The ellipsoidal gaussian basis in molecular orbital theory

New analytic integral formulas are presented for the potential energy integrals over ellipsoidal Gaussian basis functions [ exp (-x² - y² - z²)] that enter into solving the conventional expansion self-consistent field equations. Near minimal atomic orbital bases combined from large nuclear-centered primitive Gaussian sets are used in test calculations on the HF and CO molecules. The ellipsoidal exponential parameters for the valence atomic orbitals are fully optimized using a single scale factor for each atomic orbital and nuclear coordinate. The results are compared with those obtained using an unoptimized nuclear centered double-zeta spherical Gaussian basis.     

Expansion of linear combinations of slater-type orbitals in eigenfunctions of the three-dimensional isotropic harmonic oscillator

Several classes of functions related to the Gaussian have been used with success as basis sets for the representation of atomic and molecular orbitals. We have compared the representation of a hydrogen 1s orbital by a sum of Gaussian lobe functions with its expansion in eigenfunctions of the three-dimensional isotropic harmonic oscillator. The lobe functions are shown to achieve better expectation values of the energy, with fewer terms. The lobe functions have the further computational advantage of not containing high powers of the radius. It is concluded that the lobe functions are a superior basis set for use in calculations of the electronic structure of atoms and molecules.     

Compact basis sets for LCAO-LSD calculations. Part II: Tests for Cr2 and Ni4

The compact orbital and auxiliary basis sets for LCAO-LSD calculations introduced in Part I are tested in molecular calculations on Cr₂ and Ni₄. The present results for spectroscopic constants and valence orbital energies obtained using medium size orbital expansions with a double-zeta representation for valence orbitals are in very good agreement with those previously calculated with very extended sets. Since the computational time of the present calculations is reduced severalfold compared with the extended basis set calculations, the present basis sets allow increased efficiency of the LCAO-LSD calculations and allow the method to be extended to larger systems.     

Newly developed basis sets for density functional calculations

Optimized contracted Gaussian basis sets of double-zeta valence polarized (DZVP) quality for first-row transition metals are presented. The DZVP functions were optimized using the PWP86 generalized gradient approximation (GGA) functional and the B3LYP hybrid functional. For a careful analysis of the basis sets performance the transition metal atoms and cations excitation energies were calculated and compared with the experimental ones. The calculated values were also compared with those obtained using the previously available DZVP basis sets developed at the local-density functional level. Because the new basis sets work better than the previous ones, possible reasons of this behavior are analyzed. The newly developed basis sets also provide a good estimation of other atomic properties such as ionization energies.     

Study of the quality of Gaussian basis sets for carbon and silicon: Calculations on methane and silane

A number of Gaussian basis sets for carbon and silicon have been examined in terms of the one-electron properties of methane and silane. The convergence of the properties to their limiting values is not monotonic but, in general, a representation that involves five Gaussian functions per occupied atomic orbital on the heavy atom is sufficient to closely approach the limits. A relationship between the sizes and partitioned electronic energies is shown to hold to a good approximation for the Boys spatially localized molecular orbitals employed in this study.     

Ab initio calculations on large molecules using molecular fragments. Generalization of the molecular fragment basis at the minimum basis set level

By determining basis set parameters in molecular environments using other criteria than total energy, it is shown that a generalization of the molecular fragment basis can be obtained in which calculated geometric and electronic structural properties are predicted substantially better than with other basis sets of similar size. As a first step in the development of a series of basis sets having successively greater flexibility and accuracy, several single-zeta basis sets are created, using a two-Gaussian contraction for each basis orbital. The best of these basis sets produced calculated geometric and electronic properties for a series of molecules that model a wide variety of organic molecules that are of better accuracy than the corresponding STO -2G basis, and similar in most cases to STO -3G. In addition, the basis set is shown to be applicable in either a Cartesian Gaussian basis or a floating spherical Gaussian basis.     

Binding energies at different momenta for the valence orbitals of HCl by the binary (e, 2e) method

The binding energy spectra for the valence orbitals of hydrogen chloride have been obtained using the binary (e,2e) method at 1200 eV. The strength of the innermost valence orbital (4σ) is severely split among several ion states in the energy range 25 to 41 eV. The measured cross sections are compared with results of calculations using contracted Gaussian basis sets of double-zeta quality, and with a one-particle Green's function calculation.     

Compact contracted Gaussian-type basis sets for halogen atoms. Basis-set superposition effects on molecular properties

Compact, contracted Gaussian basis sets for halogen atoms are generated and tested in ab initio molecular calculations. These basis sets have similar structure to that of Huzinaga and co-workers' (HTS ) sets; however, they give both better atomic total energies and better properties of atomic valence orbitals. These sets, after splitting of valence orbitals and augmenting with polarization functions, provide molecular results that agree well with those given by extended calculations. Basis set superposition error (BSSE ) is calculated using the counterpoise method. BSSE has only slight influence on calculated equilibrium geometry, shape of potential curve, and electric properties (dipole and quadrupole moments) of molecules. However, atomization energies may be significantly changed by the BSSE .     

