Three key enhancements were made to a semiempirical molecular orbital program to develop a fast, accurate method of calculating chemical properties of large (> 1000 atom) molecular systems, through the use of quantum theory. In this thesis the key enhancements are presented which are: the implementation of a divide-and-conquer approach to a self-consistent field procedure, in an effort to improve capability; the use of the novel technology, GPU technology, to parallelize the divide-and-conquer self-consistent field procedure, in an effort to improve the speed; the implementation of a newly developed semiempirical model, the Polarized Molecular Orbital Model, in an effort to improve the accuracy. The development of a divide-and-conquer approach to the SCF (DC-SCF) procedure (enhancement 1) was carried out using saturated hydrocarbon chains whereby the saturated hydrocarbon chain is partitioned into small overlapping subsystems and the Roothaan equations solved for each subsystem. An investigation was carried out to find the optimal partitioning scheme for saturated hydrocarbon chains in order to minimize the loss of energy experienced from neglecting some of the interactions in the system whilst maintaining near linear scaling with system size. The DC-SCF procedure was shown to be accurate to 10-3 kcal mol-1 per atom whilst calculating the SCF-energy nearly 6 times faster than using the standard SCF procedure, for a 698-atom system. The development of a parallel DC-SCF procedure and Cartesian forces calculation for use on a GPU (enhancement 2), resulted in a hybrid CPU/GPU DC-SCF implementation that calculated the energy of a 1997-atom saturated hydrocarbon chain 21 times faster than the standard serial SCF implementation and a accelerated Cartesian forces calculation that performed 7 times faster for a saturated hydrocarbon chain of 1205-atoms, when accelerated using an NVidia Tesla C2050 GPU. The hybrid CPU/GPU algorithm made use of commercially accelerated linear algebra libraries, CULA and CUBLAS. A comparison was made between CULA’s accelerated eigensolver routine and the accelerated DC-eigensolver (developed in this research) and it was found that for saturated hydrocarbon chains of > 350 atoms, the accelerated DC-eigensolver performed around twice as fast as the accelerated CULA eigensolver. The implementation of the Polarized Molecular Orbital model (enhancement 3) was validated against published isomerization energies and benchmarked against the non-nitrogen containing complexes in the S66 database. The benchmark complexes were categorized according to dominant intermolecular interactions namely, hydrogen bonding, dispersion interactions and mixed interactions. After assessment it was found that the PMO model predicts interaction energies of complexes with a mixture of dispersive and electrostatic interactions to the highest accuracy (0.69 kcal mol-1 with respect to CCSD(T)/CBS). The dispersion correction within the PMO model was found to ‘overcorrect’ the dispersive contribution for most complexes tested. The outcome of this research is a semiempirical molecular orbital program that calculates the energy of a closed-shell saturated hydrocarbon chain of ~2000 atoms in under 4 minutes instead of 1.5 hours when using a PM3-Hamiltonian and can calculate interaction energies of systems exhibiting a mixture of electrostatic and dispersive interactions to an accuracy of within 1 kcal mol-1 (relative to high-level quantum methods). To demonstrate a suitable application for the enhanced SE-MO program, interaction energies of a series of PAHs with water, phenol and methanol have been investigated. The resultant program is suitable for use in calculating the energy and forces of large material and (in future) biological systems by a fast and accurate method that would be impractical or impossible to do without these enhancements.

