Theoretical Treatment of the Coriolis Effect Using Hyperspherical Coordinates, with Application to the Ro-Vibrational Spectrum of Ozone
Theoretical Treatment of the Coriolis Effect Using Hyperspherical Coordinates, with Application to the Ro-Vibrational Spectrum of Ozone
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DOI：
10.1021/acs.jpca.0c00893
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发表时间：
2020-04-09
影响因子：
2.9
通讯作者：
Babikov, Dmitri
中科院分区：
文献类型：
--
作者：
Gayday, Igor;Teplukhin, Alexander;Babikov, Dmitri
对于一个三原子分子，使用超球坐标对几种描述转动与振动之间相互作用的替代方法进行了比较和对比。这些方法因z轴的选择以及对分子是长球形还是扁球形转子形状的假设不同而有所差异。对于每种情况，推导并分析了转动 - 振动哈密顿矩阵的块结构，并明确了每种方法的优缺点。然后运用该理论计算单取代臭氧的振转光谱；大致上，结合了（OOO）-O - 16 - O - 18 - O - 16和（OOO）-O - 16 - O - 16 - O - 18异构体的约600个振动态，转动激发高达J = 5以及两种宇称（总共21600个耦合的振转态）。计算并分析了不同宇称态之间的分裂，即所谓的K - 加倍。分别确定了不对称顶转子项和科里奥利耦合项的作用，发现它们都影响这些分裂，但方向相反。因此，这两种效应部分抵消，剩余的分裂相对较小。本工作中报道的（OOO）-O - 16 - O - 18 - O - 16和（OOO）-O - 16 - O - 16 - O - 18的振转态能量与文献（对于低振动激发情况可用）非常吻合。这里获得的高激发振动态的新数据使得能够对臭氧的对称和不对称同位素异构体中的科里奥利效应进行首次系统研究。
Several alternative methods for the description of the interaction between rotation and vibration are compared and contrasted using hyperspherical coordinates for a triatomic molecule. These methods differ by the choice of the z-axis and by the assumption of a prolate or oblate rotor shape of the molecule. For each case, a block-structure of the rotational-vibrational Hamiltonian matrix is derived and analyzed, and the advantages and disadvantages of each method are made explicit. This theory is then employed to compute ro-vibrational spectra of singly substituted ozone; roughly, 600 vibrational states of (OOO)-O-16-O-18-O-16 and (OOO)-O-16-O-16-O-18 isomers combined, with rotational excitations up to J = 5 and both inversion parities (21600 coupled ro-vibrational states in total). Splittings between the states of different parities, so-called K-doublings, are calculated and analyzed. The roles of the asymmetric-top rotor term and the Coriolis coupling term are determined individually, and it is found that they both affect these splittings, but in the opposite directions. Thus, the two effects partially cancel out, and the residual splittings are relatively small. Energies of the ro-vibrational states reported in this work for (OOO)-O-16-O-18-O-16 and (OOO)-O-16-O-16-O-18 are in excellent agreement with literature (available for low-vibrational excitation). New data obtained here for the highly excited vibrational states enable the first systematic study of the Coriolis effect in symmetric and asymmetric isotopomers of ozone.