Adapted Gaussian basis sets for atoms Cs to Lr based on the generator coordinate Hartree–Fock method

We have applied a discretized version of the generator coordinate Hartree–Fock method to generate adapted Gaussian basis sets for atoms Cs (Z=55) to Lr (Z=103). Our Hartree–Fock total energy results, for all atoms studied, are better than the corresponding Hartree–Fock energy results attained with previous Gaussian basis sets. For the atoms Cs to Lr we have obtained an energy value within the accuracy of 10⁻⁴ to 10⁻³ hartree when compared with the corresponding numerical Hartree–Fock total energy results. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 858–865, 1998     

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.     

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     

Molecule‐adapted basis sets optimized with a quantum Monte Carlo method

The Monte Carlo simulated annealing method is adapted to optimize correlated Gaussian‐type functions in nonrelativistic molecular environments. Starting from an atom‐centered atomic Gaussian basis set, the uncontracted functions are reoptimized in the molecular environments corresponding to the H₂O, CN^?, N₂, CO, BF, NO⁺, CO₂, and CS systems. These new molecular adapted basis sets are used to calculate total energies, harmonic vibrational frequencies, and equilibrium geometries at a correlated level of theory. The present methodology is a simple and effective way to improve molecular correlated wave functions, without the need to enlarge the molecular basis set. Additionally, this methodology can be used to generate hierarchical sequences of molecular basis sets with increasing size, which are relevant to establish complete basis set limits. © 2014 Wiley Periodicals, Inc.     

Accurate relativistic adapted Gaussian basis sets for Cesium through Radon without variational prolapse and to be used with both uniform sphere and Gaussian nucleus models

Accurate relativistic adapted Gaussian basis sets (RAGBSs) from Cs (Z = 55) through Rn (Z = 86) without variational prolapse were developed by using the polynomial version of the Generator Coordinate Dirac-Fock method. The RAGBSs presented here can be used with any of two popular finite nucleus models, the uniform sphere and the Gaussian models. The largest RAGBS error is 4.5 mHartree for Radon with a size of 30s27p17d11f.     

Accurate relativistic adapted Gaussian basis sets for hydrogen through xenon without variational prolapse and to be used with both uniform sphere and Gaussian nucleus models

Accurate relativistic adapted Gaussian basis sets (RAGBSs) from H (Z = 1) through Xe (Z = 54) without variational prolapse have been developed by employing a polynomial version of the Generator Coordinate Dirac‐Fock (p‐GCDF) method. Two nuclear models have been used in this work: (1) the finite nucleus of uniform proton‐charge distribution, and (2) the finite nucleus with a Gaussian proton–charge distribution. The largest errors observed are only 1.5 mHartree (silver and cadmium) and the RAGBS sizes are much smaller than previous accurate relativistic Gaussian basis sets that were shown to be free of variational prolapse. © 2005 Wiley Periodicals, Inc. J Comput Chem 27: 61–71, 2006     

Gaussian basis sets for transition metals of the second series

A Gaussian basis set consisting of (15s, 9p, 8d) Gaussian functions has been optimized for the transition metal atoms of the second series (fourth-row atoms).     

Efficiency of numerical basis sets for predicting the binding energies of hydrogen bonded complexes: evidence of small basis set superposition error compared to Gaussian basis sets

Binding energies of selected hydrogen bonded complexes have been calculated within the framework of density functional theory (DFT) method to discuss the efficiency of numerical basis sets implemented in the DFT code DMol3 in comparison with Gaussian basis sets. The corrections of basis set superposition error (BSSE) are evaluated by means of counterpoise method. Two kinds of different numerical basis sets in size are examined; the size of the one is comparable to Gaussian double zeta plus polarization function basis set (DNP), and that of the other is comparable to triple zeta plus double polarization functions basis set (TNDP). We have confirmed that the magnitudes of BSSE in these numerical basis sets are comparative to or smaller than those in Gaussian basis sets whose sizes are much larger than the corresponding numerical basis sets; the BSSE corrections in DNP are less than those in the Gaussian 6-311+G(3df,2pd) basis set, and those in TNDP are comparable to those in the substantially large scale Gaussian basis set aug-cc-pVTZ. The differences in counterpoise corrected binding energies between calculated using DNP and calculated using aug-cc-pVTZ are less than 9 kJ/mol for all of the complexes studied in the present work. The present results have shown that the cost effectiveness in the numerical basis sets in DMol3 is superior to that in Gaussian basis sets in terms of accuracy per computational cost.     

