Vibrational corrections to geometries of transition metal complexes from density functional theory

Zero-point vibrational corrections are computed at the BP86/AE1 level for the set of 50 transition-metal/ligand bonds that have recently been proposed as testing ground for DFT methods, because of the availability of precise experimental gas-phase geometries (Bühl and Kabrede, J Chem Theory Comput 2006, 2, 1282). These corrections are indicated to be transferable to a large extent between various density-functional/basis-set combinations, so that they can be used to estimate zero-point averaged r0g distances from re values optimized at other theoretical levels. Applying this approach to a number of popular DFT levels does not, in general, improve their overall accuracy in terms of mean and standard deviations from experiment. The hybrid variant of the meta-functional TPSS is confirmed as promising choice for computing structures of transition-metal complexes.     

Ab initio and coupled-perturbed density functional theory estimation of zero-field splittings in MnII transition metal complexes

The paper presents a method comparison for the prediction of zero-field splitting (ZFS) parameters in a series of Mn (II) coordination complexes. The test set consists of Mn (II) complexes that are experimentally well-characterized by X-ray diffraction and high-field electron paramagnetic resonance. Their ZFS parameters have been calculated using density functional theory (DFT) as well as complete active space self-consistent field (CASSCF) methods. It is shown that the recently introduced coupled-perturbed spin-orbit coupling (CP-SOC) approach [ Neese, F. J. Chem. Phys. 2007, 127, 164112 ] together with hybrid-DFT functionals leads to a slope of the correlation line (plot of experimental vs calculated D values) that is essentially unity provided that the direct spin-spin interaction is properly included in the treatment. This is different from our previous DFT study on the same series of complexes where a severe overestimation of the D parameter has been found [ Zein, S. ; Duboc, C. ; Lubitz, W. ; Neese, F. Inorg. Chem. 2008, 47, 134 ]. CASSCF methods have been used to evaluate the ZFS in an "ab initio ligand-field" type treatment. The study demonstrates that a substantial part of the relevant physics is lost in such a treatment since only excitations within the manganese d-manifold are accounted for. Thus, a severe underestimation of the D parameter has been found. Because the CASSCF calculations in combination with quasidegenerate perturbation theory treats the SOC to all orders, we have nevertheless verified that second-order perturbation theory is an adequate approximation in the case of the high-spin d (5) configuration.     

Zeolite-Y entrapped bivalent transition metal complexes as hybrid nanocatalysts: density functional theory investigation and catalytic aspects

The intriguing research toward the exploitation of zeolite-Y-based hybrid nanocatalysts for catalytic oxidation reactions has been growing significantly. In the present investigation, we describe the synthesis of zeolite-Y entrapped transition metal complexes of the general formulae [M(SFCH)·xH₂O]-Y (where, M = Mn, Fe, Co, Ni (x = 3) and Cu (x = 1)); H₂SFCH = (E)-N′-(2-hydroxybenzylidene)furan-2-carbohydrazide]. These nanocatalysts have been characterized by various physicochemical techniques. Density functional theory calculations are performed to address the relaxed geometry, bond angle, bond length, dihedral angle, highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) energy gap, and electronic density of states of H₂SFCH ligand and their neat transition metal complexes. The observed HOMO–LUMO gap and the Fermi energy is higher for Cu(II) complexes, which demonstrates the better catalytic activity of this nanocatalyst. The catalytic activity was performed in liquid-phase oxidation of cyclohexane using hydrogen peroxide as oxidant to give cyclohexanone (CyONE) and cyclohexanol (CyOL). Among them, [Cu(SFCH)·H₂O]-Y catalyst has the highest selectivity toward CyONE (84.5%).     

Time-dependent density functional theory applied to ligand-field excitations and their circular dichroism in some transition metal complexes

Ligand-field transitions in [Co(en)₃]³⁺ and [Rh(en)₃]³⁺ as well as the low-energy part of the electronic spectrum of [Fe(phen)₃]²⁺ are investigated with time-dependent density functional theory (TDDFT). There is a strong functional dependence for [Co(en)₃]³⁺ and [Fe(phen)₃]²⁺. ΔSCF methods reproduce the ligand-field singlet excitation energies of [Co(en)₃]³⁺ and [Rh(en)₃]³⁺ very well. The case of [Co(en)₃]³⁺ is analyzed in some detail, in particular regarding the possibility of applying a charge-transfer (CT) correction [M.E. Casida, F. Gutierrez, J. Guan, F.-X. Gadea, D.R. Salahub, J.-P. Daudey, J. Chem. Phys. 113 (2000) 7062]. A simple CT correction would not be sufficient, but the magnitude of the charge transfer correction term in comparison with the calculated excitation energy appears to be indicative of self-interaction problems in the ground state electronic structure and in the calculated excitation energies. For the ligand-field transition of [Co(en)₃]³⁺ a hybrid functional with about 25% exact exchange performs well. Range separation/long range correction/Coulomb attenuation offers little improvement for the ligand-field transitions in [Co(en)₃]³⁺ because the occupied and unoccupied orbitals involved are in close spatial proximity.     

