On the Use of an Interpolation Approach for the Choice of Gaussian Polarization Functions (original) (raw)
Related papers
Journal of Computational Methods in Sciences and Engineering, 2004
The rational design rules for atomic Gaussian basis sets, tailored for the calculations of molecular polarizabilities αij and hyperpolarizabilities β ijk at the SCF level, are elaborated. The sequence of the optimized polarization sets (2d), (3d), (4d), (3d1f), (4d3f) for the first-row atoms from B to F is constructed, the optimization technique is supposed to provide a rapid convergence of both αij and β ijk with the size of the polarization set. Adding of these polarization sets to the [6s4p] and [6s5p] substrates, derived from the energy-optimized (10s6p) primitive set of Huzinaga, gives the [6s4pNdMf] and [6s5pNdMf] bases families. They are combined with the corresponding [4sNpMd] and [5sNpMd] bases for Hydrogen built up in the same manner. The convergence of SCF results with the size of the basis set has been thoroughly investigated by the examples of H2CO, CH3CN, and HCN molecules. It has been established that both αij and β ijk values converge to their saturation limits at the [6s4p3d/4s3p] level. This basis set provides the results, which are very close to near HF limit values, estimated with the most sophisticated polarized Gaussian basis sets used up to now.
Effect of the basis set on the computation of molecular polarization
The Journal of Physical Chemistry, 1993
The effect of the basis set on the polarization contribution to the interaction energy was studied by means of the polarization energy maps for hydrogen cyanide, formaldehyde, and urea. The study was carried out at the SCFlevel. Basis sets included in the present study were the split-valence 3-21G, 6-31G, 6-31G*, and 6-31G** basis sets and Dunning's 9s5p contracted to a double zeta (DZ), the DZ plus one set of polarization functions (DZP), or two (DZPP'). A DZ plus one set of polarization functions with exponents optimized to yield reliable polarizabilities (DZP') was also used. The polarization a t each point was calculated as the difference between the interaction energy of the molecule with a positive point charge and the molecular electrostatic potential at this point. Maps were computed for three different planes at 2, 4, and 8 bohrs from the plane containing the heavy atoms of the molecule. Comparison of the results shows a correlation between the percentage of the polarization achieved with the ability of a basis set to provide reasonable estimates of dipole polarizabilities. Thus, a basis set with polarization functions optimized to obtain reliable polarizabilities was necessary to achieve good quantitative descriptions of molecular polarization potentials.
Theoretical Chemistry Accounts, 2005
Following the recent studies of basis sets explicitly dependent on oscillatory external electric field we have investigated the possibility of some further truncation of the so-called polarized basis sets without any major deterioration of the computed data for molecular dipole moments, dipole polarizabilities, and related electric properties of molecules. It has been found that basis sets of contracted Gaussian functions of the form [3s1p] for H and [4s3p1d] for the first-row atoms can satisfy this requirement with particular choice of contractions in their polarization part. With m denoting the number of primitive GTOs in the contracted polarization function, the basis sets devised in this article will be referred to as the ZmPol sets. In comparison with earlier, medium-size polarized basis sets (PolX), these new ZmPol basis sets are reduced by 2/3 in their size and lead to the order of magnitude computing time savings for large molecules. Simultaneously, the dipole moment and polarizability data remain at almost the same level of accuracy as in the case of the PolX sets. Among a variety of possible applications in computational chemistry, the ZmPolX are also to be used for calculations of frequencies and intensities in the Raman spectra of large organic molecules (see Part II, this issue).
Polarization functions for gaussian basis sets for the first row atoms
Theoretica Chimica Acta, 1977
Exponent optimization was performed for a single set of d-type Gaussians on the first row atoms C, N, and O in fifteen small molecules. The hydrogen p-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.
Theoretica Chimica Acta, 1992
The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of Bill 3 (-0. 4 9 9 a.u.), Poll 2 (-0. 2 0 7 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to-0.230a.u.,-0.177a.u., and-0. 0 9 7 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system.
