Accurate Thermochemistry from Corrected Hartree Fock Results: Rapid Estimation of Nearly Experimental Quality Total Energy Using the Small 6-31G(d) Basis Set

Sándor Kristyán, Adrienn Ruzsinszky, and Gábor I. Csonka *

Starting idea

The method can be constructed from the basic idea that the electron correlation energy is roughly proportional to the number of electrons. The essence of the method is the use of partial atomic charges to estimate the number of electrons around the atoms.

Basic Equation

It is supposed that the quasi-linear dependence of the correlation energy on the (fractional) number of electrons is conserved in the molecules.

Ecorr(RECEP)  S(A=1,M)Ecorr(NA, ZA). (eq 1)

In eq 1, NA is the electron content around atom A, calculated from partial charge par(A).

How to calculate the values for the Ecorr(NA,ZA) terms in eq 1?

Our suggestion:

Ecorr(NA, ZA, method, charge definition) =

= (NA – N1) Epar(N2, ZA, method) + (N2 – NA) Epar(N1, ZA, method), (eq 2)

where N1 and N2 are integer numbers of electrons with N1 < NA < N2, (the value of NA depends on the charge definition, e.g. Mulliken, NPA, ChelpG, Bader etc.). Epar(N, ZA, method) are the corresponding atomic correlation parameters.

Next Question:

How to provide useful atomic parameters?

  1. Select a good quality total energy (e.g. G3 or experimental)
  2. Define the energy correction (basis set error + correlation energy) as:
    Ecorr(G3) = ET(G3) – ET(HF/6-31G(d))
  3. Find the minimum of
    S (i=1,L) (Ecorr(G3)i - Ecorr(REBECEP)i)2 in a set of L molecules. The solution yields the desired. Ecorr(NA, ZA), values

Results

The best results were obtained using the natural population analysis although the other three are also recommended for use.

References