Pub Date : 2024-06-11DOI: 10.1088/2516-1075/ad4b80
William Dawson, Louis Beal, Laura E Ratcliff, Martina Stella, Takahito Nakajima, Luigi Genovese
Literate programming—the bringing together of program code and natural language narratives—has become a ubiquitous approach in the realm of data science. This methodology is appealing as well for the domain of Density Functional Theory (DFT) calculations, particularly for interactively developing new methodologies and workflows. However, effective use of literate programming is hampered by old programming paradigms and the difficulties associated with using high performance computing (HPC) resources. Here we present two Python libraries that aim to remove these hurdles. First, we describe the PyBigDFT library, which can be used to setup materials or molecular systems and provides high-level access to the wavelet based BigDFT code. We then present the related remotemanager library, which is able to serialize and execute arbitrary Python functions on remote supercomputers. We show how together these libraries enable transparent access to HPC based DFT calculations and can serve as building blocks for rapid prototyping and data exploration.
{"title":"Exploratory data science on supercomputers for quantum mechanical calculations","authors":"William Dawson, Louis Beal, Laura E Ratcliff, Martina Stella, Takahito Nakajima, Luigi Genovese","doi":"10.1088/2516-1075/ad4b80","DOIUrl":"https://doi.org/10.1088/2516-1075/ad4b80","url":null,"abstract":"Literate programming—the bringing together of program code and natural language narratives—has become a ubiquitous approach in the realm of data science. This methodology is appealing as well for the domain of Density Functional Theory (DFT) calculations, particularly for interactively developing new methodologies and workflows. However, effective use of literate programming is hampered by old programming paradigms and the difficulties associated with using high performance computing (HPC) resources. Here we present two Python libraries that aim to remove these hurdles. First, we describe the PyBigDFT library, which can be used to setup materials or molecular systems and provides high-level access to the wavelet based BigDFT code. We then present the related <monospace>remotemanager</monospace> library, which is able to serialize and execute arbitrary Python functions on remote supercomputers. We show how together these libraries enable transparent access to HPC based DFT calculations and can serve as building blocks for rapid prototyping and data exploration.","PeriodicalId":42419,"journal":{"name":"Electronic Structure","volume":"5 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-06DOI: 10.1088/2516-1075/ad43d0
Vladislav Borisov
Solid state theory, density functional theory and its generalizations for correlated systems together with numerical simulations on supercomputers allow nowadays to model magnetic systems realistically and in detail and can be even used to predict new materials, paving the way for more rapid material development for applications in energy storage and conversion, information technologies, sensors, actuators etc. Modeling magnets on different length scales (between a few Ångström and several micrometers) requires, however, approaches with very different mathematical formulations. Parameters defining the material in each formulation can be determined either by fitting experimental data or from theoretical calculations and there exists a well-established approach for obtaining model parameters for each length scale using the information from the smaller length scale. In this review, this approach will be explained step-by-step in textbook style with examples of successful scale-bridging modeling of different classes of magnetic materials from the research literature as well as based on results newly obtained for this review.
