Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX
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MoCo and MoWNi Clusters as Models for Hydrodesulfurization: A DFT Study of the Geometric, Electronic, and Magnetic Properties of MomCon (3 ≤ m + n ≤ 8) and MoxWyNiz (3 ≤ x + y + z ≤ 8) Clusters Julian Del Plá, Leandro P. Bof, and Reinaldo Pis Diez* CEQUINOR, Centro de Química Inorgánica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CONICET, 1900 La Plata, Argentina
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ABSTRACT: The geometric, electronic, and magnetic properties of MomCon (3 ≤ m + n ≤ 8) and MoxWyNiz (3 ≤ x + y + z ≤ 8) clusters, as models for the hydrodesulfurization process, are investigated from a computational point of view. Optimized geometries of stable MoCo isomers show that Mo and Co atoms tend to segregate from each other. Charge transfer occurs from Mo to Co. Optimized geometries of stable MoWNi isomers display MoW cores with Ni atoms decorating triangular faces. Charge transfer takes place from W atoms to Mo and to Ni atoms. Various aggregates are identified as candidates to participate in the hydrodesulfurization process according to the change in Mulliken atomic charges after the removal and the addition of an electron to neutral clusters. For MoCo species, it is found that both Mo and Co atoms would be involved in the active sites of the catalyst. For MoWNi clusters, instead, the active sites of the catalyst would be formed by Mo and W atoms exclusively, whereas the Ni atom would be responsible for modifying the local electronic structure of Mo and W atoms.
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INTRODUCTION Since the beginning of the 20th century, Mo and W sulfides supported on alumina and containing Co and/or Ni as promoters have been the main catalysts used for both hydrodesulfurization (HDS) and hydrodenitrogenation (HDN) processes.1,2 Despite some studies changing the support or adding new elements, there seem to be no doubts that the active sites of these catalysts have to do with Mo(W)S2 nanoparticles or crystallites with their edges decorated with the promoters. Also, it is accepted that the active sites in HDS and HDN catalysts are vacancies created by the removal of sulfur atoms by molecular hydrogen.3 Moreover, it is a well-known fact that CoMo catalysts are more efficient in HDS processes than in HDN ones, whereas NiMo systems show better activities for HDN reactions.4 By mid-1990s, some authors observed an increase of the HDS activity of CoMo catalysts after the addition of amounts of tungsten.5,6 In 2001, a novel unsupported catalyst based on NiMoW was reported to exhibit a 4 times greater HDS activity than that observed for catalysts usually used in industry.7 Several computational works and other combined experimental and theoretical studies on the CoMo system exist in the literature. Hinnemann et al. performed periodic density functional theory (DFT) calculations on MoS and CoMoS structures to show that the presence of metal-support linkages increases the energy required to form sulfur vacancies.8 Thus, their reactivity toward HDS becomes reduced as few sulfur © XXXX American Chemical Society
vacancies are formed. Costa et al. used periodic DFT to study the effect of Co as a promoter on the interaction of MoS nanoparticles with supports such as γ-alumina and anatase.9 They found that Co decreases the interaction with the supports. Badawi et al. carried out a combined experimental and theoretical study on the effect of water on the stability of MoS and CoMoS catalysts in hydrodeoxygenation of phenolic compounds, finding that Co plays both a promoting role for the catalytic reaction and a passivating role against the presence of water.10,11 Borges and Silva used DFT and a Coulomb model to estimate bond strengths to investigate the effect of Co and Ni on MoS isolated clusters against thiophene adsorption. They found that the effect of the promoters is mainly the weakening of surface metal−sulfur bonds.12 Costa et al. used a combination of X-ray photoelectron spectroscopy, transmission electron microscopy, and catalytic tests with periodic DFT calculations to study toluene hydrogenation on (Co)MoS catalysts supported on γ-alumina.13 The authors report that the catalytic activity correlates with the number of mixed CoMo sites present at the MoS2 edges. Liu et al. investigated thiophene HDS on (Co)MoS catalysts supported on zeolite L using DFT.14 The authors found that the pore size of the support plays a fundamental role in the process. Ding et Received: October 6, 2018 Revised: December 9, 2018
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DOI: 10.1021/acs.jpcc.8b09773 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
considered as active site models rather than models for the whole catalyst.
