STATES

BACKGROUND

Heterogeneous catalysis reactions like photocatalytic/electrochemical water splitting (HER/OER), ammonia synthesis, CO ₂ reduction, and oxygen reduction reaction (ORR) in fuel cells, are getting increasing attention because of their advantages in facing the energy crisis and environmental issues. With the aid of these technologies, hydrogen can be produced from water and then used directly in fuel cells without any emission of pollutants. CO ₂ and N ₂ can be transformed into specific carbon products or ammonia, which are important for industry and fertilizers. Unfortunately, all these reactions require that the corresponding catalysts lower the activation energy for scalable production. The design of and search for high-performance catalysts are strongly dependent on the understanding of the catalysis reaction details and the physical properties of the catalysts. At present, d-band theory (J. Nørskov, et al. PNAS, 2011, 108, 937; L. Pettersson, et al., Top. Catal. 2014, 57, 2) has had great success in explaining of the catalytic efficiency of a selected catalyst. Within the framework of d-band theory, the reaction kinetics is determined by the adsorption energy between the reaction intermediates and catalyst active sites. However, a fundamental and unanswered question is why the adsorption energy is different for different crystal surfaces of a same catalyst, and how one can identify the active sites for a selected catalyst.

Transition metal dichalcogenides such as MoS ₂ are potential alternatives to noble-metal based catalysts because of their high catalytic efficiency and stability. It is experimentally very well proven that the (001) basal plane of a MoS ₂ crystal is inert for the catalytic process of the photocatalytic/electrochemical water splitting reaction. It is the edges of the crystal which serve as active sites (see Figure 1). Only if defects such as elemental vacancies are introduced into the basal plane, the basal plane can be activated for catalysis. The same phenomenon is observed in other materials such as PtSe ₂ , PtTe ₂ , and PdTe ₂ . However, it is still not clear why the catalytic efficiency is markedly different at different crystal surfaces of the same catalyst and what the factor is that determines the adsorption energy. This is of great importance to the design of new high-performance catalysts. PRIOR ART

US20140353166A1 discloses a method for scalable synthesis of molybdenum disulfide monolayer and few-layer films. When deposited on SiO ₂ /Si substrates and used as electrocatalyst for hydrogen evolution, they exhibit high efficiency with large exchange current densities and low Tafel slopes. The reference states that the mono and few-layer films have more active sites than nanoparticles and bulk phase.

WO2018165449 A 1 discloses the formation of molybdenum disulfide nanosheets on a carbon fiber substrate. These nanosheets have a plurality of catalytically active edge sites along basal planes and show good activity towards hydrogen evolution.

JP2009252412A relates to the use of RuTe ₂ as an active ingredient for direct methanol fuel cells. The fuel cell with RuTe ₂ as a catalyst can be used for portable electrical products.

M. Asadi, K. Kim, C. Liu, A. V. Addepalli, P. Abbasi, P. Yasaei, P. Phillips, A. Behranginia, J. M. Cerrato, R. Haasch, P. Zapol, B. Kumar, R. F. Klie, J. Abiade, L. A. Curtiss, A. Salehi- Khojin (Science, 2016, 353, 467) report that nanostructured transition metal dichalcogenides such as MoS ₂ , WS ₂ , MoSe ₂ , and WSe ₂ are excellent electrocatalysts for CO ₂ reduction. The authors found that the metallic edge sites of the nanoflakes are active centers because of the strong binding to CO molecules.

C. Tsai, K. Chan, F. Abild-Pedersen, J. K. Nørskov (Phys. Chem. Chem. Phys. 2014, 16, 13156); T. F. Jaramillo, K. P. Jørgensen, J. Bonde, J. H. Nielsen, S. Horch, lb Chorkendorff (Science, 2007, 317, 100); R. Abinaya J. Archana, S. Harish, M. Navaneethan, S. Ponnusamy, C. Muthamizhchelvan, M. Shimomura and Y. Hayakawa (RSC Adv., 2018, 8, 26664) report that the photocatalytic and electrochemical efficiency of transition metal dichalcogenides (MoS ₂ ) is correlated to the number of edge sites of the crystal, while the (001) basal plane of MoS ₂ crystal is inert towards hydrogen evolution,