On polarization functions for Gaussian basis sets
Journal of Molecular Modeling, 2020
In this work, we introduce a technique to choose polarization functions directly from the primitive set of Gaussian exponent without the necessity to optimize or even reoptimized them. For this purpose, initially, we employed Gaussian basis sets generated by using the Polynomial Generator Coordinate Hartree-Fock (PGCHF) method, and later we extended our technique to the cc-pVQZ and pc-3 Gaussian basis sets in order to show how our technique works and how good it is. Using the new polarized basis sets, from our technique, total electronic energies, equilibrium geometries, and vibrational frequencies were calculated for a set of molecules containing atoms from H(Z = 1) to Ba(Z = 56). The technique presented here can be used with any Gaussian basis set flexible (large) enough and also can be used to choose Gaussian basis set exponents from one basis set to another as polarization functions.
Polarization consistent basis sets: Principles
The Journal of Chemical Physics, 2001
The basis set convergence of Hartree-Fock energies for the H 2 , H 3 ϩ , C 2 , N 2 , N 4 , O 2 , O 3 , F 2 , HF, and CH 4 molecules is analyzed using optimized basis functions. Based on these analysis a sequence of polarization consistent basis sets are proposed which should be suitable for systematically improving Hartree-Fock and density functional energies. Analogous to the correlation consistent basis sets designed for correlation energies, higher angular momentum functions are included based on their energetical importance. In contrast to the correlation consistent basis sets, however, the importance of higher angular momentum functions decreases approximately geometric, rather than arithmetic. It is shown that it is possible to design a systematic sequence of basis sets for which results converge monotonic to the Hartree-Fock limit. The primitive basis sets can be contracted by a general contraction scheme. It is found that polarization consistent basis sets provide a faster convergence than the correlation consistent basis sets. Results obtained with polarization consistent basis sets can be further improved by extrapolation.
Newly developed basis sets for density functional calculations
Journal of Computational Chemistry, 2005
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.
Accurate Gaussian basis sets for atoms from H to Ba were obtained by means of the generator coordinate Hartree-Fock (GCHF) method based on a polynomial expansion to discretize the Griffin-Wheeler-Hartree-Fock equations (GWHF). The discretization of the GWHF equations in this procedure is based on a mesh of points not equally distributed in contrast with the original GCHF method. The results of atomic Hartree-Fock energies demonstrate the capability of these polynomial expansions in designing compact and accurate basis sets to be used in molecular calculations and the maximum error found when compared to numerical values is only 0.788 mHartree for indium. Some test calculations with the B3LYP exchange-correlation functional for N2, F2, CO, NO, HF, and HCN show that total energies within 1.0 to 2.4 mHartree compared to the cc-pV5Z basis sets are attained with our contracted bases with a much smaller number of polarization functions (2p1d and 2d1f for hydrogen and heavier atoms, respectively). Other molecular calculations performed here are also in very good accordance with experimental and cc-pV5Z results. The most important point to be mentioned here is that our generator coordinate basis sets required only a tiny fraction of the computational time when compared to B3LYP/cc-pV5Z calculations
Contracted Gaussian bases for the first-row atoms applied to neutral and charged diatomic molecules
Journal of Molecular Structure THEOCHEM
A set of contracted Gaussian bases generated with the Generator Coordinate Hartree–Fock method for first-row atoms (H, Li–Ne) is applied to perform molecular ab initio calculations. The primitives 18s 12p Gaussian basis sets were contracted to (5s) for H atom and (7s 5p) for Li–Ne atoms by a standard procedure and enriched with polarization functions in order to perform the calculations. The contracted Gaussian basis sets are then tested for H2, BH, B2, C2, N2, O2, F2, HF, LiF, BeO, BF, CN−, CO and NO+ molecular species. The molecular properties of interest are Koopmans' ionization potential, bond distances and vibrational frequencies at MP2 level and dipole moments at HF and MP2 levels. The results obtained show that the contracted Gaussian bases used in this work is a useful alternative for ab initio molecular calculations, and that the Generator Coordinate Hartree–Fock method is a legitimate alternative for selection of contracted and polarized Gaussian basis sets.