<p>This thesis is divided into two parts. In the first part we study thermodynamics of the two-dimensional Heisenberg ferromagnet with dipolar interaction. This interaction breaks the conditions of the Mermin-Wagner theorem, resulting in a finite transition temperature. Our calculations are done within the framework of the self-consistent spin-wave theory (SSWT), which is modified in order to include the dipolar interaction. Both quantum and classical versions of the Heisenberg model are considered.</p><p>The second part of the thesis investigates the chemical bonding in solids from the first principles calculations. A new chemical bonding indicator called balanced crystal orbital overlap population (BCOOP) is developed. BCOOP is less basis set dependent than the earlier indicators and it can be used with full-potential density-functional theory (DFT) codes. We apply BCOOP formalism to the chemical bonding in the high-T_c superconductor MgB2 and the theoretically predicted MAX phase Nb3SiC2. We also study how the chemical bonding results in a repulsive hydrogen–hydrogen interaction in metal hydrides. The role of this interaction in the structural phase transition in Ti3SnHx is investigated.</p>

This thesis is divided into two parts. In the first part we study thermodynamics of the two-dimensional Heisenberg ferromagnet with dipolar interaction. This interaction breaks the conditions of the Mermin-Wagner theorem, resulting in a finite transition temperature. Our calculations are done within the framework of the self-consistent spin-wave theory (SSWT), which is modified in order to include the dipolar interaction. Both quantum and classical versions of the Heisenberg model are considered. The second part of the thesis investigates the chemical bonding in solids from the first principles calculations. A new chemical bonding indicator called balanced crystal orbital overlap population (BCOOP) is developed. BCOOP is less basis set dependent than the earlier indicators and it can be used with full-potential density-functional theory (DFT) codes. We apply BCOOP formalism to the chemical bonding in the high-T_c superconductor MgB2 and the theoretically predicted MAX phase Nb3SiC2. We also study how the chemical bonding results in a repulsive hydrogen–hydrogen interaction in metal hydrides. The role of this interaction in the structural phase transition in Ti3SnHx is investigated.

Dipolar couplings are one of the major source of structural information. Due to their dependence on the distance between the nuclei and the angle of orientation of the dipolar vector with respect to the magnetic field, they provide significant insight into the geometry and topology of molecules. As the dipolar interactions are in general present in the solid phase of the compounds, solid state NMR experiments have gained significant popularity and is widely used. Separated Local Field NMR spectroscopy based on cross-polarization technique has been used to measure the heteronuclear dipolar couplings in solid state. However, the technique undergoes many experimental challenges and requires further development. This thesis is concerned mainly with the development of techniques to measure the dipolar couplings accurately in oriented molecules. In this regard, a method for fast data acquisition is also proposed. The first chapter briefly introduces the basics of NMR spectroscopy, methodologies applied for obtaining a high resolution NMR spectrum in the solid state. An introduction to liquid crystals is presented and the nature of NMR interaction in the liquid crystalline phases is described. In chapter-2, a new pulse scheme has been proposed that includes the X-nucleus polarization in the SLF experiments and is shown to provide better sensitivity and resolution. A quantitative analysis with simulation and experimental results are also presented. In chapter-3, the performance of various homonuclear decoupling pulse schemes incorporated into SLF experiments tested on oriented systems are compared. The proposed pulse schemes are shown to provide high resolution spectrum with accurate dipolar coupling measurement for natural abundant samples and for uniformly labeled compounds as well. Theoretical description with simulation and experimental results shown here are found to provide optimum results under several technical complications seen with respect to the conventional methods used for SLF experiments. Chapter-4, an attempt is made to reconstruct 2D J-resolved and 2D- SLF spectra from several 1D experimental data. This is achieved with the help of projection reconstruction method and is shown to provide high resolution 2D spectrum with saving of experimental time by an order of two. Chapter-5, high resolution spectra from SLF experiments under phase alternating pulses and using amplitude and time averaged nutation techniques are shown for accurate dipolar coupling measurement with a dramatic reduction in rf power. This is important as the use of low rf power leads to low sample heating and can be applied suitably for the study of liquid crystals and salty biomolecules. Chapter-6, attempts are made to characterize two novel thiophene based liquid crystals using both solution and solid state NMR spectroscopy. C-H dipolar couplings measured from SLF experiments are mainly used to find the order parameters and geometry of the molecules.

