Geometric and electronic properties of small vanadium clusters: A density functional study

Probing adsorption of methane onto vanadium cluster cations via vibrational spectroscopy

Photofragment spectroscopy is used to measure the vibrational spectra of V2+(CH4)n (n = 1-4), V3+(CH4)n (n = 1-3), and Vx+(CH4) (x = 4-8) in the C-H stretching region (2550-3100 cm-1). Spectra are measured by monitoring loss of CH4. The experimental spectra are compared to simulations at the B3LYP+D3/6-311++G(3df,3pd) level of theory to identify the geometry of the ions. Multi-reference configuration interaction with Davidson correction (MRCI+Q) calculations are also carried out on V2+ and V3+. The methane binding orientation in V2+(CH4)n (n = 1-4) evolves from η3 to η2 as more methane molecules are added. The IR spectra of metal-methane clusters can give information on the structure of metal clusters that may otherwise be hard to obtain from isolated clusters. For example, the V3+(CH4)n (n = 1-3) experimental spectra show an additional peak as the second and third methane molecules are added to V3+, which indicates that the metal atoms are not equivalent. The Vx+(CH4) show a larger red shift in the symmetric C-H stretch for larger clusters with x = 5-8 than for the small clusters with x = 2, 3, indicating increased covalency in the interaction of larger vanadium clusters with methane.

Trimetallic clusters in the sumanene bowl for dinitrogen activation

It is of great importance to find catalysts for the nitrogen reduction reaction (NRR) with high stability and reactivity. A series of M₃ clusters (M = Ti, Zr, V, and Nb) supported on sumanene (C₂₁H₁₂) were designed as potential catalysts for the NRR by taking advantage of the high reactivity of trimetallic clusters and the unique geometric and electronic properties of sumanene, a bowl-like organic molecule. Detailed mechanisms of NN bond cleavage on C₂₁H₁₂-M₃ were investigated by DFT calculations and compared with those on bare M₃ clusters. M₃ in the sumanene bowl is very stable with large binding energies, which prohibits the cohesion of M₃ into M₆. In the bowl, M₃ has a (quasi-) equilateral triangle structure with lengthened M-M bonds, which is particularly beneficial to the N₂ transfer process on Ti₃ and V₃ clusters. The N-N bond can be dissociated by both M₃ and C₂₁H₁₂-M₃ clusters without the overall energy barriers. A blurring effect is found in which some geometric and electronic properties of different metal types become similar when M₃ is supported on the substrate. Our work demonstrates that sumanene is a suitable substrate to support M₃ in the activation of N₂ with enhanced stability and maintained a high level of reactivity compared to bare M₃.

On the influence of exact exchange on transition metal superatoms

The electronic structure of A7C (A = Hg, Pd, V, Cr, Mn, Fe, Ni, Cu; C = 0, ±1, ±2) clusters has been determined using density functional theory methods. The A7C (A = Hg, Pd, Cr, Cu; C = 0, ±1, ±2) clusters all conform to the existing superatomic model, with a sufficiently stabilised local structure to prevent perturbation upon the introduction of exact exchange to the exchange correlation functional. For the A7C (A = Mn, Fe, Ni; C = 0, ±1, ±2) clusters the incorporation of exact exchange separates the atomic s- and d-electrons, leading to a net increase in the number of superatomic electrons. Conversely the incorporation of exact exchange into the exchange correlation functional decreases the number of superatomic electrons for the V7C (C = 0, ±1, ±2) clusters, owing to the radial extension of the d-orbitals influencing their ability to contribute into superatomic shells.

Thermodynamically accessible titanium clusters TiN, N = 2–32

We have performed a genetic algorithm search on the tight-binding interatomic potential energy surface (PES) for small Ti_N (N = 2–32) clusters.

Evolution of the structural, energetic, and electronic properties of the 3d, 4d, and 5d transition-metal clusters (30 TMn systems for n = 2–15): a density functional theory investigation

Subnanometric transition-metal (TM) clusters have attracted great attention due to their unexpected physical and chemical properties, leastwise compared to their bulk counterparts.