La réduction de taille réalisée dans les hétérostructures mène à des états électroniques, fondamental et excité, largement différents de ceux du cristal en volume, et a ouvert la voie à une nouvelle génération de dispositifs optoélectroniques et photonique. Les super-réseaux diélectriques sont par exemple développés pour leurs propriétés non linéaires. Ces effets sont également trouvés dans des hétérostructures de semi-conducteur basées sur GaAs, qui a par lui-même les propriétés optiques non linéaires importantes. Dans la recherche de nouvelles sources optiques, l'anisotropie optique des super-réseaux de GaAs/AlAs-oxidé a été exploitée pour produire la conversion des fréquences optiques. Les super-réseaux de type GaAs/AlAs constituent donc un prototype pour la compréhension des structures artificielles, et leurs propriétés optiques ont été à fond étudiées expérimentalement et théoriquement. En particulier, la réduction de la symétrie cubique initiale de la structure diamant ou zinc-blende provoque une anisotropie optique. Le comportement des composents du tenseur diélectrique du super-réseaux GaAs/AlAs en fonction de la période de barrière/puits est une question qui suscite un très grand intérêt. Expérimentalement, on a observé une baisse remarquable de la biréfringence quand la période décroît. Pour étudier la réponse optique de ces systèmes, les détails de la structure électronique doivent être pris en considération, y compris des effets comme le repliement des bandes et le confinement. Une analyse simple en termes de particules indépendantes est insuffisante: les effets à plusieurs corps peuvent jouer un rôle crucial et tendent à être particulièrement importants quand l'échelle du système est réduite. Les calculs utilisant des pseudopotentiels semi-empiriques sur de super-réseaux de grande période ont récemment fourni une analyse détaillée des effets du repliement des bandes et du confinement. Néanmoins, il n'y avait aucun accord quantitatif avec l'expérience au sujet de la biréfringence statique, et ces calculs n'ont pas pu expliquer l'augmentation de cette quantité avec l'augmentation de la période du super-réseau même qualitativement. Aussi, nous avons calculé la biréfringence statique de super-réseaux (001) (GaAs)$_n$/(AlAs)$_n$ pour une période de barrière/puits variant de n=1 à n=8, en utilisant la théorie de la fonctionnelle de densité dépendante du temps (TDDFT). Nous confirmons les résultats des calculs semi-empiriques précédents basés sur un calcul à particules indépendantes, en exécutant des calculs ab initio dans la même approximation. Cependant, nous montrons que l'inclusion des effets de champs locaux change complètement les composants du tenseur diélectrique: la biréfringence théorique en maintenant en bon accord avec l'expérience. En fait, on obtient l'accord qualitatif, et quantitatif avec l'expérience, en incluant les effets de champs locaux. On montre en particulier que l'anisotropie des champs locaux explique les tendances expérimentales observées. Étonnamment, l'utilisation de l'approche de milieu effectif, ou le super-réseau est modelisé par un empilement de couches ayant la permittivité GaAs ou AlAs, est justifiée dans la direction d'empilement même pour les petites périodes, car les effets de champs locaux et de confinement s'annulent. Par contraste, les effets de confinement sont trouvés plus grands dans le plan perpediculaire à la direction d'empilement, et la théorie de milieu effectif est insuffisante.

Anxiolytics, sedative-hypnotics and antipsychotics are drugs with similar chemical structures (nitrogenous heterocycles) and the Benzodiazepines (BZDs) are part of this group. Discovering by “luck”, his class of drugs, the BZDs, presents mostly anxiolytic and hypnotic actions, and is the class of drugs most consumed worldwide. In this dissertation, quantum molecular modeling techniques were used, seeking to understand the behavior of these drugs, since they have similar chemical structure. The method of calculation used was semiempirical PM6 (Sixth parameterization) and 26 compounds were analyzed. Changes in the values of the electrostatic charges of the atoms that contribute to the formation of the HOMO orbital were calculated, with the compounds in the ground state and without 1 electron (oxidation reaction), seeking indicate activity/oxidation sites and were also generated maps of molecular electrostatic potential, maps of the HOMO orbital and some electronic properties of benzodiazepines were also calculated. Knowing that benzodiazepines are metabolized in the liver, initially suffering oxidation reactions, it was possible with the calculations, analyze the substituent effect on its activity and show that this oxidation reaction occurs at the benzodiazepine ring. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Ansiolíticos, sedativo-hipnóticos e antipsicóticos são fármacos que apresentam estruturas químicas semelhantes (heterociclos nitrogenados) e os Benzodiazepínicos (BZDs) participam deste grupo. Descoberta ao “acaso”, essa classe de fármacos, os BZDs, apresenta, em sua maioria, ação ansiolítica e hipnótica, sendo a classe de medicamentos mais consumida mundialmente. Nesta dissertação foram utilizadas técnicas de modelagem molecular quântica, buscando entender o comportamento desses fármacos, já que apresentam estrutura química semelhante. O método de cálculo utilizado foi o Semiempírico PM6 (Sexta Parametrização) e 26 compostos foram analisados. Variações nos valores das cargas eletrostáticas dos átomos que contribuem para a formação do orbital HOMO foram calculados, com os compostos no estado fundamental e retirando-se 1 elétron (reação de oxidação), buscando indicar sítios de atividade/oxidação, bem como também foram gerados os mapas de potencial eletrostático molecular, mapa do orbital HOMO e algumas propriedades eletrônicas dos BZDs também foram calculadas. Sabendo-se que as benzodiazepinas são metabolizadas no fígado, sofrendo inicialmente reações de oxidação, foi possível com os cálculos, analisar o efeito do substituinte na sua atividade e mostrar que esta reação de oxidação ocorre no anel benzodiazepínico.