H. Li, M. Du, M. J. Mleczko, A. Koh, Y. Nishi, E. Pop, A. J. Bard, and X. Zheng (J. Am. Chem. Soc. 2016, 138, 5123); S. Kang, S. Han, Y. Kang (ChemSusChem, 2019, 12, 2671); L. Zeng, S. Chen, J. van der Zalm, X. Li, A. Chen (Chem. Commun., 2019, 55, 7386) found that by introducing sulfur vacancies in the (001) basal plane of MoS ₂ crystals, the catalytic activity of MoS ₂ can be boosted in the hydrogen evolution reaction, CO ₂ reduction, and NH ₃ synthesis.

A. Politano, G. Chiarello, C. Kuo, C. Lue, R. Edla, P. Torelli, V. Pellegrini, D. W. Boukhvalov (Adv. Funct. Mater.2018, 28, 1706504); H. Huang, X. Fan, D. J. Singh, and W. Zheng (ACS Omega 2018, 3, 10058) found that the pristine surface of layered transition-metal dichalcogenides (PtSe ₂ , PtTe ₂ ) are chemically inert toward most common ambient gases, including O ₂ , H ₂ O, and even in the air. However, by doping or introducing selenium or tellurium vacancies, a large density of active sites can be created in the (001) basal plane for water splitting and water-gas shift reaction. Despite all these efforts, it is still not understood what the active site(s) is/are for the various catalytic processes. For example, it is not understood why the adsorption energy can be altered significantly by introducing defects such as vacancies. The answer to these questions is very important for the design of high-performance catalysts with controllable active sites for a given heterogeneous reaction. OBJECT OF THE INVENTION

It is, therefore, an object of the invention to provide - a method for controllably making catalysts with active surface site(s), and/or - a method for improving the efficiency of a known catalysts which has hitherto not been made available with access to its most active surface site(s); - catalysts exhibiting active surface site(s), determined by the above method.

BRIEF DESCRIPTION OF THE INVENTION

The above object is achieved by selecting from the Inorganic Crystal Structure Database, FIZ Karlsruhe, Germany (ICSD, https://icsd.fiz-karlsruhe.de ) those topological insulators, specifically topological trivial insulators, wherein the position of WCCs (Wannier Charge Centers) is not occupied by an atom. These compounds are characterized by a metallic surface state at a predefined specified crystal surface determined by the method according to the present invention. In order to expose the metallic surface state to a potential reactant for photocatalytic/electrochemical reaction a crystal of the selected insulator compound is cut or grown in a predefined crystallographic direction (characterized by its Miller index (h,k,l)). It has been found that a given obstructed atomic insulator (OAI) with atoms sitting at WP _occ = {x _i ,y _i ,z _i │ i ∈ occupied position} and obstructed WCCs localized at WP _0AI = {x _i ,y _i ,z _i │ i ∉ occupied position } has metallic surface states on surface planes characterized by the equation f{x,y,z) = 0 with Miller index (or normal vector) (h,k,l) when it satisfies the following conditions:

This means that the surface plane f(x,y,z) = 0 with normal vector (h,k,l) cuts through the position of obstructed WCCs ( X _j , Y _j , Z _j ), but stays away from the atoms’ positions (x _i ,y _i ,z _i ).

Topological trivial insulators, i.e. those insulators without topological electronic structures, are characterized by an indirect band gap (of about 0.001 - 7.000 eV) in the bulk with different crystal momentum (k-vector) for the conduction and valence band. Using the Topological quantum chemistry theory (Nature 547.7663 (2017): 298-305), and the Real Space Invariants (RSI) disclosed in “Science 367 (6479), 794-797 (2020)”, it was found that some of the topological insulators, specifically topological trivial insulators, have crystalline symmetry- protected metallic surface states on certain crystallographic surfaces and that these metal surface states can explain the catalytic performance.

Thus, the present invention can provide new and/or improved catalysts, especially for photocatalytic/electrochemical reactions, such as water splitting (Oxygen Evolution Reaction, OER, or Hydrogen Evolution Reaction, HER), ammonia synthesis, CO ₂ reduction, and oxygen reduction reaction (ORR) in fuel cells.

