<p><strong>ABSTRACT </strong> Approximating the kinetic energy as a functional of the electron density is a daunting, but important, task. For molecules in equilibrium geometries, the kinetic energy is equal in magnitude to the total electronic energy, so achieving the exquisite accuracy in the total energy that is needed for chemical applications requires similar accuracy for the kinetic energy functional. For this reason, most density functional theory (DFT) calculations use the Kohn-Sham method, which provides a good estimate for the kinetic energy. But the computational cost of Kohn-Sham DFT calculations has a direct dependence on the total number of electrons because the Kohn-Sham method is based on the orbital picture, with one orbital per electron. Explicit density functionals, where the kinetic energy is written explicitly in terms of the density, and not in terms of orbitals, are much faster to compute. Unfortunately, the explicit density functionals in the literature had disappointing accuracy. This dissertation introduces several new approaches for orbital-free density functional methods. One can try to include information about the Pauli principle using the exchange hole. In the weighted density approximation (WDA), a model for the exchange hole is used to approximate the one-electron density matrix, which is then used to compute the kinetic energy. This thesis introduces a symmetric, normalized, weighted density approximation using the exchange hole of the uniform electron gas. Though the key results on kinetic energy are not accurate enough, an efficient algorithm is introduced which, with a more sophisticated hole model, might give better results. The effects of electron correlation on the kinetic energy can be modeled by moving beyond the one-electron distribution function (the electron density) to higherorder electron distributions (k-electron DFT). For example, one can model electron correlation directly using the pair electron density. In this thesis, we investigated two different functionals of the pair density, the Weizsäcker functional and the March-Santamaria functional. The Weizsäcker functional badly fails to describe the accurate kinetic energy due to the N-representability problem. The March-Santamaria functional is exact for a single Slater determinant, but fails to adequately model the effects of electron correlation on the kinetic energy. Finally, we established a relation between Fisher information and Weizsäcker kinetic energy functional. This allowed us to propose generalisations of the Weizsäcker kinetic energy density functional. It is hoped that the link between information theory and kinetic energy might provide a new approach to deriving improved kinetic energy functionals. <strong> Keywords: </strong><em>Kinetic energy functional, Density functional theory (DFT), von-Weizsäcker</em> <em> functional, March-Santamaria functional, Thomas-Fermi model, density matrix, Twopoint normalization, Pair-density functional theory (PDFT). </em></p> / Doctor of Science (PhD)

The Electron Localization Function (ELF) measures electron localization within matter and provides insights into the nature of bonds in materials and molecules. This thesis examines the relationship between ELF and binding energy in bimolecular systems, focusing on van der Waals interactions—specifically Keesom forces, Debye forces, and London dispersion forces—which play significant roles in molecular and crystalline materials. This research addresses the challenge of accurately calculating binding energies in crystalline materials by exploring their correlation with ELF. Using Density Functional Theory (DFT) with two exchange-correlation functionals, rev-vdW-DF2 and PBE-D3(BJ), this study proposes a method for calculating binding energies in crystalline materials with promising accuracy. By analysing the ELF and its correlation with binding energies in 75 bimolecular systems, the research demonstrates a strong linear correlation, with a coefficient of determination (R2) reaching up to 0.956. The findings suggest that ELF can effectively differentiate between weak and strong van der Waals interactions, providing a reliable metric for evaluating interaction strengths. The results indicate that ELF is a valuable tool for understanding the strength of molecular interactions, with potential applications in materials science and electronic structure theory. The study highlights the importance of refining the accuracy of the ELF-based method and expanding its scope to include other types of non-covalent interactions, such as halogen bonds. The main contribution of this thesis is the exploration of methodologies for analysing and predicting molecular interaction strengths within crystalline materials, which may improve computational approaches in the field. Deriving binding energies within the unit cell directly from the ELF has the potential to simplify practical calculations.