Understanding excited-state structure in metal polypyridyl complexes using resonance Raman excitation profiles,time-resolved resonance Raman spectroscopy and density functional theory

This article discusses the use of Raman spectroscopy, in concert with density functional theory, as a strategy for understanding excited-state structure in metal polypyridyl complexes. The first sections of the article discuss how one can use resonance Raman spectra of the ground-state molecule to understand the resonant Franck-Condon excited state. The theories behind these analyses are based on the sum-over-states and time-dependent approaches; a brief introduction to each of these methods is given. The use of density functional theory and its use in the determination of normal modes of vibration and infrared and Raman band intensities are discussed, with reference to a number of recent papers. The application of these methods is illustrated through the analysis of a number of selected examples which exemplify the strategies used to extract data from probing the Franck-Condon region. These data include the displacements of the resonant excited state with respect to the electronic ground state, the reorganisation energies associated with photoexcitation, bond length changes with excitation and other electronic parameters. The use, and limitations, of these methods are discussed. The direct calculation of resonance Raman band intensities is introduced. The direct measurement of excited-state vibrational spectra through time-resolved methods is discussed in the latter section of the article; with particular regard to the use of transient resonance Raman and time-resolved resonance Raman techniques to probe structural changes in metal polypyridyl complexes.     

Molecular-orbital-free algorithm for the excited-state force in time-dependent density functional theory

Starting from the equation of motion in the density matrix formulation, we reformulate the analytical gradient of the excited-state energy at the time-dependent density functional theory level in the nonorthogonal Gaussian atom-centered orbital (AO) basis. Analogous to the analytical first derivative in molecular-orbital (MO) basis, a Z-vector equation has been derived with respect to the reduced one-electronic density matrix in AO basis, which provides a potential possibility to exploit quantum locality of the density matrix and avoids the matrix transformation between the AO and the MO basis. Numerical tests are finished for the excited-state geometry optimization and adiabatic excitation energy calculation of a series of small molecules. The results demonstrate the computational efficiency and accuracy of the current AO-based energy gradient expression in comparison with the MO-based scheme.     

Electronic structures of 4d transition metal monoxides by density functional theory

Bond distances, dissociation energies, ionization potentials and electron affinities of 4d transition metal monoxides from YO to CdO and their positive and negative ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, SVWN, MPW1PW91 and PBE1PBE. It was found that calculated properties are highly dependent on the functionals employed, especially for dissociation energy. For most neutral species, pure density functionals BLYP, BPW91 and BP86 have good performance in predicting dissociation energy than hybrid density functionals B3LYP, B3PW91 and B3P86. In addition, BLYP gives the largest bond distance compared with other density functional methods, while SVWN gives shortest bond distance, largest dissociation energy and electron affinity. For the ground state, the spin multiplicity of the charged species can be obtained by ± 1 of their corresponding neutral species.     

Matrix infrared spectra and density functional calculations of transition metal hydrides and dihydrogen complexes

Metal hydrides are of considerable importance in chemical synthesis as intermediates in catalytic hydrogenation reactions. Transition metal atoms react with dihydrogen to produce metal dihydrides or dihydrogen complexes and these may be trapped in solid matrix samples for infrared spectroscopic study. The MH(2) or M(H(2)) molecules so formed react further to form higher MH(4), (H(2))MH(2), or M(H(2))(2), and MH(6), (H(2))(2)MH(2), or M(H(2))(3) hydrides or complexes depending on the metal. In this critical review these transition metal and dihydrogen reaction products are surveyed for Groups 3 though 12 and the contrasting behaviour in Groups 6 and 10 is discussed. Minimum energy structures and vibrational frequencies predicted by Density Functional Theory agree with the experimental results, strongly supporting the identification of novel binary transition metal hydride species, which the matrix-isolation method is well-suited to investigate. 104 references are cited.     

