Sarkar Biplab, Adhikari Satrajit, Baer Michael
Department of Chemistry, Indian Institute of Technology, Guwahati, North Guwahati, Guwahati 781039, India.
J Chem Phys. 2007 Jul 7;127(1):014302. doi: 10.1063/1.2743438.
This second article in the two back-to-back articles presents a numerical application to support and strengthen two theoretical findings extensively discussed in the previous article (article I). In I, we found that introducing the space-time contours enables to distinguish between N, the number of nuclear Schrodinger equations to be solved, and L, the number of field-free states that become populated by the external field (in the ordinary, perturbative approaches this distinction is not apparent). In the numerical study we show, employing the electronic transition probability matrix P(s,t) [which closely is related to the transformation matrix omega(s,t)--see Eqs. (21) and (25) in I], that the N=L case is rare and in most cases we have N<L. Since the perturbative approach can be shown to follow when N=L (see Sec. III C in I) the numerical study implies that in most cases the perturbative approach is not reliable. The second issue that is studied is related to the diabatization process. It is shown, numerically, that the N<L case, in general, does not lead to field-dressed diabatic potentials which are single valued. However, if N is chosen to be identical to the number of field-free states that yield field-free single-valued diabatic potentials in a given spatial region then the corresponding N field-dressed states also yield single-valued (field-dressed) diabatic potentials. This result is independent of L. The numerical study is carried out for an eigenvalue problem based on the Mathieu equation.
这两篇相继发表的文章中的第二篇给出了一个数值应用，以支持和强化前一篇文章（文章I）中广泛讨论的两个理论发现。在文章I中，我们发现引入时空轮廓能够区分需要求解的核薛定谔方程的数量N和由外场填充的无场态的数量L（在普通的微扰方法中，这种区别并不明显）。在数值研究中，我们利用电子跃迁概率矩阵P(s,t)（它与变换矩阵omega(s,t)密切相关——见文章I中的式(21)和(25)）表明，N = L的情况很少见，在大多数情况下我们有N < L。由于当N = L时可以证明微扰方法是适用的（见文章I的第三节C），所以数值研究表明在大多数情况下微扰方法不可靠。研究的第二个问题与 diabatic 化过程有关。数值结果表明，一般来说，N < L的情况不会导致场修饰的 diabatic 势是单值的。然而，如果选择N等于在给定空间区域中产生无场单值 diabatic 势的无场态的数量，那么相应的N个场修饰态也会产生单值的（场修饰的）diabatic 势。这个结果与L无关。数值研究是针对基于马蒂厄方程的本征值问题进行的。
