Quantum theory of QSAR

Es discuteix aquí la forma de desenvolupar un formalisme on les mesures de semblança quàntiques (QSM) es transformen en un producte natural, que sorgeix d'un marc de treball específic relacionat amb la teoria quàntica. Aquesta fita s'empra per establir una connexió fonamental entre la teoria quàntica i les QSAR, que s'estudien més endavant des del punt de vista de la química quàntica discreta. A fi d'assolir aquest objectiu es revisen en un primer pas diverses eines teòriques. D'aquesta manera la primera secció s'associa a la construcció del concepte de conjunt etiquetat. Més tard, la definició d'objecte quàntic (QO) s'aclareix emprant tant el rerefons de la teoria quàntica com els conceptes previs, que formen part del formalisme de conjunt etiquetat. Per definir un QO, es demostra que les funcions de densitat (DF) tenen un paper principal i es presenta una possible forma matemàtica simplificada amb propòsits computacionals. En el camí de preparar les eines per dilucidar el problema, els conjunts convexos resulten ser prominents, mentre que la noció de semiespai vectorial, apareix com a conseqüència. Les regles de transformació, un aparell dissenyat per connectar les funcions d'ona amb les DF, es defineixen en un proper pas. També es descriuen diversos aspectes d'aquest tipus de discussió preliminar, entre altres el concepte de distribucions d'energia cinètica, que apareixen dins la definició dels espais de Hilbert generals i els espais de Sobolev. Les QSM, com una font de la representació discreta de les estructures moleculars, es fan evidents dins d'aquest concepte. Un desenvolupament posterior de la teoria intenta estudiar els processos de discretització; això és: la transformació dels espais funcionals d'infinites dimensions en espais n-dimensionals. Aquest resultat afegeix noves perspectives a la representació discreta de QO, ja que: a) esdevé una font de nous descriptors, b) descriu el fonament de les QSAR, cosa que permet la construcció de models adequats comWays of developing the formalism where Quantum Similarity Measures (QSM) become a natural product issuing from a specific mathematical framework related to quantum theory are discussed. This fact is used to establish a fundamental connection between Quantum Theory and QSAR, which is analysed in turn within the realm of discrete quantum chemistry. In order to achieve such an objective several theoretical tools are revised in a previous step. The first section is devoted to constructing the concept of the Tagged Set. Next, the definition of Quantum Object (QO) is clarified by means of Quantum Theory background ideas and the previous Tagged Set formalism. In the definition of QO, Density Functions (DF) are shown to play a fundamental role and a possible simplified mathematical picture is presented for possible computational purposes. In the process of preparing the problem-solving tools, convex sets become prominent, and the notion of Vector Semispace appears as a consequence. The Transformation Rule, a device to connect Wavefunctions with DF, is defined in a new step. Various products of this preliminary discussion are described, among them the concept of Kinetic Energy distributions, issuing from the background concept of extended Hilbert and Sobolev spaces. QSM as a source of discrete representation of molecular structures is made evident in this context. Further theoretical development undertakes precise study of discretization, that is, the transformation of infinite-dimensional functional spaces into n-dimensional ones. This result adds new perspectives to the discrete representation of QO, because a) It provides a source of new QO descriptors, b) It describes the QSAR theoretical background enabling the construction of adequate models like tuned-QSAR, and c) It allows the construction of sound and general alternatives of Hammet?s ó or log P parameters. In this context, QSM appear to produce QSAR models constructed with unbiased descriptors, deducible from quant