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.     

Polarized basis sets of Slater-type orbitals: H to Ne atoms

We present three Slater-type atomic orbital (STO) valence basis (VB) sets for the first and second row atoms, referred to as the VB1, VB2, and VB3 bases. The smallest VB1 basis has the following structure: [3, 1] for the H and He atoms, [5, 1] for Li and Be, and [5, 3, 1] for the B to Ne series. For the VB2 and VB3 bases, both the number of shells and the number of functions per shell are successively increased by one with respect to VB1. With the exception of the H and Li atoms, the exponents for the VB1 bases were obtained by minimizing the sum of the Hartree-Fock (HF) and frozen-core singles and doubles configuration interaction (CISD FC) energies of the respective atoms in their ground state. For H and Li, we minimized the sum of the HF and CISD FC energies of the corresponding diatoms (i.e., of H(2) or Li(2)) plus the ground-state energy of the atom. In the case of the VB2 basis sets, the sum that was minimized also included the energies of the positive and negative ions, and for the VB3 bases, the energies of a few lowest lying excited states of the atom. To account for the core correlations, the VBx (x = 1, 2, and 3) basis sets for the Li to Ne series were enlarged by one function per shell. The exponents of these extended (core-valence, CV) basis sets, referred to, respectively, as the CVBx (x = 1, 2, and 3) bases, were optimized by relying on the same criteria as in the case of the VBx (x = 1, 2, and 3) bases, except that the full CISD rather than CISD FC energies were employed. We show that these polarized STO basis sets provide good HF and CI energies for the ground and excited states of the atoms considered, as well as for the corresponding ions.     

Adaptation of one‐electron basis sets to spatial confinements

A method that generates out of a given orbital basis set its analog appropriate for describing the effects of a spatial confinement is presented. The method is based on the requirement that the one‐particle model spaces for the confined and for the unconfined systems are equivalent in the sense of a criterion derived from the basis‐set‐generating eigenvalue equations. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 341–347, 1999     

Spatially restricted Double Z-Simplified Box Orbital basis sets: Optimization and comparison with some standard basis sets

As part of previous studies, we introduced a new type of basis function named Simplified Box Orbitals (SBOs) that belong to a class of spatially restricted functions which allow the zero differential overlap (ZDO) approximation to be applied with complete accuracy. The original SBOs and their Gaussian expansions SBO-3G form a minimal basis set, which was compared to the standard Slater-type orbital basis set (STO-3G). In the present paper, we have developed the SBO basis functions at double-zeta (DZ) level, and we have assessed the option of expanding the SBO-DZ as a combination of Gaussian functions. Finally, we have determined the quality of the new basis set by comparing the molecular properties calculated with SBO-nG with those achieved with some standard basis sets.     

An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000     

Relativistic Gaussian basis sets for molecular calculations: Fully optimized single‐family exponent basis sets for H?Hg

Relativistic single‐family exponent Gaussian basis sets for molecular calculations are presented for the 80 atoms ₁H through ₈₀Hg. The exponent parameters shared by Gaussian basis functions of all symmetry species are fully optimized. Two nucleus models of uniformly charged sphere and Gaussian charge distribution are considered and two kinds of basis sets are generated accordingly. The total energy errors are less than 2 mhartree in any atoms. Some of the present basis sets include small variational collapse (or prolapse), but test calculations show that they could be reliably applied to molecular calculations. © 2005 Wiley Periodicals, Inc. J Comput Chem 27: 48–52, 2006     

Gaussian basis sets for first‐, third‐, and fourth‐row positive and negative ions

An improved generator coordinate Hartree–Fock (HF) method is used to generate accurate triple‐optimized Gaussian basis sets for the cations from He⁺ (Z=2) through Ne⁺ (Z=10) and from K⁺ (Z=19) through Xe⁺ (Z=54), and for the anions from H⁻ (Z=1) through F⁻ (Z=9) and from K⁻ (Z=19) through I⁻ (Z=53). For all ions here studied, our ground‐state HF total energies are better than those calculated with the generator coordinate HF method, using optimized Gaussian basis sets of the same size. For all ions studied, the largest difference between our total energy values and the corresponding results obtained with a numerical HF method is equal to 3.434 mhartrees for Te⁺. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 126–130, 2001