Calculation of the zero-field splitting tensor on the basis of hybrid density functional and Hartree-Fock theory

The zero-field splitting (ZFS) (expressed in terms of the D tensor) is the leading spin-Hamiltonian parameter for systems with a ground state spin S>12. To first order in perturbation theory, the ZFS arises from the direct spin-spin dipole-dipole interaction. To second order, contributions arise from spin-orbit coupling (SOC). The latter contributions are difficult to treat since the SOC mixes states of different multiplicities. This is an aspect of dominant importance for the correct prediction of the D tensor. In this work, the theory of the D tensor is discussed from the point of view of analytic derivative theory. Starting from a general earlier perturbation treatment [F. Neese and E. I. Soloman, Inorg. Chem. 37, 6568 (1998)], straightforward response equations are derived that are readily transferred to the self-consistent field (SCF) Hartree-Fock (HF) or density functional theory (DFT) framework. The main additional effort in such calculations arises from the solution of nine sets of nonstandard coupled-perturbed SCF equations. These equations have been implemented together with the spin-orbit mean-field representation of the SOC operator and a mean-field treatment of the direct spin-spin interaction into the ORCA electronic structure program. A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values. The slope of the correlation line is essentially unity for the B3LYP and BLYP functionals compared to approximately 0.5 in previous treatments.     

An ab initio and density functional theory study of radical-clock reactions

Density functional theory (DFT) and ab initio (CBS-RAD) calculations have been used to investigate a series of "radical clock" reactions. The calculated activation energies suggest that the barriers for these radical rearrangements are determined almost exclusively by the enthalpy effect with no evidence of significant polar effects. The ring-closure reactions to cyclopentylmethyl radical derivatives and the ring opening of cyclopropylmethyl radicals give different correlations between the calculated heat of reaction and barrier, but the two types of reaction are internally consistent.     

A systematic density functional study of the zero-field splitting in Mn(II) coordination compounds

This work presents a detailed evaluation of the performance of density functional theory (DFT) for the prediction of zero-field splittings (ZFSs) in Mn(II) coordination complexes. Eighteen experimentally well characterized four-, five-, and six-coordinate complexes of the general formula [Mn(L)nL'2] with L' = Cl, Br, I, NCS, or N3 (L = an oligodentate ligand) are considered. Several DFT-based approaches for the prediction of the ZFSs are compared. For the estimation of the spin-orbit coupling (SOC) part of the ZFS, it was found that the Pederson-Khanna (PK) approach is more successful than the previously proposed quasi-restricted orbitals (QRO)-based method. In either case, accounting for the spin-spin (SS) interaction either with or without the inclusion of the spin-polarization effects improves the results. This argues for the physical necessity of accounting for this important contribution to the ZFS. On average, the SS contribution represents approximately 30% of the axial D parameters. In addition to the SS part, the SOC contributions of d-d spin flip (alphabeta) and ligand-to-metal charge transfer excited states (betabeta) were found to dominate the SOC part of the D parameter; the observed near cancellation between the alphaalpha and betaalpha parts is discussed in the framework of the PK model. The calculations systematically (correlation coefficient approximately 0.99) overestimate the experimental D values by approximately 60%. Comparison of the signs of calculated and measured D values shows that the signs of the calculated axial ZFS parameters are unreliable once E/D > 0.2. Finally, we find that the calculated D and E/D values are highly sensitive to small structural changes. It is observed that the use of theoretically optimized geometries leads to a significant deterioration of the theoretical predictions relative to the experimental geometries derived from X-ray diffraction. The standard deviation of the theoretical predictions for the D values almost doubles from approximately 0.1 to approximately 0.2 cm-1 upon using quantum chemically optimized structures. We do not find any noticeable improvement in considering basis sets larger than standard double- (SVP) or triple-zeta (TZVP) basis sets or using functionals other than the BP functional.     