Low-energy excited states of divanadium: a matrix isolation and MRCI study

The ground and excited electronic states of the vanadium dimer (V2) have been studied using Ne matrix isolation experiments and quantum chemical calculations (multireference configuration interaction based on complete active space self-consistent orbitals). In the near infrared absorption spectrum, two vibrational progressions of a new electronic term with a large number of members have been observed with the origin at 1.08 eV and a fundamental vibrational quantum of 475 cm(-1). With the aid of calculations, it has been assigned to a (3)Πu electronic term. The calculations yield potential energy curves for a large number of singlet, triplet, and quintet electronic terms.

Gas-phase perspective on the thermodynamics and kinetics of heterogeneous catalysis

Gas-phase studies of small transition metal cluster cations provide thermochemistry of utility to surface science and heterogeneous catalysis.

Structures, spectra, and energies of niobium clusters from Nb13 to Nb20

A comprehensive theoretical investigation on structures and properties of niobium clusters in the range from 13 to 20 atoms, in three different charged states, is performed by using the BPW91 and M06 functionals and the cc-pVDZ-PP basis set. These species are predicted to prefer low spin ground state, i.e., singlet (for even electron) and doublet (for odd electron) systems. In terms of growth mechanism, a compact structure with one Nb encapsulated by a cage formed from five and six triangles is found to be favored over an icosahedral evolution. Unlike many 3d metals, whose volumes are much smaller, 13 and 19 Nb atoms clusters do not exist as icosahedra and double-icosahedra. A distinct case is Nb(15) as it bears a slightly distorted bcc structure. For some systems, several lower lying isomers are computed to be so close in energy that DFT computations cannot clearly establish their ground electronic states. The existence of structural isomers with comparable energy content is established for Nb(n) species with n = 13, 18, 19, and 20 in both neutral and charged states. The vibrational (IR) spectra are also calculated. While the spectra of smaller systems are strongly dependent on addition or removal of an electron from the neutral, the spectra of the larger size clusters are mostly independent of the charged state. The neutrals and their corresponding ions usually have a quite similar IR pattern. Electron affinities (EA), ionization energies (IE), average binding energies, dissociation energies, and frontier orbital energy gaps are evaluated. The computed EAs and IEs are generally in fair agreement with experiment. The Nb(15) system is observed to be stable and it can form a highly symmetric structure in all charged states with both open and closed electron shells.

Reactivity of group 5 bielement clusters with H2

Bielement metal clusters composed of the group 5 elements, A(n)B(m) (A, B = V, Nb, Ta), were prepared in the gas phase over the wide n and m ranges. We measured reactivities of the attachment reaction of the neutral clusters to H(2), which were plotted as a function of a map with n and m. The clusters with n + m = 4 and 5 were found to be more reactive than the other clusters. The measurement of the ionization energies reveals that there is no strong correlation between the reactivity and the ionization energy. In addition, the reactivities of the cations, A(n)B(m)(+), were also highest at n + m = 4 and 5. These findings suggest that the electronic structure does not totally determine the reactivity of the neutral clusters. On the other hand, theoretical calculations for A(n)B(m) (n + m = 4) reported by Metha et al. showed that the optimized geometrical structures of the congener group 5 bielement clusters do not change significantly by changing n and m within n + m = 4. Hence, it is highly likely that the pyramidal (n + m = 4) and bipyramidal (n + m = 5) structures of A(n)B(m) determine the high reactivity of the clusters.

