Pople-Karplus equations

For the halogens, with the exception of fluorine, d-orbitals are in many cases suspected to take part in chemical bonding and may a priori be assumed to contribute to a. Jameson and Gutowsky have extended the Karplus-Pople treatment to also include d-orbitals [170]. The general expressions for in this more general case become rather lengthy and are not reproduced here. However, when only atomic orbitals centered on atom A are considered, the Jameson-Gutowsky equation for essentially takes the form... 

A number of investigations have led to the conclusion that most NMR chemical shifts are largely dependent upon the paramagnetic term [1,8,9]. The description of Karplus and Pople is often used to describe the paramagnetic term, shown as Equation 2, for an oxygen nucleus (O) bound to another nucleus (X) [11]. 

Letcher and Van Wazer applying LCAO theory first developed by Pople and Karplus and Das, have expressed the shielding (which was dominated by the magnitude of (7 ), in terms of localized bond parameters, e.g., ionic character, hybridization and double bonding. Using expressions for (7 obtained by Jameson and Gutowsky and taking account of both phosphorus p and d orbital occupation, the phosphorus chemical shift, <5 —was related to four parameters and/by equation (11)—... 

Despite these difficulties, Lasaga and Karplus have discussed the calculation of excitation energies based on an operator equation related to (3). Simons and Dalgaard have proposed a perturbation approach to a similar operator problem. To date, however, numerical applications have been limited to the analysis of the singlet excitation of ethylene in Pariser-Parr-Pople (PPP) model, a two-level problem. ... 

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