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Several functionals namely the local spin density (LSD) approximation, the Perdew-Burke-Ernzerhof (PBE), generalised gradient approximation (GGA), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta GGA are studied for the symmetric and asymmetric stretching potential energy curves of H3. The PBE GGA and TPSS meta GGA are found to be useful not only for chemical applications but also for the construction of higher-rung nonempirical functionals.

The binding energy curves for Ne2, Ar2 and Be2 are computed with several nonempirical density functionals, including the local spin density (LSD) approximation, the Perdew-Burke-Ernzerhof (PBE), generalized gradient approximation (GGA), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta GGA. Binding energy curves in reasonable agreement with those constructed from experiment are found from PBE and TPSS describing the short-range part of van der Waals interaction.

A study is conducted with an aim to show the performance and applicability of the nonempirical functionals for molecular geometry and zero-point energy calculations. The ability of the density functionals is tested to predict accurate equilibrium bond lengths and angles for a data set of 21 mostly polyatomic molecules.

The Gaussian-3 total energies was approximated using single-point Hartree-Fock-self-consistent field (HF-SCF) total energies plus the correlation energy corrections calculated from the HF-SCF partial atomic charges according to the rapid estimation of correlation energy from partial charges (RECEP) method. The parameters of the RECEP method are recommended to estimate total correlation energies of closed-shell ground-state neutral molecules at stationary points of the potential-energy surface.

Four new REEF-HF parameter sets are developed for HF/6-31G(d) or HF/6-311+G(2d,p) energies and the corresponding NPA or mulliken charges. All parameter sets were developed and tested on the same molecular database set of 161 closed-shell neutral molecules composed of H, C, N, O, F, Si, S, and Cl atoms.

The rapid estimation of basis set error and correlation energy from partial charges method is improved to make superfluous the explicit zero-point energy and thermal correction calculations. The new method is faster than the previous rapid estimation of basis set error and correlation energy from partial charges method, without losing the precision.

The rapid estimation of basis set error and correlation energy from partial charges (REBECEP) method is discussed which is improved further in several ways by introducing total energies derived from experimental enthalpies of formation instead of G3 energies in the fitting procedure. It was found the REBECEP method performed better for the 117 molecules with a moderate 6-31G(d) basis set than the B3LYP method with large 6-311+G(3df,2p) basis set.