al. carried out a series of nonperiodic DFT calculations with numerical atomic orbitals to represent valence states on isolated (Co)MoS clusters to study hydrogen adsorption and dissociation and thiophene adsorption.15 The authors conclude that corner sites containing both Co and Mo are the most efficient from the catalytic point of view. Finally, the only work made on isolated CoMo clusters was performed by Liebing et al.16 The authors studied geometric, electronic, and magnetic properties of ConMom clusters, with n + m = x and 2 ≤ x ≤ 6 using nonperiodic DFT calculations. It must be noted, however, that the authors are more interested in the potential use of those bimetallic clusters in spintronics than in their possible catalytic activities. An important amount of experimental work on NiMoW systems can be found in the literature in recent years.17−24 On the other hand, computational works or combined experimental and theoretical studies are scarce. Thomazeau et al. carried out a combined experimental and computational investigation on a γ-Al2O3-supported Mo1−xWxS2 system promoted with both Co and Ni.25 The authors found an improvement of about 30% in thiophene HDS activity for the NiMo0.5W0.5S2 catalyst with respect to the nonpromoted system. Olivas et al. used semiempirical tight binding calculations to complement experimental data for dibenzothiophene HDS on NiMoW sulfide catalysts.26 They found that the role of Ni is to increase the electronic charge around the Fermi level, thus increasing the metallic character of the catalysts. Finally, Cervantes-Gaxiola et al. also complement a series of experimental measurements on the HDS activities of supported NiMoW, NiMo, and NiW sulfide catalysts with periodic DFT calculations. The calculations were restricted to unsupported surfaces of those systems. Interestingly, the authors found that the catalyst surface becomes more easily formed in the trimetallic system than in the bimetallic ones and, moreover, the NiMoW surface exhibits the largest population of d states around the Fermi level, which is in good agreement with the findings made by Olivas et al.26 To the best of our knowledge, there are no studies concerning the properties of isolated NiMoW clusters. Transition-metal clusters are important in diverse fields such as nanotechnology and materials science.27 Catalysis is not an exception. Active sites in catalysts are closely related to metal sites as it is clear from the previous paragraph. Such an activity will depend on the nature of the metal atoms forming the site, on the geometric arrangement of those atoms, and on their formal atomic charges, among other factors. Thus, transitionmetal clusters are excellent models to investigate processes of importance in catalysis, both from an experimental point of view and from a computational viewpoint. As a continuation of our studies on the properties of transition-metal clusters with potential catalytic activity in HDS, a systematic study of selected MomCon and MoxWyNiz clusters, with 3 ≤ m + n ≤ 8 and 3 ≤ x + y + z ≤ 8, is accomplished in this work using DFT. Geometric, electronic, and magnetic properties are calculated for the aggregates mentioned above. Moreover, atomic charge rearrangements undergone in stable clusters due to ionization processes are taken as reactivity indexes that can be used to predict potential activity against thiophene HDS. It is important to emphasize that the clusters studied in this work include neither sulfur atoms nor the support effect in an attempt to isolate geometric and/or electronic effects due to dopant species. Also, the small cluster sizes investigated in this work should be better
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COMPUTATIONAL DETAILS The stoichiometry for MomCon clusters, with 2 ≤ m ≤ 6, 1 ≤ n ≤ 3, and 3 ≤ m + n ≤ 8, is selected according to the optimal experimental ratios, namely, 0.25 ≤ n/m ≤ 0.60, for MomConS structures supported on γ-alumina.1 Thus, Mo2Co, Mo3Co, Mo4Co, Mo4Co2, Mo5Co2, Mo6Co2, and Mo5Co3 aggregates are studied in this work. On the other hand, the composition of MoxWyNiz clusters, with 1 ≤ x ≤ 2, 1 ≤ y ≤ 3, 1 ≤ z ≤ 3, and 3 ≤ x + y + z ≤ 8, is fixed according to the optimal experimental ratios of 0.75 ≤ x/ y ≤ 0.95 and 0.5 ≤ z/(x + y) ≤ 0.7.26 This way, the trimetallic clusters investigated in this work are MoWNi, Mo2W2Ni2, Mo2W2Ni3, and Mo2W3Ni3. Geometry optimizations are addressed using starting structures generated from well-known geometries of pure metal clusters28−31 and a few highly symmetrical common structures. For every cluster size, one or more atoms of a given type are replaced by atoms of the other type until the desired stoichiometry is reached. Optimizations are considered complete when the maximum element of the gradient vector of the total electronic energy with respect to the atomic coordinates is less than 3 × 10−4 atomic units. Because of the non-negligible number of competing electronic states present in transition-metal clusters, the total electronic energy is also minimized with respect to the electron spin multiplicity, which is kept fixed during geometry optimizations. Optimizations are performed without symmetry constraints. The Hessian matrix of the total electronic energy with respect to the atomic coordinates is constructed and diagonalized for optimized geometries. The eigenvalues of the Hessian matrix are used to check whether the optimized geometry is a local minimum on the potential-energy surface of the given cluster. When negative eigenvalues of the Hessian matrix are found, the corresponding eigenvectors are used to distort the optimized geometry, thus obtaining a new starting structure, which is then reoptimized. The procedure is repeated until a local minimum is found. Eigenvalues of the Hessian matrix for all of the stable clusters reported in this work are converted to harmonic vibrational frequencies and are shown in Tables S1−S4 in the Supplementary Information. The atomization energies reported in this work are calculated as follows Eat(MomCon) =
m × E(Mo) + n × E(Co) − E(MomCon) n+m
(1)
and Eat(Mox WyNiz) =
x × E(Mo) + y × E(W) + z × E(Ni) − E(Mox WyNiz) x+y+z (2)
where E(MomCon) and E(MoxWyNiz) are the total electronic energies of the clusters and E(Mo), E(Co), E(W), and E(Ni) are the total electronic energies of the atoms in their ground states as calculated with the present level of theory. Ionization energies (IE) and electron affinities (EA) are calculated as B
