Electron correlation effects/contributions

Electron correlation effects contribute considerably to the stability of clusters. Binding energies per atom of neutral and charged species exhibit even-odd oscillations with larger values for clusters with an even number of valence electrons. Consequently the ground-state properties such as ionization potentials and electron affinities do not change smoothly with the cluster size [6]. 

Three-membered ring-forming processes involving X-CH2-CH2-F or CH2-C(Y)-CH2F (X = CH2, O, or S and Y = O or S) in the gas phase have been treated by the ab initio MO method with a 6-31+G basis set." When electron correlation effects were considered, the activation (AG ) and reaction (AG°) free energies were lowered by about lOkcal mol indicating the importance of electron correlation in these reactions. The contribution of entropy of activation -TAS ) at 298 K to AG is very small the reactions are enthalpy controlled. 

Much larger differences occur for the X parameter. There are also large differences between the two DF calculations for X, which cannot be explained by the small change in internuclear separation. The value of X may be expected to be less stable than M [127]. The conclusion in [19] is that the RCC-S value for X, which is higher than that of [89, 127], is more correct. The electron correlation effects are calculated by the RCC-SD method at the molecular equilibrium internuclear distance Rg. A major correlation contribution is observed, decreasing M by 17% and X by 22%. 

Recent work improved earlier results and considered the effects of electron correlation and vibrational averaging [278], Especially the effects of intra-atomic correlation, which were seen to be significant for rare-gas pairs, have been studied for H2-He pairs and compared with interatomic electron correlation the contributions due to intra- and interatomic correlation are of opposite sign. Localized SCF orbitals were used again to reduce the basis set superposition error. Special care was taken to assure that the supermolecular wavefunctions separate correctly for R —> oo into a product of correlated H2 wavefunctions, and a correlated as well as polarized He wavefunction. At the Cl level, all atomic and molecular properties (polarizability, quadrupole moment) were found to be in agreement with the accurate values to within 1%. Various extensions of the basis set have resulted in variations of the induced dipole moment of less than 1% [279], Table 4.5 shows the computed dipole components, px, pz, as functions of separation, R, orientation (0°, 90°, 45° relative to the internuclear axis), and three vibrational spacings r, in 10-6 a.u. of dipole strength [279]. 

Significant changes in optimized geometries due to electron correlation contributions are also of relevance for systems which present intramolecular hydrogen bonds. We shall present here, as a suitable example, the case of monothiomalonaldehyde (la) and its thienol tautomer (lb), since in this case the characteristics of the intramolecular hydrogen bonds depend strongly on the inclusion of electron correlation effects in the theoretical treatment. 

In practice, one often has to restrict the active space to include only a few of the highest occupied and lowest unoccupied molecular orbitals. The correlation effects not included in the CASSCF calculation can then be recovered by a multireference Cl (MRCI) calculation, in which all single and double excitations from the CASSCF reference are taken into account [27], A computationally more efficient way of including dynamical electron correlation effects is perturbation theory with respect to the CASSCF reference. The most widely employed method of this type is the CASPT2 method developed by Roos and collaborators [28], The CASSCF and CASPT2 methods have been essential tools for the calculations described in this contribution. 

The solvent effect on V° can be significant. It derives from the modification of the donor and acceptor transitions densities by the medium, and is in effect regardless of whether or not the molecules interact with each other. V° is therefore the solvent-modified electronic coupling described in Equation (3.139), and as such, can be explicitly dissected into contributions from Coulombic and short-range interactions as well as electron correlation effects. According to the results reported in ref. [47], the solvent modification of Vshort is minor but VCoul is strongly influenced by the medium. In Figure 3.49 we plot results reported in ref. [47] to illustrate that. 

Electron correlation introduces basically two effects into ab initio calculations on intermolecular forces. Hartree-Fock calculations do not account for dispersion forces and hence the dispersion energy is included only in Cl calculations. A second contribution comes from a correction of monomer properties through electron correlation effects. Again, the correlation correction of the electric dipole moment is the most important contribution. In the case of (HF)2 these two effects are of opposite sign and hence the influence of electron correlation on the calculated results is rather small (Table 3). 

This qualitative picture is taken into account in the unrestricted Hartree-Fock (UHF) approach, but it is found that UHF calculations normally overestimate Ajgo drastically. To obtain reliable results, the interactions between the electrons must be described much more accurately. Furthermore, in difference to most other electronic properties, such as dipole moments etc., a proper treatment of the hfcc s also requires special consideration of the inner valence and the Is core regions, since these electrons possess a large probability density at the position of the nucleus. Because the contributions from various shells are similar in magnitude but differ in sign, a balanced description of the electron correlation effects for all occupied shells is essential. All this explains the strong dependence of A on the atomic orbital basis and on the quality of the wavefunction used for the calculation. 

The estimates for Sfj cited above were all for thermal ground-state systems, based on self-consistent field (SCF) wavefunctions. Studies with more elaborate wave-function models have provided examples where electron-correlation effects (relative to the mean-field SCF level) make appreciable contributions to T,y magnitudes (e.g., [110, 116]). Furthermore, for the important case of excited state ET processes, where the SCF approach is not generally applicable, the viability of a one-particle model for T// becomes less clear. 

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