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. 2023 Jun 21;158(23). doi: 10.1063/5.0156976.
We present the computational methodology, which for the first time allows rigorous twelve-dimensional (12D) quantum calculations of the coupled intramolecular and intermolecular vibrational states of hydrogen-bonded trimers of flexible diatomic molecules. Its starting point is the approach that we introduced recently for fully coupled 9D quantum calculations of the intermolecular vibrational states of noncovalently bound trimers comprised of diatomics treated as rigid. In this paper, it is extended to include the intramolecular stretching coordinates of the three diatomic monomers. The cornerstone of our 12D methodology is the partitioning of the full vibrational Hamiltonian of the trimer into two reduced-dimension Hamiltonians, one in 9D for the intermolecular degrees of freedom (DOFs) and another in 3D for the intramolecular vibrations of the trimer, and a remainder term. These two Hamiltonians are diagonalized separately, and a fraction of their respective 9D and 3D eigenstates is included in the 12D product contracted basis for both the intra- and intermolecular DOFs, in which the matrix of the full 12D vibrational Hamiltonian of the trimer is diagonalized. This methodology is implemented in the 12D quantum calculations of the coupled intra- and intermolecular vibrational states of the hydrogen-bonded HF trimer on an ab initio calculated potential energy surface (PES). The calculations encompass the one- and two-quanta intramolecular HF-stretch excited vibrational states of the trimer and low-energy intermolecular vibrational states in the intramolecular vibrational manifolds of interest. They reveal several interesting manifestations of significant coupling between the intra- and intermolecular vibrational modes of (HF)3. The 12D calculations also show that the frequencies of the v = 1, 2 HF stretching states of the HF trimer are strongly redshifted in comparison to those of the isolated HF monomer. Moreover, the magnitudes of these trimer redshifts are much larger than that of the redshift for the stretching fundamental of the donor-HF moiety in (HF)2, most likely due to the cooperative hydrogen bonding in (HF)3. The agreement between the 12D results and the limited spectroscopic data for the HF trimer, while satisfactory, leaves room for improvement and points to the need for a more accurate PES.
我们提出了一种计算方法，该方法首次能够严格地对氢键三聚物的分子内和分子间振动态进行十二维（12D）量子计算，这些三聚物由柔性双原子分子组成。其出发点是我们最近引入的方法，用于对由刚性双原子组成的非共价键三聚物的分子间振动态进行完全耦合的 9D 量子计算。在本文中，它被扩展到包括三个双原子单体的分子内伸缩坐标。我们 12D 方法的基石是将三聚物的完整振动哈密顿量分解为两个降维哈密顿量，一个是用于分子间自由度（DOF）的 9D 哈密顿量，另一个是用于三聚物分子内振动的 3D 哈密顿量，以及剩余项。这两个哈密顿量分别对角化，它们各自的 9D 和 3D 本征态的一部分被包含在三聚物的内-分子间 DOF 的 12D 乘积收缩基中，其中三聚物的完整 12D 振动哈密顿量的矩阵被对角化。该方法应用于氢键 HF 三聚物的内-分子间耦合振动态的 12D 量子计算，该三聚物基于从头算计算的势能面（PES）。计算涵盖了三聚物的单量子和双量子 HF 伸缩激发振动态以及感兴趣的分子内振动能级中的低能分子间振动态。它们揭示了（HF）3 中分子内和分子间振动模式之间存在显著耦合的几个有趣表现。12D 计算还表明，与孤立的 HF 单体相比，HF 三聚物的 v = 1、2 HF 伸缩态的频率发生了强烈的红移。此外，这些三聚物红移的幅度比（HF）2 中供体-HF 部分的伸缩基频的红移幅度大得多，这很可能是由于（HF）3 中的协同氢键作用。12D 结果与 HF 三聚物的有限光谱数据之间的一致性虽然令人满意，但仍有改进的空间，并指出需要更准确的 PES。
