Electronic Structure最新文献

筛选
英文 中文
Exploratory data science on supercomputers for quantum mechanical calculations 超级计算机上用于量子力学计算的探索性数据科学
IF 2.6
Electronic Structure Pub Date : 2024-06-11 DOI: 10.1088/2516-1075/ad4b80
William Dawson, Louis Beal, Laura E Ratcliff, Martina Stella, Takahito Nakajima, Luigi Genovese
{"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}
引用次数: 0
From electronic structure to magnetism and skyrmions 从电子结构到磁性和天膜
IF 2.6
Electronic Structure Pub Date : 2024-06-06 DOI: 10.1088/2516-1075/ad43d0
Vladislav Borisov
{"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}
引用次数: 0
Molecular NMR shieldings, J-couplings, and magnetizabilities from numeric atom-centered orbital based density-functional calculations 基于原子中心轨道的密度函数数值计算得出的分子核磁共振屏蔽、J-耦合和磁化率
IF 2.6
Electronic Structure Pub Date : 2024-05-29 DOI: 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
{"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}
引用次数: 0
Impact of nuclear effects on the ultrafast dynamics of an organic/inorganic mixed-dimensional interface 核效应对有机/无机混维界面超快动力学的影响
IF 2.6
Electronic Structure Pub Date : 2024-05-29 DOI: 10.1088/2516-1075/ad4d46
Matheus Jacobs, Karen Fidanyan, Mariana Rossi and Caterina Cocchi
{"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}
引用次数: 0
In-plane magnetization orientation driven topological phase transition in OsCl3 monolayer 面内磁化取向驱动的 OsCl3 单层拓扑相变
IF 2.6
Electronic Structure Pub Date : 2024-05-27 DOI: 10.1088/2516-1075/ad4b81
Ritwik Das, Subhadeep Bandyopadhyay and Indra Dasgupta
{"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}
引用次数: 0
Computation of the expectation value of the spin operator S^2 for the spin-flip Bethe–Salpeter equation 计算自旋翻转贝特-萨尔佩特方程的自旋算子 S^2 的期望值
IF 2.6
Electronic Structure Pub Date : 2024-05-20 DOI: 10.1088/2516-1075/ad48ed
B A Barker, A Seshappan and D A Strubbe
{"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}
引用次数: 0
Excited-state downfolding using ground-state formalisms 利用基态形式的激发态下折
IF 2.6
Electronic Structure Pub Date : 2024-05-14 DOI: 10.1088/2516-1075/ad46b6
Nicholas P Bauman
{"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}
引用次数: 0
Density functional theory beyond the Born–Oppenheimer approximation: exact mapping onto an electronically non-interacting Kohn–Sham molecule 超越玻恩-奥本海默近似的密度泛函理论:电子非相互作用科恩-沙姆分子的精确映射
IF 2.6
Electronic Structure Pub Date : 2024-05-12 DOI: 10.1088/2516-1075/ad45d5
Emmanuel Fromager and Benjamin Lasorne
{"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}
引用次数: 0
Ensemble variational Monte Carlo for optimization of correlated excited state wave functions 优化相关激发态波函数的集合变异蒙特卡洛算法
IF 2.6
Electronic Structure Pub Date : 2024-04-08 DOI: 10.1088/2516-1075/ad38f8
William A Wheeler, Kevin G Kleiner, Lucas K Wagner
{"title":"Ensemble variational Monte Carlo for optimization of correlated excited state wave functions","authors":"William A Wheeler, Kevin G Kleiner, Lucas K Wagner","doi":"10.1088/2516-1075/ad38f8","DOIUrl":"https://doi.org/10.1088/2516-1075/ad38f8","url":null,"abstract":"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 <italic toggle=\"yes\">N</italic> 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 <italic toggle=\"yes\">ab initio</italic> variational Monte Carlo to calculate the degenerate first excited state of a CO molecule.","PeriodicalId":42419,"journal":{"name":"Electronic Structure","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140612143","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}
引用次数: 0
Importance profiles. Visualization of atomic basis set requirements 重要性剖面图原子基集要求的可视化
IF 2.6
Electronic Structure Pub Date : 2024-04-02 DOI: 10.1088/2516-1075/ad31ca
Susi Lehtola
{"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 &lt;inline-formula&gt;\u0000&lt;tex-math&gt;&lt;?CDATA $|alpharangle$?&gt;&lt;/tex-math&gt;\u0000&lt;mml:math overflow=\"scroll\"&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;⟩&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;/mml:math&gt;\u0000&lt;inline-graphic xlink:href=\"estad31caieqn1.gif\" xlink:type=\"simple\"&gt;&lt;/inline-graphic&gt;\u0000&lt;/inline-formula&gt; centered on some nucleus can be visualized by projecting &lt;inline-formula&gt;\u0000&lt;tex-math&gt;&lt;?CDATA $|alpharangle$?&gt;&lt;/tex-math&gt;\u0000&lt;mml:math overflow=\"scroll\"&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;⟩&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;/mml:math&gt;\u0000&lt;inline-graphic xlink:href=\"estad31caieqn2.gif\" xlink:type=\"simple\"&gt;&lt;/inline-graphic&gt;\u0000&lt;/inline-formula&gt; on the set of numerically represented occupied orbitals &lt;inline-formula&gt;\u0000&lt;tex-math&gt;&lt;?CDATA $|psi_{i}rangle$?&gt;&lt;/tex-math&gt;\u0000&lt;mml:math overflow=\"scroll\"&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;ψ&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;⟩&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;/mml:math&gt;\u0000&lt;inline-graphic xlink:href=\"estad31caieqn3.gif\" xlink:type=\"simple\"&gt;&lt;/inline-graphic&gt;\u0000&lt;/inline-formula&gt; as &lt;inline-formula&gt;\u0000&lt;tex-math&gt;&lt;?CDATA $I_{0}(alpha) = sum_{i}langlealpha|psi_{i}ranglelanglepsi_{i}|alpharangle$?&gt;&lt;/tex-math&gt;\u0000&lt;mml:math overflow=\"scroll\"&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;I&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;0&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;&lt;mml:mo&gt;=&lt;/mml:mo&gt;&lt;mml:munder&gt;&lt;mml:mo&gt;∑&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:munder&gt;&lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;⟨&lt;/mml:mo&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;ψ&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;⟩&lt;/mml:mo&gt;&lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;⟨&lt;/mml:mo&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;ψ&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;⟩&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;/mml:math&gt;\u0000&lt;inline-graphic xlink:href=\"estad31caieqn4.gif\" xlink:type=\"simple\"&gt;&lt;/inline-graphic&gt;\u0000&lt;/inline-formula&gt;. Choosing &lt;italic toggle=\"yes\"&gt;α&lt;/italic&gt; 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}
引用次数: 0
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信