DOI: 10.1021/acs.jpcc.8b09773 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C Table 1. Some Structural and Electronic Properties of the Stable MomCon Isomers Found in This Worka cluster (label)
Eat
M
dMo−Mo
dMo−Co
Mo2Co (21-1) Mo2Co (21-2) Mo2Co (LMTK) Mo3Co (31-1) Mo3Co (31-2) Mo3Co (31-3) Mo3Co (LMTK) Mo4Co (41-1) Mo4Co (41-2) Mo4Co (LMTK) Mo4Co2 (42-1) Mo4Co2 (42-2) Mo4Co2 (42-3) Mo4Co2 (42-4) Mo4Co2 (LMTK) Mo5Co2 (52-1) Mo5Co2 (52-2) Mo5Co2 (52-3) Mo5Co2 (52-4) Mo5Co2 (52-5) Mo5Co3 (53-1) Mo5Co3 (53-2) Mo5Co3 (53-3) Mo5Co3 (53-4) Mo5Co3 (53-5) Mo6Co2 (62-1) Mo6Co2 (62-2) Mo6Co2 (62-3) Mo6Co2 (62-4) Mo6Co2 (62-5) Mo6Co2 (62-6)
2.016 1.975 1.78 2.338 2.324 2.321 2.05 2.834 2.771 2.38 3.021 3.006 3.003 2.990 2.68 3.191 3.190 3.187 3.186 3.181 3.267 3.259 3.246 3.242 3.238 3.356 3.353 3.350 3.343 3.337 3.337
2 4 2 4 2 6 4 2 4 2 5 3 5 7 5 5 3 5 3 7 2 4 4 2 6 3 7 3 5 5 1
2.016 2.004 2.07 2.272 2.270 2.314 2.42 2.403 2.396 2.55 2.397 2.404 2.324 2.396 2.45 2.479 2.486 2.491 2.533 2.505 2.502 2.498 2.452 2.456 2.459 2.543 2.475 2.560 2.541 2.472 2.547
2.386 2.516 2.47 2.531 2.516 2.516 2.43 2.536 2.549 2.46 2.411 2.396 2.559 2.569 2.49 2.485 2.385 2.426 2.486 2.497 2.492 2.500 2.433 2.432 2.429 2.403 2.492 2.477 2.444 2.449 2.376
dCo−Co
Qav(Co)
EA
IE
−0.133 −0.078
0.84 1.11 0.8 1.16 1.13 1.20 1.0 1.18 1.30 0.9 1.41 1.41 1.20 1.42 0.5 1.47 1.51 1.45 1.67 1.51 1.42 1.53 1.59 1.60 1.58 1.48 1.46 1.43 1.48 1.52 1.54
5.80 5.74 5.9 5.46 5.46 5.51 5.6 5.66 5.44 5.2 5.52 5.41 5.59 5.45 5.6 5.35 5.41 5.41 5.18 5.32 5.59 5.52 5.29 5.23 5.36 5.24 5.26 5.22 5.24 5.22 5.22
−0.004 −0.031 −0.003 0.066 0.150 2.456 2.388 2.178 2.26 2.262 2.266 2.256 2.235 2.281 2.417 2.423 2.321 2.312 2.331 2.276 2.370 2.367 2.312
0.036 0.054 −0.018 0.028 −0.035 −0.055 −0.065 −0.027 −0.030 0.025 0.016 −0.038 −0.034 −0.054 −0.138 −0.037 −0.029 −0.071 −0.055 −0.129
a
Atomization energies (Eat, in eV/atom), electronic spin multiplicity (M), equilibrium bond lengths (dA−B, in Å. The average bond length is provided when more than one A−B bond exists.), average Mulliken atomic charge on Co atoms, electron affinity (EA, in eV), and ionization energy (IE, in eV) for the ground-state and for those lower-lying isomers up to about 60 meV/atom above the ground state are shown. See Figures 1 and 2 for labels. Results obtained by Liebing et al. (LMTK for short)16 are also shown for comparison.
IE = E + − E 0
All of the calculations are carried out using the exchange− correlation density functional based on Perdew, Burke, and Ernzerhof33 within the context of the generalized gradient approximation to the density functional theory (DFT).34−36 The Def2-TZVP basis set is used for all atoms.37 This is an allelectron basis set for Co and Ni. For Mo and W, on the other hand, the valence atomic orbitals of the basis set are accompanied by a pseudopotential, which is utilized to mimic the effect of 28 and 60 inner electrons, respectively.38 To accelerate the calculations, the resolution of identity is exploited in the RI-J version using an auxiliary basis set to fit the electron density during the calculation of the Coulomb repulsion.39 All calculations are accomplished with the ORCA program.40
(3)
and EA = E 0 − E−
(4)
where E0, E+, and E− are the total electronic energies of neutral clusters and positively and negatively charged clusters, respectively. The geometries of neutral clusters are kept fixed during the ionization processes. On the other hand, electron spin multiplicities of charged species are reoptimized after the removal or addition of the electron. It is argued that metal clusters interact with thiophene through a two-step process, that is, a charge-donation step from the S lone electron pair to empty sp atomic states in the cluster and a back-donation step from filled or partially filled d states of the cluster to antibonding C−S bonds. Then, the atomic charge rearrangement in the sp atomic states undergone by metal atoms during the attachment of an electron, a process closely associated with the EA, could be taken as a model for the charge-donation step. On the other hand, atomic charge rearrangement in metal d atomic states during the removal of an electron, a process that resembles the IE, could mimic the charge-back-donation step. A former application of this model can be found elsewhere.32
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RESULTS AND DISCUSSION A large amount of stable isomers was obtained for all of the MoCo and MoWNi clusters studied, especially for the larger ones. For simplicity, only those stable isomers lying up to about 60 meV/atom above the lowest-energy isomer are reported and described. Geometric, Electronic, and Magnetic Properties of MoCo Clusters. Two isomers are found for the Mo2Co triatomic. The lowest-energy isomer presents a doublet C
DOI: 10.1021/acs.jpcc.8b09773 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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energy isomers are found to be 15, 18, and 31 meV/atom above the ground state, and their electronic states are a triplet, a quintet, and a septet, respectively. In the case of Mo5Co2, five isomers separated by only 10 meV/atom are reported. All of the structures are derived from a pentagonal bipyramid, in which the pentagonal base shows different degrees of distortion. The most appreciable distortion is found in 52-2 and 52-3, see Figure 1 for labels, where a Co atom diminishes its coordination number from four to three as a consequence of the out-of-plane position of a Mo atom. The ground state is characterized by a quintet electronic state. Interestingly, the two Co atoms are bonded in the five isomers. Five stable isomers are reported in Table 1 for Mo5Co3. The ground-state and the first low-lying isomer, which is 8 meV/ atom above in energy, can be described as bicapped octahedra with two Co atoms bonded to each other. The other three, high-lying isomers, which are found between 21 and 29 meV/ atom above the ground state, exhibit a structure that resembles a capped pentagonal bipyramid with the three Co atoms in a row; see Figure 2. The ground state is characterized by a doublet electronic state, whereas doublet, quartet, and sextet electronic states are found for the other four isomers.