Thesis (Ph.D.); Submitted to the University of California, Berkeley, CA (US); 21 Dec 2004. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--56768" Urban, Jeffry Todd. USDOE Director. Office of Science. Office of Basic Energy Sciences (US) 12/21/2004. Report is also available in paper and microfiche from NTIS.

Cette thèse a pour objet l’étude et le contrôle de la photo-réactivité d’interrupteurs moléculaires, en particulier la photo-isomérisation des spiropyranes. Ce travail théorique a été réalisé en collaboration étroite avec l’équipe expérimentale PFL de l’ICB à Dijon. Des simulations de dynamique quantique non-adiabatique ont été réalisées afin de reproduire et rationaliser les résultats expérimentaux de spectroscopie d’absorption transitoire résolue en temps. Ces expériences ont montré une photo-réactivité ultra-rapide (~ 100 fs) suite à une excitation par une pulse LASER ultra-court. Celle-ci est interprétée comme un mécanisme de conversion interne entre le premier état électronique excité singulet et l’état fondamental via une intersection conique. L’étude théorique a utilisé la réaction d’ouverture de cycle du benzopyrane comme modèle. Les développements réalisés ont porté sur : (1) L’exploration du mécanisme réactionnel et le calcul de surfaces d’énergie potentielle via des méthodes de chimie quantique post-CASSCF perturbatives (XMCQDPT2). Cette analyse a montré des résultats variant fortement par rapport à ceux relevés dans la littérature à des niveaux de calcul moins élevés. (2) Le développement d’un modèle de surfaces d’énergie potentielle électronique par la construction d’un hamiltonien diabatique à partir de données ab initio XMCQDPT2. Du fait de l’importante anharmonicité de l’état électronique fondamental, nous avons mis en place une approche effective en rupture avec les études antérieures. (3) La réalisation de simulations de dynamique quantique non-adiabatique par la méthode MCTDH. Les résultats obtenus sont en très bon accord avec les résultats expérimentaux. L’inclusion explicite du pulse LASER a permis de reproduire et de rationaliser l’effet de contrôle par mise en forme d’impulsion observé expérimentalement. Ce travail a ainsi permis la mise en place d’une collaboration et d’un dialogue théorie/expérience effectifs. / This thesis adresses the study and control of the photo-reactivity of molecular switches, here the photo-isomerisation of spiropyrans. This theoretical work has been achieved in close collaboration with the experimental team PFL within the ICB in Dijon. Non-adiabatic quantum dynamics simulations were carried out so as to reproduce and rationalise the experimental results from time-resolved transient absorption spectroscopy. Such experiments have demonstrated ultra-fast photo-reactivity (~ 100 fs) following excitation by an ultra-short LASER pulse. It is interpreted as an internal conversion mechanism between the first singlet excited eletronic state and the ground state via a conical intersection. The theoretical study used the ring-opening reaction of benzopyran as a model. Developments were made regarding: (1) The exploration of the reaction mechanism and the computation of potential energy surfaces with perturbative, post-CASSCF quantum chemistry methods (XMCQDPT2). This investigation showed that results changed significantly compared to those reported in the literature with lower-level calculations. (2) The generation of a diabatic Hamiltonian based on ab initio XMCQDPT2 data. Owing to the significant anharmonicity in the ground electronic state, we designed a new effective approach, quite different from the previous studies. (3) The production of non-adiabatic quantum dynamics simulations using the MCTDH method. The results thus obtained are in excellent agreement with the experimental ones. Including explicitly the LASER pulse allowed us to reproduce and rationalise the action of pulse shaping on control observed in experiments. The present work thus made possible the succesful implementation of a theoretical/experimental collaboration.

