Rapid Estimation of Basis Set Error and Correlation Energy Based on Mulliken Charges and Mulliken Matrix with the Small 6-31g* Basis Set

Good, density functional quality (B3LYP/6-31G*) ground state total electronic energies have been approximated using single point Hartree–Fock-self consistent field (HF-SCF/6-31G*) total energies and Mulliken partial charges versus. Mulliken matrix (electrons assigned to atoms and atoms pairs from Mulliken population analysis). This is a development of our rapid estimation of basis set error and correlation energy from partial charges (REBECEP) method, published earlier (see references 21,22,30]. The development is as follows: (1) A larger set of atoms (H, C, N, O, F, Si, P and S) are considered as building blocks for closed shell, neutral, ground state molecules at their equlibrium geometry; (2) geometries near equilibrium geometry are also considered; (3) A larger set, containing 115 molecules, was used to fit REBECEP parameters; (4) most importantly, electrons belonging to chemical bonds (between atom pairs) are also considered (Mulliken matrix) in addition to the atoms (Mulliken charges), using more REBECEP parameters to fit and yielding a more flexible algorithm. With these parameters a rather accurate closed shell ground state electronic total energy can be obtained from a small basis set HF-SCF calculation in the vicinity of optimal geometry. The 3.3 kcal/mol root mean square deviation of REBECEP improves to 1.5 kcal/mol when using Mulliken matrix instead of Mulliken charges.