Computational linear dependence in molecular electronic structure calculations using universal basis sets

Distributed universal even‐tempered basis sets have been developed over recent years that are capable of supporting Hartree–Fock energies to an accuracy approaching the sub‐μHartree level. These basis sets have also been exploited in correlation studies, in applications to polyatomic molecules, and in the calculation of electric properties, such as multipole moments, polarizabilities, and hyperpolarizabilities. Jorge and coworkers have also developed universal basis sets and have recently reported applications to diatomic molecular systems. In this article, we compare the molecular calculations reported by Jorge and coworkers with our previous studies. Particular attention is given to the degree of computational linear dependence associated with the various basis sets employed and the consequential effects of the accuracy of the calculated energies. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Auxiliary basis sets for density fitting-MP2 calculations: Nonrelativistic triple-zeta all-electron correlation consistent basis sets for the 3d elements Sc-Zn

Auxiliary basis sets for density fitting second-order Moller-Plesset perturbation theory (DF-MP2) have been optimized for use with the triple-zeta nonrelativistic all-electron correlation consistent orbital basis sets, cc-pVTZ-NR and aug-cc-pVTZ-NR, for the 3d elements Sc-Zn. The relative error in using these auxiliary basis sets is found to be around four orders of magnitude smaller than that from utilizing triple-zeta orbital basis sets rather than corresponding quadruple-zeta basis sets, in calculation of the correlation energy for a test set of 54 small to medium sized transition metal complexes.     

A scheme for the economical use of numerical basis sets in calculations with SIESTA

We demonstrate the effectiveness of an economical scheme that uses numerical basis sets in computations with SIESTA. The economical basis sets demonstrated, in which high-level double-zeta basis plus polarization orbitals (DZP) are applied only for atoms of strong electronegativity and metal atoms while a double-zeta basis is applied to the rest of the atoms of small proton-bound carboxylic acid clusters and sodium–organic compounds, predict correct geometric structures very close to those obtained using DZP for all atoms. The use of economical basis sets can save about 30–50% of the CPU time that is used for calculations with large basis sets. This study provides a general guideline for basis set selection in SIESTA computations of large systems.Acknowledgement. The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. CityU 1033/00P).     

A study of the performance of numerical basis sets in DFT calculations on sulfur-containing molecules

The performance of numerical basis sets in relation to Gaussian basis sets is examined, by studying 20 small sulfur-containing molecules. The results of geometry optimization calculations are reported for each molecule using both density functional and Hartee-Fock methods. In comparison with experimental data, it is shown that the use of numerical bases tend to overestimate structural parameters, particularly bond lengths, and, in most cases, more than Gaussian basis sets. It is also shown that the use of a larger Gaussian basis set in DFT calculations has the effect of reducing bond lengths. © 1996 John Wiley & Sons, Inc.     

BSSE-correction scheme for consistent gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations

Revised versions of our published pob-TZVP [Peintinger, M. F.; Oliveira, D. V. and Bredow, T., J. Comput. Chem., 2013, 34 (6), 451–459.] and unpublished pob-DZVP basis sets, denoted as pob-TZVP-rev2 and pob-DZVP-rev2, have been derived for the elements H Br. It was observed that the pob basis sets suffer from the basis set superposition error (BSSE). In order to reduce this effect, we took into account the counterpoise energy of hydride dimers as an additional parameter in the basis set optimization. The overall performance, portability, and SCF stability of the resulting rev2 basis sets are significantly improved compared to the original pob basis sets. © 2019 Wiley Periodicals, Inc.     

Correlation balance in basis sets for electronic structure calculations

The balanced addition of polarization functions to the 6–31G and 6–311G basis sets for correlated wave functions is evaluated using bond energy predictions at the MP 2 and full MP 4 levels as a measure of correlation-balanced basis sets. The homolytic dissociations of the XH bonds in H₂, CH₄, NH₃, H₂O, and HF and the XY bonds in C₂H₆, NH₂NH₂, HOOH, and CH₃OH are used as the basis for the evaluation. It is found that correlation balance is achieved for HH, XH, and XY bonds, particularly at the MP 2 level, only if at least as many polarization sets, and sometimes more, are added to the hydrogens as are added to the heavy atoms.     

Minimal basis sets in calculations of intermolecular interaction energies

Several minimal (7, 3/3) Gaussian basis sets have been used to calculate the energies and some other properties of CH₄ and H₂O. Improved basis sets developed for these molecules have been extended to NH₃ and HF and employed to H₂CO and CH₃OH. Interaction energies between XH_n molecules have been calculated using the old and the new minimal basis sets. The results obtained with the new basis sets are comparable in accuracy to those calculated with significantly more extended basis sets involving polarization functions. Binding energies calculated using the counterpoise method are not much different for the new and the old minimal basis sets, and are likely to be more accurate than the results of much more extended calculations.     

Newly developed basis sets for density functional calculations

Optimized contracted Gaussian basis sets of double-zeta valence polarized (DZVP) quality for first-row transition metals are presented. The DZVP functions were optimized using the PWP86 generalized gradient approximation (GGA) functional and the B3LYP hybrid functional. For a careful analysis of the basis sets performance the transition metal atoms and cations excitation energies were calculated and compared with the experimental ones. The calculated values were also compared with those obtained using the previously available DZVP basis sets developed at the local-density functional level. Because the new basis sets work better than the previous ones, possible reasons of this behavior are analyzed. The newly developed basis sets also provide a good estimation of other atomic properties such as ionization energies.     

