Drei numerische Feldberechnungsverfahren - die Momentenmehtode, die Einheitliche Geometrische Beugungstheorie und die Verallgemeinerte Multipoltechnik - werden schrittweise zu einer Erweiterten Hybridmethode (EHM) kombiniert. Dabei wird jeder einzelne Kombinationsschritt anschaulich anhand von Beispielen erläutert, die den Vorteil der EHM verdeutlichen: Mit diesem Verfahren lassen sich bestimmte Anordnungen äußerst effektiv analysieren.

Atomistic modeling and simulation methods enable a modern molecular approach to bio-medical research. Issues addressed range from structure-function relationships to structure-based drug design. The ability of these methods to address biologically relevant problems is largely determined by their accurate treatment of electrostatic interactions in the target biomolecular structure. In practical molecular simulations, the electrostatic charge density of molecules is approximated by an arrangement of fractional "point charges" throughout the molecule. While chemically intuitive and straightforward in technical implementation, models based exclusively on atom-centered charge placement, a major workhorse of the biomolecular simulations, do not necessarily provide a sufficiently detailed description of the molecular electrostatic potentials for small systems, and can become prohibitively expensive for large systems with thousands to millions of atoms. In this work, we propose a rigorous and generally applicable approach, Optimal Point Charge Approximation (OPCA), for approximating electrostatic charge distributions of biomolecules with a small number of point charges to best represent the underlying electrostatic potential, regardless of the distance to the charge distribution. OPCA places a given number of point charges so that the lowest order multipole moments of the reference charge distribution are optimally reproduced. We provide a general framework for calculating OPCAs to any order, and introduce closed-form analytical expressions for the 1-charge, 2-charge and 3-charge OPCA. We demonstrate the advantage of OPCA by applying it to a wide range of biomolecules of varied sizes. We use the concept of OPCA to develop a different, novel approach of constructing accurate and simple point charge water models. The proposed approach permits a virtually exhaustive search for optimal model parameters in the sub-space most relevant to electrostatic properties of the water molecule in liquid phase. A novel rigid 4-point Optimal Point Charge (OPC) water model constructed based on the new approach is substantially more accurate than commonly used models in terms of bulk water properties, and delivers critical accuracy improvement in practical atomistic simulations, such as RNA simulations, protein folding, protein-ligand binding and small molecule hydration. We also apply our new approach to construct a 3-point version of the Optimal Point Charge water model, referred to as OPC3. OPCA can be employed to represent large charge distributions with only a few point charges. We use this capability of OPCA to develop a multi-scale, yet fully atomistic, generalized Born approach (GB-HCPO) that can deliver up to 2 orders of magnitude speedup compared to the reference MD simulation. As a practical demonstration, we exploit the new multi-scale approach to gain insight into the structure of million-atom 30-nm chromatin fiber. Our results suggest important structural details consistent with experiment: the linker DNA fills the core region and the H3 histone tails interact with the linker DNA. OPC, OPC3 and GB-HCPO are implemented in AMBER molecular dynamics software package. / Ph. D.