The reparametization of semiempirical Hamiltonians is an emerging method used in direct dynamics studies. The use of semiempirical Hamiltonians in direct dynamics studies diminishes the computational cost of trajectory calculations and negates the need for an analytical potential energy surface when performing reaction dynamics studies. The reparametization of semiempirical Hamiltonians increases the agreement with experiment and high level ab initio theory. We have chosen to create one set of new parameters that apply to two related reactions, F + CH₄ → HF + CH₃ and F + C₂H₆ → HF + C₂H₅. We have performed an electronic structure study for these reactions. The ab initio data obtained from the electronic structure study is then used as the reference for a reparametization of the PM3 Hamiltonian. The reparametization has improved the ab initio and PM3 reaction energy and potential energy surface scan agreement. This new set of parameters for PM3 (SRP-PM3) is used to perform a direct quasiclassical trajectory study of the reactions. The vibrational and rotational HF distributions calculated using SRP-PM3 are compared with experiments. We have observed an improvement in the agreement with experimental vibrational distributions but have seen no change in the rotational distributions. / Master of Science

ealizaram-se cálculos ab initio e semi-empíricos em 5-hidrotriptofano (5-OH-trp), 7-aza-triptofano (7-aza-trp) e triptofano (trp), determinando as superfícies de energia potencial (SEP) do estado fundamental (EF) e do primeiro estado excitado (1EE), em função dos ângulos X IND. 1 e X IND. 2, medidos nos diedros N-C IND.alfa-C IND.beta-C IND.gama e C IND.alfa-C IND.beta-C IND.gama- C IND.delta2, respectivamente. Esses compostos foram estudados nos estados de protonação zwitteriônico, neutro e aniônico. A SEP do EF na forma zwitteriônica fo obtida pelo método semi-empírico AM1 e utilizada como referência para os cálculos ab initio. Os cálculos de 1EE foram feitos utilizando o método de Interação de Configurações com excitações simples (ICS) e orbitais internos congelados. As energias de transição entre o EF e o 1EE após as otimizações foram obtidas pelo método semi-empírico INDO/S-CIS, permitindo a obtenção dos espectros teóricos de absorção ótica, pelas energias de transição das geometrias otimizadas no EF, e de fluorescência de estado estacionário, pelas energias de transição das geometrias otimizadas no 1EE. Medidas experimentais dos espectros de absorção ótica e de fluorescência de estado estacionário e resolvida no tempo foram realizadas com o 5-OH-trp e o 7-aza-trp em solução tampão fosfato, pH 7,4. Os decaimentos fluorescentes ajustados a mais de uma exponencial foram estudados em termos das populações relativas de Boltzmann nos EF e 1EE. As taxas do decaimento não-radiativo de transferência de elétrons no 1EE foram obtidas pela implementação computacional da Teoria de Marcus e do Método da Expansão de Perturbação Renormalizada (EPR). Além disso, otimizações de estruturas de estados de transição (ET) na SEP dos 1EE foram realizadas pelo Método Sunchronous Transiti-Guided Quasi-Newton e pelo algoritmo de Berny modificado. Para aproximar as condições experimentais, foram ) realizadas simulações por dinâmica molecular (DM) usando o método híbrido QM/MM no EF do 5-OH-trp na forma zwitteriônica, na presença do solvente aquoso representado explicitamente. Os resultados obtidos dos cálculos ab initio foram usados como referência para o início dessas simulações. As conformações visitadas no EF, os espectros teóricos de absorção ótica e as camadas de solvatação do solvente aquoso em torno do reagente são discutidas. / Semi-empirical and ab-initio calculations were performed on 5-hydroxytryptophan (5-OH-trp), 7-aza-tryptophan (7-aza-trp) and tryptophan (trp). The potential energy surface (PES) of the