Relativistic well-tempered gaussian basis sets

The effectiveness of well-tempered Gaussian basis sets has been tested for the atoms He-Ar, Ag, and Xe. It has been found that orbital exponents optimized through the well-tempered scheme for non-relativistic atoms can be carried over to relativistic calculations to produce wavefunctions close to the relativistic Hartree-Fock limit.     

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.

     

Molecular integrals over generalized gaussian basis sets

A method is given for obtaining the common molecular integrals over generalized gaussian functions: The present algorithms are expected to be more efficient than those given in earlier work by the same author.     

The ellipsoidal gaussian basis in molecular orbital theory

New analytic integral formulas are presented for the potential energy integrals over ellipsoidal Gaussian basis functions [ exp (-x² - y² - z²)] that enter into solving the conventional expansion self-consistent field equations. Near minimal atomic orbital bases combined from large nuclear-centered primitive Gaussian sets are used in test calculations on the HF and CO molecules. The ellipsoidal exponential parameters for the valence atomic orbitals are fully optimized using a single scale factor for each atomic orbital and nuclear coordinate. The results are compared with those obtained using an unoptimized nuclear centered double-zeta spherical Gaussian basis.     

Property-optimized gaussian basis sets for molecular response calculations

With recent advances in electronic structure methods, first-principles calculations of electronic response properties, such as linear and nonlinear polarizabilities, have become possible for molecules with more than 100 atoms. Basis set incompleteness is typically the main source of error in such calculations since traditional diffuse augmented basis sets are too costly to use or suffer from near linear dependence. To address this problem, we construct the first comprehensive set of property-optimized augmented basis sets for elements H-Rn except lanthanides. The new basis sets build on the Karlsruhe segmented contracted basis sets of split-valence to quadruple-zeta valence quality and add a small number of moderately diffuse basis functions. The exponents are determined variationally by maximization of atomic Hartree-Fock polarizabilities using analytical derivative methods. The performance of the resulting basis sets is assessed using a set of 313 molecular static Hartree-Fock polarizabilities. The mean absolute basis set errors are 3.6%, 1.1%, and 0.3% for property-optimized basis sets of split-valence, triple-zeta, and quadruple-zeta valence quality, respectively. Density functional and second-order M?ller-Plesset polarizabilities show similar basis set convergence. We demonstrate the efficiency of our basis sets by computing static polarizabilities of icosahedral fullerenes up to C(720) using hybrid density functional theory.     

Uniform quality gaussian basis sets for molecular calculations. III. Charge optimized basis sets

Gradient optimized constrained (2s ≠ 2p) and unconstrained (2s ≠ 2p) Gaussian 3G basis sets are reported for the first-row atoms and ions X^O, for Q = ?2 to +4. Analytic equations have been fitted to the logarithm of the exponents as a function of the nuclear charge Z and formal charge Q. Consequently only two parameters Z and Q have to be specified in order to completely define a basis set.     

Accurate relativistic adapted gaussian basis sets for francium through ununoctium without variational prolapse and to be used with both uniform sphere and gaussian nucleus models

Accurate relativistic adapted Gaussian basis sets (RAGBSs) for ₈₇Fr up to ₁₁₈Uuo atoms without variational prolapse were developed here with the use of a polynomial version of the Generator Coordinate Dirac‐Fock method. Two finite nuclear models have been used, the Gaussian and uniform sphere models. The largest RAGBS error, with respect to numerical Dirac‐Fock results, is 15.4 miliHartree for Ununoctium with a basis set size of 33s30p19d14f functions. © 2013 Wiley Periodicals, Inc.     

Atomic orbital basis sets for molecular interactions

We describe a general approach to the parametrization of linear combinations of Gaussian atomic orbitals, useful for atomic and molecular interactions. We use a Gaussian transform method and Gauss-Legendre quadratures to express hydrogenic atomic orbitals, with varying effective charges, in terms of Gaussian-type orbitals. This procedure provides well-defined rules for calculating exponent factors and combination coefficients of the linear combinations of Gaussians in problems where nuclear distances may vary over large ranges during interactions. © 1994 by John Wiley & Sons, Inc.     

