An accurate relativistic universal Gaussian basis set for hydrogen through Nobelium without variational prolapse and to be used with both uniform sphere and Gaussian nucleus models

An accurate relativistic universal Gaussian basis set (RUGBS) from H through No without variational prolapse has been developed by employing the Generator Coordinate Dirac-Fock (GCDF) method. The behavior of our RUGBS was tested with two nuclear models: (1) the finite nucleus of uniform proton-charge distribution, and (2) the finite nucleus with a Gaussian proton-charge distribution. The largest error between our Dirac-Fock-Coulomb total energy values and those calculated numerically is 8.8 mHartree for the No atom.     

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.     

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     

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.     

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     

Relativistic Gaussian basis sets for the elements K – Uuo

A series of energy-minimized relativistic Gaussian basis sets for the elements with atomic numbers 19–118 is presented. The basis sets have been derived at the self-consistent field level as weighted average energies of the respective electronic configurations. A spherical Gaussian charge distribution has been used to model the nucleus. The basis sets are constructed as interleaving dual family sets with shared exponents within each family. The quality of the basis sets is better than double zeta. Received: 7 July 2000 / Accepted: 21 September 2000 / Published online: 21 December 2000     

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin‐free (scalar) and two‐component (spin–orbit) relativistic density functional calculations of indirect NMR nuclear spin–spin coupling (J‐coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J‐couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg₂²⁺, and Tl? X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite‐nucleus effects.     

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     

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.     

Core correlating basis functions for elements 31–118

Gaussian functions for correlation of all core shells of elements from Z = 31 to Z = 118 have been optimized in relativistic singles and doubles CI calculations, performed on the shell of highest angular momentum for each principal quantum number. The SCF functions were derived from the double-zeta, triple-zeta, and quadruple-zeta basis sets previously optimized by the author. Only those Gaussian functions that are not represented in the SCF basis sets were optimized. The functions are available from the Dirac program web site, .     

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     

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.     

1H NMR spectra of ethane‐1,2‐diol and other vicinal diols in benzene: GIAO/DFT shift calculations

The proton NMR spectra of several 1,2‐diols in benzene have been analysed so as to associate each magnetically nonequivalent proton with its chemical shift. The shifts and coupling constants of the OH and methylene protons of ethane‐1,2‐diol have been determined in a wide range of solvents. The conformer distribution and the proton NMR shifts of these 1,2‐diols in benzene have been computed on the basis of density functional theory. The solvent is included using the integral–equation–formalism polarizable continuum model implemented in Gaussian 09. Relative Gibbs energies for all stable conformers are calculated at the Perdew, Burke and Enzerhof (PBE)0/6‐311 + G(d,p) level, and shifts are calculated using the gauge‐including atomic orbital method with the PBE0/6‐311 + G(d,p) geometry but using the cc‐pVTZ basis set. Previous calculations on ethane‐1,2‐diol and propane‐1,2‐diol have been corrected and extended. New calculations on tert‐butylethane‐1,2‐diol, phenylethane‐1,2‐diol, butane‐2,3‐diols (dl and meso) and cyclohexane‐1,2‐diols (cis and trans) are presented. Overall, the computed NMR shifts are in good agreement with experimental values for the OH protons but remain systematically high for CH protons. Some results based on the Gaussian 03 solvation model are included for comparison. Copyright © 2012 John Wiley & Sons, Ltd.     

Near-Dirac–Hartree–Fock results for first-row atoms calculated with GTO basis sets

Relativistic basis sets for first-row atoms have been constructed by using the near-Hartree–Fock (nonrelativistic) eigenvectors calculated by Partridge. These bases generate results of near-Dirac–Hartree–Fock quality. Relativistic total and orbital energies, relativistic corrections to the total energy, and magnetic interaction energies for the first-row atoms have been presented. The smallest Gaussian expansions (13s8 p expansions) yield Dirac–Hartree–Fock total energies accurate through six significant digits, while the largest expansions (18s13p expansions) give these energies accurate through seven significant digits. These results are more accurate than some of the results reported earlier, particularly for the open-shell atoms, indicating that the basis employed is reasonably economical for relativistic calculations. © 1995 John Wiley & Sons, Inc.     

Combined experimental and computational modeling studies on 3,5‐dimethyl‐pyrazole‐1‐carbodithioic acid benzyl ester

The title compound, 3,5‐Dimethyl‐pyrazole‐1‐carbodithioic acid benzyl ester, has been synthesized and structurally characterized by X‐ray single crystal diffraction, elemental analysis, IR spectra, and UV‐Vis spectrum. The crystal belongs to orthorhombic, space group P212121, with a = 5.3829(15), b = 11.193(3), c = 21.824(6) Å, V = 1315.0(6) ų, and Z = 4. The molecules are connected via intermolecular C–H···N hydrogen bonds into 1D infinite chains. The crystal structure is consolidated by the intramolecular C–H···S hydrogen bonds. Furthermore, Density functional theory (DFT) calculations of the structure, stabilities, orbital energies, composition characteristics of some frontier molecular orbitals and Mulliken charge distributions of the title compound were performed by means of Gaussian 03W package and taking B3LYP/6‐31G(d) basis set. The time‐dependent DFT (TD‐DFT) calculations have been employed to calculate the electronic spectrum of the title compound, and the UV‐Vis spectra has been discussed on this basis. The results show that DFT method at B3LYP/6‐31G(d) level can well reproduce the structure of the title compound. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

The use of gaussian nuclear charge distributions for the calculation of relativistic electronic wavefunctions using basis set expansions

It is demonstrated that the use of a Gaussian charge distribution to represent the nucleus is advantageous in relativistic quantum chemical basis set expansion calculations. It removes the singularity at the origin of the Dirac wavefunction, leading to a more rapid convergence of the ground-state energy expectation value as a function of basis set size and to a large reduction in the exponents of the optimized basis sets. Hence, smaller basis sets can be used for HFD calculations.     

Gaussian basis sets for molecular applications

The choice of basis set in quantum chemical calculations can have a huge impact on the quality of the results, especially for correlated ab initio methods. This article provides an overview of the development of Gaussian basis sets for molecular calculations, with a focus on four popular families of modern atom‐centered, energy‐optimized bases: atomic natural orbital, correlation consistent, polarization consistent, and def2. The terminology used for describing basis sets is briefly covered, along with an overview of the auxiliary basis sets used in a number of integral approximation techniques and an outlook on possible future directions of basis set design. © 2012 Wiley Periodicals, Inc.     

Structures and properties of lanthanide and actinide complexes by a new density functional approach: Lanthanum,gadolinium, lutetium,and thorium halides as case studies

The LaX₃, GdX₃, LuX₃, and ThX₄ systems (X = F, Cl, Br, and I) have been chosen as test cases to analyze the performances of a computational protocol, resting on a recently proposed density functional method, the so‐called PBE0 model. Relativistic effects were taken into account by means of two different sets of quasi‐relativistic effective core potentials. All static data were found to be in very good agreement with those provided by post‐HF methods. Because experimental geometries have been determined at high temperature (1000–1800 K), the effect of nuclear motions have been considered through a variational numerical procedure. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1153–1166, 2000