Inner shell energy-level calculation

The structural parameters and vibrational frequencies of three selected examples, namely, H2O, O2F2, and B2H6, are summarized in Tables 5.6.1 to 5.6.3, respectively. Experimental results are also included for easy comparison. In each table, the structural parameters are optimized at ten theoretical levels, ranging from the fairly routine HF/6-31G(d) to the relatively sophisticated QCISD(T)/6-31G(d). In passing, it is noted that, in the last six correlation methods employed, CISD(FC), CCSD(FC),..., QCISD(T)(FC), FC denotes the frozen core approximation. In this approximation, only the correlation energy associated with the valence electrons is calculated. In other words, excitations out of the inner shell (core) orbitals of the molecule are not considered. The basis of this approximation is that the most significant chemical changes occur in the valence orbitals and the core orbitals remain essentially intact. On... 

Figure 7.2 Quasi-chemical contributions of the hydration free energy of Be (aq). Cluster geometries were optimized using the B3LYP hybrid density functional (Becke, 1993) and the 6-31- -G(d, p) basis set. Frequency calculations confirmed a true minimum, and the zero point energies were computed at the same level of theory. Single-point energies were calculated using the 6-311- -G(2d, p) basis set. A purely inner-shell n = 5 cluster was not found the optimization gave structures with four (4) inner-sphere water molecules and one (1) outer-sphere water molecule. For n = 6 both a purely inner-shell configuration, and a structure with four (4) inner-shell and two (2) outer-shell water molecules were obtained. The quasi-chemical theory here utilizes only the inner-shell structure. O - rin [/ff -f (left ordinate) vs. n. A ...

Solvation effects have been incorporated into the calculations of anionic proton transfer potentials in a number of ways. The simplest is the microsolvation model where a few solvent molecules are included to form a supermolecular system that is directly characterized by quantum mechanical calculations. This has the advantage of high accuracy, but is limited to small systems. Moreover, one must assume that a limited number of solvent molecules can adequately model a tme solution. A more realistic approach is to explicitly describe the inner solvation shell with quantum calculations and then treat the outer solvation sphere and bulk solvent as a continuum (infinite polarizable dielectric medium). In this way, the specific interactions can be treated by high-level calculations, but the effect of the bulk solvent and its dielectric is not neglected. An ej tension of this approach is to characterize the reaction partners by quantum mechanics and then treat the solvent with a molecular mechanics approach (hybrid quantum mechanics/molecular mechanics QM/MM). The low-cost of the molecular mechanics treatment allows the solvent to be involved in molecular dynamics simulations and consequently free energies can be calculated. In more recent work, solvent also has been treated with a frozen or constrained density functional theory approach. ... 

The inner core electrons occupy closed shells. The only exchange part of the two-electron Breit interaction between the valence, outer core and inner core electrons, Bf and P/c, gives non-zero contribution. The contributions from Bfy and P/c, are quite essential for calculation at the level of chemical accuracy (about 1 kcal/mol or 350 cm for transition energies). This accuracy level is, in general, determined by the possibilities of modern correlation methods and computers already for compounds of light elements. Note, that the contribution from the exchange interaction is not smaller than that from the Coulomb part [29]. The inner core electrons can be considered as frozen in most physical-chemical processes of interest. Therefore, the effective operators for P/ and P/c acting on the valence and... 

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