Combination Of Gaussian-type Orbitals Research Articles

Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry

Atomic-like basis functions provide a natural, physically motivated description of electronic states, among which Gaussian-type orbitals are the most widely used basis functions in molecular simulations. This paper aims at developing a systematic analysis of numerical approximations based on linear combinations of Gaussian-type orbitals. We derive a priori error estimates for Hermite-type Gaussian bases as well as for even-tempered Gaussian bases. Numerical results are presented to support the theory.

Ab Initio Study of 2H Nuclear Quadrupole Coupling Constants in Deuterated Crystalline Oxalic Acid Dehydrated Polymorphs

We report calculated 2H nuclear quadrupole coupling constants and asymmetry parameter in deuterated crystalline oxalic acid dihydrated polymorphs within a full-potential linear combination of Gaussian-type orbitals employing both Density Functional Theory and Hartree-Fock approximation. The Becke's hybrid exchange B3 and the Lee, Yang and Parr correlation functionals were employed. Their dependence with basis set, interelectronic correlation, structural changes and crystal field environment are reported.

Ab initio density functional approach for noncollinear molecular magnetism of multicenter metal clusters

Abstract We investigated the spin structure of a bi-pyramidal Cr5 cluster using ab initio linear combination of Gaussian type orbitals generalized spin density functional theory. We found that a three-dimensional spin state is most stable among several candidates for stable spin structures.

Predicted spin-orbit coupling effect on the magnetic ordering of crystalline uranium dioxide

The magnetic ordering of fluorite structure uranium dioxide has been investigated using fully-relativistic linear combinations of Gaussian type orbitals - fitting function (LCGTO-FF) calculations, within the generalized gradient approximation (GGA) to density functional theory. Three types of collinear spin-orderings were considered; ferromagnetic with spins aligned in the (001) direction and two antiferromagnetic (001) layer structures with spins aligned either perpendicular to each plane (001) or parallel to each plane (100). For each ordering, the total energy and spin-moment were calculated both with and without spin-orbit coupling. The ferromagnetic ordering is found to be energetically preferred to the antiferromagnetic orderings, contrary to experiment, whether or not spin-orbit coupling is included. Spin-orbit coupling is shown to have a significant quenching effect on the spin-moment and also introduces a strong magnetic anisotropy in the antiferromagnetic state that favors the (001) alignment over the (100) alignment.

Full potential calculations on the electron bandstructures of Sphalerite, Pyrite and Chalcopyrite

The bulk electronic structures of Sphalerite, Pyrite and Chalcopyrite have been calculated within an ab initio, full potential, density functional approach. The exchange term was approximated with the Dirac exchange functional, the Vosko–Wilk–Nusair parameterization of the Cepler–Alder free electron gas was used for correlation and linear combinations of Gaussian type orbitals were used as basis functions. The Sphalerite (zinc blende) band gap was calculated to be direct with a width of 2.23 eV. The Sphalerite valence band was 5.2 eV wide and composed of a mixture of sulfur and zinc orbitals. The band below the valence band located around −6.2 eV was mainly composed of Zn 3d orbitals. The S 3s orbitals gave rise to a band located around −12.3 eV. Pyrite was calculated to be a semiconductor with an indirect band gap of 0.51 eV, and a direct gap of 0.55 eV. The valence band was 1.25 eV wide and mainly composed of non-bonding Fe 3d orbitals. The band below the valence band was 4.9 eV wide and composed of a mixture of sulfur and iron orbitals. Due to the short inter-atomic distance between the sulfur dumbbells, the S 3s orbitals in Pyrite were split into a bonding and an anti-bonding range. Chalcopyrite was predicted to be a conductor, with no band-crossings at the Fermi level. The bands at −13.2 eV originate from the sulfur 3s orbitals and were quite similar to the sulfur 3s bands in Sphalerite, though somewhat shifted to lower energy. The top of the valence band consisted of a mixture of orbitals from all the atoms. The lower part of the same band showed metal character. Computational modeling as a tool for illuminating the flotation and leaching processes of Pyrite and Chalcopyrite, in connection with surface science experiments, is discussed.