L'adsorption de CO dans la faujasite échangée au CuI et au Na+ a été modélisée à l'aide des approches quantiques (DFT) et classiques (Monte Carlo). Grâce à l'approche DFT, la surface d'énergie potentielle de la faujasite a été explorée. Différents types d'interactions de CO avec les cations ont été identifiés, pour chacune les effets induits par l'adsorption de CO aux niveaux structural et énergétique ont été analysés, et le calcul de la fréquence de vibration de CO a été réalisé. Grâce aux valeurs obtenues, une nouvelle attribution des spectres d'adsorption de CO dans CuY et NaY a été établie. D'un autre côté, grâce aux simulations Monte Carlo dans l'ensemble Grand Canonique, les propriétés d'adsorption (isothermes et enthalpies) de la faujasite vis-à-vis de CO ont été modélisées, et le mécanisme microscopique d'adsorption de CO a été établi. La mise en œuvre de ces simulations a nécessité de paramétrer un nouveau champ de force destiné à décrire les interactions CO/faujasite et CO/CO. / CO adsorption in CuI and Na+ exchanged faujasite has been modeled by mean of quantum (DFT) and classical (Monte Carlo) approaches. By mean of the DFT calculations, faujasite potential energy surface has been explored. Different types of CO interactions with the cations have been highlighted, for each one of them CO adsorption effects on the structural and energetic parameters have been analyzed, and calculations of the CO stretching frequency have been performed. Thanks to our calculated values, a new attribution of CO adsorption spectra in CuY and NaY has been established. On another side, by mean of Monte Carlo simulations in the Grand Canonical ensemble, faujasite adsorption properties regarding CO (isotherms and enthalpies) have been modeled, and the CO adsorption mechanism has been established at the microscopic level. The implementation of these simulations has required the derivation of a new force field describing the CO/faujasite and CO/CO interactions.

The possibility of using methylamines instead of ammonia as a nitrogen precursor for the CVD of nitrides is studied using quantum chemical computations of reaction energies: reaction electronic energy (Δ𝑟𝐸𝑒𝑙𝑒𝑐) reaction enthalpy (Δ𝑟𝐻) and reaction free energy (Δ𝑟𝐺). The reaction energies were calculated for three types of reactions: Uni- and bimolecular decomposition to more reactive nitrogen species, adduct forming with trimethylgallium (TMG) and trimethylaluminum (TMA) followed by a release of methane or ethane and surface adsorption to gallium nitride for both the unreacted ammonia or methylamines or the decomposition products. The calculations for the reaction entropy and free energy were made at both STP and CVD conditions (300°C-1300°C and 50 mbar). The ab inito Gaussian 4 (G4) theory were used for the calculations of the decomposition and adduct reactions while the surface adsorptions were calculated using the Density Functional Theory method B3LYP. From the reactions energies it can be concluded that the decomposition was facilitated by the increasing number of methyl groups on the nitrogen. The adducts with mono- and dimethylamine were more favorable than ammonia and trimethylamine. 𝑁𝐻2 was found to be most readily to adsorb to 𝐺𝑎𝑁 while the undecomposed ammonia and methylamines was not willingly to adsorb.

