Quasirelativistic energy-consistent 5f-in-core pseudopotentials for divalent and tetravalent actinide elements

Quasirelativistic energy-consistent 5f-in-core pseudopotentials modeling divalent (5f ⁿ⁺¹ occupation with n = 5–13 for Pu–No) respectively tetravalent (5f ^n-1 occupation with n = 1–9 for Th–Cf) actinides together with corresponding core-polarization potentials have been generated. Energy-optimized (6s5p4d) and (7s6p5d) valence basis sets as well as 2f1g correlation functions have been derived and contracted to polarized double, triple, and quadruple zeta quality. Corresponding smaller (4s4p) and (5s5p) respectively (4s4p3d) and (5s5p4d) basis sets suitable for calculations on actinide(II) respectively actinide(IV) ions in crystalline solids form subsets of these basis sets designed for calculations on molecules. Results of Hartree–Fock test calculations for actinide di- and tetrafluorides show a satisfactory agreement with calculations using 5f-in-valence pseudopotentials. Electronic Supplementary Material The online version of this article doi: contains supplementary material, which is available to authorized users.     

Optimization of Gaussian basis sets for Dirac-Hartree-Fock calculations

We investigate the optimization of Gaussian basis sets for relativistic calculations within the framework of the restricted Dirac-Hartree-Fock (DHF) method for atoms. We compare results for Rn of nonrelativistic and relativistic basis set optimizations with a finite nuclear-size. Optimization of separate sets for each spin-orbit component shows that the basis set demands for the lower j component are greater than for the higher j component. In particular, the p _1/2 set requires almost as many functions as the s _1/2 set. This implies that for the development of basis sets for heavy atoms, the symmetry type for which a given number of functions is selected should be based on j, not on l, as has been the case in most molecular calculations performed to date.     

Fully relativistic calculations of ThF4

Based on the results of first‐principles density functional theory calculations of the electronic structure of ThF₄ in solid state and molecular form, the study of the Th6p, 5f, 6d, 7s and F2s, 2p states was done. We used the fully relativistic cluster discrete variational method with the local exchange‐correlation potential. The hybridization of F2p and Th5f, 6d, 7s, 7p states in the valence molecular orbitals (VMOs) in the region 0–10 eV and of F2s and Th6p states in the inner valence molecular orbitals (IVMOs) in the region 10–50 eV was studied. The results of relativistic cluster calculations are compared with those obtained for ThF₄ molecule. The energies of ionization of VMOs and of IVMOs were evaluated on the basis of the ground‐state and Slater's transition‐state calculations. The MO energy levels provide a satisfactory interpretation of experimental photoelectron spectra. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Self-consistent relativistic effective core potentials for transition metal atoms: Cu,Ag, and Au

A development of the RECP method for the case of transition and rare earth elements is suggested. New terms with projectors on the occupation numbers ofd andf outermost shells respectively (which can be determined in SCF iterations) are added to the standard RECP operator and the corresponding self-consistent RECP terms are generated for atoms Cu, Ag and Au. Significant improvement is achieved in reproduction of atomic excitation energies as compared with the conventional shape-consistent RECP calculation.     

Core and valence electrons in atoms and ions: configuration interaction calculations

Summary The partitioning of ground-state atoms or ions into inner spherical cores with radius _b and outer valence regions extending from _b to infinity is explored with the help of the expression for the valence-region energy (where T ^v and V ^v are, respectively, the kinetic and potential energies of the valence electrons N ^v found beyond the boundary surface defined by _b) using also the appropriate expression for E ^ion, the energy of the ion left behind after removal of the valence electrons. E ^v and E ^ion are meaningful only for discrete numbers, N ^c, of electrons assigned to the core, namely, when the exchange integrals, K ^cv, between N ^c and N ^v total (or at least closely approach) 0, i.e., for N ^c = 2 e or N ^c = 2 and 10 e for the first- or second-row elements, respectively.Part of the projected Ph.D. dissertation of N. D.     

A diagrammatic valence bond method for configuration interaction calculations in atoms and molecules

A diagrammatic valence bond method based on Rumer-Pauling rules for configuration interaction calculations is described. The advantages of this method are that it is simple and flexible and is expected to be computationally efficient as the basis functions can be coded as increasing integers. Evaluation of Hamiltonian matrix elements involves simple bit manipulations and binary searches. The basis, being represented pictorially, should also help in utilizing spatial symmetries for further block-diagonalizing the Hamiltonian matrix. The eigenfunctions of the Hamiltonian can also be used to compute matrix elements between different electronic states.     

