Density functional calculation of thermal expansion of γ-GeSe

김선아 Graduate School, Yonsei University 2023 국내석사

In present Master’s Thesis, , I report the magnitude and the anisotropy of the thermal expansion of γ-GeSe. Chapter 1 provides an overview of my research and includes a review of density functional theory and density functional perturbation theory, which I utilize to determine the thermal expansion properties. In Chapter 2, we discuss the quasi-harmonic approximation and the framework for obtaining thermal expansion. In Chapter 3, we obtain and compare linear thermal expansion coefficients and volume thermal expansion coefficients of non-central symmetry γ-GeSe and central symmetry γ-GeSe. We obtain lattice constants of γ-GeSe as a function of temperature based on the density function theory. γ-GeSe is a hexagonal layered material whose unit cell consists of two quadruple layers of Se-Ge-Ge-Se. To obtain lattice constants as a function of temperature, we calculate the total energy of the system as a function of lattice constants without considering any atomic vibration by using the density functional theory and we calculate phonon frequencies in the full Brillouin zone as functions of lattice constants by using the density functional perturbation theory. With these results, we obtain the Helmholtz free energy as a function of lattice constants and temperature. Finally, by finding lattice constants which minimize the free energy at each temperature, we obtain the lattice constants as a function of temperature. Chapter 4 summarizes the study of thermal expansion coefficients for two stacked of γ-GeSe and concludes this Master’s Thesis. The conclusion of this Master’s Thesis provide a the thermal properties of γ- GeSe.

A Density Functional Odyssey Beyond Ground State Energies

Hait, Diptarka University of California, Berkeley ProQuest Disser 2022 해외박사(DDOD)

소속기관이 구독 중이 아닌 경우 오후 4시부터 익일 오전 9시까지 원문보기가 가능합니다.

Density functional theory or DFT is presently the most popular route for computing the electronic structure of chemical systems. Although DFT is formally exact, the exact functional that maps the electron density to the energy remains unknown to date. A large number of density functional approximations (DFAs) have consequently been developed to compute the energies of molecules and extended materials. Use of exact constraints, large amounts of highly accurate benchmark data, and intelligent data-driven design schemes have resulted in modern functionals that provide an excellent balance between computational cost and predictive accuracy. However, nearly all the DFA development efforts in recent years had focused on improving chemically relevant energy differences in the ground state. Even the electron density, which is the central quantity of the theory, has been mostly neglected. This dissertation tries to explore usage of DFT beyond ground state energies through the investigation of electrical response properties and electronic excited states. Information from these regimes should prove helpful extending the applicability of DFT beyond computation of ground state energy differences, and also assist in designing more transferable DFAs that better approximate the exact functional.The first half of the dissertation assesses the accuracy of modern DFAs in predicting molecular properties associated with the response of the energy to electric fields. The exact functional is formally capable of predicting exact energies even when the system is subjected to arbitrary electric fields. However, approximate functionals only model the electrical response well if the density is accurate. The ability of DFAs to compute electrical response properties thus indicate their accuracy in modeling densities. The dissertation therefore studies dipole moments (Chapter 4), second cumulants of the density (Chapter 5) and static dipole polarizabilities (Chapter 6). High level coupled cluster benchmarks at the complete basis set limit for ≥ 100 chemical species has been generated for all the three properties. These benchmark datasets are used to evaluate the performance of several popular and recent functionals, in order to gauge performance. This analysis reveals that some of the most accurate modern DFAs for ground state energies yield suboptimal predictions for electrical response properties. Future DFA development therefore should utilize these benchmark datasets for training and assessment purposes, in order to obtain functionals that simultaneously yield accurate energies and densities. In addition, we use the static dipole polarizability as a sensitive probe for electronic structure in Chapter 7, to identify qualitative problems in DFAs. This demonstrates that several modern DFAs are challenged by homolytic single bond dissociation, as they fail to completely unpair electrons over the right distance scales. The material in this half of the dissertation therefore provides information about how existing functionals struggle to model density, and should be helpful for the design of more accurate DFAs.The second half of the dissertation examines behavior for electronic excited states, focusing on the popular linear-response time-dependent DFT (TDDFT) and the less well known orbital optimized DFT (OO-DFT) approaches. Chapter 10 shows that TDDFT methods cannot describe bond dissociations in the excited state, developing unphysical derivative discontinuities at the onset of spin unpairing in the ground state. The other chapters focus on OO-DFT, and applications to core spectroscopy. Chapter 11 presents a robust new algorithm for excited state OO, that ensures the optimization process remains on the chosen state and does not undergo ‘variational collapse’, to a lower energy state. This SquareGradient Minimization or SGM algorithm is used to model core-level excitations for closed-shell systems (Chapter 12) and radicals (Chapter 13), using OO-DFT. Chapter 13 also presents a scheme to recouple three unpaired electrons to obtain spin-pure doublets, which are relevant for core to unoccupied orbital transitions in radicals. The results of Chapter 12 and 13 demonstrate the OO-DFT with the SCAN DFA can model core-level spectra of second period elements to semiquantitative accuracy of ∼ 0.3 eV, against experimental values with ∼ 0.1 eV uncertainty. This is a dramatic improvement over the ∼ 15 eV errors observed from TDDFT, indicating that OO-DFT/SCAN is a cheap and reliable way to model core-level spectra. Indeed, OO-DFT/SCAN can be directly used to simulate experimental spectra, such as time-resolved X-ray transient absorption studies of chemical dynamics. The energies and densities of these core-excited states also provide new information for functional training beyond ground state energies. Incorporation of this very distinct form of data in the DFA development process thus can help better approximate the exact functional.

