No description available.

In electronic structure calculations the computational cost is of great importance because large systems can contain a huge number of electrons. One effective method to make such calculations is by density matrix purification. Although, the cost for this method is relatively low compared to other existing methods there is room for improvements. In this paper one method proposed by Emanuel Rubensson and one method proposed by Jaehoon Kim & Yousung Jung was compared to each other with respect to efficiency, simplicity and robustness. Both are improved methods to compute the density matrix by accelerated polynomial expansion. Rubensson’s method consists of two different algorithms and results showed that both performed better than Kim & Jung’s method in terms of efficiency, which is the property both methods directs their main focus on. The major differences between them was identified in terms of adaptivity. The methods require different inputs that demands separate levels of knowledge about the system. Kim & Jung’s method which require less knowledge can however benefit efficiency-wise from more information in order to optimize the algorithm for the system. Results also showed that both methods were stable, but since they only were tested with arbitrarily assumed input arguments no conclusion about their general stability could be drawn.

A fundamental understanding of ultrafast nonequilibrium dynamical processes in molecular aggregates is crucially important for the design of nanodevices that utilize quantum mechanical effects. However, understanding the coupled electron-phonon dynamics of such high-dimensional systems remains a challenging issue. As a result of the ever-growing computational power that is available, realistic parameterization of model Hamiltonians and implementation of sophisticated quantum dynamics algorithms have become indispensable tools for gaining insight into these processes. The focus of this dissertation is the development and implementation of approximate path integral-based methods to compute the time-evolution as well as linear and nonlinear spectroscopic signals of molecular aggregates following photo-excitation. The developments and applications presented here are geared toward gaining a better understanding of the role that electron-phonon coupling plays in framing ultrafast excitation energy transfer networks in photosynthetic light-harvesting complexes. The ultrafast excitation energy transfer dynamics that occurs upon photo-excitation of a network of electronically coupled chromophores is remarkably sensitive to the strength of electronic coupling as well as the frequencies and coupling strengths that characterize electron-phonon interactions. Based on approximations to the diabatic representation of molecular Hamiltonians, energetic models of condensed phase molecular aggregates can be parameterized from a first principles description. Often times, computational parameterization of these models reveals comparable magnitudes for intermolecular electronic couplings and electron-phonon couplings, negating the applicability of popular perturbative algorithms (such as those based on Forster or Redfield theory) for describing their time-evolution. Moreover, non-perturbative exact methods (e.g. stochastic Schrodinger equations and the Hierarchical Equations of Motion) are generally inefficient for all but a few specific limiting forms of electron-phonon coupling, or make assumptions about autocorrelation timescales of the vibrational environment. Because of the failure of the energetic parameters determined through recent ab initio studies of natural molecular aggregates to abide by the rather restrictive requirements for efficient application of the above-mentioned methods, the development of approximate non-perturbative algorithms for predicting nonequilibrium dynamical properties of such systems is a central theme in this dissertation. Following a general introductory section describing the basic concepts that are fundamental to the remainder of the thesis, the derivation of path integral dynamics methods is presented. These include a cartesian phase space path integral derivation of the truncated Wigner approximation as applied to the Meyer-Miller-Stock-Thoss mapping model for describing vibronic systems as well as a novel derivation of the Partially Linearized Density Matrix algorithm, highlighting its emergence as a leading order approximation to an, in principle, exact expression for the density matrix. An algorithm for computing the nonlinear response function for higher-order optical spectroscopy signals is presented within the framework of the partially linearized density matrix formalism. Time-resolved two-dimensional electronic spectra are computed and compared with exact results as well as standard perturbation theory-based results, highlighting the accuracy and efficiency of the developed method. Additionally, the recently popularized symmetrical quasi-classical method for computing the reduced density matrix dynamics is extended for computing linear optical spectroscopy signals, and compared with results from the partially linearized density matrix treatment. A generalization of the model Hamiltonian form utilized in recent ab initio studies is presented, allowing for direct vibrational energy relaxation due to coupling between intramolecular normal modes and their environment. The consequences of including these interactions within a model Hamiltonian that is inspired by energetic parameters found in studies of a photosynthetic light-harvesting complex are highlighted in the context of density matrix dynamics and time-resolved two-dimensional electronic spectroscopy. The results indicate that this physical process can be utilized as a means of optimizing the efficiency of excitation energy transfer and localization. Inspired by ab initio characterization of model Hamiltonians for molecular aggregates, a new approximate semiclassical propagator for describing the time-evolution of a system consisting of discrete electronic states in the presence of both high-frequency harmonic vibrational modes as well as slow environmental DOFs with arbitrary potentials is presented. Results indicate that this algorithm provides a more accurate description in this parameter regime than standard linearized path integral methods such as the partially linearized density matrix algorithm and the truncated Wigner approximation. Finally, preliminary results of dynamics involving non-perturbative field-matter interactions is presented with emphasis on strategically shaped pulses, field design through optimal control, and non-perturbative pump-probe spectroscopy.