Differences between ab initio and density functional electron densities

We analyzed the energy contributions and the spatial distribution differences of several electron densities of atoms and small molecules. The results show the insensitivity of local spin density correlation functionals in respect to differences in the electron densities. On the other hand, significant changes in one-electron and two-electron energy contributions are observed, although both compensate each other. The projection of the differences between these electron densities, referred to as the Hartree-Fock density, shows a qualitative resemblance between multideterminantal and Kohn-Sham wavefunctions. Finally, a comparative analysis of the optimized conformational parameters obtained using several methods shows that the inclusion of the correlation energy in SCF or in post-SCF procedures gives similar results and that the exchange potential is more important than is the correlation potential to improve these conformational parameters. © 1997 John Wiley & Sons, Inc.     

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.     

The exchange-correlation potential in ab initio density functional theory

From coupled-cluster theory and many-body perturbation theory we derive the local exchange-correlation potential of density functional theory in an orbital dependent form. We show the relationship between the coupled-cluster approach and density functional theory, and connections and comparisons with our previous second-order correlation potential [OEP-MBPT(2) (OEP-optimized effective potential)] [I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett, J. Chem. Phys. 116, 4415 (2002)]. Starting from a general theoretical framework based on the density condition in Kohn-Sham theory, we define a rigorous exchange-correlation functional, potential and orbitals. Specifying initially to second-order terms, we show that our ab initio correlation potential provides the correct shape compared to those from reference quantum Monte Carlo calculations, and we demonstrate the superiority of using Fock matrix elements or more general infinite-order semicanonical transformations. This enables us to introduce a method that is guaranteed to converge to the right answer in the correlation and basis set limit, just as does ab initio wave function theory. We also demonstrate that the energies obtained from this generalized second-order method [OEP-MBPT2-f] and [OEP-MBPT2-sc] are often of coupled-cluster accuracy and substantially better than ordinary Hartree-Fock based second-order MBPT=MP2.     

Dimers, trimers and oligomers of sulfur oxides: an ab initio and density functional study

Ab initio (HF/3-21G^*), DFT (B3LYP with basis sets 6-31G^*, 6-311+G^* and 6-311+G(2d)) and, in some cases, MP2/6-31G^* calculations, were done on cyclic dimers, trimers, etc. and on acyclic oligomers (with OH and H on the ends) of sulfur monoxide and sulfur dioxide. The four cyclic (SO)_n molecules were (S–O)₂ (1,3,2,4-dioxadithietane, 1a), (S–O)₃ (1,3,5,2,4,6-trioxatrithiane, 2a), (S(=O))₄ (tetrathietane 1,2,3,4-tetraoxide, 1b), and (S(=O))₆ (hexathiane 1,2,3,4,5,6-hexaoxide, 2b). The four cyclic (SO₂)_n molecules were the dioxide of 1a (1,3,2,4-dioxadithietane 2,4-dioxide, 1c), the trioxide of 2a (1,3,5,2,4,6-trioxatrithiane 2,4,6-trioxide, 2c), the tetraoxide of 1b (tetrathietane 1,1,2,2,3,3,4,4-octaoxide, 1d) and the hexaoxide of 2b (hexathiane 1,1,2,2,3,3,4,4,5,5,6,6-dodecaoxide, 2d). The 16 acyclic molecules (oxides of disulfane, trisulfane, etc. and oxides of oxadisulfane, dioxatrisulfane, etc.) were (–S–O–)_n, (–S(=O)–)_n, (–S(=O)O–)_n, and (–S(=O)₂–)_n, with n from 2 to 5 and HO, H at the ends. Most of these species are relative minima on the B3LYP/6-31G^* potential energy surface. In energy content, the SO dimer, etc. lie below, and the SO₂ dimer, etc. above, their SO_x components, at all the electron-correlated levels.     