Hybrid functional study on electronic structure of d⁰ and d¹ titanates

Bora Lee 서울대학교 대학원 2012 국내박사

The density functional theory (DFT) has been successfully applied to studying a wide range of properties in various materials. However, the application of the conventional DFT has been particularly limited for several cases. The typical drawback of the conventional DFT is the band gap underestimation. In addition, the electronic structure of the strongly correlated system, such as transition metal oxide, shows a large discrepancy in the experimental results. Several methods have been employed to go beyond the conventional DFT, for example, the LDA + U method, Hartree-Fock approximation, and dynamic mean-field theory. Recently, the hybrid functional method is also attracting interests as it allows for correctly estimating the energy gap of the material. In this method, a part of the exact exchange energy is mixed with a semilocal functional. The basic recipe for the mixing coefficient is to add 25% of the exact exchange term, and 25% is determined based on the perturbation theory. This choice has been shown to produce reasonable energy gaps for many materials. By using the hybrid functional method, we exploit the theoretical ground state properties of rutile and anatase TiO2 and SrTiO3 (d0-titanate), Ti2O3 (d1-titanate), and Ti4O7 (mixed-valence titanate). We find not only the electronic property but also the atomic structure is improved by hybrid functional for d0-titanate. However, we introduce the modified mixing coefficient in order to fit the energy gap to the exact experimental value. In addition, the adjusted lattice parameters are used for the accurate dielectric constant of high-k titanates. For Ti2O3 and Ti4O7, which are metal-insulator transition material with a small energy gap of 0.1 eV for low temperature structure, we observe the theoretical band gap is almost ten times larger than experimental values by the hybrid functional with the mixing coefficient of 0.25. In the same manner of d0-titanates, we reduce the mixing coefficient for the narrow energy gap. The optimized hybrid functional provides the improved structural parameters as well as the electronic structures. In addition, we discuss the magnetic properties and the high temperature structure by the optimized hybrid functional.

