Within the ZDO approximation

Finally, according to Equation (1.39) the transition moment also vanishes if the differential overlap is zero everywhere in space. This is not strictly possible (except within the ZDO approximation), but the product lvery small values if the amplitude of MO only is large in those regions of space where the amplitude of tpi is very small, and vice versa. Consequently the transition dipole moment will also be very small in such a case. This is true for n- r transitions, where an electron is excited from a lone-pair orbital in the molecular plane into a n orbital of an unsaturated system, for which the molecular plane is also a nodal plane. Similar reasoning applies to so-called charge transfer transitions, that is, those in which an electron is transferred from one subsystem to another, the orbitals different regions of space. Such transitions are overlap forbidden. This is not, however, a very strict selection rule, since it is not based on a vanishing but only on a small value of the transition moment. The differential overlap is never exactly zero in practice. 

Within the ZDO approximation only one-center contributions are considered and all neglected terms are lumped into the empirical spin-orbit coupling parameters (iy.. Then,... 

Coordinate System Dependence Hartree-Fock Approximation Atomic and Bond Dipoles Within the ZDO Approximation How to Calculate the Dipole Polarizability (4[Pg.720]

The calculation of the two-electron integrals in the standard CCSD scheme, even within the ZDO approximation, involves a time-consuming calculation, which precludes the applicability of the CC theory to larger systems. The use of the cue approach in the evaluation of expression (3.13) in the CCSD scheme can be illustrated with the following example concerning polyene molecules (see Fig. 3.2). The calculation of the [AA BB ] integral using the cue basis is reduced to a simple expression ... 

In several works the NDDO approximation was maintained, i.e. the original ZDO MNDO type wavefunction was used without deorthogoanlization for calculating MEP maps [40-44]. Within the NDDO approximation Eq. (3) is modified as follows ... 

Under the ZDO approximation the orthogonalization procedure gives rise to significant changes in the core Hamiltonian matrix. There is also an observation that the interactions between neighboring atoms are too large for the usual parametric schemes within the... 

The important observation here was that approximations such as ZDO implied certain consistency requirements. Foremost among these was the requirement for rotational invariance that is, the same answer should result regardless of the molecule s orientation. As obvious a requirement as this may seem, the way in which to achieve this invariance is, perhaps, not so obvious within a semiempiri-cal scheme. 

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