This work addresses the question of the efficient numerical solution of time-domain boundary integral equations with retarded potentials arising in the problems of acoustic and electromagnetic scattering. The convolutional form of the time-domain boundary operators allows to discretize them with the help of Runge-Kutta convolution quadrature. This method combines Laplace-transform and time-stepping approaches and requires the explicit form of the fundamental solution only in the Laplace domain to be known. Recent numerical and analytical studies revealed excellent properties of Runge-Kutta convolution quadrature, e.g. high convergence order, stability, low dissipation and dispersion. As a model problem, we consider the wave scattering in three dimensions. The convolution quadrature discretization of the indirect formulation for the three-dimensional wave equation leads to the lower triangular Toeplitz system of equations. Each entry of this system is a boundary integral operator with a kernel defined by convolution quadrature. In this work we develop an efficient method of almost linear complexity for the solution of this system based on the existing recursive algorithm. The latter requires the construction of many discretizations of the Helmholtz boundary single layer operator for a wide range of complex wavenumbers. This leads to two main problems: the need to construct many dense matrices and to evaluate many singular and near-singular integrals. The first problem is overcome by the use of data-sparse techniques, namely, the high-frequency fast multipole method (HF FMM) and H-matrices. The applicability of both techniques for the discretization of the Helmholtz boundary single-layer operators with complex wavenumbers is analyzed. It is shown that the presence of decay can favorably affect the length of the fast multipole expansions and thus reduce the matrix-vector multiplication times. The performance of H-matrices and the HF FMM is compared for a range of complex wavenumbers, and the strategy to choose between two techniques is suggested. The second problem, namely, the assembly of many singular and nearly-singular integrals, is solved by the use of the Huygens principle. In this work we prove that kernels of the boundary integral operators $w_n^h(d)$ ($h$ is the time step and $t_n=nh$ is the time) exhibit exponential decay outside of the neighborhood of $d=nh$ (this is the consequence of the Huygens principle). The size of the support of these kernels for fixed $h$ increases with $n$ as $n^a,a<1$, where $a$ depends on the order of the Runge-Kutta method and is (typically) smaller for Runge-Kutta methods of higher order. Numerical experiments demonstrate that theoretically predicted values of $a$ are quite close to optimal. In the work it is shown how this property can be used in the recursive algorithm to construct only a few matrices with the near-field, while for the rest of the matrices the far-field only is assembled. The resulting method allows to solve the three-dimensional wave scattering problem with asymptotically almost linear complexity. The efficiency of the approach is confirmed by extensive numerical experiments.

<p>U ovoj doktorskoj disertaciji izloženi su rezultati&nbsp;analize eksperimentalno i teorijski dobijene&nbsp;raspodele gustine naelektrisanja dva derivata&nbsp;tiosemikarbazida, 4-metil-3-tiosemikarbazida&nbsp;(MeTSC) i 4-metil-3-tiosemikarbazon 2-piridinformamida (TSC4). &nbsp;Analiza&nbsp;eksperimentalno dobijene gustine naelektrisanja je&nbsp;zasnovana&nbsp; na preciznim &nbsp;podacima dobijenim&nbsp;difrakcijom rendgenskog zračenja visoke&nbsp;rezolucije. Teorijska istraživanja bazirana su na&nbsp;teorijskim strukturnim faktorima dobijenim&nbsp;primenom programa CRYSAL09 polazeći od&nbsp;geometrije&nbsp; molekula određene nakon multipol&nbsp;utačnjavanja eksperimentalno dobijene gustine&nbsp;naelektrisanja. Za opisivanje eksperimentalne i&nbsp;teorijske ukupne elektronske gustine kori&scaron;ćen je&nbsp;Hansen-Coppens-ov multipol-model.&nbsp; Takođe je&nbsp;urađena i topolo&scaron;ka analizahemijskih veza i&nbsp;interakcija &nbsp;i ispitivana su elektrostatička svojstva&nbsp;atoma sumpora.</p><p>Analizom eksperimentalne gustine&nbsp;naelektrisanja kristalnih struktura MeTSC i TSC4&nbsp;uočeno je da deformaciona gustina slobodnih&nbsp;elektronskih parova S atoma ima &nbsp;oblik torusa, da&nbsp;je unutar njega raspodela elektronske gustine&nbsp;nehomogena i da položaj samog torusa može biti&nbsp;ortogonalan (SalTSC) ili pod uglom (MeTSC,&nbsp;<br />TSC4).&nbsp; Na osnovu raspodele deformacione&nbsp;gustine i elektrostatičkog potencijala, kao &nbsp;i na&nbsp;osnovu topolo&scaron;ke analize ukupne eksperimentalne&nbsp;gustine naelektrisanja &rho;_ktv&nbsp; i njenog Laplasijana &nabla;²&rho;_ktv zaključeno je da atom sumpora ima izrazitu&nbsp;fleksibilnost i sposobnost da prilagodi svoju&nbsp;elektronsku gustinu slobodnih elektronskih &nbsp;parova&nbsp;prostornom rasporedu donornih grupa koje&nbsp;učestvuju u interakcijama sa S akceptorom.