Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA.
J Chem Phys. 2012 Aug 21;137(7):074115. doi: 10.1063/1.4746156.
The approach of defining quantum corrections on nuclear dynamics of molecular systems incorporated approximately into selected degrees of freedom, is described. The approach is based on the Madelung-de-Broglie-Bohm formulation of time-dependent quantum mechanics which represents a wavefunction in terms of an ensemble of trajectories. The trajectories follow classical laws of motion except that the quantum potential, dependent on the wavefunction amplitude and its derivatives, is added to the external, classical potential. In this framework the quantum potential, determined approximately for practical reasons, is included only into the "quantum" degrees of freedom describing light particles such as protons, while neglecting with the quantum force for the heavy, nearly classical nuclei. The entire system comprised of light and heavy particles is described by a single wavefunction of full dimensionality. The coordinate space of heavy particles is divided into spatial domains or subspaces. The quantum force acting on the light particles is determined for each domain of similar configurations of the heavy nuclei. This approach effectively introduces parametric dependence of the reduced dimensionality quantum force, on classical degrees of freedom. This strategy improves accuracy of the quantum force and does not restrict interaction between the domains. The concept is illustrated for two-dimensional scattering systems, where the quantum force is required to reproduce vibrational energy of the quantum degree of freedom.
描述了一种将分子系统的核动力学近似纳入选定自由度的量子修正的方法。该方法基于马德隆-德布罗意-玻姆形式的含时量子力学，该理论用轨迹的集合来表示波函数。轨迹遵循经典运动定律，只是除了外部经典势之外，还添加了依赖于波函数幅度及其导数的量子势。在这个框架中，为了实际原因而近似确定的量子势仅包含描述质子等轻粒子的“量子”自由度，而忽略了重核的量子力，重核几乎是经典的。由轻粒子和重粒子组成的整个系统由全维的单个波函数描述。重粒子的坐标空间被划分为空间域或子空间。对于重核相似构型的每个域，确定作用在轻粒子上的量子力。这种方法有效地引入了降低维量子力对经典自由度的参数依赖性。这种策略提高了量子力的准确性，并且不限制域之间的相互作用。该概念通过二维散射系统进行说明，其中需要量子力来再现量子自由度的振动能。
