Comparison of cartesian and lobe function Gaussian basis sets

The lobe function and cartesian (spherical harmonic) gaussian are compared with reference to calculations for second-row atoms. Single and grouped gaussian basis sets which have been reported for cartesian functions are taken over directly to construct corresponding lobe function bases with identical sets of exponents and with lobe separations chosen by a scaling procedure. Total and orbital energies and SCF coefficients resulting from calculations on the second-row atoms using the two types of functions for both primitive and grouped gaussian basis sets are seen to be in excellent agreement, thereby emphasizing the essential equivalence of lobe functions and cartesian gaussians, at the very least with respect to calculation of energy surfaces.

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Zusammenfassung Die Lobe-Funktionen und kartesischen (Kugelfunktions-) Gaußfunktionen werden in Berechnungen von Atomen der zweiten Reihe des periodischen Systems verglichen. Schon bekannte einfache und gruppierte Gaußfunktionsbasissätze für kartesische Funktionen werden direkt übernommen, um entsprechende Lobe-Funktionsbasen mit identischen Exponenten zu konstruieren, wobei die zugehörigen Lobe-Abstände nach einer Koordinatenstreckungs-(scaling) Methode berechnet werden. Gesamt- und Orbitalenergien sowie SCF-Koeffizienten für die Atome der zweiten Reihe stimmen bei Benutzung der beiden verschiedenen Funktionstypen, sowohl bei einfacher als auch bei gruppierter Gaußfunktionsbasis, außerordentlich gut überein, wodurch die wesentliche Gleichwertigkeit von Lobe-Funktionen und kartesischen Gaußfunktionen betont wird, zum allermindesten hinsichtlich der Berechnung von Energieflächen.

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Résumé La fonction de lobe et la gaussienne cartésienne (harmonique sphérique) sont comparées sur des calculs d'atomes de la seconde ligne. Des bases de gaussiennes simples et groupées utilisées pour les fonctions cartésiennes sont directement employées pour construire les bases correspondantes de fonctions à lobes avec des ensembles d'exposants identiques et des séparations de lobes choisis par calibrage. L'emploi de ces deux types de fonctions donne des résultats concordants pour l'énergie totale, les énergies orbitales et les coefficients SCF, mettant l'accent sur l'équivalence essentielle des fonctions à lobe et des gaussiennes cartésiennes, tout au moins pour le calcul des surfaces d'énergie.

     

An ab initio study of the ground and low-lying excited states of the permanganate ion

The results of ab-initio self-consistent field calculations for the ground state and configuration interaction calculations for the excited states of the permanganate ion are presented and discussed. The calculations were performed using two large basis sets of contracted gaussian functions, and singly excited configurations were used in the calculations of the excited states. Fair agreement is obtained between these results and the experimental absorption spectra.     

Extended floating spherical gaussian basis sets for molecules. Generation procedure and result for H2O

A procedure is proposed to generate extended floating spherical gaussian orbital (FSGO) basis sets for molecular SCF calculations by projecting large basis set SCF results onto FSGOs. This replaces the need for repeated evaluation of energy integrals and SCF iterations for extensive non-linear optimizations of FSGOs.     

The Hylleraas-CI method in molecular calculations. III. Implementation and numerical verification of a three-electron many-center theory

The general theory of three-electron Hylleraas-Configuration-Interaction method using linear correlation factors of the form r_ij has been implemented for molecular systems using cartesian Gaussians as basis sets. A brief review of the theory and the form of the three-electron integrals is presented. Additionally, a table of numerical values of some selected three-electron integrals is given. Results from test calculations on H₃ using the full form of the theory are presented for some simple basis sets. A discussion of the computational problems that need to be overcome before this approach is competitive with traditional methods is included.     

Economical geometry optimization in first row molecules with bond function augmented basis sets

Ab initio MO geometry optimization studies on a number of molecules containing first row atoms show that the use of gaussian bond functions in conjunction with the standard 4-31G basis sets enables geometry calculations closely approaching the accuracy of calculations using more extensive basis sets.     

