Assigning signs to the electronic nonadiabatic coupling terms: the H2,O system as a case study.
Assigning signs to the electronic nonadiabatic coupling terms: the H2,O system as a case study.
复制标题
为电子非绝热耦合项分配符号：以 H2,O 系统为例。
作者：
Á. Vibók;G. Halász;S. Suhai;M. Baer
本文讨论了电子非绝热耦合项（NACT）的一个特殊困难，即如何正确确定其符号。众所周知，正确的NACT，包括它们的符号，对于核薛定谔方程的任何数值处理都是至关重要的[参见，即，A. Kuppermaan和R. Abrol，Adv.Chem.Phys.124，283（2003）]。在大多数情况下，非绝热耦合矩阵（NACM）的正确符号的推导是采用各种连续性程序。然而，在某些情况下，这些程序并不足够，对于这些情况，我们建议应用基于数学引理的附加程序，该引理断言产生D矩阵的指数线积分相对于积分的初始点是不变的[M]。Baer，J.Phys.Chem.A104，3181（2000）]。在数值研究中，我们应用这个引理来确定{H（2），O}系统的三个激发态的3 × 3 NACM元的符号（其中一些NACTs是首次提出的）。事实证明，从头计算处理产生的结果可以形成八种不同的3x 3 NACM。然而，这个引理的应用（不需要任何显著的额外数值工作）将这个数字减少到2。最后的选择是通过一个增强的数值研究，这需要更准确的计算。
This paper is devoted to a specific difficulty related to the electronic nonadiabatic coupling terms (NACT), namely, how to determine correctly their signs. It is well known that correct NACTs, including their signs, are crucial for any numerical treatment of the nuclear Schrodinger equation [see, i.e., A. Kuppermaan and R. Abrol, Adv. Chem. Phys. 124, 283 (2003)]. In most cases the derivation of the correct sign of the nonadiabatic coupling matrix (NACM) is done employing various continuity procedures. However, there are cases where these procedures do not suffice and for these cases we suggest to apply an additional procedure based on a mathematical lemma which asserts that the exponentiated line integral which yields the D matrix is invariant with respect to the initial point of the integration [M. Baer, J. Phys. Chem. A 104, 3181 (2000)]. In the numerical study we apply this lemma to determine the signs of the 3x3 NACM elements for the three excited states of the {H(2),O} system (some of these NACTs are presented here for the first time). It turns out that the ab initio treatment yields results from which one can form eight different 3x3 NACMs. However the application of this lemma (which does not require any significant additional numerical effort) reduces this number to two. The final selection is done by an enhanced numerical study which requires more accurate calculations.