Die vorliegende Arbeit verallgemeinert die Methode der Wellenpaketpropagation fuer isolierte molekulare Systeme auf molekulare Systeme mit Umgebungswechselwirkung. Im Rahmen der Dichtematrixtheorie werden am Beispiel des linearen Absorptionskoeffizienten und des Raman-Streuquerschnitts Ausdruecke fuer stationaere optische Funktionen abgeleitet. Diese Ausdruecke lassen sich als Fouriertransformation einer durch Dichtematrixpropagation erhaltenen Groesse verstehen, deren Dynamik auch durch die Umgebung des molekularen Systems beeinflusst wird. Am Beispiel von drei Modellsystemen (OH-Streckschwingung von Wasser, NO in Ar-Matrizen, HCl in Ar-Matrizen) wird der lineare Absorptionskoeffizient im infraroten und ultravioletten Spektralbereich berechnet. Die Ergebnisse werden mit experimentellen Daten verglichen. Aus der numerisch ansruchsvollen drei-dimensionalen Behandlung des HCl in Ar werden zusaetzlich Schluesse ueber die Dynamik des H-Atoms bei der Photodissoziation gezogen. Der Ausdruck fuer den Raman-Streuquerschnitt wird an einem theoretischen Modellsystem untersucht. Insbesondere wird die Temperatur- und Feldstaerkeabhaengigkeit des Spektrums diskutiert. / The well-known wave paket propagation method is extended from isolated molecular systems to molekular systems interacting with a dissipative environment. In the framework of density matrix theory formulations of stationary optical properties (linear absorption and Raman scattering cross section) are found. Essentially these formulations contain the Fourier-transform of a term given by density matrix propagation which is influenced by the environment. For three examples (OH stretching vibration in liquid water, NO in Ar-matrices, HCl in Ar-matrices) the linear absorption coefficient is calculated in the infrared and ultraviolett spectral range. Comparisons with experimental data are given. For the case of HCl in Ar-matrices additional information concerning the dynamics of the H-atom during the photodissociation is given. The Raman scattering cross section is calculated for a theoretical model system. Especially temperature dependence and the influence of the electric field strength on the spectra is discussed.

No description available.

No description available.

This thesis deals with quantum chemistry methods for large systems. In particular, the thesis focuses on the efficient construction of the Coulomb and exchange matrices which are important parts of the Fock matrix in Hartree-Fock calculations. Density matrix purification, which is a method used to construct the density matrix for a given Fock matrix, is also discussed. The methods described are not only applicable in the Hartree-Fock case, but also in Kohn-Sham Density Functional Theory calculations, where the Coulomb and exchange matrices are parts of the Kohn-Sham matrix. Screening techniques for reducing the computational complexity of both Coulomb and exchange computations are discussed, including the fast multipole method, used for efficient computation of the Coulomb matrix. The thesis also discusses how sparsity in the matrices occurring in Hartree-Fock and Kohn-Sham Density Functional Theory calculations can be used to achieve more efficient storage of matrices as well as more efficient operations on them. / QC 20100817