electronic state, whereas the other one, characterized by a quartet electronic state, is found to be 41 meV/atom above in energy. The equilibrium geometry of both isomers is a scalene triangle with short Mo−Mo bonds of 2.016 Å in 21-1 and 2.004 Å in 21-2, and larger Mo−Co bonds of 2.386 and 2.516 Å in 21-1 and 21-2, respectively. Results are summarized in Table 1, and equilibrium geometries are shown in Figure 1.
Figure 1. Equilibrium geometries of the stable MomCon (3 ≤ m + n ≤ 7) isomers reported in this work. Light-blue and pink circles represent molybdenum and cobalt atoms, respectively. Cluster labels are defined in Table 1.
Three stable isomers are reported in the case of Mo3Co. A deformed tetrahedron is the geometry adopted by all of the isomers; see Figure 1. As expected, average Mo−Co and Mo− Mo bond distances are larger than the ones found for the triatomics. The lowest-energy isomer presents a quartet electronic state, whereas a doublet state and a sextet one are found to be 14 and 17 meV/atom above in energy, respectively. Two low-energy isomers were found for Mo4Co. The two isomers exhibit the same geometry, that is, an out-of-plane rhombus conformed by Mo atoms, with the Co atom at the top, giving place to a sort of distorted square pyramid. The isomers are separated by 63 meV/atom, the lowest-energy one with a doublet electronic state, whereas the second isomer presents a quartet electronic state. See Figure 1 and Table 1 for geometric data. As can be seen in Figure 1, the four lower-energy isomers found for Mo4Co2 are characterized by a distorted octahedron, in which Co atoms tend to be neighbors. The lowest-energy isomer presents a quintet electronic state. The three low-
Figure 2. Equilibrium geometries of the stable MomCon (m + n = 8) isomers reported in this work. Light-blue and pink circles represent molybdenum and cobalt atoms, respectively. Cluster labels are defined in Table 1.
The ground state of Mo6Co2 corresponds to an octahedron, which is capped in two adjacent triangular faces by the Co atoms. This structure can also be described as two out-of-plane rhombuses, one atop the other. Two low-lying isomers, 62-3 and 62-6, also present that equilibrium geometry; see Figure 2. On the other hand, isomers 62-2, 62-4, and 62-5 show a structure that is better described as a square face atop a slightly D
DOI: 10.1021/acs.jpcc.8b09773 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C Table 2. Some Structural and Electronic Properties of the Stable MoxWyNiz Isomers Found in This Worka cluster (label)
Eat
M
MoWNi (111-1) MoWNi (111-2) Mo2W2Ni2 (222-1) Mo2W2Ni2 (222-2) Mo2W2Ni2 (222-3) Mo2W2Ni2 (222-4) Mo2W2Ni2 (222-5) Mo2W2Ni3 (223-1) Mo2W2Ni3 (223-2) Mo2W2Ni3 (223-3) Mo2W2Ni3 (223-4) Mo2W2Ni3 (223-5) Mo2W3Ni3 (233-1) Mo2W3Ni3 (233-2) Mo2W3Ni3 (233-3) Mo2W3Ni3 (233-4) Mo2W3Ni3 (233-5)
2.424 2.384 3.591 3.580 3.577 3.574 3.568 3.708 3.692 3.683 3.661 3.660 4.108 4.098 4.082 4.078 4.060
1 3 3 1 3 1 1 1 3 3 3 1 1 1 3 3 1
dMo−Mo
2.453 2.393 2.425 2.483 2.500 2.450 2.493 2.403 2.498 2.487 2.375 2.344 2.368 2.338
dMo−W
dMo−Ni
2.030 2.062 2.424 2.468 2.420 2.442 2.409 2.463 2.421 2.474 2.441 2.442 2.534 2.545 2.565 2.566 2.443
2.534 2.391 2.545 2.683 2.670 2.604 2.562 2.612 2.496 2.557 2.545 2.543 2.594 2.574 2.527 2.609 2.584
dW−W
dW−Ni
2.443 2.350 2.432 2.374 2.473 2.411 2.585 2.446 2.478 2.447 2.520 2.537 2.509 2.511 2.673
2.337 2.436 2.468 2.435 2.479 2.427 2.452 2.463 2.494 2.447 2.439 2.463 2.475 2.489 2.475 2.478 2.449
dNi−Ni
2.376 2.585 2.474 2.424
2.487 2.494 2.520
Qav(Ni)
Qav(W)
EA
IE
−0.153 −0.095 −0.150 −0.172 −0.154 −0.178 −0.132 −0.152 −0.136 −0.138 −0.106 −0.086 −0.202 −0.123 −0.172 −0.132 −0.194
0.174 0.147 0.347 0.351 0.392 0.391 0.289 0.442 0.452 0.345 0.305 0.270 0.345 0.283 0.312 0.268 0.385
1.04 1.18 1.74 1.79 1.69 1.75 1.66 1.79 1.81 1.78 1.80 1.70 1.65 1.64 1.82 1.82 1.93
6.13 5.80 5.78 5.69 5.72 5.75 5.74 5.91 5.88 5.83 5.87 5.86 5.72 5.64 5.53 5.52 5.61
a
Atomization energies (Eat, in eV/atom), electronic spin multiplicity (M), equilibrium bond lengths (dA−B, in Å. The average bond length is provided when more than one A−B bond exists.), average Mulliken atomic charge on Ni and W atoms, electron affinity (EA, in eV), and ionization energy (IE, in eV) for the ground-state and for those lower-lying isomers up to about 60 meV/atom above the ground state are shown. See Figures 3 and 4 for labels.
