Ab initio density functional theory applied to quasidegenerate problems

Ab initio density functional theory (DFT), previously applied primarily at the second-order many-body perturbation theory (MBPT) level, is generalized to selected infinite-order effects by using a new coupled-cluster perturbation theory (CCPT). This is accomplished by redefining the unperturbed Hamiltonian in ab initio DFT to correspond to the CCPT2 orbital dependent functional. These methods are applied to the Be-isoelectronic systems as an example of a quasidegenerate system. The CCPT2 variant shows better convergence to the exact quantum Monte Carlo correlation potential for Be than any prior attempt. When using MBPT2, the semicanonical choice of unperturbed Hamiltonian, plays a critical role in determining the quality of the obtained correlation potentials and obtaining convergence, while the usual Kohn-Sham choice invariably diverges. However, without the additional infinite-order effects, introduced by CCPT2, the final potentials and energies are not sufficiently accurate. The issue of the effects of the single excitations on the divergence in ordinary OEP2 is addressed, and it is shown that, whereas their individual values are small, their infinite-order summation is essential to the good convergence of ab initio DFT.     

Ab initio and density functional theory based studies on collagen triplets

An understanding of the amino acid sequence dependent stability of polypeptides is of renowned interest to biophysicists and biochemists, in order to identify the nature of forces that stabilize the three-dimensional structure of proteins. In this study, the role of various collagen triplets influencing the stability of collagen has been addressed. It is found from this study that proline can stabilize the collagen triplet only when other residues are also in the polyproline II conformation. Solvation studies of various triplets indicate that the presence of polar residues increases the free energy of solvation. Especially the triplets containing arginine residues displays a higher solvation free energy. The chemical hardness of all the triplets in collagen-like conformation has been found to be higher than that in the extended conformation. Studies on Gly–X–Y, Gly–X–Hyp, and Gly–Pro–Y triplets confirm that there will be local variations in the stability of collagen along the entire sequence.     

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 calculations on halogen-bonded complexes and comparison with density functional methods

A systematic theoretical investigation on a series of dimeric complexes formed between some halocarbon molecules and electron donors has been carried out by employing both ab initio and density functional methods. Full geometry optimizations are performed at the Moller-Plesset second-order perturbation (MP2) level of theory with the Dunning's correlation-consistent basis set, aug-cc-pVDZ. Binding energies are extrapolated to the complete basis set (CBS) limit by means of two most commonly used extrapolation methods and the aug-cc-pVXZ (X = D, T, Q) basis sets series. The coupled cluster with single, double, and noniterative triple excitations [CCSD(T)] correction term, determined as a difference between CCSD(T) and MP2 binding energies, is estimated with the aug-cc-pVDZ basis set. In general, the inclusion of higher-order electron correlation effects leads to a repulsive correction with respect to those predicted at the MP2 level. The calculations described herein have shown that the CCSD(T) CBS limits yield binding energies with a range of -0.89 to -4.38 kcal/mol for the halogen-bonded complexes under study. The performance of several density functional theory (DFT) methods has been evaluated comparing the results with those obtained from MP2 and CCSD(T). It is shown that PBEKCIS, B97-1, and MPWLYP functionals provide accuracies close to the computationally very expensive ab initio methods.     

Ab initio benchmark calculations on Ca(II) complexes and assessment of density functional theory methodologies

A set of benchmark results for the geometries, binding energies, and protonation affinities of 24 complexes of small organic ligands with Ca(II) is provided. The chosen level of theory is CCSD(T)/CBS obtained by means of a composite procedure. The performance of four density functionals, namely, PW91, PBE, B3LYP, and TPSS and several Pople-type basis sets, namely, 6-31G(d), 6-31+G(d), 6-31+G(2d,p) and 6-311+G(d) have been assessed. Additionally, the nature of the metal ligand bonding has been analyzed by means of the Symmetry Adapted Perturbation Theory (SAPT). We have found that the B3LYP hybrid functional, in conjunction with either the polarized double-ζ 6-31+G(2d,p) or the triple-ζ 6-311+G(d) basis sets, yields the closest results compared to the benchmark data. The SAPT analysis stresses the importance of induction effects in the binding of these complexes and suggests that consideration of classical electrostatic contributions alone may not be reliable enough for the prediction of relative binding energies for Ca(II) complexes.     

