Sato Tohru, Chibotaru Liviu F, Ceulemans Arnout
Division of Quantum Chemistry, Catholic University of Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium.
J Chem Phys. 2005 Feb 1;122(5):54104. doi: 10.1063/1.1836758.
Correct boundary conditions for the E x e dynamic Jahn-Teller problem are considered explicitly for the first time to obtain approximate analytical solutions in the strong coupling limit. Numerical solutions for the decoupled equations using the finite difference method are also presented. The numerical solutions for the decoupled equations exhibit avoided crossings in the weak coupling region, which explains the oscillating behavior of the solutions obtained by Longuet-Higgins et al. for the coupled equations. The obtained analytical energy expressions show improved agreement with the numerical calculations as compared with the previous treatment in which the potentials were assumed to be harmonic. We demonstrate that the pseudorotational energy j(2)/(2g(2)), where g is the dimensionless vibronic coupling constant, and j total angular momentum: j=+/-1/2,+/-3/2,..., in the conventional strong coupling expression for the vibronic levels of the lower sheet is exact. Non-Hermitian first-order perturbation theory gives the energy which is correct up to 1/g(4). The asymptotic behavior of the wave function at the origin does not influence the corrected energy up to order of 1/g(4). At the same time the treatment of the upper sheet with correct boundary conditions gives solutions which are entirely different from the corresponding Slonczewski's solutions. Besides, the correct boundary conditions enable us to evaluate the nonadiabatic coupling between the lower and upper potential sheets. The energy correction due to the nonadiabatic coupling is estimated to be of order 1/g(6).
首次明确考虑了Eₓₑ动态 Jahn - Teller 问题的正确边界条件，以在强耦合极限下获得近似解析解。还给出了使用有限差分法对解耦方程的数值解。解耦方程的数值解在弱耦合区域呈现出避免交叉的情况，这解释了 Longuet - Higgins 等人对耦合方程所获得的解的振荡行为。与之前假设势为谐波的处理方法相比，所得到的解析能量表达式与数值计算结果的一致性有所提高。我们证明，在下层电子振动能级的传统强耦合表达式中，赝旋转能量j(²)/(2g(²))（其中g是无量纲电子 - 振动耦合常数）以及总角动量j = ±1/2, ±3/2, ... 是精确的。非厄米一阶微扰理论给出的能量在1/g(⁴)的量级上是正确的。波函数在原点处的渐近行为对直至1/g(⁴)量级的修正能量没有影响。同时，对上层使用正确边界条件进行处理得到的解与相应的 Slonczewski 解完全不同。此外，正确的边界条件使我们能够评估上下势层之间的非绝热耦合。由于非绝热耦合引起的能量修正估计为1/g(⁶)量级。
