| Due to its moderate computational consume and high precision, the first-principles calculation based on the density functional theory (DFT) has become one of the most important methods in the condensed matter physics, quantum chemistry, material science and so on, which can be applied to study the geometry, electronic structure and many other properties of small molecules to get more and accurate information. Aspirin has been widely used to treat inflammatory conditions and was subjected to a series of experimental and theoretical studies to determine whether it exhibits polymorphism for the development of pharmaceutical ingredients. As one of the type of polymorphism, many researches have been done on conformational isomerism due to its universality and importance.In the second chapter, we introduce the basic concept of DFT. Theorem of Hohenberg-Kohn is the fundament of DFT and is developed to Kohn-Sham equation, which can be used to perform real calculations with developed exchange-correlation functionals. At the end of this chapter, we introduce the main functions of Gaussian09package, and pay more attention to the basis set, identification and treatment of internal rotation in normal mode vibrational analysis and thermodynamics in Gaussian09.In the third chapter, we first constructed the initial geometry of the aspirin formI molecule, and then used the B3LYP exchange functional with6-311++G(2d,2p) basis set for the geometry optimizations. The molecular structure and calculated vibrational spectra of the optimized structure2a agree with the experimental results remarkably well, so as to prove the computational method we used can give reliable results. All conformers were searched out with using2a as the starting structure considering all the internal rotation modes and optimized by the methord B3LYP/6-311++G(2d,2p). Eleven optimized conformers of aspirin molecule are identified as stable structures and conformer1a has the lowest electronic energy followed by its rotamer2a with slightly higher energy of0.038eV at temperature of0K. Conformer7b has the highest energy which is about0.59eV above that of the conformer1a. All conformers of aspirin are tending to get an electron, because all the values of the electron affinity are positive. The electron affinity for conformer7b is the highest up to0.838eV, namely, the conformer7b is a better electron acceptor compared to the other conformers. On the contrary, conformer5a has the lowest electron affinity of0.324eV and the highest ionization potential of9.040eV stating that this conformer has stable chemical property. Compare to the previous DFT study on the conformers of aspirin molecule, we proceeded with the higher level of the first-principles calculation, and not only detect a new conformer6a to the literature, but also get the different energy ordering of conformers3a and2b and the lower relative energy between conformers. To better understand the reaction mechanism between conformers, we investigated the structures of transition state and the reaction paths followed by integrating the intrinsic reaction coordinate. Fifteen reaction paths have been identified to ensure the conformer1a having the lowest total electronic energy can transform to the any one of the other ten conformers. Furthermore, we computed the Gibbs free energies of activation and rates of reaction (i.e. the energy barrier of reaction), in which considering the effect of internal rotation in normal mode vibrational analysis. The relative energy barrier ordering means the rotation of the carboxyl group COOH is easier and the rotation of the acetyl group CH3CO is harder. All the conformers can coexist at room temperature since the energy barriers of the fifteen reactions between conformers are all lower than20kcal/mol.In the forth chapter, according to the relative energy ordering of aspirin conformers at temperature of0K, conformer1a should be the molecular structure of aspirin form I owing to its total electronic energy lower than2a, however,2a is observed experimentally. In order to explain the contradiction as well as an apparent elongation of the O-H covalent bond in the carboxylic acid hydrogen bonds (HB) dimer in aspirin as a function of temperature illustrated by Wilson, we choose the carboxylic acid HB dimer to study. We first modeled the initial geometry of the carboxylic acid HB dimer of aspirin forml, and then used the methord B3LYP/6-311++G(2d,2p) for the geometry optimizations to get the dimer2a’2a and the other stable nineteen conformational dimers of the dimer2a’2a. For more accurate energy calculations, the twenty optimized conformational dimers were optimized again by the method CAM-B3LYP/6-311++G(2d,2p) taking long range interaction into account. The geometries of the twenty dimers optimized by the two methods appear not to be distinguish from each other and the dimer having the lowest total electronic energy is always1a’1a, but the value of relative energy between dimers becomes larger. Next, the Gibbs free energies and Boltzmann factors of dimers1a’1a and2a’2a were calculated at thirty-two temperatures between2and700K. The result shows that if consider the effect of internal rotation in normal mode vibrational analysis, at the temperature of280K1a’1a can transform to2a’2a on the consequence of the Gibbs free energy of2a’2a being lower than1a’1a, which gives an explanation for the contradiction mentioned above. Otherwise, until the temperature of500K, the Gibbs free energy of2a’2a won’t be lower than1a’1a, which indicates the importance of identification and treatment of the internal rotation in normal mode vibrational analysis for thermodynamics. The O-H covalent bond in the carboxyl group of dimer1a’1a seems to be elongated contrasted with the dimer2a’2a, which make us seek an alternative explanation in terms of the relative occupancies of the dimer2a’2a and1a’1a calculated by the ratio of their Boltzmann factors for the phenomenon observed by Wilson. Above the temperature of180K, our computational results consistent with the experimental data very well, but below the temperature of100K, a significant occupancy of dimer1a’1a would be expected in our calculation, but with little evidence of it in experiment. Furthermore, we attempted to explain this inconsistent by the quantum tunnelling effect and the transition state theory. In the end, in order to analyze the relative strengths of hydrogen bonding in the aspirin conformational dimers, we started by repeating YURTSEVER’s study with the same method B3LYP/6-31G(d) and a higher precision method B3LYP/6-311++G(2d,2p), which make the aspirin conformers1a’,2a,2a’,4a’,2b’and4b held together in dimers by the different hydrogen bonding linkage. Within the obtained results, the geometries and bond lengths of hydrogen bonding appear very similar by the two methods, and the pronounced differences between them are the relative binding energy ordering of dimer C and D and the failure of optimizing the dimer A by the method B3LYP/6-311++G(2d,2p).In the final chapter, we make a conclusion for this thesis, and make a plan for the following work. |
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