Schuurman Michael S, Yarkony David R
Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA.
J Chem Phys. 2006 Jun 28;124(24):244103. doi: 10.1063/1.2206185.
A method for characterizing the degeneracy preserving seam space in the vicinity of a three state conical intersection is introduced. Second order degenerate perturbation theory is used to construct an approximately diabatic Hamiltonian whose eigenenergies and eigenstates accurately describe the vicinity of the three state conical intersection in its full dimensionality. The perturbative analysis enables the large number, 6(N(int)(N(int)+1)2), of unique second order parameters needed to construct this accurate Hamiltonian to be determined from ab initio data at a limited number of nuclear configurations, with (N(int)+10) being minimal. Using the minimum energy three state conical intersection of the pyrazolyl radical (N(int) = 18), the potential of this approach is illustrated. A Hamiltonian comprised of the ten characteristic (linear) parameters and over 1440 second order parameters is constructed and used to determine the locus of the conical intersection seam as well as to describe the 18 dimensional space in the vicinity of that point of intersection. Our results demonstrate the ability of this methodology to quantitatively reproduce the ab initio potential energy surfaces near a three state conical intersection.
介绍了一种表征三态锥形交叉点附近简并保持缝空间的方法。利用二阶简并微扰理论构建了一个近似非绝热哈密顿量，其本征能量和本征态能在全维度上精确描述三态锥形交叉点附近的情况。微扰分析使得构建这个精确哈密顿量所需的大量（6(N(int)(N(int)+1)/2)）唯一二阶参数能够从有限数量核构型的从头算数据中确定，其中(N(int)+10)为最小值。以吡唑基自由基的最低能量三态锥形交叉点（N(int)=18）为例，说明了该方法的潜力。构建了一个由十个特征（线性）参数和超过1440个二阶参数组成的哈密顿量，并用于确定锥形交叉缝的轨迹以及描述该交叉点附近的18维空间。我们的结果证明了该方法定量重现三态锥形交叉点附近从头算势能面的能力。
