title: An Infinite Order Discrete Variable Representation of an Effective Mass Hamiltonian: Application to Exciton Wave Functions in Quantum Confined Nanostructures.
abstract: We describe an extension of the conventional Fourier grid discrete variable representation (DVR) to the bound state problem of a particle with a position-dependent mass. An infinite order DVR, derived for a variable mass kinetic energy operator, coupled with an efficient grid contraction scheme yields essentially exact eigenvalues for a chosen grid spacing. Implementation of the method is shown to be very practical due to the fact that in a DVR no integral evaluation is necessary and that the resultant kinetic energy matrix is sparse. Numerical calculations are presented for exciton states of spherical, cylindrical, and toric Type I (CdSe/ZnS) core-shell quantum dots. In these examples, electron-hole interaction is treated explicitly by solving a self-consistent Schrödinger-Poisson equation on a contracted DVR grid. Prospective applications of the developed approach to calculating electron transfer rates between adsorbed molecular acceptors and quantum confined nanocrystals of generic shape, dimensionality, and composition are also discussed.
authors.affiliation: Cherry L. Emerson Center for Scientific Computation, Emory University , 1515 Dickey Dr., Atlanta, Georgia 30322, United States.
authors.forename: Alexey L
authors.initials: AL
authors.lastname: Kaledin
authors.affiliation: Department of Chemistry, Emory University , 1515 Dickey Dr., Atlanta, Georgia 30322, United States.
authors.forename: Tianquan
authors.initials: T
authors.lastname: Lian
authors.affiliation: Department of Chemistry, Emory University , 1515 Dickey Dr., Atlanta, Georgia 30322, United States.
authors.forename: Craig L
authors.initials: CL
authors.lastname: Hill
authors.affiliation: Cherry L. Emerson Center for Scientific Computation, Emory University , 1515 Dickey Dr., Atlanta, Georgia 30322, United States.
authors.forename: Djamaladdin G
authors.initials: DG
authors.lastname: Musaev