Obtaining enantio pure drug molecules is a long standing challenge in asymmetric synthesis implying that the identification of enantiomers and the determination of enantiomeric purity from a racemic mixture are of profound importance. In achieving this target NMR spectroscopy has proven to be an excellent analytical tool. It is well known that normal achiral NMR solvents do not distinguish the spectra of enantiomers. On the other hand, the conversion of substrates to diastereomers using one of the enantiopure chiral auxiliaries, such as, chiral solvating agent, chiral derivatizing agent and chiral lanthanide shift reagent, circumvents this problem. The imposition of diasteomeric interactions circumvents this problem. There is a pool of chiral auxiliaries available in the literature, each of which is specific to molecules of certain functionalities and has its own advantages and limitations. These classical methods have two limitations as they demand the presence of a targeted functional group in the chiral molecule and utilize only chemical shifts to visualize enantiomers. On the other hand in chiral anisotropic medium, due to differential ordering effect, the order-sensitive NMR observables, viz. chemical shift anisotropies (∆σi), dipolar couplings (Dij) and for nuclei with spin >1/2 the quadrupolar couplings (Qi) have enormous power of exhibiting different spectrum for each enantiomer permitting their discrimination. Numerous weakly ordered chiral aligning media have been reported in the literature. Nevertheless there is a scarcity of water compatible medium. Research work presented in this thesis is focused on various aspects, such as, the discovery of new chiral aligning medium for the enantiodiscrimination of water soluble chiral molecules, potential utility of DNA liquid crystal for discrimination of amino acids, on-the-fly monitoring of enzyme kinetics and the preparation of novel composite liquid crystals, hydrogels and thin films. The derived results are discussed in different chapters. Chapter 1 provides a brief introduction to NMR spectroscopy with special emphasis on the conceptual understanding of the tensorial interaction parameters, such as chemical shifts, scalar and dipolar couplings, quadrupolar couplings, effect of r.f pulses, basic introduction to 2D NMR experiments. Subsequently, a broad overview of the enantiomers, specification of their configurations, chirality without stereogenic carbon, chirality in molecules containing different atoms, are discussed. Following this a brief introduction to liquid crystals and their properties, their classification, their orientation in the magnetic field, order parameter are also discussed. The description on the chiral liquid crystals, the differential ordering effect, employment of the orientation dependent NMR interactions, utility of 2H NMR experiments for the visualization of enantiomers and the measurement of enantiomeric composition has been set out in brief. Chapter 2: As far as the organo soluble chiral molecules is concerned (in solvents such as, chloroform, dioxane, tetrahydrofuran and dimethylformamide), it has been well established that an ideal choice of chiral liquid crystal for enantiodiscrimination is poly-�-benzyl-L-glutamate (PBLG). Nevertheless, there is a scarcity of weak aligning medium for water soluble chiral molecules. This chapter introduces the chiral liquid crystal derived from the polysaccharide xanthan, which has numerous applications. The detailed discussion on the preparation of polysaccharide xanthan mesophase is given. The appearance of the mesophse is established by detecting the quadrupole split doublet of dissolved water. Subsequently enantiodiscrimination power of this new medium has been investigated on deuterated D/L-Alanine and (R/S)-β-butyrolactone. For such a purpose the selective 2D-SERF (SElective ReFocussing) experiment has been employed. It has been convincingly demonstrated that the medium has wide applicability for the discrimination of enantiomers, enantiotopic directions in prochiral molecules, measurement of enantiomeric excess and the RDCs in medium sized molecules. The new medium is sustainable over a wide range of temperature and concentration of ingredients, the mesophase is reversible, reproducible, easy to prepare besides being cost effective. It is possible to have the controlled tuning of the degree of order for specific application. Chapter 3: In this chapter the real discriminatory potential of DNA liquid crystalline phase has been explored. It is unambiguously established that; i) the fragmented DNA liquid crystal is able to differentiate between enantiomers of structurally different chiral amino acids; ii) the T1 (2H) values for L/D (alanine) is nearly equal indicating the similar dynamics for both the enantiomers, thus permitting the measurement of ee from the integral areas of the peaks of the contours of 2D spectrum; iii) the enantiotopic discrimination in prochiral compounds has also been successfully explored. Furthermore the analyses of NMR results yielded fruitful information on the analytical potential of DNA chiral liquid crystal, such as, (a) the chiral discrimination is effective on a large range of amino acids