&nbsp; U&nbsp;kristalnim strukturama MeTSC i TSC4 utvrđeno&nbsp;je da S atom istovremeno gradi četiri, odnosno&nbsp;prosečno &scaron;est međumolekulskih interakcija.</p><p>U cilju upotpunjavanja eksperimentalnih&nbsp;rezultata analizirana je teorijski dobijena gustina&nbsp;naelektrisanja oba molekula, a zatim su ispitivane&nbsp;karakteristike sumpora kao akceptora i to u&nbsp;sistemima različite složensti polazeći od&nbsp;izolovanih monomera, preko izdvojenih dimer do&nbsp;kristalnogokruženja. Ovom analizom je utvrđeno&nbsp;da se simultanim angažovanjem S atoma u vi&scaron;e&nbsp;interakcija ne umanjuje njegova akceptorska&nbsp;sposobnost.</p><p>Vodonične vezekoje uključuju S akceptor su&nbsp;ispitivane sa aspekta &nbsp;energijskih svojstava dimera&nbsp;koji suprisutni u MeTSCi TSC4, kaoi u dodatno&nbsp;konstruisanim&nbsp; sistemima&nbsp; MeTSC/MeOH&nbsp; i&nbsp;aceton/MeOH. Energijske&nbsp; karakteristike&nbsp; su&nbsp;proučavane u pogledu elektrostatičke energije&nbsp;interakcije (E_es) i kohezione energije(E_coh). Za&nbsp;<br />dva odabrana&nbsp; MeTSC/MeOH i aceton/MeOH&nbsp;sistema je primenjena metoda &nbsp;kuplovanih klastera&nbsp;kao&scaron;to&nbsp; je&nbsp;<em> ab initio</em>&nbsp; CCSD(T)&nbsp; metod.&nbsp; Za&nbsp;MeTSC/MeOH sistem je &nbsp;urađena potpuna&nbsp;optimizacija i za tako dobijenu ravnotežnu&nbsp;geometriju je izračunata energija sistema&nbsp;∆E_CCSD(T),CBS.</p> / <p>In this dissertation the analysis of the experimental and theoretically obtained electron &nbsp;density of two derivatives of thiosemicarbasides, 4-methyl-3-thiosemicarbaside (MeTSC) and 4-methyl-3-thiosemikabazone 2-piridinformamide (TSC4) are presented.&nbsp; The analysis of experimentally obtained electron density is based on &nbsp;accurate X-ray diffraction data of high resolution. Theoretically calculated electron densities are obtained from periodic quantum mechanical calculation using CRYSTAL09 and the accurate structural parameters from high resolution X-ray&nbsp;experiment. For the description of the theoretical and experimental electron density the Hansen-Coppens multipol model was used. Further topological analysis of chemical bonds and interactions was performed in order to explain the electrostatic properties of sulfur.</p><p>In this work it has been observed that in the experimentally obtained electron density of the MeTSC and TSC4 crystal structures, the deformational electron density of sulfur free electron pairs forms a toroidal shape. Further, this torus is not homogeneously filled but shows pronounced local accumulations and its position can be either orthogonal (like in SalTSC) or tilted (MeTSC, TSC4). Based on the distribution of the&nbsp;deformational electron&nbsp; density and electrostatic potential, as well as the topological analysis of the total electron density &rho;_ktv and its Laplasian &nabla;²&rho;_ktv&nbsp;it can be concluded that the S atom has a remarkable flexibility and ability to adapt his deformation electron density of free electron pairs into toruses corresponding to the position of donor groups surrounding him. In the crystal structures of MeTSC and TSC4 it was determined that the S atom participates in four and six interactions, respectively.</p><p>In order to supplement&nbsp; the experimentally obtained results a theoretically calculated electron density of both molecules (MeTSC and TSC4) was performed and the properties of the S atom as a hydrogen acceptor have been studied. The analysis was &nbsp;performed on systems of various complexity, starting with isolated monomers, then on &nbsp;dimers and up to the whole crystal packing. From this work it has been concluded that &nbsp;the acceptor capabilities of the S atom are not diminished with the increasing number &nbsp;of interactions.&nbsp;&nbsp;&nbsp;&nbsp;</p><p>The hydrogen bonding involving thioureido S&nbsp;acceptor is also investigated in terms of the energetic properties of the MeTSC and TSC4 dimers existing in the crystal structure, and additional MeTSC/MeOH and acetone/MeOH systems. Energetic features were thoroughly studied through electrostatic interactions energies (E_es) and &nbsp;cohesive energies (E_coh). For two selected MeTSC/MeOH and acetone/MeOH systems an ab initio approach&nbsp;employing the coupled-cluster singles and doubles augmented by a perturbational correction for connected triple excitations (CCSD(T)) method were applied. Finaly, for MeTSC/MeOH system full geometry optimization was &nbsp;performed and for resulting equilibrium geometry the energy of the system (∆E_CCSD(T),CBS) was calculated.</p>

