ALKENE CYCLOPROPANATION WITH NICKEL CATALYST ENHANCER AND IMPROVED REARRANGEMENT REACTION BACKGROUND OF THE DISCLOSURE Cyclopropanation, the conversion of a carbon-carbon double bond to a cyclopropane ring, is a chemical transformation used in the production of intermediate species in the synthesis of primary and secondary metabolites in human, plant and microorganism biology. Since the discovery that diazomethane, CH ₂ N ₂ (DAM), can achieve the cyclopropanation of alkenes under palladium catalysis in the 1960s, this reaction has been used in synthesis with the aid of diazo compounds, for example diazoalkanes, and transition metal catalysts typically comprising palladium, copper, ruthenium, or platinum complexes. The great importance of functionalized cyclopropanes in organic and biological synthesis spurs a continuing search for efficient stereo- and regio-controlled cyclopropanation methodologies. However, methods were scarce for the construction of diversely functionalized cyclopropanes from polyprenoid substrates. Intermediates containing the cyclopropyl moiety may be used inter alia in the preparation of terpene precursors such as homofarnesol. Traditional methods, however, suffer from protracted process times, high costs, demanding energy requirements, and/or the formation of side products which negatively affect product purity and overall yields. Sanhaji et al. (PCT International Publication No. WO 2017/182542) discloses that (E)-β- farnesene was subjected to traditional diazo cyclopropanation in the presence of palladium(II) bis(acetylacetonate) (Pd(acac)2) to obtain the monocycloproponated compound (E)-Δ-farnesene: (E)-Δ-farnesene. In the process of Sanhaji et al., adding the DAM required 4 hours of time to obtain a reaction mixture which was incubated for an additional 16 hours for the reaction to reach completion. The crude product contained 82% of the desired (E)-Δ-farnesene along with 9% unreacted (E)-β-farnesene and 6% of a dicyclopropanated side product. The long reaction times and low yields underscore the need for improved methods for selectively cyclopropanating olefins, especially in the instance of polyprenoid substrate molecules. SUMMARY OF THE DISCLOSURE In a first aspect, the present disclosure provides a method of carbocyclyl moiety formation across a carbon-carbon multiple bond. The method comprises combining components comprising: a substrate compound comprising a carbon-carbon multiple bond; a diazo alkylation reagent; a cyclopropanation catalyst comprising a transition metal selected from the group consisting of Pd, Pt, Cu, and Ru, and a catalyst enhancer comprising Ni, to form a reaction mixture for producing a product compound comprising a cyclopropyl moiety. Preferred catalysts include those selected from the group consisting of a Pd(II) compound, a Pt(II) compound, a Cu(II) compound, and a Ru(II) compound. Exemplary Pd(II) compounds include Pd(II) complexes such as Pd(acac) ₂ , Pd(OAc) ₂ , and PdCl ₂ . Exemplary Pt(II) compounds include Pt(II) complexes such as Pt(acac) ₂ , Pt(OAc) ₂ , and PtCl ₂ . Exemplary Cu(II) compounds include Cu(II) complexes such as Cu(acac)2, Cu(OAc)2, and CuCl2. Exemplary Ru(II) compounds include Ru(II) complexes such as Pd(acac)2, Pd(OAc)2, and PdCl2. Preferred catalyst enhancers include Ni(II) compounds. Exemplary Ni(II) compounds include Ni(acac)2, Ni(OAc)2, and NiCl2. The relative amounts of catalyst and enhancer can be adjusted to maximize yields and selectivity. Preferably, a ratio (moles of catalyst enhancer)/(moles of catalyst) is at least 0.1 to at most 10, inclusive. More preferably, a ratio (moles of catalyst enhancer)/(moles of catalyst) is at least 0.5 to at most 5, inclusive. Very preferably, a ratio (moles of catalyst enhancer)/(moles of catalyst) is at least 0.9 to at most 1.1, inclusive. In representative embodiments, the diazo alkylation reagent is a diazoalkane, for example diazomethane. In one embodiment, the product compound comprises a cyclopropylvinyl moiety. In some embodiments, the substrate is a polyprenoid compound of formula I: or an isotopically labeled compound, salt, solvate, polymorph, or co-crystal thereof, wherein n is a natural number from at least 0 to at most 10, inclusive for example 0, 1, 2, or 3. Representative substrates include isoprene, ocimene, myrcene, farnesene, and combinations thereof. (E)-β- farnesene is a preferred substrate. Exemplary products include a molecule of formula III or an isotopically labeled compound, salt, solvate, polymorph, or co-crystal thereof: III. A preferred product is (E)-Δ-farnesene or an isotopically labeled compound, salt, solvate, polymorph, or co-crystal thereof. A homoallylic compound of formula V or an isotopically labeled compound, salt, solvate, polymorph, or co-crystal thereof may be formed from the product compound of formula IV or an isotopically labeled compound, salt, solvate, polymorph, or co-crystal thereof in the presence of a Bronsted acid of formula HQ: , wherein Bronsted acid HQ is selected from R’CO ₂ H and/or a hydrogen halide selected from the group consisting of HCl, HBr, HI, and combinations thereof, wherein R’ is a C1-10 alkyl or aryl moiety, which may be linear or branched and may be substituted or unsubstituted, and wherein Q is R’CO ₂ - and/or a halide atom. A homoallylic alcohol of formula VI or an isotopically labeled compound, salt, solvate, polymorph, or co-crystal thereof may be formed by hydrolysis of a compound of formula V or an isotopically labeled compound, salt, solvate, polymorph, or co-crystal thereof: VI. In some embodiment, the Bronsted acid HQ is R’CO2H and R’ is a C1-C4 alkyl moiety, which may be substituted with 1 to 3 substituents independently selected from the group consisting of halogen, cyano, and nitro. In a preferred example, HQ is ClCH2CO ₂ H. Provided herein is also an improved of cyclopropyl moiety formation across a double bond of an alkene substrate. The method comprises forming a reaction mixture from components comprising the alkene substrate comprising a carbon-carbon multiple bond, a diazo alkylation reagent, and a Pd(II) catalyst. The improvement comprising: the addition of a Ni(II) catalyst enhancer to the reaction mixture. Preferably, a ratio (moles of catalyst enhancer)/(moles of catalyst) is at least 0.1 to at most 10, inclusive. More preferably, a ratio (moles of catalyst enhancer)/(moles of catalyst) is at least 0.5 to at most 5, inclusive. Very preferably, a ratio (moles of catalyst enhancer)/(moles of catalyst) is at least 0.9 to at most 1.1, inclusive. In some embodiments, the alkene substrate is a polyprenoid compound, for example a compound selected from the group consisting of isoprene, ocimene, myrcene, farnesene, and combinations thereof. In a preferred example, the polyprenoid compound is (E)-β-farnesene. In a further aspect, herein provided is an improved method of forming a homoallylic compound. The method includes forming a homoallylic compound of formula 2 from a cyclopropylvinyl precursor of formula 1 by incubation in the presence of a Bronsted acid HQ wherein the Bronsted acid HQ is selected from R’CO ₂ H and a hydrogen halide selected from HCl, HBr, and HI, wherein R is a C1-30 cyclic, polycyclic or acyclic alkyl moiety, or an aryl or polyaryl residue, each of which may be saturated or unsaturated, branched or linear, and substituted or unsubstituted; R’ is a C _1-30 alkyl or alkyl moiety, which may be linear or branched and may be substituted or unsubstituted, and wherein Q is an ester group and/or a halide atom. The improvement comprises: a ratio (equivalents of acid HQ)/(moles of precursor 1) being at least 0.75 to at most 1.25, inclusive and the incubation time being at least 0.75 hours to at most 1.25 hours, inclusive. In some embodiments, the reaction time at least 0.85 hours to at most 1.15 hours, inclusive or at least 0.95 hours to at most 1.05 hours, inclusive. Exemplary reaction temperature ranges from at least 50 °C to at most 80 °C, inclusive, at least 60 °C to at most 70 °C, inclusive or at least 62.5 °C to at most 67.5 °C, inclusive. DEFINITIONS Definitions of specific functional groups and chemical terms are described in more detail below. The chemical elements are identified in accordance with the Periodic Table of the Elements, CAS version, Handbook of Chemistry and Physics, 75 ^th Ed., inside cover, and specific functional groups are generally defined as described therein. Additionally, general principles of organic chemistry, as well as specific functional moieties and reactivity, are described in Thomas Sorrell, Organic Chemistry, University Science Books, Sausalito, 1999; Smith and March, March’s Advanced Organic Chemistry, 5 ^th Edition, John Wiley & Sons, Inc., New York, 2001; Larock, Comprehensive Organic Transformations, VCH Publishers, Inc., New York, 1989; and Carruthers, Some Modern Methods of Organic Synthesis, 3 ^rd Edition, Cambridge University Press, Cambridge, 1987. Compounds described herein can comprise one or more asymmetric centers, and thus can exist in various isomeric forms, e.g., enantiomers and/or diastereomers. For example, the compounds described herein can be in the form of an individual enantiomer, diastereomer or geometric isomer, or can be in the form of a mixture of stereoisomers, including racemic mixtures and mixtures enriched in one or more stereoisomer. Isomers can be isolated from mixtures by methods known to those skilled in the art, including chiral high-pressure liquid chromatography (HPLC), supercritical fluid chromatography (SFC), and the formation and crystallization of chiral salts; or preferred isomers can be prepared by asymmetric syntheses. See, for example, Jacques et al., Enantiomers, Racemates and Resolutions (Wiley Interscience, New York, 1981); Wilen et al., Tetrahedron 33:2725 (1977); Eliel, Stereochemistry of Carbon Compounds (McGraw–Hill, NY, 1962); and Wilen, Tables of Resolving Agents and Optical Resolutions p.268 (E.L. Eliel, Ed., Univ. of Notre Dame Press, Notre Dame, IN 1972). The present disclosure additionally encompasses compounds described herein as individual isomers substantially free of other isomers, and alternatively, as mixtures of various isomers. Unless otherwise provided, a formula depicted herein includes compounds that do not include isotopically enriched atoms and also compounds that include isotopically enriched atoms. Compounds that include isotopically enriched atoms may be useful as, for example, analytical tools, and/or probes in biological assays. When a range of values (“range”) is listed, it is intended to encompass each value and sub–range within the range. A range is inclusive of the values at the two ends of the range unless otherwise provided. For example, “an integer between 1 and 4” refers to 1, 2, 3, and 4. For example, “C _1–6 alkyl” is intended to encompass C ₁ , C ₂ , C ₃ , C ₄ , C ₅ , C ₆ , C _1–6 , C _1–5 , C _1–4 , C _1–3 , C _1–2 , C2–6, C2–5, C2–4, C2–3, C3–6, C3–5, C3–4, C4–6, C4–5, and C5–6 alkyl. “Alkyl” refers to a radical of a straight–chain or branched saturated hydrocarbon group having from 1 to 20 carbon atoms (“C _1–20 alkyl”). In some embodiments, an alkyl group has 1 to 12 carbon atoms (“C1–12 alkyl”). In some embodiments, an alkyl group has 1 to 10 carbon atoms (“C1–10 alkyl”). In some embodiments, an alkyl group has 1 to 9 carbon atoms (“C1–9 alkyl”). In some embodiments, an alkyl group has 1 to 8 carbon atoms (“C _1–8 alkyl”). In some embodiments, an alkyl group has 1 to 7 carbon atoms (“C1–7 alkyl”). In some embodiments, an alkyl group has 1 to 6 carbon atoms (“C1–6 alkyl”). In some embodiments, an alkyl group has 1 to 5 carbon atoms (“C _1–5 alkyl”). In some embodiments, an alkyl group has 1 to 4 carbon atoms (“C _1–4 alkyl”). In some embodiments, an alkyl group has 1 to 3 carbon atoms (“C _1–3 alkyl”). In some embodiments, an alkyl group has 1 to 2 carbon atoms (“C1–2 alkyl”). In some embodiments, an alkyl group has 1 carbon atom (“C1 alkyl”). In some embodiments, an alkyl group has 2 to 6 carbon atoms (“C2–6 alkyl”). Examples of C _1–6 alkyl groups include methyl (C ₁ ), ethyl (C ₂ ), n–propyl (C ₃ ), isopropyl (C3), n–butyl (C4), tert–butyl (C4), sec–butyl (C4), iso–butyl (C4), n–pentyl (C5), 3–pentanyl (C5), amyl (C5), neopentyl (C5), 3–methyl–2–butanyl (C5), tertiary amyl (C5), and n–hexyl (C6). Additional examples of alkyl groups include n–heptyl (C ₇ ), n–octyl (C ₈ ) and the like. Unless otherwise specified, each instance of an alkyl group is independently optionally substituted, e.g., unsubstituted (an “unsubstituted alkyl”) or substituted (a “substituted alkyl”) with one or more substituents. In certain embodiments, the alkyl group is unsubstituted C _1–12 alkyl (e.g., –CH ₃ (Me), unsubstituted ethyl (Et), unsubstituted propyl (Pr, e.g., unsubstituted n-propyl (n-Pr), unsubstituted isopropyl (i-Pr)), unsubstituted butyl (Bu, e.g., unsubstituted n-butyl (n-Bu), unsubstituted tert-butyl (tert-Bu or t-Bu), unsubstituted sec-butyl (sec-Bu or s-Bu), unsubstituted isobutyl (i-Bu)). In certain embodiments, the alkyl group is substituted C _1–12 alkyl (such as substituted C1-6 alkyl, e.g., –CH2F, –CHF2, –CF3, –CH2CH2F, –CH2CHF2, –CH2CF3, or benzyl (Bn)). The attachment point of alkyl may be a single bond (e.g., as in –CH ₃ ), double bond (e.g., as in =CH2), or triple bond (e.g., as in ≡CH). The moieties =CH2 and ≡CH are also alkyl. In some embodiments, an alkyl group is substituted with one or more halogens. “Perhaloalkyl” is a substituted alkyl group as defined herein wherein all of the hydrogen atoms are independently replaced by a halogen, e.g., fluoro, bromo, chloro, or iodo. In some embodiments, the alkyl moiety has 1 to 8 carbon atoms (“C _1–8 perhaloalkyl”). In some embodiments, the alkyl moiety has 1 to 6 carbon atoms (“C1–6 perhaloalkyl”). In some embodiments, the alkyl moiety has 1 to 4 carbon atoms (“C _1–4 perhaloalkyl”). In some embodiments, the alkyl moiety has 1 to 3 carbon atoms (“C _1–3 perhaloalkyl”). In some embodiments, the alkyl moiety has 1 to 2 carbon atoms (“C1–2 perhaloalkyl”). In some embodiments, all of the hydrogen atoms are replaced with fluoro. In some embodiments, all of the hydrogen atoms are replaced with chloro. Examples of perhaloalkyl groups include –CF ₃ , –CF2CF3, –CF2CF2CF3, –CCl3, –CFCl2, –CF2Cl, and the like. “Alkenyl” refers to a radical of a straight–chain or branched hydrocarbon group having from 2 to 20 carbon atoms, one or more (e.g., two, three, or four, as valency permits) carbon– carbon double bonds, and no triple bonds (“C _2–20 alkenyl”). In some embodiments, an alkenyl group has 2 to 10 carbon atoms (“C2–10 alkenyl”). In some embodiments, an alkenyl group has 2 to 9 carbon atoms (“C _2–9 alkenyl”). In some embodiments, an alkenyl group has 2 to 8 carbon atoms (“C _2–8 alkenyl”). In some embodiments, an alkenyl group has 2 to 7 carbon atoms (“C _2–7 alkenyl”). In some embodiments, an alkenyl group has 2 to 6 carbon atoms (“C2–6 alkenyl”). In some embodiments, an alkenyl group has 2 to 5 carbon atoms (“C _2–5 alkenyl”). In some embodiments, an alkenyl group has 2 to 4 carbon atoms (“C _2–4 alkenyl”). In some embodiments, an alkenyl group has 2 to 3 carbon atoms (“C2–3 alkenyl”). In some embodiments, an alkenyl group has 2 carbon atoms (“C2 alkenyl”). The one or more carbon–carbon double bonds can be internal (such as in 2–butenyl) or terminal (such as in 1–butenyl). Examples of C _2–4 alkenyl groups include ethenyl (C2), 1–propenyl (C3), 2–propenyl (C3), 1–butenyl (C4), 2–butenyl (C4), butadienyl (C4), and the like. Examples of C2–6 alkenyl groups include the aforementioned C2–4 alkenyl groups as well as pentenyl (C ₅ ), pentadienyl (C ₅ ), hexenyl (C ₆ ), and the like. Additional examples of alkenyl include heptenyl (C ₇ ), octenyl (C ₈ ), octatrienyl (C ₈ ), and the like. Unless otherwise specified, each instance of an alkenyl group is independently optionally substituted, e.g., unsubstituted (an “unsubstituted alkenyl”) or substituted (a “substituted alkenyl”) with one or more substituents. In certain embodiments, the alkenyl group is unsubstituted C _2–10 alkenyl. In certain embodiments, the alkenyl group is substituted C2–10 alkenyl. In an alkenyl group, a C=C double bond for which the stereochemistry is not specified (e.g., –CH=CHCH3 or ) may be in the (E)- or (Z)-configuration. “Alkynyl” refers to a radical of a straight–chain or branched hydrocarbon group having from 2 to 20 carbon atoms, one or more (e.g., two, three, or four, as valency permits) carbon– carbon triple bonds, and optionally one or more double bonds (“C2–20 alkynyl”). In some embodiments, an alkynyl group has 2 to 10 carbon atoms (“C _2–10 alkynyl”). In some embodiments, an alkynyl group has 2 to 9 carbon atoms (“C2–9 alkynyl”). In some embodiments, an alkynyl group has 2 to 8 carbon atoms (“C2–8 alkynyl”). In some embodiments, an alkynyl group has 2 to 7 carbon atoms (“C _2–7 alkynyl”). In some embodiments, an alkynyl group has 2 to 6 carbon atoms (“C2–6 alkynyl”). In some embodiments, an alkynyl group has 2 to 5 carbon atoms (“C2–5 alkynyl”). In some embodiments, an alkynyl group has 2 to 4 carbon atoms (“C2–4 alkynyl”). In some embodiments, an alkynyl group has 2 to 3 carbon atoms (“C _2–3 alkynyl”). In some embodiments, an alkynyl group has 2 carbon atoms (“C ₂ alkynyl”). The one or more carbon–carbon triple bonds can be internal (such as in 2–butynyl) or terminal (such as in 1– butynyl). Examples of C2–4 alkynyl groups include ethynyl (C2), 1–propynyl (C3), 2–propynyl (C ₃ ), 1–butynyl (C ₄ ), 2–butynyl (C ₄ ), and the like. Examples of C _2–6 alkenyl groups include the aforementioned C2–4 alkynyl groups as well as pentynyl (C5), hexynyl (C6), and the like. Additional examples of alkynyl include heptynyl (C7), octynyl (C8), and the like. Unless otherwise specified, each instance of an alkynyl group is independently optionally substituted, e.g., unsubstituted (an “unsubstituted alkynyl”) or substituted (a “substituted alkynyl”) with one or more substituents. In certain embodiments, the alkynyl group is unsubstituted C2–10 alkynyl. In certain embodiments, the alkynyl group is substituted C _2–10 alkynyl. “Carbocyclyl” or “carbocyclic” refers to a radical of a non–aromatic cyclic hydrocarbon group having from 3 to 13 ring carbon atoms (“C3–13 carbocyclyl”) and zero heteroatoms in the non–aromatic ring system. In some embodiments, a carbocyclyl group has 3 to 8 ring carbon atoms (“C _3–8 carbocyclyl”). In some embodiments, a carbocyclyl group has 3 to 7 ring carbon atoms (“C3–7 carbocyclyl”). In some embodiments, a carbocyclyl group has 3 to 6 ring carbon atoms (“C3–6 carbocyclyl”). In some embodiments, a carbocyclyl group has 5 to 10 ring carbon atoms (“C _5–10 carbocyclyl”). Exemplary C _3–6 carbocyclyl groups include cyclopropyl (C ₃ ), cyclopropenyl (C3), cyclobutyl (C4), cyclobutenyl (C4), cyclopentyl (C5), cyclopentenyl (C5), cyclohexyl (C6), cyclohexenyl (C6), cyclohexadienyl (C6), and the like. Exemplary C3–8 carbocyclyl groups include the aforementioned C _3–6 carbocyclyl groups as well as cycloheptyl (C7), cycloheptenyl (C7), cycloheptadienyl (C7), cycloheptatrienyl (C7), cyclooctyl (C8), cyclooctenyl (C8), bicyclo[2.2.1]heptanyl (C7), bicyclo[2.2.2]octanyl (C8), and the like. Exemplary C _3–10 carbocyclyl groups include the aforementioned C _3–8 carbocyclyl groups as well as cyclononyl (C9), cyclononenyl (C9), cyclodecyl (C10), cyclodecenyl (C10), octahydro–1H– indenyl (C9), decahydronaphthalenyl (C10), spiro[4.5]decanyl (C10), and the like. As the foregoing examples illustrate, in certain embodiments, the carbocyclyl group is either monocyclic (“monocyclic carbocyclyl”) or contain a fused, bridged, or spiro ring system such as a bicyclic system (“bicyclic carbocyclyl”). Carbocyclyl can be saturated, and saturated carbocyclyl is referred to as “cycloalkyl.” In some embodiments, carbocyclyl is a monocyclic, saturated carbocyclyl group having from 3 to 10 ring carbon atoms (“C3–10 cycloalkyl”). In some embodiments, a cycloalkyl group has 3 to 8 ring carbon atoms (“C3–8 cycloalkyl”). In some embodiments, a cycloalkyl group has 3 to 6 ring carbon atoms (“C _3–6 cycloalkyl”). In some embodiments, a cycloalkyl group has 5 to 6 ring carbon atoms (“C _5–6 cycloalkyl”). In some embodiments, a cycloalkyl group has 5 to 10 ring carbon atoms (“C5–10 cycloalkyl”). Examples of C5–6 cycloalkyl groups include cyclopentyl (C5) and cyclohexyl (C5). Examples of C3–6 cycloalkyl groups include the aforementioned C _5–6 cycloalkyl groups as well as cyclopropyl (C ₃ ) and cyclobutyl (C4). Examples of C3–8 cycloalkyl groups include the aforementioned C3–6 cycloalkyl groups as well as cycloheptyl (C7) and cyclooctyl (C8). Unless otherwise specified, each instance of a cycloalkyl group is independently unsubstituted (an “unsubstituted cycloalkyl”) or substituted (a “substituted cycloalkyl”) with one or more substituents. In certain embodiments, the cycloalkyl group is unsubstituted C3–10 cycloalkyl. In certain embodiments, the cycloalkyl group is substituted C _3–10 cycloalkyl. Carbocyclyl can be partially unsaturated. Carbocyclyl may include zero, one, or more (e.g., two, three, or four, as valency permits) C=C double bonds in all the rings of the carbocyclic ring system that are not aromatic or heteroaromatic. Carbocyclyl that includes one or more (e.g., two or three, as valency permits) C=C double bonds in the carbocyclic ring is referred to as “cycloalkenyl.” Carbocyclyl that includes one or more (e.g., two or three, as valency permits) C≡ triple bonds in the carbocyclic ring is referred to as “cycloalkynyl.” “Carbocyclyl” also includes ring systems wherein the carbocyclyl ring, as defined above, is fused with one or more aryl or heteroaryl groups wherein the point of attachment is on the carbocyclyl ring, and in such instances, the number of carbons continue to designate the number of carbons in the carbocyclic ring system. Unless otherwise specified, each instance of a carbocyclyl group is independently optionally substituted, e.g., unsubstituted (an “unsubstituted carbocyclyl”) or substituted (a “substituted carbocyclyl”) with one or more substituents. In certain embodiments, the carbocyclyl group is unsubstituted C _3–10 carbocyclyl. In certain embodiments, the carbocyclyl group is a substituted C3–10 carbocyclyl. In certain embodiments, the carbocyclyl is substituted or unsubstituted, 3- to 7-membered, and monocyclic. In certain embodiments, the carbocyclyl is substituted or unsubstituted, 5- to 13- membered, and bicyclic. In some embodiments, “carbocyclyl” is a monocyclic, saturated carbocyclyl group having from 3 to 10 ring carbon atoms (“C _3–10 cycloalkyl”). In some embodiments, a cycloalkyl group has 3 to 8 ring carbon atoms (“C3–8 cycloalkyl”). In some embodiments, a cycloalkyl group has 3 to 6 ring carbon atoms (“C3–6 cycloalkyl”). In some embodiments, a cycloalkyl group has 5 to 6 ring carbon atoms (“C _5–6 cycloalkyl”). In some embodiments, a cycloalkyl group has 5 to 10 ring carbon atoms (“C5–10 cycloalkyl”). Examples of C5–6 cycloalkyl groups include cyclopentyl (C5) and cyclohexyl (C5). Examples of C3–6 cycloalkyl groups include the aforementioned C5–6 cycloalkyl groups as well as cyclopropyl (C ₃ ) and cyclobutyl (C ₄ ). Examples of C _3–8 cycloalkyl groups include the aforementioned C _3–6 cycloalkyl groups as well as cycloheptyl (C ₇ ) and cyclooctyl (C8). Unless otherwise specified, each instance of a cycloalkyl group is independently unsubstituted (an “unsubstituted cycloalkyl”) or substituted (a “substituted cycloalkyl”) with one or more substituents. In certain embodiments, the cycloalkyl group is unsubstituted C _3–10 cycloalkyl. In certain embodiments, the cycloalkyl group is substituted C3–10 cycloalkyl. In certain embodiments, the carbocyclyl includes oxo substituted thereon. “Heterocyclyl” or “heterocyclic” refers to a radical of a 3– to 13–membered non– aromatic ring system having ring carbon atoms and 1 to 4 ring heteroatoms, wherein each heteroatom is independently selected from nitrogen, oxygen, and sulfur (“3–13 membered heterocyclyl”). In heterocyclyl groups that contain one or more nitrogen atoms, the point of attachment can be a carbon or nitrogen atom, as valency permits. A heterocyclyl group can either be monocyclic (“monocyclic heterocyclyl”) or a fused, bridged, or spiro ring system such as a bicyclic system (“bicyclic heterocyclyl”). A heterocyclyl group can be saturated or can be partially unsaturated. Heterocyclyl may include zero, one, or more (e.g., two, three, or four, as valency permits) double bonds in all the rings of the heterocyclic ring system that are not aromatic or heteroaromatic. Heterocyclyl bicyclic ring systems can include one or more heteroatoms in one or both rings. “Heterocyclyl” also includes ring systems wherein the heterocyclyl ring, as defined above, is fused with one or more carbocyclyl groups wherein the point of attachment is either on the carbocyclyl or heterocyclyl ring, or ring systems wherein the heterocyclyl ring, as defined above, is fused with one or more aryl or heteroaryl groups, wherein the point of attachment is on the heterocyclyl ring, and in such instances, the number of ring members continue to designate the number of ring members in the heterocyclyl ring system. Unless otherwise specified, each instance of heterocyclyl is independently optionally substituted, e.g., unsubstituted (an “unsubstituted heterocyclyl”) or substituted (a “substituted heterocyclyl”) with one or more substituents. In certain embodiments, the heterocyclyl group is unsubstituted 3– 10 membered heterocyclyl. In certain embodiments, the heterocyclyl group is substituted 3–10 membered heterocyclyl. In certain embodiments, the heterocyclyl is substituted or unsubstituted, 3- to 7-membered, and monocyclic. In certain embodiments, the heterocyclyl is