with spectral differences ΔΔʋQ‘s and ΔʋQ‘s varying from 80 to 338 Hz, and 50 to 900 Hz respectively; (b) the discrimination phenomenon remain active irrespective of the structure and the electronic nature (polarity) of the fourth substituent around the stereogenic center; (c) compared to an alkyl moiety, the presence of a terminal –OH or –SH group seems to slightly increase both the degree of alignment of the solute and the enantiodiscrimination efficiency compared to alanine; (d) The enantiodiscrimination can be detected easily not only on CD3 and CD groups, but also on CD2 sites exhibiting inequivalent diastereotopic directions; (e) discriminations with rather large differential ordering effect were obtained even for the sites that are situated far away from the asymmetric center; (f) The relative position of quadrupolar doublets from one 2H site to another can be reversed with regard to the absolute configuration (L/D). Chapter 4: Racemases recognize a chiral substrate such as (L-Alanine) and convert it into its enantiomer, i.e., (D-Alanine) and vice versa. Alanine racemase plays a vital role for certain bacteria, providing D-Alanine for peptidoglycan cell-wall biosynthesis. Elucidating the mechanism of enzymatic racemization is crucial for designing new inhibitors that may be useful as a novel class of antibiotics. This requires techniques to discriminate L-and D-Alanine and follow their concentrations as a function of time, so that one can determine the kinetic parameters and study the effect of inhibitors. In this chapter the utility of DNA liquid crystal media for in situ and real-time monitoring of the interconversion of L-and D-alanine-d3 by alanine racemase from Bacillus stearothermophilus has been demonstrated. The enantiomeric excess has been measured at different time intervals to monitor the enzymatic racemization at different time intervals in pseudo 2D NMR. The study unambiguously ascertains the reliability and robustness of utility of NMR in chiral anisotropic phase for monitoring the enzymatic racemization. The method thus provides new mechanistic insight and a better understanding of enzymatic reactions, in particular for alanine racemase. Chapter 5: In continuation with the development of weakly ordered liquid crystals, this chapter reports the spontaneous formation of composite graphene oxide (GO)/double stranded DNA (dsDNA) liquid crystals at higher concentrations of ingredients, and hydrogels at lower concentrations of ingredients, the process of which involves simple mixing in an aqueous phase has been demonstrated. The liquid crystalline phases and hydrogels have been characterized using optical polarized microscopy (OPM), scanning electron microscopy (SEM), Raman spectroscopy and 2H NMR spectroscopy. The observation of strong birefringence in the optical polarized microscope gives evidence for the formation of GO/dsDNA liquid crystals. The strong interaction between the dsDNA and GO was confirmed using Raman spectroscopic analysis. Furthermore, GO/dsDNA thin films have also been prepared and characterized using SEM and OPM. The GO/dsDNA thin film was prepared and its liquid crystal nature was established using OPM and 2H NMR. Importantly, the GO/dsDNA hydrogels were formed without any heat treatment to unwind dsDNA molecules and the porosity of hydrogels can be controlled by changing concentration of the dsDNA. This novel multifunctional composite liquid crystals and hydrogels of GO/dsDNA thus opens up new avenues for many applications like security papers, optical devices such as circular polarizers, reflective displays and drug delivery as well as tissue engineering using GO composite hydrogels.

Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems. The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain. In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations. Chapter 4 contains a digital quantum simulation of the mirror inversion propagator corresponding to the time evolution of an XY spin chain. This simulation has been used to experimentally demonstrate the mirror inversion of quantum states, proposed by Albanese et al.[Phys.Rev.Lett.93,230502(2004)], by which entangled states can be transferred from one end of the chain to the other end. The experiments have been performed in a 5-qubit dipolar coupled nuclear spin system. For simulation, we make use of the recently proposed unitary operator decomposition algorithm along with the numerical pulse optimization techniques, which assisted in achieving high experimental fidelities. Chapter 5 contains a digital quantum simulation of the unitary propagator of a transverse Ising spin chain, which has been used to experimentally demonstrate the perfect state transfer protocol of Di Franco et al. [Phys.Rev.Lett.101,230502(2008)]. The importance of this protocol arises due to the fact that it achieves perfect state transfer from one end of the chain to the other end without the necessity of initializing the intermediate spins of the chain, whereas most of the previously proposed protocols require initialization. The experiments have been performed in a 3-spin nuclear spin system. The simulation has also been used to demonstrate the generation of a GHZ state.