{"title":"From electronic structure to magnetism and skyrmions","authors":"Vladislav Borisov","doi":"10.1088/2516-1075/ad43d0","DOIUrl":"https://doi.org/10.1088/2516-1075/ad43d0","url":null,"abstract":"Solid state theory, density functional theory and its generalizations for correlated systems together with numerical simulations on supercomputers allow nowadays to model magnetic systems realistically and in detail and can be even used to predict new materials, paving the way for more rapid material development for applications in energy storage and conversion, information technologies, sensors, actuators etc. Modeling magnets on different length scales (between a few <inline-formula>\u0000<tex-math><?CDATA $mathrm{unicode{x00C5}}$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mtext>Å</mml:mtext></mml:mrow></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"estad43d0ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>ngström and several micrometers) requires, however, approaches with very different mathematical formulations. Parameters defining the material in each formulation can be determined either by fitting experimental data or from theoretical calculations and there exists a well-established approach for obtaining model parameters for each length scale using the information from the smaller length scale. In this review, this approach will be explained step-by-step in textbook style with examples of successful scale-bridging modeling of different classes of magnetic materials from the research literature as well as based on results newly obtained for this review.","PeriodicalId":42419,"journal":{"name":"Electronic Structure","volume":"38 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-29DOI: 10.1088/2516-1075/ad45d4
Raul Laasner, Iuliia Mandzhieva, William P Huhn, Johannes Colell, Victor Wen-zhe Yu, Warren S Warren, Thomas Theis and Volker Blum
This paper reports and benchmarks a new implementation of nuclear magnetic resonance shieldings, magnetizabilities, and J-couplings for molecules within semilocal density functional theory, based on numeric atom-centered orbital (NAO) basis sets. NAO basis sets are attractive for the calculation of these nuclear magnetic resonance (NMR) parameters because NAOs provide accurate atomic orbital representations especially near the nucleus, enabling high-quality results at modest computational cost. Moreover, NAOs are readily adaptable for linear scaling methods, enabling efficient calculations of large systems. The paper has five main parts: (1) It reviews the formalism of density functional calculations of NMR parameters in one comprehensive text to make the mathematical background available in a self-contained way. (2) The paper quantifies the attainable precision of NAO basis sets for shieldings in comparison to specialized Gaussian basis sets, showing similar performance for similar basis set size. (3) The paper quantifies the precision of calculated magnetizabilities, where the NAO basis sets appear to outperform several established Gaussian basis sets of similar size. (4) The paper quantifies the precision of computed J-couplings, for which a group of customized NAO basis sets achieves precision of ∼Hz for smaller basis set sizes than some established Gaussian basis sets. (5) The paper demonstrates that the implementation is applicable to systems beyond 1000 atoms in size.
{"title":"Molecular NMR shieldings, J-couplings, and magnetizabilities from numeric atom-centered orbital based density-functional calculations","authors":"Raul Laasner, Iuliia Mandzhieva, William P Huhn, Johannes Colell, Victor Wen-zhe Yu, Warren S Warren, Thomas Theis and Volker Blum","doi":"10.1088/2516-1075/ad45d4","DOIUrl":"https://doi.org/10.1088/2516-1075/ad45d4","url":null,"abstract":"This paper reports and benchmarks a new implementation of nuclear magnetic resonance shieldings, magnetizabilities, and J-couplings for molecules within semilocal density functional theory, based on numeric atom-centered orbital (NAO) basis sets. NAO basis sets are attractive for the calculation of these nuclear magnetic resonance (NMR) parameters because NAOs provide accurate atomic orbital representations especially near the nucleus, enabling high-quality results at modest computational cost. Moreover, NAOs are readily adaptable for linear scaling methods, enabling efficient calculations of large systems. The paper has five main parts: (1) It reviews the formalism of density functional calculations of NMR parameters in one comprehensive text to make the mathematical background available in a self-contained way. (2) The paper quantifies the attainable precision of NAO basis sets for shieldings in comparison to specialized Gaussian basis sets, showing similar performance for similar basis set size. (3) The paper quantifies the precision of calculated magnetizabilities, where the NAO basis sets appear to outperform several established Gaussian basis sets of similar size. (4) The paper quantifies the precision of computed J-couplings, for which a group of customized NAO basis sets achieves precision of ∼Hz for smaller basis set sizes than some established Gaussian basis sets. (5) The paper demonstrates that the implementation is applicable to systems beyond 1000 atoms in size.","PeriodicalId":42419,"journal":{"name":"Electronic Structure","volume":"88 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141193141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-29DOI: 10.1088/2516-1075/ad4d46
Matheus Jacobs, Karen Fidanyan, Mariana Rossi and Caterina Cocchi
Electron dynamics at weakly bound interfaces of organic/inorganic materials are easily influenced by large-amplitude nuclear motion. In this work, we investigate the effects of different approximations to the equilibrium nuclear distributions on the ultrafast charge-carrier dynamics of a laser-excited hybrid organic/inorganic interface. By considering a prototypical system consisting of pyrene physisorbed on a MoSe2 monolayer, we analyze linear absorption spectra, electronic density currents, and charge-transfer dynamics induced by a femtosecond pulse in resonance with the frontier-orbital transition in the molecule. The calculations are based on ab initio molecular dynamics with classical and quantum thermostats, followed by time-dependent density-functional theory coupled to multi-trajectory Ehrenfest dynamics. We impinge the system with a femtosecond (fs) pulse of a few hundred GW cm−2 intensity and propagate it for 100 fs. We find that the optical spectrum is insensitive to different nuclear distributions in the energy range dominated by the excitations localized on the monolayer. The pyrene resonance, in contrast, shows a small blue shift at finite temperatures, hinting at an electron-phonon-induced vibrational-level renormalization. The electronic current density following the excitation is affected by classical and quantum nuclear sampling through suppression of beating patterns and faster decay times. Interestingly, finite temperature leads to a longer stability of the ultrafast charge transfer after excitation. Overall, the results show that the ultrafast charge-carrier dynamics are dominated by electronic rather than by nuclear effects at the field strengths and time scales considered in this work.
