Valence Basis Sets Research Articles

The electronic spectrum of AgBr2: Ab initio benchmark calculations on the 2Πu and 2Σu+ charge transfer states including spin‐orbit effects

AbstractThe 2Πu and 2Σu+ charge transfer (CT) states of AgBr2 have been studied through benchmark ab initio HF, complete active space SCF, CASPT2, NEVPT2, and averaged coupled pair functional (ACPF) multireference calculations using especially developed valence basis sets to study the transition energies, geometries, vibrational frequencies, and Mulliken charges. The spin‐orbit (SO) effects have been included through the effective Hamiltonian formalism using the ACPF energies as |ΛSΣ> diagonal elements. The equilibrium Ag–Br distance for both CT states is larger than that of the X2Πg ground state. The ACPF adiabatic excitation energies of the 2Πu and 2Σu+ states are 4620 and 7006 cm‐1, respectively. Using previous ACPF benchmark studies showing that the 2Δg ligand field (LF) state lies more than 20,000 cm‐1 above the ground state, these new results lead to the following energetic ordering for the five lowest electronic states of AgBr2: X2Πg, 2Σg+, 2Πu, 2Σu+, and 2Δg, in sharp contradiction with Hartree–Fock theory. When considering the coupling of the LF and CT states, the inclusion of the SO effects leads to a pure Ω = 3/2 (X2Πg) ground state, Ω = 1/2 (92% 2Πg + 8% 2Σg+) A state, Ω = 3/2 (pure 2Πu) B state, Ω = 1/2 (68% 2Πu+32% 2Σu+) C state, Ω = 1/2 (8% 2Πg + 92% 2Σg+) D state, and an Ω = 1/2 (32% 2Πu + 68% 2Σu+) E state. We present here what we consider the most complete and accurate account of the electronic spectrum of AgBr2. © 2012 Wiley Periodicals, Inc.

The molecular structure of AgBr2 and AgBr2+. A benchmark CASSCF, CASPT2, and averaged coupled pair functional study

AbstractThe ground states of AgBr2 and AgBr2+ have been predicted to be 2B2 and 1A1 bent structures (θ = 67° and θ = 47°, respectively) using complete active space self‐consistent field (CASSCF) and multireference second order perturbation theory (J. Chem. Phys., 1999, 111, 8925). Because CuF2, CuCl2, and AgCl2 are known to be linear, the ground states of AgBr2 and AgBr2+ have been studied through benchmark ab initio CASSCF(21,15), multireference second‐order perturbation theory and averaged coupled pair functional calculations using very large and especially developed valence basis sets. The bent nature of the ground state of the AgBr2+ ion is confirmed, but for AgBr2 the absolute minimum of the ground state is found to be 2Πg in the linear centrosymmetric structure with the present large optimized basis sets at all levels of theory. Also, a significant Ag‐Br bond length reduction was obtained for the cation with respect to the previous value. These results show the crucial role played by the quality of the valence atomic basis sets for this type of transition metal molecules on key properties such as the equilibrium geometry. New equilibrium geometries, vibrational frequencies and ionization potentials are presented. © 2012 Wiley Periodicals, Inc.

Coupled Cluster and Møller-Plesset Perturbation Theory Calculations of Noncovalent Intermolecular Interactions using Density Fitting with Auxiliary Basis Sets from Cholesky Decompositions.

We compute noncovalent intermolecular interaction energies for the S22 test set [Phys. Chem. Chem. Phys.2006, 8, 1985-1993] of molecules at the Møller-Plesset and coupled cluster levels of supermolecular theory using density fitting (DF) to approximate all two-electron integrals. The error due to the DF approximation is analyzed for a range of auxiliary basis sets derived from Cholesky decomposition (CD) in conjunction with correlation consistent and atomic natural orbital valence basis sets. A Cholesky decomposition threshold of 10(-4)Eh for full molecular CD and its one-center approximation (1C-CD) generally yields errors below 0.03 kcal/mol, whereas 10(-3)Eh is sufficient to obtain the same level of accuracy or better with the atomic CD (aCD) and atomic compact CD (acCD) auxiliary basis sets. Comparing to commonly used predefined auxiliary basis sets, we find that while the aCD and acCD sets are larger by a factor of 2-4 with triple-ζ AO basis sets, they provide results 1-2 orders of magnitude more accurate.

