Density functional and multiconfigurational ab initio study of the ground and excited states of Os2

Multiconfigurational ab initio methods predict that the ⁵Π_u state as the ground state instead of the ⁷Δ_u state. Although multiconfigurational perturbation theory correctly predicts the ground state, they overestimate the bond dissociation energy (BDE). Only multireference configuration interaction method can reasonably calculate the BDE. The spin‐orbit effect on the spectroscopic constants is not significant. The results calculated by density functional theory (DFT) vary significantly depending on the selection of a DFT functional. No DFT functional gives the same energy ordering as calculated by the second‐order multiconfigurational perturbation theory (CASPT2). The old generalized gradient approximations functionals are well suited for predicting the ground state and calculating the bond length and the vibrational frequency of Os₂. According to the CASPT2 calculation, the ground state of Os₂ has a quadruple bond. © 2014 Wiley Periodicals, Inc.     

Ab initio calculation of the Dzyaloshinskii–Moriya parameters: Spin–orbit GSO‐HF,DFT, and CI approaches

We present ab initio methods to determine the Dzyaloshinskii–Moriya (DM) parameter, which provides the anisotropic effects of noncollinear spin systems. For this purpose, we explore various general spin orbital (GSO) approaches, such as Hartree–Fock (HF), density functional theory (DFT), and configuration interaction (CI), with one‐electron spin–orbit coupling (SOC1). As examples, two simple D_3h‐symmetric models, H₃ and B(CH₂)₃, are examined. Implications of the computational results are discussed in relation to as isotropic and anisotropic interactions of molecular‐based magnets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Spin–orbit coupling of spin‐frustrated systems

We have investigated the effects of spin–orbit (SO) interactions on noncollinear molecular magnetism by combining the classical Dzyaloshinsky–Moriya (DM) model and ab initio generalized spin orbital (GSO) method. We have derived an estimation scheme of the magnetic anisotropy energy (MAE) and the Dzyaloshinsky vector based on the SO first‐order perturbation theory (SOPT1) for GSO Hartree–Fock (GHF) solutions. We found that the fundamental results of GHF‐SOPT1 method can be reproduced by diagonalizing the core Hamiltonian plus SO terms, and that the spin topologies of odd‐ring systems can be determined by the topological indices of the singly occupied molecular orbitals. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

An animated visualization of orbital angular momentum and spin‐orbit coupling

This paper presents an approach toward visualizing a complex orbital based on animation using a time‐dependent phase factor. This makes orbital angular momentum clearly visible, in a way that reflects the nature of the orbital angular momentum wavefunction. Visualization of this quantity is also useful for examining the effects of spin‐orbit coupling (SOC), in which higher orbital angular momentum states are admixed into the orbital; in this case, however, scaling of one phase‐component is needed. The phase orientation of a complex orbital, which is generally not guaranteed by the SCF procedure, must be considered when doing this. The method of visualization presented here may prove useful when analyzing properties where SOC is important, such as magnetic resonance parameters. Animated visualizations are performed, and compared with the method of phase‐colored isosurfaces, first for a model p‐orbital to explain the idea, and then for the singly‐occupied molecular orbitals of two small doublet radicals.     

Fundamental vibrational frequencies and dominant resonances in methylamine isotopologues by ab initio and density functional theory methods

Ab initio and density functional theory (DFT) calculations were performed for obtaining fundamental vibrational frequencies of methylamine, CH3NH2, and its deuterated variants CH3ND2, CD3NH2, and CD3ND2. The calculations were carried out using the CCSD(T) coupled cluster approximation with cc-pVTZ and cc-pVQZ basis sets, and by the DFT method with the semiempirical hybrid functional B97-1 with polarization consistent pc-2 and pc-3 basis sets. Reasonable performance of the DFT harmonic and ab initio harmonic calculations was found, which improved considerably upon combination of the harmonic fundamental frequencies with anharmonic corrections from the smaller, pc-2, basis. The computed anharmonic fundamental frequencies of methylamine isotopologues agree very well with the experimental values and represent a useful tool for assignment and analysis of the dominant resonances.     

