Use In Molecular Calculations Research Articles

Improved valence basis sets for divalent lanthanide 4f-in-core pseudopotentials

Improved energy-optimized (6s5p4d) and (7s6p5d) primitive valence basis sets have been derived for energy-consistent scalar-relativistic 4f-in-core pseudopotentials of the Stuttgart-Cologne variety modeling divalent lanthanides with a \(4\hbox{f}^{n+1}\) occupation (n = 0–13 for La–Yb). Segmented contracted basis sets covering the range of polarized double-, triple-, and quadruple-zeta quality, augmented by 2f1g correlation sets, were created for use in molecular calculations. The basis sets contain smaller (4s4p3d) and (5s5p4d) primitive subsets, which are designed in particular for solid state calculations of crystals containing divalent lanthanide ions. Hartree–Fock, density functional theory and coupled cluster results obtained with the new basis sets for lanthanide atomic ionization potentials as well as of geometry optimizations of various test molecules, i.e. selected lanthanide mono- and dihydrides, mono- and difluorides, and monooxides, show a satisfactory agreement with experimental data as well as with corresponding scalar-relativistic all-electron results. Core-polarization potentials are found to improve the results, especially for the atomic first and second ionization potentials.

Energy-consistent pseudopotentials for group 11 and 12 atoms: adjustment to multi-configuration Dirac–Hartree–Fock data

Abstract Two-component relativistic pseudopotentials (i.e., scalar-relativistic and spin–orbit (SO) potentials) of the energy-consistent variety have been adjusted for the group 11 and 12 atoms Cu, Zn; Ag, Cd; Au, Hg, replacing the 1s–2p; 1s–3d; and 1s–4f cores, respectively. The adjustment has been done for the valence-energy spectrum of (near-)neutral atoms, to reference data from numerical all-electron four-component multi-configuration Dirac–Hartree–Fock (MCDHF) calculations, including the two-electron Breit interaction. For use in molecular calculations, the potentials have been supplemented by energy-optimized (12s12p9d3f2g)/[6s6p4d3f2g] valence basis sets. First benchmark applications of the potentials and basis sets are presented for atomic excitation energies and SO splittings at a correlated level, and for ground and excited state spectroscopic properties of group 11 monohalides and group 12 dimers.

Energy-adjustedab initio pseudopotentials for the second and third row transition elements

Nonrelativistic and quasirelativisticab initio pseudopotentials substituting the M(Z−28)+-core orbitals of the second row transition elements and the M(Z−60)+-core orbitals of the third row transition elements, respectively, and optimized (8s7p6d)/[6s5p3d]-GTO valence basis sets for use in molecular calculations have been generated. Additionally, corresponding spin-orbit operators have also been derived. Atomic excitation and ionization energies from numerical HF as well as from SCF pseudopotential calculations using the derived basis sets differ in most cases by less than 0.1 eV from corresponding numerical all-electron results. Spin-orbit splittings for lowlying states are in reasonable agreement with corresponding all-electron Dirac-Fock (DF) results.

Energy-adjusted pseudopotentials for the rare earth elements

Nonrelativistic and quasirelativistic energy-adjusted pseudopotentials and optimized (7s6p5d)/[5s4p3d]-GTO valence basis sets for use in molecular calculations for fixed f-subconfigurations of the rare earth elements, La through Lu, have been generated. Atomic excitation and ionization energies from numerical HF, as well as SCF pseudopotential calculations using the derived basis sets, differ by less than 0.1 eV from numerical HF all-electron results. Corresponding values obtained from CI(SD), CEPA-1, as well as density functional calculations using the quasirelativistic pseudopotentials, are in reasonable agreement with experimental data.

