Neglect of Diatomic Differential Overlap (NDDO) in Non-Empirical Quantum Chemical Orbital Theories

In order to extend the applicability of non-empirical q u a n t u m chemical methods expanding delocalized orbi tals of molecules and stereoregular crystals as a l inear combina t ion of a tomic basis functions, we revive a discussion mainly held in the sixties and seventies abou t the possibility of neglecting small integral values occurring in numerical calculations of elect ronic states and their energies with only little loss of accuracy [1]. Within the Born-Oppenheimer picture of fixed nuclear posit ions any procedure of such kind is based on the evaluat ion of four different types of integrals over some finite number N0 of atomic orbitals { 0 > / ? M ) | M = l , 2 , . . . , i V a ; / i e M } localized at Na a tomic centers [2]. Here, r is the vector of the elect ronic coordinates (x, y, z), and RM denotes the posit ion vector of a tom M to which all orbitals with index p belong (notat ion: p e M). F o r convenience, all these a tomic orbitals are taken to be real.