ground state (GS) and the lowest exited state (1ES) was determined as a function X IND. 1 e X IND. 2 angles corresponding to the dihedrals N-C IND.alfa-C IND.beta-C IND.gama e C IND.alfa-C IND.beta-C IND.gama- C IND.delta2, respectively. The compounds were studied in the zwitterionic, neutral and anionic states. The PES of the GS was obtained using the AM1 semi-empirical method and was used as a reference for the ab-initio calculations. The configuration interaction method with single excitations (CIS) was used for the calculations of the 1ES with frozen internal orbitals. After geometry optimization of GS, the transition energies to 1ES were obtained by INDO/S-CIS, giving the theoretical optical absorption spectrum. Similarly, following the geometry optimization of 1ES, the transition energies to GS were determined, giving the fluorescence emission spectrum. Experimental results were obtained for optical absorption and fluorescence spectra of 5-OH-trp and 7-aza-trp in phosphate buffer solution, pH 7.4. The fluorescence decay of the compounds was also examined. Decay profiles fitted to multiexponential function were analyzed in terms of Boltzmann relative populations in the GS and 1ES. The non-radioactive electron transfer rates in the excited state were obtained by computational implementation of the Marcus Theory with renormalized perturbation expansion method (RPE). In this study, optimizations of the transition states in the PES of the ground and lower excited states were performed by the Synchronous Transit-Guided Quasi-Newton method and the Berny algorithm modified. For further comparison with experimental conditions, molecular dynamic simulations for the zwitterionic 5-OH-trp were performed using the hybrid QM/MM method with explicit representation of the aqueous solvent. To start the simulations the results from ab-initio calculations were used. The conformations for the GS, the theoretical absorption spectrum and the solvation layers were compared to the experimental results

Dans un superréseau, le confinement modifie les états électroniques et la réduction de symétrie produit une forte anisotropie des propriétés optiques. Dans les super-réseaux GaAs/AlAs cette anisotropie, avec en plus les effets non-linéaires dans les propriétés optiques de GaAs, est un élément essentiel pour la réalisation des convertisseurs de fréquence. Dans mon travail de thèse, j'ai étudié le tenseur diélectrique statique et les spectres d'absorption des superréseaux (GaAs)p/(AlAs)p en fonction de leur période p. Le calcul de ces quantités a été commencé à l'aide de techniques semi-empiriques à l'Université de Pavia, sous la direction du Prof. L.C. Andreani. En particulier, J'ai développé un code pour appliquer la méthode «linear combination of bulk bands» au calcul des structures de bande et des fonctions diélectriques des héterostructures (superréseaux et nanofils). Dans la suite j'ai passé 12 mois au LSI sous la direction du Dr. Lucia Reining, pour réaliser des calculs ab-initio dans le cadre de la théorie de la fonctionnelle de la densité dépendante du temps. Nous avons réussi à bien décrire l'effet du confinement sur les spectres. L'anisotropie de la réponse diélectrique, mesurée par la biréfringence, est déterminée par les contributions du confinement et des champs locaux cristallins : si on tient compte des deux effets, on peut reproduire les données expérimentales. Les ultérieurs effets à N-corps ne donnent que des corrections quantitatives. La comparaison entre les résultats des calculs ab-initio et semi-empiriques, ainsi qu'avec les données de l'expérience, nous a permis de détecter les mécanismes physiques essentiels qui contribuent à l'anisotropie des propriétés optiques et, de plus, de déterminer les limites de validité de la méthode semi-empirique et de l'approche classique des milieux effectifs.

