第一性原理計算方法分析目錄TOC\o"1-3"\h\u1212第一性原理計算方法分析 124101.1薛定諤方程 2145301.2波恩-奧本海默近似（Born-OppenheimerApproximation） 3106301.3Hartree-Fock近似 4302111.4密度泛函理論（DFT） 5凝聚態(tài)物理學作為物理學中最大、最活躍的分支學科為廣大科研學者所注意，它可以從微觀角度出發(fā)研究凝聚態(tài)的結(jié)構(gòu)、動力學過程和宏觀物理性質(zhì)的學科ADDINEN.CITE<EndNote><Cite><Author>曾犟</Author><Year>2019</Year><RecNum>23</RecNum><DisplayText><styleface="superscript">[44]</style></DisplayText><record><rec-number>23</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621681296">23</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>曾犟</author></authors><tertiary-authors><author>張振宇,</author></tertiary-authors></contributors><titles><title>二維材料的生長機理與功能性設(shè)計的第一性原理研究</title></titles><keywords><keyword>二維材料</keyword><keyword>第一性原理計算</keyword><keyword>表面生長理論</keyword><keyword>二維藍磷</keyword><keyword>異質(zhì)結(jié)</keyword><keyword>自旋半金屬</keyword><keyword>分子軌道</keyword><keyword>超晶格</keyword><keyword>拓撲絕緣體</keyword></keywords><dates><year>2019</year></dates><publisher>中國科學技術(shù)大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[44]。近年來，計算機技術(shù)不斷發(fā)展，人們越來越多地借助計算機的強大計算研究能力結(jié)合基本物理學原理嘗試開發(fā)新材料，第一性原理計算方法由此而來。目前，第一性原理計算方法飛速發(fā)展，成為第三種研究凝聚態(tài)物理的方法ADDINEN.CITE<EndNote><Cite><Author>曾犟</Author><Year>2019</Year><RecNum>23</RecNum><DisplayText><styleface="superscript">[44]</style></DisplayText><record><rec-number>23</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621681296">23</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>曾犟</author></authors><tertiary-authors><author>張振宇,</author></tertiary-authors></contributors><titles><title>二維材料的生長機理與功能性設(shè)計的第一性原理研究</title></titles><keywords><keyword>二維材料</keyword><keyword>第一性原理計算</keyword><keyword>表面生長理論</keyword><keyword>二維藍磷</keyword><keyword>異質(zhì)結(jié)</keyword><keyword>自旋半金屬</keyword><keyword>分子軌道</keyword><keyword>超晶格</keyword><keyword>拓撲絕緣體</keyword></keywords><dates><year>2019</year></dates><publisher>中國科學技術(shù)大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[44]，是使實驗研究和理論指導充分結(jié)合的有利工具。第一性原理計算方法（first-princeplescalculationmethod），也稱為從頭算(ab-initio)方法ADDINEN.CITE<EndNote><Cite><Author>Li</Author><Year>2018</Year><RecNum>32</RecNum><DisplayText><styleface="superscript">[45]</style></DisplayText><record><rec-number>32</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1622309512">32</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>GuodongLi</author><author>QiAn</author><author>SergeyI.Morozov</author><author>BoDuan</author><author>WilliamA.Goddard</author><author>QingjieZhang</author><author>PengchengZhai</author><author>G.JeffreySnyder</author></authors></contributors><auth-address>0000000092913229,grid.162110.5,StateKeyLaboratoryofAdvancedTechnologyforMaterialsSynthesisandProcessing,WuhanUniversityofTechnology,430070,Wuhan,China;;0000000122993507,grid.16753.36,DepartmentofMaterialsScienceandEngineering,NorthwesternUniversity,60208,Evanston,IL,USA;;000000041936914X,grid.266818.3,DepartmentofChemicalandMaterialsEngineering,UniversityofNevadaReno,89557,Reno,NV,USA;;0000000099585862,grid.440724.1,DepartmentofComputerSimulationandNanotechnology,SouthUralStateUniversity,454080,Chelyabinsk,Russia;;0000000107068890,grid.20861.3d,MaterialsandProcessSimulationCenter,CaliforniaInstituteofTechnology,91125,Pasadena,CA,USA</auth-address><titles><title>Ductiledeformationmechanisminsemiconductorα-Ag2S</title><secondary-title>npjComputationalMaterials</secondary-title></titles><periodical><full-title>npjComputationalMaterials</full-title></periodical><volume>4</volume><number>1</number><dates><year>2018</year></dates><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[45]，可以基于材料的自身性質(zhì)，以量子力學為基礎(chǔ)，同時考慮了電子之間的相互作用ADDINEN.CITE<EndNote><Cite><Author>柳楊璐</Author><Year>2018</Year><RecNum>2</RecNum><DisplayText><styleface="superscript">[3]</style></DisplayText><record><rec-number>2</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