Curing abnormality in density functional theory : density-corrected density functional theory

김민철 Graduate School, Yonsei University 2015 국내박사

Density functional theory (DFT) is a widely used method for various fields due to its reasonable accuracy and moderate cost. However, standard approximate functionals used in DFT often give questionable results in many systems including odd-electron complexes, molecular binding and dissociation, reaction barrier heights and etc. This usually originates from self-interaction error. In this work, I go through the recently proposed scheme to classify problematic DFT calculations and fix various calculations using density-corrected density functional theory (DC-DFT)I start from a simple two-electron system to illustrate the overall scheme. By error decomposition, DFT calculations can be classified into ‘normal’ calculations and ‘abnormal’ calculations. I show that a Kohn-Sham HOMO-LUMO gap can be used as an indicator for this abnormality, and DC-DFT can be used as a simple cure in abnormal calculations. Based on this theory, I apply DC-DFT to many cases that DFT is well-known to give incorrect results.First, electron affinity of small molecular anions is calculated with both conventional Kohn-Sham DFT (KS DFT) and DC-DFT. This is a normal case where KS DFT works fairly well, but even so, DC-DFT gives slightly better electron affinities and does not suffer from positive HOMO eigenvalues.Second, potential energy surfaces (PES) of odd-electron complexes (HO?Cl? and HO?H2O) are evaluated. The comparison between calculated PES’ of KS DFT and DC-DFT clearly show this is an abnormal calculation, where DC-DFT is far superior and KS DFT results have as mall HOMO-LUMO gap.Finally I explore the reaction pathway of molecules via dissociation curve study of diatomic molecules. It shown that the HOMO difference of the dissociated fragments can be used as an indicator of abnormality, where the molecular HOMO value is not well-defined. Also it is shown that for abnormal cases, DC-DFT can cure incorrect dissociation limits and charge distributions.

Density functional theory calculations on charge density wave phases of monolayer 1T-VSe2

정지안 숙명여자대학교 대학원 2021 국내석사

그래핀 박리에 성공한 이후, 차세대 전자재료에의 응용 가능성과 벌크와는 다른 독특한 물성으로 인해 육각질화붕소, 흑린, 전이금속칼코겐화합물 (TMDCs)을 비롯한 그래핀과 유사한 2차원 층상 구조 물질에 대한 연구가 활발하게 이루어지기 시작했다. 최근 TMDCs의 일종인 1T-VSe2는 단일층에서의 자기적 성질과 전하밀도파 상이 명확히 밝혀지지 않아 새로이 관심을 받고 있다. 실험적으로 발견된 단일층 1T-VSe2의 전하밀도파 상에 대한 논의가 계속되고 있으므로 밀도범함수 계산은 전하밀도파를 밝히기 위한 좋은 수단이 될 수 있다. 우리는 밀도범함수에 기초한 제1원리 계산을 사용해 단일층 1T-VSe2의 전하밀도파에 대한 연구를 수행하였다. 우선 단일층 1T-VSe2의 원자와 전자 구조를 조사하였다. 그 후 포논 분산 밴드 계산을 수행해 가능한 전하밀도파의 주기와 포논 왜곡 구조를 얻었다. 포논 왜곡 구조를 충분히 최적화시키는 것으로 전하밀도파 구조를 얻었다. 우리는 단일층 1T-VSe2의 가장 안정한 전하밀도파 상을 에너지 비교를 통해 확인하여 제시하였다. 각각의 전하밀도파 구조의 원자와 전자 구조를 조사하여 선행 실험 연구 결과와 비교하였다. 나아가 √21×√3 전하밀도파 상에서 스핀을 고려한 시스템과 전하 도핑 된 시스템에 대해 조사하여 CDW 상에서의 단일층 1T-VSe2의 전하 도핑 되지 않은 시스템과 전하 도핑 된 시스템에서의 자성을 밝혔다. Since the exfoliation of graphene, lots of studies have been performed on graphene-like two-dimensional layered materials such as hexagonal boron nitride, black phosphorous, and transition metal dichalcogenides (TMDCs), due to their possibility in application to next-generation electronic materials and the peculiar physical properties distinct to bulk. Recently, monolayer 1T-VSe2, a type of TMDCs attracted novel interest due to its ambiguous magnetic property and charge density wave (CDW) phase. Since the experimentally discovered the CDW phase of monolayer 1T-VSe2 is still under debate, density functional theory calculations can be a good way to unveil the charge density wave phase of monolayer 1T-VSe2. In this study, we investigated the charge density wave (CDW) phases of monolayer 1T-VSe2 by applying first-principles calculations based on density functional theory. First, we investigated the atomic and electronic structures of pristine monolayer 1T-VSe2. Then we performed phonon dispersion band calculation and demonstrated the probable charge density wave periodicities and the phonon modulated structures. By relaxing the phonon distorted structures, we obtained charge density wave structures with superlattice periodicities of 4×1, 4×4, √7×√3 and √21×√3. We proposed the energetically most favorable charge density wave phase of the monolayer 1T-VSe2 system by comparing the total energies of each CDW phase. We addressed the atomic and electronic structures of each charge density wave phase and compared them with the previous studies. Moreover, we investigated the spin-polarized system and doped system of the √21×√3 CDW phase and revealed the magnetic property in both undoped and doped system proposed in the CDW phase.

