In the first part of the dissertation, we develop a theoretical approach to analyze nonlinear spectroscopy experiments based on the formalism of quantum state (QST) and process tomography (QPT). In it, a quantum system is regarded as a black box which can be systematically tested in its performance, very much like an electric circuit is tested by sending a series of inputs and measuring the corresponding outputs, but in the quantum sense. We show how to collect a series of pump-probe or photon-echo experiments, and by varying polarizations and frequency components of the perturbations, reconstruct the quantum state (density matrix) of the probed system for a set of different initial conditions, hence simultaneously achieving QST and QPT. Furthermore, we establish the conditions under which a set of two-dimensional optical spectra also yield the desired results. Simulations of noisy experiments with inhomogeneous broadening show the feasibility of the protocol. A spin-off of this work is our suggestion of a witness that distinguishes between spectroscopic time-oscillations corresponding to vibronic only coherences against their electronic counterparts. We conclude by noting that the QST/QPT approach to nonlinear spectroscopy sheds light on the amount of quantum information contained in the output of an experiment, and hence, is a convenient theoretical and experimental paradigm even when the goal is not to perform a full QPT. In the second part of the thesis, we discuss a methodology to study the electronic dynamics of complex molecular systems, such as photosynthetic units, in the framework of time-dependent density functional theory (TD-DFT). By treating the electronic degrees of freedom as the system and the nuclear ones as the bath, we develop an open quantum systems (OQS) approach to TD-DFT. We formally extend the theoretical backbone of TD-DFT to OQS, and suggest a Markovian bath functional which can be readily included in electronic structure codes.

Crystallographically solids with well defined crystal structures are normally assumed to be highly ordered. However, it is not uncommon to find considerable degree of disorder amongst many of these crystalline substances. Disorder among crystalline substances often arise from the rotational motion which leads to the well known class of plastic crystalline substances. Typically, globular molecules such as methane, carbon tetrachloride or adamantane exhibit plastic crystalline phase with significant amount of orientational disorder. In many other substances, disorder arises from torsional motion as in the case of biphenyl, p- or o-terphenyls, stilbene or azobenzenes. In case of molecules with flexible segment, such as alkanes or surfactants, motion of the terminal methyl group or terminal ethyl group is responsible for the observed disorder. Chapter 1 discusses various aspects of disorder in crystals. A new pressure induced solid phase of biphenyl is reported at room temperature. Isothermal-isobaric ensemble variable shape simulation cell Monte Carlo calculations are reported on biphenyl at 300K as a function of pressure between 0-4 GPa. The potential proposed by Williams for inter-molecular and Benkert-Heine-Simmons(BHS) for intramolecular interactions have been employed. Different properties indicating changes in the crystal structure, molecular structure, distributions of inter- and intra-molecular energy are reported as a function of pressure. With increase in pressure beyond 0.8 GPa, the dihedral angle distribution undergoes a change from a bimodal to an unimodal distribution. The changes in IR and Raman spectra across the transition computed from ab initio calculations are in agreement with the experimental measurements. It is shown that at pressures larger than 0.8 GPa, competition between inter-molecular interactions with intra-molecular terms v/z., conjugation energy and the ortho-ortho repulsion favors a planar biphenyl due to better packing and consequently a predominant inter-molecular term. The exact value of the transition pressure will depend on the accuracy of the inter- and intra-molecular potentials employed here. p-terphenyl has been modeled at 300K and atmospheric pressure with different potential models. Modified Fihppini parameters for mtermolecular interactions and BHS potential for inter-ring torsion predict the structure of p-terphenyl reasonably well. Pressure variation calculations are carried out with this combination of inter- and intra-molecular potential. The structure as a function of pressure upto 5 GPa has been compared with experimental structure provided by Puschnig et al. The transformation of functional form of the potential energy curve (associated with the inter-ring flipping) from W-shaped to [/-shaped form as a function of pressure has been observed. This is in excellent agreement with previous studies of polyphenyls including biphenyl and p-hexaphenyl. The complete planarization of molecules occurs when the pressure range is 1.0 GPa-1.5 GPa. Molecular simulation of solid stilbene in the isothermal-isobaric ensemble with variable shape simulation are reported. Structure has been characterized by means of lattice parameters and radial distribution functions. Simulations show existence of pedal-like motion at higher temperatures in agreement with the recent X-ray diffraction measurements by Ogawa and co-workers and several others previously. Difference in energy between the major and minor conformers, barrier to conformational change at both the crystallographic sites have been calculated. Temperature dependence of the equilibrium constant between the two conformers as well as the rate of conversion between the con-formers at the two sites have been calculated. These are in agreement with the recent analysis by Harada and Ogawa of non-equilibrium states obtained by rapid cooling of stilbene. Volume and total intermolecular energy suggest existence of two transitions in agreement with previous Raman phonon spectroscopic and calorimetric studies. They seem to be associated with change from order to disorder at the two sites. Ab initio calculations coupled with simulations suggest that the disorder accounts for only a small part of the observed shortening in ethylene bond ength. A Monte Carlo simulation with variable shape simulation cell has been carried out on stilbene. The study attempts to investigate the disorder at various pressures upto 4 GPa. It is seen that the population of minor conformers at sites 1 and 2 decrease with increase in pressure. Population of minor conformers at site 2 decreases to zero by 1.5 GPa. In contrast, the population of minor conformers at site 1 remains finite for the runs reported here. It is seen that the population of minor conformers at site 1 is higher than at site 2 at room temperature which is to be expected on the basis of the activation energies. Associated changes in the unit cell as well as molecular conformation are discussed. Isothermal-isobaric ensemble Monte Carlo simulation of adamantane has been earned out with variable shape simulation cell. Low temperature crystalline phase and the room temperature plastic crystalline phases have been studied employing the Williams potential. We show that at room temperature, the plastic crystalline phase transforms to the crystalline phase on increase in pressure. Further, we show that this is the same phase as the low temperature ordered tetragonal phase of adamantane. The high pressure ordered phase appears to be characterized by a slightly larger shift of the first peak towards lower value of r in C-C, C-H and H-H rdfs as compared to the low temperature tetragonal phase. Co-existence curve between the crystalline and plastic crystalline phase has been obtained approximately upto a pressure of 4 GPa. We investigate the equation of state, variation of lattice parameters and the distortion of molecular geometry of low temperature phase of adamantane upto 26 GPa pressure. A rigid and a flexible model of adamantane have been studied using variable shape simulation within the isothermal-isobaric ensemble. Including six low frequency modes obtained from density functional theory carried out on a single-molecule has incorporated the flexibility. These calculations used Becke 3-parameter method and Lee-Yang-Parr electron correlation functional with 6-31G(d) basis set. The simulated equation of state and variation of c/a ratio as a function of pressure are compared with the experimental results. The results are in good agreement with high pressure experiments. Nature of distortion in molecular geometry obtained from the calculation are also in good agreement with the experiment.