An all-electron LCGTO study of square and hexagonal plutonium monolayers

The linear combinations of Gaussian type orbitals fitting function (LCGTO-FF) method is used to study the electronic and geometrical properties of plutonium monolayers with square and hexagonal symmetry. The effects of several common approximations are examined: (1) scalar-relativity vs. full-relativity (i.e., with spin-orbit coupling included); (2) paramagnetic vs. spin-polarized; and (3) local-density approximation (LDA) vs. generalized- gradient approximation (GGA). The results indicate that spin-orbit coupling has a much stronger effect on the monolayer properties compared to the effects of spin-polarization. In general, the GGA is found to predict a larger lattice constant and a smaller cohesive energy compared to LDA predictions. We also find a significant compression of the monolayers compared to the bulk, contradicting the only other published result on a Pu monolayer. The current result supports the existence of a δ-like surface on α-Pu.

High-precision, all-electron, full-potential calculation of the equation of state and elastic constants of corundum

The all-electron, full-potential linear combinations of Gaussian type orbitals{endash}fitting function technique has been used to perform high-precision total-energy calculations on {alpha}-alumina (corundum). The calculations yield zero-pressure lattice parameters that are in 0.3{percent} agreement with experiment and symmetry-preserving elastic constants that agree with experiment to within 5{percent}. The bulk modulus and pressure derivatives of the lattice parameters are also in good agreement with existing data. The calculated energies have been used to generate an analytical equation of state (EOS) for corundum that should be valid up to at least 250 GPa. The fitted EOS agrees with room temperature diamond anvil cell data up to 175 GPa to within the known limitations of the experimental data. The c/a ratio, band gap, and tetragonal shear modulus have been determined for pressures up to 250 GPa. The c/a ratio varies by less than 3{percent} over the entire pressure range. For pressures above 150 GPa, the band gap changes from direct to indirect and the tetragonal shear modulus softens. The linear pressure coefficient of the band gap is estimated to be 5.1 meV/kbar at zero pressure. {copyright} {ital 1997} {ital The American Physical Society}

Scalar-relativistic LCGTO DFT calculations for atoms using the Douglas-Kroll transformation

Haberlen and Rosch (HR) demonstrated [Chem. Phys. Lett. 199, 491 (1992)] the feasibility of performing scalar-relativistic, density functional theory (DFT) linear combination of Gaussian-type orbitals–fitting function (LCGTO-FF) calculations on clusters of atoms using an “incomplete” Douglas–Kroll transformation. Some of the approximations used in their multiatom calculations have not yet been fully explored for isolated atoms, especially the neglect of matrix elements involving vector products of the momentum and the use of fitting functions. In this investigation, scalar-relativistic LCGTO calculations (without fitting functions) were carried out at four levels of approximation, including that employed by HR, for four atoms: Ce, Au, Pb, and Pu. The results of these calculations suggest that the HR approximation should be applicable to atoms through the light actinides, so long as spin–orbit effects are unimportant. A comparison of very large basis-set results with results obtained using ordinary-size basis sets indicates that the valence (bonding) states from scalar-relativistic LCGTO-FF calculations should be no more sensitive to the orbital basis-set size than are their nonrelativistic counterparts. Published 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 565–574, 1997

Structure and bonding of Group 13 monocarbonyls

A. J. Bridgeman, J. Chem. Soc., Dalton Trans., 1997, 1323 DOI: 10.1039/A606474D

The shapes of bis(cyclopentadienyl) complexes of the s-block metals

The structures and bonding of the bis(cyclopentadienyl) complexes of the alkaline-earth metals and the alkali metals have been studied using density functional calculations within the linear combination of Gaussian-type orbitals framework. The compounds Ca(cp) 2 and Sr(cp) 2 are predicted to have bent equilibrium structures in agreement with the experimentally determined shapes but in contrast to previous theoretical investigations; Mg(cp) 2 and the isoelectronic [M(cp) 2 ] - (M = Li, Na, K or Rb) ions are predicted to have coparallel, staggered rings. Analysis of the bonding shows that π-type interactions dominate for the complexes of the heavier metals of both groups as a result of the increased influence of the metal d functions. Their role is key to the driving force for the bent geometries of Ca(cp) 2 and Sr(cp) 2 just as it is for the anomalous shapes of some of the dihalide molecules. The key orbital interaction, however, is quite different.