This work addresses the question of the efficient numerical solution of time-domain boundary integral equations with retarded potentials arising in the problems of acoustic and electromagnetic scattering. The convolutional form of the time-domain boundary operators allows to discretize them with the help of Runge-Kutta convolution quadrature. This method combines Laplace-transform and time-stepping approaches and requires the explicit form of the fundamental solution only in the Laplace domain to be known. Recent numerical and analytical studies revealed excellent properties of Runge-Kutta convolution quadrature, e.g. high convergence order, stability, low dissipation and dispersion. As a model problem, we consider the wave scattering in three dimensions. The convolution quadrature discretization of the indirect formulation for the three-dimensional wave equation leads to the lower triangular Toeplitz system of equations. Each entry of this system is a boundary integral operator with a kernel defined by convolution quadrature. In this work we develop an efficient method of almost linear complexity for the solution of this system based on the existing recursive algorithm. The latter requires the construction of many discretizations of the Helmholtz boundary single layer operator for a wide range of complex wavenumbers. This leads to two main problems: the need to construct many dense matrices and to evaluate many singular and near-singular integrals. The first problem is overcome by the use of data-sparse techniques, namely, the high-frequency fast multipole method (HF FMM) and H-matrices. The applicability of both techniques for the discretization of the Helmholtz boundary single-layer operators with complex wavenumbers is analyzed. It is shown that the presence of decay can favorably affect the length of the fast multipole expansions and thus reduce the matrix-vector multiplication times. The performance of H-matrices and the HF FMM is compared for a range of complex wavenumbers, and the strategy to choose between two techniques is suggested. The second problem, namely, the assembly of many singular and nearly-singular integrals, is solved by the use of the Huygens principle. In this work we prove that kernels of the boundary integral operators $w_n^h(d)$ ($h$ is the time step and $t_n=nh$ is the time) exhibit exponential decay outside of the neighborhood of $d=nh$ (this is the consequence of the Huygens principle). The size of the support of these kernels for fixed $h$ increases with $n$ as $n^a,a<1$, where $a$ depends on the order of the Runge-Kutta method and is (typically) smaller for Runge-Kutta methods of higher order. Numerical experiments demonstrate that theoretically predicted values of $a$ are quite close to optimal. In the work it is shown how this property can be used in the recursive algorithm to construct only a few matrices with the near-field, while for the rest of the matrices the far-field only is assembled. The resulting method allows to solve the three-dimensional wave scattering problem with asymptotically almost linear complexity. The efficiency of the approach is confirmed by extensive numerical experiments.

Recent experimental achievements in active noise control (ANC) for cooling fans have used near-field error sensors whose locations are determined according to a theoretical condition of minimized sound power. A theoretical point source model, based on the condition previously stated, reveals the location of near-field pressure nulls that may be used to optimize error sensor placement. The actual locations of these near-field pressure nulls for both an axial cooling fan and a monopole loudspeaker were measured over a two-dimensional grid with a linear array of microphones. The achieved global attenuation for each case is measured over a hemisphere located in the acoustic far field of the ANC system. The experimental results are compared to the theoretical pressure null locations in order to determine the efficacy of the point source model. The results closely matched the point source model with a loudspeaker as the primary source, and the sound power reduction was greatly reduced when error sensors were placed in non-ideal locations. A weakness of the current near-field modeling process is that a point monopole source is used to characterize the acoustic noise from an axial cooling fan, which may have multipole characteristics. A more complete characterization of fan noise may be obtained using a procedure based on the work of Martin and Roure [J. Sound Vib. 201 (5), 577--593 (1997)]. Pressure values are obtained over a hemisphere in the far field of a primary source and the contributions from point source distributions up to the second order, centered at the primary source, may be calculated using a multipole expansion. The source information is then used in the aforementioned theoretical near-field calculation of pressure. The error sensors are positioned using the complete fan characterization. The global far-field attenuation for the multipole expansion model of fan noise is compared to that of previous experiments. Results show that the multipole expansion model yields a more accurate representation the near field, but is not successful in achieving greater sound power reductions in the far field.