All-Electron Ground-State and Time-Dependent Density Functional Theory: Fast Algorithms and Better Approximations

Kanungo, Bikash ProQuest Dissertations & Theses University of Mich 2019 해외박사(DDOD)

소속기관이 구독 중이 아닌 경우 오후 4시부터 익일 오전 9시까지 원문보기가 가능합니다.

Density functional theory (DFT), in its ground-state as well as time-dependent variant, have enjoyed incredible success in predicting a range of physical, chemical and materials properties. Although a formally exact theory, in practice DFT entails two key approximations---(a) the pseudopotential approximation, and (b) the exchange-correlation approximation. The pseudopotential approximation models the effect of sharply varying core-electrons along with the singular nuclear potential into a smooth effective potential called the pseudopotential, thereby mitigating the need for a highly refined spatial discretization. The exchange-correlation approximation, on the other hand, models the quantum many-electron interactions into an effective mean-field of the electron density (ρ(r)), and, remains an unavoidable approximation in DFT.The overarching goal of this dissertation work is ---(a) to develop efficient numerical methods for all-electron DFT and TDDFT calculations which can dispense with the pseudopotentials without incurring huge computational cost, and (b) to provide key insights into the nature of the exchange-correlation potential that can later constitute a route to systematic improvement of the exchange-correlation approximation through machine learning algorithms (i.e., which can learn these functionals using training data from wavefunction-based methods). This, in turn, involves---(a) obtaining training data mapping ρ(r) to vxc(r), and (b) using machine learning on the training data (ρ(r) Leftrightarrow vxc(r) maps) to obtain the functional form of vxc[ρ(r)], with conformity to the known exact conditions.The research efforts, in this thesis, constitute significant steps towards both the aforementioned goals. To begin with, we have developed a computationally efficient approach to perform large-scale all-electron DFT calculations by augmenting the classical finite element basis with compactly supported atom-centered numerical basis functions. We term the resultant basis as enriched finite element basis. Our numerical investigations show an extraordinary 50-300-fold and 5-8-fold speedup afforded by the enriched finite element basis over classical finite element and Gaussian basis, respectively. In the case of TDDFT, we have developed an efficient a priori spatio-temporal discretization scheme guided by rigorous error estimates based on the time-dependent Kohn-Sham equations. Our numerical studies show a staggering 100-fold speedup afforded by higher-order finite elements over linear finite elements. Furthermore, for pseudopotential calculations, our approach achieve a 3-60-fold speedup over finite difference based approaches. The aforementioned a priori spatio-temporal discretization strategy forms an important foundation for extending the key ideas of the enriched finite element basis to TDDFT. Lastly, as a first step towards the goal of machine-learned exchange-correlation functionals, we have addressed the challenge of obtaining the training data mapping ρ(r) to vxc(r). This constitute generating accurate ground-state density, ρ(r), from wavefunction-based calculations, and then inverting the Kohn-Sham eigenvalue problem to obtain the vxc(ρ) that yields the same ρ(r). This is otherwise known as the inverse DFT problem. Heretofore, this remained an open challenge owing lack of accurate and systematically convergent numerical techniques. To this end, we have provided a robust and systematically convergent scheme to solve the inverse DFT problem, employing finite element basis. We obtained the exact vxc corresponding to ground-state densities obtained from configuration interaction calculations, to unprecedented accuracy, for both weak and strongly correlated polyatomic systems ranging up to 40 electrons. This ability to evaluate exact vxc's from ground-state densities provides a powerful tool in the future testing and development of approximate exchange-correlation functionals.