Energy-adjustedab initio pseudopotentials for the second and third row transition elements: Molecular test for M2 (M=Ag,Au) and MH (M=Ru,Os)

Summary Recently published nonrelativistic and quasirelativistic energy-adjustedab initio pseudopotentials representing the M^(Z–28)+ cores of the second row transition metal atoms and the M^(Z–60)+ cores of the third row transition metal atoms have been tested in SCF, CI(SD) and CEPA1 calculations of the spectroscopic constants (R _e ,D _e , and _e ) of the ground states of the neutral and singly charged silver and gold dimers, and in state averaged CASSCF and multi-reference CI(SD) calculations of the spectroscopic constants (R _e ,D _e , _e , _e , /R). Comparison is made with experimental and reliable theoretical data where available; in the case of the hydrides, additional calculations with pseudopotentials published by other groups have been made for comparison.     

General variation method for the relativistic calculations of atoms and molecules

Use of the general variation method of Weinstein and MacDonald for the relativistic calculation of atoms and molecules is proposed. It is shown from the numerical calculations for hydrogenlike atomic systems that this method is useful in judging an accuracy of energies and wave functions obtained with a relativistic Hamiltonian whose spectra are not bounded. It is also shown that this method can be used to find spurious solutions such as 1p_½ or 2d_3/2 appearing in atomic systems. Problems in extending the method to many-electron atoms and molecules are discussed.     

Multireference configuration interaction calculations for complexes of positronium and B, C, N, and O atoms

Positronium (Ps) binding energies for complexes of Ps and atoms with open shell electrons, PsX (X=B, C, N, and O), are calculated using the multireference singly and doubly excited configuration interaction (MRSDCI) method. The effectiveness of this method for the complexes is verified. The MRSDCI calculations are carried out with a frozen-core approximation so as to incorporate only the most important valence correlation effects. Many-body correlation effects and contributions from higher angular momentum orbitals are estimated by extrapolation techniques. The resulting Ps binding energies agree well with the results of diffusion Monte Carlo simulations by Bressanini et al. (Phys Rev A 57:1678,1998) and by Jiang and Schrader (J Chem Phys 109:9430,1998). For PsO the Ps binding energy obtained by Jiang and Schrader is about 1.8 times larger than that of Bressanini et al.; the present calculated value is close to that of Jiang and Schrader.     

An application of correlation energy density functionals to atoms and molecules

Four density functionals — including that recently introduced by Perdew ((1986) Phys Rev B33: 8822)—are tested for first-row atoms, hydrides and dimers. Calculated contributions of the correlation energy to the ionization potentials and electron affinities of atoms and to the dissociation energies of molecules are compared with empirical values which were reevaluated for this purpose. An improvement over Hartree-Fock is found in all cases if the self-interaction or the gradient correction are included in the density functional, although there is a rather large variation in the accuracy of the predictions.     

A combination of quasirelativistic pseudopotential and ligand field calculations for lanthanoid compounds

Summary Improved energy-adjusted quasirelativistic pseudopotentials for lanthanoid atoms with fixed valency are presented and tested in molecular calculations for CeO, CeF, EuO, GdO, YbO, and YbF. The pseudopotential calculations treat the lanthanoid 4f shell as part of the core and yield accurate estimates for average bond lengths, vibrational frequencies and dissociation energies of all states belonging to a superconfiguration. Information for each individual state of the considered superconfiguration may be obtained from subsequent ligand field model calculations. The results of this combined pseudo-potential and ligand field approach (PPLFT) are compared to more accurate calculations with ab initio pseudopotentials that include the lanthanoid 4f orbitals explicitly in the valence shell and to available experimental data.     

Variational Monte Carlo calculations for some cations and anions of the first‐row atoms using explicitly correlated wave functions

The variational Monte Carlo method is applied to calculate ground‐state energies of some cations and anions of the first‐row atoms. Accurate values providing between 80 and 90% of the correlation energy are obtained. Explicitly correlated wave functions including up to 42 variational parameters are used. The nondynamic correlation due to the 2s ? 2p near degeneracy effect is included by using a multideterminant wave function. The variational free parameters have been fixed by minimizing the energy that has shown to be a more convenient functional than the variance of the local energy, which is the most commonly employed method in variational Monte Carlo calculations. The energies obtained improve previous works using similar wave functions. © 2002 Wiley Periodicals, Inc.; DOI 10.1002/qua.10125     

Electronic structures and bonding of CeF: a frozen-core four-component relativistic configuration interaction study

