Ab initio calculation of spin–orbit interaction in polyatomic molecules using Gaussian-type wavefunctions

A set of programs has been developed to calculate molecular spin–orbit interaction with Gaussian-type wavefunctions in connection with the popular GAUSSIAN 76 program. The spin–orbit contributions to the fine structure of O₂ (X³∑_g^?), NH (X³∑^?), and CH₂ (X³B₁) are evaluated with the standard STO -3G and 6-31G basis sets; for NH the influence of bond functions added to the latter basis set is also investigated. The results are compared to values previously obtained with other types of basis sets.     

Kramers' unrestricted Hartree–Fock and second-order Møller–Plesset perturbation methods using relativistic effective core potentials with spin–orbit operators: Test calculations for HI and CH3I

The Kramers' restricted Hartree–Fock (KRHF) and second-order Møller–Plesset perturbation (KRMP2) methods using relativistic effective core potentials (RECP) with spin–orbit operators and two-component spinors are extended to the unrestricted forms, KUHF and KUMP2. As in the conventional unrestricted methods, the KUHF and KUMP2 methods are capable of qualitatively describing the bond breaking for a single bond. As a result, it is possible to estimate spin–orbit effects along the dissociation curve at the HF and MP2 levels of theory as is demonstrated by the test calculations on the ground states of HI and CH₃I. Since the energy lowering due to spin–orbit interactions is larger for the I atom than for the closed-shell molecules, dissociation energies are reduced and bond lengths are slightly elongated by the inclusion of the spin–orbit interactions. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 91–98, 1998     

Numerical method for the open-shell restricted hartree–fock density-matrix direct calculation

A new computation procedure for direct calculation of the density matrix in the LCAO version of the restricted Hartree–Fock–Roothaan open-shell theory is analyzed. It is proved that the procedure is quadratically convergent and stable to the round-off errors independently of the Fock operator spectrum. The dependence of the limit matrix of the initial matrix is examined.     

Ab initio studies on the electronic structure of the complexes containing Mo—S bond using relativistic effective core potentials

An ab initio calculation was performed on the electronic structures of MoS, MoS^2-₄ and Mo₂S₂ using relativistic effective core potential (RECP) for molybdenum, and non-relativistic ECP for sulfur. We predicted that the equilibrium bond length and the dissociation energy of MoS in ground state are 3.89 a.u. and 4.67 eV, respectively, and that the bond is a triple-bond. The ground state of MoS^2-₄ in Td symmetry is ¹A₁ and π-bonding dominates σ-donation in the molybdenum-sulfur interaction. The Mo₂S₂ is a model contracted from bi-nuclear sulfur-bridged clusters, and the bonding orbitals 1b_1u, 1b_1g and 1b_2g make the dominant contribution to the stabilization of sulfur-bridged species.     

Electronic structure of molecules using one-component wave functions and relativistic effective core potentials

A one-component approach to molecular electronic structure is discussed that includes the dominant relativistic effects on valence electrons and yet allows the use of the traditional quantum-chemistry techniques. The approach starts with one-component Cowan–Griffin relativistic orbitals that successfully incorporate the effects of the mass-velocity and Darwin terms present in more complicated wave functions such as the Dirac–Hartree–Fock. The approach then constructs “relativistic” effective core potentials (RECPS ) from these orbitals, and uses these to bring the relativistic effects into the molecular electronic calculations. The use of effective one-electron spin-orbit operators in conjunction with these one-component wave functions to include the effects of spin-orbit coupling is discussed. Applications to molecular systems involving heavy atoms and comparisons with available spectroscopic data on molecular geometries and excitation energies are presented. Finally, a new approach to the construction of RECPS encompassing the Hamiltonian and shapeconsistent approach is presented together with a novel analysis of the long-range behavior of the RECPS .     

Ab initio relativistic effective potentials with spin-orbit operators. VI. Fr through Pu

Ab initio averaged relativistic effective core potentials (AREP ), spin-orbit (SO ) operators, and valence basis sets are reported for the elements Fr through Pu in the form of expansions in Gaussian-type functions. Gaussian basis sets with expansion coefficients for the low-energy states of each atom are given. Atomic orbital energies calculated under the j–j coupling scheme within the self-consistent field approximation and employing the AREP 'S in their unaveraged form (REP 'S) agree to within 10% of orbital energies due to numerical all-electron Dirac–Fock calculations. The accuracy of the AREP 'S and so operators is also shown to be good through comparisons of calculated so splitting energies with all-electron Dirac–Fock results.     