The theoretical part of the Master´s thesis describes ab initio methods in quantum chemistry and semiempirical methods, which represents a way in overcoming of main disadvantages in ab initio methods (costs, speed). The experimental part was focused on comparison highly accurate CCSD(T) method with used semiempirical methods (AM1, PM3, PM6, and PM7). The data were mostly compared on small model systems with ions, which are an essential part of many biological systems. Furthermore, the applicability of semiempirical methods was examined for the description of intra- and intermolecular hydrogen bonds and van der Waals interactions.

ealizaram-se cálculos ab initio e semi-empíricos em 5-hidrotriptofano (5-OH-trp), 7-aza-triptofano (7-aza-trp) e triptofano (trp), determinando as superfícies de energia potencial (SEP) do estado fundamental (EF) e do primeiro estado excitado (1EE), em função dos ângulos X IND. 1 e X IND. 2, medidos nos diedros N-C IND.alfa-C IND.beta-C IND.gama e C IND.alfa-C IND.beta-C IND.gama- C IND.delta2, respectivamente. Esses compostos foram estudados nos estados de protonação zwitteriônico, neutro e aniônico. A SEP do EF na forma zwitteriônica fo obtida pelo método semi-empírico AM1 e utilizada como referência para os cálculos ab initio. Os cálculos de 1EE foram feitos utilizando o método de Interação de Configurações com excitações simples (ICS) e orbitais internos congelados. As energias de transição entre o EF e o 1EE após as otimizações foram obtidas pelo método semi-empírico INDO/S-CIS, permitindo a obtenção dos espectros teóricos de absorção ótica, pelas energias de transição das geometrias otimizadas no EF, e de fluorescência de estado estacionário, pelas energias de transição das geometrias otimizadas no 1EE. Medidas experimentais dos espectros de absorção ótica e de fluorescência de estado estacionário e resolvida no tempo foram realizadas com o 5-OH-trp e o 7-aza-trp em solução tampão fosfato, pH 7,4. Os decaimentos fluorescentes ajustados a mais de uma exponencial foram estudados em termos das populações relativas de Boltzmann nos EF e 1EE. As taxas do decaimento não-radiativo de transferência de elétrons no 1EE foram obtidas pela implementação computacional da Teoria de Marcus e do Método da Expansão de Perturbação Renormalizada (EPR). Além disso, otimizações de estruturas de estados de transição (ET) na SEP dos 1EE foram realizadas pelo Método Sunchronous Transiti-Guided Quasi-Newton e pelo algoritmo de Berny modificado. Para aproximar as condições experimentais, foram ) realizadas simulações por dinâmica molecular (DM) usando o método híbrido QM/MM no EF do 5-OH-trp na forma zwitteriônica, na presença do solvente aquoso representado explicitamente. Os resultados obtidos dos cálculos ab initio foram usados como referência para o início dessas simulações. As conformações visitadas no EF, os espectros teóricos de absorção ótica e as camadas de solvatação do solvente aquoso em torno do reagente são discutidas. / Semi-empirical and ab-initio calculations were performed on 5-hydroxytryptophan (5-OH-trp), 7-aza-tryptophan (7-aza-trp) and tryptophan (trp). The potential energy surface (PES) of the ground state (GS) and the lowest exited state (1ES) was determined as a function X IND. 1 e X IND. 2 angles corresponding to the dihedrals N-C IND.alfa-C IND.beta-C IND.gama e C IND.alfa-C IND.beta-C IND.gama- C IND.delta2, respectively. The compounds were studied in the zwitterionic, neutral and anionic states. The PES of the GS was obtained using the AM1 semi-empirical method and was used as a reference for the ab-initio calculations. The configuration interaction method with single excitations (CIS) was used for the calculations of the 1ES with frozen internal orbitals. After geometry optimization of GS, the transition energies to 1ES were obtained by INDO/S-CIS, giving the theoretical optical absorption spectrum. Similarly, following the geometry optimization of 1ES, the transition energies to GS were determined, giving the fluorescence emission spectrum. Experimental results were obtained for optical absorption and fluorescence spectra of 5-OH-trp and 7-aza-trp in phosphate buffer solution, pH 7.4. The fluorescence decay of the compounds was also examined. Decay profiles fitted to multiexponential function were analyzed in terms of Boltzmann relative populations in the GS and 