Ab initio and DFT studies of the spin-orbit and spin-spin contributions to the zero-field splitting tensors of triplet nitrenes with aryl scaffolds

Spin-orbit and spin-spin contributions to the zero-field splitting (ZFS) tensors (D tensors) of spin-triplet phenyl-, naphthyl-, and anthryl-nitrenes in their ground state are investigated by quantum chemical calculations, focusing on the effects of the ring size and substituted position of nitrene on the D tensor. A hybrid CASSCF/MRMP2 approach to the spin-orbit term of the D tensor (D(SO) tensor), which was recently proposed by us, has shown that the spin-orbit contribution to the entire D value, termed the ZFS parameter or fine-structure constant, is about 10% in all the arylnitrenes under study and less depends on the size and connectivity of the aryl groups. Order of the absolute values for D(SO) can be explained by the perturbation on the energy level and spatial distributions of π-SOMO through the orbital interaction between SOMO of the nitrene moiety and frontier orbitals of the aryl scaffolds. Spin-spin contribution to the D tensor (D(SS) tensor) has been calculated in terms of the McWeeny-Mizuno equation with the DFT/EPR-II spin densities. The D(SS) value calculated with the RO-B3LYP spin density agrees well with the D(Exptl) -D(SO) reference value in phenylnitrene, but agreement with the reference value gradually becomes worse as the D value decreases. Exchange-correlation functional dependence on the D(SS) tensor has been explored with standard 23 exchange-correlation functionals in both RO- and U-DFT methodologies, and the RO-HCTH/407 method gives the best agreement with the D(Exptl) -D(SO) reference value. Significant exchange-correlation functional dependence is observed in spin-delocalized systems such as 9-anthrylnitrene (6). By employing the hybrid CASSCF/MRMP2 approach and the McWeeny-Mizuno equation combined with the RO-HCTH/407/EPR-II//U-HCTH/407/6-31G* spin densities for D(SO) and D(SS), respectively, a quantitative agreement with the experiment is achieved with errors less than 10% in all the arylnitrenes under study. Guidelines to the putative approaches to D(SS) tensor calculations are given.     

Combined ab initio and density functional study of ring chain tautomerism in benzofurazan-1-oxide

The ring chain tautomerism of benzofurazan-1-oxide (benzofuroxan) has been reinvestigated using ab initio as well as nonlocal density functional theory. The failure in predicting energies and geometries of this reaction by wave functions at the Hartree-Fock or even at the MP2 level could be overcome by using the nonlocal three-parameter hybrid exchange correlation functional of Becke and Lee, Young, and Parr (B3-LYP). Two possible reaction paths via ortho-dinitrosobenzene have been studied, considering both ground and transition states. At the B3-LYP level of theory, both mechanisms show very similar activation energies which are in excellent agreement with experimental results. Solvent effects, simulated by a self-consistent reaction field (SCRF) model, cause alternations in the preferred mechanism as well as in the most stable intermediates. © 1996 by John Wiley & Sons, Inc.     

An ab initio and density functional theory study of the structure and bonding of sulfur ylides

Sulfur ylides are useful synthetic intermediates that are formed from the interaction between singlet carbenes and sulfur-containing molecules. Partial double-bond character frequently has been proposed as a key contributor to the stability of sulfur ylides. Calculations at the B3LYP, MP2, and CCSD(T) levels of theory employing various basis sets have been performed on the sulfur ylides H(2)S-CH(2) and (CH(3))(2)S-CH(2) in order to investigate the structure and bonding of these systems. The following general properties of sulfur ylides were observed from the computational studies: C-S bond distances that are close in length to that of a typical C-S double bond, high charge transfer from the sulfide to the carbene, and large torsional rotation barriers. Analysis of the sulfur ylide charge distribution indicates that the unusually short C-S bond distance can be attributed in part to the electrostatic attraction between highly oppositely charged carbon and sulfur atoms. Furthermore, n --> sigma* stabilization arising from donation of electron density from the carbon lone pair orbital into S-H or S-C antibonding orbitals leads to larger than expected torsional barriers. Finally, natural resonance theory analysis indicates that the bond order of the sulfur ylides H(2)S-CH(2) and (CH(3))(2)S-CH(2) is 1.4-1.5, intermediate between a single and double bond.     