有机/无机材料弱结合界面上的电子动力学很容易受到大振幅核运动的影响。在这项工作中，我们研究了平衡核分布的不同近似值对激光激发的有机/无机混合界面的超快电荷载流子动力学的影响。通过考虑由物理吸附在 MoSe2 单层上的芘组成的原型系统，我们分析了线性吸收光谱、电子密度电流以及飞秒脉冲与分子中前沿轨道转变共振诱导的电荷转移动力学。计算基于带有经典和量子恒温器的 ab initio 分子动力学，然后是与多轨迹 Ehrenfest 动力学相耦合的时变密度泛函理论。我们用强度为几百 GW cm-2 的飞秒 (fs) 脉冲冲击该系统并传播 100 fs。我们发现，在单层局部激发的能量范围内，光谱对不同的核分布并不敏感。相反，芘共振在有限温度下显示出微小的蓝移，暗示了电子-声子诱导的振动级重正化。激发后的电子电流密度受到经典和量子核取样的影响，跳动模式受到抑制，衰变时间加快。有趣的是，有限温度导致激发后的超快电荷转移具有更长的稳定性。总之，研究结果表明，在本研究考虑的场强和时间尺度下，超快电荷载流子动力学是由电子效应而非核效应主导的。
{"title":"Impact of nuclear effects on the ultrafast dynamics of an organic/inorganic mixed-dimensional interface","authors":"Matheus Jacobs, Karen Fidanyan, Mariana Rossi and Caterina Cocchi","doi":"10.1088/2516-1075/ad4d46","DOIUrl":"https://doi.org/10.1088/2516-1075/ad4d46","url":null,"abstract":"Electron dynamics at weakly bound interfaces of organic/inorganic materials are easily influenced by large-amplitude nuclear motion. In this work, we investigate the effects of different approximations to the equilibrium nuclear distributions on the ultrafast charge-carrier dynamics of a laser-excited hybrid organic/inorganic interface. By considering a prototypical system consisting of pyrene physisorbed on a MoSe2 monolayer, we analyze linear absorption spectra, electronic density currents, and charge-transfer dynamics induced by a femtosecond pulse in resonance with the frontier-orbital transition in the molecule. The calculations are based on ab initio molecular dynamics with classical and quantum thermostats, followed by time-dependent density-functional theory coupled to multi-trajectory Ehrenfest dynamics. We impinge the system with a femtosecond (fs) pulse of a few hundred GW cm−2 intensity and propagate it for 100 fs. We find that the optical spectrum is insensitive to different nuclear distributions in the energy range dominated by the excitations localized on the monolayer. The pyrene resonance, in contrast, shows a small blue shift at finite temperatures, hinting at an electron-phonon-induced vibrational-level renormalization. The electronic current density following the excitation is affected by classical and quantum nuclear sampling through suppression of beating patterns and faster decay times. Interestingly, finite temperature leads to a longer stability of the ultrafast charge transfer after excitation. Overall, the results show that the ultrafast charge-carrier dynamics are dominated by electronic rather than by nuclear effects at the field strengths and time scales considered in this work.","PeriodicalId":42419,"journal":{"name":"Electronic Structure","volume":"88 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141193147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-27DOI: 10.1088/2516-1075/ad4b81
Ritwik Das, Subhadeep Bandyopadhyay and Indra Dasgupta
The quantum anomalous Hall effect resulting from the in-plane magnetization in the OsCl3 monolayer is shown to exhibit different electronic topological phases determined by the crystal symmetries and magnetism. In this Chern insulator, the Os-atoms form a two dimensional planar honeycomb structure with an easy-plane ferromagnetic configuration and the required non-adiabatic paths to tune the topology of electronic structure exist for specific magnetic orientations based on mirror symmetries of the system. Using density functional theory (DFT) calculations, these tunable phases