کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
503688 863797 2006 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Exact analytical expressions and numerical analysis of two-center Franck–Condon factors and matrix elements over displaced harmonic oscillator wave functions
موضوعات مرتبط
مهندسی و علوم پایه شیمی شیمی تئوریک و عملی
پیش نمایش صفحه اول مقاله
Exact analytical expressions and numerical analysis of two-center Franck–Condon factors and matrix elements over displaced harmonic oscillator wave functions
چکیده انگلیسی

A detailed study is undertaken, using various techniques, in deriving analytical formula of Franck–Condon overlap integrals and matrix elements of various functions of power (xl)(xl), exponential (exp(−2cx))(exp(−2cx)) and Gaussian (exp(−cx2))(exp(−cx2)) over displaced harmonic oscillator wave functions with arbitrary frequencies. The results suggested by previous experience with various algorithms are presented in mathematically compact form and consist of generalization. The relationships obtained are valid for the arbitrary values of parameters and the computation results are in good agreement with the literature. The numerical results illustrate clearly a further reduction in calculation times.Program summaryProgram name:FRANCKCatalogue identifier:ADXX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXX_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgramming language:Mathematica 5.0Computer:Pentium M 1.4 GHzOperating system:Mathematica 5.0RAM:512 MBNo. of lines in distributed program, including test data, etc.:825No. of bytes in distributed program, including test data, etc.:16 344Distribution format:tar.gzNature of problem:  The programs calculate the Franck–Condon factors and matrix elements over displaced harmonic oscillator wave functions with arbitrary quantum numbers (n,n1)(n,n1), frequencies (a,a1)(a,a1) and displacement (d)(d) for the various functions of power (xl)(xl), exponential (exp(−2cx))(exp(−2cx)) and Gaussian (exp(−cx2))(exp(−cx2)).Solution method:The Franck–Condon factors and matrix elements are evaluated using binomial coefficients and basic integrals.Restrictions:  The results obtained by the present programs show great numerical stability for arbitrary quantum numbers (n,n1)(n,n1), frequencies (a,a1)(a,a1) and displacement (d)(d).Unusual features:NoneRunning time:  As an example, for the value of Franck–Condon Overlap Integral Inn′(d;α,α′)=0.004405001887372332Inn′(d;α,α′)=0.004405001887372332 with n=3n=3, n1=2n1=2, a=4a=4, a1=3a1=3, d=2d=2, the compilation time in a Pentium M 1.4 GHz computer is 0.18 s. Execution time depends on the values of integral parameters n  , n′n′, d, α  , α′α′.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Physics Communications - Volume 175, Issue 3, 1 August 2006, Pages 226–231
نویسندگان
, , ,