substituted or unsubstituted, 5- to 13-membered, and bicyclic. In certain embodiments, the heterocyclyl includes oxo substituted thereon. In some embodiments, a heterocyclyl group is a 5–10 membered non–aromatic ring system having ring carbon atoms and 1–4 ring heteroatoms, wherein each heteroatom is independently selected from nitrogen, oxygen, and sulfur (“5–10 membered heterocyclyl”). In some embodiments, a heterocyclyl group is a 5–8 membered non–aromatic ring system having ring carbon atoms and 1–4 ring heteroatoms, wherein each heteroatom is independently selected from nitrogen, oxygen, and sulfur (“5–8 membered heterocyclyl”). In some embodiments, a heterocyclyl group is a 5–6 membered non–aromatic ring system having ring carbon atoms and 1–4 ring heteroatoms, wherein each heteroatom is independently selected from nitrogen, oxygen, and sulfur (“5–6 membered heterocyclyl”). In some embodiments, the 5–6 membered heterocyclyl has 1–3 ring heteroatoms selected from nitrogen, oxygen, and sulfur. In some embodiments, the 5–6 membered heterocyclyl has 1–2 ring heteroatoms selected from nitrogen, oxygen, and sulfur. In some embodiments, the 5–6 membered heterocyclyl has one ring heteroatom selected from nitrogen, oxygen, and sulfur. Exemplary 3–membered heterocyclyl groups containing one heteroatom include aziridinyl, oxiranyl, or thiiranyl. Exemplary 4–membered heterocyclyl groups containing one heteroatom include azetidinyl, oxetanyl and thietanyl. Exemplary 5–membered heterocyclyl groups containing one heteroatom include tetrahydrofuranyl, dihydrofuranyl, tetrahydrothiophenyl, dihydrothiophenyl, pyrrolidinyl, dihydropyrrolyl and pyrrolyl–2,5–dione. Exemplary 5–membered heterocyclyl groups containing two heteroatoms include dioxolanyl, oxasulfuranyl, disulfuranyl, and oxazolidin-2-one. Exemplary 5–membered heterocyclyl groups containing three heteroatoms include triazolinyl, oxadiazolinyl, and thiadiazolinyl. Exemplary 6– membered heterocyclyl groups containing one heteroatom include piperidinyl, tetrahydropyranyl, dihydropyridinyl, and thianyl. Exemplary 6–membered heterocyclyl groups containing two heteroatoms include piperazinyl, morpholinyl, dithianyl, and dioxanyl. Exemplary 6–membered heterocyclyl groups containing two heteroatoms include triazinanyl. Exemplary 7–membered heterocyclyl groups containing one heteroatom include azepanyl, oxepanyl and thiepanyl. Exemplary 8–membered heterocyclyl groups containing one heteroatom include azocanyl, oxecanyl, and thiocanyl. Exemplary 5-membered heterocyclyl groups fused to a C6 aryl ring (also referred to herein as a 5,6-bicyclic heterocyclic ring) include indolinyl, isoindolinyl, dihydrobenzofuranyl, dihydrobenzothienyl, benzoxazolinonyl, and the like. Exemplary 6- membered heterocyclyl groups fused to an aryl ring (also referred to herein as a 6,6-bicyclic heterocyclic ring) include tetrahydroquinolinyl, tetrahydroisoquinolinyl, and the like. “Aryl” refers to a radical of a monocyclic or polycyclic (e.g., bicyclic or tricyclic) 4n+2 aromatic ring system (e.g., having 6, 10, or 14 pi electrons shared in a cyclic array) having 6–14 ring carbon atoms and zero heteroatoms provided in the aromatic ring system (“C _6–14 aryl”). In some embodiments, an aryl group has six ring carbon atoms (“C ₆ aryl”; e.g., phenyl). In some embodiments, an aryl group has ten ring carbon atoms (“C10 aryl”; e.g., naphthyl such as 1– naphthyl and 2–naphthyl). In some embodiments, an aryl group has fourteen ring carbon atoms (“C ₁₄ aryl”; e.g., anthracyl). “Aryl” also includes ring systems wherein the aryl ring, as defined above, is fused with one or more carbocyclyl or heterocyclyl groups wherein the radical or point of attachment is on the aryl ring, and in such instances, the number of carbon atoms continue to designate the number of carbon atoms in the aryl ring system. Unless otherwise specified, each instance of an aryl group is independently optionally substituted, e.g., unsubstituted (an “unsubstituted aryl”) or substituted (a “substituted aryl”) with one or more substituents. In certain embodiments, the aryl group is unsubstituted C _6–14 aryl. In certain embodiments, the aryl group is substituted C _6–14 aryl. “Heteroaryl” refers to a radical of a 5–10 membered monocyclic or bicyclic 4n+2 aromatic ring system (e.g., having 6 or 10 pi electrons shared in a cyclic array) having ring carbon atoms and 1–4 ring heteroatoms provided in the aromatic ring system, wherein each heteroatom is independently selected from nitrogen, oxygen, and sulfur (“5–10 membered heteroaryl”). In heteroaryl groups that contain one or more nitrogen atoms, the point of attachment can be a carbon or nitrogen atom, as valency permits. Heteroaryl bicyclic ring systems can include one or more heteroatoms in one or both rings. “Heteroaryl” includes ring systems wherein the heteroaryl ring, as defined above, is fused with one or more carbocyclyl or heterocyclyl groups wherein the point of attachment is on the heteroaryl ring, and in such instances, the number of ring members continues to designate the number of ring members in the heteroaryl ring system. “Heteroaryl” also includes ring systems wherein the heteroaryl ring, as defined above, is fused with one or more aryl groups wherein the point of attachment is either on the aryl or heteroaryl ring, and in such instances, the number of ring members designates the number of ring members in the fused (aryl/heteroaryl) ring system. Bicyclic heteroaryl groups wherein one ring does not contain a heteroatom (e.g., indolyl, quinolinyl, carbazolyl, and the like) the point of attachment can be on either ring, e.g., either the ring bearing a heteroatom (e.g., 2–indolyl) or the ring that does not contain a heteroatom (e.g., 5–indolyl). In some embodiments, a heteroaryl group is a 5–10 membered aromatic ring system having ring carbon atoms and 1–4 ring heteroatoms provided in the aromatic ring system, wherein each heteroatom is independently selected from nitrogen, oxygen, and sulfur (“5–10 membered heteroaryl”). In some embodiments, a heteroaryl group is a 5–8 membered aromatic ring system having ring carbon atoms and 1–4 ring heteroatoms provided in the aromatic ring system, wherein each heteroatom is independently selected from nitrogen, oxygen, and sulfur (“5–8 membered heteroaryl”). In some embodiments, a heteroaryl group is a 5–6 membered aromatic ring system having ring carbon atoms and 1–4 ring heteroatoms provided in the aromatic ring system, wherein each heteroatom is independently selected from nitrogen, oxygen, and sulfur (“5–6 membered heteroaryl”). In some embodiments, the 5–6 membered heteroaryl has 1–3 ring heteroatoms selected from nitrogen, oxygen, and sulfur. In some embodiments, the 5–6 membered heteroaryl has 1–2 ring heteroatoms selected from nitrogen, oxygen, and sulfur. In some embodiments, the 5–6 membered heteroaryl has 1 ring heteroatom selected from nitrogen, oxygen, and sulfur. Unless otherwise specified, each instance of a heteroaryl group is independently optionally substituted, e.g., unsubstituted (“unsubstituted heteroaryl”) or substituted (“substituted heteroaryl”) with one or more substituents. In certain embodiments, the heteroaryl group is unsubstituted 5–14 membered heteroaryl. In certain embodiments, the heteroaryl group is substituted 5–14 membered heteroaryl. In certain embodiments, the heteroaryl group is 5-6 membered, monocyclic. In certain embodiments, the heteroaryl group is 8-14 membered, bicyclic. Exemplary 5–membered heteroaryl groups containing one heteroatom include pyrrolyl, furanyl and thiophenyl. Exemplary 5–membered heteroaryl groups containing two heteroatoms include imidazolyl, pyrazolyl, oxazolyl, isoxazolyl, thiazolyl, and isothiazolyl. Exemplary 5– membered heteroaryl groups containing three heteroatoms include triazolyl, oxadiazolyl, and thiadiazolyl. Exemplary 5–membered heteroaryl groups containing four heteroatoms include tetrazolyl. Exemplary 6–membered heteroaryl groups containing one heteroatom include pyridinyl. Exemplary 6–membered heteroaryl groups containing two heteroatoms include pyridazinyl, pyrimidinyl, and pyrazinyl. Exemplary 6–membered heteroaryl groups containing three or four heteroatoms include triazinyl and tetrazinyl, respectively. Exemplary 7–membered heteroaryl groups containing one heteroatom include azepinyl, oxepinyl, and thiepinyl. Exemplary 5,6–bicyclic heteroaryl groups include indolyl, isoindolyl, indazolyl, benzotriazolyl, benzothiophenyl, isobenzothiophenyl, benzofuranyl, benzoisofuranyl, benzimidazolyl, benzoxazolyl, benzisoxazolyl, benzoxadiazolyl, benzthiazolyl, benzisothiazolyl, benzthiadiazolyl, indolizinyl, and purinyl. Exemplary 6,6–bicyclic heteroaryl groups include naphthyridinyl, pteridinyl, quinolinyl, isoquinolinyl, cinnolinyl, quinoxalinyl, phthalazinyl, and quinazolinyl. “Partially unsaturated” refers to a group that includes at least one double or triple bond. The term “partially unsaturated” is intended to encompass rings having multiple sites of unsaturation but is not intended to include aromatic groups (e.g., aryl or heteroaryl groups) as herein defined. Likewise, “saturated” refers to a group that does not contain a double or triple bond, i.e., contains all single bonds. In some embodiments, alkyl, alkenyl, alkynyl, carbocyclyl, heterocyclyl, aryl, and heteroaryl groups, as defined herein, are optionally substituted (e.g., “substituted” or “unsubstituted” alkyl, “substituted” or “unsubstituted” alkenyl, “substituted” or “unsubstituted” alkynyl, “substituted” or “unsubstituted” carbocyclyl, “substituted” or “unsubstituted” heterocyclyl, “substituted” or “unsubstituted” aryl or “substituted” or “unsubstituted” heteroaryl group). In general, the term “substituted,” whether preceded by the term “optionally” or not, means that at least one hydrogen present on a group (e.g., a carbon or nitrogen atom) is replaced with a permissible substituent, e.g., a substituent which upon substitution results in a stable compound, e.g., a compound which does not spontaneously undergo transformation such as by rearrangement, cyclization, elimination, or other reaction. Unless otherwise indicated, a “substituted” group has a substituent at one or more substitutable positions of the group, and when more than one position in any given structure is substituted, the substituent is either the same or different at each position. The term “substituted” is contemplated to include substitution with all permissible substituents of organic compounds, any of the substituents described herein that results in the formation of a stable compound. The present disclosure contemplates any and all such combinations in order to arrive at a stable compound. For purposes of this disclosure, heteroatoms such as nitrogen may have hydrogen substituents and/or any suitable substituent as described herein which satisfy the valencies of the heteroatoms and results in the formation of a stable moiety. Exemplary carbon atom substituents include halogen, −CN, −NO2, −N3, −SO2H, −SO3H, −OH, −OR ^aa , −ON(R ^bb )2, −N(R ^bb )2, −N(R ^bb )3 ⁺ X ⁻ , −N(OR ^cc )R ^bb , −SH, −SR ^aa , −SSR ^cc , −OP(=O)(N(R ^bb ) ₂ ) ₂ , −NR ^bb P(=O)(R ^aa ) ₂ , −NR ^bb P(=O)(OR ^cc ) ₂ , −NR ^bb P(=O)(N(R ^bb ) ₂ ) ₂ , −P(R ^cc ) ₂ , −P(OR ^cc )2, −P(R ^cc )3 ⁺ X ⁻ , −P(OR ^cc )3 ⁺ X ⁻ , −P(R ^cc )4, −P(OR ^cc )4, −OP(R ^cc )2, −OP(R ^cc )3 ⁺ X ⁻ , −OP(OR ^cc ) ₂ , −OP(OR ^cc ) ₃ ⁺ X ⁻ , −OP(R ^cc ) ₄ , −OP(OR ^cc ) ₄ , −B(R ^aa ) ₂ , −B(OR ^cc ) ₂ , −BR ^aa (OR ^cc ), C _1-10 alkyl, C1-10 perhaloalkyl, C2-10 alkenyl, C2-10 alkynyl, heteroC1-10 alkyl, heteroC2-10 alkenyl, heteroC2-10 alkynyl, C3-10 carbocyclyl, 3-14 membered heterocyclyl, C6-14 aryl, and 5-14 membered heteroaryl, wherein each alkyl, alkenyl, alkynyl, heteroalkyl, heteroalkenyl, heteroalkynyl, carbocyclyl, heterocyclyl, aryl, and heteroaryl is independently substituted with 0, 1, 2, 3, 4, or 5 R ^dd groups; wherein X ⁻ is a counterion; or two geminal hydrogens on a carbon atom are replaced with the group =O, =S, =NN(R ^bb )2, =NNR ^bb C(=O)R ^aa , =NNR ^bb C(=O)OR ^aa , =NNR ^bb S(=O)2R ^aa , =NR ^bb , or =NOR ^cc ; each instance of R ^aa is, independently, selected from C1-10 alkyl, C1-10 perhaloalkyl, C2-10 alkenyl, C _2-10 alkynyl, heteroC _1-10 alkyl, heteroC _2-10 alkenyl, heteroC _2-10 alkynyl, C _3-10 carbocyclyl, 3-14 membered heterocyclyl, C _6-14 aryl, and 5-14 membered heteroaryl, or two R ^aa groups are joined to form a 3-14 membered heterocyclyl or 5-14 membered heteroaryl ring, wherein each alkyl, alkenyl, alkynyl, heteroalkyl, heteroalkenyl, heteroalkynyl, carbocyclyl, heterocyclyl, aryl, and heteroaryl is independently substituted with 0, 1, 2, 3, 4, or 5 R ^dd groups; each instance of R ^bb is, independently, selected from hydrogen, −OH, −OR ^aa , −N(R ^cc )2, −CN, −C(=O)R ^aa , −C(=O)N(R ^cc )2, −CO2R ^aa , −SO2R ^aa , −C(=NR ^cc )OR ^aa , −C(=NR ^cc )N(R ^cc )2, −SO ₂ N(R ^cc ) ₂ , −SO ₂ R ^cc , −SO ₂ OR ^cc , −SOR ^aa , −C(=S)N(R ^cc ) ₂ , −C(=O)SR ^cc , −C(=S)SR ^cc , −P(=O)(R ^aa )2, −P(=O)(OR ^cc )2, −P(=O)(N(R ^cc )2)2, C1-10 alkyl, C1-10 perhaloalkyl, C2-10 alkenyl, C2- 10 alkynyl, heteroC1-10alkyl, heteroC2-10alkenyl, heteroC2-10alkynyl, C3-10 carbocyclyl, 3-14 membered heterocyclyl, C _6-14 aryl, and 5-14 membered heteroaryl, or two R ^bb groups are joined to form a 3-14 membered heterocyclyl or 5-14 membered heteroaryl ring, wherein each alkyl, alkenyl, alkynyl, heteroalkyl, heteroalkenyl, heteroalkynyl, carbocyclyl, heterocyclyl, aryl, and heteroaryl is independently substituted with 0, 1, 2, 3, 4, or 5 R ^dd groups; wherein X ⁻ is a counterion; each instance of R ^cc is, independently, selected from hydrogen, C1-10 alkyl, C1-10 perhaloalkyl, C2-10 alkenyl, C2-10 alkynyl, heteroC1-10 alkyl, heteroC2-10 alkenyl, heteroC2-10 alkynyl, C _3-10 carbocyclyl, 3-14 membered heterocyclyl, C _6-14 aryl, and 5-14 membered heteroaryl, or two R ^cc groups are joined to form a 3-14 membered heterocyclyl or 5-14 membered heteroaryl ring, wherein each alkyl, alkenyl, alkynyl, heteroalkyl, heteroalkenyl, heteroalkynyl, carbocyclyl, heterocyclyl, aryl, and heteroaryl is independently substituted with 0, 1, 2, 3, 4, or 5 R ^dd groups; each instance of R ^dd is, independently, selected from halogen, −CN, −NO2, −N3, −SO2H, −SO3H, −OH, −OR ^ee , −ON(R ^ff )2, −N(R ^ff )2, −N(R ^ff )3 ⁺ X ⁻ , −N(OR ^ee )R ^ff , −SH, −SR ^ee , −SSR ^ee , −NR ^ff C(=O)R ^ee , −NR ^ff CO2R ^ee , −NR ^ff C(=O)N(R ^ff )2, −C(=NR ^ff )OR ^ee , −OC(=NR ^ff )R ^ee , −OC(=NR ^ff )OR ^ee , −C(=NR ^ff )N(R ^ff ) ₂ , −OC(=NR ^ff )N(R ^ff ) ₂ , −NR ^ff C(=NR ^ff )N(R ^ff ) ₂ , −NR ^ff SO ₂ R ^ee , −SO2N(R ^ff )2, −SO2R ^ee , −SO2OR ^ee , −OSO2R ^ee , −S(=O)R ^ee , −Si(R ^ee )3, −OSi(R ^ee )3, −C(=S)N(R ^ff )2, −C(=O)SR ^ee , −C(=S)SR ^ee , −SC(=S)SR ^ee , −P(=O)(OR ^ee )2, −P(=O)(R ^ee )2, −OP(=O)(R ^ee )2, −OP(=O)(OR ^ee ) ₂ , C _1-6 alkyl, C _1-6 perhaloalkyl, C _2-6 alkenyl, C _2-6 alkynyl, heteroC _1-6 alkyl, heteroC2-6alkenyl, heteroC2-6alkynyl, C3-10 carbocyclyl, 3-10 membered heterocyclyl, C6-10 aryl, 5-10 membered heteroaryl, wherein each alkyl, alkenyl, alkynyl, heteroalkyl, heteroalkenyl, heteroalkynyl, carbocyclyl, heterocyclyl, aryl, and heteroaryl is independently substituted with 0, 1, 2, 3, 4, or 5 R ^gg groups, or two geminal R ^dd substituents can be joined to form =O or =S; wherein X ⁻ is a counterion; each instance of R ^ee is, independently, selected from C _1-6 alkyl, C _1-6 perhaloalkyl, C _2-6 alkenyl, C _2-6 alkynyl, heteroC _1-6 alkyl, heteroC _2-6 alkenyl, heteroC _2-6 alkynyl, C _3-10 carbocyclyl, C6-10 aryl, 3-10 membered heterocyclyl, and 3-10 membered heteroaryl, wherein each alkyl, alkenyl, alkynyl, heteroalkyl, heteroalkenyl, heteroalkynyl, carbocyclyl, heterocyclyl, aryl, and heteroaryl is independently substituted with 0, 1, 2, 3, 4, or 5 R ^gg groups; each instance of R ^ff is, independently, selected from hydrogen, C1-6 alkyl, C1-6 perhaloalkyl, C2-6 alkenyl, C2-6 alkynyl, heteroC1-6alkyl, heteroC2-6alkenyl, heteroC2-6alkynyl, C3- ₁₀ carbocyclyl, 3-10 membered heterocyclyl, C _6-10 aryl and 5-10 membered heteroaryl, or two R ^ff groups are joined to form a 3-10 membered heterocyclyl or 5-10 membered heteroaryl ring, wherein each alkyl, alkenyl, alkynyl, heteroalkyl, heteroalkenyl, heteroalkynyl, carbocyclyl, heterocyclyl, aryl, and heteroaryl is independently substituted with 0, 1, 2, 3, 4, or 5 R ^gg groups; and each instance of R ^gg is, independently, halogen, −CN, −NO2, −N3, −SO2H, −SO3H, −OH, −OC1-6 alkyl, −ON(C1-6 alkyl)2, −N(C1-6 alkyl)2, −N(C1-6 alkyl)3 ⁺ X ⁻ , −NH(C1-6 alkyl)2 ⁺ X ⁻ , −NH ₂ (C _1-6 alkyl) ⁺ X ⁻ , −NH ₃ ⁺ X ⁻ , −N(OC _1-6 alkyl)(C _1-6 alkyl), −N(OH)(C _1-6 alkyl), −NH(OH), −SH, −SC1-6 alkyl, −SS(C1-6 alkyl), −C(=O)(C1-6 alkyl), −CO2H, −CO2(C1-6 alkyl), −OC(=O)(C1- 6 alkyl), −OCO2(C1-6 alkyl), −C(=O)NH2, −C(=O)N(C1-6 alkyl)2, −OC(=O)NH(C1-6 alkyl), −NHC(=O)( C _1-6 alkyl), −N(C _1-6 alkyl)C(=O)( C _1-6 alkyl), −NHCO ₂ (C _1-6 alkyl), −NHC(=O)N(C _1- 6 alkyl)2, −NHC(=O)NH(C1-6 alkyl), −NHC(=O)NH2, −C(=NH)O(C1-6 alkyl), −OC(=NH)(C1-6 alkyl), −OC(=NH)OC1-6 alkyl, −C(=NH)N(C1-6 alkyl)2, −C(=NH)NH(C1-6 alkyl), −C(=NH)NH2, −OC(=NH)N(C _1-6 alkyl) ₂ , −OC(NH)NH(C _1-6 alkyl), −OC(NH)NH ₂ , −NHC(NH)N(C _1-6 alkyl) ₂ , −NHC(=NH)NH ₂ , −NHSO ₂ (C _1-6 alkyl), −SO ₂ N(C _1-6 alkyl) ₂ , −SO ₂ NH(C _1-6 alkyl), −SO ₂ NH ₂ , −SO2C1-6 alkyl, −SO2OC1-6 alkyl, −OSO2C1-6 alkyl, −SOC1-6 alkyl, −Si(C1-6 alkyl)3, −OSi(C1-6 alkyl)3 −C(=S)N(C1-6 alkyl)2, C(=S)NH(C1-6 alkyl), C(=S)NH2, −C(=O)S(C1-6 alkyl), −C(=S)SC1- ₆ alkyl, −SC(=S)SC _1-6 alkyl, −P(=O)(OC _1-6 alkyl) ₂ , −P(=O)(C _1-6 alkyl) ₂ , −OP(=O)(C _1-6 alkyl) ₂ , −OP(=O)(OC1-6 alkyl)2, C1-6 alkyl, C1-6 perhaloalkyl, C2-6 alkenyl, C2-6 alkynyl, heteroC1-6alkyl, heteroC _2-6 alkenyl, heteroC _2-6 alkynyl, C _3-10 carbocyclyl, C _6-10 aryl, 3-10 membered heterocyclyl, 5-10 membered heteroaryl; or two geminal R ^gg substituents can be joined to form =O or =S; wherein X ⁻ is a counterion. In certain embodiments, the carbon atom substituents are independently halogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, −OR ^aa , −SR ^aa , −OC(=O)N(R ^bb ) ₂ , −NR ^bb C(=O)R ^aa , −NR ^bb CO ₂ R ^aa , or −NR ^bb C(=O)N(R ^bb ) ₂ . In certain embodiments, the carbon atom substituents are independently halogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, −OR ^aa , −SR ^aa , −N(R ^bb )2, –CN, −NR ^bb C(=O)R ^aa , −NR ^bb CO ₂ R ^aa , or −NR ^bb C(=O)N(R ^bb ) ₂ , wherein R ^aa is hydrogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, an oxygen protecting group when attached to an oxygen atom, or a sulfur protecting group (e.g., acetamidomethyl, t- Bu, 3-nitro-2-pyridine sulfenyl, 2-pyridine-sulfenyl, or triphenylmethyl) when attached to a sulfur atom; and each R ^bb is independently hydrogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, or a nitrogen protecting group. In certain embodiments, the carbon atom substituents are independently halogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, −OR ^aa , −SR ^aa , −N(R ^bb )2, –CN, –SCN, or –NO2. In certain embodiments, the carbon atom substituents are independently halogen, substituted (e.g., substituted with one or more halogen moieties) or unsubstituted C _1-6 alkyl, −OR ^aa , −SR ^aa , −N(R ^bb ) ₂ , –CN, –SCN, or –NO ₂ , wherein R ^aa is hydrogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, an oxygen protecting group when attached to an oxygen atom, or a sulfur protecting group (e.g., acetamidomethyl, t-Bu, 3- nitro-2-pyridine sulfenyl, 2-pyridine-sulfenyl, or triphenylmethyl) when attached to a sulfur atom; and each R ^bb is independently hydrogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, or a nitrogen protecting group. A “counterion” or “anionic counterion” is a negatively charged group associated with a positively charged group in order to maintain electronic neutrality. An anionic counterion may be monovalent (i.e., including one formal negative charge). An anionic counterion may also be multivalent (i.e., including more than one formal negative charge), such as divalent or trivalent. Exemplary counterions include halide ions (e.g., F ^– , Cl ^– , Br ^– , I ^– ), NO ₃ ^– , ClO ₄ ^– , OH ^– , H ₂ PO ₄ ^– , HCO3 ⁻ , HSO4 ^– , sulfonate ions (e.g., methanesulfonate, trifluoromethanesulfonate, p– toluenesulfonate, benzenesulfonate, 10–camphor sulfonate, naphthalene–2–sulfonate, naphthalene–1–sulfonic acid–5–sulfonate, ethan–1–sulfonic acid–2–sulfonate, and the like), carboxylate ions (e.g., acetate, propanoate, benzoate, glycerate, lactate, tartrate, glycolate, gluconate, and the like), BF ₄ ⁻ , PF ₄ ^– , PF ₆ ^– , AsF ₆ ^– , SbF ₆ ^– , B[3,5-(CF ₃ ) ₂ C ₆ H ₃ ] ₄ ] ^– , B(C ₆ F ₅ ) ₄ ⁻ , BPh ₄ ^– , Al(OC(CF3)3)4-, and carborane anions (e.g., CB11H12 ^– or (HCB11Me5Br6) ^– ). Exemplary counterions which may be multivalent include CO3 ²⁻ , HPO4 ²⁻ , PO4 ³⁻ , B4O7 ²⁻ , SO4 ²⁻ , S2O3 ²⁻ , carboxylate anions (e.g., tartrate, citrate, fumarate, maleate, malate, malonate, gluconate, succinate, glutarate, adipate, pimelate, suberate, azelate, sebacate, salicylate, phthalates, aspartate, glutamate, and the like), and carboranes. “Halo” or “halogen” refers to fluorine (fluoro, –F), chlorine (chloro, –Cl), bromine (bromo, –Br), or iodine (iodo, –I). Nitrogen atoms can be substituted or unsubstituted as valency permits, and include primary, secondary, tertiary, and quaternary nitrogen atoms. Exemplary nitrogen atom substituents include hydrogen, −OH, −OR ^aa , −N(R ^cc ) ₂ , −CN, −C(=O)R ^aa , −C(=O)N(R ^cc ) ₂ , −CO2R ^aa , −SO2R ^aa , −C(=NR ^bb )R ^aa , −C(=NR ^cc )OR ^aa , −C(=NR ^cc )N(R ^cc )2, −SO2N(R ^cc )2, −SO2R ^cc , −SO2OR ^cc , −SOR ^aa , −C(=S)N(R ^cc )2, −C(=O)SR ^cc , −C(=S)SR ^cc , −P(=O)(OR ^cc )2, −P(=O)(R ^aa )2, −P(=O)(N(R ^cc ) ₂ ) ₂ , C _1-10 alkyl, C _1-10 perhaloalkyl, C _2-10 alkenyl, C _2-10 alkynyl, heteroC _1-10 alkyl, heteroC2-10alkenyl, heteroC2-10alkynyl, C3-10 carbocyclyl, 3-14 membered heterocyclyl, C6-14 aryl, and 5-14 membered heteroaryl, or two R ^cc groups attached to an N atom are joined to form a 3-14 membered heterocyclyl or 5-14 membered heteroaryl ring, wherein each alkyl, alkenyl, alkynyl, heteroalkyl, heteroalkenyl, heteroalkynyl, carbocyclyl, heterocyclyl, aryl, and heteroaryl is independently substituted with 0, 1, 2, 3, 4, or 5 R ^dd groups, and wherein R ^aa , R ^bb , R ^cc and R ^dd are as defined above. In certain embodiments, the nitrogen atom substituents are independently substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, −C(=O)R ^aa , −CO2R ^aa , −C(=O)N(R ^bb )2, or a nitrogen protecting group. In certain embodiments, the nitrogen atom substituents are independently substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, −C(=O)R ^aa , −CO2R ^aa , −C(=O)N(R ^bb )2, or a nitrogen protecting group, wherein R ^aa is hydrogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C _1-6 alkyl, or an oxygen protecting group when attached to an oxygen atom; and each R ^bb is independently hydrogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, or a nitrogen protecting group. In certain embodiments, the nitrogen atom substituents are independently substituted (e.g., substituted with one or more halogen) or unsubstituted C _1-6 alkyl or a nitrogen protecting group. In certain embodiments, the substituent present on a nitrogen atom is a nitrogen protecting group (also referred to as an amino protecting group). Nitrogen protecting groups include –OH, –OR ^aa , –N(R ^cc ) ₂ , –C(=O)R ^aa , –C(=O)N(R ^cc ) ₂ , –CO ₂ R ^aa , –SO ₂ R ^aa , –C(=NR ^cc )R ^aa , – C(=NR ^cc )OR ^aa , –C(=NR ^cc )N(R ^cc )2, –SO2N(R ^cc )2, –SO2R ^cc , –SO2OR ^cc , –SOR ^aa , –C(=S)N(R ^cc )2, – C(=O)SR ^cc , –C(=S)SR ^cc , C _1–10 alkyl (e.g., aralkyl, heteroaralkyl), C _2–10 alkenyl, C _2–10 alkynyl, C3–10 carbocyclyl, 3–14 membered heterocyclyl, C6–14 aryl, and 5–14 membered heteroaryl groups, wherein each alkyl, alkenyl, alkynyl, carbocyclyl, heterocyclyl, aralkyl, aryl, and heteroaryl is independently substituted with 0, 1, 2, 3, 4, or 5 R ^dd groups, and wherein R ^aa , R ^bb , R ^cc , and R ^dd are as defined herein. Nitrogen protecting groups are well known in the art and include those described in detail in Protecting Groups in Organic Synthesis, T. W. Greene and P. G. M. Wuts, 3 ^rd edition, John Wiley & Sons, 1999, incorporated herein by reference. Amide nitrogen protecting groups (e.g., –C(=O)R ^aa ) include formamide, acetamide, chloroacetamide, trichloroacetamide, trifluoroacetamide, phenylacetamide, 3– phenylpropanamide, picolinamide, 3–pyridylcarboxamide, N–benzoylphenylalanyl derivative, benzamide, p–phenylbenzamide, o–nitrophenylacetamide, o–nitrophenoxyacetamide, acetoacetamide, (N’–dithiobenzyloxyacylamino)acetamide, 3–(p–hydroxyphenyl)propanamide, 3–(o–nitrophenyl)propanamide, 2–methyl–2–(o–nitrophenoxy)propanamide, 2–methyl–2–(o– phenylazophenoxy)propanamide, 4–chlorobutanamide, 3–methyl–3–nitrobutanamide, o– nitrocinnamide, N–acetylmethionine, o–nitrobenzamide, and o–(benzoyloxymethyl)benzamide. Carbamate nitrogen protecting groups (e.g., –C(=O)OR ^aa ) include methyl carbamate, ethyl carbamate, 9–fluorenylmethyl carbamate (Fmoc), 9–(2–sulfo)fluorenylmethyl carbamate, 9–(2,7–dibromo)fluorenylmethyl carbamate, 2,7–di–t–butyl–[9–(10,10–dioxo–10,10,10,10– tetrahydrothioxanthyl)]methyl carbamate (DBD–Tmoc), 4–methoxyphenacyl carbamate (Phenoc), 2,2,2–trichloroethyl carbamate (Troc), 2–trimethylsilylethyl carbamate (Teoc), 2– phenylethyl carbamate, 1–(1–adamantyl)–1–methylethyl carbamate (Adpoc), 1,1–dimethyl–2– haloethyl carbamate, 1,1–dimethyl–2,2–dibromoethyl carbamate (DB–t–BOC), 1,1–dimethyl– 2,2,2–trichloroethyl carbamate (TCBOC), 1–methyl–1–(4–biphenylyl)ethyl carbamate (Bpoc), 1–(3,5–di–t–butylphenyl)–1–methylethyl carbamate (t–Bumeoc), 2–(2’– and 4’–pyridyl)ethyl carbamate (Pyoc), 2–(N,N–dicyclohexylcarboxamido)ethyl