The Energy Correction

Making the appropriate substitution for and evaluating numerically, s is given as 

The ratio of r, to is always greater than 0 and is unlikely to be greater than 0.5. Therefore the reasonable range for/is from 1.83 to 1.93. This value is independent of the value for or the adsorbate intermolecular force. It depends on the ratio of radii but not on the absolute values of the individual radii. The recommendation, if nothing is known about the adsorbent surface, would be to use the lower number, i.e. 1.83, for this factor 

It is unlikely that this factor will be incorrect by more than 3%. 

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An essential thing to stress concerning the above development of so-called Rayleigh-Schrodinger perturbation theory (RSPT) is that each of the energy corrections... 

NOB. The energy corrected in this way is the G1 value for the electronic energy, denoted E. ... 

This is a form of Henry s law, where the Henry s law constant is simply the product of the vapor pressure of solute 2 multiplied by the energy correction term exp(Ae/ 7 ). For oleophilic substances, which do not like water, mixing is an endothermic process and the term Ae/kT is positive, so that Henry s law constant is much higher than the vapor pressure of the pure substance. 

In summary, the wave function correct to first order and the energy correct to second order are... 

Equation (187) now gives the energy correct to second order. This process of successive approximations can be continued, but in most cases it is carried no further than we have carried it in Eqs. (186) and (187). 

The energy correction (4.52) takes account of the effect of the terms (bq2 + dq4) in the perturbation (4.36). However, since the first-order correction due to the terms (aq + cq3) vanished, we must go to the second-order energy correction to take these terms into account. The contribution of (aq + cq1) to (2) will turn out to be of the same order of magnitude as the contribution of (bq2 + dq4) to (,). We have the correct zeroth-order wave functions (4.38), and we can use (1.202) for the second-order energy correction for state n ... 

As is usual, the above expressions for the energies of the two -orbital sets in the AOM have neglected the 8-bonding interaction which is allowed by symmetry. Its effects are assumed to be small. Expressions for the energies corrected for the 8-bonding by the inclusion of a parameter es are given in Appendix 2. 

This result indicates that the Rayleigh-Schrodinger PT is expected to be well applicable in those cases in which these fractions are small. Inserting eq. (1.62) into expressions for the energy corrections we get the well-known explicit expression for the second-order ones ... 

The derivatives of the energy correction (of the terms proportional to dP4rr and c)T4r) with respect to the angles J/ J/ yield additional quasi- and pseudotorques (K 4 and (V4, respectively) acting upon the hybridization tetrahedron of the frontier nitrogen atom ... 

It is important to stress here that in each order of the SRS and MSMA theories the energy correction can be separated into the polarization and exchange parts,... 

Thus, we obtain a recursive formula for the energy corrections... 

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