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Rotating full- and reduced-dimensional quantum chemical models of molecules

机译:旋转分子的全维和降维量子化学模型

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A flexible protocol, applicable to semirigid as well as floppy polyatomic systems, is developed for the variational solution of the rotational-vibrational Schr?dinger equation. The kinetic energy operator is expressed in terms of curvilinear coordinates, describing the internal motion, and rotational coordinates, characterizing the orientation of the frame fixed to the nonrigid body. Although the analytic form of the kinetic energy operator might be very complex, it does not need to be known a priori within this scheme as it is constructed automatically and numerically whenever needed. The internal coordinates can be chosen to best represent the system of interest and the body-fixed frame is not restricted to an embedding defined with respect to a single reference geometry. The features of the technique mentioned make it especially well suited to treat large-amplitude nuclear motions. Reduced-dimensional rovibrational models can be defined straightforwardly by introducing constraints on the generalized coordinates. In order to demonstrate the flexibility of the protocol and the associated computer code, the inversion-tunneling of the ammonia (~(14)NH_3) molecule is studied using one, two, three, four, and six active vibrational degrees of freedom, within both vibrational and rovibrational variational computations. For example, the one-dimensional inversion-tunneling model of ammonia is considered also for nonzero rotational angular momenta. It turns out to be difficult to significantly improve upon this simple model. Rotational-vibrational energy levels are presented for rotational angular momentum quantum numbers J 0, 1, 2, 3, and 4.
机译:针对旋转振动薛定er方程的变分解,开发了一种适用于半刚性以及软多原子系统的灵活协议。动能算子以曲线坐标表示,描述了内部运动,而旋转坐标表示了固定在非刚体上的框架的方向。尽管动能算符的解析形式可能非常复杂,但是在此方案中并不需要先验地知道它,因为它在需要时会自动且以数字方式构造。可以选择内部坐标以最好地表示感兴趣的系统,并且身体固定框架不限于针对单个参考几何体定义的嵌入。提到的技术的特点使其特别适合于处理大振幅核运动。可以通过在广义坐标上引入约束来直接定义降维旋转振动模型。为了证明协议和相关计算机代码的灵活性,使用了一个,两个,三个,四个和六个主动振动自由度,研究了氨(〜(14)NH_3)分子的反向隧穿振动和振动变分计算。例如,对于非零旋转角动量,也考虑氨的一维反转隧道模型。事实证明,很难对该简单模型进行重大改进。给出了旋转角动量量子数J 0、1、2、3和4的旋转振动能级。

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