Há, no Brasil, uma enorme diversidade de espécies vegetais, e um conhecimento popular de várias propriedades medicinais das mesmas. Dentre os estudos realizados com extratos de plantas, há um interesse especial na atividade antioxidante. Este trabalho, focado em atividade antioxidante, é dividido em duas partes: a primeira, utiliza a técnica de RPE para estudar a ação dos antioxidantes neutralizando os radicais livres, enquanto que a segunda utiliza a TFD para, em simulação computacional, ajudar a entender os resultados obtidos na primeira parte. Foram analisados 10 extratos vegetais: Swartzia langsdorffii, Machaerium villosum, Pterogyne nitens, Maytenus ilicifolia (casca de raiz), Pera glabrata, Aegiphyla sellowiana, Copaifera langsdorffii, Chrysophyllum inornatum, Iryanthera juruensis (folhas e sementes), Didymopanax vinosum. O estudo da atividade antioxidante com RPE utiliza dois métodos diferentes: o primeiro método mede a atividade antioxidante por meio do controle da quantidade de radicais livres, TEMPOL e DPPH, em contato com o extrato vegetal, enquanto que o segundo método utiliza o spin trap DMPO em conjunto com a reação de Fenton (Fe2+ + H2O2 => Fe3+ + HO- + HO) para analisar a ação dos extratos vegetais contra o radical hidroxila (OH?). A simulação computacional dos compostos TEMPOL, DPPH e DMPO é realizada em um método de primeiros princípios na Teoria do Funcional da Densidade, com uso de pseudopotenciais. O código utilizado é o SIESTA. As conclusões indicam que o extrato de Iryanthera juruensis, tanto de folhas quanto de sementes, exibe atividades antioxidantes bastante acentuadas, em todos os métodos utilizados. A simulação computacional aponta o TEMPOL menos reativo que o DPPH, devido a menor energia liberada em sua reação de redução. Sabendo que algumas destas espécies já são usadas popularmente por propriedades medicinais, estudos futuros para a correta identificação do agente antioxidante e seu possível uso, tanto na indústria alimentícia quanto na farmacêutica, deverão ser realizados. / There is, in Brazil, a great diversity of vegetable species, and a popular knowledge of several medicinal properties of the some of them. In studies carried out with plants? extracts, there is special interest in antioxidant activities. This work, focused in antioxidant activity, is divided in two parts: the first uses EPR technique to study the antioxidant activities neutralizing free radicals, while the second one uses DFT, in computational simulation, to understand the results obtained from the first part. Ten vegetable extracts were analyzed: Swartzia langsdorffii, Machaerium villosum, Pterogyne nitens, Maytenus ilicifolia (bark root extracts), Pera glabrata, Aegiphyla sellowiana, Copaifera langsdorffii, Chrysophyllum inornatum, Iryanthera juruensis (leaves and seeds), Didymopanax vinosum. The study with EPR uses two different methods: the first method measures the antioxidant activity by monitoring the amount of free radicals, DPPH and TEMPOL, that are in contact with the plant extract, the second method uses spin trap DMPO with Fenton reaction (Fe2+ + H2O2 => Fe3+ + HO- + HO) for the study of the plant extract antioxidant activity against the hydroxyl radical (OH?). The computational simulation of TEMPOL, DPPH and DMPO is carried out using a method of first principles within the Density Functional Theory and pseudopotentials. The code is SIESTA. The conclusions indicate that the Iryanthera juruensis extract, as of leaves as of seeds, exhibits accentuated antioxidants activities, in all of the used methods. The computational simulation indicated that the TEMPOL is less reactive than the DPPH, because the lower energy in its reduction reaction. As some of these species are already used popularly by medicinal properties, future studies for correct identification of the antioxidant compounds and its possible use, as in the food industry as in the pharmaceutical industry, should be realized.