are identified by changing the orientation of the magnetic moments. We argue that in contrast to the buckled system, here the Cl-ligands bring non-trivial topology into the system by breaking the in-plane mirror symmetry. The interplay between the magnetic anisotropy and electronic band-topology changes the Chern number and hence the topological phases. Our DFT study is corroborated with comprehensive analysis of relevant symmetries as well as a detailed explanation of topological phase transitions using a generic tight binding model.
{"title":"In-plane magnetization orientation driven topological phase transition in OsCl3 monolayer","authors":"Ritwik Das, Subhadeep Bandyopadhyay and Indra Dasgupta","doi":"10.1088/2516-1075/ad4b81","DOIUrl":"https://doi.org/10.1088/2516-1075/ad4b81","url":null,"abstract":"The quantum anomalous Hall effect resulting from the in-plane magnetization in the OsCl3 monolayer is shown to exhibit different electronic topological phases determined by the crystal symmetries and magnetism. In this Chern insulator, the Os-atoms form a two dimensional planar honeycomb structure with an easy-plane ferromagnetic configuration and the required non-adiabatic paths to tune the topology of electronic structure exist for specific magnetic orientations based on mirror symmetries of the system. Using density functional theory (DFT) calculations, these tunable phases are identified by changing the orientation of the magnetic moments. We argue that in contrast to the buckled system, here the Cl-ligands bring non-trivial topology into the system by breaking the in-plane mirror symmetry. The interplay between the magnetic anisotropy and electronic band-topology changes the Chern number and hence the topological phases. Our DFT study is corroborated with comprehensive analysis of relevant symmetries as well as a detailed explanation of topological phase transitions using a generic tight binding model.","PeriodicalId":42419,"journal":{"name":"Electronic Structure","volume":"24 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141167438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-20DOI: 10.1088/2516-1075/ad48ed
B A Barker, A Seshappan and D A Strubbe
Spin-flip (SF) methods applied to excited-state approaches like the Bethe–Salpeter equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are generally not eigenstates of the spin operator . Even for simple cases where the excitation vector is expected to be, for example, a triplet state, the value of may be found to differ from 2.00; this difference is called ‘spin contamination’. The expectation values must be computed for each excitation vector, to assist with the characterization of the particular excitation and to determine the amount of spin contamination of the state. Our aim is to provide for the first time in the SF methods literature a comprehensive resource on the derivation of the formulas for as well as its computational implementation. After a brief discussion of the theory of the SF Bethe–Salpeter equation (BSE) and some examples further illustrating the need for calculating , we present the derivation for the general equation for computing with the eigenvectors from an SF-BSE calculation, how it is implemented in a Python script, and timing information on how this calculation scales with the size of the SF-BSE Hamiltonian.