Organic conjugated systems are attractive because of wide range of applications, which includes stimulated emission from -conjugated polymers, optical switches, organic solar cells and organic light emitting diodes, to name a few. They have the advantage of low cost, ease of processing and tunability of their linear and nonlinear optical properties by functionalization with donor or acceptor groups. In chapter 1, we provide an introduction to the π-conjugated systems and various interesting phenomena observed in these systems, This is followed by a brief description of the application of the above mentioned -conjugated systems for organic light emitting diodes, and organic photovoltaic cells. In the last section of this chapter, we give an introduction to magnetism due to π-electron systems. In chapter 2, we begin with energy band theory in one-dimension and its drawbacks. We introduce various model Hamiltonians which incorporate electron-electron inter-actions like Hubbard model, and Pariser-Parr-Pople (PPP) model. We present numerical techniques like valence-bond (VB) and constant MS techniques that are used to exactly solve the above model Hamiltonian. This is followed by an introduction to density matrix renormalization group method (DMRG) employed for the above model Hamiltonian for larger system in one-dimension and quasi-one-dimension. We give description of linear and nonlinear optical properties followed by the oriented gas model for ensemble of molecules. Various methods for computing polarizabilities and hyperpolarizibilities of molecules includes such as Finite-Field method, Sum-Over-State Method, and Correction Vector (CV) Methods are described in detail. In chapter 3, we look into fused azulene systems as a possible organic multiferroics. Azulene molecule with fused five and seven membered π-conjugated rings has a dipole moment, and the π-framework has geometric frustration. Hence in fused azulenes we can expect both ferroelectric and magnetic ground state. To explore this, we study low-lying correlated electronic states of fused azulenes using the long-range interacting PPP model and the finite DMRG method. The ground state is a singlet for oligomers up to 5 azulene units. For oligomers with more than 5 azulene units and up to 11 azulene units the oligomers have a triplet ground state. From the excitation gaps between the lowest MS = 0 state and the lowest states in MS=1, 2, and 3 sectors we predict that the ground-state spin of the fused azulene increases with the number of azulene units. In the thermodynamic limit, we expect the fused azulene to be a ferromagnet. Charge density calculations show that the ground state of the system has ferroelectric alignment of the dipoles of the monomeric units. Thus, a fused azulene system could be the first example of an organic molecule which is both ferromagnetic and ferroelectric, in the ground state. In chapter 4, we study the linear and nonlinear optical properties of diradical systems. We have studied linear and non-linear optical properties of π-conjugated diradicals because they are expected to exhibit large non-linear responses. The system studied are oligomers of dicyclopenta-fused acenes (DPA) and the s-indaceno[1,2,3-cd;5,6,7-c'd']diphenalene (IDPL) molecule. Spin-spin correlation functions within a correlated PPP model Hamiltonian, using exact diagonalization method, are used to characterize the diradical nature of DPA-2 and similar calculations on Anthracene have been performed to contrast this with a singlet character. The diradical character of DPA-2 is also manifest as low optical gap, low spin gap and large THG coefficients compared to Anthracene molecule. Larger DPA-k, k > 2, oligomers as well as the IDPL molecule have been studied within the DMRG technique. In the DPA-4, we nd a very small spin gap (0.04 eV), while in the oligomers with k > 4, we nd that the ground state is degenerate with the lowest triplet state. The energy of the second excited triplet state decreases with increasing size k and seems to saturate at ~0.36 eV in the thermodynamic limit. The lowest optical gap in DPA-4 is at 1.94 eV and has large transition dipoles, while for DPA-k, 4 < k ≥ 28, we have not been able to access states with large transition dipoles. The weak low-energy excitations seem to saturate at 0.5 eV and the two-photon gap also seems to be saturating at~ 0.3 eV in the thermodynamic limit. These polymers will not be IR uorescent by Kasha rule. The dominant component of the THG coefficient, γxxxx, is highest for DPA-4 which reduces almost by an order of magnitude in DPA-8; for k > 8 it increases up to the largest system with k=20 for which we have computed the coe cient. The variation of the charge gap of DPA oligomer with the increase in system size is small and in the polymer limit the charge gap is 4:24 eV. For IDPL molecule spin gap is 0.20 eV and