Electron affinities reported by LMTK are smaller than the ones found in this work, notably the value for Mo4Co2. Ionization energies listed by LMTK, on the contrary, agree very well with values obtained in this work. Geometric, Electronic, and Magnetic Properties of MoWNi Clusters. The ground state of the triatomic MoWNi is found to be a scalene triangle in a singlet electronic state with bond distances of 2.030, 2.534, and 2.337 Å for Mo−W, Mo-Ni, and Ni−W bonds, respectively. A triplet state isomer, also with a triangular structure, is lying about 40 meV/atom above the ground state. Results are summarized in Table 2, and equilibrium geometries are shown in Figure 3. Five stable isomers of Mo2W2Ni2 are found within 23 meV/ atom. All of the equilibrium geometries can be described as a capped triangular bipyramid, in which the differences among them are due to both the electron multiplicity and the relative position of each atom type; see Figure 3. The ground-state and the next lower-energy isomer exhibit the same atom arrangement, differing in the electron multiplicity as 222-1 presents a triplet electronic state, whereas 222-2 shows a singlet electronic state; see Table 2 and Figure 3 for labels. Isomers 222-3 and 222-4 present the same atomic pattern, the first one being characterized by a triplet electronic state and the second one by a singlet electronic state. Finally, isomer 222-5 presents a unique atomic pattern and a singlet electronic state. In the case of Mo2W2Ni3, five stable isomers within 48 meV/ atom are found. Optimized geometries can be divided in two groups. The first one, which includes the ground-state and the next low-lying isomer, can be described either as an oblate pentagonal bipyramid or as a bicapped triangular bipyramid, in which the two capping atoms are bonded to each other; see Figure 4. The second structural type found, which includes isomers 223-3 and 223-4, can also be described as a bicapped triangular bipyramid, but in this case, the two capping atoms are unbonded. The ground state is characterized by a singlet electronic state, whereas the two closer isomers exhibit a triplet electronic state.
out-of-plane rhombus. The electronic state of the ground state is found to be a triplet, whereas the low-lying isomers are characterized by singlet, triplet, quintet, and septet electronic states. Isomers 62-2 and 62-3 are almost degenerate to the ground state, being between 3 and 6 meV/atom above in energy. The other isomers are slightly higher in energy. It can be seen from Figures 1 and 2 that Co atoms tend to segregate when there is more than one Co atom in the cluster. Exceptions are 42-3, 62-1, and 62-6, in which Co atoms are opposite to each other. For 53-1 and 53-2 clusters, only two Co atoms are bonded, whereas the third one is opposite to that Co−Co bond. It is also interesting to note that, according to Mulliken atomic charges, Mo atoms donate electronic charges to Co atoms, as can be deduced from the average atomic charges on Co atoms reported in Table 1. It is worth noting, however, that because of important charge rearrangements, some Mo atoms remain negatively charged (data not shown in the table). Exceptions to that behavior are 41 and 42 clusters, for which, in almost all cases, charge donation occurs from Co to Mo. The ionization energy of ground states exhibits an oscillating behavior with local maxima for clusters 21, 41, and 53. On the other hand, electron affinities can be separated into three groups. The first one is formed only by cluster 21, with the smallest EA value. The second group, with a value of about 1.17 eV, contains clusters 31 and 41. The third one is formed by clusters 42, 52, 53, and 62, for which an EA of about 1.45 eV is found. Finally, it can be seen from Table 1 that present results agree well with those reported by Liebing et al. (LMTK for short).16 Ground-state equilibrium geometries and electron multiplicities are in very good agreement, except for the geometry of Mo4Co, for which a distorted triangular bipyramid is found by LMTK (see ref 16 for drawings). Atomization energies reported by LMTK are consistently smaller than the values found in this work. Average Mo−Mo distances found by LMTK are larger than those reported in this work, whereas no clear tendency can be observed for average Mo−Co distances. E
DOI: 10.1021/acs.jpcc.8b09773 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 3. Equilibrium geometries of the stable MoxWyNiz (3 ≤ x + y + z ≤ 6) isomers reported in this work. Light-blue, gray, and green circles represent molybdenum, tungsten, and nickel atoms, respectively. Cluster labels are defined in Table 2.