carbamate, t–butyl carbamate (BOC), 1–adamantyl carbamate (Adoc), vinyl carbamate (Voc), allyl carbamate (Alloc), 1–isopropylallyl carbamate (Ipaoc), cinnamyl carbamate (Coc), 4–nitrocinnamyl carbamate (Noc), 8–quinolyl carbamate, N–hydroxypiperidinyl carbamate, alkyldithio carbamate, benzyl carbamate (Cbz), p– methoxybenzyl carbamate (Moz), p–nitrobenzyl carbamate, p–bromobenzyl carbamate, p– chlorobenzyl carbamate, 2,4–dichlorobenzyl carbamate, 4–methylsulfinylbenzyl carbamate (Msz), 9–anthrylmethyl carbamate, diphenylmethyl carbamate, 2–methylthioethyl carbamate, 2– methylsulfonylethyl carbamate, 2–(p–toluenesulfonyl)ethyl carbamate, [2–(1,3–dithianyl)]methyl carbamate (Dmoc), 4–methylthiophenyl carbamate (Mtpc), 2,4–dimethylthiophenyl carbamate (Bmpc), 2–phosphonioethyl carbamate (Peoc), 2–triphenylphosphonioisopropyl carbamate (Ppoc), 1,1–dimethyl–2–cyanoethyl carbamate, m–chloro–p–acyloxybenzyl carbamate, p– (dihydroxyboryl)benzyl carbamate, 5–benzisoxazolylmethyl carbamate, 2–(trifluoromethyl)–6– chromonylmethyl carbamate (Tcroc), m–nitrophenyl carbamate, 3,5–dimethoxybenzyl carbamate, o–nitrobenzyl carbamate, 3,4–dimethoxy–6–nitrobenzyl carbamate, phenyl(o– nitrophenyl)methyl carbamate, t–amyl carbamate, S–benzyl thiocarbamate, p–cyanobenzyl carbamate, cyclobutyl carbamate, cyclohexyl carbamate, cyclopentyl carbamate, cyclopropylmethyl carbamate, p–decyloxybenzyl carbamate, 2,2–dimethoxyacylvinyl carbamate, o–(N,N–dimethylcarboxamido)benzyl carbamate, 1,1–dimethyl–3–(N,N– dimethylcarboxamido)propyl carbamate, 1,1–dimethylpropynyl carbamate, di(2–pyridyl)methyl carbamate, 2–furanylmethyl carbamate, 2–iodoethyl carbamate, isobornyl carbamate, isobutyl carbamate, isonicotinyl carbamate, p–(p’–methoxyphenylazo)benzyl carbamate, 1– methylcyclobutyl carbamate, 1–methylcyclohexyl carbamate, 1–methyl–1–cyclopropylmethyl carbamate, 1–methyl–1–(3,5–dimethoxyphenyl)ethyl carbamate, 1–methyl–1–(p– phenylazophenyl)ethyl carbamate, 1–methyl–1–phenylethyl carbamate, 1–methyl–1–(4– pyridyl)ethyl carbamate, phenyl carbamate, p–(phenylazo)benzyl carbamate, 2,4,6–tri–t– butylphenyl carbamate, 4–(trimethylammonium)benzyl carbamate, and 2,4,6–trimethylbenzyl carbamate. Sulfonamide nitrogen protecting groups (e.g., –S(=O) ₂ R ^aa ) include p–toluenesulfonamide (Ts), benzenesulfonamide, 2,3,6,–trimethyl–4–methoxybenzenesulfonamide (Mtr), 2,4,6– trimethoxybenzenesulfonamide (Mtb), 2,6–dimethyl–4–methoxybenzenesulfonamide (Pme), 2,3,5,6–tetramethyl–4–methoxybenzenesulfonamide (Mte), 4–methoxybenzenesulfonamide (Mbs), 2,4,6–trimethylbenzenesulfonamide (Mts), 2,6–dimethoxy–4–methylbenzenesulfonamide (iMds), 2,2,5,7,8–pentamethylchroman–6–sulfonamide (Pmc), methanesulfonamide (Ms), β– trimethylsilylethanesulfonamide (SES), 9–anthracenesulfonamide, 4–(4’,8’– dimethoxynaphthylmethyl)benzenesulfonamide (DNMBS), benzylsulfonamide, trifluoromethylsulfonamide, and phenacylsulfonamide. Other nitrogen protecting groups include phenothiazinyl–(10)–acyl derivative, N’–p– toluenesulfonylaminoacyl derivative, N’–phenylaminothioacyl derivative, N– benzoylphenylalanyl derivative, N–acetylmethionine derivative, 4,5–diphenyl–3–oxazolin–2– one, N–phthalimide, N–dithiasuccinimide (Dts), N–2,3–diphenylmaleimide, N–2,5– dimethylpyrrole, N–1,1,4,4–tetramethyldisilylazacyclopentane adduct (STABASE), 5– substituted 1,3–dimethyl–1,3,5–triazacyclohexan–2–one, 5–substituted 1,3–dibenzyl–1,3,5– triazacyclohexan–2–one, 1–substituted 3,5–dinitro–4–pyridone, N–methylamine, N–allylamine, N–[2–(trimethylsilyl)ethoxy]methylamine (SEM), N–3–acetoxypropylamine, N–(1–isopropyl–4– nitro–2–oxo–3–pyrrolin–3–yl)amine, quaternary ammonium salts, N–benzylamine, N–di(4– methoxyphenyl)methylamine, N–5–dibenzosuberylamine, N–triphenylmethylamine (Tr), N–[(4– methoxyphenyl)diphenylmethyl]amine (MMTr), N–9–phenylfluorenylamine (PhF), N–2,7– dichloro–9–fluorenylmethyleneamine, N–ferrocenylmethylamino (Fcm), N–2–picolylamino N’– oxide, N–1,1–dimethylthiomethyleneamine, N–benzylideneamine, N–p– methoxybenzylideneamine, N–diphenylmethyleneamine, N–[(2– pyridyl)mesityl]methyleneamine, N–(N’,N’–dimethylaminomethylene)amine, N,N’– isopropylidenediamine, N–p–nitrobenzylideneamine, N–salicylideneamine, N–5– chlorosalicylideneamine, N–(5–chloro–2–hydroxyphenyl)phenylmethyleneamine, N– cyclohexylideneamine, N–(5,5–dimethyl–3–oxo–1–cyclohexenyl)amine, N–borane derivative, N–diphenylborinic acid derivative, N–[phenyl(pentaacylchromium– or tungsten)acyl]amine, N– copper chelate, N–zinc chelate, N–nitroamine, N–nitrosoamine, amine N–oxide, diphenylphosphinamide (Dpp), dimethylthiophosphinamide (Mpt), diphenylthiophosphinamide (Ppt), dialkyl phosphoramidates, dibenzyl phosphoramidate, diphenyl phosphoramidate, benzenesulfenamide, o–nitrobenzenesulfenamide (Nps), 2,4–dinitrobenzenesulfenamide, pentachlorobenzenesulfenamide, 2–nitro–4–methoxybenzenesulfenamide, triphenylmethylsulfenamide, and 3–nitropyridinesulfenamide (Npys). In certain embodiments, a nitrogen protecting group is Bn, Boc, Cbz, Fmoc, trifluoroacetyl, triphenylmethyl, acetyl, or Ts. In certain embodiments, the oxygen atom substituents are independently substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, −C(=O)R ^aa , −CO2R ^aa , −C(=O)N(R ^bb ) ₂ , or an oxygen protecting group. In certain embodiments, the oxygen atom substituents are independently substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, −C(=O)R ^aa , −CO2R ^aa , −C(=O)N(R ^bb )2, or an oxygen protecting group, wherein R ^aa is hydrogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C _1-6 alkyl, or an oxygen protecting group when attached to an oxygen atom; and each R ^bb is independently hydrogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, or a nitrogen protecting group. In certain embodiments, the oxygen atom substituents are independently substituted (e.g., substituted with one or more halogen) or unsubstituted C _1-6 alkyl or an oxygen protecting group. In certain embodiments, the substituent present on an oxygen atom is an oxygen protecting group (also referred to herein as an “hydroxyl protecting group”). Oxygen protecting groups include −R ^aa , −N(R ^bb ) ₂ , −C(=O)SR ^aa , −C(=O)R ^aa , −CO ₂ R ^aa , −C(=O)N(R ^bb ) ₂ , −C(=NR ^bb )R ^aa , −C(=NR ^bb )OR ^aa , −C(=NR ^bb )N(R ^bb )2, −S(=O)R ^aa , −SO2R ^aa , −Si(R ^aa )3, −P(R ^cc )2, wherein X ⁻ , R ^aa , R ^bb , and R ^cc are as defined herein. Oxygen protecting groups are well known in the art and include those described in detail in Protecting Groups in Organic Synthesis, T. W. Greene and P. G. M. Wuts, 3 ^rd edition, John Wiley & Sons, 1999, incorporated herein by reference. Exemplary oxygen protecting groups include methyl, methoxylmethyl (MOM), methylthiomethyl (MTM), t–butylthiomethyl, (phenyldimethylsilyl)methoxymethyl (SMOM), benzyloxymethyl (BOM), p–methoxybenzyloxymethyl (PMBM), (4–methoxyphenoxy)methyl (p–AOM), guaiacolmethyl (GUM), t–butoxymethyl, 4–pentenyloxymethyl (POM), siloxymethyl, 2–methoxyethoxymethyl (MEM), 2,2,2–trichloroethoxymethyl, bis(2–chloroethoxy)methyl, 2– (trimethylsilyl)ethoxymethyl (SEMOR), tetrahydropyranyl (THP), 3–bromotetrahydropyranyl, tetrahydrothiopyranyl, 1–methoxycyclohexyl, 4–methoxytetrahydropyranyl (MTHP), 4– methoxytetrahydrothiopyranyl, 4–methoxytetrahydrothiopyranyl S,S–dioxide, 1–[(2–chloro–4– methyl)phenyl]–4–methoxypiperidin–4–yl (CTMP), 1,4–dioxan–2–yl, tetrahydrofuranyl, tetrahydrothiofuranyl, 2,3,3a,4,5,6,7,7a–octahydro–7,8,8–trimethyl–4,7–me thanobenzofuran–2– yl, 1–ethoxyethyl, 1–(2–chloroethoxy)ethyl, 1–methyl–1–methoxyethyl, 1–methyl–1– benzyloxyethyl, 1–methyl–1–benzyloxy–2–fluoroethyl, 2,2,2–trichloroethyl, 2– trimethylsilylethyl, 2–(phenylselenyl)ethyl, t–butyl, allyl, p–chlorophenyl, p–methoxyphenyl, 2,4–dinitrophenyl, benzyl (Bn), p–methoxybenzyl, 3,4–dimethoxybenzyl, o–nitrobenzyl, p– nitrobenzyl, p–halobenzyl, 2,6–dichlorobenzyl, p–cyanobenzyl, p–phenylbenzyl, 2–picolyl, 4– picolyl, 3–methyl–2–picolyl N–oxido, diphenylmethyl, p,p’–dinitrobenzhydryl, 5– dibenzosuberyl, triphenylmethyl, α–naphthyldiphenylmethyl, p–methoxyphenyldiphenylmethyl, di(p–methoxyphenyl)phenylmethyl, tri(p–methoxyphenyl)methyl, 4–(4′– bromophenacyloxyphenyl)diphenylmethyl, 4,4′,4″–tris(4,5–dichlorophthalimidophenyl)methyl, 4,4′,4″–tris(levulinoyloxyphenyl)methyl, 4,4′,4″–tris(benzoyloxyphenyl)methyl, 3–(imidazol–1– yl)bis(4′,4″–dimethoxyphenyl)methyl, 1,1–bis(4–methoxyphenyl)–1′–pyrenylmethyl, 9–anthryl, 9–(9–phenyl)xanthenyl, 9–(9–phenyl–10–oxo)anthryl, 1,3–benzodisulfuran–2–yl, benzisothiazolyl S,S–dioxido, trimethylsilyl (TMS), triethylsilyl (TES), triisopropylsilyl (TIPS), dimethylisopropylsilyl (IPDMS), diethylisopropylsilyl (DEIPS), dimethylthexylsilyl, t– butyldimethylsilyl (TBDMS), t–butyldiphenylsilyl (TBDPS), tribenzylsilyl, tri–p–xylylsilyl, triphenylsilyl, diphenylmethylsilyl (DPMS), t–butylmethoxyphenylsilyl (TBMPS), formate, benzoylformate, acetate, chloroacetate, dichloroacetate, trichloroacetate, trifluoroacetate, methoxyacetate, triphenylmethoxyacetate, phenoxyacetate, p–chlorophenoxyacetate, 3– phenylpropionate, 4–oxopentanoate (levulinate), 4,4–(ethylenedithio)pentanoate (levulinoyldithioacetal), pivaloate, adamantoate, crotonate, 4–methoxycrotonate, benzoate, p– phenylbenzoate, 2,4,6–trimethylbenzoate (mesitoate), alkyl methyl carbonate, 9–fluorenylmethyl carbonate (Fmoc), alkyl ethyl carbonate, alkyl 2,2,2–trichloroethyl carbonate (Troc), 2– (trimethylsilyl)ethyl carbonate (TMSEC), 2–(phenylsulfonyl) ethyl carbonate (Psec), 2– (triphenylphosphonio) ethyl carbonate (Peoc), alkyl isobutyl carbonate, alkyl vinyl carbonate alkyl allyl carbonate, alkyl p–nitrophenyl carbonate, alkyl benzyl carbonate, alkyl p– methoxybenzyl carbonate, alkyl 3,4–dimethoxybenzyl carbonate, alkyl o–nitrobenzyl carbonate, alkyl p–nitrobenzyl carbonate, alkyl S–benzyl thiocarbonate, 4–ethoxy–1–napththyl carbonate, methyl dithiocarbonate, 2–iodobenzoate, 4–azidobutyrate, 4–nitro–4–methylpentanoate, o– (dibromomethyl)benzoate, 2–formylbenzenesulfonate, 2–(methylthiomethoxy)ethyl, 4– (methylthiomethoxy)butyrate, 2–(methylthiomethoxymethyl)benzoate, 2,6–dichloro–4– methylphenoxyacetate, 2,6–dichloro–4–(1,1,3,3–tetramethylbutyl)phenoxyacet ate, 2,4–bis(1,1– dimethylpropyl)phenoxyacetate, chlorodiphenylacetate, isobutyrate, monosuccinoate, (E)–2– methyl–2–butenoate, o–(methoxyacyl)benzoate, α–naphthoate, nitrate, alkyl N,N,N’,N’– tetramethylphosphorodiamidate, alkyl N–phenylcarbamate, borate, dimethylphosphinothioyl, alkyl 2,4–dinitrophenylsulfenate, sulfate, methanesulfonate (mesylate), benzylsulfonate, and tosylate (Ts). In certain embodiments, an oxygen protecting group is silyl, TBDPS, TBDMS, TIPS, TES, TMS, MOM, THP, t-Bu, Bn, allyl, acetyl, pivaloyl, or benzoyl. In certain embodiments, the sulfur atom substituents are independently substituted (e.g., substituted with one or more halogen) or unsubstituted C _1-6 alkyl, −C(=O)R ^aa , −CO ₂ R ^aa , −C(=O)N(R ^bb )2, or a sulfur protecting group. In certain embodiments, the sulfur atom substituents are independently substituted (e.g., substituted with one or more halogen) or unsubstituted C _1-6 alkyl, −C(=O)R ^aa , −CO ₂ R ^aa , −C(=O)N(R ^bb ) ₂ , or a sulfur protecting group, wherein R ^aa is hydrogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl, or an oxygen protecting group when attached to an oxygen atom; and each R ^bb is independently hydrogen, substituted (e.g., substituted with one or more halogen) or unsubstituted C _1-6 alkyl, or a nitrogen protecting group. In certain embodiments, the sulfur atom substituents are independently substituted (e.g., substituted with one or more halogen) or unsubstituted C1-6 alkyl or a sulfur protecting group. In certain embodiments, the substituent present on a sulfur atom is a sulfur protecting group (also referred to as a “thiol protecting group”). Sulfur protecting groups include −R ^aa , −P(OR ^cc ) ₃ ⁺ X ⁻ , −P(=O)(R ^aa ) ₂ , −P(=O)(OR ^cc ) ₂ , and −P(=O)(N(R ^bb ) ₂ ) ₂ , wherein R ^aa , R ^bb , and R ^cc are as defined herein. Sulfur protecting groups are well known in the art and include those described in detail in Protecting Groups in Organic Synthesis, T. W. Greene and P. G. M. Wuts, 3 ^rd edition, John Wiley & Sons, 1999, incorporated herein by reference. In certain embodiments, a sulfur protecting group is acetamidomethyl, t-Bu, 3-nitro-2-pyridine sulfenyl, 2-pyridine- sulfenyl, or triphenylmethyl. The “molecular weight” of –R, wherein –R is any monovalent moiety, is calculated by subtracting the atomic weight of a hydrogen atom from the molecular weight of the molecule R– H. The “molecular weight” of –L–, wherein –L– is any divalent moiety, is calculated by subtracting the combined atomic weight of two hydrogen atoms from the molecular weight of the molecule H–L–H. In certain embodiments, the molecular weight of a substituent is lower than 200, lower than 150, lower than 100, lower than 50, or lower than 25 g/mol. In certain embodiments, a substituent consists of