DETAILED DESCRIPTION OF THE INVENTION

It was found that the active sites for heterogeneous reactions are metallic surface states, localized at/on specific crystallographic surfaces, characterized by their surface normal expressed as (h,k, /)-index (Miller index). The metallic surface states can be imagined as “dangling bonds” which extend from the catalyst’s surface and which cause metallic conductivity. Inside the crystal body of a catalytic compound (the bulk) all bonds are saturated; the atomic orbitals (AOs) of the elements, which make up the catalytic compound, overlap each other, thereby forming molecular orbitals (MOs) with joint electrons. However, at the boundaries of the crystal certain atomic orbitals have no corresponding binding partner for forming a MO; they remain “unsaturated” and extend beyond the crystal boundary as “dangling bond”. Of course, the metallic surface states, or “dangling bonds”, can also be created through the introduction of defects in the crystal structure, such as elemental vacancies. It was found that the above-defined metal surface states increase catalytic efficiency. Thus, with the knowledge of the above finding one can a) explain the catalytic efficiency of known catalytic compounds, b) turn a given compound, which has yet uncovered catalytic potential, into an efficient catalyst by cutting or growing a crystal of this potential catalytic material in a predefined crystallographic direction (characterized by its surface normal, expressed in Miller indices (h,k,l)), thereby revealing the metal surface states, The direction is determined by the crystal surface with metallic surface states, which can be calculated (see below) or obtained from the below material list c) eventually improve the catalytic efficiency of known catalytic compounds with method b), d) screen known compounds for catalytic material, and/or e) provide a list of compounds that can be used as catalysts.

As used herein the following terms have the following meaning:

“Surface properties” means the bonding and electronic structures at the surface of a crystal.

“Topological trivial insulator” means an insulator according to the traditional definition, i.e. one that has no topological feature(s) such as band inversion between conduction and valence band. Consequently, insulators that exhibit (a) topological feature(s) are called “topological insulators”.

“Indirect band gap” means that the bottom of the conduction band and the top of the valence band have different crystal momentum (k- vector) in the Brillouin zone.

“Metallic surface states” means the dangling bonds derived electronic states, which are located between the conduction and valence band. These surface states have de-localized electrons and are highly electrically conductive. In the real space, they are at the crystal surface. In the Momentum space (k), they are located in the gap between the bulk conduction and valence band.

“Certain surfaces” means the surface of a catalyst crystal with a surface normal of a designated Miller-index (( h,k,l)-index). “Catalytic active site” means the crystal surfaces where heterogeneous catalysis reactions may occur.

“ Occupied positions” means the available Wyckoff positions in a given space group which is/are occupied by (an) atom(s). An example is given below for space group No. 25 (Pmm2):

Wyckoff Positions of Group Pmm2 (No. 25)

Thus, a Wyckoff position of a defined space group consists of all points X for which the site- symmetry groups are conjugate subgroups of the defined space group. Each Wyckoff position of a space group is labelled by a letter which is called the Wyckoff letter. The number of different Wyckoff positions of each space group is finite, the maximal numbers being 9 for plane groups (realized in p2mm) and 27 for space groups (realized in Pmmm). There is a total of 72 Wyckoff positions in plane groups and 1731 Wyckoff positions in space groups.

Heterogeneous catalytic reactions are a type of catalytic process where the catalyst and the reactants are not present in the same phase. This occurs e.g. in reactions between gases or liquids or both at the surface of a solid catalyst. Typical heterogeneous catalytic reactions include photocatalytic/electrochemical water splitting, ammonia synthesis, CO ₂ reduction, and oxygen reduction reaction (ORR) e.g. in fuel cells. According to the classic surface adsorption theory, a heterogeneous reaction comprises four stages:

1) Diffusion of a reactant to the solid catalyst surface. The diffusion rate is determined by the bulk concentration of the reactant and the thickness of the boundary layer (a layer of solution formed at the catalyst surface) surrounding the catalyst particle.

