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 ach-antages with respect to a direct cliagonalization of a
Hamiltonian matrix. especially in context of DFT-LDA 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 Born-Oppenheimer
decoupling between electronic and ionic motion and the classical approximation
for the ionic motion. Then we present the unified approach for ab-initio
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
self-trapping in diamond. To this purpose we first introduce the self-trapping
phenomena. by presenting a qualitative model for such processes. Then \Ve
illustrate the theoretical and the experimental facts which suggest the occurrence
of self-trapping processes in diamond. Finally we present the results of
our DFT-LDA 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 i1n-ersion of an overlap matrix, and whose minimum
coincides with the exact D FT-LDA minimum. (ii) The introduction of localization
constraints for the single particle wave-functions. In this Chapter
we first discuss the analytic properties of the novel energy functional within
DFT-LDA. Then we demonstrate tha.t a quantum MD algorithm with linear
system-size sea.ling can be obtained when the functional is minimized with
respect to localized waYe-functions. 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 DFT-LDA quantum l\ID and electronic structure
calculations. In particular we present a fictitious clamped second-order 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 second-order 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.