将自旋翻转（SF）方法应用于激发态方法（如贝特-萨尔佩特方程），可以获得开壳系统（如分子和固体中的缺陷）的激发能量。然而，这些解的特征状态通常不是自旋算子的特征状态。即使在激发矢量预期为三重态等简单情况下，也可能发现其值与 2.00 存在差异；这种差异被称为 "自旋污染"。必须计算每个激发矢量的期望值，以帮助确定特定激发的特征，并确定态的自旋污染量。我们的目的是首次在 SF 方法文献中提供有关公式推导及其计算实现的全面资源。在简要讨论了 SF Bethe-Salpeter 方程（BSE）的理论和一些进一步说明计算必要性的例子之后，我们介绍了用 SF-BSE 计算得出的特征向量进行计算的一般公式的推导、如何在 Python 脚本中实现该公式，以及关于该计算如何随 SF-BSE 哈密顿的大小而缩放的定时信息。
{"title":"Computation of the expectation value of the spin operator S^2 for the spin-flip Bethe–Salpeter equation","authors":"B A Barker, A Seshappan and D A Strubbe","doi":"10.1088/2516-1075/ad48ed","DOIUrl":"https://doi.org/10.1088/2516-1075/ad48ed","url":null,"abstract":"Spin-flip (SF) methods applied to excited-state approaches like the Bethe–Salpeter equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are generally not eigenstates of the spin operator . Even for simple cases where the excitation vector is expected to be, for example, a triplet state, the value of may be found to differ from 2.00; this difference is called ‘spin contamination’. The expectation values must be computed for each excitation vector, to assist with the characterization of the particular excitation and to determine the amount of spin contamination of the state. Our aim is to provide for the first time in the SF methods literature a comprehensive resource on the derivation of the formulas for as well as its computational implementation. After a brief discussion of the theory of the SF Bethe–Salpeter equation (BSE) and some examples further illustrating the need for calculating , we present the derivation for the general equation for computing with the eigenvectors from an SF-BSE calculation, how it is implemented in a Python script, and timing information on how this calculation scales with the size of the SF-BSE Hamiltonian.","PeriodicalId":42419,"journal":{"name":"Electronic Structure","volume":"4 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-14DOI: 10.1088/2516-1075/ad46b6
Nicholas P Bauman
Downfolding coupled cluster (CC) techniques are powerful tools for reducing the dimensionality of many-body quantum problems. This work investigates how ground-state downfolding formalisms can target excited states using non-Aufbau reference determinants, paving the way for applications of quantum computing in excited-state chemistry. This study focuses on doubly excited states for which canonical equation-of-motion CC approaches struggle to describe unless one includes higher-than-double excitations. The downfolding technique results in state-specific effective Hamiltonians that, when diagonalized in their respective active spaces, provide ground- and excited-state total energies (and therefore excitation energies) comparable to high-level CC methods. The performance of this procedure is examined with doubly excited states of H2, Methylene, Formaldehyde, and Nitroxyl.
下折耦合簇（CC）技术是降低多体量子问题维度的有力工具。这项工作研究了基态下折形式如何利用非奥夫波参考行列式来瞄准激发态，从而为量子计算在激发态化学中的应用铺平道路。这项研究的重点是双激发态，对于这些态，除非包含比双激发态更高的激发，否则经典的运动方程 CC 方法难以描述。下折技术产生了特定状态的有效哈密顿，在各自的活性空间中对其进行对角时，可提供与高级 CC 方法相当的基态和激发态总能量（以及激发能量）。我们用 H2、Methylene、Formaldehyde 和 Nitroxyl 的双激发态检验了这一程序的性能。
{"title":"Excited-state downfolding using ground-state formalisms","authors":"Nicholas P Bauman","doi":"10.1088/2516-1075/ad46b6","DOIUrl":"https://doi.org/10.1088/2516-1075/ad46b6","url":null,"abstract":"Downfolding coupled cluster (CC) techniques are powerful tools for reducing the dimensionality of many-body quantum problems. This work investigates how ground-state downfolding formalisms can target excited states using non-Aufbau reference determinants, paving the way for applications of quantum computing in excited-state chemistry. This study focuses on doubly excited states for which canonical equation-of-motion CC approaches struggle to describe unless one includes higher-than-double excitations. The downfolding technique results in state-specific effective Hamiltonians that, when diagonalized in their respective active spaces, provide ground- and excited-state total energies (and therefore excitation energies) comparable to high-level CC methods. The performance of this procedure is examined with doubly excited states of H2, Methylene, Formaldehyde, and Nitroxyl.","PeriodicalId":42419,"journal":{"name":"Electronic Structure","volume":"37 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-12DOI: 10.1088/2516-1075/ad45d5
Emmanuel Fromager and Benjamin Lasorne
This work presents an alternative, general, and in-principle exact extension of electronic Kohn–Sham density functional theory (KS-DFT) to the fully quantum-mechanical molecular problem. Unlike in existing multi-component or exact-factorization-based DFTs of electrons and nuclei, both nuclear and electronic densities are mapped onto a fictitious electronically non-interacting molecule (referred to as KS molecule), where the electrons still interact with the nuclei. Moreover, in the present molecular KS-DFT, no assumption is made about the mathematical form (exactly factorized or not) of the molecular wavefunction. By expanding the KS molecular wavefunction à la Born–Huang, we obtain a self-consistent set of ‘KS beyond Born–Oppenheimer’ electronic equations coupled to nuclear equations that describe nuclei interacting among themselves and with non-interacting electrons. An exact adiabatic connection formula is derived for the Hartree-exchange-correlation energy of the electrons within the molecule and, on that basis, a practical adiabatic density-functional approximation is proposed and discussed.
