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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。
Using MATLAB as the design language, a series of atomic orbitals for atomic orbital spherical harmonics Y_ (1m) (θ, φ) such as s, p, d, f and sp ~ 3 and d ~ 2sp ~ 3 hybrid orbital angle functions Visual accurate, fast and easy m library. According to the argument of sphere coordinates, we define the domain φ∈ [0,2π], θ∈ [0, π], and set the discrete independent variable T, P, the spherical harmonic function Y_ (1m) The computer program of the analytic formula for the hybrid orbital angle function is used to calculate the corresponding R value according to the analytic formula. Then the MATLAB matrix transformation command [X, Y, Z] = sph2cart (T, P, R) and the drawing command mesh , Y, Z) to visualize the spherical harmonic function Y_ (1m) (θ, φ) and the hybrid orbit angle function. The programming ideas and compiling methods are introduced in detail. The analytic array algorithm expressions of the spherical harmonic function Y_ (1m) (θ, φ) and the hybrid orbital angle function are given, and the m-file drawing program and the running results are given.