In Chapter 2 we discuss variational properties of ground and of excited states of a generic Hamiltonian and then we extend this formulation to the framework of D FT. In a \·ariational a.pp roach an eigenvalue quantum mechanical problem is recast as a minimization of a. functional. This scheme has several computational achantages with respect to a direct cliagonalization of a Hamiltonian matrix. especially in context of DFTLDA quantum 11ID. In the same Chapter we also describe the minimization schemes used in this work, with a particular emphasis on the acceleration methods reported in the Appendix. In Chapter :3 we discuss the tvvo fundamental approximations which a.re a.t the basis of quantum f\ID schemes, i.e. the adiabatic BornOppenheimer decoupling between electronic and ionic motion and the classical approximation for the ionic motion. Then we present the unified approach for abinitio molecular dynamics introduced by Car and Parrinello ( CP) [4]. which provides an efficient approach for ground state quantum MD simulations. The variational properties of the excited states discussed in Chapter :3 allows us to extend the CP scheme to excited state quantum l'vID. Finally the acceleration methods reported in Appendix allows us to increase the integration time step in CP quantum MD. In Chapter 4 \Ye use the excited state quantum MD to study the excitonic selftrapping in diamond. To this purpose we first introduce the selftrapping phenomena. by presenting a qualitative model for such processes. Then \Ve illustrate the theoretical and the experimental facts which suggest the occurrence of selftrapping processes in diamond. Finally we present the results of our DFTLDA calculations for the core exciton, the valence exciton and the valence biexciton. In Chapter 5 \re present a method for electronic structure calculations and quantum ]\ID simulations whose computational cost grows linearly with the system size. Our approach is based on two ideas: (i) The use of a novel energy functional which does not require either explicit orthogonalization of the electronic orbitals. or i1nersion of an overlap matrix, and whose minimum coincides with the exact D FTLDA minimum. (ii) The introduction of localization constraints for the single particle wavefunctions. In this Chapter we first discuss the analytic properties of the novel energy functional within DFTLDA. Then we demonstrate tha.t a quantum MD algorithm with linear systemsize sea.ling can be obtained when the functional is minimized with respect to localized waYefunctions. Finally we present a. practical implementation of this algorithm in a TB context. In Chapter 6 we use the TB quantum :MD scheme having computational cost that grmvs linearly the system size to study the impact of a C60 fullerene on a. clean ( 2x1) reconst meted ( 111) surface of diamond. In the .\ppenclix we reproduce a reprint of Ref. [.5], in which vve introduce acceleration schemes for DFTLDA quantum l\ID and electronic structure calculations. In particular we present a fictitious clamped secondorder dynamics for total energy minimizations and we show that the convergence rate of this dynamics is comparable to tha.t of conjugate gradient methods. l\foreover we increase the integration time step in damped secondorder dynamics and in CP quantum l\ID by preconditioning the fictitious electronic motion. Finally we analyse in detail a numerical instability~ usually referred to a.s charge sloshing insta.bilit:y. \\·hich could be induced by the Coulomb potential in large supercells.
New Developments in Quantum Molecular Dynamics: Excited State Dynamics and Large Scale Simulations(1994 Oct 27).
New Developments in Quantum Molecular Dynamics: Excited State Dynamics and Large Scale Simulations

19941027
Abstract
In Chapter 2 we discuss variational properties of ground and of excited states of a generic Hamiltonian and then we extend this formulation to the framework of D FT. In a \·ariational a.pp roach an eigenvalue quantum mechanical problem is recast as a minimization of a. functional. This scheme has several computational achantages with respect to a direct cliagonalization of a Hamiltonian matrix. especially in context of DFTLDA quantum 11ID. In the same Chapter we also describe the minimization schemes used in this work, with a particular emphasis on the acceleration methods reported in the Appendix. In Chapter :3 we discuss the tvvo fundamental approximations which a.re a.t the basis of quantum f\ID schemes, i.e. the adiabatic BornOppenheimer decoupling between electronic and ionic motion and the classical approximation for the ionic motion. Then we present the unified approach for abinitio molecular dynamics introduced by Car and Parrinello ( CP) [4]. which provides an efficient approach for ground state quantum MD simulations. The variational properties of the excited states discussed in Chapter :3 allows us to extend the CP scheme to excited state quantum l'vID. Finally the acceleration methods reported in Appendix allows us to increase the integration time step in CP quantum MD. In Chapter 4 \Ye use the excited state quantum MD to study the excitonic selftrapping in diamond. To this purpose we first introduce the selftrapping phenomena. by presenting a qualitative model for such processes. Then \Ve illustrate the theoretical and the experimental facts which suggest the occurrence of selftrapping processes in diamond. Finally we present the results of our DFTLDA calculations for the core exciton, the valence exciton and the valence biexciton. In Chapter 5 \re present a method for electronic structure calculations and quantum ]\ID simulations whose computational cost grows linearly with the system size. Our approach is based on two ideas: (i) The use of a novel energy functional which does not require either explicit orthogonalization of the electronic orbitals. or i1nersion of an overlap matrix, and whose minimum coincides with the exact D FTLDA minimum. (ii) The introduction of localization constraints for the single particle wavefunctions. In this Chapter we first discuss the analytic properties of the novel energy functional within DFTLDA. Then we demonstrate tha.t a quantum MD algorithm with linear systemsize sea.ling can be obtained when the functional is minimized with respect to localized waYefunctions. Finally we present a. practical implementation of this algorithm in a TB context. In Chapter 6 we use the TB quantum :MD scheme having computational cost that grmvs linearly the system size to study the impact of a C60 fullerene on a. clean ( 2x1) reconst meted ( 111) surface of diamond. In the .\ppenclix we reproduce a reprint of Ref. [.5], in which vve introduce acceleration schemes for DFTLDA quantum l\ID and electronic structure calculations. In particular we present a fictitious clamped secondorder dynamics for total energy minimizations and we show that the convergence rate of this dynamics is comparable to tha.t of conjugate gradient methods. l\foreover we increase the integration time step in damped secondorder dynamics and in CP quantum l\ID by preconditioning the fictitious electronic motion. Finally we analyse in detail a numerical instability~ usually referred to a.s charge sloshing insta.bilit:y. \\·hich could be induced by the Coulomb potential in large supercells.File  Dimensione  Formato  

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