Role of Spin-Dependent Interactions in Chemical Reactions and Molecular Physics

This work describes development of theoretical models for applications where spin-dependent interactions play a key role. Specifically, we focus on the spin-orbit and hyperfine interactions in atoms and molecules, which are important for applications in photochemistry, photophysics, materials science, quantum sensing, and quantum computing. In the first part of this work, we discuss development and application of the nonadiabatic statistical theory (NAST) to predict kinetics of spin-forbidden chemical reactions, intersystem crossings and spin-crossovers. We describe the newly developed NAST software package and its capabilities. The package predicts the microcanonical and canonical rate constants for the nonadiabatic spin-orbit coupling driven and traditional adiabatic unimolecular reactions. In addition, the NAST package can calculate the probabilities and rate constants for transitions between individual MS components of the spin multiplets, and process the results of electronic structure calculations to generate the necessary input data for the rate calculations. The second part of this work is motivated by the proposed applications of ultracold atoms in the quantum information science. The ultracold alkali atoms trapped in inert parahydrogen matrix have been shown to possess long coherence times between the hyperfine states |├ F,m_F ⟩┤. The long coherence times make these atoms promising candidates for spin-based qubits and quantum sensors. This coherence is limited by interaction between the electron spin of the alkali metal atom and the host matrix. To explain the experimental coherence times of 39K, 85Rb, 87Rb, and 133Cs atoms, we develop a model of inhomogeneous broadening of the transitions between the |├ F,m_F ⟩┤ states due to the anisotropic hyperfine interaction between the metal and the host matrix. In the third part of this work, we model the effect of extreme variations in the speed of light on the electronic and atomic structures of small molecules. This part of work is motivated by the theories beyond the Standard Model of physics that treat the fundamental constants as dynamic entities

Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials : Simple yet Efficient

Electronic structure calculations, such as in the Hartree-Fock or Kohn-Sham density functional approach, require an initial guess for the molecular orbitals. The quality of the initial guess has a significant impact on the speed of convergence of the self-consistent field (SCF) procedure. Popular choices for the initial guess include the one-electron guess from the core Hamiltonian, the extended Huckel method, and the superposition of atomic densities (SAD). Here, we discuss alternative guesses obtained from the superposition of atomic potentials (SAP), which is easily implementable even in real-space calculations. We also discuss a variant of SAD which produces guess orbitals by purification of the density matrix that could also be used in real-space calculations, as well as a parameter-free variant of the extended Huckel method, which resembles the SAP method and is easy to implement on top of existing SAD infrastructure. The performance of the core Hamiltonian, the SAD, and the SAP guesses as well as the extended Huckel variant is assessed in nonrelativistic calculations on a data set of 259 molecules ranging from the first to the fourth periods by projecting the guess orbitals onto precomputed, converged SCF solutions in single- to triple-zeta basis sets. It is shown that the proposed SAP guess is the best guess on average. The extended Huckel guess offers a good alternative, with less scatter in accuracy.Peer reviewe

Collision-induced three-body polarizability of helium

We present first-principles theoretical determination of the three-body polarizability and the third dielectric virial coefficient of helium. Coupled-cluster theory and the full configuration interaction procedure were used to perform required electronic structure calculations. The mean absolute relative uncertainty of the trace of the three-body polarizability tensor, resulting from the incompleteness of orbital basis set, was determined using extrapolation techniques. Additional uncertainty due to approximate treatment of triple and the neglect of higher excitations was estimated using full configuration interaction calculations. An analytic function was developed to describe the behavior of the polarizability and its asymptotic decay to three-atomic and atom-diatom fragmentation channels. We also developed an analytic function describing the local behavior of the total uncertainty of our calculations. Using both fits we calculated the third dielectric virial coefficient and its uncertainty using the classical and semiclassical Feynman-Hibbs approaches. The results of our calculations were compared with available experimental data and with recent Path-Integral Monte Carlo (PIMC) calculations employing the so-called superposition approximation of the three-body polarizability. For temperatures above 200 K we observed significant discrepancy between the classical results obtained using either the superposition approximation or the ab initio computed polarizability. The theoretical data reported in this work eliminate the main accuracy bottleneck of the development of optical pressure standard and are expected to facilitate further progress in the field of quantum thermal metrologyComment: 30 pages, 7 figure

