Ab initio computation of semiempirical π-electron methods. V. Geometry dependence of Hν π-electron effective integrals

Abstract

The ab initio effective valence shell Hamiltonian (ℋν) provides ab initio analogs of the correlated π-electron integrals which should appear in the traditional Pariser–Parr–Pople (PPP) semiempirical π-electron theory. In our continuing studies of the ab initio basis of an improved PPP theory, we examine the geometry dependence of the correlated ℋν π-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 π-electron parameters corresponding to the PPP αi, βi,j, and γi,j integrals. First, the one-electron, two-center resonance integrals βi,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 αi 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 γi,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 γ1,2 is 0.5 eV smaller than the ethylene γ1,2 even when the C1=C2 bond lengths are identical. Additionally, the set of γi,j for the cyclic polyenes is not even a single function of Ri,j, a feature reflecting the subtle contributions of electron correlation to the ab initio γi,j. However, plots of γ−1i,j vs Ri,j display some unforeseen regularity which may prove useful in improving current semiempirical models for cyclic polyenes.