The size and conformational complexity of proteins and other large systems represent major challenges for today's methods of quantum chemistry.This thesis is centered around the development of new computational tools to gain molecular-level insight into electronic transitions in such systems. To meet this challenge, we focus on the polarizable embedding (PE) model, which takes advantage of the fact that many electronic transitions are localized to a smaller part of the entire system.This motivates a partitioning of the large system into two regions that are treated at different levels of theory:The smaller part directly involved in the electronic process is described using accurate quantum-chemical methods, while the effects of the rest of the system, the environment, are incorporated into the Hamiltonian of the quantum region in an effective manner. This thesis presents extensions of the PE model with theaim of expanding its range of applicability to describe electronic transitions in large molecular systemsin the optical and X-ray regions. The developments cover both improvements with regardto the quantum region as well as the embedding potential representing the environment.Regarding the former, a damped linear response formulation has been implemented to allow for calculations of absorption spectra of large molecular systems acrossthe entire frequency range. A special feature of this development is its abilityto address core excitations that are otherwise not easily accessible.Another important development presented in this thesis is the coupling of the PE model to a multi-configuration self-consistent-field description of the quantum region and its further combination with response theory. In essence, this extends the PE model to the study of electronic transitions in large systems that are prone to static correlation --- a situation that is frequently encountered in biological systems. In addition to the direct environmental effects on the electronic structure of the quantum region, another important component of the description of electronic transitions in large molecular systems is an accurate account of the indirect effects of the environment, i.e., the geometrical distortions in the quantum region imposed by the environment. In thisthesis we have taken the first step toward the inclusion of geometry distortions in the PE frameworkby formulating and implementing molecular gradients for the quantum region. To identify critical points related to the environment description, we perform a theoretical analysis of the PE model starting from a full quantum-mechanicaltreatment of a composite system. Based on this, we present strategies for an accurate yet efficient construction of the embedding potentialcovering both the calculation of ground state and transition properties. The accurate representation of the environment makes it possible to reduce the size of the quantum region without compromising the overall accuracy of the final results. This further enables use of highly accurate quantum-chemical methods despite their unfavorable scaling with the size of the system. Finally, some examples of applications will be presented to demonstrate how the PE model may be applied as a tool to gain insight into and rationalize the factors influencing electronic transitions in large molecular systems of increasing complexity. / <p>The dissertation was awarded the best PhD thesis prize 2016 by the Danish Academy of Natural Sciences.</p><p></p><p>QC 20170209</p>

Das wissenschaftliche Rechnen mit der Computersimulation hat sich heute als dritte Säule der wissenschaftlichen Methodenlehre neben der Theorie und dem Experiment etabliert. Aufgabe der Informatik im wissenschaftlichen Rechnen ist es, sowohl effiziente Simulationsalgorithmen zu entwickeln als auch ihre effiziente Implementierung. Die vorliegende Arbeit richtet ihren Fokus auf die effiziente Implementierung zweier wichtiger Verfahren des wissenschaftlichen Rechnens: die Schnelle Multipolmethode (FMM) für Teilchensimulationen und die Methode der finiten Elemente (FEM), die z. B. zur Berechnung der Deformation von Festkörpern genutzt wird. Die Effizienz der Implementierung bezieht sich hier auf die Ausführungszeit der Simulationen und den zur Ausführung notwendigen Energieverbrauch der eingesetzten Rechnersysteme. Die Steigerung der Effizienz wurde durch modellbasiertes Autotuning erreicht. Beim