Improving the accuracy of ab initio methods with summation approximants and singularity analysis

The accuracy of Møller–Plesset (MP) perturbation theory and coupled‐cluster (CC) theory can be significantly improved, at essentially no increase in computational cost, by using summation approximants that model the way in which these theories converge to the full configuration interaction limit. Approximants for MP4 and CCSD(T) are presented, their size scaling is analyzed, and the functional analysis of the MP energy, on which the MP4 approximant is based, is discussed. The MP approximants are shown to have a form that is appropriate for describing resonance energies. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Interaction of acetonitrile with alkaline metal cations: A density functional,coupled‐cluster,and quadratic configuration interaction study

A systematic quantum chemical study of CH₃CN and its CH₃CN?M⁺ 1:1 model adducts (M⁺∈{Li⁺, Na⁺}) is presented, with respect to binding energetics, structural and vibrational force field changes. Several gradient‐corrected density functional levels of theory were employed (of both “pure” and “hybrid” character), together with the coupled cluster including double substitutions from the Hartree–Fock determinant (CCD) and quadratic configuration interaction including single and double substitutions (QCISD) methods [with the rather large 6‐311G(d,p) basis set], and their performances compared. The binding energy decompositions according to the Kitaura–Morokuma scheme and the reduced variational space self‐consistent field (RVS‐SCF) method have shown that the electrostatic plus polarization interaction terms are primarily responsible for overall stabilization, while the charge‐transfer term is negligibly small and virtually identical for both adducts. The computed harmonic vibrational frequencies for acetonitrile correlate excellently with the experimental ones (r²>0.9998 for almost all cases, while for the BLYP level, r²=1). It is shown for the first time that the experimentally observed blue shifts of the ν_CN mode are caused even by formation of 1:1 adducts, contrary to the previously accepted opinions. The CCD and QCISD, as well as the BPW91 and BP86 levels of theory predict almost excellently the ν_CN mode blue shift upon adduct formation, while the BLYP and B3LYP levels perform significantly poorer. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

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.     

Fully ab initio protein‐ligand interaction energies with dispersion corrected density functional theory

Dispersion corrected density functional theory (DFT‐D3) is used for fully ab initio protein‐ligand (PL) interaction energy calculation via molecular fractionation with conjugated caps (MFCC) and applied to PL complexes from the PDB comprising 3680, 1798, and 1060 atoms. Molecular fragments with n amino acids instead of one in the original MFCC approach are considered, thereby allowing for estimating the three‐body and higher many‐body terms. n > 1 is recommended both in terms of accuracy and efficiency of MFCC. For neutral protein side‐chains, the computed PL interaction energy is visibly independent of the fragment length n. The MFCC fractionation error is determined by comparison to a full‐system calculation for the 1060 atoms containing PL complex. For charged amino acid side‐chains, the variation of the MFCC result with n is increased. For these systems, using a continuum solvation model with a dielectricity constant typical for protein environments (? = 4) reduces both the variation with n and improves the stability of the DFT calculations considerably. The PL interaction energies for two typical complexes obtained ab initio for the first time are found to be rather large (?30 and ?54 kcal/mol). © 2012 Wiley Periodicals, Inc.     

Excited states of OsO4: A comprehensive time‐dependent relativistic density functional theory study

A large number of scalar as well as spinor excited states of OsO₄, in the experimentally accessible energy range of 3–11 eV, have been captured by time‐dependent relativistic density functional linear response theory based on an exact two‐component Hamiltonian resulting from the symmetrized elimination of the small component. The results are grossly in good agreement with those by the singles and doubles coupled‐cluster linear response theory in conjunction with relativistic effective core potentials. The simulated‐excitation spectrum is also in line with the available experiment. Furthermore, combined with detailed analysis of the excited states, the nature of the observed optical transitions is clearly elucidated. It is found that a few scalar states of ³T₁ and ³T₂ symmetries are split significantly by the spin‐orbit coupling. The possible source for the substantial spin‐orbit splittings of ligand molecular orbitals is carefully examined, leading to a new interpretation on the primary valence photoelectron ionization spectrum of OsO₄. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A full‐pivoting algorithm for the Cholesky decomposition of two‐electron repulsion and spin‐orbit coupling integrals

A significant reduction in the computational effort for the evaluation of the electronic repulsion integrals (ERI) in ab initio quantum chemistry calculations is obtained by using Cholesky decomposition (CD), a numerical procedure that can remove the zero or small eigenvalues of the ERI positive (semi)definite matrix, while avoiding the calculation of the entire matrix. Conversely, due to its antisymmetric character, CD cannot be directly applied to the matrix representation of the spatial part of the two‐electron spin‐orbit coupling (2e‐SOC) integrals. Here, we present a computational strategy to achieve a Cholesky representation of the spatial part of the 2e‐SOC integrals, and propose a new efficient CD algorithm for both ERI and 2e‐SOC integrals. The proposed algorithm differs from previous CD implementations by the extensive use of a full‐pivoting design, which allows a univocal definition of the Cholesky basis, once the CD δ threshold is made explicit. We show that is the upper limit for the errors affecting the reconstructed 2e‐SOC integrals. The proposed strategy was implemented in the ab initio program Computational Emulator of Rare Earth Systems (CERES), and tested for computational performance on both the ERI and 2e‐SOC integrals evaluation. © 2017 Wiley Periodicals, Inc.     

