Zero differential overlap transition

Semiempirical methods are widely used, based on zero differential overlap (ZDO) approximations which assume that the products of two different basis functions for the same electron, related to different atoms, are equal to zero [21]. The use of semiempirical methods, like MNDO, ZINDO, etc., reduces the calculations to about integrals. This approach, however, causes certain errors that should be compensated by assigning empirical parameters to the integrals. The limited sets of parameters available, in particular for transition metals, make the semiempirical methods of limited use. Moreover, for TM systems the self-consistent field (SCF) procedures are hardly convergent because atoms with partly filled d shells have many... 

Use the zero differential overlap (ZDO) approximation for the two-electron integrals to show that the singly excited configurations and transition dipoles are equal. When they are allowed to interact two states are formed ... 

The transition dipoles and dipole differences between states a) and g) can be expressed in terms of matrix elements between the MO and applying the ZDO (zero differential overlap) approximation as in (68) and (69),... 

Figure 3.10. INDO/MRDCI calculated transition densities for 5-8 between the S0 and Si on the left-hand side and between the Si and S2 on the right-hand side. The radii of the circles are proportional to the zero differential overlap (ZDO) transition densities associated with each atom. (From Ref. [284] with permission of the American Institute of Physics.)...

Xf into their sum and their difference, to the former of which a transition from the ground state is in general allowed, but to the latter forbidden. In a jmper published soon afterwards by Lefebvre and Moser 25 it was suggested that the degeneracy between Xi and x vill arise in the absence of zero differential overlap... 

Hansen, A.E. On evaluation of electric and magnetic dipole transition moments in the zero differential overlap approximation. Theor. Chim. Acta 6, 341-349 (1966)... 

Quantum-chemical calculations on conjugated hydrocarbons support the spectroscopic estimate, (3 Rq) = -2.40eV, and all-electron descriptions are appealing as soon as they become feasible. There are too many levels of theory to enumerate here, but quantitative ones are not yet applicable to conjugated polymers. Moreover, we are interested in excited states, which remain challenging even in molecules. The rationale for ct-tt separability, for the Coulomb potential V(R), and for the zero differential overlap (ZDO) approximation were discussed [1] in connection with the PPP model. Hubbard [33] considered the same issues for d electrons in transition metals. Quantum cell models [12,13,34] for frontier orbitals of any kind implicitly invoke ZDO to obtain two-center interactions. In many cases, the relevant transfer integrals t, Hubbard repulsion U, and intersite interactions V(R) are small and hence difficult to evaluate in... 

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. 

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