AB initio study of the spatial extension of the ethylene v state

An AO basis containing 108 contracted cartesian gaussian functions is employed in a CI study of the V state of ethylene. The <Ψ&z.sfnc;Σ_ix²_i&z.sfnc;Ψ > value for this state is predicted to the in the 19–20 au² range, nearly doubl ³(π,π^*) and ground states of this system.     

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     

Ab initio calculation of the dipole polarizabilities of unsaturated hydrocarbons

Finite-field SCF MO calculations of polarizability are reported for ethene, benzene and naphthalene using three good gaussian basis sets Double-zeta wavefunctions yield values of α_LL and α_MM in agreement with experiment but the calculated α_NN is half the experimental value. Polarization functions when present preferentially improve α_NN. (L,M) and N refer to the molecular long, medium and normal axes, respectively.) STO-4G results are given for benzene, naphthalene, azulene, anthracene and phenanthrene, and the agreement with the experiment is reasonable after scaling the calculated α_LL and α_MM by a constant factor. The calculated α_MM are an order of magnitude too low.     

Comparison of quantum mechanical methods to compute the biologically relevant reactivities of cyclopenta-polycyclic aromatic hydrocarbons

In computational studies to understand the interaction of polycyclic aromatic hydrocarbons (PAHs) with biomolecular systems, the semiempirical method AM 1 has been used previously to determine the geometry of the PAH and its metabolites and relevant intermediates. A number of studies have shown that AM 1 provides geometries for parent PAHs that are acceptably close to experimentally determined structures. However, many of the properties that determine the manner by which PAHs interact with biological nucleophiles depend on the structure of metabolites and reactive intermediates where less experimental information is available. In a previous study, we used AM 1 to obtain the molecular geometries of reactive intermediates of cyclopenta-PAHs (cPAHs) and then used single-point Hartree-Fock calculations, with the gaussian 3-21g basis set, to obtain molecular energies and charge distributions, in order to predict the direction of epoxide ring opening. Recent advances in the availability of computational hardware and software have provided other, more rigorous, methods for approaching this problem. In this study, we used hartree-fock methods in the gaussian series of programs employing the 3-21_g and 6-31_g basis sets and the local density functional method Dmol to obtain molecular geometries, energies, and charge distributions of the epoxides and the two potential hydroxycarbocations that could result from protonated ring opening, for a series of cPAHs. We have also performed the same calculations with AMSOL /SM 2, a semiempirical method that adds the effect of the aqueous environment to the AM 1 Hamiltonian. The division of the cPAHs into classes is not altered by these more rigorous calculations. The inclusion of water in the Hamiltonian has a greater effect on the results than using the ab initio methods to obtain the structure. © 1994 John Wiley & Sons, Inc.     

Photoelectron spectra of hydrogen peroxide and hydrogen disulphide: ab initio calculations

Koopmans' theorem ionization potentials from ab initio gaussian basis set calculations on cis, trans and skew forms of HOOH and HSSH are compared with experimental values from photoelectron spectroscopy.     

Grid‐based density functional calculations of many‐electron systems

Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many‐electron systems in the 3D cartesian coordinate grid (CCG). The atom‐centered localized gaussian basis set, electronic density, and the two‐body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange‐correlation potential, while Hay‐Wadt‐type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, and atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom‐centered grid as well as the grid‐free calculation. Results for three atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many‐electron systems. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Gaussian integral transforms of unconventional functions: contracted basis functions appropriate to molecules and metallic clusters

We report the development of new gaussian integral transforms one-electron functions. A straightforward recipe to generate gaussian contractions of these functions is introduced. The applications call into question the disseminated belief of the superiority of Slater type orbitals (STO) in molecular calculations. A first successful application of the Bessel K _v (qr) function to a molecular system is presented. One of the integral transforms that yields the 0s function is used to generate contractions that have a better performance than the STO ones in cases that diffuse functions are needed. Applications are presented to some Li _n clusters and a new conformation of the Li₃ cluster is then proposed.     

