基于MATLAB的球谐函数M函数库  

Developing the M-file library for visualization of spherical harmonic function based on MATLAB

作　　者：郭仕恒[1] 许庆陵[1] 王东耀[1] 苏育志[1] 张建华[1] 

机构地区：[1]广州大学化学化工学院,广东广州510006

出　　处：《计算机与应用化学》2011年第10期1339-1342,共4页Computers and Applied Chemistry

摘　　要：以MATLAB为设计语言,开发了系列用于原子轨道球谐函数Y_(1m)(θ,φ)如s、p、d、f原子轨道及sp^3和d^2sp^3杂化轨道角度函数可视化的精确、快速、简便的m函数库。根据球坐标的自变量定义域:φ∈[0,2π]、θ∈[0,π],设定离散的自变量值T,P,对球谐函数Y_(1m)(θ,φ)及杂化轨道角度函数的解析式进行计算机程序化,根据解析式计算对应的R值,然后由MATLAB矩阵变换命令[X,Y,Z]=sph2cart(T,P,R)和绘图命令mesh(X,Y,Z)实现球谐函数Y_(1m)(θ,φ)及杂化轨道角度函数的可视化。详细介绍了程序设计思路、编写方法,给出了球谐函数Y_(1m)(θ,φ)及杂化轨道角度函数的解析式数组算法表达式、m-file绘图程序和运行结果。A accurate, fast, simple and direct m-file library for visualization of atomic orbital spherical harmonic function Ytm（θ,φ） such as s,p,d, f and sp3, d2sp3 hybrid orbitals are designed. The matrix[T,P] from the discrete data of variablesφ（φ∈[0,2π]） and0（0 ∈[0,π]） in spherical coordinate system are used to calculate the R based on the formula expressions of atomic orbital spherical harmonic function Ytm（θ,φ） and sp^3, d2sp3 hybrid orbitals. The matrix[X,Y,Z] for plotting are obtained from the discrete data T,P,R using [X,Y,Z]=sph2cart（T,P,R） command. Thus the visualization of the atomic orbital spherical harmonic function Ytm（θ,φ） and the hybrid orbitals are realized using the mesh（X,Y,Z） command. Procedures of the visualization for the spherical harmonic functions are discussed. Finally the MATLAB readable formula expressions of atomic orbital spherical harmonic function Ytm（θ,φ） and the sp3, dZsp3 hybrid orbitals based on MATLAB array element algorithm, the concrete m-files and graphs are given here.

关 键 词：MATLAB 球谐函数Y_lm(θ φ) m-文件 

分 类 号：O413.1[理学—理论物理]