Correlation energy empirical estimates

The valence correlation energy is estimated from two-point extrapolation for CCSD, CCSD(T) and CCSDT calculations. The effects of higher order correlation effects are estimated from CCSDTQ/cc-pVDZ results scaled by an empirical factor of 1.25. 

Correct the energy from step 6 for remaining basis set deficiencies I empirically estimating the remaining correlation energy betwet spin-paired electrons with the formula ... 

The last important contribution to intermolecular energies that will be mentioned here, the dispersion energy (dEnis). is not accessible in H. F. calculations. In our simplified picture of second-order effects in the perturbation theory (Fig. 2), d mS was obtained by correlated double excitations in both subsystems A and B, for which a variational wave function consisting of a single Slater determinant cannot account. An empirical estimate of the dispersion energy in Li+...OH2 based upon the well-known London formula (see e.g. 107)) gave a... 

The numerical determination of E grr by the use of many-body theory is a formidable task, and estimates of it based on E j and E p serve as important benchmarks for the development of methods for calculating electron correlation effects. The purpose of this work is to obtain improved estimates of Epp by combining the leading-order relativistic and many-body effects which have been omitted in Eq. (1) with experimentally determined values of the total electronic energy, and precise values of Epjp. We then obtain empirical estimates of E grr for the diatomic species N2, CO, BF, and NO using Epip and E p and the definition of E g in Eq. (1). 

Two key pieces of theoretical data are required to obtain an empirical estimate of the correlation energy from the experimental data collected in the preceding section the total molecular Hartree-Fock energy and the relativistic corrections . It is implicit in the definition of the correlation energy presented in Eq. (1) that the total electronic energy ofa given molecule, Ef, may be divided into three constituent parts,... 

Our new empirical estimates of the electron correlation energy for the four species considered in this paper are collected in Table 13. 

Table 13 Empirical estimates of the correlation energy, Ecofr in atomic units. ...

Correlation energies for diatomic molecules a re-evaluation of the empirical estimates for the N2, CO, BF and NO systems... 

Let us start a survey of computational methods by beginning with the simplest conceivable approach5that of assuming a constant empirical value for each type of bond and therefore obtaining the total correlation energy by summing the bond contributions (similarly in the same way that estimates are made in chemistry, e.g. for the heats of formation and dipole moments). We think that this method can hardly be refined to a state that would approach the so-called chemical accuracy because it disregards the interpair electron correlation. 

Computationally, one first performs a semiempirical all-valence electron calculation (say CNDO/2) to obtain the electron densities P -. One-center epq are constants which were tabulated60 for H, B, C, N, O and F atoms. Two-center Wpq are evaluated by an empirical formula which is a function of the interatomic distance. Computation of the expression (153) is much shorter than a standard CNDO/2 run. It is understandable that such a simple method cannot provide highly accurate estimates of the correlation energy. Actually, this accuracy is claimed61 to be within 0.5 eV. 

In addition to the paper cited above, dealing with A10, an extended DZ basis SCF calculation of the energy spectrum has been reported by Schamps.303 Six states of AlO and three of A10+ were investigated. Correlation-energy differences were estimated semi-empirically. 

Force-field-based scoring functions use arbitrary empirical estimates of interaction energies obtained by molecular mechanics energy functions. This simple approximation, which takes into account only enthalpic contribution often correlates well with the experiment. Solvent effects are described by atom-based solvation parameters, which are computed for the surface of both ligand and receptor which is buried upon complexation. DOCK-chemical27 and CHARMm scoring functions represent this class. 

For the nitrogen molecule calculations were performed for nuclear separations of 1.75, 2.00, 2.25, and 2.50 bohr and these values interpolated to obtain a correlation energy at the equilibrium nuclear geometry. The empirical correlation energy for the nitrogen molecule is -0.538 hartree. The calculated correlation energy obtained by interpolation is -0.4501 hartree which represents 83.7% of the estimate. 

A conclusion that may be drawn on this section is that the empirical methods for estimates of the correlation energy may be profitable in applications and that their further development is worth pursuing, It should be realized that for molecules that are (by their size) of interest to chemists, they mostly represent the only feasible approach. 

In principle, equation (2) should provide a numerical estimate for Vq. However, in practice, values of w are so uncertain (see Appendix B) that equation (2) is more useful for estimating w from experimental values of Vq. A useful way to deduce an overall order and an overall activation energy for a reaction is to measure the T and p dependences of Vq and to correlate these empirically with equation (3) by adjusting n and E. ... 

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