The gaussian basis sets p-GCHF was generated for a set of atoms from Na to Cl through the Generator Coordinate Method (GCM) based on a polynomial integral expansion to discretize the Griffin-Wheeler-Hartree-Fock equations. The p-GCHF is a 7z type basis sets and was contracted through the Contract program, which works based on the Davidson's contraction model. The contraction process provided a set of 9s7p functions for Na and Mg atoms and 9s8p functions for Al, Si, P, S e Cl atoms. Polarization exponents were acquired through the Polarization program at CISD level of theory for H, B, C, N, O, F, Na, Mg, Al, Si, P, S e Cl atoms. No more than 2p1d polarization exponents were necessary to compose the p-GCHF basis set for hydrogen atom, 2d1f for the first row of the periodic table and 3d2f for the second row. Molecular calculations show that p-GCHF works like cc-pVQZ and cc-pV5Z basis sets but with smaller computational demands than the Dunning's ones. Vibrational frequency analysis and optimization geometry of the stationary points (minimum as well as transition state), revealed similarities between p-GCHF and cc-pVQZ basis sets, but again with the GCM basis sets being computationally advantageous. A basis sets capable of describing a system like the traditional gaussian basis sets known in the literature but demanding less computational effort is very helpful mainly for those who work with massive molecular systems.

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.

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The potential energy surface of [P,C,O] system in the ground state was investigated by quantum chemical methods. Four different isomers were characterized at the B3LYP/aug-cc-pVTZ: COP (i1), cPCO (i2), PCO (i3), and CPO (i4). The linear species i3 is the global minimum in the ground state surface, while i4 is a bent structure, and i2 is a cyclic isomer. In view to evaluate the bond nature of each isomer, a QTAIM and a NBO analyses were applied. The triangular species presents a ring critical point which confirms its cyclic structure instead of a T-shape one. The stability increases in the following order: i3 > i2 > i1 > i4. The energy gap between i3 and i2 ranges from 49.20 to 51.15 kcal mol(-1). The reaction barrier energies that converge into the direction of i3 showed values around 10 kcal mol(-1), while the reverse barriers are considerably large (62.85 kcal mol(-1)). The i3 heat of formation at 298 K ranges from 11.83 to 19.41 kcal mol(-1).