Calculation of molecular integrals for systems confined by hard spherical walls: Use of the single‐center expansion of floating spherical gaussians

Assuming a gaussian basis set representation of atomic and molecular wave functions, the single‐center expansion of off‐centered spherical gaussian orbitals is exploited to calculate the one and two‐electron integrals for multielectronic atoms and molecules confined within hard spherical walls. As a validating test, the ground‐state energy of a helium atom positioned off‐center in a spherical box is calculated by applying the simplest form of the floating spherical gaussian orbital (FSGO) scheme, i.e., the use of a primitive basis set consisting of a single FSGO per electron pair. Comparison with corresponding recent accurate calculations gives supporting evidence of the adequacy of the method for its application to more elaborate gaussian‐type basis set representations for confined atoms and molecules. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 271–278, 2001     

Approximate STO functions for the first-row transition metal atoms

Slater type orbital (STO) basis sets for the atoms Sc-Zn have been derived using a technique based on the distance between subspaces. The accuracy for several properties of these basis sets has been tested. Basis sets studied are of both single- and double-zeta sizes, although this technique can be generalized for any size. Uniform quality criteria through the series of atoms Sc-Zn are difficulty to establish due to the varying number of d electrons. A comparative study at the atomic level of the quality of STO basis sets (both the two new basis sets and Clementi's basis sets) for the first-row transition elements has been carried out. Results show that the new basis sets provide better simulation for several properties. Molecular calculations on compounds with these atoms using a Gaussian expansion fitted according to the new values of optimized STOs are also included. The results obtained are similar to those reported when STO-3G basis set is used.     

An approximate frozen core approach to valence only molecular calculations

A simple valence electron-only theory based on an approximate frozen core approach and an exact core-valence strong orthogonality condition is developed for atomic and molecular systems. A unique reduced basis is introduced in which both core and valence orbitals are expanded. The core representation is roughly approximated, and the valence orbital overlap with the corresponding all-electron reference functions is nearly exact. The size of the reduced basis in terms of primitive functions is practically the same as that adopted by effective core potential methods in which the valence orbitals have the correct nodal properties. Results obtained with the present approach are presented for LiO, BeO and CaO molecules, and compared with the corresponding all-electron frozen core calculations. In addition, a detailed investigation on Li _n Be clusters (n=1,..., 6) is carried out.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Molecular states of atoms. I. Orbital energy parameters

Atomic valence state energies are analyzed to obtain values of orbital energy parameters that may be used in semiempirical molecular orbital calculations. Difficulty in defining the interaction between orbitals with non-integer electron populations is systematically avoided by distinguishing between a valence state and a molecular state of an atom, only the latter state having non-integer spin paired orbital occupancy. Application of the virial theorem to the molecular state enables a value for the orbital kinetic energy to be obtained from the valence state orbital energy parameters once an arbitrary configuration is defined as reference. The orbitals then are eigenfunctions of the atomic Fock operator for that reference molecular state and, with their energy parameters, may be employed as a fixed basis set for molecular orbital calculations.     

One-Parameter double-zeta atomic functions for the hartree–fock energies of helium isoelectronic sequence

The double-zeta atomic functions are characterized by the nuclear charge z of the two-electron atomic system. The Hartree–Fock total energies and the corresponding orbital energies are calculated using various atomic wave functions for the helium isoelectronic sequence. The expectation values rⁿ of various wave functions are also examined. It is found that the accuracy of our one-parameter double-zeta functions corresponds to the accuracy of the usual five-parameter double-zeta functions.     

Physical nature of the chemical bond II. Valence atomic orbital and energy partitioning studies of linear nitriles

The valence atomic orbitals (VAO 's) of several linear nitriles are determined using non-empirical SCF –LCAO –MO wave functions expanded in a minimal (CN^?, HCN, FCN, C₂N₂), double-zeta (CN^?, HCN), or double-zeta + polarization (HCN) basis of Slater atomic orbitals (AO 's). The molecular energy of each system (except the double-zeta + polarization HCN system) is partitioned according to the procedure of Ruedenberg to obtain numerical values of nitrile C and N atomic and C?N bond components of the energy. In addition, the nitrile results are compared with minimal AO basis results obtained previously by other authors for homonuclear diatomics, diatomic hydrides and H₂O. The numerical data are used to test the internal self-consistency of the various definitions entering the partitioning method, i.e. whether or not analogous quantities assume similar values in chemically similar situations. The analysis of nitrile SCF –MO wave functions in terms of the set of VAO 's characteristic of the system under consideration is shown to be a promising approach to the problem of extracting useful information from the wave functions. In general, numerical results for the nitrile systems studied are fairly consistent with the concepts on which the partitioning method is based: promotion, quasi-classical interaction, sharing penetration, sharing interference and charge transfer. However, the VAO expansions for several energy components need to be investigated further and possibly revised.     

Ab initio SCF MO study of hydrogen bonds between H2S and H2O molecules

The hydrogen bonds between H₂S and H₂O molecules are calculated through anab initio, LCAO MO SCF method using a Gaussian type orbital double-zeta basis set. The capacity of the H₂S molecule to act as an electron acceptor is confirmed. Consultant of the Instituto Mexicano del Petróleo.     

Selected valence electron split-shell molecular orbital calculations on the diatomic interhalogen molecules

Selected valence electron split-shell molecular orbital calculations have been performed on the diatomic interhalogen molecules in order to obtain their binding energies, equilibrium internuclear distances, vibrational force constants, dipole moments and nuclear quadrupole coupling constants. The results are compared with the corresponding closedshell values and with those of some previous semiempirical and nonempirical all valence electron calculations. It is observed that the selected valence electron split-shell molecular orbital method which involves the least amount of computations yields results in better agreement with experiment than other methods.