XZP + 1d and XZP + 1d-DKH basis sets for second-row elements: application to CCSD(T) zero-point vibrational energy and atomization energy calculations

Recently, segmented all-electron contracted double, triple, quadruple, quintuple, and sextuple zeta valence plus polarization function (XZP, X = D, T, Q, 5, and 6) basis sets for the elements from H to Ar were constructed for use in conjunction with nonrelativistic and Douglas-Kroll-Hess Hamiltonians. In this work, in order to obtain a better description of some molecular properties, the XZP sets for the second-row elements were augmented with high-exponent d "inner polarization functions," which were optimized in the molecular environment at the second-order Møller-Plesset level. At the coupled cluster level of theory, the inclusion of tight d functions for these elements was found to be essential to improve the agreement between theoretical and experimental zero-point vibrational energies (ZPVEs) and atomization energies. For all of the molecules studied, the ZPVE errors were always smaller than 0.5%. The atomization energies were also improved by applying corrections due to core/valence correlation and atomic spin-orbit effects. This led to estimates for the atomization energies of various compounds in the gaseous phase. The largest error (1.2kcalmol(-1)) was found for SiH(4).

CAP/SAC-CI method for calculating resonance states of metastable anions

The complex absorbing potential (CAP)/symmetry-adapted cluster-configuration interaction (SAC-CI) method has been developed to investigate resonance states of metastable anions. The method has been implemented in the projected scheme and applied to the π∗ resonance state of formaldehyde. The dependence on both valence and diffuse basis sets up to g-function, the number of SAC-CI states in the projection, and the effect of perturbation selection are examined. The potential energy curve and decay width are calculated in the C–O stretching coordinate, and the Franck–Condon factors for transitions from neutral to resonance state are evaluated to interpret the electron transmission (ET) spectrum.

Structure and energetics of small iron clusters

Electronic properties of Fe(2-10) clusters and their ions are described by an all-electron ab initio density functional theory computational analysis using the Handy's OPTX exchange and the gradient-corrected correlation functional of Perdew, Burke and Ernzerhof with a triple-zeta valence basis set plus polarization functions. Ground state structures, magnetic moments, dissociation energies, binding energies, IR vibrational spectra, vertical and adiabatic ionization energies, and electron affinities are reported. Two possible states for Fe(2) which are separated by 81.54 meV are described as possible Fe(2), while the septet (ground state) yields an accurate bond distance (error of 0.02Å); the nonet yields a precise vibrational frequency (error of 10.1cm(-1)). Fe(2) binding energy (0.05 eV/atom error) more closely resembles experimental data than any other previously reported computational methods. In addition, the Fe(6) is found to be the most stable cluster within our set being analyzed.

Thermal Rearrangements of 1-Ethynyl-2-methylcyclopropane: A Computational Study

In this research, a comprehensive theoretical investigation of the thermal rearrangements of 1-ethynyl-2-methylcyclopropane is carried out employing density functional theory (DFT), with the B3LYP functional, and high-level ab initio methods, such as the complete active space self-consistent field (CASSCF), multireference second-order Møller-Plesset perturbation theory (MRMP2), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. In all computations Pople's polarized triple-ζ split valence basis set, 6-311G(d,p), is utilized. The potential energy surface (PES) for the relevant system is explored to provide a theoretical account of the experiments by Hopf, Ellis and Frey, Huntsman et al., and Berson. The computational results herein on the target system show that the thermal aromatization reaction does not proceed via conversion of 1,2,5-hexatriene (2) to 1,3,5-hexatriene (10a) as proposed by Hopf. Indeed, the reaction proceeds via conversion of 5 and 6 to bicyclo[3.1.0]hexene (9) as suggested by Huntsman et al.