Origin of the zero-field splitting in mononuclear octahedral dihalide MnII complexes: an investigation by multifrequency high-field electron paramagnetic resonance and density functional theory

The synthesis, structural characterization, and electronic properties of a new series of high-spin six-coordinate dihalide mononuclear MnII complexes [Mn(tpa)X2] (tpa=tris-2-picolylamine; X=I (1), Br (2), and Cl (3)) are reported. The analysis of the crystallographic data shows that in all investigated complexes the manganese ion lies in the center of a distorted octahedron with a cis configuration of the halides imposed by the tpa ligand. By a multifrequency high-field electron paramagnetic resonance investigation (95-285 GHz), the electronic properties of 1-3 were determined (DI=-0.600, DBr=-0.360, DCl=+0.115 cm-1), revealing the important effect of (i) the nature of the halide and (ii) the configuration (cis/trans) of the two halides on the magnitude of D. The spin Hamiltonian parameters obtained by density functional theory calculations initiated from the crystal structure of 1-3 are in reasonable agreement with the experimental values. The absolute value of D is consistently overestimated, but the sign and the trend over the chemical series is well reproduced. Theoretical models (cis- and trans-[Mn(NH3)4X2], X=I, Br, Cl and F) have been used to investigate the different contributions to D and also to understand the origin of the experimentally observed changes in D within the series reported here. This study reveals that the spin-spin coupling contributions to the D tensor are non-negligible for the lighter halides (F, Cl) but become insignificant for the heavier halides (I, Br). The four different types of excitations involved in the spin-orbit coupling (SOC) part of the D tensor contribute with comparable magnitudes and opposing signs. The general trend observed for halide MnII complexes (DI>DBr>DCl) can be explained by the fact that the halide SOC dominates the D value in these systems with a major contribution arising from interference between metal- and halide-SOC contributions, which are proportional to the product of the SOC constants of Mn and X.     

Ab initio studies on the zero-field splitting parameters of manganese porphyrin complexes

The magnetic property of a one-dimensional magnetic chain, 5,10,15,20-tetrakis(4-bromophenyl)porphyrinatomanganese(III) tetracyanoethenide ([MnTBrPP]⁺[TCNE]⁻), is investigated by using model complexes and ab initio calculations. In these models, MnTBrPP is reduced to a manganese porphyrin complex (MnP). The spin-polarized density functional theory (UDFT) and the hybrid UDFT were used to calculate the complexes, and Pederson’s scheme was used to calculate their zero-field splitting (ZFS) parameters. We found from the model calculations that the TCNE coordination hardly affects the magnetic anisotropy of MnP.     

Ab initio density functional theory investigation of Li-intercalated zinc oxide nanotube bundles

We have investigated the energetic, and geometric and electronic structure of Li-intercalated (5,5) zinc oxide nanotube (ZnONT) bundles via density functional theory as implemented in the code WIEN2k. Our results showed that the most prominent effect of Li intercalation on the electronic band structure is a shift of the Fermi energy which occurs as a result of charge transfer from lithium to the ZnONTs. All the Li-intercalated (5,5) ZnONT bundles are predicted to be metallic representing a substantial change in electronic properties relative to the undoped bundle, which is a wide band gap semiconductor. Both inside of the nanotube and the interstitial spaces are susceptible for intercalation. The present calculations suggest that the single-walled zinc oxide nanotube (SwZnONT) bundle is a promising candidate for the anode material in battery applications.     

