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.     

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.     

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 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.     

Outer- and inner-valence satellites of carbon dioxide: electron momentum spectroscopy compared with symmetry-adapted-cluster configuration interaction general-R calculations

The extensive study of outer- and inner-valence satellites of carbon dioxide by electron momentum spectroscopy is reported. The experiments have been performed using a high-sensitivity electron momentum spectrometer employing non-coplanar symmetric geometry at impact energy of about 1200 eV. Binding energy spectrum up to 50 eV, above the first double ionization threshold (~37.3 eV), is presented. Four main peaks and twelve satellites have been identified including four embedded in the double ionization continuum, among which the two beyond 42 eV are observed for the first time. High accuracy symmetry-adapted-cluster configuration interaction general-R calculation with aug-cc-pVTZ basis sets has also been performed and the result is in line with the experimental ionization spectrum except the relative intensities for some of the satellites in inner-valence region. The experimental momentum profiles for both the main ionization transitions and satellites have been obtained and compared with theoretical calculations by HF and B3LYP methods with 6-311++G? and aug-cc-pVTZ basis sets. Through comparison, the detailed assignments of the satellite bands have been achieved and the pole strengths for the relevant shake-up transitions are determined experimentally for the first time.     

A simulation of the exchange potential in unrestricted and restricted Hartree-Fock calculations studied on atoms

The spherical average of the Hartree-Fock exchange potential depending on each spin orbital is compared with Slater's exchange potential, V _xs, as demonstrated for the phosphorus atom. It is shown that the former potential can be simulated by (a + br)V _xs, where r is the radius and the constants a and b are calculated for each spin orbital. This simulation is tested for the iron atom and it is found that the results agree well with those obtained from unrestricted and restricted Hartree-Fock calculations, respectively. The applicability of this new method in energy band structure calculations is briefly discussed.Dedicated to Professor H. Hartmann on the occasion of his 65th birthday.     

Extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms. I. Methodological developments

An extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms is presented. In addition to the use of pseudo-potentials in the calculations, the consequences of this extension on the different components of the energy partition which is the basic idea of the method, is analysed. Particular emphasis is placed on the specific role played by the 3d orbitals in each of the energy components. First, at the zeroth order, the energy is found to be very sensitive to the optimization of the 3d polarization functions. Secondly, the internal correlation energy, calculated by CI, requires the optimization of distinct 3d correlation orbitals to describe adequately the strong near-degeneracy effects that occur within the valence space. Finally it is shown that the 3d orbitals contribute partially to the non-internal correlation energy and that, the atoms-in-molecule structures corresponding typically to all-external contributions are negligible. The concept of error energy is introduced in place of the non-internal correlation energy: it includes the relativistic contributions within the semi-empirical tables. Such tables are presented for second row atoms and for the chlorine atom. From these tables, predicted values for some atomic term energies, experimentally undetermined, are derived. The methodological tests are limited here to the chlorine atom which is chosen for further applications in the next paper of this series. The conclusions concerning the applicability of the method to third row atoms are however quite general.Boursier I.R.S.I.A     

Semiempirical and ab initio calculations on the alkaline hydrolysis of the β-lactam ring Influence of the solvent

We used semiempirical and ab initio calculations to investigate the nucleophilic attack of the hydroxyl ion on the β-lactam carbonyl group. Both allowed us to detect reaction intermediates pertaining to proton-transfer reactions. We also used ab initio calculations and the PM3 semiempirical method to investigate the influence of the solvent on the process. The AMSOL method predicts the occurrence of a potential energy barrier of 20.7 kcal mol⁻¹ due to the desolvation of the hydroxyl ion in approaching the β-lactam carbonyl group. Using the supermolecular approach and a water solvation sphere of 20 molecules around the solute, the potential energy barrier is lowered to 17.5 kcal mol⁻¹. Ab initio calculations using the SCRF method predict a potential energy barrier of 13.6 kcal mol⁻¹. These three values, especially the last two, are very close to the experimental value of 16.7 kcal mol⁻¹.