Optimization of Gaussian basis sets for Dirac-Hartree-Fock calculations

We investigate the optimization of Gaussian basis sets for relativistic calculations within the framework of the restricted Dirac-Hartree-Fock (DHF) method for atoms. We compare results for Rn of nonrelativistic and relativistic basis set optimizations with a finite nuclear-size. Optimization of separate sets for each spin-orbit component shows that the basis set demands for the lower j component are greater than for the higher j component. In particular, the p _1/2 set requires almost as many functions as the s _1/2 set. This implies that for the development of basis sets for heavy atoms, the symmetry type for which a given number of functions is selected should be based on j, not on l, as has been the case in most molecular calculations performed to date.     

Effective basis sets for calculations of exchange-repulsion energy

Usefulness of different Gaussian basis sets for reproducing the “tail” region of the SCF wavefunctions employed in calculations of the exchange-repulsion effect is investigated for the model He-He interaction. It has been shown that extension of the monomer-centered basis set in the scheme of regularized even-tempered basis sets [M. W. Schmidt and K. Ruedenberg, J. Chem. Phys. 71 , 3951 (1979)] can be more efficient than augmentation of the fully energy-optimized basis set with diffuse basis functions. It has been also found that Landshoff term vanishes and the “tail” region is well reproduced if monomer wavefunctions are calculated with the basis set of the dimer.     

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.     

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.     

Locally dense basis sets for chemical shift calculations

Calculations of chemical shifts have been carried out using “locally dense” basis sets for the resonant atom of interest, and smaller, attenuated sets on other atoms in the molecule. For carbon, calculations involving a 6-311G(d) triply split valence set with polarization on the resonant atom and 3-21G atomic bases on other heavy atoms result in good agreement with experiment, and are virtually identical to those found employing the larger basis on all atoms. For species such as nitrogen, oxygen, and fluorine where standard balanced basis sets do not agree well with experiment, use of attenuated sets fail as well. The use of locally dense basis sets permits calculations previously impractical, and the successful application to carbon suggests that the chemical shift is most dependent on the local basis set, and less so on whether or not a balanced or unbalanced calculation is being carried out.     

Choosing GTO basis sets for periodic HF calculations

We investigate numerical linear dependencies of Gaussian-type orbital basis sets employed in the framework of the Hartree-Fock self-consistent field method for periodic structures, which so far have hampered the use of extended basis sets for non-ionic crystals. These linear dependencies occur when diffuse basis functions are included in a basis set in an uncontrolled manner. We use the condition number of the overlap matrix to lead us in the construction of extended basis sets for periodic structures which avoid numerical linear dependencies. Extended basis sets of high quality are optimized for a number of periodic structures (fcc He, α-Be, α-BN, and B1 NaF) with respect to the energy of the constituent atoms or ions. The results obtained with our basis sets, which do not require reoptimization in the crystal environment, compare favorably with those obtained with other extended basis sets reported in the literature. Received: 20 July 1998/Accepted: 21 August 1998 / Published online: 19 October 1998     

Polarization consistent basis sets. V. The elements Si-Cl

Polarization consistent basis sets, optimized for density functional calculations, are proposed for the elements Si-Cl. Their performance for atomization energies, equilibrium geometries, harmonic vibrational frequencies, and associated infrared intensities is compared with other commonly used basis sets. Atomization energies can be predicted to within 0.01 kJ/mol per atom of the basis set limit by extrapolation of the pc-2, -3, and -4 results. Equilibrium bond distances and harmonic vibrational frequencies can be calculated to within 10(-5) A and 0.5 cm(-1), respectively, of the basis set limit. The pc-n basis sets are shown to give comparable or better accuracy than other alternatives, while containing fewer or equal number of primitive basis functions.     

Relativistic effects determined using the Douglas-Kroll contracted basis sets and correlation consistent basis sets with small-core relativistic pseudopotentials

The coupled cluster approximation with single, double, and quasiperturbative triple excitations [CCSD(T)] was used in combination with the Douglas-Kroll contracted correlation consistent basis sets [cc-pVnZ-DK, where n = D(2), T(3), Q(4), and 5] and small-core relativistic pseudopotentials (PP) with correlation consistent polarized valence basis sets (cc-pVnZ-PP and aug-cc-pVnZ-PP) to investigate the impact of scalar relativistic corrections on energetic and structural properties of small molecules containing third-row (Ga-Kr) atoms. These molecules were taken from the Gaussian-2 extended test set for third-row atoms. Atomization energies, ionization energies, electron affinities, and proton affinities for molecules in the test set were determined and compared with nonrelativistic results which were obtained in a recent study in which the standard and augmented correlation consistent basis sets were used in combination with CCSD(T). Several schemes were used to extrapolate the energies to the complete basis set limit.     

Cubic-grid Gaussian basis sets for electron scattering calculations IV

Summary An analytical formula has been derived for averaging the differential cross section for electron scattering with respect to isotropic target molecule orientation. It may be applied to any type ofT-matrix element k ^out|T|k ⁱⁿ in which the plane-wave functionsk ^out andk ⁱⁿ are expanded in a set ofs-type Gaussian functions. The formula for averaging was tested against results obtained by Monte-Carlo-type calculations and against experimental data for elastic electron scattering by the H₂ molecule.     

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.