Hochgenaue Berechnungen von Energien und molekularen Eigenschaften mit Hilfe der Coupled-Cluster-Theorie

Coupled-Cluster-Theorie (CC) ist in der heutigen Quantenchemie eine der erfolgreichsten Methoden zur genauen Beschreibung von Molekülen. Die in dieser Arbeit vorgestellten Ergebnisse zeigen, daß neben den Berechnungen von Energien eine Reihe von Eigenschaften wie Strukturparameter, Schwingungsfrequenzen und Rotations-Schwingungs-Parameter kleiner und mittelgrofler Moleküle zuverlässig und präzise vorhergesagt werden können. Im ersten Teil der Arbeit wird mit dem Spin-adaptierten Coupled-Cluster-Ansatz (SA-CC) ein neuer Weg zur Verbesserung der Beschreibung von offenschaligen Systemen vorgestellt. Dabei werden zur Bestimmung der unbekannten Wellenfunktionsparameter zusätzlich die CC-Spingleichungen gelöst. Durch dieses Vorgehen wird gewährleistet, daß die erhaltene Wellenfunktion eine Spineigenfunktion ist. Die durchgeführte Implementierung des Spin-adaptierten CC-Ansatzes unter Berücksichtigung von Einfach- und Zweifachanregungen (CCSD) für high-spin Triplett-Systeme wird ausführlich erläutert. Im zweiten Teil werden CC-Additionsschemata vorgestellt, die auf der Annahme der Additivität von Elektronenkorrelations- und Basissatzeffekten basieren. Die etablierte Vorgehensweise, verschiedene Beiträge zur Energie mit an den Rechenaufwand angepassten Basissätzen separat zu berechnen und aufzusummieren, wird hier auf Gradienten und Kraftkonstanten übertragen. Für eine Beschreibung von Bindungslängen und harmonischen Schwingungsfrequenzen mit experimenteller Genauigkeit ist die Berücksichtigung von Innerschalenkorrelationseffekten sowie Dreifach- und Vierfachanregungen im Clusteroperator der Wellenfunktion nötig. Die Basissatzkonvergenz wird dabei zusätzlich mit Extrapolationsmethoden beschleunigt. Die quantitative Vorhersage der Bindungslängen von 17 kleinen Molekülen, aufgebaut aus Atomen der ersten Langperiode, ist so mit einer Genauigkeit von wenigen Hundertstel Pikometern möglich. Für die Schwingungsfrequenzen dieser Moleküle weist das CC-Additionsschema basierend auf den berechneten Kraftkonstanten im Vergleich zu experimentellen Ergebnissen einen mittleren absoluten Fehler von 3.5 cm-1 und eine Standardabweichung von 2.2 cm-1 auf. Darüber hinaus werden zur Unterstützung von experimentellen Untersuchungen berechnete spektroskopische Daten einiger größerer Moleküle vorgelegt. Die in dieser Arbeit vorgestellten Untersuchungen zur Isomerisierung von Dihalogensulfanen XSSX (X= F, Cl) oder die Berechnung von Struktur- und Rotations-Schwingungs-Parametern für die Moleküle CHCl2F und CHClF2 zeigen, daß bereits störungstheoretische CCSD(T)-Näherungsmethoden qualitativ gute Vorhersagen experimenteller Resultate liefern. Desweiteren werden Diskrepanzen von experimentellen und berechneten Bindungsabständen bei den Molekülen Borhydrid- und Carbenylium durch die Berücksichtigung des elektronischen Beitrages zum Trägheitsmoment beseitigt.

The ability of the Gaussian-2, Gaussian-3, Complete Basis Set–QB3, and Complete Basis Set–APNO model chemistries to model the geometries of small water clusters

The Gaussian-2, Gaussian-3, Complete Basis Set-QB3, and Complete Basis Set-APNO methods have been used to calculate geometries of neutral clusters of water, (H2O)n, where n = 2–6. The structures are in excellent agreement with those determined from experiment and those predicted from previous high-level calculations. These methods also provide excellent thermochemical predictions for water clusters, and thus can be used with confidence in evaluating the structures and thermochemistry of water clusters.