modellbasierten Autotuning wird für die wesentlichen Teile des Algorithmus ein Modell aufgestellt, das dessen Ausführungszeit bzw. Energieverbrauch beschreibt. Dieses Modell ist abhängig von Eigenschaften des genutzten Rechnersystems, von Eingabedaten und von verschiedenen Parametern des Algorithmus. Die Eigenschaften des Rechnersystems werden durch Ausführung des tatsächlich genutzten Codes für verschiedene Implementierungsvarianten ermittelt. Diese umfassen eine CPU-Implementierung und eine Grafikprozessoren-Implementierung für die FEM und die Implementierung der Nahfeld- und der Fernfeldwechselwirkungsberechnung für die FMM. Anhand der aufgestellten Modelle werden die Kosten der Ausführung für jede Variante vorhergesagt. Die optimalen Algorithmenparameter können somit analytisch bestimmt werden, um die gewünschte Zielgröße, also Ausführungszeit oder Energieverbrauch, zu minimieren. Bei der Ausführung der Simulation werden die effizientesten Implementierungsvarianten entsprechend der Vorhersage genutzt. Während bei der FMM die Performance-Messungen unabhängig von der Ausführung der Simulation durchgeführt werden, wird für die FEM ein Verfahren zur dynamischen Verteilung der Rechenlast zwischen CPU und GPU vorgestellt, das auf Ausführungszeitmessungen zur Laufzeit der Simulation reagiert. Durch Messung der tatsächlichen Ausführungszeiten kann so dynamisch auf sich während der Laufzeit verändernde Verhältnisse reagiert und die Verteilung der Rechenlast entsprechend angepasst werden. Die Ergebnisse dieser Arbeit zeigen, dass modellbasiertes Autotuning es ermöglicht, die Effizienz von Anwendungen des wissenschaftlichen Rechnens in Bezug auf Ausführungszeit und Energieverbrauch zu steigern. Insbesondere die Berücksichtigung des Energieverbrauchs alternativer Ausführungspfade, also die Energieadaptivität, wird in naher Zukunft von großer Bedeutung im wissenschaftlichen Rechnen sein. / Computer simulation as a part of the scientific computing has established as third pillar in scientific methodology, besides theory and experiment. The task of computer science in the field of scientific computing is the development of efficient simulation algorithms as well as their efficient implementation. The thesis focuses on the efficient implementation of two important methods in scientific computing: the Fast Multipole Method (FMM) for particle simulations, and the Finite Element Method (FEM), which is, e.g., used for deformation problems of solids. The efficiency of the implementation considers the execution time of the simulations and the energy consumption of the computing systems needed for the execution. The method used for increasing the efficiency is model-based autotuning. For model-based autotuning, a model for the substantial parts of the algorithm is set up which estimates the execution time or energy consumption. This model depends on properties of the computer used, of the input data and of parameters of the algorithm. The properties of the computer are determined by executing the real code for different implementation variants. These implementation variantss comprise a CPU and a graphics processor implementation for the FEM, and implementations of near field and far field interaction calculations for the FMM. Using the models, the execution costs for each variant are predicted. Thus, the optimal algorithm parameters can be determined analytically for a minimisation of the desired target value, i.e. execution time or energy consumption. When the simulation is executed, the most efficient implementation variants are used depending on the prediction of the model. While for the FMM the performance measurement takes place independently from the execution of the simulation, for the FEM a method for dynamically distributing the workload to the CPU and the GPU is presented, which takes into account execution times measured at runtime. By measuring the real execution times, it is possible to response to changing conditions and to adapt the distribution of the workload accordingly. The results of the thesis show that model-based autotuning makes it possible to increase the efficiency of applications in scientific computing regarding execution time and energy consumption. Especially, the consideration of the energy consumption of alternative execution paths, i.e. the energy adaptivity, will be of great importance in scientific computing in the near future.

