Gaussian basis set of double zeta quality for atoms K through Kr: application in DFT calculations of molecular properties

Contracted basis sets of double zeta (DZ) quality for the atoms from K to Kr are presented. They were determined from fully optimized basis sets of primitive Gaussian-type functions generated in atomic Hartree-Fock calculations. Sets of Gaussian polarization functions optimized at the Möller-Plesset second-order level were added to the DZ basis set. This extends earlier work on segmented contracted DZ basis set for atoms H-Ar. From this set, using the BP86 nonhybrid and B3LYP hybrid functionals, dissociation energy, geometric parameters, harmonic vibrational frequency, and electric dipole moment of a set of molecules were calculated and compared with results obtained with other basis sets and with experimental data reported in the literature. In addition, ⁵⁷Fe and ⁷⁷Se nuclear magnetic resonance chemical shifts in Fe(C₅H₅)₂, H₂Se, and CSe₂ were calculated using density functional theory and gauge-including atomic orbitals and, then, compared with theoretical and experimental values previously published in the literature. Except for chemical shift, one verifies that our results give the best agreement with experimental and benchmark values. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008     

Augmented Gaussian basis sets of double and triple zeta valence qualities for the atoms K and Sc–Kr: Applications in HF, MP2, and DFT calculations of molecular electric properties

Augmented Gaussian basis sets of double and triple zeta valence qualities plus polarization functions for the atoms K and from Sc to Kr are presented. They were generated from the all-electron unaugmented sets by addition of diffuse functions (s, p, d, f, and g symmetries) that were optimized for the anion ground states. From these sets, Hartree–Fock, second-order Møller–Plesset perturbation theory, and density functional theory electric dipole moment and dipole polarizability calculations for a sample of molecules were carried out. Comparison with theoretical and experimental values available in the literature was done.     

Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy

Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 molecules representing (nearly) all elements-except lanthanides-in their common oxidation states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, density functional theory and correlated methods, for which we had chosen M?ller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.     

Consistent Gaussian basis sets of triple‐zeta valence with polarization quality for solid‐state calculations

Consistent basis sets of triple‐zeta valence with polarization quality for main group elements and transition metals from row one to three have been derived for periodic quantum‐chemical solid‐state calculations with the crystalline‐orbital program CRYSTAL. They are based on the def2‐TZVP basis sets developed for molecules by the Ahlrichs group. Orbital exponents and contraction coefficients have been modified and reoptimized, to provide robust and stable self‐consistant field (SCF) convergence for a wide range of different compounds. We compare results on crystal structures, cohesive energies, and solid‐state reaction enthalpies with the modified basis sets, denoted as pob‐TZVP, with selected standard basis sets available from the CRYSTAL basis set database. The average deviation of calculated lattice parameters obtained with a selected density functional, the hybrid method PW1PW, from experimental reference is smaller with pob‐TZVP than with standard basis sets, in particular for metallic systems. The effects of basis set expansion by diffuse and polarization functions were investigated for selected systems. © 2012 Wiley Periodicals, Inc.     

Reduced-size polarized basis sets for calculations of molecular electric properties. I. The basis set generation

Following the recent studies of basis sets explicitly dependent on oscillatory external electric field we have investigated the possibility of some further truncation of the so-called polarized basis sets without any major deterioration of the computed data for molecular dipole moments, dipole polarizabilities, and related electric properties of molecules. It has been found that basis sets of contracted Gaussian functions of the form [3s1p] for H and [4s3p1d] for the first-row atoms can satisfy this requirement with particular choice of contractions in their polarization part. With m denoting the number of primitive GTOs in the contracted polarization function, the basis sets devised in this article will be referred to as the ZmPol sets. In comparison with earlier, medium-size polarized basis sets (PolX), these new ZmPol basis sets are reduced by 2/3 in their size and lead to the order of magnitude computing time savings for large molecules. Simultaneously, the dipole moment and polarizability data remain at almost the same level of accuracy as in the case of the PolX sets. Among a variety of possible applications in computational chemistry, the ZmPolX are also to be used for calculations of frequencies and intensities in the Raman spectra of large organic molecules (see Part II, this issue).     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The basis set polarization approach is employed for the generation of medium-size polarized GTO/CGTO basis sets for calculations of molecular dipole moments and polarizabilities. The excellent performance of the [13.10.4/7.5.2] GTO/CGTO polarized basis sets derived for Si through Cl is illustrated by the atomic polarizability results and SCF and MBPT data for dipole moments and polarizabilities of the second-row atom hydrides. The possible applications of the electric-property oriented polarized basis sets are discussed. The basis set data for Si through Cl are those for H and C through F append the paper.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of BiH₃ (–0.499 a.u.), PoH₂ (–0.207 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to —0.230 a.u., –0.177 a.u., and –0.097 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