1ES. The non-radioactive electron transfer rates in the excited state were obtained by computational implementation of the Marcus Theory with renormalized perturbation expansion method (RPE). In this study, optimizations of the transition states in the PES of the ground and lower excited states were performed by the Synchronous Transit-Guided Quasi-Newton method and the Berny algorithm modified. For further comparison with experimental conditions, molecular dynamic simulations for the zwitterionic 5-OH-trp were performed using the hybrid QM/MM method with explicit representation of the aqueous solvent. To start the simulations the results from ab-initio calculations were used. The conformations for the GS, the theoretical absorption spectrum and the solvation layers were compared to the experimental results

Computational methods have been extensively developed at various levels of approximation in recent years to model biomolecular interactions and for rational drug design. This research work aims to explore the feasibility of using quantum mechanical (QM) methods within the two broad categories of in silico ligand-based and structure-based drug design. First, density functional theory at the M06L level of theory was employed to examine structure-activity relationships of boron-based heterocyclic compounds, anti-inflammatory inhibitors targetting the interleukin-1β (IL-1β) cytokine. Our findings from computed energies and shapes of the molecular orbitals provide understanding of electronic effects associated with the inhibitory activity. We also found that the boron atom, specifically its electrostatic polarity, appears to be essential for the anti-IL-1β activity as evidenced by the biological assay of non-boron analogues selected from the ligand-based virtual screening results. Secondly, we aimed to dock ligands at the active sites of zinc-containing metalloproteins with reasonable computational cost and with accuracy. Therefore, an in-house docking scheme based on a Monte Carlo sampling algorithm using the semiempirical PM6/AMBER force field scoring function was compiled for the first time within the Gaussian 09 program. It was applied to four test cases, docking to cytidine deaminase and human carbonic anhydrase II proteins. The docking results show the method’s promise in resolving false-positive docking poses and improving the predicted binding modes over a conventional docking scheme. Finally, semiempirical QM methods which include dispersion and hydrogen-bond corrections were assessed for modelling conformations of β-cyclodextrin (βCD) and their adsorption on graphene. The closed in vacuo βCD cccw conformer was found to be in the lowest energy, in good agreement with previous ab initio QM studies. DFTB3, PM6-DH2 and PM7 methods were applied to model the intermolecular interactions of large βCD/graphene complexes, over a thousand atoms in size. We found that the binding preference of βCD on graphene is in a closed conformation via its C2C3 rim, agreeing with reported experimental and computational findings.

Optimization of Semiempirical Quantum Mechanical Methods for in Silico Drug Design Doctoral thesis Kristian Kříž The subject of this thesis is the optimization of semiempirical quantum mechanical methods (SQM) for their use in in silico drug design. The thesis covers two topics - COSMO2 solvation model optimization part and PLF547, PLA15 dataset development part. The first part is devoted to the optimization of COSMO solvation model by addition of a nonpolar term and reparametrization of the model for SQM methods PM6 and PM7. We have shown that the accuracy of the resulting "COSMO2" optimized model improved on all the tested datasets and we have compared it to other selected SQM solvation models. The method has also been tested on the protein ligand complexes as a part of a scoring function, where it provides better preditction of binding affinity of drug candidates for their target protein. The second part of the thesis describes the construction of datasets for noncovalent interactions aimed speicificly to represent an environment of an enyzme active site complexed with a ligand with reliable benchmark values of interaction energies in vacuum and solvent (water). The developed PLF547 and PLA15 datasets are suitable for testing and development of methods for the use in drug design. We have...