Ces travaux de thèse portent sur la polymérisation radicalaire contrôlée (PRC) des esters et amides de vinyle. L’une des possibilités de contrôle est le piégeage dynamique réversible des chaînes radicalaires croissantes (P•) par un agent de contrôle (T) formant une espèce dormante (P─T’). La concentration en radicaux dans le milieu peut alors diminuer dramatiquement de sorte que les réactions indésirables de terminaisons soient négligeables et que le contrôle de la masse molaire des polymères soit atteint avec un faible indice de dispersité. L’utilisation de complexes métalliques, pouvant s’oxider et former une liaison métal-carbone, comme agent de piégeage des radicaux est une manière de réaliser ce contrôle. La PRC est alors appelée Polymérisation Radicalaire Contrôlée par voie Organométallique (OMRP). A ce jour, plusieurs métaux de transitions ont été utilisés avec plus ou moins de succès en OMRP. Lors de cette étude, nous avons synthétisé des complexes de cuivre(I) et testé leurs performances pour l’OMRP de l’acétate de vinyle et de l’éthylène. Nous avons également utilisé des outils de chimie théorique pour mieux comprendre pourquoi le cobalt(II) acétylacétonate est, jusqu’à aujourd’hui, le meilleur agent de contrôle pour la polymérisation de l’acétate de vinyle et des amides de vinyle. Grâce à la théorie de la fonctionnelle de densité (DFT), nous avons mis en lumière le rôle crucial de la coordination sur le cobalt des groupements carbonyles des monomères étudiés. / This thesis focus on Controlled Radical Polymerization (CRP) of vinyl esters and vinyl amides. One of the possibilities to achieve this control is a dynamic reversible trapping of the growing radical chains (P•) by a controlling agent (T) to form a dormant species (P─T’). The radical concentration in the medium can be dramatically reduced so that the unwanted terminations are disfavored and polymers with controlled molecular weights and low dispersity can be obtained. A way to achieve this control is the use of metallic complexes, which can oxidize and form a metal-carbon bond, as trapping agent in the so-called Organometallic Mediated Radical Polymerization (OMRP). So far, different transition metals have been used with gretaer or smaller success. In this study, the synthesis of copper(I) complexes and their investigation for the vinyl acetate and ethylene polymerization under OMRP conditions were performed. We also used computational chemistry as a tool to better understand why the cobalt(II) acetylacetonate (Co(acac)2) has, so far, given the best results for either vinyl acetate or vinyl amides polymerization. Thanks to Density Functional Theory (DFT), the crucial role of the monomer carbonyl group coordination to cobalt was pointed out.

This dissertation presents a study of the molecular mechanism underlying the highly efficient solar energy conversion processes that occur in the Photosystem I (PS I) reaction centers in plants and bacteria. The primary electron donor P700 is at the heart of solar energy conversion process in PS I and the aim is to obtain a better understanding of the electronic and structural organization of P700 in the ground and excited states. Static Fourier Transform Infra-Red (FTIR) difference spectroscopy (DS) in combination with site directed mutagenesis and Density Functional Theory (DFT) based vibrational frequency simulations were used to investigate how protein interactions such as histidine ligation and hydrogen bonding modulate this organization. (P700+-P700) FTIR DS at 77K were obtained from a series of mutants from the cyanobacterium Synechocystis sp. 6803 (S. 6803) where the amino acid residues near the C=O groups of the two chlorophylls of P700 where specifically changed. (P700+-P700) FTIR DS was also obtained for a set of mutants from C. reinhardtii where the axial ligand to A0-, the primary electron acceptor in PS I was modified. The FTIR DS obtained from these mutants provides information on the axial ligands, the hydrogen bonding status as well as the polarity of the environment of specific functional groups that are part of the chlorophyll molecules that constitute P700. Assignment of the FTIR bands to vibrational modes in specific types of environment is very difficult. In order to assist the assignment of the difference bands in experimental spectra DFT based vibrational mode frequency calculations were undertaken for Chl-a and Chl-a+ model molecular systems under different set of conditions; in the gas phase, in solvents using the Polarizable Continuum Model (PCM), in the presence of explicit solvent molecules using QM/MM methods, and in the presence of axial ligands and hydrogen bonds. DFT methods were also used to calculate the charge, spin and redox properties of Chl-a/Chl-a’ dimer models that are representative of P700, the primary electron donor in PS I.

