Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA.
J Phys Chem A. 2013 Aug 15;117(32):7179-89. doi: 10.1021/jp4008834. Epub 2013 May 1.
The mathematical constructs of the Dyson coordinates and geometry are introduced. The former are a unitary transformation of the normal coordinates and the anharmonic vibrational counterpart of the Dyson orbitals in electronic structure theory. The first-order Dyson coordinates bring the sums of the harmonic force constants and their first-order diagrammatic perturbation corrections (the first-order Dyson self-energy) to a diagonal form. The first-order Dyson geometry has no counterpart in electronic structure theory. It is the point on the potential energy surface at which the sums of the energy gradients and their first-order diagrammatic perturbation corrections vanish. It agrees with the vibrationally averaged geometry of vibrational self-consistent field (VSCF) theory in the bulk limit. These constructs provide a unified view of the relationship of VSCF and its diagrammatically size-consistent modifications as well as the self-consistent phonon method widely used in solid-state physics.
引入了狄森坐标和几何的数学结构。前者是正常坐标的幺正变换，也是电子结构理论中狄森轨道的非谐振动对应物。一阶狄森坐标将调和力常数及其一阶图式微扰修正（一阶狄森自能）的和对角化。一阶狄森几何在电子结构理论中没有对应物。它是势能面上的一个点，在这个点上，能量梯度及其一阶图式微扰修正的和为零。它与振动自洽场（VSCF）理论的振动平均几何在整体极限内是一致的。这些结构为 VSCF 及其图式大小一致的修正以及广泛应用于固态物理的自洽声子方法之间的关系提供了一个统一的观点。
