Theoretical structure of the low‐laying electronic states of the molecule YBr

An ab initio CASSCF and MRCI (single and double excitation plus Davidson correction) calculation have been performed for the molecule YBr. The potential energy curves of 20 electronic states in the representation ^2s+1Λ^(+/?) (neglecting the spin‐orbit effects) and 41 states in the representation Ω^(+/?) [including the spin‐orbit (SO) effects] have been calculated along with the corresponding spectroscopic constants. The SO effects are taken into account via a semi‐empirical SO pseudo‐potential for the yttrium atom, while they have been neglected for bromine. Very good agreement is displayed by comparing the present results with those obtained experimentally, up to now, of the three states X¹Σ⁺, (1)²Π, and (2)¹Σ⁺. New results have been obtained for 17 states ^2s+1Λ^(+/?), and their SO components yet not observed or calculated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Theoretical calculation of the electronic states with spin‐orbit effects of the molecule NaRb

The potential energy curves of the molecule NaRb have been calculated for the 60 low‐lying electronic states in the Ω‐representation. Using an ab‐initio method the calculation is based on nonempirical pseudo‐potential in the interval 3.0a_o ≤ R ≤ 44.0a_o of the internuclear distance. The spin‐orbit effects have been taken into account through a semiempirical spin‐orbit pseudo‐potential added to the electrostatic Hamiltonian with Gaussian basis sets for both atoms. The spectroscopic constants have been calculated for 42 states and the components of the spin‐orbit splitting have been identified for the states (1, 2, 5)³Π and (1, 2)³Δ. The comparison of the present results with those available in literature shows a good agreement, whereas the other results, to the best of our knowledge, are given here for the first time. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Theoretical electronic structure of the lowest-lying states of the YI molecule

CAS-SCF/MRCI calculations have been performed for 15 molecular states in the representation ^2S+1Λ^(+/−) (neglecting spin–orbit effects) for the molecule YI. The corresponding 33 molecular states in the representation Ω^(+/−) (including spin–orbit effects) have been calculated using a semi-empirical spin–orbit pseudopotential built up for yttrium. Calculated potential energy curves and spectroscopic constants are reported, to the best of our knowledge they are the first ones from ab initio methods for this molecule. Present results are compared to experimental accurate data available for the ground X¹Σ⁺ and 3 excited states (1)¹Π, (2)¹Σ⁺ and (2)¹Π.     

The effect of the iterative triple and quadruple cluster amplitudes on the adiabatic potential curve in the coupled cluster calculations of the ground electronic state of the Yb dimer

The dissociation energy, equilibrium internuclear distance, and spectroscopic constants for the ¹Σ ground state of the Yb₂ molecule are calculated. The relativistic effects are introduced through generalized relativistic effective core potentials with very high precision. The scalar relativistic coupled cluster method particularly well suited for closed‐shell van der Waals systems is used for the correlation treatment. Extensive generalized correlation basis sets were constructed and used. The relatively small corrections for high‐order cluster amplitudes and spin—orbit interactions are taken into account using smaller basis sets and the spin—orbit density functional theory. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

NMR spin–spin coupling constants in hydrogen‐bonded glycine clusters

The influence of the hydrogen bond formation on the NMR spin–spin coupling constants (SSCC), including the Fermi contact (FC), the diamagnetic spin‐orbit, the paramagnetic spin‐orbit, and the spin dipole term, has been investigated systematically for the homogeneous glycine cluster, in gas phase, containing up to three monomers. The one‐bond and two‐bond SSCCs for several intramolecular (through covalent bond) and intermolecular (across the hydrogen‐bond) atomic pairs are calculated employing the density functional theory with B3LYP and KT3 functionals and different types of extended basis sets. The ab initio SOPPA(CCSD) is used as benchmark for the SSCCs of the glycine monomer. The hydrogen bonding is found to cause significant variations in the one‐bond SSCCs, mostly due to contribution from electronic interactions. However, the nature of variation depends on the type of oxygen atom (proton‐acceptor or proton‐donor) present in the interaction. Two‐bond intermolecular coupling constants vary more than the corresponding one‐bond constants when the size of the cluster increases. Among the four Ramsey terms that constitute the total SSCC, the FC term is the most dominant contributor followed by the paramagnetic spin‐orbit term in all one‐bond interaction.     

Geometries,vibrational frequencies,and excitation energies of a series of fluorine‐substituted carbenes,FCX (X = H,F, Cl,Br, and I): A high‐level multireference configuration interaction study

High‐level calculations using internally contracted multireference configuration interaction including Davidson correction (icMRCI+Q) method have been carried out for the ground singlet states, the first excited states, and the lowest triplet states of a series of fluorine‐substituted carbenes FCX (X = H, F, Cl, Br, and I). Equilibrium geometries and vibrational frequencies of the three electronic states, adiabatic transition energy of the first excited singlet state, as well as the ground singlet—lowest triplet energy gap (S‐T gap) of each of FCX carbenes have been obtained. Effects of the basis set of icMRCI+Q calculation on the geometries and energies have been investigated. In addition, various corrections, including the scalar relativistic effect, spin‐orbit coupling, and core‐valence correlation, have been studied in calculating the transition energies and the S‐T gaps, especially for heavy‐atom carbenes. This results have been compared with previous calculations using a variety of methods. Our icMRCI+Q results are in very good agreement with the high‐resolution laser‐based spectroscopic results where available. Some structure and spectroscopic constants of the fluorine‐substituted carbenes which are void in the literature have been provided with consistent high‐level calculations. © 2013 Wiley Periodicals, Inc.     