Despite the success of modern quantum chemistry in predicting properties of organic molecules, the treatment of inorganic systems, which have many close lying states, remains out of quantitative reach for current methods. To treat non-dynamic correlation, we take advantage of the density matrix renormalization group (DMRG) method that has become very successful in the field of solid state physics. We present a detailed study of the DMRG method, and we pay special attention to the evolution of the understanding behind the mathematical structure of the DMRG wave function. Our primary goal is to develop a density matrix renormalization group self--consistent--field (DMRG-SCF) approach, analogous to the complete active space self--consistent field (CASSCF) method, but dealing with large active spaces that are too demanding for the full configuration interaction (FCI) method. As a first step towards such a DMRG-SCF procedure, we present a spin-adapted DMRG algorithm designed to target spin- and spatial-symmetry states that are hard to obtain while using an unrestricted algorithm. Our next step is a modification of the DMRG algorithm to obtain decreasing energy at every step during the sweep. This monotonically convergent DMRG scheme lets us obtain the two-body density matrix as a by--product of the existing procedure without any additional cost in storage. Additionally, the two-body density matrix produced at convergence using this scheme is free from the N-representability problem that is present when the two--body density matrix is produced with the two-site DMRG scheme without additional storage cost. Finally, taking advantage of the modifications developed herein, we present results obtained from our DMRG-SCF method. Lastly, we discuss possible ways of incorporating dynamical correlation into the DMRG scheme, in order to obtain a modern multireference approach.

Despite the success of modern quantum chemistry in predicting properties of organic molecules, the treatment of inorganic systems, which have many close lying states, remains out of quantitative reach for current methods. To treat non-dynamic correlation, we take advantage of the density matrix renormalization group (DMRG) method that has become very successful in the field of solid state physics. We present a detailed study of the DMRG method, and we pay special attention to the evolution of the understanding behind the mathematical structure of the DMRG wave function. Our primary goal is to develop a density matrix renormalization group self--consistent--field (DMRG-SCF) approach, analogous to the complete active space self--consistent field (CASSCF) method, but dealing with large active spaces that are too demanding for the full configuration interaction (FCI) method. As a first step towards such a DMRG-SCF procedure, we present a spin-adapted DMRG algorithm designed to target spin- and spatial-symmetry states that are hard to obtain while using an unrestricted algorithm. Our next step is a modification of the DMRG algorithm to obtain decreasing energy at every step during the sweep. This monotonically convergent DMRG scheme lets us obtain the two-body density matrix as a by--product of the existing procedure without any additional cost in storage. Additionally, the two-body density matrix produced at convergence using this scheme is free from the N-representability problem that is present when the two--body density matrix is produced with the two-site DMRG scheme without additional storage cost. Finally, taking advantage of the modifications developed herein, we present results obtained from our DMRG-SCF method. Lastly, we discuss possible ways of incorporating dynamical correlation into the DMRG scheme, in order to obtain a modern multireference approach.

The electron transport through a molecular wire under the influence of an external laser field is studied using a reduced density matrix formalism. The full system is partitioned into the relevant part, i.e. the wire, electron reservoirs and a phonon bath. An earlier second-order perturbation theory approach of Meier and Tannor for bosonic environments which employs a numerical decomposition of the spectral density is used to describe the coupling to the phonon bath and is extended to deal with the electron transfer between the reservoirs and the molecular wire. Furthermore, from the resulting time-nonlocal (TNL) scheme a time-local (TL) approach can be determined. Both are employed to propagate the reduced density operator in time for an arbitrary time-dependent system Hamiltonian which incorporates the laser field non-perturbatively. Within the TL formulation, one can extract a current operator for the open quantum system. This enables a more general formulation of the problem which is necessary to employ an optimal control algorithm for open quantum systems in order to compute optimal control fields for time-distributed target states, e.g. current patterns. Thus, we take a fundamental step towards optimal control in molecular electronics. Numerical examples of the population dynamics, laser controlled current, TNL vs. TL and optimal control fields are presented to demonstrate the diverse applicability of the derived formalism.