프로그램

 

 

1월 17일 (화)

 

13:50~14:00

개회 및 인사말 

 

 

14:00~17:00

강의제목 Fundamentals of Density Functional Theory  

강사 유재준 교수 (서울대학교)

강의 소개 We will discuss basic concepts, theories, and methods behind density functional theory (DFT). DFT is a computational quantum mechanical modeling method used in physics, chemistry, and materials science to investigate the electronic structure of many-body systems, particularly atoms, molecules, and condensed phases. We hope to provide a broad perspective on current electronic structure theory and background for practical computations, starting points of advanced topics such as exchange-correlational functional, pseudopotential theory, time-dependent DFT, many-body perturbation theory, and DFT-DMFT (dynamical mean-field theory). This course aims at graduate and post-graduate students in theoretical and computational condensed matter physics.

참고자료

• Richard M. Martin, Electronic Structure: basic theory and practical methods (Cambridge University Press, 2004) (ISBN 0 521 78285 6)
• ICTP Workshop “Hands-on Workshop on Density Functional Theory and Beyond: Computational Materials Science for Real Materials,” (6-15 August 2013), http://th.fhi-berlin.mpg.de/sitesub/meetings/DFT-workshop-2013/index.php?n=Meeting.Program

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1월 18일 (수)

 

10:00 ~ 12:00

강의제목 Time dependent density functional theory in real time: linear and nonlinear optical respons

강사 Prof. Kazuhiro Yabana (Univ of Tsukuba)

강의 소개 Time-dependent density functional theory (TDDFT) is a framework that extends the usual static density functional theory to describe the motion of electrons when a time-dependent external field is applied. In this lecture, I will explain how TDDFT can be used to calculate the motion of electrons caused by light irradiating an isolated system (molecules and nanoparticles) or a periodic system (crystals). 
I will then present the applications of TDDFT to the ultrafast motion of electrons and nonlinear optical responses caused by the interaction of intense ultrashort pulsed light and matter, which are actively studied in the field of advanced optical science. 

Furthermore, an attempt to describe the propagation of intense pulsed light by coupling TDDFT with Maxwell's equations for electromagnetic fields will be presented. 

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14:00~17:00

강의제목 Ab initio DMFT methodologies for correlated quantum materials

강사 최상국 교수 (KIAS)

강의 소개 In materials with a large number of electrons, the quantum mechanical interactions between these electrons often dictate the material’s properties. These so-called correlated quantum materials display a range of exceptional emergent phenomena, including transitions from metal to insulator states, colossal magnetoresistance, and high-temperature superconductivity and even topological superconductivity.

The prediction of correlated quantum materials properties from first principles poses a grand challenge for condensed matter physics and materials science. Correlated quantum materials defy current band-picture-based ab initio methodologies, such as density functional theory. In these materials, there are fine details beyond band-picture descriptions due to their quantum many electron nature. To illustrate, quasiparticle peak comes with finite width and there can be a satellite peak next to the quasiparticle peak. In some cases, there is no one-to-one correspondence between mean-field band structure and measured one-electron spectra and band-picture description fails.

In this lecture, we present ab initio DMFT as one of the most successful methodologies to understand correlated quantum materials. This Green's function based method goes beyond the band-picture and has been successful in explaining many features of correlated quantum materials. We discuss the theoretical basis of this Green's function based approach and introduce multiple variations of ab initio DMFT. Additionally, we provide supportive data to validate ab initio DMFT.

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1월 19일 (목)

 

10:00~12:00

강의제목 Understanding and Overcoming Systematic Errors in Density Functional Theory

강사 Prof. Weitao Yang (Duke Univ)

강의 소개 The systematic delocalization and static/strong correlation errors underlie many challenges in density functional theory (DFT) calculations. These errors can be understood based on the fractional perspectives: they are the systematic deviation of the density functional approximations from the exact conditions on fractional charges and spins derived from the principle of quantum mechanics on degenerate states.   This will be presented in the first part of the lecture.

The second part of the lecture covers current effort in addressing these errors. We developed a localized orbital scaling correction (LOSC): it accurately characterizes the distributions of global and local fractional electrons and spins, and is thus capable of correcting system energy, energy derivative and electron density in a size-consistent manner. Our approach introduces the explicit derivative discontinuity and largely restores the flat-plane behavior of electronic energy at fractional charges and fractional spins. The LOSC–DFAs lead to systematically improved results, including the dissociation of ionic species, single bonds, multiple bonds without breaking the space or spin symmetry, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra, and energy-level alignments for interfaces. The LOSC DFA orbital energies are excellent approximations to quasiparticle energies, comparable to or better than GW. This also leads to the QE-DFT (quasiparticle energies from DFT) approach: the calculations of excitation energies of the N-electron systems from the ground state DFA calculations of the (N - 1)-electron systems. Results show good performance with accuracy similar to TDDFT for valence excitations with commonly used DFAs with or without LOSC. For charge transfer and Rydberg states, good accuracy was obtained only with the use of LOSC DFA.  The QE-DFT method has been further developed to describe excited-state potential energy surfaces (PESs), conical intersections, and the analytical gradients of excited-state PESs. We have also made the LOSC software available for the community. 

참고자료

• J. Cohen, P. Mori-Sanchez, and W. Yang. Insights into current limitations of density functional theory. Science, 321:792, 2008.

• P. Mori-Sánchez, A. J. Cohen, and W. Yang, “Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction,” Physical Review Letters, 100: 146401, 2008.

• P. Mori-Sanchez, A. J. Cohen, and W. Yang. Discontinuous Nature of the Exchange-Correlation Functional in Strongly Correlated Systems, Physical Review Letters, 102:066403, 2009.