In this thesis, theoretical and computer simulation studies of vibrational phase relaxation in various molecular liquids are presented. That includes liquid nitrogen, both along the coexistence line and the critical isochore, binary liquid mixture and liquid water. The focus of the thesis is to understand the dependence of the vibrational relaxation on the density, temperature, composition and the role of different interactions among the molecules. The density fluctuation of the solute particles in a solvent is studied systematically, where the computer simulation results are compared with the mode coupling theory (MCT). The classical density functional theory (DFT) is used to study the vibrational relaxation dynamics in molecular liquids with an aim to understand the heterogeneous nature of the dynamics commonly observed in experiments. Chapter 1 contains a brief overview of the earlier relevant theories, their successes and shortcomings in the light of the problems discussed in this thesis. This chapter discusses mainly the basic features of the vibrational dynamics of molecular liquids and portrays some of the theoretical frameworks and formalisms which are widely recognized to have contributed to our present understanding. Vibrational dephasing of nitrogen molecules is known to show highly interesting anomalies near its gas–liquid critical point. In Chapter 2, we present the results of extensive computer simulation studies and theoretical analysis of the vibrational phase relaxation of nitrogen molecules both along the critical isochore and the gas–liquid coexistence line. The simulation includes the different contributions (density (ρ), vibration–rotation (VR), and resonant transfer (Rs)) and their cross–correlations. Following Everitt and Skinner, we have included the vibrational coordinate (q) dependence of the inter–atomic potential, which is found to have an important contribution. The simulated results are in good agreement with the experiments. The linewidth (directly proportional to the rate of the vibrational phase relaxation) is found to have a lambda shaped temperature dependence near the critical point. As observed in the experimental studies, the calculated lineshape becomes Gaussian–like as the critical temperature (Tc) is approached while being Lorentzian–like at the temperatures away from Tc. Both the present simulation and a mode coupling theory (MCT) analysis show that the slow decay of the enhanced density fluctuations near the critical point (CP), probed at the sub–picosecond timescales by the vibrational frequency modulation, and an enhanced vibration–rotation coupling, are the main causes of the observed anomalies. Dephasing time (тv) and the root mean square frequency fluctuation (Δ) in the supercritical region are calculated. The principal results are: 1. a crossover from a Lorentzian–like to a Gaussian–like lineshape is observed as the critical point is approached along the critical isochore, 2. the root mean square frequency fluctuation shows a non–monotonic dependence on the temperature along the critical isochore, 3. the temperature dependent linewidth shows a divergence–like (λ–shaped) behavior along the coexistence line and the critical isochore. It is found that the linewidth calculated from the time integral of the normal coordinate time correlation function (CQ(t)) is in good agreement with the known experimental results. The origin of the anomalous temperature dependence of linewidth can be traced to simultaneous effects of several factors, (i) the enhancement of the negative cross–correlations of ρ with VR and Rs and (ii) the large density fluctuations as the critical point (CP) is approached. Due to the negative cross–correlations of ρ with VR and Rs the total decay becomes faster (correlation times are in the femtosecond scale). The reason for the negative cross–correlation between ρ and VR is explored in detail. A mode coupling theory (MCT) analysis shows a slow decay of the enhanced density fluctuations near the critical point. The MCT analysis demonstrates that the large enhancement of VR–coupling near CP may arise from a non–Gaussian behavior of the equilibrium density fluctuations. This enters through a non–zero value of the triplet direct correlation function. Many of the complex systems found in nature and used routinely in industry are multi–component systems. In particular, binary mixtures are highly non–ideal and play an important role in the industry. The dynamic properties are strongly influenced by composition fluctuations which are absent in the one component liquids. In Chapter 3, isothermal–isobaric (NPT) ensemble molecular dynamics simulation studies of vibrational phase relaxation (VPR) in a model system are presented. The model considers strong attractive interaction between the dissimilar species to prevent phase separation. The model reproduces the experimentally observed non–monotonic, nearly symmetric, composition dependence of the dephasing rate. In addition, several other experimentally observed features, such as the maximum of the frequency modulation correlation time (т c) at a mole fraction near 0.5 and the maximum rate enhancement by a factor of about 3 above the pure component value, are also reproduced. The product of the mean square frequency modulation ((Δω2(0))) with тc indicates that the present model is in the intermediate regime of the