Using phase-space localized basis functions to obtain vibrational energies of molecules

For decades scientists have attempted to use ideas of classical mechanics to choose basis functions for calculating spectra. The hope is that a classically-motivated basis set will be small because it covers only the dynamically important part of phase space. One popular idea is to use phase space localized (PSL) basis functions. This thesis improves on previous efforts to use PSL functions and examines the usefulness of these improvements. Because the overlap matrix, in the matrix eigenvalue problem obtained by using PSL functions with the variational method, is not an identity, it is costly to use iterative methods to solve the matrix eigenvalue problem. We show that it is possible to circumvent the orthogonality (overlap) problem and use iterative eigensolvers. We also present an altered method of calculating the matrix elements that improves the performance of the PSL basis functions, and also a new method which more efficiently chooses which PSL functions to include. These improvements are applied to a variety of single well molecules. We conclude that for single minimum molecules, the PSL functions are inferior to other basis functions. However, the ideas developed here can be applied to other types of basis functions, and PSL functions may be useful for multi-well systems.

Dynamic texture reconstruction from sparse codes for unusual event detection in crowded scenes

Unusual event detection in crowded scenes remains challenging because of the diversity of events and noise. In this paper, we present a novel approach for unusual event detection via sparse reconstruction of dynamic textures over an overcomplete basis set, with the dynamic texture described by local binary patterns from three orthogonal planes (LBPTOP). The overcomplete basis set is learnt from the training data where only the normal items observed. In the detection process, given a new observation, we compute the sparse coefficients using the Dantzig Selector algorithm which was proposed in the literature of compressed sensing. Then the reconstruction errors are computed, based on which we detect the abnormal items. Our application can be used to detect both local and global abnormal events. We evaluate our algorithm on UCSD Abnormality Datasets for local anomaly detection, which is shown to outperform current state-of-the-art approaches, and we also get promising results for rapid escape detection using the PETS2009 dataset.

Formation of single-walled carbon nanotube via the interaction of graphene nanoribbons : ab initio density functional calculations

The interaction of bare graphene nanoribbons (GNRs) was investigated by ab initio density functional theory calculations with both the local density approximation (LDA) and the generalized gradient approximation (GGA). Remarkably, two bare 8-GNRs with zigzag-shaped edges are predicted to form an (8, 8) armchair single-wall carbon nanotube (SWCNT) without any obvious activation barrier. The formation of a (10, 0) zigzag SWCNT from two bare 10-GNRs with armchair-shaped edges has activation barriers of 0.23 and 0.61 eV for using the LDA and the revised PBE exchange correlation functional, respectively, Our results suggest a possible route to control the growth of specific types SWCNT via the interaction of GNRs.

Role of lithium vacancies in accelerating the dehydrogenation kinetics on a LiBH4(010) surface : an Ab initio study

In this work, ab initio density functional calculations were performed to explore the effect of surface lithium vacancies on the initial dehydrogenation kinetics of lithium borohydride. We found that some B−H bonds in neighboring BH4-1 complexes around the vacancy became elongated (weakened). The activation barriers for the recombination of H atoms to form H2 were decreased from 3.64 eV for the stoichiometrically complete LiBH4(010) surface to 1.53 and 0.23 eV in the presence of mono- and di-vacancies, respectively. Our results indicate that the creation of Li vacancies may play a critical role in accelerating the dehydrogenation kinetics of LiBH4.

Mechanisms of glycerol dehydration

Dehydration of neutral and protonated glycerol was investigated using quantum mechanical calculations (CBS-QB3). Calculations on neutral glycerol show that there is a high barrier for simple 1,2-dehydration, E-a = 70.9 kcal mol(-1), which is lowered to 65.2 kcal mol(-1) for pericyclic 1,3-dehydration. In contrast, the barriers for dehydration of protonated glycerol are much lower. Dehydration mechanisms involving hydride transfer, pinacol rearrangement, or substitution reactions have barriers between 20 and 25 kcal mol(-1). Loss of water from glycerol via substitution results in either oxirane or oxetane intermediates, which can interconvert over a low barrier. Subsequent decomposition of these intermediates proceeds via either a second dehydration step or loss of formaldehyde. The computed mechanisms for decomposition of protonated glycerol are supported by the gas-phase fragmentation of protonated glycerol observed using a triple-quadrupole mass spectrometer.

A mass spectrometry study of XCO+, X = Si, Ge : Is SiCO+ a main group carbonyl? Comments on the bonding in ground state SiCO and the Si,C,O (+) potential energy surface