Dynamics of Clusters Initiated by Photon and Surface Impact

Clusters of atoms/molecules show dynamics characteristic of the method of excitation. Two contrasted processes are discussed: (1) electronic excitation via single-photon absorption and (2) impulsive excitation of nuclear motions by surface impact. Process 1 is exemplified by photodissociation dynamics of size-selected metal cluster ions. The electronic energy is converted most likely to vibrational energy of internal modes; dissociation follows via statistical mechanism to produce energetically favored fragments. Exceptionally, a silver cluster ion, Ag4(+), is shown to undergo nonstatistical dissociation along the potential-energy surface of the excited state. Energy partitioning to translational and vibrational modes of fragments is analyzed as well as bond dissociation energies. Furthermore, the spectrum of the photodissociation yield provides electronic and geometrical structures of a cluster with the aid of ab initio calculations; manganese, Mn(N)(+), and chromium, Cr(N)(+), cluster ions are discussed, where the importance of magnetic interactions is manifested. On the other hand, momentum transfer upon surface impact plays a role in process 2. An impulsive mechanical force triggers extraordinary chemical processes distinct from those initiated by atomic collision as well as photoexcitation. Experiments on aluminum, Al(N)(-), silicon, SiN(-), and solvated, I(2)(-)(CO2)(N), cluster anions provide evidence for reactions proceeding under extremely high temperatures, such as pickup of surface atoms, annealing of products, and mechanical splitting of chemical bonds. In addition, a model experiment to visualize and time-resolve the cluster impact process is performed by using a micrometer-sized liquid droplet. Multiphoton absorption initiates superheating of the droplet surface followed by a shock wave and disintegration into a number of small fragments (shattering). These studies further reveal how the nature of chemical bonds influences the dynamics of clusters.

Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems

Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.

Coexistence of ferroelectricity and ferromagnetism in tantalum clusters

The atomic and electronic structures of Ta(N) (N=2-23) clusters have been determined in the framework of pseudopotential density-functional calculations, based upon an unbiased global search with guided simulated annealing to an empirical potential. It is found that the ground-state structures of Ta(N) are very similar to those of Nb(N), showing no preference for the icosahedral growth. Also, a size- and structure-dependent ferroelectricity is found in these tantalum clusters. More importantly, it is found that the ferroelectricity and ferromagnetism can coexist in the homogeneous transition-metal cluster, offering a possibility to obtain a new type of "multiferroic" materials composed of the clusters. Finally, the far-infrared spectroscopy is suggested to be an efficient tool to distinguish the ferroelectric clusters.

Preparing transition-metal clusters in known structural forms: The mass-analyzed threshold ionization spectrum of V3

The first results are presented of a new experiment designed both to generate and characterize spectroscopically individual isomers of transition-metal cluster cations. As a proof of concept the one-photon mass-analyzed threshold ionization (MATI) spectrum of V3 has been recorded in the region of 44,000-45,000 cm-1. This study extends the range of a previous zero-kinetic-energy (ZEKE) photoelectron study of Yang et al. [Chem. Phys. Lett. 231, 177 (1994)] with which the current results are compared. The MATI spectra reported here exhibit surprisingly high resolution (0.2 cm-1) for this technique despite the use of large discrimination and extraction fields. Analysis of the rotational profile of the origin band allows assignment of the V3 ground state as and the V3+ ground state as , both with D3h geometry, in agreement with the density-functional theory study of the V3 ZEKE spectrum by Calaminici et al. [J. Chem. Phys. 114, 4036 (2001)]. There is also some evidence in the spectrum of transitions to the low-lying excited state of the ion. The vibrational structure observed in the MATI spectrum is, however, significantly different to and less extensive than that predicted in the density-functional theory study. Possible reasons for the discrepancies are discussed and an alternative assignment is proposed which results in revised values for the vibrational wave numbers of both the neutral and ionic states. These studies demonstrate the efficient generation of cluster ions in known structural (isomeric) forms and pave the way for the study of cluster reactivity as a function of geometrical structure.

Homonuclear transition-metal trimers

Density-functional theory has been used to determine the ground-state geometries and electronic states for homonuclear transition-metal trimers constrained to equilateral triangle geometries. This represents the first application of consistent theoretical methods to all of the ten 3d block transition-metal trimers, from scandium to zinc. A search of the potential surfaces yields the following electronic ground states and bond lengths: Sc3(2A1',2.83 A), Ti3(7E',2.32 A), V3(2E",2.06 A), Cr3(17E',2.92 A), Mn3(16A2',2.73 A), Fe3(11E",2.24 A), Co3(6E",2.18 A), Ni3(3A2",2.23 A), Cu3(2E',2.37 A), and Zn3(1A1',2.93 A). Vibrational frequencies, several low-lying electronic states, and trends in bond lengths and atomization energies are discussed. The predicted dissociation energies DeltaE(M3-->M2+M) are 49.4 kcal mol(-1)(Sc3), 64.3 kcal mol(-1)(Ti3), 60.7 kcal mol(-1)(V3), 11.5 kcal mol(-1)(Cr3), 32.4 kcal mol(-1)(Mn3), 61.5 kcal mol(-1)(Fe3), 78.0 kcal mol(-1)(Co3), 86.1 kcal mol(-1)(Ni3), 26.8 kcal mol(-1)(Cu3), and 4.5 kcal mol(-1)(Zn3).

