<p>This thesis is part of an effort to enable large-scale Hartree-Fock/Kohn-Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. This method involves two computationally intensive steps. These steps are the construction of the Fock/Kohn-Sham potential matrix from a given electron density and the subsequent update of the electron density usually represented by the so-called density matrix. In this thesis the focus lies on the representation of potentials and electron density and on the density matrix construction step in the SCF method. Traditionally a diagonalization has been used for the construction of the density matrix. This diagonalization method is, however, not appropriate for large systems since the time complexity for this operation is σ(n³). Three types of alternative methods are described in this thesis; energy minimization, Chebyshev expansion, and density matrix purification. The efficiency of these methods relies on fast matrix-matrix multiplication. Since the occurring matrices become sparse when the separation between atoms exceeds some value, the matrix-matrix multiplication can be performed with complexity σ(n).</p><p>A hierarchic sparse matrix data structure is proposed for the storage and manipulation of matrices. This data structure allows for easy development and implementation of algebraic matrix operations, particularly needed for the density matrix construction, but also for other parts of the SCF calculation. The thesis addresses also truncation of small elements to enforce sparsity, permutation and blocking of matrices, and furthermore calculation of the HOMO-LUMO gap and a few surrounding eigenpairs when density matrix purification is used instead of the traditional diagonalization method.</p>

<p>In this thesis I have theoretically studied electron recombination processes with small molecular ions.</p><p>In these kind of processes resonant states are involved. To calculate the potential energy for these states as a function of internuclear distance, structure calculations and scattering calculations have to be performed.</p><p>So far I have been studying the ion-pair formation with in electron recombination with H₃⁺. The cross section for this process has been calculated using different kind of models, both a time dependent quantum mechanical and a semiclassical.</p><p>I have also studied the direct process of dissociative recombination of HF⁺. To calculate the total cross section for this process, we have performed wave packet propagation on thirty resonant states and summed up the individual cross sections for these states.</p><p>The cross sections for both these processes have a similar appearance to those measured experimentally in the ion storage ring CRYRING in Stockholm.</p>

Recent research has shown that small hydrogen bonding catalysts can catalyze the hetero Diels-Alder reaction. In this thesis such hydrogen bonding catalysts in conjunction with varying functional groups and their effect on the hetero Diels-Alder reaction have been investigated. The influence of the different solvents has been investigated as well. The activation barriers for the different region- and stereo isomeric pathways have been compared in order to determine the stereo specificity of the reactions. These calculations have been done using the B3LYP functional for the geometry optimizations and then M06-2X for single point calculations. For the solvated cases the cPCM model and the M06-2X functional were used. It was shown that for the catalyzed systems bulkier groups in the endo position tend to have a lower activation barrier, allowing for control over the stereoselectivity. Electron withdrawing groups have an activating effect and are also synergistic with the hydrogen bonding catalysts. The solvent with the lowest dielectric constant gave the lowest activation barrier.

In this study, quantum chemical methods have been used to study two isomers of the proposed high energy density material N8. It has been suggested as a green substitute for conventional solid rocket fuel. Several techniques were used to study the barrier height towards decomposition along reaction path of four N8 isomers. The potential energy surfaces around the transition states of two of the isomers were further investigated. Results show that the bond length of the isomers may have been overestimated, and one of the isomers has a lower barrier and may have a more complicated reaction route. Furthermore, there is a rather large difference in barrier height between calculations at the CCSD and CCSD(T) levels of theory / I den här studien har kvantkemiska beräkningsmetoder använts för att studera två isomerer av N8. På grund av sitt höga energiinnehåll har N8 föreslagits som ett grönt alternativ till konventionellt fast racketbränsle. Flera tekniker har använts för att studera barriären för nedbrytning utefter reaktionskoordinaten för fyra N8-isomerer. Potentialytan runt aktiveringstillståndet för två av isomererna studerades närmare. Resultaten visar att bindningslängden hos isomererna kan ha överskattats och en av isomererna har en lägre barriär samt kan ha en mer komplicerad reaktionsväg. Vidare är det en tämligen stor skillnad i aktiveringsenergi mellan CCSD- och CCSD(T)- nivåerna.