Basis set convergence of molecular correlation energy differences within the random phase approximation

The basis set convergence of energy differences obtained from the random phase approximation (RPA) to the correlation energy is investigated for a wide range of molecular interactions. For dispersion bound systems the basis set incompleteness error is most pronounced, as shown for the S22 benchmark [P. Jurecka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The use of very large basis sets (> quintuple-zeta) or extrapolation to the complete basis set (CBS) limit is necessary to obtain a reliable estimate of the binding energy for these systems. Counterpoise corrected results converge to the same CBS limit, but counterpoise correction without extrapolation is insufficient. Core-valence correlations do not play a significant role. For medium- and short-range correlation, quadruple-zeta results are essentially converged, as demonstrated for relative alkane conformer energies, reaction energies dominated by intramolecular dispersion, isomerization energies, and reaction energies of small organic molecules. Except for weakly bound systems, diffuse augmentation almost universally slows down basis set convergence. For most RPA applications, quadruple-zeta valence basis sets offer a good balance between accuracy and efficiency.

Potential Energy Surfaces for Rearrangements of Berson Trimethylenemethanes

In this research, thermal rearrangements of the Berson trimethylenemethanes (Berson-TMMs) have been investigated by employing density functional theory (DFT) and high-level ab initio methods, such as the complete active space self-consistent field (CASSCF), multireference second-order Møller-Plesset perturbation theory (MRMP2), multireference configuration interaction singles and doubles (MRCISD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. In all computations Pople's polarized triple-ζ split valence basis set, 6-311G(d,p), is utilized. The relevant portions of the lowest-energy, singlet-spin potential energy surface of the C(4)H(6) (parent TMM), C(6)H(8) (Berson-TMMa), and C(8)H(12) (Berson-TMMc) chemical systems have been explored in order to determine the reaction energies and activation parameters accurately, with the ultimate objective of providing a theoretical account of experiments by Berson on TMMc. The nature of the orthogonal and the planar structures of the parent TMM have been clarified in this study. We have concluded that the orthogonal TMM (1)B(1) minimum has a C(2v) symmetry structure, and there is no pyramidalization in the unique methylene group. It lies at 13.9 kcal mol(-1) above the triplet minimum (3)B(2) at MRCISD level. The closed-shell (1)A(1) state of the planar TMM is not a true minimum but a transition structure (TS) for 180° rotation of the unique methylene group in the orthogonal TMM minimum. It lies at 3.0 kcal mol(-1) above (1)B(1). The planar structures are also involved in the interchange of equivalent orthogonal TMMs (o(1), o(2), o(3)). Many features of the parent TMM are retained in TMMa and TMMc, despite the constraints imposed by the five-membered ring in the latter species. Thus, ring closure to the bicyclic molecules 3a (3c) and 5a (5c) takes place similarly to that in the parent TMM. Likewise, planar TMMa (TMMc) structures are TSs, while orthogonal ones are true minima. The adiabatic singlet-triplet gaps are also similar, being 14.7 (13.0) and 16.5 (16.2) kcal mol(-1) in the orthogonal (o(1)) and planar TMMa (TMMc), respectively. It has been shown here that the substantial reductions in the ring-opening barriers of MCP derivatives 3a (3c) and 5a (5c) can be largely attributed to ring strain in the former and π-bond strain in the latter species.

The fate of branched and linear isomers in the rhodium-catalyzed hydroformylation of 3,4,4-trimethylpent-1-ene

In nonreversible hydroformylations, the computational evaluation of regio- and stereoselectivities from the relative energy barriers of the transition states (TS) for the alkyl-Rh intermediate formation step is possible, provided all low energy conformers are considered. In contrast, in reversible hydroformylations, also the subsequent reaction steps need to be taken into account to shed some light on mechanistic details. Thus, an extensive comparison of branched (B) and linear (L) reaction pathways for the Rh-catalyzed hydroformylation of 3,4,4-trimethylpent-1-ene (a bulky chiral substrate), going from a number of reactant complexes to products, has been carried out to rationalize the experimental result that pointed to reaction reversibility, although the value of the regioselectivity ratio (B:L = 15:85), based on alkyl-Rh TS free energies, computed under the hypothesis of nonreversibility, was in satisfactory agreement with the experimental one (5:95). A density functional theory approach at the B3P86/6-31G* level coupled to effective core potentials for Rh in the LanL2DZ valence basis set has been employed. By comparing the activation free energies involved in the various steps for the different reactant adducts, interestingly a similar behavior along all the linear pathways is found: the alkyl-Rh formation TS presents the highest barrier; thus, the reaction is nonreversible for all the linear isomers that invariably proceed to yield the linear aldehyde. Conversely, the behavior is quite different along the branched pathways. While some branched isomers eventually produce the corresponding aldehydes, two of the others follow distinct competing pathways, because β-hydride elimination occurs (a) to the terminal olefin-Rh complex (the starting material) that reacts again with the original regioselectivity, increasing the linear fraction, when the CO addition and insertion TS are higher than the alkyl-Rh TS and (b) to the internal olefin-Rh complex when the CO addition and insertion TS are higher than the relevant β-hydride elimination TS, but not than the alkyl-Rh TS. The solvent effect on the reversible profile, evaluated either in the supermolecule approach by adding a benzene molecule to the calculations or in the IEF-PCM framework (e = 2.247), does not bring about any substantial change in the profile, leaving unaltered the conclusions reached.

