State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, China.
J Chem Phys. 2012 Sep 7;137(9):094101. doi: 10.1063/1.4748137.
We present an efficient and accurate grid method to study the strong field dynamics of planar H(2)(+) under Born-Oppenheimer approximation. After introducing the elliptical coordinates to the planar H(2)(+), we show that the Coulomb singularities at the nuclei can be successfully overcome so that both bound and continuum states can be accurately calculated by the method of separation of variables. The time-dependent Schrödinger equation (TDSE) can be accurately solved by a two-dimensional discrete variable representation (DVR) method, where the radial coordinate is discretized with the finite-element discrete variable representation for easy parallel computation and the angular coordinate with the trigonometric DVR which can describe the periodicity in this direction. The bound states energies can be accurately calculated by the imaginary time propagation of TDSE, which agree very well with those computed by the separation of variables. We apply the TDSE to study the ionization dynamics of the planar H(2)(+) by short extreme ultra-violet (xuv) pulses, in which case the differential momentum distributions from both the length and the velocity gauge agree very well with those calculated by the lowest order perturbation theory.
我们提出了一种高效准确的网格方法，用于在玻恩-奥本海默近似下研究平面 H(2)(+)的强场动力学。在将椭圆坐标引入平面 H(2)(+)后，我们表明可以成功克服原子核处的库仑奇点，从而通过变量分离方法准确计算束缚态和连续态。通过二维离散变量表示（DVR）方法可以准确求解含时薛定谔方程（TDSE），其中径向坐标采用有限元离散变量表示，便于并行计算，而角坐标则采用三角 DVR，可描述该方向的周期性。通过 TDSE 的虚时传播可以准确计算束缚态能量，与通过变量分离计算的结果非常吻合。我们应用 TDSE 研究了短极端紫外（xuv）脉冲下平面 H(2)(+)的离化动力学，在这种情况下，长度和速度规范的微分动量分布与最低阶微扰理论计算的结果非常吻合。