Nuclear quadrupole coupling constants from the Gaussian density-functional method.

~Received 29 September 1995! The reliability of density-functional theory in predicting nuclear quadrupole resonance ~NQR! frequencies and nuclear quadrupole coupling constants was tested for a series of straight-chain chloroalkenes ~vinyl chloride, 2-chloropropane, cis- and trans-1-chloropropene, cis-dichloroethylene, and tetrachloroethylene!. The calculations were performed using the linear combination of Gaussian-type orbitals local-spin-density method and the generalized gradient approximation. The calculated NQR frequencies are in good agreement with experimental data. Less satisfactory agreement is found in the prediction of quadrupole coupling constants. The results show that the calculated NQR frequencies and nuclear quadrupole coupling constants can be used to study the electron distribution in molecular systems. @S1050-2947~96!06905-3# PACS number~s!: 31.15.2p I. INTRODUCTION

Gaussian density-functional study for small neutral (Al n ), positive (Al n + ) and negative (Al n ? ) aluminium clusters (n=2?5)

The structures and properties of Aln, Aln+, Aln− (n=1,5) clusters have been investigated by using the Linear Combination of Gaussian Type Orbitals (LCGTO) method, considering Local (LSD) and Non Local (NLSD) Spin Density Approximations and employing a Model Core Potential (MCP) that allows the explicit treatment of 3s2 3p1 valence electrons. For each system different geometrical structures and electronic states have been considered. For Al3, Al3+, Al3− the most stable geometry proved to be the equilateral triangle (D3h). Al4 and Al4+ prefer the rhombus (D2h) structure, while the corresponding anion prefers the square (D4h) one. The trapezoidal form (C2v) is the most stable isomer for Al5, Al5+ and Al5− clusters. The analysis of vibrational frequencies shows that these structures are minima in the potential energy surface. The binding energies (De), the adiabatic ionization potentials (IP) and electron affinities (EA), the chemical potentials or absolute hardnesses (η) and electronegativities (χ) have been computed. Results are in good agreement with the available experimental data and the previous high level theoretical computations.

Density functional theory and quantum chemistry: Metals and metal oxides

The LCGTO-MCP-LSD (linear combination of Gaussian type orbitals - model core potential - local spin density) method has already been tested in a wide range of applications, including transition metals, transition-metal clusters, transition-metal oxide molecules and clusters. In this contribution a very brief overview of the density functional methodology, some remarks on the program deMon, developed in our laboratory, and a survey on recent applications aimed at delimiting the possibilities and limitations are given. The most recent applications of DFT to transition-metal oxide diatomics are discussed focusing on the usefulness of the methodology in theoretical spectroscopy as well as in describing metal-oxygen bonding.

Binding energies of excitons and donors in a double quantum well in a magnetic field.

We study binding energies of both excitons and donors in a symmetric double quantum well in the presence of a magnetic field applied parallel to the growth direction. We express wave functions as combinations of Gaussian-type orbitals and subband wave functions of even and odd parities, with variationally determined expansion parameters. By varying the interwell barrier width and well sizes (hence varying the interwell coupling), we obtain binding energies ranging in character from that for a strongly coupled double well to that for a system of two isolated single wells. The behavior of the binding energies as function of the interwell coupling, well sizes, and the magnetic field, as well as the donor position is consistently described with our formalism with naturally included subband mixing effects. The magnetic field leads to stronger confinement of the wave functions and enhances binding energies.