Explicitly Correlated Coupled Cluster Calculations for Molecules Containing Group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) Elements: Optimized Complementary Auxiliary Basis Sets for Valence and Core–Valence Basis Sets

Compact auxiliary basis sets matched to the standard aug-cc-pVnZ-PP and aug-cc-pwCVnZ-PP orbital basis sets have been developed for the coinage metals (Cu, Ag, Au) and group 12 elements (Zn, Cd, Hg) for use in the resolution of the identity (RI) approximation in explicitly correlated F12 calculations. The CCSD(T)-F12b method has been utilized with these auxiliary basis sets to carry out molecular benchmark calculations on homonuclear coinage metal diatomics (Cu2, Ag2, Au2), as well as mono- (CuF, AgF, AuF) and difluorides (CuF2, AgF2, AuF2). The resulting equilibrium geometries, harmonic vibrational frequencies, and atomization energies demonstrate that CCSD(T)-F12b calculations using double-ζ-quality basis sets produce results comparable in accuracy to conventional CCSD(T) quadruple-ζ calculations, while F12b with triple-ζ-quality sets yields results close to 5-ζ, which is near the conventional complete basis set (CBS) limit estimates. Analogous trends are observed for the group 12 monofluorides (ZnF, Cd...

Electrically polarized valence basis sets for the SBKJC effective core potential developed for calculations of dynamic polarizabilities and Raman intensities

Sadlej’s electric polarization method of Gaussian basis functions was applied to the double-zeta effective core potential basis sets of Stevens, Basch, Krauss, Jasien and Cundari to generate a new augmented polarized valence double-zeta set, named as pSBKJC, which is appropriate for the calculation of dynamic polarizabilities and Raman intensities. The pSBKJC basis set was developed for the atoms of families 14–17 (from C to F, Si to Cl, Ge to Br and Sn to I). In order to assess the performance of this new basis set, these properties were compared to those evaluated using Sadlej’s set, available in the EMSL online library under the name of Sadlej-pVTZ. In these tests, Hartree-Fock/pSBKJC calculations have proved to be less demanding of the computer than the Hartree-Fock/Sadlej-pVTZ ones but give results in excellent agreement with those from the Sadlej-pVTZ basis set. Since the Stevens et al. pseudopotential can represent the scalar relativistic effects, the results obtained at the Hartree-Fock/pSBKJC level show a better agreement with the results of Dirac-Hartree-Fock/Sadlej-pVTZ relativistic calculations using Dyall’s spin-free Hamiltonian. When comparing Hartree-Fock/pSBKJC data of Raman scattering activities, at the excitation wavelength of 488 nm, with those of spin-free Dirac-Hartree-Fock/Sadlej-pVTZ calculations, a very good agreement is observed, where the RMS error is 8.5 A4a.m.u.−1 and the averaged percentage error is 3.4%. In terms of computer savings in calculations of dynamic Raman intensities, a 20% reduction in the CPU time in the coupled cluster singles and doubles intensities of C6H6 and about 40% reduction in the time-dependent Hartree-Fock intensities for C6F6 molecules were attained.

