用指数函数拟合长链分子超极化率时目标函数的选择

Correct target function for hyperpolarizability of per unit cell of long chain molecules when exponential function used to fit

长链体系的轴向单元(超)极化率的饱和值Δp(∞),需要对有限的计算数据用函数拟合,再根据拟合函数外推求得。以a-be-cn作为拟合函数,有两拟合公式:p(n)-p(n-1)=a-be-cn和p(n)/n=a-be-cn。从理论上探讨了两公式目标函数不同存在的本质区别,结论是应该使用p(n)-p(n-1)作为目标函数,即合理的公式是前者。并用氢分子链,氟化氢分子链和聚乙烯为例,表明后者在链增长时没有正确的渐近行为,原因是当后者还原为对p(n)的拟合函数时含有一个ne-cn的项,而这一项会影响拟合后外推的饱和值的正确性。

To obtain the asymptotic value of the component of （hyper） polarizability tensor oritened along the backbone of polymeric systems, an approach is to follow the evolution of the longitudinal （hyper） polarizability in larger and larger oligomers and then to extrapolate to the infinite polymer limit. Set a-be^-cn as the fitting function, then the longitudinal hyperpolarizability per unit values of polymeric chains can be expressed in two ways：γ（ n）-γ（ n-1 ） = a-be^-cn and γ（ n）/n = a-be^-cn. There are essential differences between them when studying them theoritically. And three linear polymers： （H-H） n, （F-H） n, and （ CH = CH） n have been employed to compare these two formulae. It shows that γ（ n ）--γ（ n-1 ） yields a consistently improved accuracy and a better theoretical justification than γ（ n）/n. The reason is that the latter formula comes from a representation for γ（n） , which has a nbe＂on term. This term gives wrong effection to the asymptotic behavior.