Optimized Gaussian basis sets for excited states of Ar, Ar + and He

Gaussian basis sets for use in molecular calculations are optimized for electronic states which possess partial occupation of the 3 s, 3 p, 3 d, 4 s and 4 p shells in argon and its positive ion. The significant influence of d polarization/correlation functions is discussed and it is shown that various 3 d-type functions are necessary for a proper description of 3 d-excitations. Rydberg-like functions are sufficiently different in the neutral and ionic system so that separate exponents are necessary. Contraction of d-type functions is possible without loss of accuracy but considerable saving in computer cost. Numerous Ar and Ar + states are calculated in the final AO basis recommended for molecular calculations which include argon atoms and ions; it consists of 14 s, 10 p, 5 d Gaussians in an (8 s, 6 p, 4 d) contraction. Gaussian functions for a number of Rydberg states up to 4 s, 3 p and 3 d in helium are optimized; the corresponding excited states evaluated in an AO basis in the (8 s, 4 p, 1 d) contraction show very good agreement with measured data.

Energy-adjusted a b i n i t i o pseudopotentials for the first row transition elements

Nonrelativistic and quasirelativistic ab-initio pseudopotentials representing the Ne-like X(Z−10)+ cores (X=Sc–Zn) of the first row transition metals and optimized (8s7p6d1f )/[6s5p3d1f ]-GTO valence basis sets for use in molecular calculations have been generated. Excitation and ionization energies of the low lying states of Sc through Zn from numerical HF- as well as SCF- and CI(SD)-pseudopotential calculations using the derived basis sets differ by less than 0.1 eV from corresponding all-electron results.

Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals

Ab initio effective core potentials (ECP’s) have been generated to replace the innermost core electron for third-row (K–Au), fourth-row (Rb–Ag), and fifth-row (Cs–Au) atoms. The outermost core orbitals—corresponding to the ns2np6 configuration for the three rows here—are not replaced by the ECP but are treated on an equal footing with the nd, (n+1)s and (n+1)p valence orbitals. These ECP’s have been derived for use in molecular calculations where these outer core orbitals need to be treated explicitly rather than to be replaced by an ECP. The ECP’s for the forth and fifth rows also incorporate the mass–velocity and Darwin relativistic effects into the potentials. Analytic fits to the potentials are presented for use in multicenter integral evaluation. Gaussian orbital valence basis sets are developed for the (3s, 3p, 3d, 4s, 4p), (4s, 4p, 4d, 5s, 5p), and (5s, 5p, 5d, 6s, 6p) ortibals of the three respective rows.

Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi

A consistent set of ab initio effective core potentials (ECP) has been generated for the main group elements from Na to Bi using the procedure originally developed by Kahn. The ECP’s are derived from all-electron numerical Hartree–Fock atomic wave functions and fit to analytical representations for use in molecular calculations. For Rb to Bi the ECP’s are generated from the relativistic Hartree–Fock atomic wave functions of Cowan which incorporate the Darwin and mass–velocity terms. Energy-optimized valence basis sets of (3s3p) primitive Gaussians are presented for use with the ECP’s. Comparisons between all-electron and valence-electron ECP calculations are presented for NaF, NaCl, Cl2, Cl2−, Br2, Br2−, and Xe2+. The results show that the average errors introduced by the ECP’s are generally only a few percent.

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.

An optimum minimal basis of exponential atomic orbitals

An analysis of some of the energetic properties of the conventional minimal STO basis is used to suggest a new optimum set of exponential functions for use in molecular calculations.

Unconventional basis sets in quantum mechanical calculations

Recent years have seen the introduction of several new and sophisticated basis sets in quantum mechanical calculations. Most applications of these basis sets have been to atomic systems, but since modern computing technology makes numerical integration a feasible alternative to analytical integration, they may be attractive for use in molecular calculations as well. In this paper we investigate six of these sets for approximating the ground-state wave-function of the hydrogen molecule. We conclude, on the basis of accuracy and computational time, that the traditional Slater type orbital (particularly with non-integer-n) still gives the best value for money.