inhomogeneous broadening. The non–monotonic composition (χ) dependence of тv is found to be primarily due to the non–monotonic χ dependence of тc, rather than due to a similar dependence in the amplitude of (Δω2(0)). The probability distribution of Δω shows a markedly non–Gaussian behavior at intermediate composition (χ - 0.5). We have also calculated the composition dependence of the viscosity (η∗) in order to explore the correlation between the viscosity with that of тv and тc. It is found that both the correlation times essentially follow the nature of the composition dependence of the viscosity. A mode coupling theory (MCT) analysis is presented to include the effects of the composition fluctuations in binary mixture. Water is an interesting and attractive object for research, not only because of its great importance in life processes but also due to its unusual and intriguing properties. Most of the anomalous properties of water are related to the presence of a three–dimensional network of hydrogen bonds, which is constantly changing at ultrafast, sub–picosecond timescales. Vibrational spectroscopy provides the means to study the dynamics of processes involving only certain chemical bonds. The dynamics of hydrogen bonding can be probed via its reflection on molecular vibrations, e.g., the stretching vibrational mode of the O–H bond. Recently developed femtosecond infrared vibrational spectroscopy has proved to be valuable to study water dynamics because of its unique temporal resolution. Recent studies have shown that the vibrational relaxation of the O–H stretch of HDO occurs at an extremely fast timescale with time constant being less than 100 femtosecond. Here, in Chapter 4, we investigate the origin of this ultrafast vibrational dephasing using computer simulation and appropriate theoretical analysis. In addition to the usual fast vibrational dynamics due to the hydrogen bonding excitations, we find two additional reasons: (a) the large amplitude of angular jumps of the water molecules (with 30–40 fs time intervals) provide large contribution to the mean square vibrational frequency and (b) the projected force along the O–H bond due to the solvent molecules, on the oxygen (FO(t)) and hydrogen (FH (t)) atoms of the O–H bond exhibit a large negative cross–correlation (NCC) between FO(t) and FH (t). This NCC is shown to be partly responsible for a weak, non–Arrhenius temperature dependence of the relaxation rate. In the concluding note, Chapter 5 starts with a brief summary of the outcome of this thesis and ends up with suggestions of a few relevant problems that may prove worthwhile to be addressed in the future.

In this work, the electronic band structure of III (In, Al, Ga) - V (N, As, Sb) compounds and their ternary alloys have been investigated by density functional theory (DFT) within generalized gradient approximation (GGA) and empirical tight binding (ETB) calculations, respectively. The present DFT-GGA calculations have shown direct band gap structures in zinc-blende phase for InN, InAs, InSb, GaN, and GaAs. However, indirect band gap structures have been obtained for cubic AlN, AlSb and AlAs com- pounds / here, the conduction band minima of both AlN and AlAs are located at X symmetry point, while that of AlSb is at a position lying along Gamma- X direction. An important part of this work consists of ETB calculations which have been parameterized for sp3d2 basis and nearest neighbor interactions to study the band gap bowing of III(In / Al)- V(N / As / Sb) ternary alloys. This ETB model provides a satisfactory electronic properties of alloys within reasonable calculation time compared to the calculations of DFT. Since the present ETB energy parameters reproduce successfully the band structures of the compounds at &iexcl / and X symme- try points, they are considered reliable for the band gap bowing calculations of the ternary alloys. In the present work, the band gap engineering of InNxAs1&iexcl / x, InNxSb1&iexcl / x, InAsxSb1&iexcl / x, Al1&iexcl / xInxN, Al1&iexcl / xInxSb and Al1&iexcl / xInxAs alloys has been studied for total range of constituents (0 &lt / x &lt / 1). The downward band gap bowing seems the largest in InNxAs1&iexcl / x alloys among the alloys considered in this work. A metallic character of InNxAs1&iexcl / x, InNxSb1&iexcl / x and InAsxSb1&iexcl / x has been ob- tained in the present calculations for certain concentration range of constituents (N / As) as predicted in the literature. Even for a small amount of contents (x), a decrease of the electronic e&reg / ective mass around &iexcl / symmetry point appears for InNxAs1-x, InNxSb1-x and InAsxSb1-x alloys manifesting itself by an increase of the band curvature. The calculated cross over from indirect to direct band gap of ternary Al alloys has been found to be consistent with the measurements. As a last summary, the determinations of the band gaps of alloys as a function of contents, the concentration range of con- stituents leading to metallic character of the alloys, the change of the electronic effective mass around the Brillioun zone center (Gamma) as a function of alloy contents, the cross over from indirect to direct band gap of the alloys which are direct on one end, indirect on the other end, are main achievements in this work, indispensable for the development of mate- rials leading to new modern circuit components.

