Strong electron correlations in electronic structure theory are purely quantum effects arising as a result of degeneracies in molecules and materials, and exhibit significantly different yet interesting characters than do weak correlations. Although weak correlations have recently been able to be described very efficiently and accurately within single particle pictures, less known are good prescriptions for treating strong correlations efficiently. Brute-force calculations of strong correlations in wave function theories tend to be very computationally-intensive, and are usually limited to small molecules for applications. Breaking symmetry in a mean-field approximation is an efficient alternative to acquire strong correlations with, in many cases, qualitatively accurate results. The symmetry broken in quantum chemistry has been traditionally of spin, in so-called unrestricted methods, which typically break spatial symmetry as a consequence, and vice versa, in most situations. In this work, we present a novel approach to accurately describing strong correlations with a mean-field cost by means of Hartree- Fock-Bogoliubov (HFB) theory. We are inspired by the number-symmetry-breaking in HFB, which, with an attractive particle interaction, accounts for strong correlations, while maintaining spin and spatial symmetry. We show that this attractive interaction must be restricted to the chemically-relevant orbitals in an active space to obtain physically meaningful results. With such constraints, our constrained pairing mean-field theory (CPMFT) can accurately describe potential energy curves of various strongly-correlated molecular systems, by cleanly separating strong and weak correlations. To achieve the correct dissociation limits in hetero-atomic molecules, we have modified our CPMFT functional by adding asymptotic constraints. We also include weak correlations by combining CPMFT with density functional theory for chemically accurate results, and reveal the connection between CPMFT and traditional unrestricted methods. The similarity between CPMFT and unrestricted methods leads us to the idea of constrained active space unrestricted mean-field approaches. Motivated by CPMFT, we partially retrieve spin-symmetry that has been fully broken in unrestricted methods. We allow symmetry breaking only in an active space. This constrained unrestricted Hartree-Fock (CUHF) is an interpolation between two extrema: the fully broken-symmetry solution and the symmetry preserved solution. This thesis defines the theory behind and reports the results of CUHF. We first show that, if an active space is chosen to include only open-shell electrons, CUHF reduces to restricted open-shell Hartree-Fock (ROHF), and such CUHF proves in many ways significantly

Density-functional theory has become an indispensible tool for studying matter on the atomic level, being routinely applied across diverse disciplines from solid-state physics to chemistry and molecular biology. Its failure to account for dispersion interactions has spurred intensive research over the past decade. In this thesis, a semilocal density-functional approximation including dispersion is developed by combining standard functionals for exchange and correlation with the nonempirical “exchange-hole dipole moment“ (XDM) dispersion model of Becke and Johnson. With a minimum of empiricism, the method accurately describes all types of noncovalent interactions, from the extremely weak dispersion forces in rare-gas systems to the hydrogen bonding and stacking interactions responsible for the structure and function of biological macromolecules such as DNA and proteins. The method is compatible with a wide variety of standard Gaussian basis sets, and is easily applied to any system that can be modeled with density-functional theory.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第14868号 / 工博第3136号 / 新制||工||1470(附属図書館) / 27290 / UT51-2009-K664 / 京都大学大学院工学研究科分子工学専攻 / (主査)教授 榊 茂好, 教授 今堀 博, 教授 杉野目 道紀 / 学位規則第4条第1項該当

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23220号 / 工博第4864号 / 新制||工||1759(附属図書館) / 京都大学大学院工学研究科分子工学専攻 / (主査)教授 佐藤 啓文, 教授 佐藤 徹, 教授 田中 勝久 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

Over the years electronic structure theory has proven to be a powerful method with which one can probe the behaviour of materials, making it possible to predict properties that are difficult to measure experimentally. The numerical tools needed for these methods are always in need of development, since the desire to calculate more complex materials pushes this field forward. This thesis contains work on both this implementational and developmental aspects. In the first part we investigate the structural properties of the 6d transition metals using the exact muffin-tin orbitals method. It is found that these elements behave similarly to their lighter counterparts, except for a few deviations. In these cases we argue that it is relativistic effects that cause this anomalous behaviour. In the second part we assess the Padé approximant, which is used in several methods where one wants to include many-body effects into the electronic structure. We point out difficulties that can occur when using this approximant, and propose and evaluate methods for their solution. / <p>QC 20130219</p>