On the structure and torsional potential of trifluoromethoxybenzene: an ab initio and density functional study

The torsional potential of trifluoromethoxybenzene around the aryl–O bond was investigated with the aid of large-scale ab initio calculations performed at the Møller–Plesset second order (MP2) level, with several post-MP2 methods, and with a hybrid density functional method (B3LYP). Contrary to several recent reports, we do not find substantial qualitative differences between MP2 and B3LYP results, provided sufficiently large basis sets are used. The results are confronted with analogous MP2 and B3LYP data for methoxybenzene, for hypothetical anions as obtained by deprotonation at the para-position, and for ethylbenzene. The trends in the calculated torsional potentials, barrier heights and energy differences between conformers are discussed and correlated with selected structural parameters.     

Vibrational spectroscopy investigation using ab initio and density functional theory on p-anisaldehyde

The FTIR and FT Raman spectra of p-anisaldehyde has been recorded in the regions 4,000-400 and 3,500-100 cm(-1), respectively. The optimized geometry, frequency and intensity of the vibrational bands of p-anisaldehyde were obtained by ab initio and DFT levels of theory with complete relaxation in the potential energy surface using 6-31G(d,p) basis set. A complete vibrational assignment aided by the theoretical harmonic frequency analysis has been proposed. The harmonic vibrational frequencies calculated have been compared with experimental FTIR and FT Raman spectra. The observed and the calculated frequencies are found to be in good agreement. The experimental spectra also coincide satisfactorily with those of theoretically constructed bar type spectrograms.     

A density functional treatment of organolithium compounds: Comparison to ab initio,semiempirical, and experimental results

Density functional calculations on several classes of organolithium compounds are described. The compounds studied include lithium bonds to carbon, oxygen, and nitrogen and are representative of most types of organolithium compounds that have appeared in the recent literature. The computational results are compared to those using MNDO, which has been shown to have some serious deficiencies in compounds involving carbon–lithium bonds, and to PM3 results, which offer some improvement over MNDO for many organolithium compounds. Most of the density functional calculations with a large basis set are in good agreement with available ab initio and experimental data. Calculated carbon–lithium bond lengths were slightly shorter than those calculated by other ab initio methods and were substantially longer than those calculated by MNDO, which is known to underestimate carbon–lithium bond lengths severely. Dimerization energies of methyllithium, calculated by DMol, were also in good agreement with those of other ab initio calculations. Lithium–nitrogen bonds in lithium amides were calculated to be slightly shorter by DMol than by MNDO, although the two methods were in qualitative agreement for this type of compound. © 1995 by John Wiley & Sons, Inc.     

FT-Raman and FT-IR spectra, ab initio and density functional studies of 3,4-dichlorobenzyl alcohol

The Fourier transform Raman and Fourier transform infrared spectra of 3,4-dichlorobenzyl alcohol were recorded in the solid phase. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities, depolarization ratios, reduced masses were calculated by HF and density functional B3LYP method with the 6-311 G** basis set. The scaled theoretical wavenumbers showed very good agreement with the experimental values. The thermodynamic functions of the title compound were also performed at HF/6-311G** and B3LYP/6-311G** levels of theory. A detailed interpretations of the infrared and Raman spectra of 3,4-dichlorobenzyl alcohol is reported. The theoretical spectrograms for FT-IR spectra of the title molecule have been constructed.     

Intramolecular hydrogen-bonding interactions in 2-nitrosophenol and nitrosonaphthols: ab initio, density functional, and nuclear magnetic resonance theoretical study

Intramolecular hydrogen bonding (IHB) interactions and molecular structures of 2-nitrosophenol, nitrosonaphthols, and their quinone-monooxime tautomers were investigated at ab initio and density functional theory (DFT) levels. The geometry optimization of the structures studied was performed without any geometrical restrictions. Possible conformations with different types of the IHB of the tautomers were considered to understand the nature of the HB among these conformers. The effect of solvent on hydrogen bond energies, conformational equilibria, and tautomerism in aqueous solution were studied. Natural bond orbital analysis was performed to study the IHB in the gaseous phase and in aqueous medium. The NMR 1H, 13C, 15N, and 17O chemical shifts in the gaseous phase and in solution for the studied compounds were calculated using the gauge-including atomic orbitals approach implemented in the Gaussian 03 program package. The optimized geometrical parameters and 1H NMR chemical shifts are in good agreement with previous theoretical and experimental data.     