Computational studies on the electron-phonon interaction of intrinsic and doped semiconductors

임재모 서울대학교 대학원 2024 국내박사

Semiconductors are arguably the most important group of materials in modern electronics. The interaction between the electrons and the lattice, i.e., the electron-phonon interaction, is present in all semiconductors and plays a decisive role in shaping the electronic properties of semiconductors. Since the electron-phonon coupling depends on various material-dependent parameters, a first-principles method that can give quantitative predictions without any empirical input is highly desirable. In recent years, there has been much interest and development in ab initio methods for calculating electron- phonon interactions. Density functional perturbation theory,Wannier functions, and Boltzmann transport equations have become well-established, standard methods in the ab initio community. However, these methods are still limited in their scope in terms of systems or properties that they can address. Further theoretical and methodological efforts are needed to expand the scope of first- principles electron-phonon calculations. In this thesis, we present computational studies on the electron-phonon coupling in intrinsic and doped semiconductors. We focus on the method- ological aspect of this subject and present advancements in each of the three fundamental aspects of electron-phonon calculations: screening, downfolding, and response calculations. In the first part, we study the dynamical screening of phonons and electron-phonon coupling in polar doped semiconductors due to plasmons. The non-adiabatic plasmon-phonon coupling has not been studied from first principles due to its complicated frequency dependence. We develop a simple yet accurate extended adiabatic model that captures the frequency dependence as well as the broadening of the plasmon-phonon hybrid modes. We also analyze how these hybrid excitations couple to the electrons. The developed method is applied to study plasmon-phonon coupling and electron spectral functions in GaAs and TiO2. In the second part, we develop a new downfolding method, which we termed Wannier function perturbation theory, that can incorporate the response of the Wannier basis functions to the atomic displacements. This method provides a localized representation of the wavefunction perturbation due to phonons, enabling an efficient interpolation of this quantity in momentum space. Using this method, we compute the phonon-induced band structure renormalization of silicon with a speedup of three orders of magnitude compared to the state-of-the- art method. Utilizing this large speedup, we perform a predictive calculation of the indirect optical absorption