Thermal denitrogenation of 7-isopropylidene-2,3-diaza-norbornene: formation of substituted 3-methylene-(1,4)-pentadienes

A theoretical study of the thermal denitrogenation of 7-isopropylidene-2,3-diaza-norbornene is carried out by employing density functional theory and high level ab initio methods, such as the complete active space self-consistent field, multi-reference second-order Møller-Plesset perturbation theory, and coupled-cluster singles and doubles with perturbative triples. In all computations Pople's polarized triple-ζ split valence basis set, 6-311G(d,p), is utilized. The potential energy surface for the relevant system is explored to provide a theoretical account for the formation of trienes (major products). For this purpose, a mechanism has been proposed and theoretically studied. The rate constant for each isomerization reaction is computed using the transition state theory. The simultaneous first-order ordinary-differential equations are solved numerically for the considered system to obtain time-dependent concentrations, hence the product distributions at a given temperature. Our results demonstrate that E- and Z-2-methyl-3-ethylidene-1,4-pentadienes are formed via a reaction path originating from 3-isopropylidene-1,4-pentadiene. The result of kinetic analysis agrees well with the experimental observations of Berson et al. (M. R. Mazur, S. E. Potter, A. R. Pinhas and J. A. Berson, J. Am. Chem. Soc., 1982, 104, 6823-6824). Further, the computed percentage of trienes is in general agreement with experiment. Therefore, we conclude that our proposed mechanism satisfactorily explains the experimental observations.

High linear regioselectivity in the rhodium-catalyzed hydro(deuterio)formylation of 3,4,4-trimethylpent-1-ene: The role of β-hydride elimination

The regioselectivity in the hydroformylation reaction catalyzed by an unmodified Rh catalyst has been investigated for a number of α-methylsubstituted alk-1-enes (3-methylbut-1-ene MB1, 3-methylpent-1-ene MP1, 3,4-dimethylpent-1-ene DMP1, and 3,4,4-trimethylpent-1-ene TMP1) experimentally (at 20°C and 100atm CO/H2 total pressure) and theoretically at the B3P86/6-31G* level with Rh described by effective core potentials in the LanL2DZ valence basis set. For all substrates the formation of the linear aldehyde (L) with respect to the branched one (B) in a prevailing amount has been observed (L/B>62/38); the L isomer was formed as the almost exclusive product in the case of TMP1 (L/B=95/5). 2H NMR investigations of crude reaction mixtures, coming from analogous deuterioformylation experiments interrupted at partial substrate conversion, showed that in the case of TMP1 only the branched alkyl-rhodium intermediate, precursor of the branched aldehyde, via β-hydride elimination mainly generates terminal deuterated olefins and, to a lesser extent, internal ones. The reversibility of the branched alkyl-Rh intermediates accounts for the high regioselectivity in favor of the linear aldehyde. Computational studies confirm the importance of the alkyl-Rh transition state (TS) stability to reproduce the experimental regioselectivity, or even to predict it, when the reaction is nonreversible (i.e. for MB1, MP1, and DMP1). In the case of TMP1, the free energy profiles for further reaction steps along branched and linear pathways have been examined to elucidate the origin of reaction reversibility. The TS for the alkyl migratory insertion onto the CO coordinated to rhodium, higher than that for the alkyl-Rh intermediate formation, explains the reason why in deuterioformylation experiments at partial conversion the monodeuterated terminal olefin TMP1-1-d1 is obtained. This occurs for one out of two most populated reactant conformers of TMP1, although for the Curtin–Hammett principle reactant populations are not particularly important. For the other, the reaction proceeds to the branched aldehyde. Only for a less populated reactant conformer the internal olefin is obtained. Conversely, along the linear pathway the CO addition and alkyl migratory insertion steps occur, respectively, in a practically spontaneous way and with very low TS in any case. Agostic interactions (using the QTAIM theory) and kinetic isotope effects have been evaluated and discussed. The examination of further reaction steps for DMP1 allowed us to demonstrate that the reaction is nonreversible for that substrate, despite the similarity between DMP1 and TMP1. The tert-butyl group exerts its steric hindrance mainly on the very first branched reaction steps, favoring an alkyl-Rh TS arrangement lower in free energy than the alkyl-Rh migratory insertion onto the coordinated CO. In part the branched material returns to the reactant complex, thus enriching the linear fraction.

Performance of Effective Core Potentials for Density Functional Calculations on 3d Transition Metals.

