Linear Combination Of Gaussian-type Orbitals Research Articles

Range-Separated Hybrid Functionals with Variational Fitted Exact Exchange

This work presents a variationally fitted long-range exact exchange algorithm that can be used for the computation of range-separated hybrid density functionals in the linear combination of Gaussian type orbital (LCGTO) approximation. The obtained LCGTO energy and gradient expressions are free of four-center integrals and employ modified three-center integral recurrence relations to obtain optimal computational performance. The accuracy and performance of selected range-separated hybrid functionals with variational fitted long-range exact exchange are analyzed and discussed. A parallel implementation is presented and benchmarked.

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.

First-principle study of solid neon under high compression

Crystal structure, metallization and equation of state of solid neon at extremely high pressures are studied with first-principle simulations. Density functional (DFT) calculations based on the generalized gradient approximation (GGA) show that solid neon adopts the fcc phase up to pressures of 256 TPa. Solid fcc neon exhibits a direct band gap at low densities and an indirect band gap at high densities. The band gap of solid fcc neon closes at a density of 74.9 g/cm 3 and a pressure of 142 TPa, which is about 8% larger than the prediction of linear combination of Gaussian-type orbital (LCGTO) [3]. Further, GW approximation calculations predict that the metallization density and metallization pressure of solid fcc neon are 83.1 g/cm 3 and 176 TPa, respectively. Finally, the equation of state of solid neon up to 3800 TPa are calculated and fit functions are presented.

Generalized Spin Orbital Density Functional Study of Multicenter Metal Systems

We have firstly developed the ab initio linear combination of gaussian type orbital (LCGTO) program of generalized spin orbital (GSO) density functional theory (DFT) and applied it for multicenter metal clusters with noncollinear spin structures. It was found that two- and three-dimensional spin states becomes ground-states for Cr 3 (D 3h ) and CR 4 (T d ) respectively, indicating importance of GSO treatment of DFT for these clusters. Generalized spin orbital density functional theory multicenter metal clusters noncollinear molecular magnetism

Generalized spin orbital GW theory for spin‐frustrated and spin‐degenerate systems

AbstractWe proposed the ab initio linear combination of Gaussian type orbital (LCGTO) generalized spin orbital GW (GSO–GW) method and calculated triangular hydrogen molecules as models of the noncolinear magnetic clusters. A remarkable improvement of ionized potentials (IPs) by the GW procedure for GHFS solutions is observed in comparison with calculational results by full CI. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 369–374, 2001

LDA calculations of the Young's moduli of polyethylene and six polyfluoroethylenes

The Young's moduli of the linear chain polymers, polyethylene and six polyfluoroethylenes, constrained to the planar conformation, are calculated by means of the local density approximation (LDA) using the Perdew–Zunger (PZ) correlation potential and a linear combination of Gaussian-type orbitals (LCGTO).

Generalized Spin-Density Functional Calculation for the Spin Frustrated Systems

We developed the ab initio Linear Combination of Gaussian Type Orbital (LCGTO) program with generalized Hartree-Fock-Slater functional and calculate the hydrogen cluster as models of the noncollinear systems. Calculational results are compared with that of ab initio GHF and the difference between them are discussed.

Relativistic effects on the structural phase stability of molybdenum

The relative stabilities of the fcc, bcc, and hcp structures of molybdenum (Mo) are studied as functions of volume with both nonrelativistic and scalar-relativistic linear combinations of Gaussian-type orbitals (LCGTO) fitting function calculations. Relativity is shown to have a significant effect on the bcc-fcc structural energy difference that first increases, then decreases, with pressure, but has only a negligible effect on the hcp-fcc structural energy difference. The scalar-relativistic bcc-fcc energy difference curve obtained here is in good agreement with an earlier fully relativistic calculation using the all-electron full-potential linear muffin-tin orbital method. Unlike previous theoretical work, this investigation finds no region of hcp phase stability at T = 0. Instead, the bcc phase transforms directly into the fcc phase at a pressure of about 6.6 Mbar.

All-electron full-potential calculation of the electronic band structure, elastic constants, and equation of state for graphite

The all-electron full-potential linear combinations of Gaussian-type orbitals---fitting-function technique has been used to calculate the electronic structure, equation of state (EOS), and elastic constants for crystalline graphite. An analysis of the zero-pressure band structure is used to resolve inconsistencies between previous local-density-approximation (LDA) calculations. The calculated band structure is consistent with experimental data to the extent expected given the known limits of LDA one-electron energies. The in-plane lattice constant found here exhibits the usual LDA-induced contraction, whereas the interlayer separation and the unit-cell volume exhibit an anomalous expansion due to a LDA underestimate of the weak interlayer bonding. The calculated values of ${\mathrm{C}}_{11}$+${\mathrm{C}}_{12}$ and ${\mathrm{C}}_{33}$ are in good agreement with ultrasound measurements, while the value of ${\mathrm{C}}_{13}$ (\ensuremath{\approx}0) is much smaller than the ultrasound value. The bulk modulus and pressure derivatives of the lattice constants derived from the theoretical elastic constants are in very good agreement with diamond anvil cell (DAC) data, suggesting that the theoretical value for ${\mathrm{C}}_{13}$ is more reliable than the ultrasound measurement. An analytical EOS has been determined for pressures up to 50 GPa, well beyond the range of stability for the graphite structure. The EOS and the pressure dependencies of c/a and the optical transition energies (${\mathrm{A}}_{1}$ and ${\mathrm{A}}_{2}$) are in reasonable agreement with DAC data up to 14 GPa.

