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>

No description available.

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)

Accurate correlated electronic structure methods involve a significant amount of computations and can be only employed to small molecular systems. For example, the coupled-cluster singles, doubles, and perturbative triples model (CCSD(T)), which is known as the ``gold standard" of quantum chemistry for its accuracy, usually can treat molecules with 20-30 atoms. To extend the reach of accurate correlated electronic structure methods to larger molecular systems, we work towards two directions: parallel computing and reduced-cost/scaling approaches. Parallel computing can utilize more computational resources to handle systems that demand more substantial computational efforts. Reduced-cost/scaling approaches, which introduce approximations to the existing electronic structure methods, can significantly reduce the amount of computation and storage requirements. In this work, we introduce a new distributed-memory massively parallel implementation of standard and explicitly correlated (F12) coupled-cluster singles and doubles (CCSD) with canonical bigO{N^6} computational complexity ( C. Peng, J. A. Calvin, F. Pavov{s}evi'c, J. Zhang, and E. F. Valeev, textit{J. Phys. Chem. A} 2016, textbf{120}, 10231.), based on the TiledArray tensor framework. Excellent strong scaling is demonstrated on a multi-core shared-memory computer, a commodity distributed-memory computer, and a national-scale supercomputer. We also present a distributed-memory implementation of the density-fitting (DF) based CCSD(T) method. (C. Peng, J. A. Calvin, and E. F. Valeev, textit{in preparation for submission}) An improved parallel DF-CCSD is presented utilizing lazy evaluation for tensors with more than two unoccupied indices, which makes the DF-CCSD storage requirements always smaller than those of the non-iterative triples correction (T). Excellent strong scaling is observed on both shared-memory and distributed-memory computers equipped with conventional Intel Xeon processors and the Intel Xeon Phi (Knights Landing) processors. With the new implementation, the CCSD(T) energies can be evaluated for systems containing 200 electrons and 1000 basis functions in a few days using a small size commodity cluster, with even more massive computations possible on leadership-class computing resources. The inclusion of F12 correction to the CCSD(T) method makes it converge to basis set limit much more rapidly. The large-scale parallel explicitly correlated coupled-cluster program makes the accurate estimation of the coupled-cluster basis set limit for molecules with 20 or more atoms a routine. Thus, it can be used rigorously to test the emerging reduced-scaling coupled-cluster approaches. Moreover, we extend the pair natural orbital (PNO) approach to excited states through the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method. (C. Peng, M. C. Clement, and E. F. Valeev, textit{submitted}) We simulate the PNO-EOM-CCSD method using an existing massively parallel canonical EOM-CCSD program. We propose the use of state-averaged PNOs, which are generated from the average of the pair density of excited states, to span the PNO space of all the excited states. The doubles amplitudes in the CIS(D) method are used to compute the state-averaged pair density of excited states. The issue of incorrect states in the state-averaged pair density, caused by an energy reordering of excited states between the CIS(D) and EOM-CCSD, is resolved by simply computing more states than desired. We find that with a truncation threshold of $10^{-7}$, the truncation error for the excitation energy is already below 0.02 eV for the systems tested, while the average number of PNOs is reduced to 50-70 per pair. The accuracy of the PNO-EOM-CCSD method on local, Rydberg and charge transfer states is also investigated. / Ph. D.

No description available.

Accurate energetic modeling of large molecular systems is always desired by chemists. For example, ligand-protein binding simulations and enzymatic catalysis studies all involve with a small energy difference. The energetic accuracy depends largely on a proper handling of electronic correlations. Molecular mechanics (MM) methods deliver a parameterized Newtonian treatment to these problems. They show great capability in handling large calculations but give only qualitatively good results. Quantum mechanics (QM) methods solve Schrödinger equations and exhibit much better energy accuracy, though the computational cost can be prohibitive if directly applied to very large systems. Fragment-based methods have been developed to decompose large QM calculations into fragment calculations. However, most current schemes use a self- consistent field (SCF) method on fragments, in which no electronic correlation is accounted for. The super-system energy is computed as a sum of fragment energies plus two-body corrections and, possibly, three-body corrections (a "body" is a fragment). Higher order corrections can be added. Nevertheless, many problems require the treatment of high order electronic correlations. The coupled-cluster (CC) theory is the state-of-the-art QM method for handling electronic correlations. The CC wavefunction contains correlated excitations up to a given truncated level and coincidental excitations for all possible electronic excitations. It is a brilliant way of including more electronic correlations while maintaining a low-order scaling. In the proposed excitonic coupled-cluster (X-CC) theory, substantial modifications have been made to allow CC algorithms to act on the collective coordinates of fragment fluctuations to obtain super-system energy. The X-CC theory is designed to achieve accurate energetic modeling results for large chemical systems with much improved affordability and systematic improvability. The test system used in this work is a chain of beryllium atoms. A 30-fragment X-CCSD(2) calculation delivered matching accuracy with traditional CCSD method. An X-CCSD(2) calculation on a chain of 100 bonded fragments finished in 7 hours on a single 2.2 GHz CPU core. The X-CC scheme also demonstrates the ability in handling charge transfer problems. Due to the use of fluctuation basis in the test cases, the excitonic algorithms can be easily generalized to inhomogeneous systems. This will be investigated in future work.