Lourderaj Upakarasamy, Martínez-Núñez Emilio, Hase William L
Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA.
J Phys Chem A. 2007 Oct 18;111(41):10292-301. doi: 10.1021/jp073317v. Epub 2007 Sep 8.
Linear molecules with degenerate bending modes have states, which may be represented by the quantum numbers N and L. The former gives the total energy for these modes and the latter identifies their vibrational angular momentum jz. In this work, the classical mechanical analog of the N,L-quantum states is reviewed, and an algorithm is presented for selecting initial conditions for these states in quasiclassical trajectory chemical dynamics simulations. The algorithm is illustrated by choosing initial conditions for the N = 3 and L = 3 and 1 states of CO2. Applications of this algorithm are considered for initial conditions without and with zero-point energy (zpe) included in the vibrational angular momentum states and the C-O stretching modes. The O-atom motions in the x,y-plane are determined for these states from classical trajectories in Cartesian coordinates and are compared with the motion predicted by the normal-mode model. They are only in agreement for the N = L = 3 state without vibrational angular momentum zpe. For the remaining states, the Cartesian O-atom motions are considerably different from the elliptical motion predicted by the normal-mode model. This arises from bend-stretch coupling, including centrifugal distortion, in the Cartesian trajectories, which results in tubular instead of elliptical motion. Including zpe in the C-O stretch modes introduces considerable complexity into the O-atom motions for the vibrational angular momentum states. The short-time O-atom motions for these trajectories are highly irregular and do not appear to have any identifiable characteristics. However, the O-atom motions for trajectories integrated for substantially longer period of times acquire unique properties. With C-O stretch zpe included, the long-time O-atom motion becomes tubular for trajectories integrated to approximately 14 ps for the L = 3 states and to approximately 44 ps for the L = 1 states.
具有简并弯曲模式的线性分子具有一些状态，这些状态可用量子数N和L来表示。前者给出这些模式的总能量，后者确定其振动角动量jz。在这项工作中，回顾了N、L量子态的经典力学类似物，并提出了一种算法，用于在准经典轨迹化学动力学模拟中为这些状态选择初始条件。通过为二氧化碳的N = 3、L = 3和1状态选择初始条件来说明该算法。考虑了该算法在振动角动量态和C - O伸缩模式中不包含零点能量（zpe）和包含零点能量的初始条件下的应用。通过笛卡尔坐标中的经典轨迹确定这些状态下x、y平面中O原子的运动，并与正常模式模型预测的运动进行比较。它们仅在不具有振动角动量zpe的N = L = 3状态下一致。对于其余状态，笛卡尔坐标中O原子的运动与正常模式模型预测的椭圆运动有很大不同。这是由笛卡尔轨迹中的弯曲 - 伸缩耦合（包括离心畸变）引起的，这导致管状运动而非椭圆运动。在C - O伸缩模式中包含zpe会给振动角动量态的O原子运动带来相当大的复杂性。这些轨迹的短时间O原子运动非常不规则，似乎没有任何可识别的特征。然而，对于积分时间长得多的轨迹，O原子运动获得了独特的性质。包含C - O伸缩zpe时，对于L = 3状态积分到约14 ps、对于L = 1状态积分到约44 ps的轨迹，长时间O原子运动变为管状。