2) The adsorption of reactants onto the surface of the catalyst through chemical or physical bonding.

3) Oxidation or reduction at the catalyst surface, which is characterized by an electron transfer between the catalyst and adsorbates.

4) Desorption of the reaction product. This process is accompanied by a breaking of (a) bond(s) as the product(s) desorb from the surface of the catalyst.

The catalytic efficiency generally depends on the adsorption energy of the adsorbates/reaction intermediates and the catalytic active site(s). A good catalyst requires that the adsorption energy is “just right” so that the products can be formed and released as quickly as possible. Adsorption energy can be positive or negative; positive energy means the adsorption is weak, while negative energy means good, i.e. strong adsorption. However, an adsorption energy which is too positive will lead to a low concentration of reactants at the catalyst surface(s) and therefore will increase the reaction kinetics. On the other hand, if the adsorption energy is too negative the products remain on the catalyst surface too long and may act as “poison” to the active site(s).

It was now found that the catalytic efficiency of topological insulators, specifically topological trivial insulators, directly correlates with its metallic surface states. Using the Topological Quantum Chemistry (TQC) Theory (Nature 547.7663 (2017): 298-305), all of the topological trivial, as well as the topologically nontrivial, band insulators in the Inorganic Crystal Structure Database (ICSD) (Nature 566.7745) (2017): 480-485) were identified. Topologically trivial insulators come in two distinct categories: with and without surface states,

The Band Representations (BRs) of the valence bands of all these topological band insulators were identified (see: Nature 566.7745) (2017): 480-485; and in the Topological materials database, see: https://www.topologicalquantumchemistrv.com). For a given topological band insulator with atoms sitting at the Wyckoff positions WP _occ = {x _i , y _i , Z _i │ i ∈ occ = occupied position}, using the BRs and the formulae of Real Space Invariants (RSI) e.g. disclosed in “Science 367 (6479), 794-797 (2020)”, one can calculate the RSIs of all the Wyckoff positions (WPs) of the crystal symmetry group. Thus, for a given space group, one can define RSIs for each of the Wyckoff positions of that space group. For a topological band insulator, the RSI defined at a Wyckoff position is always an integer, which stands for the number of irreducible Wannier orbitals (=irreducible Wannier Charge Centers (WCCs)) at that Wyckoff position.

The Wyckoff positions with nonzero RSI give the positions of irreducible Wannier Charge Centers (WCCs) (Physical Review B 89.11 (2014)), WP _wcc = {x _k ,y _k ,z _k │RSI _k ≠ 0}. Any BRs of a topological band insulator, which have at least one irreducible WCC localized at the empty Wyckoff position (i.e, a Wyckoff position which is not occupied by atom), is in the obstructed atomic limit phase, i.e. ∃ (X _j , Y _j ,Z _j ) ∈ WP _wcc , (X _j , Y _j ,Z _j ) ∉ WP _occ . Thus, all of the Wyckoff positions, which have nonzero RSI and which are not occupied by the atoms of the material are called “obstructed Wyckoff positions”, WP _0AI = {x _j ,y _j ,z _j │RSI _j ≠ 0 , J ∉ occupied positions }. A band insulator is a not obstructed atomic insulator when all of its irreducible WCCs are occupied by atoms. Otherwise, it is an Obstructed Atomic Insulator (OAI).

For Obstructed Atomic Insulators with occupied Wyckoff Positions WP _occ = {x _i , y _i , Z _i │ i ∈ occupied positions] and obstructed Wyckoff positions WP _0AI = {X _j ,Y _j ,Z _j │RSI _j ≠ 0 , J ∉ occupied positions], their surface planes f(x,y, z) = 0 with Miller index (or normal vector) (h,k,l) have metallic surface states when (h,k,l) satisfy the following conditions:

This means that the surface plane f{x,y,z) = 0 with normal vector (h,k,l) cuts through the position of obstructed Wyckoff positions, but stays away from the occupied positions in a crystal.