of silicon. Our calculation is the first calculation that reproduces both the redshift and smoothening of the kink of the absorption spectra due to an increase in the temperature. In the last part, we incorporate the effect of electronic Berry curvature in the study of phonon-limited electronic transport using the Boltzmann transport equation. We find a large increase and a sizable frequency dependence in the nonlinear Hall conductivity of n-doped GeTe which are not captured by the widely-used Berry curvature dipole theory. We decompose the conductivities into the contribution of relaxons, normal modes of the dynamics with well- defined lifetimes. We find that long-lived relaxons whose eigenstate represent the polarization of carriers in different valleys lead to the enhanced and frequency-dependent nonlinear Hall response. Keywords: Density functional theory, Wannier functions, electron-phonon coupling, nonlinear Hall effect Student ID: 2018-20336 반도체는 현대 전자공학에 가장 중요한 물질군 중 하나이다. 반도체 내부의 전자와 반도체를 이루는 격자의 상호작용은 전기적 성질에 매우 중요한 영향을 미친다. 전자와 양자화된 격자 진동인 포논 사이의 상호작용은 물질에 따라 매우 다양한 양상을 띄기 때문에, 이를 기술하기 위해서는 실험에 의한 입력값 없이도 정량적인 예측을 줄 수 있는 제일원리 방법의 사용이 필요하다. 최근 수 년간 제일원리 전자구조계산 분야에서 전자-포논 계산이 많은 관심을 받고 있으며, 밀도 범함수 섭동 이론, 바니어 함수, 볼츠만 수송 방정식 등이 표준적인 방법론으로 자리잡았다. 그러나, 이러한 방법들은 이론의 한계 상 다룰 수 있는 물질이나 물성의 종류에 한계가 있으며, 이를 극복하고 전자-포논 상호작용 계산의 적용 범위를 확장하기 위해서는 새로운 이론 및 방법론을 개발하는 연구가 필요하다. 본 학위논문에서는 반도체에서의 전자-포논 상호작용에 대한 계산 연구를 진행하였으며, 특히 방법론 개발에 주목하여 전자-포논 계산의 중요한 세 단계인 가리기, 모델 만들기, 반응 특성 계산 각각에 대해 기존 이론의 한계를 극복한 새로운 방법론을 제안하였다. 첫째로, 도핑된 반도체에서의 플라즈몬에 의한 동적 가리기 효과를 연구하였다. 포논과 플라즈몬은 비슷한 에너지 영역을 차지아므로, 그 상호작용은 단열 근사로 기술되지 않으며, 복잡한 주파수 의존성을 띄고, 이로 인해 제일원리 계산으로 거의 연구되지 않았다. 이 연구에서는 단순하지만 정확한 확장 단열 근사 모형을 개발하여 플라즈몬-포논 복합 모드의 에너지 및 분산, 그리고 이 복합 모드와 전자와의 상호작용을 계산하였다. 개발된 방법론을 통해 도핑된 비소화 갈륨 및 이산화 타이타늄의 플라즈몬-포논 복합 모드와 전자 스펙트럼 함수를 계산하였다. 둘째로, 원자 움직임에 따른 기저 함수의 변화를 묘사할 수 있는 새로운 모델화 방법인 바니어 함수 섭동 이론을 개발하였다. 이 방법을 이용하면 기존의 바니어 함수 방법과 달리 파동함수 뿐 아니라 포논에 의한 파동함수 섭동 역시 국소화된 기저 함수로 표현하고 운동량 공간에서 효율적으로 내삽할 수 있다. 바니어 함수 섭동 이론을 이용하여 규소의 포논에 의한 전자 밴드 구조의 재규격화를 계산하였으며, 기존의 방법과 비교하여 1,000배 이상 계산 속도가 향상됨을 확인하였다. 또한, 이를 바탕으로 규소의 적외선 영역 흡광 스펙트럼을 계산하였는데, 이는 온도에 따른 흡광 스펙트럼 변화의 특징인 적색편이와 기울기 변화를 처음으로 모두 재현한 제일원리 계산 결과이다. 마지막으로, 전자 베리 곡률의 효과를 볼츠만 수송 계산에 적용하는 방법론을 개발하였다. 이를 이용하여 전자가 도핑된 저마늄 텔루라이드의 비선형 홀 전도도가 기존의 예측에 비해 커지고 또한 독특한 주파수 의존성을 갖게 됨을 예측하였다. 이 결과의 물리적 원인을 분석하기 위해서 릴랙손 방법을 도입하여 전도도를 여러 정규 모드가 주는 기여의 합으로 분해하였다. 이를 통해 밴드 구조의 여러 골짜기에 전자 밀도를 편극시키는 정규 모드가 특히 긴 수명을 가지며 비선형 홀 전도도에 큰 영향을 준다는 것을 발견하였다.

Multi-State Density Functional Theory (MS-DFT) and Multi-State Energy Decomposition Analysis (MS-EDA)

Hettich, Christian Peter University of Minnesota ProQuest Dissertations & T 2025 해외박사(DDOD)

소속기관이 구독 중이 아닌 경우 오후 4시부터 익일 오전 9시까지 원문보기가 가능합니다.