Reaction of a Mo Atom with H2, N2, and O2: A Density Functional Study

The reactivity of a Mo atom with H2, N2, and O2 is investigated with the all-electron Linear Combination of Gaussian Type-Orbitals−Kohn−Sham−Density Functional Theory (LCGTO-KS-DFT) method. We used MoH2 to validate the DFT methodology, comparing with accurate relativistic CI results. After this validation we studied the reaction of a Mo atom with N2 and O2 in order to obtain an explanation of the different observed reactivities. The equilibrium geometries are characterized by their binding energies, electronic states, and harmonic frequencies. For MoN2 we found two local minima under the dissociation limit on the quintet surface that are very weakly bonded. For MoO2 we found several local minima on different potential energy surfaces. The lowest minimum for this system is a bent structure on the triplet potential energy surface. A detailed analysis of the molecular orbitals is given. We suggest a two-step charge transfer process as the mechanism of the reaction, and we found that the Mo atom is always the electron donor. The theoretical explanation of the experimental results provide a better understanding of the electronic structure and the reaction mechanism.

Investigation of M�ssbauer parameters for a set of iodine compounds using gradient-corrected density functional theory

In the present work we show the first application of density functional theory (DFT) with gradient-corrected exchange-correction functionals within the linear combination of Gaussian-type orbitals (LCGTO) formalism to the calculation of isomer shifts and quadrupole couplings for a large and varied set of iodine compounds: I2, ICl, IBr, ICN, HI, KI, CH3I, CH2I2, CHI3, CI4, SiI4, GeI4, and SnI4. The results are compared with experimental data from Mossbauer spectroscopy. The overall agreement with experiment is most satisfactory, with the exception of the highly dipolar systems ICl, IBr, and ICN. For these systems it is believed that the free molecule assumption of the calculations is not an entirely valid model of the crystalline environment of the experiments. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 575–583, 1997

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

Persistent quantum-size effect in aluminum films up to twelve atoms thick.

Total energies and work functions have been calculated for unrelaxed, free-standing Al(111) films, 1--12 layers thick, using the all-electron, full-potential linear combination of Gaussian-type orbitals--fitting-function technique. The work function exhibits a significant quantum-size effect (at least 0.1 eV) over the entire range of thickness considered. This result contradicts an old prediction that the work function of an Al(111) N-layer film will converge to within a few hundredths of an eV by N=6. The present result, which is consistent with earlier jellium calculations, demonstrates the risk of mistaking an accidental coincidence of work functions for two films, differing in thickness by one layer, for a true convergence with respect to thickness. The implications for thin-film calculations of surface properties are discussed. A linear fit to the film binding energy vs thickness is used to extract the Al(111) surface energy (0.45 eV) and the binding energy of bulk Al (4.06 eV). \textcopyright{} 1996 The American Physical Society.

On the electronic structures and spectra of NiCl2 and CuCl2

The geometry and ground state of NiCl2 have been studied using local density-functional (LDF) calculations within the linear combination of Gaussian-type orbitals (LCGTO) framework. The molecule is found to be linear with a 3Σg– ground state in agreement with recent experimental results but contrary to previous theoretical studies. The calculated bond length and vibrational frequencies are in excellent agreement with experiment. A cellular ligand-field (CLF) analysis of the spectrum has been performed. The LDF and CLF calculations provide a consistent description of the bonding and suggest that the chloride ions are acting as good σ and π donors in this molecule with both roles enhanced compared to systems with higher co-ordination numbers. A proper account of the important interaction of the dσ orbital with the antibonding σg+ orbital is given using a cylindrically symmetric ‘void’ cell. A recent CLF analysis of CuCl2 is shown to be incorrect because of the treatment of the void interaction. A new study of the ligand-field spectrum of CuCl2 is presented, the results of which are consistent with the LDF and CLF studies on NiCl2 and with recent molecular orbital and LDF calculations on CuCl2.

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.

Charge separation and covalent bonding in metal oxide surfaces: A local density functional study on the MgO(001) surface

A first principles local density functional investigation on extended, two-dimensional periodic slab models of the MgO(001) surface is performed, using the linear combination of Gaussian-type orbitals (LCGTO) technique as implemented in the FILMS program package. Stimulated by recent theoretical evidence for a reduced charge separation in MgO(001), a detailed analysis of the charge distribution and its influence on the electrical field above the surface is carried out. Two different methods to quantify the charge separation in the ionic substrate are employed, a local one based on the topological atom approach and a global one derived from the Madelung field of the surface near potential adsorbates. Both procedures lead to a charge separation significantly (10%–20%) below the nominal ionic value of ±2 a.u. A variational atomic orbital analysis is utilized to discuss the origin of the Mg 3s and 3p structures discernible in the crystal orbitals of the MgO slab systems. They are identified as covalent magnesium valence orbital admixtures to the oxygen dominated valence bands in consistence with the reduced charge separation. Their influence on the cohesive energy of crystalline MgO, however, is found to be only 5% (∼0.5 eV).