carbon, hydrogen, fluorine, chlorine, bromine, iodine, oxygen, sulfur, nitrogen, and/or silicon atoms. In certain embodiments, a substituent consists of carbon, hydrogen, fluorine, chlorine, bromine, and/or iodine atoms. In certain embodiments, a substituent consists of carbon, hydrogen, and/or fluorine atoms. In certain embodiments, a substituent does not comprise one or more, two or more, or three or more hydrogen bond donors. In certain embodiments, a substituent does not comprise one or more, two or more, or three or more hydrogen bond acceptors. The term “salt” refers to ionic compounds that result from the neutralization reaction of an acid and a base. A salt is composed of one or more cations (positively charged ions) and one or more anions (negative ions) so that the salt is electrically neutral (without a net charge). Salts of the compounds of this invention include those derived from inorganic and organic acids and bases. Examples of acid addition salts are salts of an amino group formed with inorganic acids, such as hydrochloric acid, hydrobromic acid, phosphoric acid, sulfuric acid, and perchloric acid, or with organic acids, such as acetic acid, oxalic acid, maleic acid, tartaric acid, citric acid, succinic acid, or malonic acid or by using other methods known in the art such as ion exchange. Other salts include adipate, alginate, ascorbate, aspartate, benzenesulfonate, benzoate, bisulfate, borate, butyrate, camphorate, camphorsulfonate, citrate, cyclopentanepropionate, digluconate, dodecylsulfate, ethanesulfonate, formate, fumarate, glucoheptonate, glycerophosphate, gluconate, hemisulfate, heptanoate, hexanoate, hydroiodide, 2–hydroxy–ethanesulfonate, lactobionate, lactate, laurate, lauryl sulfate, malate, maleate, malonate, methanesulfonate, 2– naphthalenesulfonate, nicotinate, nitrate, oleate, oxalate, palmitate, pamoate, pectinate, persulfate, 3–phenylpropionate, phosphate, picrate, pivalate, propionate, stearate, succinate, sulfate, tartrate, thiocyanate, p-toluenesulfonate, undecanoate, valerate, hippurate, and the like. Salts derived from appropriate bases include alkali metal, alkaline earth metal, ammonium, and N ⁺ (C _1–4 alkyl) ₄ salts. Representative alkali or alkaline earth metal salts include sodium, lithium, potassium, calcium, magnesium, and the like. Further salts include ammonium, quaternary ammonium, and amine cations formed using counterions such as halide, hydroxide, carboxylate, sulfate, phosphate, nitrate, lower alkyl sulfonate, and aryl sulfonate. The term “solvate” refers to forms of the compound that are associated with a solvent, usually by a solvolysis reaction. This physical association may include hydrogen bonding. Conventional solvents include water, methanol, ethanol, acetic acid, DMSO, THF, diethyl ether, and the like. The provided compounds may be prepared, e.g., in crystalline form, and may be solvated. Suitable solvates include pharmaceutically acceptable solvates and further include both stoichiometric solvates and non-stoichiometric solvates. In certain instances, the solvate will be capable of isolation, for example, when one or more solvent molecules are incorporated in the crystal lattice of a crystalline solid. “Solvate” encompasses both solution-phase and isolable solvates. Representative solvates include hydrates, ethanolates, and methanolates. The term “hydrate” refers to a compound that is associated with water. Typically, the number of the water molecules contained in a hydrate of a compound is in a definite ratio to the number of the compound molecules in the hydrate. Therefore, a hydrate of a compound may be represented, for example, by the general formula R⋅x H2O, wherein R is the compound and wherein x is a number greater than 0. A given compound may form more than one type of hydrates, including, e.g., monohydrates (x is 1), lower hydrates (x is a number greater than 0 and smaller than 1, e.g., hemihydrates (R⋅0.5 H ₂ O)), and polyhydrates (x is a number greater than 1, e.g., dihydrates (R⋅2 H ₂ O) and hexahydrates (R⋅6 H ₂ O)). The term “tautomers” refers to compounds that are interchangeable forms of a particular compound structure, and that vary in the displacement of hydrogen atoms and electrons. Thus, two structures may be in equilibrium through the movement of π electrons and an atom (usually H). For example, enols and ketones are tautomers because they are rapidly interconverted by treatment with either acid or base. Another example of tautomerism is the aci- and nitro- forms of phenylnitromethane, that are likewise formed by treatment with acid or base. Tautomeric forms may be relevant to the attainment of the optimal chemical reactivity and biological activity of a compound of interest. It is also to be understood that compounds that have the same molecular formula but differ in the nature or sequence of bonding of their atoms or the arrangement of their atoms in space are termed “isomers.” Isomers that differ in the arrangement of their atoms in space are termed “stereoisomers.” Stereoisomers that are not mirror images of one another are termed “diastereomers,” and those that are non-superimposable mirror images of each other are termed “enantiomers.” When a compound has an asymmetric center, for example, it is bonded to four different groups, a pair of enantiomers is possible. An enantiomer can be characterized by the absolute configuration of its asymmetric center and is described by the R- and S-sequencing rules of Cahn and Prelog, or by the manner in which the molecule rotates the plane of polarized light and designated as dextrorotatory or levorotatory (i.e., as (+) or (-)-isomers respectively). A chiral compound can exist as either individual enantiomer or as a mixture thereof. A mixture containing equal proportions of the enantiomers is called a “racemic mixture.” The term “polymorphs” refers to a crystalline form of a compound (or a salt, hydrate, or solvate thereof) in a particular crystal packing arrangement. All polymorphs have the same elemental composition. Different crystalline forms usually have different X-ray diffraction patterns, infrared spectra, melting points, density, hardness, crystal shape, optical and electrical properties, stability, and solubility. Recrystallization solvent, rate of crystallization, storage temperature, and other factors may cause one crystal form to dominate. Various polymorphs of a compound can be prepared by crystallization under different conditions. The term “co-crystal” refers to a crystalline structure comprising at least two different components (e.g., a provided compound and an acid), wherein each of the components is independently an atom, ion, or molecule. In certain embodiments, none of the components is a solvent. In certain embodiments, at least one of the components is a solvent. A co-crystal of a provided compound and an acid is different from a salt formed from a provided compound and the acid. In the salt, a provided compound is complexed with the acid in a way that proton transfer (e.g., a complete proton transfer) from the acid to a provided compound easily occurs at room temperature. In the co-crystal, however, a provided compound is complexed with the acid in a way that proton transfer from the acid to a provided herein does not easily occur at room temperature. In certain embodiments, in the co-crystal, there is no proton transfer from the acid to a provided compound. In certain embodiments, in the co-crystal, there is partial proton transfer from the acid to a provided compound. Co-crystals may be useful to improve the properties (e.g., solubility, stability, and ease of formulation) of a provided compound. The terms "incubating" and "incubation" refer to a process of mixing two or more chemical or biological entities (such as a chemical compound and an enzyme) and allowing them to interact under conditions favorable for producing a desired product. The term “catalyst enhancer” includes any component which when added to a method of cyclopropanation improves one or more of its yield, selectivity, reaction times, and energy requirements, suitably in the presence of a transition metal catalyst. The term excludes components which would otherwise act as cyclopropanation catalysts. The term “equivalent weight” of an acid refers to the molecular weight of the acid divided by its basicity. By way of example, the equivalent weight of monobasic acid HCl is equal to its molecular weight, while the equivalent weight of dibasic acid H2SO4 is equal to half its molecular weight. Hence, one equivalent of an acid is equal to a mole of the compound in the instance of a monobasic acid, half a mole in that of a dibasic acid, and a third of a mole for a tribasic acid. BRIEF DESCRIPTION OF THE DRAWINGS FIG.1 shows a ¹ H NMR (400 MHz, CDCl3) of a purified (E)-Δ- farnesene product. FIG.2 shows a ¹³ C NMR (400 MHz, CDCl3) of a purified (E)-Δ-farnesene product. FIG.3 shows a ¹ H NMR (400 MHz, CDCl ₃ ) of a purified homofarnesol chloroacetate product. FIG.4 shows a ¹³ C NMR (400 MHz, CDCl3) of a purified homofarnesol chloroacetate product. FIG.5 shows a ¹ H NMR (400 MHz, CDCl ₃ ) of a purified homofarnesol product. FIG.6 shows a ¹³ C NMR (400 MHz, CDCl3) of a purified homofarnesol product. FIG.7 shows a GC/MS spectrum of (E)-β-farnesene. FIG.8 shows a GC/MS spectrum of a crude (E)-Δ-farnesene product. FIG.9 shows a GC/MS spectrum of a crude homofarnesol chloroacetate product. FIG.10 shows a GC/MS spectrum of a crude homofarnesol product. DETAILED DESCRIPTION OF CERTAIN ASPECTS AND EMBODIMENTS OF THE DISCLOSURE In a first aspect, the present disclosure provides a method of ring formation across carbon-carbon multiple bonds, and in particular the cyclopropanation of alkenes. The disclosure also relates to the regioselective cyclopropanation of polyprene substrates to yield compounds comprising a terminal cyclopropylvinyl moiety. Applicant has found a novel, surprising manner for catalyzing the cyclopropanation of alkenes, and in particular polyprenes. Specifically, Applicant has discovered that certain nickel-based compounds perform the function of catalytic enhancers in whose presence the reaction proceeds more rapidly, with higher regioselectivity, at higher yields, and with fewer side products than in traditional methods. The foregoing beneficial effects have been found to occur in instances where the enhancer is added to known transition metal catalysts. For example, Applicant has demonstrated that the process of cyclopropanation of alkenes in the presence of Pd(II) catalysts increases in yield and selectivity while shortening reaction times upon the addition of a Ni(II)-based catalyst enhancer to the reaction mixture. Moreover, the cyclopropanation reaction no longer requires high pressures or temperatures, thereby facilitating scale-up and minimizing energy expenditures, and the product compounds are easier to purify. Cyclopropanation On the basis of this unexpected finding, the present disclosure provides an organic synthetic method featuring ring formation across a carbon-carbon multiple bond in a substrate compound to convert an alkene or an alkyne moiety to a cyclopropane ring or a cyclopropene ring, respectively. Notably, the process is particularly suitable to selectively cyclopropanate terminal alkenes such as polyprenoid compounds. According to an aspect of the invention, the method includes forming a reaction mixture from components comprising a substrate compound that comprises a carbon-carbon multiple bond, a diazo alkylating reagent, a cyclopropanation catalyst, and a nickel-based catalyst enhancer. The reaction mixture thus formed is incubated for a sufficient amount of time to yield a product comprising a cyclopropyl moiety. Mixing of the components may be performed in any suitable order, i.e., the components in their respective phases may all be mixed together in one mixing step or the mixing may be performed in more than one step. In one embodiment, a first mixture is formed by mixing the substrate and the nickel catalyst enhancer, optionally in the presence of a solvent, e.g., an ether such as diethyl ether or tetrahydrofuran. The palladium catalyst is then combined with the first mixture, yielding a second mixture to which the diazo compound is added optionally portion-wise. The resulting reaction mixture is left to incubate for a duration of time sufficient to produce a desired amount of a compound that comprises a cyclopropyl moiety. The reaction ingredients need not necessarily be combined in the above order, provided that the desired cyclopropanation reaction takes place at acceptable rates and yields. As anticipated above, the cyclopropanation method of the invention does not require high temperatures, resulting in energy savings over traditional synthetic routes. In certain embodiments, the temperature of the reaction mixture is between -50 and 30, between -40 and 25, between -30 and 15, between -20 and 10, or between -5 and 5 ºC, inclusive. In certain embodiments, the temperature of the reaction mixture is substantially constant during the mixing steps and the subsequent incubation time. In exemplary embodiments, the incubation time is between 0.3 and 3 hours, between 0.5 to and 2 hours, between 0.75 and 1.5 hours, or between 0.9 and 1.1 hours, inclusive. Well-known olefin cyclopropanation catalysts include transition metal compounds and especially coordination complexes of generic formula ML2, M being a metal atom and each L being a ligand. Most prominent among such catalysts are Pd(II) compounds which are well established and known in the art. Examples of suitable palladium catalysts are described by Nefedov et al. in Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya 8, 1861 - 1869 (1989). Pd(II) compounds. Palladium(II) coordination complexes, e.g., palladium(II) bis(acetylacetonate) (Pd(acac)2), palladium(II) acetate (Pd(OAc)2), and palladium(II) chloride (PdCl2) are particularly useful when ethylene and mono- or disubstituted alkene substrates are to be cyclopropanated. Other traditional alkene transition metal cyclopropanation catalysts include compounds based on Pt(II), e.g., platinum(II) bis(acetylacetonate) (Pt(acac)2), platinum(II) acetate (Pt(OAc)2), and platinum(II) chloride (PtCl2); compounds based on Cu(II), e.g., copper(II) bis(acetylacetonate) (Cu(acac) ₂ ), copper(II) acetate (Cu(OAc) ₂ ), and copper(II) chloride (CuCl ₂ ); and compounds based on Ru(II), e.g., rhodium(II) bis(acetylacetonate) (Ru(acac)2), rhodium(II) acetate (Ru(OAc)2), and rhodium(II) chloride (RuCl2). Nickel compounds which find use as catalyst enhancers include coordination complexes of Ni(II), for example nickel(II) bis(acetylacetonate) (Ni(acac) ₂ ), nickel(II) acetate (Ni(OAc) ₂ ), and nickel(II) chloride (NiCl2). The amount of transition metal catalyst employed in the cyclopropanation reaction is, in representative embodiments, about 1 x 10 ^-4 to 1 x 10 ^-1 per mole of the substrate compound, which in this type of reaction is typically the limiting reagent. In some embodiments, about 1 x 10 ^-3 to 1 x 10 ^-1 moles catalyst per mole of substrate compound are used. The ratio of the moles of nickel catalyst enhancer to the moles of cyclopropanation catalyst may be in the range of at least 0.1 to at most 10. Narrower ranges, for example at least 0.5 to at most 5 or at least 0.9 to at most 1.1, are also contemplated. In exemplary embodiments, the diazo alkylation reagent is a diazoalkane (such as diazomethane, diazoethane, diazopropane, diazobutane and homologs) and diazomethane in particular. Diazo compounds tend be unstable and toxic so are usually prepared in situ from precursors. The majority of precursors contain as N-alkyl-N-nitroso group, which generates diazoalkane upon treatment with base. In one example, diazomethane can be obtained from N- methyl-N-nitroso compounds (MNC's) with the general formula R(N(NO)Me)x such as N- methyl-N-nitrosourea (MNU). The MNU can also be synthesized in situ or provided in liquid phase and its conversion to diazomethane is attractive for subsequent cyclopropanation reactions. The substitution of MNU by N-nitroso compounds of lower toxicity such as N-methyl-N-nitroso- p-toluenesulfonamide (Diazald®) or relatively more stable silyl compounds such as (trimethylsilyl)diazomethane (TMSDAM) is well known to chemists, although transportation and dissolution of Diazald® and TMSDAM can be economically undesirable due to their relatively high molecular weights. Beside N-methyl-N-nitroso compounds and (trimethylsilyl)diazomethane, one can employ other N-alkyl-N-nitroso compounds, wherein the alkyl group is ethyl, or higher alkyl groups such as propyl, butyl or higher alkyl groups, which may be linear or branched and may be substituted or unsubstituted, such as N-ethyl- N-nitroso urea, N-butyl-N-nitroso urea, 4- (ethylnitrosoamino)-4-methyl-2 pentanone (CAS 5569-45-9) or N-nitroso-N-2-propyn-l-yl- acetamid (CAS 90927-84-7). In order to illustrate the invention however, in the remainder of the specification, reference will mainly be made to MNC's and to reactions concerned with the cyclopropanation of alkenes. Typically, the N-alkyl-N-nitroso compound is generated in situ or in liquid phase from a mixture of an HNRR compound (R in this instance being an alkyl group), water, NaNO ₂ and an acid. The MNC's are generated in liquid phase from an aqueous mixture comprising a methyl amine or a derivative of a methylamine, NaNO2, and an acid. An organic solvent can be added to the MNC once it is formed to facilitate phase separation. In particular, MNU may be generated in liquid phase from an aqueous mixture comprising methylurea, NaNO ₂ , and an acid. Alternatively, instead of using methylurea, one can generate this using methylamine or its salts, and urea. Once the MNC is formed, it partitions into the organic solvent provided for that purpose. A biphasic mixture is formed, and the organic phase can be separated from the aqueous phase in a phase separation step. Thereafter, the organic phase containing the MNC is added to an alkene substrate, without having first to isolate the MNC in pure form. As the MNC is in an organic solvent, it can be cleanly and simply transferred into a reaction vessel containing the alkene substrate. Suitable N-Methyl-N-nitroso compounds (MNC's) in organic liquid phase are such which can be easily prepared as such from inexpensive components and comprise preferably but not limiting MNC's such as N-methyl-N-nitroso urea (MNU), ethyl N-Methyl-N-nitroso urethane (nitroso-EMU) or N-nitroso-methylaminoisobutyl methyl ketone (NMK). The term "N-methyl-N-nitroso compound generated in organic liquid phase" includes the generation of N-alkyl-N-nitroso compounds as organic liquid phase, such as nitroso-EMU or NMK. Alternatively, a N-alkyl-N-nitroso compound, which can exist in solid form, can be dissolved in an organic liquid phase. The method according to this aspect of the invention can be used to cyclopropanate substrate compounds which comprise a carbon-carbon multiple bond, inclusive of any type of mono- and disubstituted alkene substrates. In some embodiments, the alkene substrate is terminal (mono-substituted) alkene, i.e., an alkene wherein R ² is an H atom. R ¹ may be an alkyl, alkylidene, or aryl, which may be branched or unbranched and substituted or unsubstituted. Other alkene substrates are exo-methylene compounds (i.e. those in which R ¹ and R ² are independently alkyl, alkylidene or aryl). In terminal non-activated isoprenes, wherein R ³ is alkyl, alkylidene, or aryl, the method can achieve the cyclopropanation of the terminal double bond while the exo- methylene double bond only reacts at lower than detectable levels. Terminal isoprenoid compounds, with one or more trisubstituted double bonds in the substituent R ³ , can be cyclopropanated with high selectivity at the monosubstituted double bond, leaving the other double bonds untouched. This provides a selective access to mono- cyclopropanated myrcene, farnesene or higher polyprenoid derivatives. Especially the vinylcyclopropanes (monocyclopropanated) are valuable intermediates for further transformations, e.g., to homofarnesol and other terpene precursors. The above capability for selective monocyclopropanation provides a method for preparing cyclopropanating isoprenoids substrates of formula I to obtain cyclopropylvinyl derivatives of formula II: I II, in which n is a natural number 0 to 10, inclusive, for example n = 0, 1, 2, or 3. In a particular embodiment, the cyclopropanated product is a molecule of formula III or an isotopically labeled compound, salt, solvate, polymorph, or co-crystal thereof: III, where n is 0, 1, 2, or 3. In a preferred example of the embodiment, (E)-β-farnesene is monocyclopropanated at its terminal double bond to yield [(4E)-5,9-dimethyl-1-methylene-4,8- decadien-1-yl]cyclopropane ((E)-Δ-farnesene) with strong regioselectivity and at high yields. The method may further comprises isolating the cyclopropanated reaction product, or a tautomer, stereoisomer, isotopically labeled compound, salt, solvate, polymorph, or co-crystal thereof. In certain embodiments, the step of isolating described in this paragraph comprises liquid-liquid phase separation, drying, filtration, concentration, chromatography, decolorization, or recrystallization, or a combination thereof. Liquid-liquid phase separation typically entails a separation of an organic phase and an aqueous phase. In certain embodiments, the drying is drying an organic phase over a solid drying agent (e.g., anhydrous Na2SO4, anhydrous MgSO4, anhydrous CaSO4, anhydrous CaCl2, or activated molecular sieves). In certain embodiments, the filtration is a filtration of a mixture of an organic phase and a solid drying agent to remove the solid drying agent and hydrates thereof. Concentration usually includes concentration of an organic phase to remove part or substantially all of the volatiles (e.g., organic solvents). In exemplary instances, the concentration is performed under a pressure lower than 1 atmosphere (“atm”; e.g., between 0.001 and 0.01, between 0.01 and 0.1, or between 0.1 and 1 atm, inclusive). In certain embodiments, the concentration is performed under a temperature of between 0 and 10, between 10 and 20, between 20 and 25, between 25 and 35, between 35 and 50, or between 50 and 80 ºC, inclusive. In some applications, the chromatography is flash chromatography (e.g., normal-phase flash chromatography (e.g., over silica gel)). In certain embodiments, the chromatography is high-performance liquid chromatography (HPLC) (e.g., reverse-phase HPLC or normal-phase HPLC). Depending on the requirement of the application at hand, the step of isolating described in this paragraph may or may not comprise chromatography. In certain embodiments, the decolorization comprises redissolving in an organic solvent, decolorization, and concentration. In certain embodiments, the decolorization comprises contacting with a solid decolorization agent (e.g., activated charcoal). In some instances, the recrystallization is a single- solvent recrystallization. In other instances, the recrystallization is a multi-solvent (e.g., bi- solvent or tri-solvent) recrystallization. In certain embodiments, the recrystallization is a hot filtration-recrystallization. Rearrangement Reaction In a second aspect, a cyclopropanated product of the method as disclosed in the above first aspect is subjected to a rearrangement reaction to form one or more homoallylic compounds. The rearrangement reaction of 1-substituted cyclopropyl precursor β-1 to compounds of structure 2 using various conditions and reagents has been reported in the literature and substituted benzenesulfonamides under Au(I)- or triflic acid-catalysis (A. Togni et al., Adv. Synth. & Cat. 349, 1619 (2007); triethylsilane or triethoxysilane and Wilkinson's catalyst (I. P. Beletskaya et al., Tetrahedron Lett. 3, 7901, 1995); ethyl propiolate and diphenyl diselenide (A. Ogawa et al., J. Org. Chem. 65, 7682, 2000); Wilkinson's catalyst in dichloromethane or chloroform (R. I. Khusnutdinov et al., Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, 1373, 1991) and trimethylsilyl halides (W-D. Z. Li, J-H. Yang, Org. Lett. 6, 1849, 2004) have been used for this transformation. Schroeder (International PCT Application Publication No. WO 2015/059293) reports having carried out the above rearrangement reaction with high E/Z selectivity without the need for transition catalysis, or any other reagent or solvent (in particular, additional non-polar organic solvents such as dichloromethane) other than water and/or alkanoic acid HQ. As reported on Table 1 of Schroeder, the highest E/Z selectivity achieved with its rearrangement reaction was 77/23. Applicant has discovered that E/Z selectivity can be further improved by carrying out the method of Schroeder at relatively low acid concentrations and for relatively short reaction times. Accordingly, the invention provides in this second aspect a method of forming homoallylic compounds 2 from cyclopropylvinyl precursors 1 in the presence of a Bronsted acid HQ: wherein the Bronsted acid HQ is selected from R'CO ₂ H and/ or a hydrogen halide selected from HCl, HBr or HI, wherein R is a C1-30 cyclic, polycyclic or acyclic alkyl residue, or an aryl or polyaryl residue, each of which may be saturated or unsaturated, branched or linear, and substituted or unsubstituted; R' is a C _1-30 alkyl or aryl residue, which may be linear or branched and may be substituted or unsubstituted, and wherein Q is an ester group and/or a halide atom. It was surprisingly found that E/Z selectivity is improved over Schroeder’s method if the ratio of the equivalents of Bronsted acid to the moles of cyclopropylvinyl precursor is 1:1 and the reaction time is about 1 hour. Without being bound to any particular theory, it