Potential energy curves for ground and excited states of NaLi from ab initio calculations with effective core polarization potentials

Sixteen low-lying electronic states of NaLi are investigated by SCF/valence Cl calculations including core polarization effects by means of an effective potential. Spectroscopic constants are obtained with estimated uncertainties of ΔR_e ? 0.01 Å, Δω_e ? 0.6 cm^?1 and ΔD_e ? 80 cm^?1. From a comparison of experimental and theoretical G(υ) values, we suggest a ground-state dissociation energy of 7093 ± 5 cm^?1. Using our rovibrational energies and recently measured excitation lines, we are able to improve the T_e values and dissociation energies of five excited states to an accuracv of ±8 cm^?1.     

Structures and vibrational frequencies of vanadium (V) oligomers: An ab initio study using effective core potentials

Ab initio molecular geometries and vibrational frequencies of various isolated vanadate species (VO³⁻₄, HVO²⁻₄, H₂VO⁻₄, and V₂O⁴⁻₇) were calculated using different pseudopotentials. The relative merits of these were assessed by comparing the calculated molecular parameters with the corresponding values obtained from calculations at all-electron levels and, whenever available, from X-ray studies for the salts. The calculations were extended to higher oligomers (V₃O⁵⁻₁₀, V₄O⁶⁻₁₃, and V₄O⁴⁻₁₂) using the pseudopotential whose basis functions are (10s5p5d)/[2s1p1d] (55/5/5) on vanadium and (4s4p)/[2s2p] (31/31) on oxygen, which yielded the best compromise between accuracy and computational effort. The results indicate a linear centrosymmetric geometry for the isolated V₂O⁴⁻₇ anion. The higher oligomers have less than 180° V(SINGLE BOND)O(SINGLE BOND)V angles, except the noncyclic tetraoligomer which has a linear central V(SINGLE BOND)O(SINGLE BOND)V angle (180°). The cyclic V₄O⁴⁻₁₂ species presents a planar structure with all the vanadium and bridging oxygen atoms in the same plane. This structure was alrea dy reported for the [(CH₃)CNH₃][V₄O₁₂] salt. The results suggest a lower stability of the linear V₄O⁶⁻₁₃ species, in agreement with previous reports. © 1996 by John Wiley & Sons, Inc.     

A new method for modelling spectator chemical groups in ab initio calculations: effective group potentials

 A new method for an increased numerical efficiency of ab initio calculations is proposed. It is based on the assumption that in most cases chemical properties of functional groups in molecules are mainly controlled by a few electrons. This statement allows one to distinguish between two classes of nuclei and electrons: active and inactive ones. The effective group potential (EGP) method presupposes that the effect of inactive electrons in a functional chemical group can be described by a pseudopotential, in the same way that core electrons are replaced by effective core potentials in atoms. It is shown that EGPs are able to predict chemical and structural features of the active part of a molecule and at a fraction of the ordinary computational cost. The preliminary results reported here concern the determination of EGPs for ammonia, the methyl radical and the cyclopendadienyl ligand, which represent different types of bonding. Received: 15 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Optimized Gaussian basis sets for use with relativistic effective (core) potentials: K,Ca, Ga—Kr

Correlation-consistent valence basis sets were developed for the third-row main block elements (K, Ca, Ga—Kr) for use with relativistic effective core potentials. These basis sets are somewhat larger than double-zeta in size, with polarization functions, and are balanced for use in both Hartree–Fock and correlation calculations. Spin–orbit splittings for atoms and molecules are calculated and compared to experiment. These calculations use the approximate spin–orbit operator from the relativistic effective core potentials. The use of these results in the calculation of accurate thermochemical data is discussed. © 1997 John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

AB initio effective core potentials including relativistic effects. A procedure for the inclusion of spin-orbit coupling in molecular wavefunctions

The first ab initio procedure for the treatment of spin-orbit coupling in molecules based on the use of relativistic effective potentials derived from Dirac-Fock atomic wavefunctions is presented. A rigorous definition for the spin-orbit operator is given and its use in molecular calculations discussed.     

