Time-Dependent Density Functional Perturbation Theory: new algorithms with applications to molecular spectra

This thesis is organized as follows. In Chapter 1 we will illustrate the basic concepts of DFT and TDDFT; the most common computational approaches will be also considered. In Chapter 2 our new formalism will be introduced together with the numerical algorithm and a first application to benzene. In chapter 3 we will illustrate a technique for extrapolating the Lanczos coefficients and to accelerate the convergence of the method. The resulting methodology will be applied to more challenging problems, such as fullerene and chlorophyll spectra. In Chapter 4 the method will be applied to the study of dye-sensitized solar cells. In appendix A and B we will give the technical details of our specific implementation in the plane-wave pseudopotential framework

ENVIRONMENTAL SUSTAINABILITY OF OIL INDUSTRY

Similarly to most industrial activities, the oil industry can affect the environment at several stages. The greatest impact is the release of waste into the environment in concentrations that are not natural. Virtually in all cases, the adverse impact can be minimized or eliminated through the implementation of a proper waste management plan. Over the past few years the oil industry has placed greater emphasis on minimizing the environmental impact of its operations in all the main phases of a hydrocarbon reservoir life: from appraisal to field development, from production and recovery to reservoir decommissioning. As a consequence, the oil industry is facing important technical challenges, approaching with great interest and expectation new emerging technologies, such as nanotechnologies and alternative solutions, like CO2 underground storage. This study provides an overview of the most interesting solutions that have been proposed and critically highlights their potential benefits and drawbacks. The following paper focuses on some of the new approaches that have already changed the routine operation workflow, while others are currently being tested and may yet require further improvement

Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods

We report a systematic study of the weak chemical bond between two benzene molecules. We first show that it is possible to obtain a very good description of the C_2 dimer and the benzene molecule, by using pseudopotentials for the chemically inert 1s electrons, and a resonating valence bond wave function as a variational ansatz, expanded on a relatively small Gaussian basis set. We employ an improved version of the stochastic reconfiguration technique to optimize the many-body wave function, which is the starting point for highly accurate simulations based on the lattice regularized diffusion Monte Carlo (LRDMC) method. This projection technique provides a rigorous variational upper bound for the total energy, even in the presence of pseudopotentials, and allows to improve systematically the accuracy of the trial wave function, which already yields a large fraction of the dynamical and non-dynamical electron correlation. We show that the energy dispersion of two benzene molecules in the parallel displaced geometry is significantly deeper than the face-to-face configuration. However, contrary to previous studies based on post Hartree-Fock methods, the binding energy remains weak (~ 2 kcal/mol) also in this geometry, and its value is in agreement with the most accurate and recent experimental findings

Density-functional perturbation theory goes time-dependent

The scope of time-dependent density-functional theory (TDDFT) is limited to the lowest portion of the spectrum of rather small systems (a few tens of atoms at most). In the static regime, density-functional perturbation theory (DFPT) allows one to calculate response functions of systems as large as currently dealt with in ground-state simulations. In this paper we present an effective way of combining DFPT with TDDFT. The dynamical polarizability is first expressed as an off-diagonal matrix element of the resolvent of the Kohn-Sham Liouvillian super-operator. A DFPT representation of response functions allows one to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is finally conveniently evaluated using a newly developed non-symmetric Lanczos technique, which allows for the calculation of the entire spectrum with a single Lanczos recursion chain. Each step of the chain essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian or, for that matter, as a single time step of a Car-Parrinello molecular dynamics run. The method will be illustrated with a few case molecular applications

Solution of the Bethe-Salpeter equation without empty electronic states: Application to the absorption spectra of bulk systems

An approach recently developed to solve the Bethe-Salpeter equation within density matrix perturbation theory is extended to the calculation of optical spectra of periodic systems. This generalization requires numerical integrations within the first Brillouin zone that are efficiently performed by exploiting point group symmetries. The technique is applied to the calculation of the optical spectra of bulk Si, diamond C, and cubic SiC. Numerical convergence and the accuracy of the Tamm-Dancoff approximation are discussed in detail

Substrate screening approach for quasiparticle energies of two-dimensional interfaces with lattice mismatch

Two-dimensional (2D) materials are outstanding platforms for exotic physics and emerging applications by forming interfaces. In order to efficiently take into account the substrate screening in the quasiparticle energies of 2D materials, several theoretical methods have been proposed previously, but only applicable to interfaces of two systems' lattice constants with certain integer proportion. In this work, we analytically showed the equivalence and distinction among different approximate methods for substrate dielectric matrices. We evaluated the accuracy of these methods, by applying them to calculate quasi-particle energies of hexagonal boron nitride interface systems (heterojunctions and bilayers), and compared with explicit interface calculations. Most importantly, we developed an efficient and accurate interpolation technique for dielectric matrices that made quasiparticle energy calculations possible for arbitrarily mismatched interfaces, which is extremely important for practical applications.Comment: 9 pages, 7 figures, one tabl

Turbo charging time-dependent density-functional theory with Lanczos chains

We introduce a new implementation of time-dependent density-functional theory which allows the \emph{entire} spectrum of a molecule or extended system to be computed with a numerical effort comparable to that of a \emph{single} standard ground-state calculation. This method is particularly well suited for large systems and/or large basis sets, such as plane waves or real-space grids. By using a super-operator formulation of linearized time-dependent density-functional theory, we first represent the dynamical polarizability of an interacting-electron system as an off-diagonal matrix element of the resolvent of the Liouvillian super-operator. One-electron operators and density matrices are treated using a representation borrowed from time-independent density-functional perturbation theory, which permits to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is evaluated through a newly developed algorithm based on the non-symmetric Lanczos method. Each step of the Lanczos recursion essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian. Suitable extrapolation of the Lanczos coefficients allows for a dramatic reduction of the number of Lanczos steps necessary to obtain well converged spectra, bringing such number down to hundreds (or a few thousands, at worst) in typical plane-wave pseudopotential applications. The resulting numerical workload is only a few times larger than that needed by a ground-state Kohn-Sham calculation for a same system. Our method is demonstrated with the calculation of the spectra of benzene, C$_{60}$ fullerene, and of chlorofyll a.Comment: 15 pages, 7 figures, to be pdflatex + bibte

turboTDDFT - A code for the simulation of molecular spectra using the Liouville-Lanczos approach to time-dependent density-functional perturbation theory

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Time-dependent density functional theory study of squaraine dye-sensitized solar cells

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