{"title":"Density functional theory beyond the Born–Oppenheimer approximation: exact mapping onto an electronically non-interacting Kohn–Sham molecule","authors":"Emmanuel Fromager and Benjamin Lasorne","doi":"10.1088/2516-1075/ad45d5","DOIUrl":"https://doi.org/10.1088/2516-1075/ad45d5","url":null,"abstract":"This work presents an alternative, general, and in-principle exact extension of electronic Kohn–Sham density functional theory (KS-DFT) to the fully quantum-mechanical molecular problem. Unlike in existing multi-component or exact-factorization-based DFTs of electrons and nuclei, both nuclear and electronic densities are mapped onto a fictitious electronically non-interacting molecule (referred to as KS molecule), where the electrons still interact with the nuclei. Moreover, in the present molecular KS-DFT, no assumption is made about the mathematical form (exactly factorized or not) of the molecular wavefunction. By expanding the KS molecular wavefunction à la Born–Huang, we obtain a self-consistent set of ‘KS beyond Born–Oppenheimer’ electronic equations coupled to nuclear equations that describe nuclei interacting among themselves and with non-interacting electrons. An exact adiabatic connection formula is derived for the Hartree-exchange-correlation energy of the electrons within the molecule and, on that basis, a practical adiabatic density-functional approximation is proposed and discussed.","PeriodicalId":42419,"journal":{"name":"Electronic Structure","volume":"41 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140933329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-08DOI: 10.1088/2516-1075/ad38f8
William A Wheeler, Kevin G Kleiner, Lucas K Wagner
Variational Monte Carlo methods have recently been applied to the calculation of excited states; however, it is still an open question what objective function is most effective. A promising approach is to optimize excited states using a penalty to minimize overlap with lower eigenstates, which has the drawback that states must be computed one at a time. We derive a general framework for constructing objective functions with minima at the the lowest N eigenstates of a many-body Hamiltonian. The objective function uses a weighted average of the energies and an overlap penalty, which must satisfy several conditions. We show this objective function has a minimum at the exact eigenstates for a finite penalty, and provide a few strategies to minimize the objective function. The method is demonstrated using ab initio variational Monte Carlo to calculate the degenerate first excited state of a CO molecule.