The basis set polarization method is used to generate the first-order polarized basis sets for Sn, Sb, Te, and I. The standard (spd) and extended (spdf) versions of those basis sets are derived for the purpose of calculations of dipole moments and dipole polarizabilities for molecules involving the fourth-row atoms. The verification of the performance of the generated polarized basis sets is achieved mainly by a cross-examination of different atomic and molecular results calculated in this paper. The role of the core-polarization and relativistic effects is investigated. It is shown that the relativistic contribution to dipole moments of the fourth-row hydrides is commensurate with the contribution due to electron correlation and must be explicitly considered in accurate calculations. The detailed basis set data for Sn through I are presented in the Appendix.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The basis set polarization method is used to derive the first-order polarized basis sets for Ge through Br for calculations of atomic and molecular electric properties. The performance of the [15.12.9/9.7.4] GTO/CGTO basis sets generated in this study is verified in calculations of atomic dipole polarizabilities and dipole moments and polarizabilities of the third-row atom hydrides. Whenever accurate reference data are available for comparison, the excellent performance of the derived first-order polarized basis sets is demonstrated. The role of the core polarization and relativistic contributions to atomic and molecular is also investigated. The detailed basis set data for Ge through Br are given in Appendix.     

Distributed basis sets of s-type Gaussian functions for molecular electronic structure calculations: Applications of the Gaussian cell model to one-electron polycentric linear molecular systems

A particular formulation of the distributed Gaussian basis-set approach, the extended Gaussian cell model, is applied to the simplest polycentric molecule, the linear H₃²⁺ ion. Calculations of the total energy using two extensions of the original Gaussian cell model are described and results are reported for the ground state and the first excited state. A comparison with recently reported finite element calculations is made for a number of nuclear geometries. © 1996 John Wiley & Sons, Inc.     

On the basis set superposition error in supermolecular calculations of interaction-induced electric properties: many-body components

In the present paper we analyze basis set superposition error (BSSE) removal methods from many-body components of interaction-induced electric properties. The Valiron–Mayer function counterpoise (VMFC), site–site function counterpoise (SSFC) and TB methods have been employed in order to obtain the incremental optical components of linear hydrogen fluoride clusters (HF)n, where n = {3,4}. Following Mierzwicki and Latajka, who have performed similar calculations for the interaction energy, we compare those three methods of eliminating BSSE using several Dunning’s correlation consistent basis sets.     

Gaussian expansions of minimal STO basis for calculations in molecular quantum mechanics

By means of minimal basis SCF calculations for HF, H₂O, NH₃ and CH₄ different expansions of Slater orbitals (STO) in terms of Gaussian orbitals (GTO) are tested in order to find an appropriate compromise between sufficient accuracy of the results and reasonable computing times. The least squares fit of the GTO expansion to STO does not appear to have any advantages over the expansion based on a variational procedure. It turns out that for hydrogens an expansion of the 1s orbital in terms of three GTO is quite sufficient, whereas for first row atoms an expansion of the 1s orbital in terms of three to five GTO, of the 2s orbital in terms of two GTO and of the 2p orbitals in terms of three GTO seems to be adequate.

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Zusammenfassung An Hand von SCF-Rechnungen mit minimaler Basis für die Moleküle HF, H₂O, NH₃ und CH₄ wurden verschiedene Entwicklungen von Slater-Orbitalen (STO) nach Gauß-Orbitalen (GTO) getestet, um einen geeigneten Kompromiß zwischen ausreichender Genauigkeit der Ergebnisse und vertretbaren Rechenzeiten zu finden. Es zeigt sich, daß die Entwicklung der STO nach GTO mit Hilfe der Methode der kleinsten Fehlerquadrate keine Vorteile gegenüber der auf einem Variationsverfahren basierenden Entwicklung aufweist. Für H-Atome erweist sich eine Entwicklung des 1s-Orbitals nach drei GTO als ausreichend, für Atome der 1. Periode erscheint eine Entwicklung des 1s-Orbitals nach drei bis fünf GTO, des 2s-Orbitals nach zwei GTO und der 2p-Orbitale nach drei GTO als geeignet.

