Small gaussian basis sets for second-row atoms

6s-type and 4p-type gaussian basis sets are obtained for the second row atoms by fitting, using a least squares criterion, to 12s-type and 9p-type gaussian basis sets which are close to the self-consistent field atomic orbital wave functions. The small gaussian expansions are considered to be more suited for molecular calculations using double basis sets. The differences between these sets and the 10s-type, 6p-type and 9s-type, 5p-type are analysed. For molecular calculations using single gaussian basis sets the 10s-type and 6p-type would seem to be the best compromise.

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Zusammenfassung Ein Basissatz von Gaußfunktionen vom 6s- bzw. 4p-Typ für Atome der zweiten Reihe wird erhalten, indem die Funktionen mit Hilfe des Kriteriums der kleinsten quadratischen Abweichung einem Satz von Gaußfunktionen vom 12s- bzw. 9p-Typ angepaßt werden; dabei ist der letztgenannte Satz der selbstkonsistenten Wellenfunktion aus Atomorbitalen stark angenähert. Die kürzeren Entwicklungen nach Gaußfunktionen werden für geeigneter bei Berechnungen mit zweifachen Basissätzen gehalten. Die Unterschiede zwischen diesen Sätzen und solchen vom 10s- bzw. 6p-Typ sowie vom 9s- und 5p-Typ werden untersucht. Für Molekülrechnungen mit einfachen Basissätzen von Gaußfunktionen scheint der Satz vom 10s- bzw. 6p-Typ den besten Kompromiß darzustellen.

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Résumé On obtient des bases gaussiennes de type 6s et 4p pour les atomes de la seconde ligne par ajustement selon un critère de moindre carré à des bases gaussiennes de type 12s et 9p proches des orbitales atomiques SCF. Les petits développements en gaussiennes sont plus adaptés à des calculs moléculaires en bases doubles. Analyse des différences entre cas bases et les bases de types 10s et 6p, 9s et 5p. Pour des calculs moléculaires à base simple, 10s et 6p semble le meilleur compromis.

     

High-quality Gaussian basis sets for fourth-row atoms

Summary Energy-optimized Gaussian basis sets of triple-zeta quality for the atoms Rb-Xe have been derived. Two series of basis sets are developed; (24s 16p 10d) and (26s 16p 10d) sets which we expand to 13d and 19p functions as the 4d and 5p shells become occupied. For the atoms lighter than Cd, the (24s 16p 10d) sets with triple-zeta valence distributions are higher in energy than the corresponding double-zeta distribution. To ensure a triple-zeta distribution and a global energy minimum the (26s 16p 10d) sets were derived. Total atomic energies from the largest basis sets are between 198 and 284E _H above the numerical Hartree-Fock energies.     

Geometry optimization calculations in molecules containing second row atoms with various polarization function basis sets

Ab initio MO geometry optimization studies on a number of molecules containing second-row atoms using various polarization basis sets are presented. In particular the use of gaussian bond functions is shown to be a good substitute for the more conventional (and expensive) atom-centered d functions. Molecules examined to a double zeta plus polarization basis set level are HCP, P₂, SO, SO₂, H₂S, SF₂, CIF, HCl and Cl₂.     

Gaussian basis sets for the first and second row atoms

Gaussian basis sets consisting for first row atoms of 7 s-type and 3 p-type and for second row atoms of 10 s-type and 6 p-type functions with optimized exponents are reported. These basis sets consists of at least two functions per atomic orbital.

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Zusammenfassung Es werden für die Atome der ersten und zweiten Reihe Basissätze aus Gaußfunktionen mitgeteilt, die aus 7 Funktionen vom s-Typ und 3 Funktionen vom p-Typ für die Elemente der ersten Reihe und 10 Funktionen vom s-Typ und 6 Funktionen vom p-Typ für die Elemente der zweiten Reihe mit optimierten Exponenten bestehen. Diese Basissätze bestehen aus wenigstens zwei Funktionen pro Atomorbital.

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Résumé Une base de 7 gaussiens du type s et 3 du type p est presenté pour les éléments du premier rang et de 10 gaussiens du type s et 6 du type p pour des éléments du deuxième rang; les exposants sont optimisés. Les bases consistent au moins en deux fonctions par orbital atomique.

     

New relativistic ANO basis sets for transition metal atoms

New basis sets of the atomic natural orbital (ANO) type have been developed for the first, second, and third row transition metal atoms. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive and negative ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies, electron affinities, and excitation energies for all atoms and polarizabilities for spherically symmetric atoms. These calculations include spin-orbit coupling using a variation-perturbation approach. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The accuracy of computed electron affinities is the same except in cases where the experimental values are smaller than 0.5 eV. Accurate results are obtained for the polarizabilities of atoms with spherical symmetry. Multiplet levels are presented for some of the third row transition metals.     

Gaussian basis sets for calculation of spin densities in first-row atoms

Summary The suitability of Gaussian basis sets for ab initio calculation of Fermi contact spin densities is established by application to the prototype first-row atoms B-F having open shell p electrons. Small multiconfiguration self-consistent-field wave functions are used to describe relevant spin and orbital polarization effects. Basis sets are evaluated by comparing the results to highly precise numerical grid calculations previously carried out with the same wave function models. It is found that modest contracted Gaussian basis sets developed primarily for Hartree-Fock calculations can give semiquantitative results if augmented by diffuse functions and if further uncontracted in the outer core-inner valence region.     