Ab initio study of intriguing coordination complexes: a metal field theory picture

Two noninnocent ligands are theoretically studied using wave function based methods to demonstrate their ability to undergo singlet-triplet transition under the effect of an external charge mimicking the electrostatic role of a metal ion. It is shown that the singlet-triplet energy difference is very sensitive to the metal ion charge which tunes the HOMO-LUMO energy difference of these ligands. While the latter is reduced as the charge is enhanced in the glyoxal-bis-(2-mercaptoanil) (gma) ligand, it is increased in the bis(imino)pyridine diradical ligand. This result shows a strong analogy with the crystal field theory, interchanging the roles played by the metal ion and the ligand. As the metal ion is explicitly treated in the Fe(gma)CN complex, this analogy can be pushed further resulting in a "metal field theory" conceptualization.     

Chirality and spin density: Ab initio and density functional approaches

The spin distribution in a stable nitroxide biradical that shows ferromagnetic interactions in the solid phase has been studied at three levels of theory: First, at the UHF level; then, including correlation effects in UMP 2 calculations; and finally, the results are compared with the spin density obtained using the local density functional (LDF ) approximation. It is shown that LDF spin densities are closer to UMP 2 than to UHF predictions; the difference between the UHF and the (UMP 2, LDF ) results points to a redistribution of the spin repartition between N and O due to electronic correlation. For planar conformations of the NO group, there is symmetric distribution (D_2d) of the spin density on the adamantane skeleton. For nonplanar nitroxides, the molecule is chiral (C₂), which results in a breakdown of the spin transmission on part of the adamantane cage. © 1993 John Wiley & Sons, Inc.     

Ab initio and density functional theory evidence on the rate-limiting step in the Morita-Baylis-Hillman reaction

The first ab initio and DFT studies on the mechanism of the MBH reaction show that the rate-limiting step involves an intramolecular proton transfer in the zwitterionic intermediate generated by the addition of enolate to electrophile. The activation barrier for the C-C bond-formation is found to be 20.2 kcal/mol lower than the proton-transfer step for the MBH reaction between methyl vinyl ketone and benzaldehyde catalyzed by DABCO.     

Relativistic molecular orbital theory of zero-field splittings in triplets

A method of calculating matrix elements of 1/r₁₂ in a basis of Dirac scattered-wave (DSW) orbitals is outlined. In the limit c → ∞, this method reduces to that described by Cook and Karplus for non-relativistic orbitals. For triplet states that can be described by a single configuration with two unpaired electrons, the relativistic exchange integrals give not only the singlet—triplet splittings (as in non-relativistic theory), but also the spin—orbit contributions to the triplet zero-field splittings. Results are reported for the ³ (n → π*) excited state of γ-thiopyrone (4H-pyran-4-thione), which has a very large value of D (calc. ?31 cm^?1, exp. ?24 to ?28 cm^?1).     

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.     

Ab initio and density functional theory calculations of molecular structure and vibrational spectrum of ethyl azidoacetate

Here we report ab initio and density functional results for molecular properties of ethyl azidoacetate (N₃CH₂COOC₂H₅) and for the corresponding singly ionized structure (N₃CH₂COOC₂H₅⁺). Ab initio ionization energies based on Koopmans’ theorem are in excellent agreement with the experimental data from ultraviolet photoelectron spectroscopy. DFT adiabatic energy differences between neutral and ionized structures are very sensitive to electronic correlation effects and are not in very good agreement with experiment. The results for the structure and vibrational frequencies are compared with the experimental data of related molecular structures.     

Ab initio and density functional theory reinvestigation of gas-phase sulfuric acid monohydrate and ammonium hydrogen sulfate