Accurate quantum-chemical calculations using Gaussian-type geminal and Gaussian-type orbital basis sets: applications to atoms and diatomics

We have implemented the use of mixed basis sets of Gaussian one- and two-electron (geminal) functions for the calculation of second-order M?ller-Plesset (MP2) correlation energies. In this paper, we describe some aspects of this implementation, including different forms chosen for the pair functions. Computational results are presented for some closed-shell atoms and diatomics. Our calculations indicate that the method presented is capable of yielding highly accurate second-order correlation energies with rather modest Gaussian orbital basis sets, providing an alternative route to highly accurate wave functions. For the neon atom, the hydrogen molecule, and the hydrogen fluoride molecule, our calculations yield the most accurate MP2 energies published so far. A critical comparison is made with established MP2-R12 methods, revealing an erratic behaviour of some of these methods, even in large basis sets.     

Small gaussian basis sets for AB initio calculations on large molecules

Gaussian basis sets of (5s, 2p) for carbon, nitrogen, and oxygen, and (7s, 4p) for phosphorous and sulfur have been developed for ab initio calculations of biological molecules. Double zeta contracted bases are given for all five atoms. Minimum bases are given for carbon, nitrogen and oxygen, and a method is developed for replicating primitives in order to minimize the energy loss when contracting small bases. The contracted bases are applied to formamide and the results are compared with those obtained from other small basis sets.     

Accurate Coulomb-fitting basis sets for H to Rn

A series of auxiliary basis sets to fit Coulomb potentials for the elements H to Rn (except lanthanides) is presented. For each element only one auxiliary basis set is needed to approximate Coulomb energies in conjunction with orbital basis sets of split valence, triple zeta valence and quadruple zeta valence quality with errors of typically below ca. 0.15 kJ mol(-1) per atom; this was demonstrated in conjunction with the recently developed orbital basis sets of types def2-SV(P), def2-TZVP and def2-QZVPP for a large set of small molecules representing (nearly) each element in all of its common oxidation states. These auxiliary bases are slightly more than three times larger than orbital bases of split valence quality. Compared to non-approximated treatments, computation times for the Coulomb part are reduced by a factor of ca. 8 for def2-SV(P) orbital bases, ca. 25 for def2-TZVP and ca. 100 for def2-QZVPP orbital bases.     

Atomic natural orbital basis sets for transition metals

Summary We show that atomic natural orbitals are an excellent way to contract transition-metal basis sets, even though the different low-lying electronic states may have very different basis set requirements.     

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.     

Uniform quality gaussian basis sets for molecular calculations. IV. Gradient and charged optimized basis sets for CH4

Comparison of the molecular Q-optimized and molecular gradient optimized carbon basis sets for CH 4 showed that molecular Q optimization is an excellent substitute to the more expensive molecular gradient optimization. The parameter Q of the Q optimization is related to the population (i.e., net charge) on the atom.     

A comparison of lobe and cartesian gaussian basis sets for molecular calculations

Lobe gaussian and cartesian gaussian basis sets, of approximately minimal basis Slater accuracy, have been compared for molecular calculations. The basis sets were constructed so that they only differed in the representation of the angular dependence of the p function. Calculation of total energy and several one-electron properties for a series of nine molecules shows that, for molecular calculations, the lobe and cartesian gaussian representations are equivalent.     

