V3: Structure and vibrations from density functional theory, Franck–Condon factors, and the pulsed-field ionization zero-electron-kinetic energy spectrum

Density functional theory methods applied to homogeneous and heterogeneous catalysis: a short review and a practical user guide

The application of density functional theory (DFT) methods in catalysis has been growing fast in the last few decades thanks to both the availability of more powerful high computing resources and the development of new efficient approximations and approaches. DFT calculations allow for the understanding of crucial catalytic aspects that are difficult or even impossible to access by experiments, thus contributing to faster development of more efficient and selective catalysts. Depending on the catalytic system and properties under investigation, different approaches should be used. Moreover, the reliability of the obtained results deeply depends on the approximations involved in both the selected method and model. This review addresses chemists, physicists and materials scientists whose interest deals with the application of DFT-based computational tools in both homogeneous catalysis and heterogeneous catalysis. First, a brief introduction to DFT is presented. Then, the main approaches based on atomic centered basis sets and plane waves are discussed, underlining the main differences, advantages and limitations. Eventually, guidance towards the selection of the catalytic model is given, with a final focus on the evaluation of the energy barriers, which represents a crucial step in all catalytic processes. Overall, the review represents a rational and practical guide for both beginners and more experienced users involved in the wide field of catalysis.

How important is the amount of exact exchange for spin-state energy ordering in DFT? Case study of molybdenum carbide cluster, Mo4C2

Since the form of the exact functional in density functional theory is unknown, we must rely on density functional approximations (DFAs). In the past, very promising results have been reported by combining semi-local DFAs with exact, i.e. Hartree-Fock, exchange. However, the spin-state energy ordering and the predictions of global minima structures are particularly sensitive to the choice of the hybrid functional and to the amount of exact exchange. This has been already qualitatively described for single conformations, reactions, and a limited number of conformations. Here, we have analyzed the mixing of exact exchange in exchange functionals for a set of several hundred isomers of the transition metal carbide, Mo4C2. The analysis of the calculated energies and charges using PBE0-type functional with varying amounts of exact exchange yields the following insights: (1) The sensitivity of spin-energy splitting is strongly correlated with the amount of exact exchange mixing. (2) Spin contamination is exacerbated when correlation is omitted from the exchange-correlation functional. (3) There is not one ideal value for the exact exchange mixing which can be used to parametrize or choose among the functionals. Calculated energies and electronic structures are influenced by exact exchange at a different magnitude within a given distribution; therefore, to extend the application range of hybrid functionals to the full periodic table the spin-energy splitting energies should be investigated.

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.

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.

Nature of valence transition and spin moment in Ag(n)V(+) clusters

Evolution in the atomic structure, bonding characteristics, stability, and the spin magnetic moment of neutral and cationic AgnV clusters has been investigated using first-principles density functional approach with gradient corrected functional. It is shown that at small sizes, the V 4s states hybridize with Ag states to form 1S and 1P like superatomic orbitals, whereas the 3d states are localized on V giving the V atom an effective valence of 1 or 2. Starting from Ag8V(+), the V 3d states begin to participate in the bonding by hybridizing with the nearly free electron gas to form 1D superatomic orbitals increasing the V atom effective valence toward 5. For the cationic clusters, this changing valence results in three shell closures that lead to stable species. These occur for cationic clusters containing 5, 7, and 14 Ag atoms. The first two stable species correspond to filled 1S and 1P shells in two and three dimensions with a valence of 2 for V, whereas the closure at 14 Ag atoms correspond to filled 1S, 1P, and 1D shells with V site exhibiting a valence of 5. The transition from filled 1S and 1P shells to filled 1S, 1P, and 1D shells is confirmed by a quenching of the spin magnetic moment. The theoretical findings are consistent with the observed drops in intensity in the mass spectrum of AgnV(+) clusters after 5, 7, and 14 Ag atoms.

A density functional study of Rh13

A density functional study was performed for the Rh13 cluster using the linear combination of Gaussian-type orbitals density functional theory (LCGTO-DFT) approach. The calculations employed both the local density approximation (LDA) as well as the generalized gradient approximation (GGA) in combination with a quasi-relativistic effective core potential (QECP). Initial structures for the geometry optimization were taken along Born–Oppenheimer molecular dynamics (BOMD) trajectories. The BOMD trajectories were performed at different temperatures and considered different potential energy surfaces (PES). As a result, several hundred isomers of the Rh13 cluster in different spin multiplicities were optimized with the aim to determine the lowest energy structures. All geometry optimizations were performed without any symmetry restriction. A vibrational analysis was performed to characterize these isomers. Structural parameters, relative stability energy, harmonic frequencies, binding energy, and most relevant Kohn–Sham (KS) molecular orbitals are reported. The obtained results are compared with available data from the literature. This study predicts a low symmetry biplanarlike structure as the ground-state structure of Rh13 with 11 unpaired electrons. This isomer was first noticed by inspection of first-principle Born–Oppenheimer molecular dynamics (BOMD) simulations between 300 and 600 K. This represents the most extensive theoretical study on the ground-state structure of the Rh13 cluster and underlines the importance of BOMD simulations to fully explore the PES landscapes of complicated systems.