Relativistic Gaussian basis sets for the atoms hydrogen to neon

Gaussian basis sets for use in relativistic molecular calculations are developed for atoms and ions with one to ten electrons. A relativistic radial wavefunction coupled to an angular function of l-symmetry is expanded into a linear combination of spherical Gaussians of the form r ^l exp (–r ²). One set of basis functions is used for all large and small components of the same angular symmetry. The expansion coefficients and the orbital exponents have been determined by minimizing the integral over the weighted square of the deviation between the Dirac or Dirac-Fock radial wavefunctions and their analytical approximations. The basis sets calculated with a weighting function inversely proportional to the radial distance are found to have numerical constants very similar to those of their energy-optimized non-relativistic counterparts. Atomic sets are formed by combining l-subsets. The results of relativistic and non-relativistic calculations based on these sets are analyzed with respect to different criteria, e.g. their ability to reproduce the relativistic total energy contribution and the spin-orbit splitting. Contraction schemes are proposed.Dedicated to Prof. Dr. A. Neckel on occasion of his 60th birthday     

A study on universal Gaussian basis sets for first-row atoms

Analysis of various optimum and non-optimum Gaussian basis sets for firstrow elements have indicated that with a minimum increase of the basis set size and without loss of accuracy of the calculated total energy, a single universal Gaussian basis set may replace individually optimized Gaussian basis sets for a series of atoms. Such a universal Gaussian basis set may substantially reduce the computational work required for the calculation of molecular integrals in ab initio MO calculations.     

Polarization functions for gaussian basis sets for the first row atoms

Exponent optimization was performed for a single set ofd-type Gaussians on the first row atoms C, N, and O in fifteen small molecules. The hydrogenp-exponents were kept at the fixed value of 1.0. For the underlying valence shell basis sets, Dunning's double zeta basis sets were used. Standard exponents of polarization functions are suggested for the most common valence states of the C, N, and O atoms.     

Using many-particle basis sets for electronic energy calculations of molecules

A method of calculating the electronic energies of molecules using a many-particle basis set is proposed. In this case, the many-particle Schrödinger equation may be solved without resorting to the one-electron approximation. The results of the electronic energy calculations of some two-electron systems are in good agreement with experimental results.     

Optimization of basis sets for isoelectronic series of closed-shell atoms in Hartree-Fock-Roothaan calculations

Optimization of the nonlinear parameters (orbital exponents) of basis functions in Hartree-Fock-Roothaan calculations may be canied out with a high degree of accuracy. A scheme using second-order methods is suggested for optimization of the orbital exponents of Slater type basis functions defining the ground state of closed-shell atoms. An exact fomula is derived for calculating the partial second derivatives of energy with respect to nonlinear parameters in temis of the density matrix. In bases of isoelectronic series, the orbital exponents are shown to be the linear functions of the charge of the ion nucleus. Optimization calculations are reported for He, Be, Ne, and Mg atoms and their isoelectronic series. Translated fromZhumal Struktumoi Khimii, Vol. 41, No. 2, pp. 217–228, March–April, 2000     

On the existence of a natural common gauge-origin for the calculation of magnetic properties of atoms and molecules via gaugeless basis sets

It is proven that, within the conventional approach using a common origin and gaugeless basis sets for the calculation of atomic magnetizability and Larmor current density induced by an external magnetic field, the natural gauge origin coincides with the nucleus. Recipes for defining an optimal gauge origin for the calculation of magnetizability and magnetic shielding at the nuclei of a molecule are given. Within the common origin approach, the paramagnetic contributions to the components of magnetic tensors of a molecule are represented by a minimum number of non-vanishing parameters if the gauge origin is chosen at a point characterized by the total molecular symmetry, e.g., the center of electronic charge for magnetizabilities. It is shown that total values of diagonal components of the magnetic shielding tensor σ(I) at a nucleus I in a molecule, as well as separate diamagnetic σ(dI) and paramagnetic σ(pI) contributions, calculated via the common origin method, are origin independent for a number of local point group symmetries. The diagonal components (and the average value) of σ(I) depend on the gauge origin only for nuclear site symmetries C(1), C(s), C(n), C(nv), n = 2, 3.... Group-theoretical methods show interesting features, e.g., for S(4) local symmetry, in a coordinate transformation, the paramagnetic contribution to the zz component and to the trace of the shielding tensor is origin independent, whereas the xx and yy components mix into one another, in such a way that their sum remains constant.     

Large atomic natural orbital basis sets for the first transition row atoms

Large atomic natural orbital (ANO) basis sets are tabulated for the Sc to Cu atoms. The primitive sets are taken from the large sets optimized by Partridge, namely (21s13p8d) for Sc and Ti and (20s12p9d) for V to Cu. These primitive sets are supplemented with threep, oned, sixf, and fourg functions. The ANO sets are derived from configuration interaction density matrices constructed as the average of the lowest states derived from the 3d ⁿ 4s ² and 3d ⁿ⁺¹4s ¹ occupations. For Ni, the¹ S(3d ¹⁰) state is included in the averaging. The choice of basis sets for molecular calculations is discussed.