Energy pairing

Petersson and coworkers have extended this two-electron formulation of asymptotic convergence to many-electron atoms. They note that the second-order MoUer-Plesset correlation energy for a many-electron system may be written as a sum of pair energies, each describing the energetic effect of the electron correlation between that pair of electrons ... 

For aP electron pairs, the coefficient matrix C may be diagonalized, yielding the pair natural orbital (PNO) expansion of the pair energies ... 

The parameter 8,y serves to retain size consistency in the CBS extrapolation for finite values of N. Full Cl pair energies, (N), may be obtained from the... 

The sum over Cl coefficients is an interference factor resulting from the fact that the full Cl pair energies converge faster than the second-order pair energies. 

In calculating a pair potential for dineon, we have to take the separated atom energy as one half of the pair energy for an arbitrarily large distance. 

LFSE s for tetrahedral species are computed in a similar manner. They are compared with the results for octahedral systems in Fig. 8-7. No illustration of LFSE s for low-spin tetrahedral ions is included here because, as noted in Chapter 5, the much smaller values of Aet relative to oct ensures that pairing energies P always outweigh the ligand-field terms in practice. 

Note phen is 1, 10 orthophenanthroline. Note the change to low-spin, paired d electron, states gains tr-acceptor and /r-donoi strength offsetting spin-pairing energy. 

For a given series the value of D, the spin-pairing energy, does not in fact stay constant, but its average value for a given dq configuration is 7/6 (5/2 B + C), and for MF ions D ranges only between 3.9 and 4.7 kK. 

Crystal field splitting energy compared to the electron pairing energy. 

Figure 2 Different electronic configurations arising from the relative strengths of orbital overlap (AE) and pairing energy (PE) AE > PE favours a closed-shell diamagnetic singlet (a) whereas AE

While the first electrochemical reduction potential provides an estimate for Ac (assuming it is a reversible process), the second and higher reduction potentials do not provide the spectrum of single electron affinity levels. Rather, they provide information about two-electron, three-electron, and higher electron reduction processes, and, therefore, depend on electron pairing energy. Thus, the utility of solution-phase reduction potentials for estimating solid-state affinity levels is... 

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