Determination of spin-orbit coupling contributions in the framework of density functional theory

We present a noniterative method to calculate spin-orbit coupling by means of a theoretical approach that provides the use of the full Breit-Pauli operator. This method was applied to compute one and two-electron spin-orbit coupling contributions between singlet and triplet, and doublet and doublet states, respectively. These states have been represented by monodeterminantal wave functions and optimized using the PW91 gradient-corrected exchange-correlation functional and the hybrid B3LYP one. They have been supplied by the conventional density functional theory packages, and thus coupled by our spin-orbit coupling code. Different size basis sets have been employed and the obtained results have been compared with the corresponding ones provided by some of the already existing methods and with the experimental data. They have been found to be in good quantitative agreement.     

Ab initio calculations of the ground and excited states of the ZrN molecule including spin‐orbit effects

The electronic structures with spin‐orbit effects of the zirconium nitride ZrN molecule are investigated by the methods of multireference single and double configuration interaction. The potential energy curves are calculated along with the spectroscopic constants for the lowest‐lying 34 spin‐orbit states Ω in ZrN. A good agreement is displayed by comparing the calculated spectroscopic constants with those available experimentally. The permanent dipole moments are calculated along with the vibrational energies. New results are obtained in this work for 29 spin‐orbit states and their spectroscopic constants calculated. © 2015 Wiley Periodicals, Inc.     

Development of spin‐orbit coupling for stochastic configuration interaction techniques

To perform spin‐orbit coupling calculations on atoms and molecules, good zeroth‐order wavefunctions are necessary. Here, we present the software development of the Monte Carlo Configuration Interaction (MCCI) method, to enable calculation of such properties, where MCCI iteratively constructs a multireference wavefunction using a stochastic procedure. In this initial work, we aim to establish the efficacy of this technique in predicting the splitting of otherwise degenerate energy levels on a range of atoms and small diatomic molecules. It is hoped that this work will subsequently act as a gateway toward using this method to investigate singlet‐triplet interactions in larger multireference molecules. We show that MCCI can generate very good results using highly compact wavefunctions compared to other techniques, with no prior knowledge of important orbitals. Higher‐order relativistic effects are neglected and spin‐orbit coupling effects are incorporated using first‐order degenerate perturbation theory with the Breit‐Pauli Hamiltonian and effective nuclear charges in the one‐electron operator. Results are obtained and presented for B, C, O, F, Si, S, and Cl atoms and OH, CN, NO, and C₂ diatomic radicals including spin‐orbit coupling constants and the relative splitting of the lowest energy degenerate state for each species. Convergence of MCCI to the full configuration interaction result is demonstrated on the multireference problem of stretched OH. We also present results from the singlet‐triplet interaction between the and both the and states of the O₂ molecule. © 2017 Wiley Periodicals, Inc.     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

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.     

Noncollinear spin density functional theory for spin‐frustrated and spin‐degenerate systems

We have implemented ab initio linear combinations of Gaussian‐type orbital calculations with generalized localized spin density approximation (GLSDA) for a dimer of equilateral H₃ as a model of the noncollinear magnetic clusters. It has been found that the GLSDA solution with the three‐dimensional noncollinear spin structure is, contrary to prior band calculations by other groups, the ground state near the O_h conformation. Further computational results are compared to that of ab initio generalized Hartree–Fock. The difference between them and the influence of the correlation correction were discussed. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Exchange coupling and magnetic anisotropy in a family of bipyrimidyl radical‐bridged dilanthanide complexes: Density functional theory and ab initio calculations

The origin of the magnetic anisotropy energy barriers in a series of bpym^? (bpym = 2,2′‐bipyrimidine) radical‐bridged dilanthanide complexes [(Cp*₂Ln)₂(μ‐bpym)]⁺ [Cp* = pentamethylcyclopentadienyl; Ln = Gd^III ( 1 ), Tb^III ( 2 ), Dy^III ( 3 ), Ho^III ( 4 ), Er^III ( 5 )] has been explored using density functional theory (DFT) and ab initio methods. DFT calculations show that the exchange coupling between the two lanthanide ions for each complex is very weak, but the antiferromagnetic Ln‐bpym^? couplings are strong. Ab initio calculations show that the effective energy barrier of 2 or 3 mainly comes from the contribution of a single Tb^III or Dy^III fragment, which is only about one third of a single Ln energy barrier. For 4 or 5 , however, both of the two Ho^III or Er^III fragments contribute to the total energy barrier. Thus, it is insufficient to only increase the magnetic anisotropy energy barrier of a single Ln ion, while enhancing the Ln‐bpym^? couplings is also very important. © 2014 Wiley Periodicals, Inc.