Journal of Chemical Physics, Vol.105, No.4, 1437-1450, 1996
Ab-Initio Computation of Semiempirical Pi-Electron Methods .5. Geometry Dependence of H-Nu Pi-Electron Effective Integrals
The ab initio effective valence shell Hamiltonian (H(n)u) provides ab initio analogs of the correlated pi-electron integrals which should appear in the traditional Pariser-Parr-Pople (PPP) semiempirical pi-electron theory. In our continuing studies of the nb initio basis of an improved PPP theory, we examine the geometry dependence of the correlated H-nu pi-electron effective integrals (also called parameters) for the linear polyenes, ethylene, the allyl radical, trans-butadiene, and hexatriene, and the cyclic polyenes, cyclobutadiene and benzene. We find particularly interesting features for each of the true pi-electron parameters corresponding to the PPP alpha(i), beta(i,j), and gamma(i,j) integrals. First, the one-electron, two-center resonance integrals beta(i,j) differ from the so-called "theoretical" values by roughly a constant shift of 0.3-0.4 eV for nearest neighbors i and j and not at all for more distant neighbors. Second, the correlated alpha(i) parameters conform to the standard point charge model fairly well, except the slopes and intercepts lack the transferability typically ascribed to them. A more accurate PPP model therefore must model the one-center, one-electron interactions more carefully. Finally, the effective Coloumb interactions gamma(i,j) follow the standard Mataga-Nishimoto distance dependence quite well for the linear polyenes, although there is a small breakdown of transferability due to long range correlation effects. For instance, the hexatriene gamma(1,2) is 0.5 eV smaller than the ethylene gamma(1,2) even when the C1=C2 bond lengths are identical. Additionally, the set of gamma(i,j) for the cyclic polyenes is not even a single function of R(i,j), a feature reflecting the subtle contributions of electron correlation to the ab initio gamma(i,j). However, plots of gamma(i,j)(-1) vs R(i,j) display some unforeseen regularity which may prove useful in improving current semiempirical models for cyclic polyenes.
Keywords:SHELL HAMILTONIAN METHOD;TRANS-BUTADIENE;VALENCE STATES;ABINITIO;CYCLOBUTADIENE;TRANSFERABILITY;PARAMETERS