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.     

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.     

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.     

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.     

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.     

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.     

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     

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.     

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.     

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.     

Using many-particle basis sets for electronic energy calculations of molecules

A method of calculating the electronic energies of molecules using a many-particle basis set is proposed. In this case, the many-particle Schrödinger equation may be solved without resorting to the one-electron approximation. The results of the electronic energy calculations of some two-electron systems are in good agreement with experimental results.     

Molecular structure–biological activity relationships on the basis of quantum-chemical calculations

Detailed quantum-chemical calculations by means of semiempirical all-valence electrons methods and a generalized (multivariable) rank correlation analysis are the fundamentals of a novel strategy of search for QSAR within homologous series of compounds. The set of molecular parameters (describing the electronic and conformational properties as well as potential interactions of the drugs) is calculated theoretically. Owing to the rank correlation method, no linear model (like LFER ) for the dependence of the biological activity upon the molecular parameters is presumed. The computed correlation coefficients are valued by carefully determined levels of statistical significance. Significant correlations are used to predict unknown activities in terms of ranks relative to the basic sample.     

Auxiliary basis sets for density-fitted correlated wavefunction calculations: weighted core-valence and ECP basis sets for post-d elements

We report optimised auxiliary basis sets for the resolution-of-the-identity (or density-fitting) approximation of two-electron integrals in second-order M?ller-Plesset perturbation theory (MP2) and similar electronic structure calculations with correlation-consistent basis sets for the post-d elements Ga-Kr, In-Xe, and Tl-Rn. The auxiliary basis sets are optimised such that the density-fitting error is negligible compared to the one-electron basis set error. To check to which extent this criterion is fulfilled we estimated for a test set of 80 molecules the basis set limit of the correlation energy at the MP2 level and evaluated the remaining density-fitting and the one-electron basis set errors. The resulting auxiliary basis sets are only 2-6 times larger than the corresponding one-electron basis sets and lead in MP2 calculations to speed-ups of the integral evaluation by one to three orders of magnitude. The density-fitting errors in the correlation energy are at least hundred times smaller than the one-electron basis set error, i.e. in the order of only 1-100 μH per atom.     

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.