Any cleaved crystal surface that cuts through theses obstructed Wyckoff Positions must have metallic surface states on that crystal surface. The location of these metallic surface states on the surface of a catalyst crystal can be predicted with the above theory. This is illustrated in Figures 1 and 2 for a MoS ₂ crystal. The surface states are located at the edge sites with dangling bonds. The (001) basal plane has no surface states and is inert for catalytic reactions. However, edge sites which are normal to the (001) face, like (100), or (010), or (110) etc. are active towards catalytic reactions such as hydrogen evolution. When these metallic surface states are located near the Fermi level (i.e. up to about 0.5 eV below or above the Fermi level) they can be transferred easily in catalytic reactions, and can serve as active centers for chemical reactions.

The position of the metallic surface state in a MoS ₂ crystal is shown in Figure 3. MoS ₂ crystallizes in space group P6 ₃ /mmc (#194) with Mo and S at Wyckoff position 2c (1/3, 2/3, 1/4) and 4f (1/3, 2/3, z) (where z is a general position not equal to 1/4), respectively. Using the Topological quantum chemistry (TQC) theory, the Real Space Invariants (RSI) at Wyckoff position 2b (0,0, 1/4) is δ(b) = 1.0. Thus, there is an irreducible WCC localized at the 2b position, which is not occupied by an atom. This shows, that with the above theory one can identify the surface plane in MoS ₂ which has metallic surface states (indicated by its Miller index (1,0,0)) as shown in Figure 3(a). On the other hand, the surface with Miller index (0,0,1) cuts the 2c position which is occupied with an atom. Therefore, the (001) surface does not have metallic surface states within the energy gap, as shown in Figure 3(b).

The prediction of the catalytic behavior of MoS ₂ crystal has been proven experimentally. Figure 4 shows the experimental setup for the HER. The bulk MoS ₂ single crystal is attached to a titanium wire with silver paint. The edges and basal plane can be seen clearly in Figure 4. Figure 5a shows the linear polarization curves for the whole crystal (Edge + basal plane), Edges only, and basal plane. It can be seen that the activity of the whole crystal is almost the same as that of the edges. The activities decrease significantly when the edges are partially covered with a gel. Figure 5b shows a photo taken at an overpotential of -0.57 vs RHE. Hydrogen bubbles are formed at the edges, but not on the basal plane. Thus, it can be concluded that the HER activity comes from the crystal edges.

Accordingly, the invention provides a method of selecting a potentially catalytic active compound which method comprises identifying all the topological insulators in the ICSD, preferably all the topological trivial insulators, calculating the Real Space Invariants of the valence bands for all these topological insulators in order to identify in all these topological insulators the Wyckoff Positions where the irreducible Wannier Charge Centers (WCCs) are localized, and then selecting as potentially catalytic active compound a topological insulator wherein the position of WCCs is not occupied by any atom.

This method was applied to all compounds in the ICSD and the potentially catalytic active compounds have been identified. These compounds are listed in the attached Table labelled “OAI" Many compounds in this table have multiple listings. Multiple listings of the same compound (meaning the same stoichiometry) may occur when different contributors to the ICSD have reported (slightly) varying data like varying lattice parameter, different space group allocations or Wyckoff allocations etc. The condensed list of unique compounds (= one listing only) is reproduced in the following Table 1 :

Table 1

In one aspect of the invention, a method is provided for controllably making catalysts with the active surface site(s), which method comprises selecting a potentially catalytic active compound either according to the above selection process or from the above Table 1 , synthesizing a crystal of this potentially catalytic active compound either so that it is grown in a predefined crystallographic direction (characterized by its h,k, l-indices) which exposes the metallic surface state; or cutting the crystal in a predefined crystallographic direction (characterized by its h,k, l-indices), so that the metallic surface state is exposed, wherein the predefined crystallographic direction is the direction of the normal vector ( h,k,l ) of the surface plane f(x,y,z) = 0 which cuts through the position of obstructed WCCs, but stays away from the atoms’ positions, condition which is fulfilled when:

\h,k, l) ^■ (x — X _j , y — Y _j ,z — Z,·) = 0,

" (h, k, 0 · (x - x _it y - y _it z - ¾) ¹ 0, ^ h, k, l e Z with the obstructed WCCs localized at WP _0Al = {X _j , Y _j ,Z _j │RSI _j ≠ 0 , J ∉ occupied positions } and atoms occupying WP _occ = {x _i ,y _i ,z _i │i ∈ occupied positions).

