第一讲交叉点的计算.ppt

量化进展课 主要内容 势能面的交叉点理论及实际计算 溶剂化理论 耦合簇理论(CCSD) QM/MM计算 FORTRAN语言在计算化学中的应用 Conical Intersections De-Cai Fang The study of chemical systems is based on the separation of nuclear and electronic motion The potential energy surfaces (PES) are generated by the solution of the electronic part of the Schrodinger equation. This solution gives an energy for every fixed position of the nuclei. When the energy is plotted as a function of geometries it generates the PES as a(3N-6) dimensional surface. Every electronic state has its own PES. On this potential energy surface, we can treat the motion of the nuclei classically or quantum mechanically Hamiltonian for molecules Derivative coupling What is a conical intersection The Noncrossing Rule Conical intersections and symmetry Symmetry required conical intersections, Jahn-Teller effect H12=0, H11=H22 by symmetry seam has dimension N of high symmetry Example: E state in H3 in D3h symmetry Symmetry allowed conical intersections (between states of different symmetry) H12=0 by symmetry Seam has dimension N-1 Example: A1-B2 degeneracy in C2v symmetry in H2+OH Accidental same-symmetry conical intersections Seam has dimension N-2 Example: X3 system The Branching Plane Topography of a conical intersection Adiabatic and Diabatic represenation Adiabatic representation uses the eigenfunctions of the electronic hamiltonian. The derivative coupling then is present in the total Schrodinger equation Diabatic representation is a transformation from the adiabatic which makes the derivative coupling vanish. Off diagonal matrix elements appear. Better for dynamics since matrix elements are scalar but the derivative coupling is a vector. Strickly diabatic bases don’t exist. Only quasidiabatic where f is very small. Locating the minimum energy point on the seam of conical intersections Projected gradient technique: M. J. Baerpack, M. Robe and H.B. Schlegel Chem. Phys. Lett. 223, 269, (1994) Lagrange multiplier technique: M. R. Manaa and D.