We study the electronic structure of the ground and several low-lying states of the CeF molecule using Dirac-Fock-Roothaan (DFR) and four-component relativistic single and double excitation configuration interaction (SDCI) calculations in the reduced frozen-core approximation (RFCA). The ground state and two low-lying excited states are calculated to have (4f)1(5d)1(6s)1 configurations with Omega = 3.5, 4.5, and 3.5, and the resulting excitation energies, T0, are, respectively, 0.319 and 0.518 eV. The experimental configurations for these states are the same, although the experimental T0 values are approximately 0.3 eV smaller than those calculated. Experimentally, the red-degraded band was observed to be 2.181 eV above the ground state, having the configuration (4f)1(5d)1(6p)1 with Omega = 4.5. The calculation for this state gives 2.197 eV and configuration (4f)1.0(5d)1.7(6p)0.3 with Omega = 4.5. We found that Omega, Re, and nu(1-0) obtained by CI agree well with experiment. Bonding between the Ce and the F is highly ionic. The 4f, 5d, and 6s valence electrons are localized at the Ce+ ion, because they are attracted by the Ce4+ ion core, and are excluded from the bonding region because of the electronic cloud around the negatively charged fluoride anion. The bonding in the ground and excited states of the CeF molecule is significantly influenced by the 6s and 5d electron distributions between the Ce and the F.     

A comparison of variational and non-variational internally contracted multiconfiguration-reference configuration interaction calculations

Summary The internally contracted multiconfiguration-reference configuration interaction (CMRCI) method and several non-variational variants of this method (averaged coupled pair approximation (ACPF), quasidegenerate variational perturbation theory (QD-VPT), linearized coupled pair many electron theory (LCPMET)) have been employed to compute potential energy functions and other properties for a number of diatomic molecules (F₂, O₂, N₂, CN, CO) using large basis sets and full valence CASSCF reference wavefunctions. In most cases the variational CMRCI wavefunctions yield more accurate spectroscopic constants than any of the employed non-variational methods. Several basis sets are compared for the N₂ molecule. It is found that atomic natural orbital (ANO) contractions led to significant errors in the computedr _e , _e , andD _e values.     

The quest for best suited references for configuration interaction singles calculations of core excited states

Near edge X‐ray absorption fine structure (NEXAFS) simulations based on the conventional configuration interaction singles (CIS) lead to excitation energies, which are systematically blue shifted. Using a (restricted) open shell core hole reference instead of the Hartree Fock (HF) ground state orbitals improves (Decleva et al., Chem. Phys., 1992, 168, 51) excitation energies and the shape of the spectra significantly. In this work, we systematically vary the underlying SCF approaches, that is, based on HF or density functional theory, to identify best suited reference orbitals using a series of small test molecules. We compare the energies of the K edges and NEXAFS spectra to experimental data. The main improvement compared to conventional CIS, that is, using HF ground state orbitals, is due to the electrostatic influence of the core hole. Different SCF approaches, density functionals, or the use of fractional occupations lead only to comparably small changes. Furthermore, to account for bigger systems, we adapt the core‐valence separation for our approach. We demonstrate that the good quality of the spectrum is not influenced by this approximation when used together with the non‐separated ground state wave function. Simultaneously, the computational demands are reduced remarkably. © 2016 Wiley Periodicals, Inc.     

The use of average natural orbitals for configuration interaction calculations on the Boron Hydride molecule

The use of average natural orbitals is compared to some better known methods of performing limited and restricted CI calculations. It is found that a moderately extensive restricted valence shell CI computation using a subset of these orbitals is an efficient and accurate method for the calculation of state wavefunctions. Total and electronic excitation energies have been calculated for the BH molecule.Taken in part from a Ph. D. thesis submitted to the University of Toronto in 1971.     

Electronic structure and relative stability of 1:1 Cu-O2 adducts from difference-dedicated configuration interaction calculations

A computational strategy to analyze Cu-O(2) adducts based on the use of difference-dedicated configuration interaction (DDCI) calculations is presented. The electronic structure, vertical gaps and nature of the metal-O(2) interaction, and the extension of the charge transfer between both fragments have been investigated. Relative stabilities between isomers are determined from triplet states CCSD(T) calculations. The key point of the here proposed strategy rests on the use of a rationally designed active space, containing only those orbitals, which optimize the interaction pathways between LCu and O(2) fragments. The procedure has been tested on a broad set of model and synthetic biomimetic systems, the results compared with previous theoretical evaluations and/or available experimental data. Our study indicates that this strategy can be considered as an alternative approach to multireference second-order perturbation theory methods to deal with this type of systems with remarkable biradical nature.