Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA.
J Chem Phys. 2012 Oct 21;137(15):154107. doi: 10.1063/1.4757935.
A new classical model for the general second-quantized many-electron Hamiltonian in Cartesian coordinates and momenta is presented; this makes semiclassical (SC) calculations using an initial value representation (IVR) more useful than the classical Hamiltonian in action-angle variables given earlier by Miller and White [J. Chem. Phys. 84, 5059-5066 (1986)]. If only 1-electron terms are included in this Hamiltonian, the classical equations of motion for the Cartesian variables are linear, and the SC-IVR gives exact results for the propagator (and thus for transition probabilities, the energy spectrum, etc.), as confirmed by analytic proof and numerical calculations. Though this new Hamiltonian is not exact when 2-electron interactions are included, we observe good results for the SC-IVR transition probabilities for times that are not too long. Test calculations, for example, show that the SC-IVR is accurate for times long enough to obtain good result for the eigenvalue spectrum (i.e., the energy levels of the electronic system).
提出了一种新的笛卡尔坐标和动量下的通用二次量子化多电子哈密顿量经典模型；与之前 Miller 和 White [J. Chem. Phys. 84, 5059-5066 (1986)]给出的作用角变量中的经典哈密顿量相比，使用初始值表示（IVR）进行半经典（SC）计算更为有用。如果仅包含此哈密顿量中的 1 电子项，则笛卡尔变量的经典运动方程是线性的，SC-IVR 为传播子（因此为跃迁概率、能谱等）给出精确结果，这已通过分析证明和数值计算得到证实。尽管当包含 2 电子相互作用时此新哈密顿量不精确，但我们观察到 SC-IVR 跃迁概率在不太长的时间内有良好的结果。例如，测试计算表明，SC-IVR 对于足够长的时间是准确的，以获得电子系统的本征值谱（即能级）的良好结果。