The thesis entitled “Addressing subtle physicochemical features exhibited by molecular crystals via Experimental and Theoretical Charge Density Analysis” consists of five chapters. An introductory note provides a brief description of experimental and theoretical charge density methodology, followed by its utilization in obtaining certain physical and chemical properties in molecular crystals. Chapter 1 addresses not so easily accessed molecular property arising due to electron conjugation, highlighting antiaromaticity in tetracyclones. A systematic study of six tetracyclone derivatives with electron withdrawing and electron donating substituents has been carried out using experimental and theoretical charge density analysis. A three pronged approach based on quantum theory of atoms in molecules (QTAIM), nucleus independent chemical shifts (NICS), and source function (SF) has been employed to establish the degree of antiaromaticity of the central five-membered ring in all the derivatives. Electrostatic potentials mapped on the is density surface reveal the finer effects of different electron withdrawing and electron donating substituents on the carbonyl group. Chapter 2 presents a temperature induced reversible first order single crystal to single crystal phase transition (Room temperature Orthorhombic, P22121 to low temperature Monoclinic, P21) in a  hybrid peptide, Boc-γ4(R)Val-Val-OH. The thermal behavior accompanying the phase transition of the dipeptide crystal was characterized by differential scanning calorimetry, visual changes in birefringence of the sample during heating and cooling cycles on a hot-stage microscope with polarized light. Variable-temperature unit cell check measurements from 300 to 100 K showed discontinuity in the volume and cell parameters near the transition temperature, supporting the first-order behavior. The reversible nature of the phase transition is traced to be due to an interplay between enthalpy and entropy. Chapter 3 brings out an unusual stabilizing interaction involving a cooperative -hole and ¬hole character in a short NCS···NCS bond. This chapter describes structural features of four isothiocyanate derivatives, FmocXCH2NCS; X=Leu, Ile, Val and Ala. Among these it is observed that only FmocLeuCH2NCS which crystallizes in a tetragonal space group, P41, (a=b=12.4405(5) Å; c= 13.4141(8) Å) transforms isomorphously to a low temperature form, P41, (a=b=17.4665(1) Å; c= 13.1291(1) Å). The characteristics of the phase transition have been monitored by Differential Scanning Calorimetry, variable temperature IR and temperature dependent unit cell measurements. The short NCS···NCS intermolecular interaction (3.296(1) Å) is analyzed based on detailed experimental charge density analysis which reveals the nature of this stabilizing interaction. Chapter 4 explains a comparative study of syn and anti conformations of carboxylic acids in peptides from both structural aspect and charge density features. Single crystal structures of four peptides having syn conformations [BocLeuγ4(R)Valγ4(R)ValOH, BocLeuγ4(R)ValLeuγ4(R)ValOH, Boc3(S)Leu3(S)LeuOH] and one with anti conformation, BocLeuγ4(R)ValValOH have been analyzed. Experimental charge density analysis has been carried out exclusively on BocLeuγ4(R)ValValOH having anti form, because of its rare occurrence in literature. However, low temperature datasets on the four peptides with syn conformations were collected and theoretical charge density analysis has been carried out on two of these compounds. Electrostatic potentials mapped on is density surface bring out a significant difference at the oxygen atoms of the carboxyl group in the two conformations. However, lone pair orientation of different types of Oxygen atoms in the two forms (urethane, amide, acid) doesn’t exclusively indicate the differences in the corresponding charge density features. Chapter 5 addresses the issue of how sensitive are the charge density features associated with amino acid residues when the backbone conformational angles are varied. Three model systems, 1, L-alanyl–L-alanyl–L-alanine dehydrate; 2, anhydrous L-alanyl–L-alanyl–L¬alanine and 3, cyclo-(D,L-Pro)2(L-Ala)4 monohydrate have been chosen for this evaluation. Compound 1 has ant parallel alignment of tripe tide strands, and compound 2 has parallel alignment. All the alanine residues in compound 1 and 2 are in the -sheet region of the Ramachandran plot, whereas, the four Alanine residues in the cyclic hex peptide 3 span different regions of the Ramachandran plot. Theoretical multipole modelling has been carried out in order to explore the plausibility of transferring multipole parameters across different regions of Ramachandran Plot. Appendix I contains a brief description of charge shift bonding in Ph-CH2-Se-Se-CH2-Ph, as determined based on both experimental and theoretical charge density analysis. Appendix II contains a reprint of a published article on “Conformation-Changing Aggregation in Hydroxyacetone: A Combined Low-Temperature FTIR, Jet, and Crystallographic Study”.