Figure 4. Equilibrium geometries of the stable MoxWyNiz (7 ≤ x + y + z ≤ 8) isomers reported in this work. Light-blue, gray, and green circles represent molybdenum, tungsten, and nickel atoms, respectively. Cluster labels are defined in Table 2.
Five stable isomers within 48 meV/atom are also found for Mo2W3Ni3. The optimized geometries are derivatives of the ones found for the Mo2W2Ni3 aggregates. Thus, the ground state (233-1), 233-3, and 233-5 can be described as a triangular bipyramid, in which three faces are capped by different atoms; see Figure 4. On the other hand, isomers 233-2 and 233-4 are better described as a capped pentagonal bipyramid. The ground state presents a singlet electronic state, whereas the remaining low-lying isomers are characterized by singlet and triplet electronic states. Interestingly, a sort of distorted Mo2W2 tetrahedron can be easily identified as a common core in the stable isomers reported both for Mo2W2Ni2 and for Mo2W2Ni3; see Figures 3 and 4. This behavior seems to be reflected on the relatively low dispersion found for the average dMo−Mo, dMo−W, and dW−W distances; see Table 2. Ni atoms, on the other hand, decorate triangular faces in almost all cases, except for the 223-1, 223-2, and 223-5 isomers, in which a Ni atom also decorates an edge of the Mo2W2 tetrahedron. In the case of Mo2W3Ni3, the Mo2W2 tetrahedron seems to evolve to form a Mo2W3 triangular bipyramid, which is also present as a common core in all of the isomers reported. The exception is 233-5, in which the two Mo atoms occupy the axial positions of the triangular bipyramid and, thus, they are not adjacent. As in the former cases, Ni atoms tend to locate both on triangular faces and on edges of the trigonal bipyramid. It is also worth noting that according to Mulliken atomic charges, W atoms donate electronic charges both to Mo and to Ni atoms, as can be deduced from the average atomic charges
reported in Table 2. No exceptions to that behavior are observed. The ionization energy of ground states also exhibits an oscillating behavior, but the values are much less dispersed than the values of MoCo clusters. Those are found from about 5.7−6.1 eV. Electron affinities of MoWNi are considerably smaller than the EA of larger clusters, which are found to be within a range of about 1.65−1.80 eV. Catalytic Activity of MoCo Clusters from Their Electronic Properties. As mentioned above, the charge rearrangement undergone by bi- and trimetallic clusters after the ionization processes can be used to predict their HDS activities. This is valid if it is accepted that the interaction with a sulfur-containing molecule occurs through electron transfers via σ donation and π back-donation. This way, an increase in the sp orbital population of a neutral cluster after the addition of an electron, as in the EA process, would indicate a favorable charge donation from the sulfur-containing molecule. On the other hand, a decrease in the d orbital population after the removal of an electron, as in the IE process, would favor the charge back-donation to the molecule that is involved in the HDS process. Thus, an a priori HDS activity index for a given cluster can be estimated when an increase in the sp population and a decrease in the d population take place simultaneously. As mentioned before, the change in atomic populations is obtained as the difference in Mulliken atomic charges after and before the ionization processes. Table 3 summarizes the change in sp and d populations undergone by all of the bimetallic clusters reported previously. As expected, almost all clusters exhibit the desired behavior, F
DOI: 10.1021/acs.jpcc.8b09773 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C Table 3. Change in sp and d Populations of the MoCo Bimetallic Clusters Studied in This Work after the Addition of an Electron (Δsp(−), in Units of Electrons) and after the Removal of an Electron (Δd(+), in Units of Electrons), Respectivelya cluster
Δsp(−)
Δd(+)
21-1 21-2 31-1 31-2 31-3 41-1 41-2 42-1 42-2 42-3 42-4 52-1 52-2 52-3 52-4 52-5 53-1 53-2 53-3 53-4 53-5 62-1 62-2 62-3 62-4 62-5 62-6
1.420 1.099 1.142 1.265 0.808 1.255 1.241 1.047 1.054 0.983 0.980 0.988 1.061 0.931 1.203 0.790 0.851 0.926 0.908 0.925 0.873 0.979 0.885 0.981 0.902 0.961 1.080
−0.646 −0.045 0.058 −0.201 −0.004 −0.288 −0.087 −0.055 −0.076 0.004 −0.114 −0.181 −0.164 −0.186 −0.356 −0.040 0.050 −0.277 −0.067 −0.036 −0.142 −0.306 −0.340 −0.271 −0.101 −0.379 −0.369
Figure 5. Atom labels for clusters 21-1, 31-2, 41-1, 52-4, and 62-6. These clusters are candidates to successfully take part in the HDS process. Light-blue and pink circles represent molybdenum and cobalt atoms, respectively. Cluster labels are defined in Table 1.