Spin–Orbit Contributions in High‐Spin Nitrenes/Carbenes: A Hybrid CASSCF/MRMP2 Study of Zero‐Field Splitting Tensors

Zero‐field splitting (ZFS) tensors ( D tensors) of organic high‐spin oligonitrenes/oligocarbenes up to spin‐septet are quantitatively determined on the basis of quantum chemical calculations. The spin–orbit contributions, D ^SO tensors are calculated in terms of a hybrid CASSCF/MRMP2 approach, which was recently proposed by us. The spin–spin counterparts, D ^SS tensors are computed based on McWeeny–Mizuno’s equation in conjunction with the RODFT spin densities. The present calculations show that more than 10 % of ZFS arises from spin–orbit interactions in the high‐spin nitrenes under study. Contributions of spin‐bearing site–site interactions are estimated with the aid of a semi‐empirical model for the D tensors and found to be ca. 5 % of the D ^SO tensor. The analysis of intermediate states reveal that the largest contributions to the calculated D ^SO tensors are attributed to intra‐site spin flip excitations and delocalized π and π* orbitals play an important role in the inter‐site spin–orbit interactions.     

Accurate spectroscopic constants of the lowest three electronic states in halonitrenes with multireference configuration interaction

Internally contracted multireference configuration interaction (icMRCI) calculations of the ground state (X³Σ⁻), the first excited state (a¹Δ) as well as the second excited state (b¹Σ⁺) have been performed for a series of halogenated nitrenes NXs (X = Cl, Br, and I). Accurate spectroscopic constants of these lowest three electronic states of each NX were obtained in this work using MRCI methods with aug‐cc‐pVXZ (X = T, Q, 5) basis sets and complete basis set (CBS) limit. In addition, various corrections, including the Davidson correction, scalar relativistic effect, core‐valence correlation, and spin‐orbit coupling effect, have been studied in calculating spectroscopic constants, especially for heavy‐atom nitrenes. Comparisons have been made with previous computational and experimental results where available. The icMRCI + Q calculations presented in this work provide a comprehensive series of results at a consistent high level of theory for all of the halogenated nitrenes.     

Spin—orbit and vibronic perturbations on the chiroptical spectra of dissymmetric pseudo-tetragonal metal complexes

The influence of spin—orbit and vibronic interactions upon the chiroptical properties of nearly degenerate dd transitions in metal complexes of pseudo-tetragonal symmetry is investigated. A model system is considered in which three nearly degenerate dd excited states are coupled via both spinorbit and vibronic interactions. Vibronic interactions among the three nearly degenerate dd electronic states are assumed to arise from a pseudo-Jahn—Teller (PJT) mechanism involving three different vibrational modes (each nontotally symmetric in the point group of the undistorted model system).A vibronic hamiltonian is constructed (for the excited states of the model system) which includes linear coupling terms in each of the three PJT-active vibrational modes as well as a linear coupling term in one totally symmetric mode of the system and a spin—orbit interaction term. Wavefunctions and eigenvalues for the spin—orbit/vibronic perturbed excited states. of the model system are obtained by diagonalizing this hamiltonian in a basis constructed of uncoupled vibrational and electronic (orbital and spin) wavefunctions.Rotatory strengths associated with transitions to vibronic levels of the perturbed system are calculated and “rotatory strength spectra” are computed assuming gaussian shaped vibronic spectral components. Calculations are carried out for a number of vibronic and spin—orbit coupling parameters and for various splitting energies between the interacting electronic states. The calculated results suggest that chiroptical spectra associated with transitions to a set of nearly degenerate dd excited states of a chiral transition metal complex cannot be interpreted directly without some consideration of the effects introduced by spin—orbit and vibronic perturbations. These perturbations can lead to substantial alterations in the sign patterns and intensity distributions of rotatory strength among vibronic levels derived from the interacting electronic states and it is generally not valid to assign specific features in the observed circular dichroism spectra to transitions between states with well-defined electronic (orbital and spin) identities.Our theoretical model is conservative with respect to the total (or net) rotatory strength associated with transitions to levels derived from the three interacting electronic states; the vibronic and spin—orbit coupling operators are operative only within this set of states. That is, the total (or net) rotatory strength associated with these transitions remains invariant to the vibronic and spin—orbit coupling parameters of the model.     

Molecular orbital calculation of spin-orbit splittings in some halogeno-compounds

CNDO and INDO calculations incorporating the spin—orbit operator in the Hamiltonian have been carried out to obtain the spin—orbit splittings of ionization potentials of some halogen compounds. Two sets of spin—orbit coupling constants were tested. The calculated splittings are compared with photoelectron spectroscopy experimental results from the literature.     