Das wissenschaftliche Rechnen mit der Computersimulation hat sich heute als dritte Säule der wissenschaftlichen Methodenlehre neben der Theorie und dem Experiment etabliert. Aufgabe der Informatik im wissenschaftlichen Rechnen ist es, sowohl effiziente Simulationsalgorithmen zu entwickeln als auch ihre effiziente Implementierung. Die vorliegende Arbeit richtet ihren Fokus auf die effiziente Implementierung zweier wichtiger Verfahren des wissenschaftlichen Rechnens: die Schnelle Multipolmethode (FMM) für Teilchensimulationen und die Methode der finiten Elemente (FEM), die z. B. zur Berechnung der Deformation von Festkörpern genutzt wird. Die Effizienz der Implementierung bezieht sich hier auf die Ausführungszeit der Simulationen und den zur Ausführung notwendigen Energieverbrauch der eingesetzten Rechnersysteme. Die Steigerung der Effizienz wurde durch modellbasiertes Autotuning erreicht. Beim modellbasierten Autotuning wird für die wesentlichen Teile des Algorithmus ein Modell aufgestellt, das dessen Ausführungszeit bzw. Energieverbrauch beschreibt. Dieses Modell ist abhängig von Eigenschaften des genutzten Rechnersystems, von Eingabedaten und von verschiedenen Parametern des Algorithmus. Die Eigenschaften des Rechnersystems werden durch Ausführung des tatsächlich genutzten Codes für verschiedene Implementierungsvarianten ermittelt. Diese umfassen eine CPU-Implementierung und eine Grafikprozessoren-Implementierung für die FEM und die Implementierung der Nahfeld- und der Fernfeldwechselwirkungsberechnung für die FMM. Anhand der aufgestellten Modelle werden die Kosten der Ausführung für jede Variante vorhergesagt. Die optimalen Algorithmenparameter können somit analytisch bestimmt werden, um die gewünschte Zielgröße, also Ausführungszeit oder Energieverbrauch, zu minimieren. Bei der Ausführung der Simulation werden die effizientesten Implementierungsvarianten entsprechend der Vorhersage genutzt. Während bei der FMM die Performance-Messungen unabhängig von der Ausführung der Simulation durchgeführt werden, wird für die FEM ein Verfahren zur dynamischen Verteilung der Rechenlast zwischen CPU und GPU vorgestellt, das auf Ausführungszeitmessungen zur Laufzeit der Simulation reagiert. Durch Messung der tatsächlichen Ausführungszeiten kann so dynamisch auf sich während der Laufzeit verändernde Verhältnisse reagiert und die Verteilung der Rechenlast entsprechend angepasst werden. Die Ergebnisse dieser Arbeit zeigen, dass modellbasiertes Autotuning es ermöglicht, die Effizienz von Anwendungen des wissenschaftlichen Rechnens in Bezug auf Ausführungszeit und Energieverbrauch zu steigern. Insbesondere die Berücksichtigung des Energieverbrauchs alternativer Ausführungspfade, also die Energieadaptivität, wird in naher Zukunft von großer Bedeutung im wissenschaftlichen Rechnen sein. / Computer simulation as a part of the scientific computing has established as third pillar in scientific methodology, besides theory and experiment. The task of computer science in the field of scientific computing is the development of efficient simulation algorithms as well as their efficient implementation. The thesis focuses on the efficient implementation of two important methods in scientific computing: the Fast Multipole Method (FMM) for particle simulations, and the Finite Element Method (FEM), which is, e.g., used for deformation problems of solids. The efficiency of the implementation considers the execution time of the simulations and the energy consumption of the computing systems needed for the execution. The method used for increasing the efficiency is model-based autotuning. For model-based autotuning, a model for the substantial parts of the algorithm is set up which estimates the execution time or energy consumption. This model depends on properties of the computer used, of the input data and of parameters of the algorithm. The properties of the computer are determined by executing the real code for different implementation variants. These implementation variantss comprise a CPU and a graphics processor implementation for the FEM, and implementations of near field and far field interaction calculations for the FMM. Using the models, the execution costs for each variant are predicted. Thus, the optimal algorithm parameters can be determined analytically for a minimisation of the desired target value, i.e. execution time or energy consumption. When the simulation is executed, the most efficient implementation variants are used depending on the prediction of the model. While for the FMM the performance measurement takes place independently from the execution of the simulation, for the FEM a method for dynamically distributing the workload to the CPU and the GPU is presented, which takes into account execution times measured at runtime. By measuring the real execution times, it is possible to response to changing conditions and to adapt the distribution of the workload accordingly. The results of the thesis show that model-based autotuning makes it possible to increase the efficiency of applications in scientific computing regarding execution time and energy consumption. Especially, the consideration of the energy consumption of alternative execution paths, i.e. the energy adaptivity, will be of great importance in scientific computing in the near future.