Topics in Modern Quantum Optics

This is the written version of lectures presented at "The 17th Symposium on Theoretical Physics - Applied Field Theory", 29 June - 1 July, 1998, the Sangsan Mathematical Science Building, Seoul National University, Seoul, Korea.Comment: 97 pages, 23 figures, 187 references. Misprints corrected, most figures redrawn and references update

Theoretical studies of molecular machines

Only volume 2 has been digitized.Molecular machines are essential components of living organisms. They are highly efficient and robust, much more than their macroscopic analogs. This stimulated growing interest in construction of artificial molecular machines with a set of functions which may be controlled in a specific way. Such man-made molecular complexes are designed as the building blocks for future nanotechnological devices. During the last decades many new molecular machines have been synthesized and characterized by various experimental techniques. This significantly increased our knowledge about systems of such kind and their functioning. However, there are only a few real applications of molecular machines. This is because the fundamental principles of operation of such single-molecule systems are not well understood. Existing theoretical studies, although very helpful, are still very sparse. This is because the molecular machines are very complex systems, comprising up to thousands atoms. Thus the progress in our understanding of nanoscale materials is tightly related to development of efficient computational and theoretical methodologies. In this work we studied two large classes of molecular machines: surface-moving nanocars and molecular rotors/motors, working on the surfaces and in crystalline state. In particular we studied the role of the internal interactions of these machines as well as their interactions with the environment. This included the flexibility of the molecules, including the rotation of the nanocars' wheels, effects of surface and rotors symmetry, charge transfer effects as well as many other factors. We have found out relations which determine the properties of studied classes of molecular machines. The development of computational and theoretical methods was another essential part of this work. In particular we have developed a family of the surface-molecule interaction potentials, aimed to performing long time scale and molecular simulations of complex systems. We also developed a physics-based model of the charge transfer happening between metals and the nanocars. This opened new ways to control such molecular machines. We also developed a theoretical framework to predict response of molecular rotors on various types of driving. Finally, we developed new and improved existing rigid-body molecular dynamics methods and extensively used them in our studies of molecular machines

Molecular simulations as test beds for bridging high throughput and high performance computing

