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arXiv 0903.0971physics.chem-ph
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三原子分子振动能级的代数矩阵计算

Algebraic-matrix calculation of vibrational levels of triatomic molecules

T. Sedivcova-Uhlikova, Hewa Y. Abdullah, Nicola Manini

摘要:

我们介绍了一种准确和有效的代数技术的三原子分子的振动光谱的计算,线性和弯曲的平衡几何。的完整的三维势能面(PES),它可以完全基于{ \it从头计算}数据,被参数化为一个产品的莫尔斯余弦展开,表示在键角的内部坐标,并包括明确的本地模式之间的相互作用。我们描述的拉伸自由度的框架中的Morse型扩展在一个合适的代数基础上,它提供了一个稀疏的哈密顿矩阵的元素的精确的解析表达式。同样,我们使用一个余弦功率展开的球谐函数的弯曲自由度的基础上。所得矩阵表示的产品空间是非常稀疏的振动水平和本征函数可以通过有效的对角化技术。我们将此方法应用于羰基硫OCS、氰化氢HCN、水H $_2$ O和二氧化氮NO $_2$。当我们基于高质量的PES调谐到实验数据的计算,计算的光谱与观察到的带的起源非常好的协议。

英文摘要:

We introduce an accurate and efficient algebraic technique for the computation of the vibrational spectra of triatomic molecules, of both linear and bent equilibrium geometry. The full three-dimensional potential energy surface (PES), which can be based on entirely {\it ab initio} data, is parameterized as a product Morse-cosine expansion, expressed in bond-angle internal coordinates, and includes explicit interactions among the local modes. We describe the stretching degrees of freedom in the framework of a Morse-type expansion on a suitable algebraic basis, which provides exact analytical expressions for the elements of a sparse Hamiltonian matrix. Likewise, we use a cosine power expansion on a spherical harmonics basis for the bending degree of freedom. The resulting matrix representation in the product space is very sparse and vibrational levels and eigenfunctions can be obtained by efficient diagonalization techniques. We apply this method to carbonyl sulfide OCS, hydrogen cyanide HCN, water H$_2$O, and nitrogen dioxide NO$_2$. When we base our calculations on high-quality PESs tuned to the experimental data, the computed spectra are in very good agreement with the observed band origins.

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