is believed that such improvements are conducive to milder reaction conditions which result in higher E/Z selectivity rates than previously achieved. In representative embodiments, the ratio of the equivalents of Bronsted acid to the moles of cyclopropylvinyl precursor is from at least 0.75 to at most 1.25. Narrower ranges, for example at least 0.85 to 1.15, or at least 0.95 to at most 1.05, are also contemplated. Typical reactions times may vary from at 0.75 hours to at most 1.25 hours, at least 0.85 hours to at most 1.15 hours, or at least 0.95 hours to at most 1.05 hours. Exemplary reaction temperature range from at least 50 °C to at most 80 °C, at least 60 °C to at most 70 °C, or at least 62.5 °C to at most 67.5 °C. The compound 2 may be hydrolyzed under conditions known to those of ordinary in the art to a homoallylic alcohol 3: When hydrogen halides (HQ = HX) are added to vinylcyclopropane 1 the rearrangement products are homoallylic halides 2' (with Q = X = CI, Br, I) which can be easily converted through nucleophilic substitution with a potassium carboxylates R'CO ₂ - K ⁺ to esters of the general structure 2 (Q = R'CO ₂ ) in the presence of a phase transfer catalyst (PTC), as described for example for X = Br in the literature (Nefedov et al., Org. Prep. Proc. Int. 22, 215, 1990). The resulting esters of the general structure 2 (Q = R'CO2) can be hydrolyzed with aqueous base to homoallylic alcohols of the general structure 3. The whole sequence (from 2' to 3) proceeds without erosion of the E/Z-ratio, so that the E/Z-ratio of 3 is the same one as in 2' under the usual reaction conditions. The improved rearrangement reaction of the present invention starting from vinylcyclopropane substituted substrates 1, gives rearranged 4,4-disubstituted homoallylic halides and esters 2 with unexpectedly high E/Z-selectivities. These selectivities have been found to be as high as 85:15. In one application of this second aspect of the disclosure, a cyclopropylvinyl precursor of formula IV yields the rearrangement products of formula V when reacted with the Bronsted acid

where n is 0, 1, 2, or 3. Compounds of formula V may be hydrolyzed under conditions known from the literature to a homoallylic alcohol of formula VI VI. EXAMPLES In order that the invention described herein may be more fully understood, the following examples are set forth. The examples are offered to illustrate the methods and uses described herein and are not to be construed in any way as limiting their scope. Exemplary Synthesis of Homofarnesol from Farnesene (E)-β-farnesene was subjected to cyclopropanation in the presence of a palladium catalyst followed by rearrangement via reaction with chloroacetic acid. The product was then hydrolyzed to form final product homofarnesol, according to the following synthetic strategy: Chemical Formula: C ₁₅ H ₂₄ Chemical Formula: C ₁₆ H ₂₆ Exact Mass: 204.19 Exact Mass: 218.20 Molecular Weight: 204.36 Molecular Weight: 218.38 Chemical Formula: C ₁₈ H ₂₉ ClO ₂ Exact Mass: 312.19 Molecular Weight: 312.88 Chemical Formula: C ₁₆ H ₂₈ O Exact Mass: 236.21 Molecular Weight: 236.40 As reported below, the presence of the nickel-based catalytic enhancer resulted in a process that proved faster, higher-yielding, and with fewer side products than the traditional synthetic route. Of note, the enhancer did not exhibit appreciable cyclopropanating activity in the absence of the palladium catalyst. Chemicals, Reagents, and Instrumental Analysis All chemicals and reagents were obtained from Sigma-Aldrich (St. Louis, MO) and used without further purification unless noted otherwise. GC-Mass: all samples were analyzed on a SHIMADZU Nexis GC-2030 with a MS- QP2020NX. A 30 m Rtx-5MS column with an inner diameter of 0.25mm was used. The analytical method included a 1:10 split injection at 265 °C with a column flow of 1.35 mL/min. Column injection temperature was set to 80 °C with a hold time of 3 min. Following this duration of time, the column temperature was ramped up to 260 °C at a rate of 45 °C per minute. The MS was set to only scan for ions within the range of 50-400 m/z with a 2000 scan speed. Analysis via MS only commenced after 4.25 minutes of the run. NMR: All the samples were analyzed by Custom NMR Services, Inc. (150V New Boston Street, Woburn, MA 01801, USA) . Proton and ¹³ C spectra were acquired on Bruker AVANCE 400 MHZ instruments, using standard pulse sequences. (all the conditions show on the spectra). Example 1. Synthesis of (4E)-5,9-Dimethyl-1-methylene-4,8-decadien-1-yl]cyclopropane ((E)-Δ- farnesene) (E)-β-farnesene (2.00 g, 9.79 mmol) and nickel (II) acetylacetonate (25 mg, 0.097 mmol) were mixed with tetrahydrofuran (10 ml). Palladium (II) acetylacetonate (29 mg, 0.095 mmol) pre-dissolved in dichloromethane was added. The mixture was stirred at 0 ⁰C and diazomethane (0.82 g, 19.58 mmol) in diethyl ether (10 ml) was added dropwise over 30 minutes. The mixture was stirred at 0 ⁰C for another hour and the reaction was quenched by adding acetic acid (2 ml). Most of the solvents was evaporated under reduced pressure. The residue was mixed with hexane (50 ml) and brine (50 ml) and separated. The organic layer was dried over anhydrous magnesium sulfate, filtered and concentrated under reduced pressure. The residue was purified by a silver nitrate (~10 wt. % loading) on silica gel column with pentane as elute to give 2.01 g of colorless oil product which was dissolved in CDCl3 and analyzed by ¹ H and ¹³ C NMR (FIGS.1 and 2, respectively) As illustrated in the spectrum of FIG. 8, the crude product was also analyzed by GC/MS, which documented the formation of desired (E)-Δ-farnesene (peak at 218, 6.66 min) at previously unattained yields and purity and in the absence of detectable amounts of unreacted substrate or dicyclopropanated side product. Molecular Formula: C ₁₆ H ₂₆ ; Exact Mass: 218.20; GC/MS peak: 218. ¹ H NMR (400 MHz, CDCl3): 5.13 (2 m, 2 H), 4.63(m, 2 H), 2.19 (m, 2 H), 2.07 (m, 4 H), 1.99 (m, 2 H), 1.69 (s, 3 H), 1.62 (2 s, 6 H), 1.30 (m, 1 H), 0.62 (m, 2 H), 0.45 (m, 2 H). ¹³ C NMR (400 MHz, CDCl3): 151.13, 135.33, 131.47, 124.62, 124.40, 106.26, 39.94, 36.22, 26.99, 26.96, 25.89, 17.89, 16.33, 16.24, 6.22. Example 2. Synthesis of (3E,7E)-4,8,12-Trimethyl-3,7,11-tridecatrien-1-yl 2-chloroacetate (homofarnesol chloroacetate) (E)-Δ-farnesene (2.00 g, 9.16 mmol) and chloroacetic acid (2.00 g, 21.16 mmol) were mixed. The mixture was stirred and heated to 65 ⁰C for one hour. After cooled to room temperature, hexane (50 ml) and water (50 ml) were added and separated. The organic layer was washed with saturated sodium bicarbonate solution (50 ml × 2), brine, dried over anhydrous magnesium sulfate, filtered and concentrated under reduced pressure. The residue was purified through a silica gel column with hexane/ethyl acetate (97.5/2.5) as elute to give 2.76 g of colorless oil product. As shown in the GC/MS spectrum of FIG.9, a 3E/3Z product ratio of 85/15 was achieved. Molecular Formula: C18H29ClO2; Exact Mass:312.19; GC/MS peak: 312 at 8.26 min and 8.39 min). ¹ H NMR (400 MHz, CDCl ₃ ): 5.10 (m, 3 H), 4.15 (t, 2 H), 4.05 (s, 2 H),2.37 (m, 2H), 1.95-2.11 (m, 8 H), 1.68 (s, 3 H), 1.63 (s, 3H), 1.59 (s, 6 H). ¹³ C NMR (400 MHz, CDCl3): 167.54, 139.05, 135.40, 131.51, 124.52, 124.09, 118.57, 66.02, 41.12, 39.90, 39.85, 27.55, 26.94, 26.66, 25.89, 17.88, 16.35, 16.20. Example 3. (3E,7E)- 4,8,12-Trimethyl-(3,7,11-Tridecatrien-1-ol (homofarnesol) Homofarnesol chloroacetate (2.00 g, 6.39 mmol) was dissolved in methanol (10 ml). Sodium hydroxide solution (0.50 g in 10 ml water) was added. The mixture was stirred at room temperature for one hour and most of the methanol was evaporated under reduced pressure. The residue was mixed with hexane (50 ml) and water (50 ml) and separated. The organic layer was washed with brine, dried over anhydrous magnesium sulfate, filtered and concentrated under reduced pressure. The residue was purified through a silica gel column with hexane/ethyl acetate (from 100/0 to 95/5) as elute to yield 1.42 g of colorless oil product. As seen in the GC/MS spectrum of FIG.10, the product consisted mostly of the desired trans product (tall peak) with small amounts of the cis side product (low peak). Molecular Formula: C ₁₆ H ₂₈ O; Exact Mass: 236.21; GC/MS peak: 236 at 7.27 min. ¹ H NMR (400 MHz, CDCl3): 5.13 (m, 3 H), 3.60 (t, 2 H), 2.28 (m, 2 H), 1.95-2.13 (m, 8 H), 1.68 (s, 3 H), 1.64 (s, 3 H), 1.59 (s, 6 H). ¹³ C NMR (400 MHz, CDCl3): 139.02, 135.45, 131.47, 124.53, 124.17, 120.08, 62.60, 39.98, 39.89, 31.70, 26.93, 26.67, 25.88, 17.85, 16.38, 16.19. Conclusion Homofarnesol and other homoallylic alcohols are used as synthetic precursors in terpene chemistry and are of interest within the flavor, fragrance, and pharmaceutical sectors. As documented herein, the inclusion of a Ni(II)-based catalyst enhancer resulted in shorter reaction times, better yields and higher selectivity in the synthesis of cyclopropyl intermediates from typical alkene, e.g., polyprenoid compounds. In one example, cyclopropylvinyl intermediates were formed which were reacted with Bronsted acids then hydrolyzed to form homoallylic alcohols. EQUIVALENTS AND SCOPE In the claims, articles such as “a,” “an,” and “the” may mean one or more than one unless indicated to the contrary or otherwise evident from the context. Claims or descriptions that include “or” between one or more members of a group are considered satisfied if one, more than one, or all of the group members are present in, employed in, or otherwise relevant to a given product or process unless indicated to the contrary or otherwise evident from the context. The present disclosure includes embodiments in which exactly one member of the group is present in, employed in, or otherwise relevant to a given product or process. The present disclosure includes embodiments in which more than one, or all of the group members are present in, employed in, or otherwise relevant to a given product or process. Furthermore, the present disclosure encompasses all variations, combinations, and permutations in which one or more limitations, elements, clauses, and descriptive terms from one or more of the listed claims is introduced into another claim. For example, any claim that is dependent on another claim can be modified to include one or more limitations found in any other claim that is dependent on the same base claim. Where elements are presented as lists, e.g., in Markush group format, each subgroup of the elements is also disclosed, and any element(s) can be removed from the group. It should it be understood that, in general, where the present disclosure, or aspects of the present disclosure, is/are referred to as comprising particular elements and/or features, certain embodiments of the present disclosure or aspects of the present disclosure consist, or consist essentially of, such elements and/or features. For purposes of simplicity, those embodiments have not been specifically set forth in haec verba herein. It is also noted that the terms “comprising” and “containing” are intended to be open and permits the inclusion of additional elements or steps. Where ranges are given, endpoints are included. Furthermore, unless otherwise indicated or otherwise evident from the context and understanding of one of ordinary skill in the art, values that are expressed as ranges can assume any specific value or sub-range within the stated ranges in different embodiments of the present disclosure, to the tenth of the unit of the lower limit of the range, unless the context clearly dictates otherwise. This application refers to various issued patents, published patent applications, journal articles, and other publications, all of which are incorporated herein by reference. If there is a conflict between any of the incorporated references and the instant specification, the specification shall control. In addition, any particular embodiment of the present invention that falls within the prior art may be explicitly excluded from any one or more of the claims. Because such embodiments are deemed to be known to one of ordinary skill in the art, they may be excluded even if the exclusion is not set forth explicitly herein. Any particular embodiment of the present disclosure can be excluded from any claim, for any reason, whether or not related to the existence of prior art. Those skilled in the art will recognize or be able to ascertain using no more than routine experimentation many equivalents to the specific embodiments described herein. The scope of the present embodiments described herein is not intended to be limited to the above Description, but rather is as set forth in the appended claims. Those of ordinary skill in the art will appreciate that various changes and modifications to this description may be made without departing from the spirit or scope of the present invention, as defined in the following claims.