The performance of popular Hartree-Fock-based effective core potentials in Hartree-Fock and density functional calculations of 3d transition metals has been evaluated by basis-set convergence studies for ten cases: the equilibrium bond dissociation energy (De) for dissociation of ground-state Ti2 to ground and excited atoms, the ground-state dissociation energies of FeO, Cu2, ScH, TiH, Sc2, Fe2, and TiV(+), and the first excitation energy (Ex) of Ti atom. Each case is studied with 11 or 13 density functionals. For comparison, the accuracy of the all-electron def2-TZVP basis set is tested with both relativistic and nonrelativistic treatments. Convergence and accuracy are assessed by comparing to relativistic all-electron calculations with a nearly complete relativistic basis set (NCBS-DK, which denotes the cc-pV5Z-DK basis set for 3d metals and hydrogen and the ma-cc-pV5Z-DK basis set for oxygen) and to nonrelativistic all-electron calculations with a nearly complete nonrelativistic basis set (NCBS-NR, which denotes the cc-pV5Z basis set for 3d metals and hydrogen and the ma-cc-pV5Z basis set for oxygen). As compared to NCBS-DK results, all ECP calculations perform worse than def2-TZVP all-electron relativistic calculations when averaged over all 130 data (13 functionals and ten test cases). The compact effective potential (CEP) relativistic effective core potential (RECP) combined with a valence basis set developed for the many-electron Dirac-Fock (MDF10) RECP performs best in effective core potential calculations and has an average basis-set incompleteness error of 3.7 kcal/mol, which is much larger than that (0.9 kcal/mol) of def2-TZVP relativistic all-electron results. Hence, the def2-TZVP relativistic all-electron calculations are recommended for accurate DFT calculations on 3d transition metals. In addition to our general findings, we observed that all kinds of density functionals do not show the same trends. For example, when ECPs are used with hybrid functionals, which sometimes are not recommended for calculations of transition metal systems, they are found to perform better at achieving the basis-set limit than when used with local functionals and meta-GGA functionals. The most successful combination of RECP and basis set has a basis-set incompleteness error of 1.7-2.4 kcal/mol for hybrid generalized gradient approximations, which is smaller than that of nonrelativistic NCBS calculations (whose average basis-set incompleteness error for hybrid functionals is 2.7-2.9 kcal/mol). The average basis-set incompleteness error in Hartree-Fock calculations is 1.0-4.4 kcal/mol for five of the ECP basis sets but is 5.8-10.8 kcal/mol for six others.

Performance of Conventional and Range-Separated Hybrid Density Functionals in Calculations of Electronic Circular Dichroism Spectra of Transition Metal Complexes

A number of density functionals, including 'pure' (nonhybrid) functionals, global hybrids, and range-separated hybrids, were used to calculate the electronic circular dichroism (CD) spectra of 10 tris-bidentate transition metal complexes. The results are compared to one another and to experimental CD spectra, in an effort to illustrate the shortcomings of particular approximations in time-dependent density functional theory (TDDFT). The use of an origin invariant formalism to calculate magnetic transition dipole moments with the help of gauge-including atomic orbitals (GIAOs) is also investigated. With valence basis sets of moderate flexibility, good agreement between GIAO results and rotatory strengths calculated from the dipole-velocity representation is obtained for selected test cases. Empirically broadened vertical CD spectra calculated with the global hybrid functionals B3LYP and PBE0 are found to agree overall the best with experimental CD spectra.

Many-body calculations of molecular electric polarizabilities in asymptotically complete basis sets

The static dipole polarizabilities of Ne, CO, N2, F2, HF, H2O, HCN, and C2H2 (acetylene) have been determined close to the Full-CI limit along with an asymptotically complete basis set (CBS), according to the principles of a Focal Point Analysis. For this purpose the results of Finite Field calculations up to the level of Coupled Cluster theory including Single, Double, Triple, Quadruple and perturbative Pentuple excitations [CCSDTQ(P)] were used, in conjunction with suited extrapolations of energies obtained using augmented and doubly-augmented Dunning's correlation consistent polarized valence basis sets of improving quality. The polarizability characteristics of C2H4 (ethylene) and C2H6 (ethane) have been determined on the same grounds at the CCSDTQ level in the CBS limit. Comparison is made with results obtained using lower levels in electronic correlation, or taking into account the relaxation of the molecular structure due to an adiabatic polarization process. Vibrational corrections to electronic polarizabilities have been empirically estimated according to Born–Oppenheimer Molecular Dynamical simulations employing Density Functional Theory. Confrontation with experiment ultimately indicates relative accuracies of the order of 1 to 2%.