Developing magnetic and metallic behavior in high-nuclearity nickel cluster carbonyls. A LCGTO-LDF study of [Ni9(CO)18]n-, [Ni10Ge(CO)20]n-, [Ni32C6(CO)36]n-, and [Ni44(CO)48]n- compounds

We have performed all-electron calculations on the electronic structure of medium- and high-nuclearity bare and carbonylated nickel cluster compounds by means of the linear combination of Gaussian type orbitals (LCGTO) local density functional (LDF) method. The transition from the molecular state to the metallic state as a function of the cluster size was studied by determining the one-electron energy spectra and the magnetic properties of naked and ligated Ni clusters

Calculation of equilibrium geometries and harmonic frequencies by theLCGTO-MCP-local spin density method

Results are presented from linear combination of Gaussian type orbitals–model core potential–local spin density calculations on equilibrium geometries and harmonic frequencies of several small main group and organometallic molecules. The equilibrium geometries were obtained by minimizing the norm of an approximate analytical energy gradient while the frequencies were obtained by numerical differentiation of these gradients. Comparison with experimental data indicates that the approximate gradients yield accurate results which typically agree better with experiment than those of the Hartree–Fock method and compare favorably with commonly used correlated techniques.

Geometry optimization of molecules within anLCGTO local-density functional approach

We describe our implementation of geometry optimization techniques within the linear combination of Gaussian-type orbitals (LCGTO) approach to local-density functional theory. The algorithm for geometry optimization is based on the evaluation of the gradient of the total energy with respect to internal coordinates within the local-density functional scheme. We present optimization results for a range of small molecules which serve as test cases for our approach.

Interaction potential between a hydrogen atom and a silicon (100) surface

The adsorption of a hydrogen atom on a (100) silicon surface has been modelled using a cluster of 11 silicon atoms with the linear combination of Gaussian type orbitals - local spin density method (LCGTO-LSD), which is well adapted to surface problems. From the spin-polarized total energy calculation, the interaction potential has been obtained as a function of distance between H and the silicon surface, and fitted by an analytic polynomial expression. This potential models properly the dissociation of H from the silicon surface at long distances. Our results agree with the experimental structural and spectroscopic data that are available for this system, so the potential should be appropriate for molecular dynamics calculations.

Highly localised excitons in sodium halides: a linear combination of Gaussian-type orbitals Xαmodel cluster study

A cluster model that takes relaxation and Madelung effects into account is found suitable for the investigation of strongly localised excitations of alkali halide crystals in the soft-X-ray range. Application to NaCl and NaF confirms that the structures below the photoconduction threshold are due to excitonic quasi-atomic 'inner-well' states but, based on these cluster calculations, new assignments are given for all excitations except the first excited state. For NaCl, the two peaks assigned to Na 3d-type final states which split in the octahedral environment show an ordering eg<t2g at variance with the well known level ordering in transition-metal complexes. This is attributed to their rather diffuse character which leads to a dominant pi -type metal-ligand interaction. The hitherto postulated 'inversion' of the Na 3p and 3d final states is not supported by the cluster calculations.

Toward a chemisorption cluster model using theLCGTO-X? method: Application to Ni(100)/Na

A modified cluster approach for modeling local chemisorption phenomena is suggested on the basis of the linear combination of Gaussian-type orbitals (LCGTO) Xα method. Contractions of the fitting bases are employed to take into account the reduced polarizability of a surface cluster and to access larger cluster sizes. Furthermore, embedding of a cluster in the surface is mimicked by Gaussian broadening of the one-electron levels leading to fractional occupation numbers via a self-consistently determined Fermi energy of the cluster. As a first application results are presented for the clusters NinNa (n = 5, 9, 17) modeling the low coverage limit of the chemisorption system Ni(100)/Na. Calculated bond length, binding energy, and induced “surface” dipole moment show fair agreement with experimental values, indicating a substantial covalent character of alkali bonding on transition metal surfaces even in the zero coverage limit.