Extrapolation of the linear and nonlinear polarizabilities from ab initio finite oligomer calculations

Abstract

AbstractDifferent definitions of property per unit cell and different fitting functions are employed to obtain the asymptotic limit values per unit cell of the polarizability (α), the first (β), and the second (γ) hyperpolarizabilities of an infinite oligomer. A 1/n power series function is found to be suitable for the average value and logarithmic average value per unit cell definition, and an exponentially decreasing function is found to be suitable for the difference value per unit cell definition. These conclusions are derived based on an equation expressing the total energy per unit cell of a finite linear oligomer as a power series of 1/n, presented from a perturbation treatment. Several calculations of long chain systems have been carried out to reach our conclusions. An equation of p(n)/n = a + b/n + c/n2 is strongly recommended for a least‐squares fitting of the properties per unit cell to achieve a stabilization behavior when the chain length is increased. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006