对Mulliken布居数分析中重叠积分的研究

通过对任意2个1s型高斯函数重叠积分的计算,明确了轨道重叠过程中影响重叠积分大小的2个主要因素——核间距及轨道指数的作用,并得出核间距越大重叠积分越小、轨道指数越小重叠积分越大的结论;其次,通过固定2个原子间距离和其中1个高斯函数的轨道指数,以及改变另1个高斯函数的轨道指数来观察重叠积分的变化情况,从而确定引入弥散函数对计算重叠积分的影响.得出当使用弥散函数来描述原子轨道时,高斯函数图像延伸范围广,使得轨道的形变程度增加,重叠区域增大.若此时使用Mulliken布居数分析方法对重叠区域的电子进行“均分”处理可能就会产生与事实不符的结果,认为对于确定的2个原子轨道重叠积分的计算,轨道指数起着至关重要的作用.

Study on the overlap integral of Mulliken population analysis

In this paper, according to the calculation of overlap integral between any two ls-type Gauss function, we find two main factors the nuclear distance and power exponent, which can affect the size of the overlap integral during the process of orbital overlap. It is concluded that the greater the nuclear distance is, the smaller the overlap integral will be and the smaller the power exponent is, the greater the overlap integral will be. In addition, by observing the overlap integral, we con- firm the influence of dispersion function to the overlap. We can draw conclusion that： Describing a- tomic orbit by dispersion function, Gauss function extends widely, wich makes the degree of deform- ation and the overlap increasing. In this circumstance, it may cause unreasonable result dividing the overlap on average in Mulliken method compared to the reality. Thus the power exponent is impor- tant to the calculation of overlap integral.