621310840">2</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>柳楊璐</author></authors><tertiary-authors><author>潘復生,</author></tertiary-authors></contributors><titles><title>Mg-Al和Mg-Y合金的第一性原理計算及實驗研究</title></titles><keywords><keyword>鎂合金</keyword><keyword>合金元素</keyword><keyword>臨界剪切應力</keyword><keyword>力學性能</keyword><keyword>變形機制</keyword></keywords><dates><year>2018</year></dates><publisher>重慶大學</publisher><work-type>碩士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[3]，能夠較為準確高效地幫助我們在研究過程中預測材料的光學和力學等性質(zhì)，經(jīng)過多年的發(fā)展，整個計算體系較為完整，理論也可以完全自洽，具有非常好的普適性ADDINEN.CITE<EndNote><Cite><Author>Pengfei</Author><Year>2021</Year><RecNum>44</RecNum><DisplayText><styleface="superscript">[46]</style></DisplayText><record><rec-number>44</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1622399561">44</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>ChenPengfei</author><author>HuangYiao</author><author>ShiZuhao</author><author>ChenXingzhu</author><author>LiNeng</author></authors></contributors><auth-address>StateKeyLaboratoryofSilicateMaterialsforArchitectures,WuhanUniversityofTechnology,Wuhan430070,China(P.C.)(Y.H.)(Z.S.)(X.C.);CenterofInnovationandEntrepreneurship,WuhanUniversityofTechnology,Wuhan430070,China;ShenzhenResearchInstitute,WuhanUniversityofTechnology,Shenzhen518000,China;StateCenterforInternationalCooperationonDesignerLow-Carbon&ampEnvironmentalMaterials(CDLCEM),SchoolofMaterialsScienceandEngineering,ZhengzhouUniversity,Zhengzhou450001,China</auth-address><titles><title>ImprovingtheCatalyticCO2ReductiononCs2AgBiBr6byHalideDefectEngineering:ADFTStudy</title><secondary-title>Materials</secondary-title></titles><periodical><full-title>Materials</full-title></periodical><volume>14</volume><number>10</number><keywords><keyword>halideperovskite</keyword><keyword>CO2catalyticreduction</keyword><keyword>defectengineering</keyword><keyword>computationalresearch</keyword></keywords><dates><year>2021</year></dates><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[46]。目前，我們使用第一性原理計算方法時，往往需要引入一些近似方法以降低計算的難度并提高計算的速度。因此，在第一性原理計算的整個發(fā)展歷程中，人們一直在尋找更為恰當和準確的近似與算法ADDINEN.CITE<EndNote><Cite><Author>曾犟</Author><Year>2019</Year><RecNum>23</RecNum><DisplayText><styleface="superscript">[44]</style></DisplayText><record><rec-number>23</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621681296">23</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>曾犟</author></authors><tertiary-authors><author>張振宇,</author></tertiary-authors></contributors><titles><title>二維材料的生長機理與功能性設(shè)計的第一性原理研究</title></titles><keywords><keyword>二維材料</keyword><keyword>第一性原理計算</keyword><keyword>表面生長理論</keyword><keyword>二維藍磷</keyword><keyword>異質(zhì)結(jié)</keyword><keyword>自旋半金屬</keyword><keyword>分子軌道</keyword><keyword>超晶格</keyword><keyword>拓撲絕緣體</keyword></keywords><dates><year>2019</year></dates><publisher>中國科學技術(shù)大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[44]，以求使第一性原理計算結(jié)果更加準確、完善。第一性原理是基于量子力學提出的，而量子力學的基本方程為薛定諤方程，薛定諤方程描述了粒子的波函數(shù)和運動方程ADDINEN.CITE<EndNote><Cite><Author>H.</Author><Year>2021</Year><RecNum>45</RecNum><DisplayText><styleface="superscript">[47]</style></DisplayText><record><rec-number>45</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1622399691">45</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Rojas-ChávezH.</author><author>MiralrioA.</author><author>Hernández-RodríguezY.M.</author><author>Cruz-MartínezH.</author><author>Pérez-PérezR.</author><author>Cigarroa-MayorgaO.E.