A further aspect of the invention comprises a method for converting a compound, which o either has been selected with the above method or o has been selected from Table 1, and which compound does not provide a surface with a metal surface state into a compound which provides a surface with a metal surface state, by cutting or growing a crystal of this compound in a predefined crystallographic direction thereby revealing metal surface slates, wherein the predefined crystallographic direction is determined as described above. Moreover, the present invention comprises a catalyst selected from the compounds listed in Table 1 wherein a crystal of the selected compound is grown in a predefined crystallographic direction (characterized by its h,k, l-indices); or is cut in a predefined crystallographic direction (characterized by its h,k, l-indices), wherein the predefined crystallographic direction is the direction of the normal vector (h,k,l) of the surface plane f(x,y, z) = 0 which cuts through the position of obstructed WCCs, but stays away from the atoms’ positions, condition which is fulfilled when: with the obstructed WCCs localized at WP _0AI = {X _j , Y _j ,Z _j │RSI _j ≠ 0 , J ∉ occupied positions] and atoms occupying WP _occ = {x _i ,y _i ,z _i │i ∈ occupied positions].

METHOD OF MAKING THE COMPOUNDS

The compounds of the present invention can e.g. be grown out of a stoichiometric mixture of the elements of the compound. The elements may be mixed together and then heated, preferably to a temperature of about 300°C, preferably 200°C, most preferred 100°C above the melting point of the lowest melting element over a period of lh to 10h, preferably 2h to Bh, more preferably 3h to 7h and then kept for 5h to 50h, preferably 10h to 30h, more preferably about 20h at that temperature. Preferably, the mixture is placed in an inert crucible for heating, e.g. an alumina crucible which preferably is sealed, e.g. in a quartz tube under a partial pressure of an inert gas, e.g. Ar. Thereafter the mixture is slowly cooled to a temperature of about 450 °C, preferably 400 °C, more preferably 350 °C over a period of 40h to 90h, preferably 50h to 80h, more preferably 55h to 65h. In an alternative method first, a polycrystalline ingot is prepared, e.g. using induction or arc melting technique with the stoichiometric mixture of the elements. The polycrystalline ingot is then crushed into microcrystalline powders and filled preferably in an alumina tube with a cone shape end and then fully sealed in a tantalum tube. The tube is then heated up to a temperature higher than the melting point of the compound to obtain a fully molten state and then slowly cooled to about 650 °C and then to room temperature.

In general, the compounds are manufactured so that they grow in a predefined crystallographic direction (characterized by its (h,k,l)-indices) which exposes the metallic surface state. It is known that the morphology of the crystal is closely related to the surface energy of each crystal surface. In the crystal growth process, the crystal surface with high surface energy has a faster growth rate than the lower one. Thus, according to the thermodynamic equilibrium theory, those surfaces with high surface energy will disappear while the surfaces with the lowest total energy will survive (M. Khan, et al. CrystEngComm, 2013, 15, 2631). Thus, one can design a catalyst if the metallic surface states coincide with the surface with the lowest surface energy. If the metallic surface states are located at the crystal surface with high surface energy, it is possible to control the surface energy by using additives. The additives, such as polyvinylpyrrolidone, sodium dodecyl sulfate, and hypophosphorous acid, can bind to a specific crystallographic surface and decrease the surface energy. This will reduce the crystal growth rate and alter morphology, exposing the desired crystal surface with metallic surface states (J. P. van der Eerden, et al. Electrochim. Acta, 1986, 31, 1007; A. Ballabh, et al, Cryst. Growth Des., 2006, 6, 1591). A crystal can also be “cut” in a predefined crystallographic direction (characterized by its h,k, 1-indices), so that the metallic surface state is exposed. For catalysts in the form of a bulk crystal, the crystal structure and crystal orientation can be determined by single- crystal X-ray diffraction. After the orientation has being determined, one can cut the crystal along a specified direction and expose the desired crystal surface. OAI Table