In this thesis I have theoretically studied electron recombination processes with small molecular ions. In these kind of processes resonant states are involved. To calculate the potential energy for these states as a function of internuclear distance, structure calculations and scattering calculations have to be performed. So far I have been studying the ion-pair formation with in electron recombination with H3+. The cross section for this process has been calculated using different kind of models, both a time dependent quantum mechanical and a semiclassical. I have also studied the direct process of dissociative recombination of HF+. To calculate the total cross section for this process, we have performed wave packet propagation on thirty resonant states and summed up the individual cross sections for these states. The cross sections for both these processes have a similar appearance to those measured experimentally in the ion storage ring CRYRING in Stockholm. / QC 20101103

This thesis is part of an effort to enable large-scale Hartree-Fock/Kohn-Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. This method involves two computationally intensive steps. These steps are the construction of the Fock/Kohn-Sham potential matrix from a given electron density and the subsequent update of the electron density usually represented by the so-called density matrix. In this thesis the focus lies on the representation of potentials and electron density and on the density matrix construction step in the SCF method. Traditionally a diagonalization has been used for the construction of the density matrix. This diagonalization method is, however, not appropriate for large systems since the time complexity for this operation is σ(n3). Three types of alternative methods are described in this thesis; energy minimization, Chebyshev expansion, and density matrix purification. The efficiency of these methods relies on fast matrix-matrix multiplication. Since the occurring matrices become sparse when the separation between atoms exceeds some value, the matrix-matrix multiplication can be performed with complexity σ(n). A hierarchic sparse matrix data structure is proposed for the storage and manipulation of matrices. This data structure allows for easy development and implementation of algebraic matrix operations, particularly needed for the density matrix construction, but also for other parts of the SCF calculation. The thesis addresses also truncation of small elements to enforce sparsity, permutation and blocking of matrices, and furthermore calculation of the HOMO-LUMO gap and a few surrounding eigenpairs when density matrix purification is used instead of the traditional diagonalization method. / <p>QC 20101123</p>

Produktion av nya energetiska material är dyrt. Målet med detta arbete är att utveckla en metod som uppskattar Chapman-Jouget detonationstrycket och detonationshastigheten hos nya CHNO-sprängämnen. En sådan metod möjliggör valet att bara syntetisera och testa de mest lovande kandidaterna som nya energetiska material, därmed undviks resursslösande arbete. Den här metoden använder sig av density functional theory (DFT) och den elektrostatiska potentialen till att uppskatta bildningsentalpier och kristalldensiteter. Beräkningarna gjordes på traditionella sprängämnen och de beräknade detonationstrycken och detonatioshastigheterna visade bra överensstämmelse med experimentell data. Detonationstrycken hamnade inom ±10% och detonatioshastigheterna inom ±5% av experimentell data. / Producing new energetic materials is expensive. This work aims to develop a method of estimating the Chapman-Jouget detonation pressure and the detonation velocity of potential new CHNO explosives. This would allow choosing the most promising candidates for synthesis and testing thus avoiding wasting resources. This method utilizes density functional theory (DFT) and the electrostatic potential to estimate heats of formation and crystal densities. The calculations were performed on traditionally used explosives and the calculated detonation pressures and detonation velocities showed good accordance with experimental data. The calculated detonation pressures fell within ±10% and the detonation velocities within ±5% of experimental data.

The aim of this project was to investigate a potential connection between a molecule's capacity to penetrate the blood-brain barrier and its electrostatic potential on the surface of the molecule. A molecule's capacity to penetrate the blood-brain barrier is quantified by their log BB value. This was done by creating a set of 58 molecules, divided into a test set and a calibration set, in Gaussian 16. The molecules were then optimized and their quantum chemical properties were calculated by using HS-95. By using stepwise regression in both Matlab and Excel these different parameters were then used to search for a correlation between the parameters and experimental log BB values. This resulted in an equation with 10 variables with an adjusted R2 value of 0,6456. When tested against the test set the mean fault was 0,1443. Outliers were then identified and removed and stepwise regression was executed once more. This resulted in an equation with 10 variables with an adjusted R2 0,8749. When this was tested against the test set the mean fault was 0,0798. The results showed that the variables that were important were the electrostatic potential, surface area and volume.