LANL2DZ basis sets recontracted in the framework of density functional theory

In this paper we report recontracted LANL2DZ basis sets for first-row transition metals. The valence-electron shell basis functions were recontracted using the PWP86 generalized gradient approximation functional and the hybrid B3LYP one. Starting from the original LANL2DZ basis sets a cyclic method was used in order to optimize variationally the contraction coefficients, while the contraction scheme was held fixed at the original one of the LANL2DZ basis functions. The performance of the recontracted basis sets was analyzed by direct comparison between calculated and experimental excitation and ionization energies. Results reported here compared with those obtained using the original basis sets show clearly an improvement in the reproduction of the corresponding experimental gaps.

Assessment of density functional theory optimized basis sets for gradient corrected functionals to transition metal systems: The case of small Nin (n⩽5) clusters

Density functional calculations have been performed for small nickel clusters, Ni(n), Ni(n) (+), and Ni(n)(-) (n<or=5), using the linear combination of Gaussian-type orbital density functional theory approach. Newly developed nickel all-electron basis sets optimized for generalized gradient approximation (GGA) as well as an all-electron basis set optimized for the local density approximation were employed. For both neutral and charged systems, several isomers and different multiplicities were studied in order to determine the lowest energy structures. A vibrational analysis was performed in order to characterize these isomers. Structural parameters, harmonic frequencies, binding energies, ionization potentials, and electron affinities are reported. This work shows that the employed GGA basis sets for the nickel atom are important for the correct prediction of the ground state structures of small nickel clusters and that the structural assignment of these systems can be performed, with a good resolution, over the ionization potential.

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.

Relaxation dynamics and structural isomerism in Nb10 and Nb10+

The structure, energetics, and interconversion of isomers of Nb10 and Nb10+ are studied using density functional theory with Gaussian basis sets, using guess structures derived from basin-hopping simulations with the Finnis-Sinclair [Philos. Mag. A 50, 45 (1984)] potential. These results are used as input to a master equation approach to model the relaxation of these clusters. Ionization potentials are calculated for all relevant minima, as are the infrared spectra. On the basis of these data, and known experimental results, plausible explanations are given for the biexponential reaction kinetics observed for Nb10 and Nb10+ with respect to small molecule adsorbates. In principle, this approach could be extended to investigate any midsized transition metal cluster that exhibits structural isomerism.

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 and Magnetism of VnBzn+1 Sandwich Clusters

Results on structural, energetic, electronic, and magnetic properties of linear sandwich VnBzn+1 clusters obtained using high-accuracy density functional computations are presented and analyzed. Energetically close-lying configurations and states of different spin-multiplicities are identified. The computed characteristics are in good agreement with the available experimental data. The computations predict that the most stable forms of the clusters in the size range n >/= 4 are chiral. This feature, combined with the magnetism of these systems, makes them of potential importance as building blocks of nanosystems with coupled optical and magnetic functionalities.

Structures and vibrations of Nb3O and Nb3O−: A density functional study

Density functional calculations of neutral and anionic niobium trimer monoxides are presented. The calculations were performed employing scalar quasirelativistic effective core potentials. In order to test the accuracy of the used effective core potentials in the framework of density functional theory the pulsed field ionization-zero electron kinetic energy photoelectron spectrum of Nb(3)O was simulated and compared to experiment. Different isomers of Nb(3)O and Nb(3)O(-) were studied in order to determine the ground state structures. For both neutral and anionic systems a planar C(2v) structure with an edge-bound oxygen atom was found as a ground state. Equilibrium structure parameters, harmonic frequencies, and adiabatic electron affinity are reported. The calculated electron affinity and frequencies are in good agreement with the available experimental data obtained recently from vibrationally resolved negative ion photoelectron spectroscopy.

Newly developed basis sets for density functional calculations

Optimized contracted Gaussian basis sets of double-zeta valence polarized (DZVP) quality for first-row transition metals are presented. The DZVP functions were optimized using the PWP86 generalized gradient approximation (GGA) functional and the B3LYP hybrid functional. For a careful analysis of the basis sets performance the transition metal atoms and cations excitation energies were calculated and compared with the experimental ones. The calculated values were also compared with those obtained using the previously available DZVP basis sets developed at the local-density functional level. Because the new basis sets work better than the previous ones, possible reasons of this behavior are analyzed. The newly developed basis sets also provide a good estimation of other atomic properties such as ionization energies.

Reaction of Bare VO+ and FeO+ with Ammonia: A Theoretical Point of View

The potential energy surfaces corresponding to the dehydration reaction of NH(3) by VO(+) ((3)Sigma, (1)Delta, (5)Sigma) and FeO(+) ((6)Sigma, (4)Delta) metal oxide cations have been investigated within the framework of the density functional theory in its B3LYP formulation and by employing new optimized basis sets for iron and vanadium. The reaction is proposed to occur through two hydrogen shifts from the nitrogen to the oxygen atom giving rise to multicentered transition states. Possible spin crossing between surfaces at different spin multiplicities has been considered. The energy profiles are compared with the corresponding ones for the insertion of bare cations to investigate the influence on reactivity of the presence of the oxygen ligand. The topological analysis of the gradient field of the electron localization function has been used to characterize the nature of the bonds for all the minima and transition states along the paths.