Core-valence correlation effects for molecules containing first-row atoms. Accurate results using effective core polarization potentials

The accuracy of employing effective core polarization potentials (CPPs) to account for the effects of core-valence correlation on the spectroscopic constants and dissociation energies of the molecules B₂, C₂, N₂, O₂, F₂, CO, CN, CH, HF, and C₂H₂ has been investigated by comparison to accurate all-electron benchmark calculations. The results obtained from the calculations employing CPPs were surprisingly accurate in every case studied, reducing the errors in the calculated valence D _e values from a maximum of nearly 2.5 kcal/mol to just 0.3 kcal/mol. The effects of enlarging the basis set and using higher-order valence electron correlation treatments were found to have only a small influence on the core-valence correlation effect predicted by the CPPs. Thus, to accurately recover the effects of intershell correlation, effective core polarization potentials such as the ones used in the present work provide an attractive alternative to carrying out computationally demanding calculations where the core electrons are explicitly included in the correlation treatment. Received: 11 May 1998 / Accepted: 27 July 1998 / Published online: 28 October 1998     

Use of the normal coordinates in variational and perturbative ab initio handling of the vibronic and spin–orbit couplings in Π electronic states of linear tetra‐atomic molecules

Avariational and a perturbative approach are developed to handle the combined effect of the vibronic and spin–orbit couplings in Π electronic states of tetra‐atomic molecules with linear equilibrium geometry. Both of them are based on the use of the normal vibrational bending coordinates. The perturbative treatment is carried out via two schemes for partition of the model Hamiltonian: In the first, the spin–orbit coupling term is treated as a perturbation; in the second, it is included in the zeroth‐order Hamiltonian. It is demonstrated that both perturbative approaches lead to the same second‐order formulae when the spin–orbit coupling constant is small compared to the bending frequency, but much larger than the splitting of potential surfaces upon bending. These approaches are used to calculate the vibronic and spin–orbit structure in the X²Π electronic state of HCCS by employing the ab initio‐computed potential energy surfaces. Complete numerical equivalence of the results obtained with the present variational approach and those generated by the algorithms employing internal vibrational coordinates is demonstrated. The restrictions concerning the applicability of the perturbative approaches are discussed in terms of the agreement between the results obtained by means of them with those generated in the corresponding variational computations. The general reliability of the model employed is checked by comparing the theoretical results with the available experimental data. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Accounting for correlations with core electrons by means of the generalized relativistic effective core potentials: atoms Hg and Pb and their compounds

A way to account for correlations between the chemically active (valence) and innermore (core) electrons in the framework of the generalized relativistic effective core potential (GRECP) method is suggested. The "correlated" GRECP's (CGRECP's) are generated for the Hg and Pb atoms. Only correlations for the external 12 and 4 electrons of them, correspondingly, should be treated explicitly in the subsequent calculations with these CGRECP's whereas the innermore electrons are excluded from the calculations. Results of atomic calculations with the correlated and earlier GRECP versions are compared with the corresponding all-electron Dirac-Coulomb values. Calculations with the above GRECP's and CGRECP's are also carried out for the lowest-lying states of the HgH molecule and its cation and for the ground state of the PbO molecule, as compared to earlier calculations and experimental data. The accuracy for the vibrational frequencies is increased up to an order of magnitude and the errors for the bond lengths (rotational constants) are decreased in about two times when the correlated GRECP's are applied instead of earlier GRECP versions employing the same innercore-outercore-valence partitioning.     

Theoretical determination of the X 2Σ+ and A 2Π potentials of CsO using relativistic effective core potentials

Theoretical potential energy curves are computed for the X ²Σ⁺ and A ²Π states of CsO using a relativistic effective core potential and a large valence Gaussian basis set. Seventeen electrons are correlated by a CI (SD ) calculation from each HF reference. We find the X ²Σ⁺ state lower by 497 and 726 cm^?1 at the HF and CI(SD) levels. Our calculated ω_e of 312 cm^?1 for the X ²Σ⁺ state agrees well with experimental values deduced from studies in matrices.     

Optimized Gaussian basis sets for use with relativistic effective (core) potentials: Li?Ar

Balanced atomic basis sets, at the double-zeta level with d functions, have been developed for the elements Li? Ar within the relativistic effective core potential procedure. The number of primitive functions, their orbital exponents, and the number of contractions were chosen for use in both Hartree–Fock and correlated calculations. Spin-orbit splittings have been obtained using the approximate operator corresponding to relativistic effective potentials and are compared with experimental values.     

A local density functional—LCAO method with effective potentials for obtaining the electronic structure of molecules and clusters

The introduction of effective core potentials into the Xα LCAO method can greatly expand the size of the molecular system which may be feasibly treated. Therefore, we have incorporated norm-conserving effective potentials into this framework, using a gaussian basis set, for calculations of the electronic structure of molecules and cluster models of solids and surfaces. This combined methodology makes possible the determination of equilibrium geometries and certain aspects of potential surfaces required for a large class of electronic structure problems.