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Résumé En vue de trouver un compromis approprié entre la précision et la durée des calculs, différents développements des orbitales de Slater (STO) en termes d'orbitales gaussiennes (GTO) sont testés au moyen de calculs SCF en bases minimales pour HF, H₂O, NH₃ et CH₄. L'ajustement par les moindres carrés du développement des STO en GTO ne présente apparemment d'avantages sur le développement fondé sur un procédé variationnel. Il apparaît que pour l'hydrogène un développement de l'orbitale 1s en fonction de trois gaussiennes est largement suffisant, alors que pour les atomes de la première rangée il semble nécessaire de développer l'orbitale 1s en 3 à 5 GTO, l'orbitale 2s en 2 GTO et les orbitales 2p en 3 GTO.

     

A mixed basis set of slater and gaussian functions for molecular calculations

A procedure for using simultaneously Slater and Gaussian basis functions in molecular calculations is presented here. The analytic expressions of the integral prototypes involving both Slater and Gaussian functions are explicitly derived.     

Reduced-size polarized basis sets for calculations of molecular electric properties. IV. First-row transition metals

Recent studies of the perturbation-dependent basis sets have indicated the possibility of a significant reduction of the size of the usual CGTO sets without considerable loss of accuracy in calculations of molecular electric properties. The resulting (ZPolX) basis sets have been developed for several atoms of the first and second row of the Periodic Table. The same method of the ZPolX basis set generation is extended for the first-row transition metals and the corresponding contracted ZPolX basis sets of the size [6s5p3d1f] are determined for both nonrelativistic and scalar relativistic calculations. The performance of the ZPolX basis sets is verified in calculations on the first-row transition metal oxides at the level of the ROHF, ROHF/CASPT2, and ROHF/CCSD(T) approximations. Also the study of the dipole polarizability of TiCl₄ confirms the excellent features of these very compact basis sets. The ZPolX basis sets for nonrelativistic and relativistic calculations of molecular electric properties are available on the web page http://www.chem.uni.torun.pl/zchk/basis-sets.html.     

Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases

We present a library of Gaussian basis sets that has been specifically optimized to perform accurate molecular calculations based on density functional theory. It targets a wide range of chemical environments, including the gas phase, interfaces, and the condensed phase. These generally contracted basis sets, which include diffuse primitives, are obtained minimizing a linear combination of the total energy and the condition number of the overlap matrix for a set of molecules with respect to the exponents and contraction coefficients of the full basis. Typically, for a given accuracy in the total energy, significantly fewer basis functions are needed in this scheme than in the usual split valence scheme, leading to a speedup for systems where the computational cost is dominated by diagonalization. More importantly, binding energies of hydrogen bonded complexes are of similar quality as the ones obtained with augmented basis sets, i.e., have a small (down to 0.2 kcal/mol) basis set superposition error, and the monomers have dipoles within 0.1 D of the basis set limit. However, contrary to typical augmented basis sets, there are no near linear dependencies in the basis, so that the overlap matrix is always well conditioned, also, in the condensed phase. The basis can therefore be used in first principles molecular dynamics simulations and is well suited for linear scaling calculations.     

Implementation of atomic basis set composed of 1s Gaussian and 1s Slater-type orbitals to carry out quantum mechanics molecular calculations

A mixed atomic basis set formed with ls Slater-type orbitals and 1s floating spherical Gaussian orbitals is implemented. Evaluation of multicenter integrals is carried out using a method based on expansion of binary products of atomic basis functions in terms of a complete basis set, and a systematic analysis is performed. The proposed algorithm is very stable and furnishes fairly good results for total energy and geometry. An LCAO-SCF test calculation is carried out on LiH. The trends observed show that there are some combinations of mixed orbitals that are appropriate to describe the system. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 604–609, 1999