next excited triplet state is at 1.48 eV. Two lowest singlet states in B space are nearly degenerate and have large transition dipole moments. Optical gaps to the above states are 2.20 eV and 2.22 eV. Two-photon gap in this system is 1.29 eV, hence this system is also non- uorescent. We calculated the dispersion of the major component of the THG coefficient, γxxxx, over a wide frequency range for this molecule, and we observe resonances corresponding to the 21Ag and 11Bu states. Extrapolated value of γxxxx at zero frequency is 15:58 x 106 a.u which is very large and the system does not have any donor or acceptor substituent groups. In chapter 5, we study absorption spectra and two photon absorption coefficient of expanded porphyrins (EPs). We nd that in the 4n+2 EPs there are two prominent low-lying one-photon excitations while in 4n systems there is only one such excitation. The two-photon gaps in both these types of systems are at energies close to the one-photon excitations. The spin gap in 4n+2 EPs are very small although the spin-1/2 Heisenberg calculations show that a pure spin system in this geometry will not have vanishing spin-gap. The charge density rearrangement in the one-photon excited state is most at the aza nitrogen site and at the meso carbon sites. In the two-photon states also the charge density rearrangement occurs mostly at the aza-ring sites. The bond order changes in these states is much more striking. In the one-photon state, the C-C bond length in the aza rings show a tendency to become uniform. Similar qualitative trend is also observed for the two-photon state. In chapter 6, we study linear and nonlinear optical properties of two push-pull polyenes stacked in head to head (HtH) and head to tail con gurations (HtT), at different stacking angles, exactly within the PPP model. Varying the stacking angle between polyenes, we nd that the optical gap varies slightly, but transition dipoles show large variation. The dominant component of first-order hyperpolarizability, βxxx for HtH and βyyy for HtT arrangement strongly depend on the distance between molecules. The βxxx for HtH configuration shows a maximum at a nonzero stacking angle, which varies with inter polyene distance. ZINDO study on two monomers, (4-hydroxy-40-nitro-azobenzene) connected by a conjugated bridge shows that βav is more than twice the monomer value and with a red-shift in the optical gap. In chapter 7, we have calculated the shifts in optical gaps and band edges as a function of the distance between two monomers within a correlated PPP model Hamiltonian for various stacking geometries. We have used as model monomers, both unsubstituted polyenes and push-pull substituted polyenes. We have carried out calculations with and without inter-chain hopping between sites on different molecules. We note that in the absence of inter-chain hopping, the energy level shifts are almost independent of the distances between the chains in all stacking geometries. It is also interesting to note that only electron-electron interactions yield a blue shift in the optical gaps for parallel stacking, but red shift in the gap for all other stacking geometries. We note that most of the shift in the gap is due to shifts in the excited state energy and the ground-state energy remains almost the same. With interchain transfer the shift in the optical gap increases with decrease in the interchain distance. We observe red-shifts in parallel stacking geometry when inter-chain electron hopping is turned on, at small interchain separations. In general interchain hopping increases significantly the red shift in the optical gaps for all geometries. Even for push-pull polyenes of | e| =2.0 eV, we observe the same trend in the shift in the optical gap for various stacking geometries. In this case the shift in optical gap is an order of magnitude higher when interchain hopping is turned on compared to that in the absence of interchain hopping. We find that the optical gap shifts are largest for the parallel stacking geometry, and it also shows stronger distance dependence. This is in close conformity with experimental observation of red-shift in absorption maxima when hydrostatic pressure is applied on the system. The shift in the HOMO (LUMO) level is small in the absence of t?, and the largest shift is in the case of parallel stacking compared to other stacking geometries. The distance dependence of the HOMO shifts is also rather weak. When t? is turned on, the level shifts become large by a factor of five or more. When we have push-pull groups electron-hole symmetry is broken and the shift is different for the HOMO and the LUMO level. Depending upon stacking geometry, the HOMO shifts vary from 0:1 ~ eV to 0.3 eV, which is larger than the shifts observed in unsubstituted polyenes. This large shift in the LUMO reduces the efficiency of exciton dissociation.