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.     

First‐principles study of the TiN(111)/ZrN(111) interface

The TiN(111)/ZrN(111) interface was studied by first‐principles method to provide the theoretical basis for developing the TiN/ZrN coatings. Twelve geometry structures of TiN(111)/ZrN(111) interfaces were established. The calculated interfacial work of adhesion reveals that the N‐terminated TiN/N‐terminated ZrN interface with TL site shows the strongest stability. For this TiN(111)/ZrN(111) interface, the results of the partial density of state indicate that the chemical bonding at the interface appeals both ionic and covalent characteristic, which is same as that in the bulk materials. The partial density of states for Zr, Ti, and N atoms at the interface are very similar with those in the bulk, which reveals that the electronic structure transition at the interface is smooth. The results of charge density and charge density difference demonstrate that the lost charge of Ti atom is larger than that of Zr atom, indicating that TiN is more ionic than ZrN. Calculations of the work of fracture indicate that the mechanical failure of the ZrN(111)/TiN(111) interface will take place at the interface. Besides that, the calculation result of the TiN(111)/ZrN(111) interface implies that the TiZrN₂ phase might be formed at the interface because the contacting of the N―N bond is the most stable.     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the CH Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C? H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

Ab initio prediction of the structure and vibration‐rotation spectroscopic properties of Na2OH and K2OH

The equilibrium structures and potential energy surfaces of the Na₂OH and K₂OH radicals and the corresponding cations in their electronic ground states have been determined from accurate ab initio calculations. The vibration‐rotation energy levels and spectroscopic constants of various isotopic species were calculated by a perturbational approach. The predicted spectroscopic constants may serve as a useful guide for detecting these species by vibration‐rotation spectroscopy and for assigning their spectra. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

GRECP/MRD‐CI calculations of spin‐orbit splitting in ground state of Tl and of spectroscopic properties of TlH

The generalized relativistic effective core potential (GRECP) approach is employed in the framework of multireference single‐ and double‐excitation configuration interaction (MRD‐CI) method to calculate the spin‐orbit splitting in the ²P^o ground state of the Tl atom and spectroscopic constants for the 0⁺ ground state of TlH. The 21‐electron GRECP for Tl is used, and the outer core 5s and 5p pseudospinors are frozen with the help of the level shift technique. The spin‐orbit selection scheme with respect to relativistic multireference states and the corresponding code are developed and applied in the calculations. In this procedure both correlation and spin‐orbit interactions are taken into account. A [4,4,4,3,2] basis set is optimized for the Tl atom and employed in the TlH calculations. Very good agreement is found for the equilibrium distance, vibrational frequency, and dissociation energy of the TlH ground state (R_e=1.870 Å, ω_e=1420 cm⁻¹, D_e=2.049 eV) as compared with the experimental data (R_e=1.872 Å, ω_e=1391 cm⁻¹, D_e=2.06 eV). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 409–421, 2001     

Ab initio surface hopping excited-state molecular dynamics approach on the basis of spin–orbit coupled states: An application to the A-band photodissociation of CH3I

Ab initio molecular dynamics approach has been extended to multi-state dynamics on the basis of the spin–orbit coupled electronic states that are obtained through diagonalization of the spin–orbit coupling matrix with the multi-state second-order multireference perturbation theory energies in diagonal elements and the spin–orbit coupling terms at the state-averaged complete active space self-consistent field level in off-diagonal elements. Nonadiabatic transitions over the spin–orbit coupled states were taken into account explicitly by a surface hopping scheme with utilizing the nonadiabatic coupling terms calculated by numerical differentiation of the spin–orbit coupled wavefunctions and analytical nonadiabatic coupling terms. The present method was applied to the A-band photodissociation of methyl iodide, CH₃I + hv → CH₃ + I (²P_3/2)/I* (²P_1/2), for which a pioneering theoretical work was reported by Amatatsu, Yabushita, and Morokuma. The present results reproduced well the experimental branching ratio and energy distributions in the dissociative products. © 2018 Wiley Periodicals, Inc.     

Two‐component calculations of spin–orbit effects for a van der Waals molecule Rn2

Electronic structures of the weakly bound Rn₂ were calculated by the two‐component Møller–Plesset second‐order perturbation and coupled‐cluster methods with relativistic effective core potentials including spin–orbit operators. The calculated spin–orbit effects are small, but depend strongly on the size of basis sets and the amount of electron correlations. Magnitudes of spin–orbit effects on D_e (0.7–3.0 meV) and R_e (−0.4∼−2.2 Å) of Rn₂ are comparable to previously reported values based on configuration interaction calculations. A two‐component approach seems to be a promising tool to investigate spin–orbit effects for the weak‐bonded systems containing heavy elements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 139–143, 1999     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

AB initio calculations of the electronic structure and doubling parameters of BS

Ab initio calculations have been performed to understand the influence of spin—orbit interaction upon the fine structure of the observed valence doublet states of the BS molecules: spin—orbit splittings, γ-type and Λ-type doublings. Configuration interaction is shown to be an essential feature in order to account for the observed data. Other properties of the electronic states (transition energies) have also been calculated.