变异蒙特卡洛方法最近被应用于激发态的计算；然而，什么目标函数最有效仍是一个悬而未决的问题。一种很有前途的方法是利用惩罚来优化激发态，以尽量减少与低特征态的重叠，但这种方法的缺点是必须一次计算一个态。我们推导出一个通用框架，用于构建在多体哈密顿最低 N 个特征状态处具有最小值的目标函数。目标函数使用能量的加权平均值和重叠惩罚，必须满足几个条件。我们证明了在罚金有限的情况下，该目标函数在精确特征点处具有最小值，并提供了几种最小化目标函数的策略。我们利用 ab initio 变分蒙特卡洛计算一氧化碳分子的退化第一激发态来演示该方法。
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Pub Date : 2024-04-02DOI: 10.1088/2516-1075/ad31ca
Susi Lehtola
Recent developments in fully numerical methods promise interesting opportunities for new, compact atomic orbital (AO) basis sets that maximize the overlap to fully numerical reference wave functions, following the pioneering work of Richardson and coworkers from the early 1960s. Motivated by this technique, we suggest a way to visualize the importance of AO basis functions employing fully numerical wave functions computed at the complete basis set limit: the importance of a normalized AO basis function <inline-formula> <tex-math><?CDATA $|alpharangle$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mo stretchy="false">|</mml:mo><mml:mi>α</mml:mi><mml:mo fence="false" stretchy="false">⟩</mml:mo></mml:mrow></mml:math> <inline-graphic xlink:href="estad31caieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula> centered on some nucleus can be visualized by projecting <inline-formula> <tex-math><?CDATA $|alpharangle$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mo stretchy="false">|</mml:mo><mml:mi>α</mml:mi><mml:mo fence="false" stretchy="false">⟩</mml:mo></mml:mrow></mml:math> <inline-graphic xlink:href="estad31caieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula> on the set of numerically represented occupied orbitals <inline-formula> <tex-math><?CDATA $|psi_{i}rangle$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo fence="false" stretchy="false">⟩</mml:mo></mml:mrow></mml:math> <inline-graphic xlink:href="estad31caieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula> as <inline-formula> <tex-math><?CDATA $I_{0}(alpha) = sum_{i}langlealpha|psi_{i}ranglelanglepsi_{i}|alpharangle$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>α</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:munder><mml:mo fence="false" stretchy="false">⟨</mml:mo><mml:mi>α</mml:mi><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo fence="false" stretchy="false">⟩</mml:mo><mml:mo fence="false" stretchy="false">⟨</mml:mo><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>α</mml:mi><mml:mo fence="false" stretchy="false">⟩</mml:mo></mml:mrow></mml:math> <inline-graphic xlink:href="estad31caieqn4.gif" xlink:type="simple"></inline-graphic> </inline-formula>. Choosing <italic toggle="yes">α</italic> to be a continuous parameter describing the AO basis, such as the exponent of a Gaussian-type orbital or Slater-type orbital basis function, one is then able to visualize the importance of various functions. The proposed visuali
{"title":"Importance profiles. Visualization of atomic basis set requirements","authors":"Susi Lehtola","doi":"10.1088/2516-1075/ad31ca","DOIUrl":"https://doi.org/10.1088/2516-1075/ad31ca","url":null,"abstract":"Recent developments in fully numerical methods promise interesting opportunities for new, compact atomic orbital (AO) basis sets that maximize the overlap to fully numerical reference wave functions, following the pioneering work of Richardson and coworkers from the early 1960s. Motivated by this technique, we suggest a way to visualize the importance of AO basis functions employing fully numerical wave functions computed at the complete basis set limit: the importance of a normalized AO basis function <inline-formula>\u0000<tex-math><?CDATA $|alpharangle$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>α</mml:mi><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"estad31caieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> centered on some nucleus can be visualized by projecting <inline-formula>\u0000<tex-math><?CDATA $|alpharangle$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>α</mml:mi><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"estad31caieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> on the set of numerically represented occupied orbitals <inline-formula>\u0000<tex-math><?CDATA $|psi_{i}rangle$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"estad31caieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> as <inline-formula>\u0000<tex-math><?CDATA $I_{0}(alpha) = sum_{i}langlealpha|psi_{i}ranglelanglepsi_{i}|alpharangle$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>α</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:munder><mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo><mml:mi>α</mml:mi><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo><mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>α</mml:mi><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"estad31caieqn4.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>. Choosing <italic toggle=\"yes\">α</italic> to be a continuous parameter describing the AO basis, such as the exponent of a Gaussian-type orbital or Slater-type orbital basis function, one is then able to visualize the importance of various functions. The proposed visuali","PeriodicalId":42419,"journal":{"name":"Electronic Structure","volume":"30 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140584593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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