In this thesis H-bonded systems (natural gas hydrates, water clusters, and crystal ice) are studied by density functional theory (DFT) computations. Natural gas hydrates (NGHs) play an important role in energy and environmental fields: NGHs are considered as a promising backup energy resource in the near-future due to their tremendous carbon content; improper exploration of NGHs could induce geological disasters and aggravate the greenhouse effect. In addition, many technologies based on gas hydrates are being applied and developed. The thermodynamic stabilities of various water cavities in different clathrate crystalline phases occupied by hydrocarbon gas molecules are studied by dispersion-corrected hybrid functionals. The Raman spectra of C-C and C-H stretching vibrations of hydrocarbon molecules in various water cavities in the solid state are derived. The trends of C-H stretching vibrational frequencies are found to follow the prediction by the “loose cage ─| tight cage” model. In addition, the trends and origins of 13C NMR chemical shifts of hydrocarbon molecules in various NGHs are presented. These theoretical results will enlarge the database of C-C and C-H stretching vibrational frequencies and 13C NMR parameters of hydrocarbon molecules in NGHs, and provide valuable information to help identify the types of clathrate phases and varieties of guest molecules included in NGHs samples taken from natural sites. The behavior of water clusters may help to understand the properties of its liquid and solid states. The thermodynamic stabilities and IR spectra of a small-, medium-, and large-sized water cluster are studied in this work. After full optimization of (H2O)20,54,100 using the hybrid functional B3LYP, the electronic energies, zero-point energies, internal energies, enthalpies, entropies, and Gibbs free energies of the water clusters are computed. The OH stretching vibrational IR spectra of (H2O)20,54,100 are also presented and split into sub-spectra for different H-bond types based on the specific contributions from each group. It is found that the OH stretching vibrational frequencies of water are sensitive to the conformations of the H-bonds and the vibrations of the H-bonds belonging to different types are located in separated regions in the IR spectra. Thus, the spectroscopic fingerprints will reflect the H-bond topology of the water molecules in a water cluster. Ice XI has been suggested to be involved in the process of planetary formation as a considerable electric field might be formed from the ferroelectric ice XI in space. IR and Raman spectroscopic technology can be directly used to identify the occurrence of ferroelectric ice XI in laboratory or extraterrestrial settings. Due to the difficulty for DFT to describe non-covalent systems, the performance of 16 different DFT methods applied on the ice Ih, VIII, IX, and XI crystal phases are assessed. Based on the computational accuracy and cost, the IR and Raman spectra of ice Ih and XI are derived and compared. The librational vibrations are found to be the identifier which can be used to distinguish ice Ih and ice XI in the universe. In addition, the existence only one kind of H-bond in ice Ih is demonstrated from the overlapping sub-spectra for different types of H-bonded pair configurations in 16 isomers of ice Ih. The region of water under negative pressure is an exotic land in lack of exploitation. Guest free clathrate hydrate (clathrate ice) of sII type has been recently confirmed experimentally at negative pressure. Does any other clathrate ice phase exist at negative pressure region? Since clathrate hydrate are isostructural with silica clathrate minerals and semiconductor clathrates, and crystal structure prediction by analogy with known structures and first-principles computations is an effective way to find new crystalline phases of solid materials, we are motived to look for new clathrate ice phases from silica or semiconductor clathrate materials based on first-principles computations. Borrowing the idea new clathrate frameworks of ZnO and SiC can be constructed by connecting their bubble clusters in different ways, new clathrate ice phases (sL, sL_I, sL_II, and sL_III) are generated by connecting the water bubble clusters according to different rules. Using the non-local dispersion-corrected vdW-DF2 functional, clathrate ice sL with ultralow density (0.6 g/cm3) is predicted by first-principles phase diagram computations to be stable under larger negative pressures than the sII phase. The phase diagram of water is thus extended into the lower negative pressure region.

Ground state destabilization is a hypothesis to explain enzyme catalysis. The most popular interpretation of it is the entropic effect, which states that enzymes accelerate biochemical reactions by bringing the reactants to a favorable position and orientation and the entropy cost of this is compensated by enthalpy of binding. Once the enzyme-substrate complex is formed, the reaction could proceed with negligible entropy cost. Deamination of cytidine catalyzed by E.coli cytidine deaminase appears to agree with this hypothesis. In this reaction, the chemical transformation occurs with a negligible entropy cost and the initial binding occurs with a large entropy penalty that is comparable to the entropic cost of the uncatalyzed reaction. Our calculations revealed that this reaction occurs with different mechanisms in the cytidine deaminase and water. The uncatalyzed reaction involves a concerted mechanism and the entropy cost of this reaction appears to be dominated by the reacting fragments and first solvation shell. The catalyzed reaction occurs via a stepwise mechanism in which a hydroxide ion acts as the nucleophile. In the active site, the entropy cost of hydroxide ion formation is eliminated due to pre-organization of the active site. Hence, the entropic effect in this reaction is due to a pre-organized active site rather than ground state destabilization. In the second part of this thesis, we investigated peptide bond formation and peptidyl-tRNA hydrolysis at the peptidyl transferase center of the ribosome. Peptidyl-tRNA hydrolysis occurs by nucleophilic attack of a water molecule on the ester carbon of peptidyl-tRNA. Our calculations showed that this reaction proceeds via a base catalyzed mechanism where the A76 O2’ is the general base and activates the nucleophilic water. Peptide bond formation occurs by nucleophilic attack of the α-amino group of aminoacyl-tRNA on the ester carbon of peptidyl-tRNA. For this reaction we investigated two mechanisms: i) the previously proposed proton shuttle mechanism which involves a zwitterionic tetrahedral intermediate, and ii) a general base mechanism that proceeds via a negatively charged tetrahedral intermediate. Although both mechanisms resulted in reasonable activation energies, only the proton shuttle mechanism found to be consistent with the pH dependence of peptide bond formation.