Knowledge of the dissociation constants of the ionizable protons of weak acids in aqueous media is of fundamental importance in many areas of chemistry and biochemistry. The pKa value, or equilibrium dissociation constant, of a molecule determines the relative concentration of its protonated and deprotonated forms at a specified pH and is therefore an important descriptor of its chemical reactivity. Considerable efforts have been devoted to the determination of pKa values by deferent experimental techniques. Although in most cases the determination of pKa values from experimental is straightforward, there are situations where interpretation is difficult and the results ambiguous. It is, therefore, not surprising that the capability to provide accurate estimates of the pKa value has been a central goal in theoretical chemistry and there has been a large effort in developing methodologies for predicting pKa values for a variety of chemical systems by differing quantum chemical techniques. A prediction accuracy within 0.5 pKa units of experiment is the desirable level of accuracy. This is a non-trivial exercise, for an error of 1 kcal/mol in estimates of the free energy value would result in an error of 0.74 pKa units. In this thesis ab initio Car-Parrinello molecular dynamics (CPMD) has been used for investigating the Brϕnsted acid-base chemistry of weak acids in aqueous solution. A key issue in any dissociation event is how the solvating water molecules arrange themselves spatially and dynamically around the neutral and dissociated acid molecule. Ab initio methods have the advantage that all solvent water molecules can, in principle, be con- sidered explicitly. One of the factors that has inhibited the widespread use of ab initio MD methods to study the dissociation reaction is that dissociation of weak acids are rare events that require extremely long simulation times before one is observed. The metady- namics formalism provides a solution to this conundrum by preventing the system from revisiting regions of configuration space where it has been in the past. The formalism allows the system to escape the free-energy minima by biasing the dynamics with a history dependent potential (or force) that acts on select degrees of freedom, referred to as collective variables. The bias potentials, modeled by repulsive inverted Gaussians that are dropped during propagation, drive the system out of any free-energy minima and allow it to explore the configuration space by a relatively quick and efficient sampling. The the- sis deals with a detailed investigation of the Brϕnsted acid-base chemistry of weak acids in aqueous solutions by the CPMD-metadynamics procedure. In Chapter 1, current approaches for the theoretical estimation of pKa values are summarized while in Chapter 2 the simulation methodology and the metadynamics sampling techniques used in thisstudy are described. The potential of the CPMD-metadynamics procedure to provide estimates of the acid dissociation constant (pKa) is explored in Chapter 3, using acetic acid as a test sys- tem. Using the bond-distance dependent coordination number of protons bound to the dissociating carboxylic groups as the collective variable, the free-energy profile for the dissociation reaction of acetic acid in water was computed. Convergence of the free-energy profiles and barriers for the simulations parameters is demonstrated. The free-energy profiles exhibit two distinct minima corresponding to the dissociated and neutral states of the acid and the deference in their values provides the estimate for pKa. The estimated value of pKa for acetic acid from the simulations, 4.80, is in good agreement with the experiment at value of 4.76. It is shown that the good agreement with experiment is a consequence of the cancellation of errors, as the pKa values are computed as the difference in the free energy values at the minima corresponding to the neutral and dissociated state. The chapter further explores the critical factors required for obtaining accurate estimates of the pKa values by the CPMD-metadynamics procedure. It is shown that having water molecules sufficient to complete three hydration shells as well as maintaining water density in the simulation cell as close to unity is important. In Chapter 4, the CPMD-metadynamics procedure described in Chapter-3 has been used to investigate the dissociation of a series of weak organic