The cation\[Si,C,O](+) has been generated by 1) the electron ionisation (EI) of tetramethoxysilane and 2) chemical ionisation (CI) of a mixture of silane and carbon monoxide. Collisional activation (CA) experiments performed for mass-selected \[Si,C,O](+), generated by using both methods, indicate that the structure is not inserted OSiC+; however, a definitive structural assignment as Si+-CO, Si+-OC or some cyclic variant is impossible based on these results alone. Neutralisation-reionisation (+NR+) experiments for EI-generated \[Si,C,O](+) reveal a small peak corresponding to SiC+, but no detectable SiO+ signal, and thus establishes the existence of the Si+-CO isomer. CCSD(T)//B3LYP calculations employing a triple-zeta basis set have been used to explore the doublet and quartet potential-energy surfaces of the cation, as well as some important neutral states The results suggest that both Si+-CO and Si+ - OC isomers are feasible; however, the global minimum is (2)Pi SiCO+. Isomeric (2)Pi SiOC+ is 12.1 kcal mol(-1) less stable than (2)Pi SiCO+, and all quartet isomers are much higher in energy. The corresponding neutrals Si-CO and Si-OC are also feasible, but the lowest energy Si - OC isomer ((3)A") is bound by only 1.5 kcal mol(-1). We attribute most, if nor all, of the recovery signal in the +NR' experiment to SiCO+ survivor ions. The nature of the bonding in the lowest energy isomers of Si+ -(CO,OC) is interpreted with the aid of natural bond order analyses, and the ground stale bonding of SiCO+ is discussed in relation to classical analogues such as metal carbonyls and ketenes.

Ground and Excited State Intramolecular Proton Transfer in Salicylic Acid: an Ab Initio Electronic Structure Investigation

Energetics of the ground and excited state intramolecular proton transfer in salicylic acid have been studied by ab initio molecular orbital calculations using the 6-31G** basis set at the restricted Hartree-Fock (RHF) and configuration interaction-single excitation (CIS) levels and also using the semiempirical method AM1 at the RHF level as well as with single and pair doubles excitation configuration interaction spanning eight frontier orbitals (PECI = 8). The ab initio potential energy profile for intramolecular proton transfer in the ground state reveals a single minimum corresponding to the primary form, in the first excited singlet state, however, there are two minima corresponding to the primary and tautomeric forms, separated by a barrier of similar to 6 kcal/mol, thus accounting for dual emission in salicylic acid. Electron density changes with electronic excitation and tautomerism indicate no zwitterion formation. Changes in spectral characteristics with change in pH, due to protonation and deprotonation of salicylic acid, are also accounted for, qualitatively. Although the AM1 calculations suggest a substantial barrier for proton transfer in the ground as well as the first excited state of SA, it predicts the transition wavelength in near quantitative accord with the experimental results for salicylic acid and its protonated and deprotonated forms.

Theoretical studies of lithium bonding in lithium chloride/aliphatic amine complexes

In the systematic study of amine … LiCl [amines = NH3, CH3NH2, (CH3)2NH] complexes the possibility of an ion-pair structure and the effect of methylation on the stabilization energy is investigated. ΔEis evaluated by the SCF/4-31G method and augmented by the approximate dispersion energy calculated perturbationally. The interaction energy decreases with the increasing number of methyl groups in the amine. The dispersion energy plays a negligible role in the stabilization of complexes. None of the systems studied are ion pairs; their Li bonds are of a so-called molecular type. Due to the divergence of the multipole expansion, the attempt to correct the 4-31G stabilization energies via the electrostatic energy fails. The relative order of the ΔE in the series of complexes is verified instead in the extended basis set calculation. The lithium bonds are compared with their H-bonded analogues.

Computational studies on new chemical species in the gas-phase and the solid-state.

There is intense activity in the area of theoretical chemistry of gold. It is now possible to predict new molecular species, and more recently, solids by combining relativistic methodology with isoelectronic thinking. In this thesis we predict a series of solid sheet-type crystals for Group-11 cyanides, MCN (M=Cu, Ag, Au), and Group-2 and 12 carbides MC2 (M=Be-Ba, Zn-Hg). The idea of sheets is then extended to nanostrips which can be bent to nanorings. The bending energies and deformation frequencies can be systematized by treating these molecules as an elastic bodies. In these species Au atoms act as an 'intermolecular glue'. Further suggested molecular species are the new uncongested aurocarbons, and the neutral Au_nHg_m clusters. Many of the suggested species are expected to be stabilized by aurophilic interactions. We also estimate the MP2 basis-set limit of the aurophilicity for the model compounds [ClAuPH_3]_2 and [P(AuPH_3)_4]^+. Beside investigating the size of the basis-set applied, our research confirms that the 19-VE TZVP+2f level, used a decade ago, already produced 74 % of the present aurophilic attraction energy for the [ClAuPH_3]_2 dimer. Likewise we verify the preferred C4v structure for the [P(AuPH_3)_4]^+ cation at the MP2 level. We also perform the first calculation on model aurophilic systems using the SCS-MP2 method and compare the results to high-accuracy CCSD(T) ones. The recently obtained high-resolution microwave spectra on MCN molecules (M=Cu, Ag, Au) provide an excellent testing ground for quantum chemistry. MP2 or CCSD(T) calculations, correlating all 19 valence electrons of Au and including BSSE and SO corrections, are able to give bond lengths to 0.6 pm, or better. Our calculated vibrational frequencies are expected to be better than the currently available experimental estimates. Qualitative evidence for multiple Au-C bonding in triatomic AuCN is also found.