</author></authors></contributors><auth-address>TecnológicoNacionaldeMéxico,InstitutoTecnológicodeTláhuacII,CaminoReal625,Col.JardinesdelLlano,SanJuanIxtayopan.AlcaldíaTláhuac,CDMX13508,Mexico;TecnologicodeMonterrey,EscueladeIngenieríayCiencias,Ave.EugenioGarzaSada2501,Monterrey64849,N.L.,Mexico;Dept.AdvancedTechnologies,UPIITA-InstitutoPolitécnicoNacional,Av.IPN2580,Col.Ticomán,GustavoA.Madero,CDMX07360,Mexico;TecnológicoNacionaldeMéxico,InstitutoTecnológicodelValledeEtla,AbasoloS/N,BarriodelAguaBuena,SantiagoSuchilquitongo,Oaxaca68230,Mexico;TecnológicoNacionaldeMéxico,InstitutoTecnológicodePuebla,DepartamentodeMetalMecánica,Av.Tecnológico420,Col.Maravillas,Puebla,Pue72220,Mexico</auth-address><titles><title>Needle-andcross-linkedZnOmicrostructuresandtheirphotocatalyticactivityusingexperimentalandDFTapproach</title><secondary-title>MaterialsLetters</secondary-title></titles><periodical><full-title>MaterialsLetters</full-title></periodical><volume>291</volume><keywords><keyword>Thermaloxidation</keyword><keyword>ZnO</keyword><keyword>Chemicaletching</keyword><keyword>DFT</keyword><keyword>Photocatalyticactivity</keyword></keywords><dates><year>2021</year></dates><isbn>0167-577X</isbn><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[47]。第一性原理計算方法主要由兩類方法構(gòu)成，分別為Hartree-Fock方法和密度泛函理論方法ADDINEN.CITE<EndNote><Cite><Author>姜朋</Author><Year>2021</Year><RecNum>25</RecNum><DisplayText><styleface="superscript">[48]</style></DisplayText><record><rec-number>25</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621686270">25</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>姜朋</author></authors><tertiary-authors><author>鄭小宏,</author></tertiary-authors></contributors><titles><title>低維自旋電子材料和器件的第一性原理研究</title></titles><keywords><keyword>自旋電子學</keyword><keyword>自旋熱電效應</keyword><keyword>光學伽伐尼效應</keyword><keyword>完全自旋極化流</keyword><keyword>(純)自旋流</keyword><keyword>范德瓦爾斯多鐵異質(zhì)結(jié)</keyword></keywords><dates><year>2021</year></dates><publisher>中國科學技術(shù)大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[48]。原則上來說，薛定諤方程能夠?qū)崿F(xiàn)嚴格求解，但是當我們的實驗對象為多粒子系統(tǒng)時，求解薛定諤方程變得十分復雜ADDINEN.CITE<EndNote><Cite><Author>曾犟</Author><Year>2019</Year><RecNum>23</RecNum><DisplayText><styleface="superscript">[44]</style></DisplayText><record><rec-number>23</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621681296">23</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>曾犟</author></authors><tertiary-authors><author>張振宇,</author></tertiary-authors></contributors><titles><title>二維材料的生長機理與功能性設(shè)計的第一性原理研究</title></titles><keywords><keyword>二維材料</keyword><keyword>第一性原理計算</keyword><keyword>表面生長理論</keyword><keyword>二維藍磷</keyword><keyword>異質(zhì)結(jié)</keyword><keyword>自旋半金屬</keyword><keyword>分子軌道</keyword><keyword>超晶格</keyword><keyword>拓撲絕緣體</keyword></keywords><dates><year>2019</year></dates><publisher>中國科學技術(shù)大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[44]，于是人們提出在求解方程時采用近似處理，以提高求解效率。于是，波恩-奧本海默近似被提出，但是也具有很大的局限性。因此，科研工作者研發(fā)出了當代計算化學中常用的算法——Hartree-Fock近似，這是很多計算方法的基石ADDINEN.CITE<EndNote><Cite><Author>余海山</Author><Year>2020</Year><RecNum>22</RecNum><DisplayText><styleface="superscript">[43]</style></DisplayText><record><rec-number>22</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621672199">22</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>余海山</author></authors><tertiary-authors><author>江俊,</author></tertiary-authors></contributors><titles><title>結(jié)合第一性原理計算和機器學習的材料理論研究</title></titles><keywords><keyword>密度泛函理論</keyword><keyword>機器學習</keyword><keyword>硼烯</keyword><keyword>化學改性</keyword><keyword>帶隙</keyword><keyword>解離能</keyword></keywords><dates><year>2020</year></dates><publisher>中國科學技術(shù)大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[43]，但這個近似也難以解決多原子體系計算復雜的問題。