Ab Initio Effective Potentials for Use in Molecular Calculations

We have investigated the efficacy of ab initio effective potentials in replacing the core electrons of atoms for use in molecular calculations. The effective potentials are obtained from ab initio GI calculations on atoms and are unique and local. We find that the use of these effective potentials to replace the core orbitals of such molecules as LiH, Li2, BH, or LiH2, leads to wavefunctions in excellent agreement with all-electron ab initio results. The use of such effective potentials should allow ab initio quality wave-functions to be obtained for systems too large for the ab initio consideration of all the electrons.

Gaussian Basis Functions for Use in Molecular Calculations. IV. The Representation of Polarization Functions for the First Row Atoms and Hydrogen

The representation of polarization functions for the first row atoms and hydrogen is investigated by means of Hartree—Fock calculations on the water and nitrogen molecules. It is found that a two-term Gaussian expansion is required to adequately represent the 3d polarization functions of the first row atoms, whereas for the 2p polarization functions of hydrogen, a single Gaussian function is sufficient. The interaction of oxygen and hydrogen polarization functions in the water molecule is briefly discussed.

Gaussian Basis Functions for Use in Molecular Calculations. III. Contraction of (10s6p) Atomic Basis Sets for the First-Row Atoms

Contracted [5s3p] and [5s4p] Gaussian basis sets for the first-row atoms are derived from the (10s6p) primitive basis sets of Huzinaga. Contracted [2s] and [3s] sets for the hydrogen atom obtained from primitive sets ranging in size from (4s) to (6s) are also examined. Calculations on the water and nitrogen molecules indicate that such basis sets when augmented with suitable polarization functions should yield wavefunctions near the Hartree–Fock limit.

Gaussian basis functions for use in molecular calculations. Contraction of (12s9p) atomic basis sets for the second row atoms

The contraction of the (12s9p) primitive basis sets of Veillard for the second row atoms is investigated. Contracted [7s], [6s], [5p], and [4p] basis sets are proposed. The [6s4p] contracted set gives a Hartree-Fock energy of −459.1706 au for the ground state of the chlorine atom. This is a substantial improvement over results previously reported for contracted gussian basis sets, even those obtained with much larger primitive sets.

Gaussian Basis Functions for Use in Molecular Calculations. I. Contraction of (9s5p) Atomic Basis Sets for the First-Row Atoms

The contraction of Gaussian basis functions for use in molecular calculations is investigated by considering the effects of contraction on the energies and one-electron properties of the water and nitrogen molecules. The emphasis is on obtaining principles which can be used to predict optimal contraction schemes for other systems without the necessity of such exhaustive calculations. Using these principles, contractions are predicted for the first-row atoms.

Self-Consistent Molecular-Orbital Methods. I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals

Least-squares representations of Slater-type atomic orbitals as a sum of Gaussian-type orbitals are presented. These have the special feature that common Gaussian exponents are shared between Slater-type 2s and 2p functions. Use of these atomic orbitals in self-consistent molecular-orbital calculations is shown to lead to values of atomization energies, atomic populations, and electric dipole moments which converge rapidly (with increasing size of Gaussian expansion) to the values appropriate for pure Slater-type orbitals. The ζ exponents (or scale factors) for the atomic orbitals which are optimized for a number of molecules are also shown to be nearly independent of the number of Gaussian functions. A standard set of ζ values for use in molecular calculations is suggested on the basis of this study and is shown to be adequate for the calculation of total and atomization energies, but less appropriate for studies of charge distribution.

Gaussian Lobe Function Expansions of Hartree—Fock Solutions for the First-Row Atoms and Ethylene

Gaussian expansions of ground-state Hartree—Fock solutions for the first-row atoms are determined by a self-consistent-field minimization of atomic energies. Wavefunctions are constructed from a basis set designed primarily for use in molecular calculations which consists only of functions of the form exp(—ar2). Angular dependence is achieved by defining origins for the basis functions at points in space determined in part by the symmetry of the orbital to be expanded. A use of atomic information in molecular problems is discussed in a SCF treatment of the ethylene molecule.