Nonempirical calculations of dipole moments of molecules in semifloating gaussian basis sets

For the example of the calculation of the dipole moments of the HF, HCl, H₂O, NH₃, CO, H₂CO, CH₃F molecules in two-exponent and three-exponent Gaussian basis sets, we have studied the effect of including floating functions in the basis, directly giving the effect of polarization of the electron shell of the atom in the molecule. We have established a weak dependence of the calculated dipole moment on the dimensionality of the basis, the number of floating functions, and also the orbital exponents of the hydrogen atoms. The correction introduced by the floating functions in molecules with polar bonds is considerably greater than the correlation correction. The proposed approach allows us to decrease the dimensionality of the orbital basis by a factor of 1.5–2 without making the agreement with experiment worse.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 4, pp. 481–485, July–August, 1990.     

Proper gaussian basis sets for density functional studies of water dimers and trimers

The accuracy of the Perdew-Burke-Ernzerhof and Tao-Perdew-Staroverov-Scuseria density functionals for describing noncovalent interaction energies in small water clusters is studied by testing 11 basis sets on a reduced test set proposed by Dahlke and Truhlar (J. Phys. Chem. B 2005, 109, 15677). We have also tested variants of the Perdew-Burke-Ernzerhof functional and the Becke98 hybrid functional. While moderate basis sets give converged density functional theory results for covalent dissociation energies, this is not true for noncovalent interaction energies. Our results show that density functionals give converged interaction energies with aug-cc-pVTZ and aug-cc-pVQZ basis sets. Gradual simplification of the basis set introduces an increasing overbinding effect. The best agreement with the high-level result was obtained by the Perdew-Burke-Ernzerhof functional at the basis set limit. The converged Tao-Perdew-Staroverov-Scuseria interaction energies show a systematic underbinding effect that can be compensated by a somewhat systematic overbinding basis set effect of smaller basis sets such as 6-31+G(d,2p). The inclusion of the diffuse functions in the oxygen basis set is very important, while the inclusion of the f functions practically does not influence the results. Improvement can be obtained by adding more hydrogen p functions to the 6-31+G basis set.     

Accurate extrapolation of electron correlation energies from small basis sets

A new two-point scheme is proposed for the extrapolation of electron correlation energies obtained with small basis sets. Using the series of correlation-consistent polarized valence basis sets, cc-pVXZ, the basis set truncation error is expressed as deltaE(X) proportional, variant(X + xi(i))(-gamma). The angular momentum offset xi(i) captures differences in effective rates of convergence previously observed for first-row molecules. It is based on simple electron counts and tends to values close to 0 for hydrogen-rich compounds and values closer to 1 for pure first-row compounds containing several electronegative atoms. The formula is motivated theoretically by the structure of correlation-consistent basis sets which include basis functions up to angular momentum L = X-1 for hydrogen and helium and up to L = X for first-row atoms. It contains three parameters which are calibrated against a large set of 105 reference molecules (H, C, N, O, F) for extrapolations of MP2 and CCSD valence-shell correlation energies from double- and triple-zeta (DT) and triple- and quadruple-zeta (TQ) basis sets. The new model is shown to be three to five times more accurate than previous two-point schemes using a single parameter, and (TQ) extrapolations are found to reproduce a small set of available R12 reference data better than even (56) extrapolations using the conventional asymptotic limit formula deltaE(X) proportional, variantX(-3). Applications to a small selection of boron compounds and to neon show very satisfactory results as well. Limitations of the model are discussed.     

Accurate estimation of correlation energies using locally dense basis sets

Locally dense basis sets using the mixed 6-311G(d, p)/3-21G basis can be used to reproduce total energies and correlation energies after empirical adjustment to 2–4 kcal/mol for a variety of small and medium size molecules containing hydrog en, carbon, and oxygen. Post-Hartree\–Fock methods can be calculated faster by this method by factors of 2–3, in general, and higher in the presence of high molecular symmetry; density functional approaches take longer and are impractical in th e locally dense basis set approach. It is shown that the correlation energy in two of the better characterized density functional approaches is generally significantly larger than that of the post-Hartree–Fock treatments studied here and appears to be insensitive to the basis set employed. © 1996 by John Wiley & Sons, Inc.