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.     

Density functional and ab initio study of the free radical MgNC

A new “non-terrestrial” molecule present in the envelope of the carbon star IRC + 10216 was described for the first time in 1986. Recently, this molecule was identified as the free radical MgNC, the first Mg-containing molecule in space. We present here the first density functional study performed on this radical, as well as on its isomer MgCN and the transition state connecting these species. It is shown that the optimum geometry obtained at the Becke3LYP/6-311+G(3df) level leads to the most exact rotational constants B_e and B_o calculated up to now. It is also shown that the energy differences between the three species are completely in agreement with the best ab initio calculations available. Furthermore, it is shown that the popular MP2 method fails for this system in the same way that has been demonstrated for other radicals.     

Binding of CO, NO, and O2 to heme by density functional and multireference ab initio calculations

Using the CASSCF/CASPT2 approach, along with several DFT methods (PBE0, B3LYP, BP86, OLYP), we have investigated the bonding of CO, NO, and O2 molecules to two model heme systems: an iron(II) porphyrin with and without an axial imidazole ligand. The experimentally available binding energies are best reproduced by the CASPT2 method and with the OLYP functional. The other functionals considered perform much worse, either severely overbinding (BP86) or underbinding (B3LYP, PBE0). Significant discrepancies between the different density functionals are observed, not only for the energetics but sometimes also for structure predictions. This confirms our viewpoint that a balanced treatment of the electronic exchange and correlation is vital to describe the weak metal-ligand bond between heme and CO, NO, or O2. The binding energies DeltaEb were split into two contributions: the so-called spin-pairing energy DeltaE sp and the "inherent" binding energy DeltaEb0, and both contributions were analyzed in terms of method and basis set effects. We have also investigated the spin density distributions resulting from the bonding of the NO molecule (a noninnocent ligand) to heme. Our analysis at the DFT and CASSCF level shows that, while various density functionals predict qualitatively very different spin distributions, the CASSCF spin populations most closely correspond to the results obtained with the pure BP86 or OLYP rather than with the hybrid functionals.     

Equilibrium structure of the carbon dioxide-water complex in the gas phase: an ab initio and density functional study

High-level ab initio (MP2/6-311++G(2d,2p) geometry, Gaussian-2, MP4(SDTQ) and QCISD(T) binding energies) and density-functional (Becke3LYP/6-311++G(2df,2pd)) calculations have been performed on the charge-transfer complex between water and carbon dioxide. The complex appears to have two equivalent non-planar minima of C_s symmetry. Minima are separated by transition states with C₁ symmetry, whereas the totally planar structure with C_2v symmetry is a second-order transition state. All the critical points lie at approximately the same energy (less than 0.05 Kj mol⁻¹ difference). Therefore, the experimentally observable structure should be planar. The best equilibrium intermolecular distance for this complex calculated at the MP2/6-311++G(2d,2p) level is 2.800 Å. Our best estimate of the observable intermolecular distance (corrected for anharmonicity) is 2.84 Å, in agreement with the experimentally derived value of 2.836 Å. Our best estimate of the binding energy at the QCISD(T) level, taking into account the variation of the distance owing to anharmonicity and the use of more sophisticated theoretical treatments, is −12.0 ± 0.2 kJ mol⁻¹. Our best estimate of the barrier to internal rotation, also at the MP2/6-311++G(2d,2p) level, is 4.0 kJ mol⁻¹, outside the error limits of the experimental determination (3.64 ± 0.04 kJ mol⁻¹). Density functional theory at the level employed here gives an equilibrium intermolecular distance that is too large (2.857 Å), a binding energy that is too small (8.1 kJ mol⁻¹), attributable neither to geometry nor to the basis set, and also a barrier to internal rotation that is slightly too small (3.39 kJ mol⁻¹). The overall picture is, however, reasonably good.