whereas in cluster 52-4, one Mo atom decreases its d population more than the Co atoms do. These results seem to suggest that for cluster sizes and stoichiometries studied in this work for the MoCo system, both atoms are of importance in the first step related to the charge donation. Co atoms, on the other hand, play a more relevant role in the π backdonation step of the proposed mechanism, indicating that they are part of the active sites needed for a successful HDS process. Catalytic Activity of MoWNi Clusters from Their Electronic Properties. The change in sp and d populations shown by the trimetallic clusters reported in this work is listed in Table 5. Again, almost all clusters show an increase in their sp population (Δsp(−)) and a decrease in their d population (Δd(+)) after the ionization processes, the only exception being cluster 222-1, which exhibits a rise in its d population. A detailed examination of the table shows that the average values for Δsp(−) and Δd(+) are 0.97 electrons and −0.18 electrons, respectively. Thus, as in the case of bimetallic clusters, an increase in the sp population larger than 1.0 electrons and a decrease in the d population smaller than −0.2 electrons taking place simultaneously could be indicative of a successful candidate for HDS. It can be seen from the table that clusters 111-1, 111-2, 222-2, 222-4, 222-5, 223-1, 223-3, and 233-4 are characterized by an increase larger than 1.0 electrons in Δsp(−). Moreover, clusters 111-1, 222-4, 222-5, 223-1, 233-1, 233-3, 233-4, and 233-5 exhibit a decrease larger than −0.2 electrons in Δd(+). After combining these findings, only five clusters fulfill the two conditions, namely, 111-1, 222-4, 222-5, 223-1, and 233-4 (Figure 6). They can be considered a priori candidates to successfully take part in the hydrodesulfurization process. Table 6 shows the Δsp(−) and Δd(+) values per atom for clusters 111-1, 222-4, 222-5, 223-1, and 233-4. Interestingly, the behavior of the MoWNi system seems to be quite different from that of the MoCo catalyst model. It can be observed in
a
See Figures 1 and 2 for labels.
that is, an increase in their sp population (Δsp(−)) and a decrease in their d population (Δd(+)) as a consequence of the ionization processes. A closer look at the table shows that the average values for Δsp(−) and Δd(+) are 1.02 electrons and −0.17 electrons, respectively. Thus, to simplify the comparisons, when an increase in the sp population larger than 1.0 electrons and a decrease in the d population smaller than −0.2 electrons occur simultaneously, then the aggregate undergoing these changes can be considered as a candidate for HDS. It is observed in Table 3 that various clusters show an increase larger than 1.0 electrons for Δsp(−), namely, 21-1, 21-2, 31-1, 31-2, 41-1, 41-2, 42-1, 42-2, 52-2, 52-4, and 62-6. On the other hand, clusters 21-1, 31-2, 41-1, 52-4, 53-2, 62-1, 62-2, 62-3, 625, and 62-6 exhibit a decrease larger than −0.2 electrons in Δd(+). It is then clear that only five clusters can be found in the two lists, that is, 21-1, 31-2, 41-1, 52-4, and 62-6(Figure 5). Thus, they are proposed as candidates to successfully carry forward the hydrodesulfurization process. To achieve a deeper understanding of the ionization processes and of the role played by Co atoms, Table 4 shows the Δsp(−) and Δd(+) values per atom for clusters 21-1, 31-2, 41-1, 52-4, and 62-6. It can be seen that Mo atoms show the larger Δsp(−) values for clusters 21-1, 31-2, and 52-4, whereas Co atoms present the larger Δsp(−) values for clusters 41-1 and 62-6. On the other hand, Co atoms display the larger Δd(+) decrease for 21-1, 41-1, and 62-2. In cluster 31-2, the Co atom and two Mo atoms present very similar Δd(+) values, G
DOI: 10.1021/acs.jpcc.8b09773 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C Table 4. Change in sp and d Populations Per Atom after the Addition of an Electron (Δsp(−), in Units of Electrons) and after the Removal of an Electron (Δd(+), in Units of Electrons), Respectively, for Clusters 21-1, 31-2, 41-1, 52-4, and 62-6a cluster 21-1 Co Mo1 Mo2 31-2 Co Mo Mo Mo 41-1 Co Mo1 Mo2 Mo3 Mo4 52-4 Co1 Co2 Mo1 Mo2 Mo3 Mo4 Mo5 62-6 Co1 Co2 Mo1 Mo2 Mo3 Mo4 Mo5 Mo6
Δsp(−)
Table 5. Change in sp and d Populations of the MoWNi Trimetallic Clusters Studied in This Work after the Addition of an Electron (Δsp(−), in Units of Electrons) and after the Removal of an Electron (Δd(+), in Units of Electrons), Respectivelya
Δd(+)
0.374 0.515 0.532
−0.230 −0.207 −0.208
0.224 0.359 0.353 0.328
−0.062 −0.066 −0.067 −0.006
0.289 0.269 0.219 0.208 0.269
−0.110 −0.019 −0.066 −0.056 −0.037
0.074 0.140 0.173 0.166 0.222 0.194 0.234
−0.004 −0.092 −0.036 −0.017 −0.085 −0.020 −0.103
0.128 0.221 0.083 0.144 0.193 0.027 0.158 0.126
−0.062 −0.149 −0.005 −0.026 −0.001 −0.020 −0.063 −0.043
a
cluster
Δsp(−)
Δd(+)
111-1 111-2 222-1 222-2 222-3 222-4 222-5 223-1 223-2 223-3 223-4 223-5 233-1 233-2 233-3 233-4 233-5
1.298 1.063 0.969 1.106 0.855 1.071 1.113 1.024 0.812 1.103 0.867 0.693 0.909 0.911 0.822 1.026 0.897
−0.536 −0.038 0.015 −0.176 −0.027 −0.205 −0.231 −0.318 −0.143 −0.077 −0.043 −0.038 −0.320 −0.139 −0.229 −0.260 −0.313
See Figures 3 and 4 for labels.
