Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, USA.
Department of Chemistry, New York University, New York, New York 10003, USA.
J Chem Phys. 2020 Jan 7;152(1):014108. doi: 10.1063/1.5138992.
We present a method for efficient calculation of intramolecular vibrational excitations of HO inside C, together with the low-energy intermolecular translation-rotation states within each intramolecular vibrational manifold. Apart from assuming rigid C, this nine-dimensional (9D) quantum treatment is fully coupled. Following the recently introduced approach [P. M. Felker and Z. Bačić, J. Chem. Phys. 151, 024305 (2019)], the full 9D vibrational Hamiltonian of HO@C is partitioned into two reduced-dimension Hamiltonians, a 6D one for the intermolecular vibrations and another in 3D for the intramolecular degrees of freedom, and a 9D remainder term. The two reduced-dimension Hamiltonians are diagonalized, and their eigenvectors are used to build up a product contracted basis in which the full vibrational Hamiltonian is diagonalized. The efficiency of this methodology derives from the insight of our earlier study referenced above that converged high-energy intramolecular vibrational excitations of weakly bound molecular complexes can be obtained from fully coupled quantum calculations where the full-dimensional product contracted basis includes only a small number of intermolecular vibrational eigenstates spanning the range of energies much below those of the intramolecular vibrational states of interest. In this study, the eigenstates included in the 6D intermolecular contacted basis extend to only 410 cm above the ground state, which is much less than the HO stretch and bend fundamentals, at ≈3700 and ≈1600 cm, respectively. The 9D calculations predict that the fundamentals of all three intramolecular modes, as well as the bend overtone, of the caged HO are blueshifted relative to those of the gas-phase HO, the two stretch modes much more so than the bend. Excitation of the bend mode affects the energies of the low-lying HO rotational states significantly more than exciting either of the stretching modes. The center-of-mass translational fundamental is virtually unaffected by the excitation of any of the intramolecular vibrational modes. Further progress hinges on the experimental measurement of the vibrational frequency shifts in HO@C and ab initio calculation of a high-quality 9D potential energy surface for this endohedral complex, neither of which is presently available.
我们提出了一种高效计算 HO 分子内振动激发的方法，同时计算了每个分子内振动模式内的低能分子间平移-旋转态。除了假设 C 是刚性的，这个九维（9D）量子处理是完全耦合的。按照最近提出的方法[P. M. Felker 和 Z. Bačić，J. Chem. Phys. 151, 024305 (2019)]，HO@C 的全 9D 振动哈密顿量被分成两个降维哈密顿量，一个 6D 哈密顿量用于分子间振动，另一个 3D 哈密顿量用于分子内自由度，以及一个 9D 剩余项。这两个降维哈密顿量被对角化，它们的本征向量被用来构建一个乘积收缩基，其中全振动哈密顿量被对角化。这种方法的效率源于我们之前研究的一个见解，即从完全耦合的量子计算中可以得到弱束缚分子复合物的收敛高能分子内振动激发，其中全维乘积收缩基仅包括一小部分跨越远低于感兴趣的分子内振动态的能量范围的分子间振动本征态。在这项研究中，包含在 6D 分子间接触基中的本征态仅延伸到比 HO 伸缩和弯曲基态高 410cm，分别约为 3700cm 和 1600cm。9D 计算预测，笼状 HO 的所有三个分子内模式的基频，以及弯曲泛音，都会相对于气相 HO 的基频蓝移，两个伸缩模式比弯曲模式更明显。弯曲模式的激发比激发任何一个伸缩模式更显著地影响低能 HO 转动态的能量。质心平移基态几乎不受任何分子内振动模式激发的影响。进一步的进展取决于对 HO@C 中振动频率位移的实验测量和对这个内包络复合物的高质量 9D 势能面的从头计算，目前这两者都不可用。