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京都大学 / 新制・課程博士 / 博士(工学) / 甲第24634号 / 工博第5140号 / 新制||工||1982(附属図書館) / 京都大学大学院工学研究科分子工学専攻 / (主査)教授 佐藤 啓文, 教授 佐藤 徹, 教授 松田 建児 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

Kohn-Sham density functional theory is a rigorous formulation of many-electron quantum mechanics which, for practical purposes, requires approximation of one term in its total energy expression: the exchange-correlation energy. This work elucidates systematic methods for constructing approximations to the exchange-correlation energy solely from first-principles physics. We review the constraints that can be built into approximate density functionals, and use thermochemical data to argue that satisfaction of these constraints permits a more general description of electronic matter. Contact with semiclassical physics is made by studying the turning surfaces of Kohn-Sham potentials in solids. Perfect metals and covalently-bound, narrow-gap insulators do not have turning surfaces at equilibrium, but do under expansive strain. Wide-gap insulators, ionic crystals, and layered solids tend to have turning surfaces at equilibrium. Chemical bonds in solids are classified using the turning surface radii of its constituent atoms. Depletion of the charge density, such as near a monovacancy in platinum, is shown to produce a turning surface. Further, this work demonstrates why generalized gradient approximations (GGAs) are often able to describe some properties of sp-bonded narrow-gap insulators well. A Laplacian-level pure-density functional is developed with the goal of describing metallic condensed matter. This functional is derived from the r2SCAN orbital-dependent meta-GGA, and reduces its tendency to over-magnetize ferromagnets; improves its description of the equation of state properties of alkali metals; and improves its description of intermetallic thermodynamics. It is constructed to enforce the fourth-order exchange gradient expansion constraint (not satisfied by r2SCAN), and a few free parameters are fitted to paradigmatic metallic systems: jellium surfaces and closed-shell jellium clusters. Last, we modify an exchange-correlation kernel that describes the density-density response of jellium to better satisfy known frequency sum rules. We also constrain the kernel to reproduce the correlation energies of jellium, and compare it to a wide variety of common kernels in use for linear response, time-dependent density functional theory calculations. / Physics

Electronic structure methods aim to accurately describe the behaviour of the electrons in molecules and materials. To be applicable to arbitrary systems, these methods cannot depend on observations of specific chemical phenomena and must be derived solely from the fundamental physical constants and laws that govern all electrons. Such methods are called ab initio methods. Ab initio methods directly solve the electronic Schrödinger equation to obtain the electronic energy and wavefunction. For more than one electron, solving the electronic Schrödinger equation is impossible, so it is imperative to develop approximate methods that cater to the needs of their users, which can vary depending on the chemical systems under study, the available computational resources and time, and the desired level of accuracy. The most accessible ab initio approaches, including Hartree-Fock methods and Kohn-Sham density functional theory methods, assume that only one electronic configuration is needed to describe the system. While these single-reference methods are successful when describing systems where a single electron configuration dominates, like most closed-shell ground-state organic molecules in their equilibrium geometries, single-reference methods are unreliable for molecules in nonequilibrium geometries (e.g., transition states) and molecules containing unpaired electrons (e.g., transition metal complexes and radicals). For these types of multireference systems, accurate results can only be obtained if multiple electronic configurations are accounted for. Wavefunctions that incorporate many electronic configurations are called multideterminant wavefunctions. This thesis presents a systematic approach to developing multideterminant wavefunctions. First, we establish a framework that outlines the structural components of a multideterminant wavefunction and propose several novel wavefunction ansätze. Then, we present a software package that is designed to aid the development of new wavefunctions and algorithms. Using this approach, we develop an algorithm for evaluating the geminal wavefunctions, a class of multideterminant wavefunctions that are expressed with respect to electron pairs. Finally, we explore using machine learning to solve the Schrödinger equation by presenting a neural network wavefunction ansatz and optimizing its parameters using stochastic gradient descent. / Thesis / Doctor of Science (PhD)

<p dir="ltr">Theoretical development and implementation of Partition Density Functional Theory, a quantum density embedding framework for electronic structure simulation.</p>