Accurate Gaussian basis sets for second-row atoms and ions generated with the improved generator coordinate Hartree–Fock method

Generation, contraction, and polarisation of Gaussian basis sets for atomic and molecular calculations using the generator coordinate method with polynomial discretisation: atoms from Na through Cl

The polynomial Generator Coordinate Hartree-Fock Gaussian basis sets, pGCHF, for the atoms Na, Mg, Al, Si, P, S, and Cl were generated using the generator coordinate method based on polynomial integral expansion to discretise the Griffin-Wheeler-Hartree-Fock equations. The pGCHF basis sets were contracted with the CONTRACT program based on the Davidson contraction model through which a set of 9s8p functions for the atoms Na through Cl were obtained. Polarisation exponents generated using the POLARIZATION program were added to the contracted pGCHF Gaussian basis sets. Molecular calculations at the DFT level of theory showed that the pGCHF basis sets can be used to calculate the atomisation energy with accuracy comparable to the well-established pcseg-3, def2-QZVP, and Sapporo-QZP basis sets; also, the complete basis set (CBS) limit estimate was obtained with the pcseg-3/pcseg-4 basis sets.

Accurate Gaussian basis sets for atomic and molecular calculations obtained from the generator coordinate method with polynomial discretization

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.

Gaussian basis sets for low-lying excited states of neutral atoms with 2 ≤ Z ≤ 36

The improved generator coordinate Hartree–Fock method is used to generate Gaussian basis sets for low-lying excited states of neutral atoms from He (Z = 2) to Kr (Z = 36). Then, excitation energies and orbital energies of the outermost orbitals of each symmetry are calculated and compared with the corresponding values obtained with numerical Hartree–Fock calculations. Besides this, the basis sets for Be (3P) and F (2P) are contracted by a standard procedure and, then, enriched with polarization functions. From these basis sets, total energies, dissociation energy, and bond length for BeF are calculated and compared with results obtained with other basis sets and with experimental values. The sets for He–Kr are useful in constructing basis sets for molecular calculations. Key words: improved generator coordinate Hartree–Fock method, Gaussian basis sets, low-lying excited states, neutral atoms.

Gaussian basis sets for the atoms from K through Xe

An improved generator coordinate Hartree-Fock (IGCHF) method is used to generate Gaussian basis sets for the atoms from K (Z = 19) through Xe (Z = 54). The Griffin-Hill-Wheeler-HF equations are integrated using the integral discretization technique. The ground state HF total energies obtained by us are compared with those calculated with the original GCHF method and with other approaches reported in the literature. The largest difference between our energy values and the corresponding ones computed with a numerical HF method is equal to 6.003 mhartree for Kr (Z = 36).Key words: improved generator coordinate Hartree-Fock method, Gaussian basis sets, total energies.