acids in aqueous solutions. The acids studied were chosen to highlight some of the major factors that influence the dissociation constant. These include the influence of the inductive effect, the stabilization of the dissociated anion by H-bonding as well as the presence of multiple ionizable groups. The acids investigated were aliphatic carboxylic acids, chlorine-substituted carboxylic acids, cid and trans-butenedioic, the isomers of hydroxybenzoic acid and phthalic acids and its isomers. It was found that in each of these examples the CPMD-metadynamics procedure correctly estimates the pKa values, indicating that the formulism is capable of capturing these influences and equally importantly indicating that the cancellation of errors is indeed universal. Further, it is shown that the procedure can provide accurate estimates of the successive pKa values of polypro tic acids as well as the subtle deference in their values for deterrent isomers of the acid molecule. Changes in protonation-deprotonation of amino acid residues in proteins play a key role in many biological processes and pathways. It is shown that CPMD simulations in conjunction with metadynamics calculations of the free energy profile of the protonation- deprotonation reaction can provide estimates of the multiple pKa values of the 20 canonical α-amino acids in aqueous solutions in good agreement with experiment (Chapter 5). The distance-dependent coordination number of the protons bound to the hydroxyl oxygen of the carboxylic and the amine groups is used as the collective variable to explore the free energy profiles of the Brϕnsted acid-base chemistry of amino acids in aqueous solutions. Water molecules, sufficient to complete three hydration shells surrounding the acid molecule were included explicitly in the computation procedure. The method works equally well for amino acids with neutral, acidic and basic side chains and provides estimates of the multiple pKa values with a mean relative error with respect to experimental results, of 0.2 pKa units. The tripeptide Glutathione (GSH) is one of the most abundant peptides and the major repository for non-protein sulfur in both animal and plant cells. It plays a critical role in intracellular oxidative stress management by the reversible formation of glutathione disulfide with the thioldisulfide pair acting as a redox buffer. The state of charge of the ionizable groups of GSH can influences the redox couple and hence the pKa value of the cysteine residue of GSH is critical to its functioning. In Chapter 6, it has been reported that ab initio Car-Parrinello Molecular Dynamics simulations of glutathione solvated by 200 water molecules, all of which are considered in the simulation. It is shown that the free-energy landscape for the protonation - deprotonation reaction of the cysteine residue of GSH computed using metadynamics sampling provides accurate estimates of the pKa and correctly predicts the shift in the dissociation constant values as compared to the isolated cysteine amino acid. The dissociation constants of weak acids are commonly determined from pH-titration curves. For simple acids the determination of the pKa from the titration curves using the Henderson-Hasselbalch equation is relatively straightforward. There are situations, however, especially in polypro tic acids with closely spaced dissociation constants, where titration curves do not exhibit clear inflexion and equivalence stages and consequently the estimation of multiple pKa values from a single titration curve is no longer straightfor- ward resulting in uncertainties in the determined pKa values. In Chapter 7, the multiple dissociation constant of the hexapeptide glutathione disulfide (GSSG) with six ionizable groups and six associated dissociation constants has been investigated. The six pKa values of GSSG were estimated using the CPMD-metadynamics procedure from the free-energy profiles for each dissociation reaction computed using the appropriate collective variable. The six pKa values of GSSG were estimated and the theoretical pH-titration curve was then compared with the experimentally measured pH-titration curve and found to be in excellent agreement. The object of the exercise was to establish whether interpretation of pH-titration curves of complex molecules with multiple ionizable groups could be facilitated using results of ab initio molecular dynamics simulations.