This work presents the theory and application of a multistate energy decomposition analysis (MS-EDA), making use of multistate density functional theory (MSDFT). Through this research, a method has been developed that can be conveniently used to elucidate the energy terms contributing to intermolecular interactions of molecular complexes in electronically excited states. Multistate density functional theory is a novel quantum theory that employs matrix density as the fundamental variable both for the ground state and for excited states. The method goes beyond the Hohenberg-Kohn theorems for one electronic state and treats all electronic states on an equal footing. Chapter 1 reviews the fundamental principles and theorems of MSDFT and introduces the concepts of minimal active space (MAS) and matrix correlation functional. In addition, the computational procedure and approximations of non-orthogonal state interaction (NOSI) are presented, upon which the remainder of the research and calculation is built.Chapter 2 summarizes the development of a block-localized excitation (BLE) approach for self-consistent-field (SCF) optimization of excited state (non-aufbau) configurations. The BLE method is a form of delta SCF (∆SCF) procedure using a projection scheme in molecular orbital basis that matches the order and occupation of the initial, predefined electronic configuration. The main novelty of the BLE method is to allow block localization of molecular orbitals on individual molecules in a molecular complex or a subset of atomic orbitals belonging to a given symmetry. Consequently, it is possible to optimize a set of non-orthogonal block-localized molecular orbitals for a system in which one molecule is excited to an excited configuration in the presence of other molecules in the ground state. The individually optimized excited configurations are used to form a minimal active space for subsequent MSDFT-NOSI calculations to determine the energies of the adiabatic ground and excited state as well as their densities. The BLE method is illustrated in the study of excimer formation for a naphthalene dimer and a preliminary analysis of energy terms of binding interactions was presented. The BLE method was further applied in Chapter 3 to a group of bi-molecular complexes that have low-lying charge transfer states. It was shown that both local covalent and intermolecular charge-transfer excited states can be adequately treated by using MSDFT-NOSI along with MAS in which individual configurations are optimized by the BLE method.The computed excitation energies, including charge-transfer states, from NOSI calculations employing the M06-2X functional to approximate the diagonal terms of the matrix correlation functional along with the cc-pVDZ basis functions are in good accord with results from EOM-CCSDT benchmarks.Chapters 4 and 5 rigorously formulate the theory, define energy terms for intermolecular interactions in excited states, and present findings from applications of energy decomposition analyses on a range of molecular complexes in excited states. In the present MS-EDA approach, energy terms associated with interactions in the ground state are grouped into a single term called local interaction energy and the focus of the energy decomposition analysis is placed on energy terms unique to excited states. These include the exciton resonance energy due to the electronic coupling interactions among locally excited states of individual monomers, the super-exchange stabilization energy due to forward and backward charge transfer states between two monomers, and orbital and configuration delocalization energy as a result of expanding the molecular orbitals from block-localized states to full molecular orbitals over the entire molecular complex and determinant configurations that specifically included in the MAS. A key feature in the MS-EDA method is that all intermediate states are variationally optimized using the BLE technique. It was found that molecular complexes in excited states can be categorized into three types: (1) encounter excited-state complex, (2) charge-transfer exciplex, and (3) intimate excimer or exciplex. For all examples, MS-EDA's decomposition of the binding energy allows for an unambiguous identification of the excitation character.Finally, in Chapter A, the bond dissociation process of methyl radical in excited states is summarized, providing insights into the interplay of diabatic states corresponding to different electronic states of the dissociated species. The active space in this chapter has one noteworthy difference from the examples in all other chapters. In all of those examples, the off-diagonal elements of the Hamilton matrix functional have generally small contributions from their WFT-style terms. In this methyl dissociation example however, the NOSI-MSDFT procedures and TDFs that we developed are applied to valence-bond style determinants. This demonstrates that these procedures and TDFs are also applicable to such an active space, which is characterized by strong WFT-style contributions to the interactions between determinants (and by a large overlap between determinants).In summary, this work illustrates the computational method, accuracy and the wide range of applications of nonorthogonal state interaction in multistate density functional theory. It is hoped that the MS-EDA method will be a useful tool for understanding the nature of intermolecular interactions of excimers and exciplexes.