Gaussian basis set of sextuple zeta quality for hydrogen through argon

Segmented all-electron contracted sextuple zeta valence plus polarization function (6ZP) basis sets for the elements from H to Ar were constructed to be used in conjunction with the non-relativistic and Douglas–Kroll–Hess Hamiltonians. The scalar relativistic effect at the coupled cluster level of theory on atomization energy for a sample of molecules was discussed. Additional improvements in the atomization energies were achieved by applying corrections due to core/valence correlation, atomic spin–orbit effects, and addition of tight d and f functions on second-row elements. This leads to estimates for the heat of formation of gaseous boron and carbon tetrafluoride.

Performance of Density Functionals for the Calculation of Gold Clusters

Clusters and nanoparticles of gold have received considerable attention during the past decade. The exceptional catalytic properties of small gold aggregates have motivated research aimed at providing insights into the molecular origins of this unexpected reactivity. The experimental observations have stimulated many theoretical studies of the electronic, structural, and chemical properties of gold clusters. Since it is not practical to calculate gold clusters using high-level ab initio correlation methods, density functional theory (DFT)-based approaches have usually been employed in such calculations, but it is not clear which functionals provide the best performance. Herein we report the results of calculations on the structure and stability of Au2 and Au8, as a model study, using various density functionals. To the best of our knowledge, there has been no previous systematic study for DFT performance on the structure and stability of gold clusters. Although the performance of density functionals is widely known for light element systems, certain functionals successful in light element chemistry may not work effectively in heavy element chemistry. This is due to the strikingly different bonding nature of heavy element systems from their light element analogues. Thus, the results of this work may be useful for future work in choosing the most appropriate density functional for gold clusters when performing DFT calculations. Kohn-Sham DFT calculations were performed with 16 different exchange correlation functionals, namely, the local density approximation (LDA:SVWN), the generalized gradient approximation (GGA:BLYP, BP86, BPW91, PW91, PBE, HCTH, tHCTH, LC-BPW91, LC-PW91 and LCPBE), and the hybrid GGA functionals (B3LYP, B3PW91, mPW1PW91, PBE0 and X3LYP). We used the relativistic effective core potentials derived by Stevens et al. and valence basis sets employed in previous works. All the calculations were carried out using the program package GAUSSIAN 09. Au2 Cluster. We compare the calculated spectroscopic constants, bond length (Re), vibrational frequency (ωe), and dissociation energy (De) with the experimental data 20 in Table 1. Overall, the LDA and several GGA functionals provide good performance for bond length (and vibrational frequency) and dissociation energy, respectively. The use of hybrid GGA functionals, i.e., the inclusion of Hartree-Fock exchange, does not improve the pure GGA results. These observations are in contrast to the known performance of functionals in light element chemistry: in general, LDA < GGA < hybrid GGA. It was reported, for instance, that the performance of the pure BP86 functional is very poor for light element systems, but its performance is observed to be one of the most effective for Au2. It is evident from our calculations that any one functional could not provide reliable spectroscopic constants of Au2. The poor performance of hybrid GGA functionals may be partly ascribed to the functional parameterization optimal to light-element systems only. Intriguingly, the long range correction to the GGA functionals (LC-GGA) improves the performance for bond lengths. Au8 Cluster. There are no experimental data for the structures and energies of Au8. Han 10 reported the relative

Geometries and electronic properties of NbnV(0, ±1) (n = 1−6) clusters studied by density-functional theory

Using density functional theory (DFT) with valence basis set LANL2TZ to study the relative stabilities and electronic properties of the most stable structures of NbnV(0, ±1) (n = 1−6) clusters. The ground state structures of NbnV (0, ±1) keep the similar geometric structure as the host Nbn clusters. The doping of vanadium atom enhances the chemical activities of Nbn clusters. The Nb3V and Nb6V are more stable than other clusters. The average binding energy of charged systems (NbnV+ and NbnV− clusters) are generally larger than neutral NbnV clusters natural population analysis shows that there are charge transfers from niobium to vanadium atoms in the small Nb1−4V, however, for larger clusters (Nb5V and Nb6V), the charge transfers are from vanadium to niobium atoms. The vertical and adiabatic ionization potentials (VIP and AIP) are estimated and the vertical one is more close to experimental results.