With much more powerful quantum mechanical computations available (i.e., Gaussian 98), the method was applied to a variety of photochemical reactions (note Scheme 1.12). The expression in Equation 1.12 for the delta-density matrix elements includes overlap integrals to take care of basis set definitions. Weinhold NHOs (i.e., hybrids) were used in order to permit easy analysis in terms of basis orbital pair bonds comprising orbital pairs. Note A refers to a reactant and B refers to the corresponding excited state in this study. [Pg.23]

To obtain eqs. (7.2.4) and (7.2.5) from eq. (7.2.6), we only need to set angle a to be 90° and 0°, respectively. It is not difficult to show that the five hybrids form an orthonormal set of wavefunctions. The parameter a in the coefficient matrix in eq. (7.2.6) may be determined in a number of ways, such as by the maximization of overlap between the hybrids and the ligand orbitals, or by the minimization of the energy of the system. In any event, such procedures are clearly beyond the scope of this chapter (or this book) and we will not deal with them any further. [Pg.236]

Self-consistent paramagnetic total energy calculations are performed to study the ground state properties. In this case the 4f-electrons are treated as localized core states. Since the local density approximation is known to overestimate the extent of the 4f-orbitals, and hence the effects of interatomic hybridization and overlap, these terms in the matrix elements are neglected the f-states are now atomic-like and in that respect can be called core-like. The fee structure for the lanthanides are assumed, except for bcc Eu, because that is the simplest closed packed structure which approximates the real structure. [Pg.173]

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