High-Accuracy and Low-Cost Electronic Structure Theory for Strongly Correlated Systems

Zhang, Dayou University of Minnesota ProQuest Dissertations & T 2023 해외박사(DDOD)

소속기관이 구독 중이 아닌 경우 오후 4시부터 익일 오전 9시까지 원문보기가 가능합니다.

Electronic structure theory is a powerful tool to study chemical systems, but it is very challenging to apply accurately to strongly correlated systems. Despite significant recent progress, a high-accuracy and low-cost electronic structure theory for strongly correlated systems is not available. This is partly related to the scarcity of accurate reference data for developing and testing improved theories, but it is also due to insufficient fundamental understanding of the ingredients necessary for a theory of a strongly correlated system to be accurate. This thesis addresses these issues. It includes benchmark studies on the spin-splitting energy of transition metals and their use to test a variety of wave function theories and density functionals in Kohn– Sham density functional theory, providing guidance as to which electronic structure method might be accurate for practical calculations, as well as providing accurate reference data for future theory development. It also contains the development of several analysis tools for improving fundamental understanding of existing theories. The results provide insight into the sources of errors in correlation energies and into improvements of existing theories. Finally, based on the discoveries of this work, a new theoretical framework named multiconfiguration density-coherence functional theory (MC-DCFT) is presented. The new theoretical framework provides an alternative approach to combining multiconfiguration wave functions with density functional theory, making it a promising method for further development.

Effect of electron density on torsional energy profile in density functional theory

조은별 Graduate School, Yonsei University 2020 국내석사

분자의 회전에너지는 분자 내 단일 결합의 회전에 의해 달라지는 에너지를 의미한다. 회전장벽은 특히 전체 최저 에너지와 국소 최고 에너지 혹은 전체 최고 에너지와의 차이를 뜻한다. 회전에너지의 전체 크기는 크지 않지만 다양한 이론 연구 연구 혹은 실험에 대한 분석에 있어서 정확히 알아야 할 필요가 있다. 본 연구에서는 그 동안 밀도범함수의 한계점 중 하나로 알려진 회전에너지의 오류가 어디서 기인했는지를 분석하였다. 이 때 효율적인 오류 분석을 위해 회전장벽 3가지를 새롭게 정의하였다. 하트리폭 밀도를 사용한 밀도보정-밀도범함수법을 사용하면 회전에너지의 오류가 감소한다는 사실을 통해 오류의 주요한 원인으로 밀도가 작용한다는 가능성을 확인했다. 이것을 회전 에너지의 모양에 상관없이 비틀린 구조에서 밀도 민감도 값이 최대가 된다는 결과를 통해 사실로 확인했다. 또한 하트리폭 밀도와 콘샴 밀도를 2가지 에너지 선 위에서 측정한 밀도기인오류 비교를 통해 하트리폭 밀도가 정답 밀도와 더 가까이 존재함을 확인했다. 이런 결과들을 종합해 회전에너지 계산에서 더 정확한 하트리폭 밀도를 사용하여 하트리폭-밀도범함수법의 오류를 개선할 수 있음을 알아냈다. I show that density-driven error affects the accuracy of density functional calculations not only for strong intermolecular interactions but also for weak intramolecular torsion. Density-driven errors are caused by inaccurate self-consistent density and can be corrected using exact density rather than approximate density. For the data set of glyoxal and its derivatives, self-consistent density-functional theory (SC-DFT) lacks quantitative accuracy and sometimes fails to predict the correct equilibrium conformation. The density-corrected calculation by Hartree-Fock density-functional theory (HF-DFT),which evaluates DFT energy on Hartree-Fock density, not only reduces the error of torsional barriers by half but also achieves highly accurate torsional energy profiles at all angles.