多原子分子简正振动频率的量化计算  

Quantum chemical calculation of normal vibration frequencies of polyatomic molecules

作　　者：徐又捷 郭迎春[1] 王兵兵[2,3] Xu You-Jie;Guo Ying-Chun;Wang Bing-Bing(School of Physics and Electronic Science,East China Normal University,Shanghai 200241,China;Beijing National Laboratory of Condensed Matter Physics,Laboratory of Optical Physics,Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]华东师范大学物理与电子科学学院,上海200241 [2]中国科学院物理研究所光物理实验室,北京凝聚态物理国家研究中心,北京100190 [3]中国科学院大学,北京100049

出　　处：《物理学报》2022年第9期63-70,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12074418,11774411)资助的课题。

摘　　要：针对较大分子振动频率的量化计算,提出了一个节省计算成本的方法.含N个原子的分子的振动频率的计算通常需要计算3N维势能超曲面及其二阶导数构成的Hessian矩阵,然后解其特征方程得到全部简正振动模式的振动频率.N越大,计算成本越大.本文提出,针对那些由平衡结构和对称性就能完全确定的振动模式,可以逐个计算其振动频率.当仅考虑一个振动模式时,3N维的Hessian矩阵的计算转化为一维的势能曲线的计算.基于简谐振子近似推导单一振动模式下分子势能曲线的表达式,接着量化计算势能曲线,将势能曲线拟合到表达式中以获得振动频率.相比计算3N维势能超曲面及其二阶导数的Hessian矩阵,仅计算一维势能曲线而节省下来的计算资源可以允许选择更高级别的计算方法和采用更为完备的基组,提高计算的精度.本文首先以计算水分子的B_(2)振动模式的振动频率为例,说明了这种方法的可行性.接着将这种方法应用到SF_(6)分子中.多参考组态相互作用(MRCI)方法是计算电子相关能的有效方法,本文采用MRCI/6-311G^(*)基组分别计算了SF_(6)的A_(1g),E_(g),T_(2g)和T_(2u)四个振动模式的振动频率,通过与其他方法的结果以及实验结果相比较,本文计算的四个频率的相对误差最小.Quantum calculation of molecular vibrational frequency is important in investigating infrared spectrum and Raman spectrum.In this work,a low computational cost method of calculating the quantum chemistry of vibrational frequencies for large molecules is proposed.Usually,the calculation of vibrational frequency of a molecule containing N atoms needs to deal with the Hessian matrix,which consists of second derivatives of the 3N-dimensional potential hypersurface,and then solve secular equations of the matrix to obtain normal vibration modes and the corresponding frequencies.Larger N implies higher computational cost.Therefore,for a limited computational hardware condition,higher-level computations for large N atomic molecule’s vibrational frequencies cannot be implemented in practice.Here we solve this problem by calculating the vibrational frequency for only one vibrational mode each time instead of calculating the Hessian matrix to obtain all vibrational frequencies.When only one vibrational mode is taken into consideration,the molecular potential hypersurface can be transformed into one-dimensional curve.Hence,we can calculate the curve with high-level computational method,then deduce the expression of one-dimensional curve by using harmonic oscillating approximation and obtain the vibrational frequency by using the expression to fit the curve.It should be noted that this method is applied to vibrational modes whose vibrational coordinates can be completely determined by equilibrium geometry and the molecular symmetry and be independent of the molecular force constants.It requires that there exists no other vibrational mode with the same symmetry but with different frequencies.The lower computational cost for a one-dimensional potential curve than that for 3N-dimensional potential hypersurface’s second derivatives permits us to use higher-level method and larger basis set for a given computational hardware condition to achieve more accurate results.In this paper we take the calculation of B_(2) vibrational f

关 键 词：量化计算 振动频率 分子对称性 势能函数 

分 类 号：O56[理学—原子与分子物理]