This thesis focuses on two aspects of Quantum Information Processing (QIP) and contains experimental implementation by Nuclear Magnetic Resonance (NMR) spectroscopy. The two aspects are: (i) development of novel methodologies for improved or fault tolerant QIP using longer lived states and geometric phases and (ii) implementation of certain quantum algorithms and theorems by NMR. In the first chapter a general introduction to Quantum Information Processing and its implementation using NMR as well as a description of NMR Hamiltonians and NMR relaxation using Redfield theory and magnetization modes are given. The second chapter contains a study of relaxation of Pseudo Pure States (PPS). PPS are specially prepared initial states from where computation begins. These states, being non-equilibrium states, relax with time and hence introduce error in computation. In this chapter we have studied the role of Cross-Correlations in relaxation of PPS. The third and fourth chapters, respectively report observation of cyclic and non-cyclic geometric phases. When the state of a qubit is subjected to evolution either adiabatically or non-adiabatically along the surface of the Bloch sphere, the qubit sometimes gain a phase factor apart from the dynamic phase. This is known as the Geometric phase, as it depends only on the geometry of the path of evolution. Geometric phase is used in Fault tolerant QIP. In these two chapters we have demonstrated how geometric phases of a qubit can be measured using NMR. The fifth and sixth chapters contain the implementations of “No Deletion” and “No Cloning” (quantum triplicator for partially known states) theorems. No Cloning and No Deletion theorems are closely related. The former states that an unknown quantum states can not be copied perfectly while the later states that an unknown state can not be deleted perfectly either. In these two chapters we have discussed about experimental implementation of the two theorems. The last chapter contains implementation of “Deutsch-Jozsa” algorithm in strongly dipolar coupled spin systems. Dipolar couplings being larger than the scalar couplings provide better opportunity for scaling up to larger number of qubits. However, strongly coupled systems offer few experimental challenges as well. This chapter demonstrates how a strongly coupled system can be used in NMR QIP.

Les systèmes dynamiques qui évoluent sur un grand intervalle de temps (dynamique moléculaire, prédiction astronomique, turbulence...) occupent une place importante dans le domaine de la science de l'ingénieur. Leur résolution numérique constitue, jusqu'à l'heure actuelle, un défi. En effet, la simulation de la solution nécessite un solveur non seulement rapide mais aussi qui respecte les propriétés physiques du problème, pour garantir la stabilité. Dans cette thèse, on se propose d'étudier, vis-à-vis de cette problématique, un schéma d'intégration temporelle basée sur la décomposition de la solution en série temporelle, suivie de la technique de resommation de Borel des séries divergentes. On analyse alors la rapidité du schéma sur des problèmes modèles. Ensuite, on montre sa capacité à préserver la structure des équations (symplecticité, iso-spectralité, conservation de l'énergie...) à un ordre arbitrairement élevé. Par la suite, on applique le schéma à la résolution d'équations aux dérivées partielles issues de la mécanique, dont les équations de la chaleur, de Burgers et de Navier-Stokes bidimensionnelles. Pour cela, on associe le schéma à une méthode de discrétisation par éléments finis en espace. Enfin, dans le but de rendre l'algorithme plus robuste, on s'intéresse à la représentation de la somme de Borel par une série de factorielle généralisée. / Dynamical systems which evolve in a large time interval (molecular dynamic, astronomical prediction, turbulence…) take an important place in engineering science. Their numerical resolution has so far constituted a challenge. Indeed, the simulation of the solution requires a solver which is not only fast but also respects the physical properties of the problem, to ensure the stability. In this thesis, we propose to study, regarding this issue, a time integration scheme based on the decomposition of the solution into time series, followed by Borel's resummation technique of divergent series. We analyse the speed of scheme on model problems. Next, we show its capability to preserve the structure of the equation (symplecticity, iso-spectrality, conservation of energy…) up to an arbitrary high order. Thereafter, we use the scheme to resolve partial differential equations coming from mechanics, including the two-dimensional heat equation, Burger’s equation and the Navier-Stokes equation. To this aim, we choose a finite element method for space discretisation. Finally, and in order to make the algorithm more robust, we are interested in the representation of the Borel sum by a generalized factorials series.