A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
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DOI：
10.1016/0022-2852(88)90164-6
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发表时间：
1988-04
影响因子：
1.4
通讯作者：
P. Jensen
中科院分区：
文献类型：
--
作者：
P. Jensen
三原子分子的转动振动哈密顿量是根据两个键长位移Δr12和Δr32和弯曲坐标ϱ导出的，如J.T.Hougen，P.R.Bunker和J.W.C.Johns[J.Mol.光谱34,136-172(1970)]。哈密顿量在变量ϱj=1−exp(−ajΔrj2)中展开为幂函数，其中主要是从势能函数获得的分子常数。该哈密顿量的本征值是变分的，即通过直接矩阵对角化而不使用微扰理论。作为振动基函数，我们使用P.Jensen[Comp.太棒了。参考文献1-55(1983)]与Morse振子伸缩函数相结合[V.ŠPirko，P.Jensen，P.R.Bunker，和A.Čejchan，J.Mol.光谱112,183-202(1985)]。根据已发表的亚甲基自由基CH2的从头算势能面[A.D.McLean，P.R.Bunker，R.Ecribano和P.Jensen，J.Chem.Phys.87,2166-2169(1987)]我们计算了该分子的最低振动能。结果表明，用较小的基组就可以得到能量收敛的结果。由于在目前的工作中我们使用Morse振子函数和刚性本底基函数来描述三原子分子的内部动力学，所以我们将这种新方法命名为MOBID。
The rotation-vibration Hamiltonian for a triatomic molecule is derived in terms of two bond-length displacements Δr12and Δr32and a bending coordinate ϱ defined as in the approach described by J. T. Hougen, P. R. Bunker, and J. W. C. Johns [J. Mol. Spectrosc.34, 136–172 (1970)]. The Hamiltonian is expanded as a power series in the variablesϱj= 1 − exp(−ajΔrj2), where theajare molecular constants obtained from the potential energy function. The eigenvalues of this Hamiltonian are obtainedvariationally, i.e., through direct matrix diagonalization without the use of perturbation theory. As vibrational basis functions we use numerically integrated bending functions obtained as described by P. Jensen [Comp. Phys. Rep.1, 1–55 (1983)] combined with Morse oscillator stretching functions [V. Špirko, P. Jensen, P. R. Bunker, and A. Čejchan,J. Mol. Spectrosc.112, 183–202 (1985)]. On the basis of a published ab initio potential energy surface for the methylene radical CH2[A. D. McLean, P. R. Bunker, R. Escribano, and P. Jensen,J. Chem. Phys.87, 2166–2169 (1987)] we have calculated the lowest vibrational energies for this molecule. The results indicate that converged energies can be obtained with a relatively small basis set. Since in the present work we useMorse oscillatorandrigid benderbasis functions to describe theinternal dynamicsof the triatomic molecule, we name the new approach by the acronym MORBID.