La forte connotation de la chimie computationnelle en termes de technologies informatiques est en même temps la force et la faiblesse des simulations moléculaires. En effet, dans le but de réaliser des études de ce type(même pour les systèmes contenant un petit nombre d'atomes), il faut d'abord procéder à des calculs de structure électronique de haut niveau. Ces calculs nécessitent généralement des nœuds (ou clusters de nœuds) équipés de mémoires de grande taille (de l'ordre de plusieurs Go), et de processeurs performants au niveau de plusieurs Gigaflops. Celà parce que la surface d'énergie potentielle ensemble (PES) qui régît le mouvement nucléaire doit être élaborée préalablement. Sur des plate-formes High Performance Computing (HPC) avec des capacités parallèles améliorées nous pouvons exécuter simultanément, sur plusieurs single (ou clusters de) processeurs multicœurs, le calculs requis par le grand nombre des valeurs d'énergie potentielles nécessaires pour décrire les PES explorés par une processus de réactivité chimique. Le véritable goulot d'étranglement dans la réalisation des calculs nécessaires, en effet, est représentée par la disponibilité d'une plate-forme informatique ayant des exigences informatiques appropriées en matière de temps de calcul et de mémoire physique. Les capacités de calcul (limitée) en général accessibles à la communauté scientifique, en fait, a toujours fixé des limites sévères à l'élaboration d'un système informatique complet de simulation a priori des processus moléculaires. Heureusement, des technologies informatiques innovantes, alliant la concurrence et la mise en réseau (tels que l'informatique distribuée, les laboratoires virtuels, le calcul intensif, le "Grid computing") ouvrent des perspectives nouvelles à la possibilité de réaliser d'importants débits de calcul et, par conséquent, de développer des simulations moléculaires a priori des systèmes réels. Les fondements théoriques et les paradigmes informatiques utilisés pour l'assemblage des composants du "Grid Empowered Molecular Simulator" (GEMS) sont décrits dans le Chapitre 1. Dans ce chapitre, nous illustrons le développement de workflows basés sur la grille, qui permettent l'évaluation ab initio des propriétés observables des systèmes chimiques petits à partir du calcul des propriétés électroniques. Dans le chapitre 2 nous abordons la question de l'interopérabilité entre codes de calcul à travers les différentes étapes du flux de travail (workflow). Ce chapitre propose les formats Q5cost et D5cost comme modèles "standard de facto" pour les calculs de chimie quantique. Le Chapitre 3 porte sur les résultats de calculs ab initio autonomes effectués sur des différents systèmes chimiques (petits clusters X_4 (X=Li,Na,K,Cu) ainsi que le dimère BeH-). Le chapitre traite des liaisons chimiques particulières et intéressantes présentes dans ces systèmes, qui nécessitent de méthodes quantiques de haut niveau à fin d'une possible rationalisation. Enfin, les chapitre 4 et 5 concernent respectivement les résultats de notre travail sur deux problèmes de combustion et la chimie atmosphérique (l'isomérisation CH3CH2OO• et la réaction N2+N2). Ils visent tous les deux à la construction des PES pour un processus réactif. Une fois la PES générée, les données cinétiques et dynamiques doivent être calculées pour un grand nombre de conditions initiales, et cela peut être fait sur des plateformes HTC. L'assemblage des workflows informatiques pour l'utilisation couplée des systèmes HPC et HTC est également traitée dans cette thèse.The strong connotation of computational chemistry in terms of computer technologies is at the same time the strength and the weakness of molecular simulations. As a matter of fact, in order to perform such studies (even for few-atom systems) we first need to carry out high-level electronic structure calculations. These calculations typically require nodes (or clusters of nodes) equipped with large (of the order of many GB) memories and processors performing at the level of several Gigaflops. This is because the whole Potential Energy Surface (PES) governing the nuclear motion needs to be worked out first. On the High Performance Computing (HPC) platforms with enhanced parallel capabilities we can run concurrently, on several single multicore (or clusters of) processors, the calculations required by the (large number of) potential energy values necessary to describe the PES explored by a reactive chemical process. The real bottleneck in carrying out related computational campaigns, indeed, is represented by the availability of a computing platform having the proper computational requirements in terms of computing time and physical memory. The (limited) computing capabilities in general available to the scientific community, in fact, still set severe limitations to the development of full a priori computational simulations of molecular processes. Fortunately, innovative computing technologies combining concurrency and networking (such as distributed computing, virtual laboratories, supercomputing, Grid computing) are opening new prospects to the possibility of achieving significant computational throughputs and, therefore, of developing a priori molecular simulations of real systems. The theoretical foundations and the computing paradigms employed for the assemblage of the components of the Grid Empowered Molecular Simulator GEMS are described in Chapter 1. In that chapter the development of grid based workflows allowing the ab initio evaluation of the observable properties of small chemical systems starting from the calculation of the electronic properties is illustrated. In Chapter 2 the issue of the of interoperability between computational codes across different stages of the workflow is faced. The Chapter proposes Q5cost and D5cost common data models as de facto standard formats for quantum chemistry calculations. Chapter 3 relates to the results of standalone ab initio calculations performed on different small chemical systems (X4 clusters and BeH- dimer). The Chapter discusses particular and interesting chemical bonds requiring high-level quantum methods to the end of being rationalized. Finally Chapter 4 and Chapter 5 report the results of our work on two combustion and atmospheric chemistry problems (CH3CH2OO• isomerization and N2+N2 reaction) respectively. They both aim at constructing the PES for a reactive process. Once a PES is generated, the kinetic and dynamical data need to be calculated for a large number of initial conditions, and can be computed on HTC platforms. The assemblage of the computational workflows for the coupled use of HPC and HTC systems is also dealt there