a
See Figure 5 for atom labels.
the table that Mo atoms show the larger Δsp(−) values for all of the clusters under study. Tungsten atoms also exhibit a large Δsp(−) value for 222-5 and 233-4. On the other hand, the larger Δd(+) decreases are observed for Mo and W atoms, except for cluster 222-5, in which the Ni atom shows the most important decrease in the d population. Present findings, then, suggest that for cluster sizes and stoichiometries investigated in this work for the MoWNi system, Mo atoms participate in the charge-transfer step through σ-donation, whereas both Mo and W atoms would be involved in the π back-donation step. Thus, it could be argued that Ni atoms play a role by modifying the local electronic structure of Mo and W atoms without joining the active sites.
Figure 6. Atom labels for clusters 111-1, 222-4, 222-5, 223-1, and 233-4. These clusters are candidates to successfully take part in the HDS process. Light-blue, gray, and green circles represent molybdenum, tungsten, and nickel atoms, respectively. Cluster labels are defined in Table 2.
of the catalyst with a sulfur-containing molecule through electron-transfer steps via σ donation and π back-donation. Although cluster sizes are relatively small, optimized geometries of the more stable isomers showed that Mo and Co atoms tend to segregate from each other and charge transfer occurs from Mo atoms to Co atoms. In the case of trimetallic MoWNi clusters, optimized geometries exhibited MoW cores with Ni atoms decorating triangular faces. Both a Mo2W2 tetrahedron and a Mo2W3 triangular bipyramid were identified as core structures in almost all cases. Charge transfer took place from W atoms both to Mo and to Ni atoms. Using the change in Mulliken atomic charges after the removal and the addition of an electron to neutral clusters, several bimetallic and trimetallic aggregates were identified as candidates to successfully take part in the hydrodesulfurization process. For MoCo species, both atom types are involved in
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CONCLUSIONS The geometric, electronic, and magnetic properties of MomCon (3 ≤ m + n ≤ 8) and MoxWyNiz (3 ≤ x + y + z ≤ 8) clusters were computationally investigated. Moreover, a list of candidates for the hydrodesulfurization process was proposed on the basis of changes in atomic charges after one electron is both added and removed from the clusters. These processes could be thought of as a basic representation of the interaction H
DOI: 10.1021/acs.jpcc.8b09773 J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
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Table 6. Change in sp and d Populations Per Atom after the Addition of an Electron (Δsp(−), in Units of Electrons) and after the Removal of an Electron (Δd(+), in Units of Electrons), Respectively, for Clusters 111-1, 222-4, 222-5, 223-1, and 233-4a cluster 111-1 Mo W Ni 222-4 Mo1 Mo2 W1 W2 Ni1 Ni2 222-5 Mo1 Mo2 W1 W2 Ni1 Ni2 223-1 Mo1 Mo2 W1 W2 Ni1 Ni2 Ni3 233-4 Mo1 Mo2 W1 W2 W3 Ni1 Ni2 Ni3
Δsp(−)
Δd(+)
0.663 0.323 0.311
−0.188 −0.187 −0.160
0.236 0.229 0.158 0.159 0.118 0.170
−0.083 −0.030 −0.012 −0.012 −0.017 −0.049
0.239 0.253 0.227 0.157 0.107 0.131
−0.010 −0.055 −0.021 −0.037 −0.075 −0.033
0.236 0.232 0.136 0.163 0.083 0.058 0.116
−0.042 −0.067 −0.038 −0.090 −0.017 −0.003 −0.062
0.173 0.178 0.114 0.048 0.164 0.126 0.113 0.109
−0.009 −0.078 −0.083 0.007 −0.034 −0.005 −0.028 −0.030
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Reinaldo Pis Diez: 0000-0003-2476-8463 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank CONICET and UNLP for the financial support. J.D.P. and L.P.B. enjoy a Ph.D. scholarship from CONICET. R.P.D. is a member of the Scientific Researcher Career of CONICET.
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a
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the σ-donation process when clusters become negatively charged. When aggregates become positively charged, as in a π back-donation process, Co atoms play the more important role. This suggests that both Mo and Co atoms would be involved in the active sites of the catalyst. For MoWNi clusters, Mo atoms are involved in the σ-donation step. The π backdonation step, on the other hand, involves both Mo and W atoms. These findings suggest that Ni atoms take no part in the active sites of the catalyst. Instead, they would be responsible for modifying the local electronic structure of Mo and W atoms.
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Article
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b09773. Vibrational frequencies of the stable MomCon and MoxWyNiz isomers (PDF) I
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