• J. Cohen, P. Mori-Sanchez, and W. Yang. Challenges for Density Functional Theory.  Chem. Rev.   112:289, 2012

• C. Li, X. Zheng, N. Q. Su, and W. Yang, “Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations,” National Science Review, 5: 203–215, 2018.

• N. Q. Su, C. Li, and W. Yang, “Describing strong correlation with fractional-spin correction in density functional theory,” Proceedings of the National Academy of Sciences, 115:9678–9683, 2018.

• Y. Mei, C. Li, N. Q. Su, and W. Yang, “Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn-Sham Calculations,” arXiv:1810.09906 2018; J. Phys. Chem. A, 123(3), 666–673, 2019

• 8.Y. Mei and W. Yang, “Excited-State Potential Energy Surfaces, Conical Intersections, and Analytical Gradients from Ground-State Density Functional Theory,” J. Phys. Chem. Lett. 10, 2538–2545, 2019. 

• Mei, Y.; Chen, Z.; Yang, W. Self-Consistent Calculation of the Localized Orbital Scaling Correction for Correct Electron Densities and Energy-Level Alignments in Density Functional Theory. J. Phys. Chem. Lett., 11 (23), 10269, 2020

• 10.Mei, Y.; Yu, J.; Chen, Z.; Su, N. Q.; Yang, W. LibSC: Library for Scaling Correction Methods in Density Functional Theory. J. Chem. Theory Comput. 2022, 18 (2), 840–850.

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14:00~17:00

강의제목 극성/강유전 산화물 기초 이론과 제일원리 계산 및 응용

강사 이재광 교수 (부산대학교)

강의 소개 본 강의에서는 극성 산화물에서 나타나는 특이한 charge compensation 현상과 강유전 산화물에서의 depolarization/magnetoelectric effect 기초 이론을 제일원리 계산 결과와 함께 소개하고자 한다. Ferroelectric tunneling junction (FTJ) 기초 이론과 강유전성 산화물을 이용한 FTJ 터널링 전류 simulation에 대해서 소개하고자 한다.

참고자료

• Claudine Noguera, J. Phys.: Condens. Matter 12 R367 (2000).

• Jaekwang Lee, Na Sai, Tianyi Cai, Qian Niu, Alexander A Demkov, PRB 81 144425 (2010).

• Vincent Garcia & Manuel Bibes, Nature Communications 5 4289 (2014).

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1월 20일 (금)

 

09:30~12:30

강의제목 양자수송 계산의 이론과 실제(Theory and pracitce of quantum transport calculations)

강사 김용훈 교수 (KAIST)

강의 소개 본 강의에서는 표준적인 밀도범함수론(density funcitonal theory, DFT)과는 다르게 (1) 열린 계(open system), (2) 비평형 계(non-equilibrium system)를 다룬다는 관점에서 나노소자 양자수송(quantum transport) 계산의 기초 개념과 실제 계산법을 소개한다. 

   첫번째 강의에서는 열린 계를 기술한다는 관점에서 섭동이론적으로 행렬 그린함수(matrix Green's function)를 정의하고 자체에너지(self-energy) 등의 연관 개념을 확립한다. 양자수송 계산의 표준적인 이론인 비평형 그린함수론(non-equilibrium Green's function, NEGF)과 광여기(optical excitaion) 상황에서의 준입자(quasi-particle)를 다루는 표준적인 이론인 GW 방법론 간의 연결 고리 등이 강조될 것이다. 

   두번째 강의에서는 비평형 상황에서 작동하는 나노소자를 다루는 표준적 틀(framework)인 란다우어 관점(Landauer picture)을 설명하고 이를 기반으로 하는 DFT-NEGF 이론을 소개한다. NEGF 이론의 원형이 닫힌 비평형 계 이론이라는 점이 상기될 것이며 이 관점에서 양자수송 현상이 나타나는 열린 비형형 계를 다루기 위한 개발된 DFT-NEGF 방법론은 란다우어 관점과 NEGF 이론의 접목으로 파생되는 별도의 이론 체계임이 강조될 것이다. 이러한 이해를 바탕으로 전압이 인가된 상황의 DFT-NEGF 계산을 엄밀히 수행하기 위한 전제 조건들을 제시할 것이다. 

   마지막 강의에서는 우리 그룹에서 개발한 다공간 범함수론(multi-space DFT, MS-DFT)을 바탕으로 양자수송 계산 이론 체게의 더욱 깊은 이해를 도모한다. 구체적으로 DFT-NEGF 방법론의 기반인 란다우어 관점이 MS-DFT 이론에서는 양자수송의 다공간 여기(multi-space excitation) 관점으로 치환됨을 설명하고 그 결과 대정준(grand canonical) 계를 소정준(microcanonical) 계로 다룰 때 주어지는 장점들을 구체적인 예들을 들어 설명한다. 

  DFT 및 다체계 섭동이론으로 대표되는 beyond DFT 이론들의 장단점에 대한 고찰을 바탕으로 차세대 제1원리 계산의 바람직한 방향에 대한 질문을 던지며 본 강의를 마무리 하고자 한다. 

강의록

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14:00~17:00

강의제목 제1원리 양자수송 계산 실습

강사 이룡규 박사과정 (KAIST)

강의 소개 앞선 이론 강의에 이어 이번 시간에는 TranSIESTA 코드를 활용한 양자수송 계산 실습을 진행합니다. 코드 설치를 포함한 실습 자료가 아래 wiki 사이트에 업로드 될 예정이므로 수강생들은 실습 전까지 해당 사이트를 지속적으로 체크해 주시기를 바랍니다.

참고자료 

• https://yhkimlab.github.io/yhkimlabwiki/site/