C-N coupling on transition metal surfaces: a density functional theory study

We have investigated the formation of C-N bonds from individual atoms and single hydrogenated moieties on a series of transition metals. These reactions play a role in HCN formation at high oxygen coverage, also known as Andrussow oxidation, and they are fundamental to understand the ability of other materials to form part of alloys where Pt is the major component. Dehydrogenations take place quite easily under these high oxygen conditions and thus, the C+N, HC+N, and N+CH recombinations to form HCN or its isomer CNH might represent the rate-limiting steps for the reaction. For all the metals in the present study we have found that the activation energy for the reactions between H(x)C and NH(y) (x,y = 0,1) involved in C-N formation follow a linear relationship with the adsorption energy of the N atom. This is due to the common nature of all these transition states, where N-containing fragments get activated from three-fold hollow sites to bridge positions. The slopes of the linear dependence, though, depend on the valence of the N fragment, i.e., smaller slopes are found for NH moieties with respect to N ones.     

Stannaborate transition metal chemistry: ligand properties, reactivity, and density functional theory calculations of platinum and palladium complexes

Three stannaborate complexes of platinum(II) and a novel stannoborate palladium(II) derivative have been prepared in excellent yield. The tin transition metal bond is formed through nucleophilic substitution and the resulting complexes [Bu3MeN] [trans-[(Et3P)2Pt(SnB11H11)H]] (6), [trans-[(Et3P)2Pt(SnB11H11)(CNtBu)]] (7), [Bu3MeN]2[trans-[(Et3P)2Pt(SnB11H11)2-(CNtBu)]] (8), and [Bu3MeN][(dppe)-Pd(SnB11H11)Me] (12) (dppe = 1,2-bis-(diphenylphosphanyl)ethane) were characterized by NMR spectroscopy and elemental analysis. In the cases of the zwitterion 7, the pentacoordinated complex 9, the palladium salt 12 and [(triphos)Pt(SnB11H11)] (10) (triphos = 1,1,1-tris(diphenylphosphanylmethyl)ethane), their solid-state structures are determined by X-ray crystal structure analyses. The trans influence of the [SnB11H11] ligand is evaluated from the results of the IR spectroscopy and X-ray crystallographic structures of complexes 6, 7, and 12. The dipole moment of the zwitterion 7 is calculated by density functional theory (DFT) methods. The alignment of the dipole moments of the polar molecules 7 and 12 in the solid state is discussed.     

Simultaneous benchmarking of ground- and excited-state properties with long-range-corrected density functional theory

We present benchmark calculations using several long-range-corrected (LRC) density functionals, in which Hartree-Fock exchange is incorporated asymptotically using a range-separated Coulomb operator, while local exchange is attenuated using an ansatz introduced by Iikura et al. [J. Chem. Phys. 115, 3540 (2001)]. We calculate ground-state atomization energies, reaction barriers, ionization energies, and electron affinities, each as a function of the range-separation parameter mu. In addition, we calculate excitation energies of small- and medium-sized molecules, again as a function of mu, by applying the LRC to time-dependent density functional theory. Representative examples of both pure and hybrid density functionals are tested. On the basis of these results, there does not appear to be a single range-separation parameter that is reasonable for both ground-state properties and vertical excitation energies. Reasonable errors in atomization energies and barrier heights are achieved only at the expense of excessively high excitation energies, at least for the medium-sized molecules, whereas values of mu that afford reasonable excitation energies yield some of the largest errors for ground-state atomization energies and barrier heights in small molecules. Notably, this conclusion is obscured if the database of excitation energies includes only small molecules, as has been the case in previous benchmark studies of LRC functionals.     

2+3] Cycloaddition of ethylene to transition metal oxo compounds. analysis of density functional results by marcus theory.

Density functional results on the [2+3] cycloaddition of ethylene to various transition metal complexes MO(3)(q) and LMO(3)(q) (q = -1, 0, 1) with M = Mo, W, Mn, Tc, Re, and Os and various ligands L = Cp, CH(3), Cl, and O show that the corresponding activation barriers DeltaE(double dagger) depend in quadratic fashion on the reaction energies DeltaE(0) as predicted by Marcus theory. A thermoneutral reaction is characterized by the intrinsic reaction barrier DeltaE(0) of 25.1 kcal/mol. Both ethylene [2+3] cycloaddition to an oxo complex and the corresponding homolytic M-O bond dissociation are controlled by the reducibility of the transition metal center. Indeed, from the easily calculated M-O bond dissociation energy of the oxo complex one can predict the reaction energy DeltaE(0) and hence, by Marcus theory, the corresponding activation barrier DeltaE. This allows a systematic representation of more than 25 barriers of [2+3] cycloaddition reactions that range from 5 to 70 kcal/mol.     