We have calculated the thermochemical parameters for the reactions H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O and H(2)SO(4) + NH(3) <--> H(2)SO(4).NH(3) using the B3LYP and PW91 functionals, MP2 perturbation theory and four different basis sets. Different methods and basis sets yield very different results with respect to, for example, the reaction free energies. A large part, but not all, of these differences are caused by basis set superposition error (BSSE), which is on the order of 1-3 kcal mol(-1) for most method/basis set combinations used in previous studies. Complete basis set extrapolation (CBS) calculations using the cc-pV(X+d)Z and aug-cc-pV(X+d)Z basis sets (with X = D, T, Q) at the B3LYP level indicate that if BSSE errors of less than 0.2 kcal mol(-1) are desired in uncorrected calculations, basis sets of at least aug-cc-pV(T+d)Z quality should be used. The use of additional augmented basis functions is also shown to be important, as the BSSE error is significant for the nonaugmented basis sets even at the quadruple-zeta level. The effect of anharmonic corrections to the zero-point energies and thermal contributions to the free energy are shown to be around 0.4 kcal mol(-1) for the H(2)SO(4).H(2)O cluster at 298 K. Single-point CCSD(T) calculations for the H(2)SO(4).H(2)O cluster also indicate that B3LYP and MP2 calculations reproduce the CCSD(T) energies well, whereas the PW91 results are significantly overbinding. However, basis-set limit extrapolations at the CCSD(T) level indicate that the B3LYP binding energies are too low by ca. 1-2 kcal/mol. This probably explains the difference of about 2 kcal mol(-1) for the free energy of the H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O reaction between the counterpoise-corrected B3LYP calculations with large basis sets and the diffusion-based experimental values of S. M. Ball, D. R. Hanson, F. L Eisele and P. H. McMurry (J. Phys. Chem. A. 2000, 104, 1715). Topological analysis of the electronic charge density based on the quantum theory of atoms in molecules (QTAIM) shows that different method/basis set combinations lead to qualitatively different bonding patterns for the H(2)SO(4).NH(3) cluster. Using QTAIM analysis, we have also defined a proton transfer degree parameter which may be useful in further studies.     

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%).     

Ab initio and density functional theory studies of the catalytic mechanism for ester hydrolysis in serine hydrolases

We present results from ab initio and density functional theory studies of the mechanism for serine hydrolase catalyzed ester hydrolysis. A model system containing both the catalytic triad and the oxyanion hole was studied. The catalytic triad was represented by formate anion, imidazole, and methanol. The oxyanion hole was represented by two water molecules. Methyl formate was used as the substrate. In the acylation step, our computations show that the cooperation of the Asp group and oxyanion hydrogen bonds is capable of lowering the activation barrier by about 15 kcal/mol. The transition state leading to the first tetrahedral intermediate in the acylation step is rate limiting with an activation barrier (ΔE₀) of 13.4 kcal/mol. The activation barrier in the deacylation step is smaller. The double-proton-transfer mechanism is energetically unfavorable by about 2 kcal/mol. The bonds between the Asp group and the His group, and the hydrogen bonds in the oxyanion hole, increase in strength going from the Michaelis complex toward the transition state and the tetrahedral intermediate. In the acylation step, the tetrahedral intermediate is a very shallow minimum on the energy surface and is not viable when molecular vibrations are included. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 89–103, 1998     

Ab initio studies of a water layer at transition metal surfaces

This paper presents a detailed study of a water adlayer adsorbed on Pt(111) and Rh(111) surfaces using periodic density functional theory methods. The interaction between the metal surface and the water molecules is assessed from molecular dynamics simulation data and single point electronic structure calculations of selected configurations. It is argued that the electron bands around the Fermi level of the metal substrate extend over the water adlayer. As a consequence in the presence of the water layer the surface as a whole still maintains its metallic conductivity-a result of a crucial importance for understanding the process of electron transfer through the water/metal interface and electrochemical reactions in particular. Our results also indicate that there exists a weak bond between the hydrogen of the water and the Rh metal atoms as opposed to the widespread (classical) models based on purely repulsive interaction. This suggests that the commonly used classical interactions potentials adopted for large scale molecular dynamics simulations of water/metal interfaces may need revision. Two adsorption models of water on transition metals with the OH bonds pointing towards or away of the surface are also examined. It is shown that due to the very close values of their adsorption energies one should consider the real structure of water on the surface as a mixture of these simple "up" and "down" models. A model for the structure of the adsorbed water layer on Rh(111) is proposed in terms of statistical averages from molecular dynamics simulations.