Structure determination of small vanadium clusters by density-functional theory in comparison with experimental far-infrared spectra

The far-infrared vibrational spectra for charged vanadium clusters with sizes of 3-15 atoms have been measured using infrared multiple photon dissociation of Vn+Ar-->Vn(+)+Ar. Using density-functional theory calculations, we calculated the ground state energy and vibrational spectra for a large number of stable and metastable geometries of such clusters. Comparison of the calculated vibrational spectra with those obtained in the experiment allows us to deduce the cluster size specific atomic structures. In several cases, a unique atomic structure can be identified, while in other cases our calculations suggest the presence of multiple isomers.

Ab initio calculations for the photoelectron spectra of vanadium clusters

We report ab initio calculations for the electronic and structural properties of V(n), V(n) (-), and V(n) (+) clusters up to n=8. We performed the calculations using a real-space pseudopotential method based on the local spin density approximation for exchange and correlation. This method assumes no explicit basis. Wave functions are evaluated on a uniform grid; only one parameter, the grid spacing, is used to control convergence of the electronic properties. Charged states are easily handled in real space, in contrast to methods based on supercells where Coulombic divergences require special handling. For each size and charge state, we find the lowest energy structure. Our results for the photoelectron spectra, using the optimized structure, agree well with those obtained by experiment. We also obtain satisfactory agreement with the measured ionization potential and electron affinity, and compare our results to calculations using an explicit basis.

DFT Calculations on Group 5 Mixed Metal Tetramers: TaxNbyVz (x + y + z = 4)

We report Density Functional Theory (DFT) calculations on mixed-metal tetramers comprised of the Group 5 (Vb) elements V, Nb, and Ta. Our results show that the lowest energy structures for Nb4 and Ta4 are regular tetrahedra with Td symmetry and singlet multiplicity whereas V4 is a triplet state with C2v symmetry. The monosubstituted isomers, A3B, all have C3v symmetry but several higher energy Cs structures have been found that are approximately 100 kJ mol−1 higher in energy. The disubstituted isomers all posses arachno-butterfly structures; the A2B2 types with C2v symmetry and the A2BC types with Cs symmetry. However, the relative openness of the arachno structures is found to be specific to the composition of the mixed-metal cluster.

Reactions and thermochemistry of small transition metal cluster ions

This review discusses the reactivities and thermodynamics of small-size-specific transition metal clusters and focuses on thermodynamic information, which has not been comprehensively discussed before. Because of this focus, guided-ion-beam mass spectrometry was used to acquire much of the data. The details of this technique and the associated data analysis methods are provided. Results on the stabilities of bare transition metal clusters are provided for neutral, cationic, and anionic species. Implications for the electronic and geometrical structures are discussed, as well as the extrapolation of these values to bulk phase behavior. Detailed results for reactions of transition metal clusters with D2 and the oxygen donors O2 and CO2 are reviewed. Available bond energies between size-specific clusters and one D atom and one and two O atoms are compiled, and their implications are evaluated and favorably compared with bulk phase analogs. Several additional thermodynamic studies of various cluster systems are also discussed.

REACTIONS OFTRANSITIONMETALCLUSTERS WITHSMALLMOLECULES

Atoms and small molecules react with transition metal clusters in ways that are analogous to the physisorption and chemisorption reactions observed on the corresponding extended metal surface. However, often underlying these similarities are size-dependent variations in the reaction mechanisms and rates, the interpretation of which requires a detailed understanding of the structures of both the bare metal cluster substrates and the cluster-molecule complexes. Although polyatomic transition metal clusters cannot be characterized by the traditional methods of molecular spectroscopy, the combination of other physical and chemical probes can provide qualitative and semiquantitative structural information. These techniques, when combined with equilibrium geometries calculated using ab initio or semiempirical methods, provide a detailed picture of the structural origin of metal cluster reactivity and its variation with size.