Investigation of inter-ion interactions in N,N,N',N'-tetramethylethylenediammonium dithiocyanate via experimental and theoretical charge density studies

The crystal structure of the N,N,N',N'-tetramethylethylenediammonium dithiocyanate salt has been examined by experimental charge density studies from high-resolution X-ray diffraction data. The corresponding results are compared with multipole refinements, using theoretical structure factors obtained from a periodic density functional theory calculation at the B3LYP level with a 6-31G** basis set. The salt crystallizes in space group P (1) over bar and contains only a single ion pair with an inversion center in the cation. The salt has thus one unique classical N+-H center dot center dot center dot(NCS)(-) hydrogen bond but also has six other weaker interactions: four C-H center dot center dot center dot S, one C-H center dot center dot center dot N, and one C-H center dot center dot center dot C-pi. The nature of all these interactions has been examined topologically using Bader's quantum theory of "atoms in molecules" and all eight of the Koch-Popelier criteria. The experimental and theoretical approaches agree well and both show that the inter-ion interactions, even in this simplest of systems, play an integrated and complex role in the packing of the ions in the crystal. Electrostatic potential maps are derived from experimental charge densities. This is the first time such a system has been examined in detail by these methods.

Topological analysis off charge density distribution in concomitant polymorphs of 3-acetylcoumarin, a case off packing polymorphism

Detailed investigation of the charge density distribution in concomitant polymorphs of 3-acetylcoumarin in terms of experimental and theoretical densities shows significant differences in the intermolecular features when analyzed based on the topological properties via the quantum theory of atoms in molecules. The two forms, triclinic and monoclinic (Form A and Form B), pack in the crystal lattice via weak C-H---O and C-H---pi interactions. Form A results in a head-to-head molecular stack, while Form B generates a head-to-tail stack. Form A crystallizes in PI (Z' = 2) and Form B crystallizes in P2(1)/n (Z = 1). The electron density maps of the polymorphs demonstrate the differences in the nature of the charge density distribution in general. The charges derived from experimental and theoretical analysis show significant differences with respect to the polymorphic forms. The molecular dipole moments differ significantly for the two forms. The lattice energies evaluated at the HF and DFT (B3LYP) methods with 6-31G** basis set for the two forms clearly suggest that Form A is the thermodynamically stable form as compared to Form B. Mapping of electrostatic potential over the molecular surface shows dominant variations in the electronegative region, which bring out the differences between the two forms.

Bond length distortions associated with torsion potentials; ab-initio studies on methanedio

The 4-31G basis set is used to study the bond length variations as functions of dihedral angels in methanediol. This study is compared with O---C---O bond angle optimization studies by Gorenstein and Kar and the possible reason for bond length shorteing in the trans---trans configuration is analysed.

Computational Methods for Studies of Quantum Dots and Boson Condensates

This thesis presents ab initio studies of two kinds of physical systems, quantum dots and bosons, using two program packages of which the bosonic one has mainly been developed by the author. The implemented models, \emph{i.e.}, configuration interaction (CI) and coupled cluster (CC) take the correlated motion of the particles into account, and provide a hierarchy of computational schemes, on top of which the exact solution, within the limit of the single-particle basis set, is obtained. The theory underlying the models is presented in some detail, in order to provide insight into the approximations made and the circumstances under which they hold. Some of the computational methods are also highlighted. In the final sections the results are summarized. The CI and CC calculations on multiexciton complexes in self-assembled semiconductor quantum dots are presented and compared, along with radiative and non-radiative transition rates. Full CI calculations on quantum rings and double quantum rings are also presented. In the latter case, experimental and theoretical results from the literature are re-examined and an alternative explanation for the reported photoluminescence spectra is found. The boson program is first applied on a fictitious model system consisting of bosonic electrons in a central Coulomb field for which CI at the singles and doubles level is found to account for almost all of the correlation energy. Finally, the boson program is employed to study Bose-Einstein condensates confined in different anisotropic trap potentials. The effects of the anisotropy on the relative correlation energy is examined, as well as the effect of varying the interaction potential.}