Some investigations of the MP2-R12 method

Summary The MP2-R12 method was introduced by Kutzelnigg and Klopper to overcome the problem caused by truncation of the one electron basis set in correlation energy calculations at the Møller-Plesset second order level of approximation. Here, we have evaluated the integrals required by their simplest scheme using the Rys-quadrature procedure. Results are presented for Ne, H₂O, and HF using largespdf gaussian basis sets.     

Simultaneous ab initio calculations of isoelectronic diatomic molecules

Large gaussian basis sets are employed in simultaneous configuration interaction calculations for the ground states of isoelectronic diatomic molecules. The resulting potential energy curves for three members respectively of four different isoelectronic molecule sequences show the applicability of the method. Comparisons with available results of standard configuration interaction calculations for selected molecules are given. Using our method we often get lower upper bounds for the electronic energy, save computer time and treat physically totally different molecules simultaneously.     

On the X-ray and UV photoelectron spectra of the difluorobenzenes

Ab initio calculations with a double zeta contracted gaussian basis are used to discuss the ionization potentials of o-, m- and p-difluorobenzene, and the correlation with benzene. Interpretations of the experimental X-ray and UV photoelectron spectra are given.     

A study of the interaction energy between a glycoluril molecular clip and dihydroxybenzenes or diaminobenzenes: a justification for easy separation by affinity chromatography

Theoretical calculations were performed to determine the interaction energy between a glycoluril (GL) molecular clip and hydroxybenzenes (HBs) and aminobenzenes (ABs). The theoretical calculations on the GL and its interactions were carried out using the hybrid functional closed-shell RB3LYP and the 6-31G* basis set, employing gaussian 03. The stability in energy of the guest inside the GL, ΔE_T(1), was in the following order: m-DHB-GL > o-DHB-GL > m-THB-GL > m-DAB-GL > o-THB-GL. The geometric parameters, in particular the bond lengths are discussed for the host molecule GL and guest molecules DHB and DAB and their parameters are compared with the host-guest molecules DHB-GL and DAB-GL, respectively.     

The electronic structure of polymers by the FSGO (Floating Spherical Gaussian Orbital) method

Non-empirical band-structure calculations have been performed on polyethylene using two basis sets introduced by Christoffersen. Both basis sets had to be optimised with respect to the carbon-carbon framework bond in order to yield solutions within the nearest-neighbour approximations. The valence bands of polyethylene are well reproduced by both basis sets whilst the conduction bands are only in fair agreement with those produced by conventional gaussian calculations. The use of the unsplit basis set was considered unsatisfactory for the representation of the core bands. The effect of increasing the number of interacting unit cells on the energy terms is discussed. Some of the energy terms converge when five unit cells are used and almost all of the terms reach a constant value when nine unit cells are employed.     

Accurate hyperfine couplings for C59N

We identify the shortcomings of existing ab initio quantum chemistry calculations for the hyperfine couplings in the recently characterized azafullerene, C₅₉N. Standard gaussian basis sets in the context of all-electron calculations are insufficient to resolve the spin density near the cores of the atoms. Using the projector augmented wave (PAW) method implemented on top of a standard pseudo-potential plane-wave density-functional framework, we compute significantly more accurate values for the Fermi contact interaction.     

An ab initio study of the nuclear spin-spin coupling constants in the second-row hydrides

Ab initio SCF perturbation theory calculations have been performed for the contact, orbital and dipolar contributions to the nuclear spin—spin coupling constants in A1H₃, SiH₄ PH₃, H₂S and HCl, using large, stable gaussian basis sets. The results for J(XH) are in reasonably good agreement with experiment, those for. J(HH) are rather less good.