Determination of absolute configuration of chiral hemicage metal complexes using time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is applied to the UV-vis absorption and circular dichroism (CD) spectra of a series of transition metals (M=Ru, Zn, Fe) complexed with an enantiopure hemicage ligand, (-)-(5R,5'R,5' 'R,7R,7'R,7' 'R,8S,8'S,8' 'S)-8,8',8' '-[(2,4,6-trimethyl-1,3,5-benzenetriyl)tris(methylene)]tris[5,6,7,8-tetrahydro-6,6-dimethyl-3-(2-pyridinyl)-5,7-methanoisoquinoline (1). The electronic spectra of the Ru and Fe complexes contain two regions, one featuring low-energy 1MLCT transitions and the other higher energy 1LC transitions; the Zn analog possesses only the 1LC transitions due to its filled 3d shell. TD-DFT is able to identify correctly these transitions in the spectra, as well as to reproduce experimental spectra accurately, with regard to both the transition energies and the relative intensities of the different transitions. Additionally, it is possible to use TD-DFT to assign the absolute configuration at the metal center with high confidence by matching the experimental and calculated spectra.     

Semi-empirical LCAO-Xα theory for transition metal complexes. I. An outline of the theory

A semi-empirical theory for transition metal complexes is presented. Unusual aspects of the theory are (1) employment of Xα theory, (2) adoption of theoretical exchange parameter, (3) exclusion of (n + 1)s and (n + 1)p atomic orbitals of a nd-transition metal, and (4) variation of atomic orbitals in LCAO method. Also, an improved Mulliken approximation is proposed and used to simplify the LCAO-Xα equations.     

Some applications of local density functional theory to the calculation of reaction energetics

Summary We report the results of a local density functional investigation of the energetics of some isomerization reactions, involving the conversions of several unsaturated systems to highly strained molecules related to triprismane and tetrahedrane. The program DMol was used at the DNP level to compute the activation barriers and total energy changes associated with these processes. We also show, for more than 70 first- and second-row atoms and molecules, that the errors (non-local corrections) in their energies correlate very well with the number of electrons, within isonuclear series. This should provide a useful empirical means for improving dissociation energies obtained within the local approximation.     

Benchmarking approximate density functional theory. I. s/d excitation energies in 3d transition metal cations

The performance of a number of different implementations of density functional theory (DFT) for predicting the s/d interconfigurational energies of the 3d transition metal cations is investigated. Systematic comparisons of computed results with experimental data indicate that gradient corrected correlation functionals, like the LYP GGA, efficiently correct the flaws of the LDA, but reveal shortcomings in the treatment of exchange by currently available GGAs. The admixture of exact exchange in hybrid functionals eventually leads to largely reduced errors. Several basis sets available for the 3d elements are tested in combination with the B3LYP functional. Finally, the influence of variations of the admixture of exact exchange is systematically tested. The results reveal that computed s/d excitation energies obtained for the individual ions depend in markedly different ways on the amount of exact exchange admixture and that there is no single optimal and transferable exchange parameter to create a hybrid functional that yields improved results for all ions alike. Several of the recently devised functionals perform as good as or slightly better than the B3LYP functional in the present study. But given the fact that the B3LYP functional has been identified as the most successful DFT method in an overwhelming number of systematic investigations in very many areas of chemical research, there is no persuasive motivation to recommend its replacement by one of the other functionals, as much less is known about their robustness.     

CASPT2 investigation of ethane dissociation and methyl recombination using canonical variational transition state theory

Ethane dissociation and the reverse recombination reactions were investigated based on CASPT2 and CASSCF calculations. The CASPT2 (partial) geometry optimization calculations and the CASSCF frequency calculations provided geometrical parameters, potential energies, and vibrational frequencies along the reaction pathway. For determining dissociation and recombination rate constants at a temperature range from 200 to 2000 K, two models (models 1 and 2) were used on the basis of the canonical variational transition state theory. The different methods for accounting for the five transitional modes were proposed in the two models. Dissociation activation parameters evaluated using the two models are in good agreement with the data available in the literature. Model 1 predicts reasonable rate constant values for methyl recombination at high temperature, and model 2 predicts reasonable values in both high‐ and low‐temperature ranges. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 161–173, 2008