圖2.1基于密度泛函理論的第一性原理計算的由來ADDINEN.CITE<EndNote><Cite><Author>柳楊璐</Author><Year>2018</Year><RecNum>2</RecNum><DisplayText><styleface="superscript">[3]</style></DisplayText><record><rec-number>2</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621310840">2</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>柳楊璐</author></authors><tertiary-authors><author>潘復生,</author></tertiary-authors></contributors><titles><title>Mg-Al和Mg-Y合金的第一性原理計算及實驗研究</title></titles><keywords><keyword>鎂合金</keyword><keyword>合金元素</keyword><keyword>臨界剪切應力</keyword><keyword>力學性能</keyword><keyword>變形機制</keyword></keywords><dates><year>2018</year></dates><publisher>重慶大學</publisher><work-type>碩士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[3]隨后，Tomas-Femi模型提出，將薛定諤方程簡化為波動方程ADDINEN.CITE<EndNote><Cite><Author>柳楊璐</Author><Year>2018</Year><RecNum>2</RecNum><DisplayText><styleface="superscript">[3]</style></DisplayText><record><rec-number>2</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621310840">2</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>柳楊璐</author></authors><tertiary-authors><author>潘復生,</author></tertiary-authors></contributors><titles><title>Mg-Al和Mg-Y合金的第一性原理計算及實驗研究</title></titles><keywords><keyword>鎂合金</keyword><keyword>合金元素</keyword><keyword>臨界剪切應力</keyword><keyword>力學性能</keyword><keyword>變形機制</keyword></keywords><dates><year>2018</year></dates><publisher>重慶大學</publisher><work-type>碩士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[3]，這也是DFT的雛形。在這些近似的基礎(chǔ)上，Hohenberg和Kohn提出了非均勻電子氣理論ADDINEN.CITE<EndNote><Cite><Author>張茜</Author><Year>2020</Year><RecNum>24</RecNum><DisplayText><styleface="superscript">[49]</style></DisplayText><record><rec-number>24</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621685146">24</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>張茜</author></authors><tertiary-authors><author>侯華,</author><author>張高龍,</author></tertiary-authors></contributors><titles><title>Mg-Gd合金中時效強化相的結(jié)構(gòu)穩(wěn)定性及熱力學性質(zhì)的第一性原理計算</title></titles><keywords><keyword>Mg-Gd合金</keyword><keyword>金屬間化合物</keyword><keyword>第一性原理</keyword><keyword>熱力學性質(zhì)</keyword><keyword>力學性能</keyword></keywords><dates><year>2020</year></dates><publisher>中北大學</publisher><work-type>碩士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[49]，推動創(chuàng)立了第一性原理計算的核心——密度泛函理論，也即DFT。如圖2.1所示，為基于密度泛函理論的第一性原理計算的由來ADDINEN.CITE<EndNote><Cite><Author>柳楊璐</Author><Year>2018</Year><RecNum>2</RecNum><DisplayText><styleface="superscript">[3]</style></DisplayText><record><rec-number>2</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621310840">2</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>柳楊璐</author></authors><tertiary-authors><author>潘復生,</author></tertiary-authors></contributors><titles><title>Mg-Al和Mg-Y合金的第一性原理計算及實驗研究</title></titles><keywords><keyword>鎂合金</keyword><keyword>合金元素</keyword><keyword>臨界剪切應力</keyword><keyword>力學性能</keyword><keyword>變形機制</keyword></keywords><dates><year>2018</year></dates><publisher>重慶大學</publisher><work-type>碩士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[3]。1.1薛定諤方程奧地利物理學家Schrodinger首先提出了薛定諤方程，這個方程主要用來描述微觀粒子的運動ADDINEN.CITE<EndNote><Cite><Author>張靜</Author><Year>2020</Year><RecNum>26</RecNum><DisplayText><styleface="superscript">[50]</style></DisplayText><record><rec-number>26</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621689716">26</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>張靜</author></authors><tertiary-authors><author>王春明,</author><author>于元烈,</author></tertiary-authors></contributors><titles><title>六方氮化硼納米片表面改性與性能研究的第一性原理計算</title></titles><keywords><keyword>密度泛函理論</keyword><keyword>六方氮化硼納米片</keyword><keyword>表面改性</keyword><keyword>性能調(diào)控</keyword><keyword>微納機電系統(tǒng)</keyword></keywords><dates><year>2020</year></dates><publisher>山東大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[50]。這個方程分為含時公式（2.1）和定時公式（2.2）兩種形式ADDINEN.CITE<EndNote><Cite><Author>曾犟</Author><Year>2019</Year><RecNum>23</RecNum><DisplayText><styleface="superscript">[44]</style></DisplayText><record><rec-number>23</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621681296">23</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>曾犟</author></authors><tertiary-authors><author>張振宇,</author></tertiary-authors></contributors><titles><title>二維材料的生長機理與功能性設(shè)計的第一性原理研究</title></titles><keywords><keyword>二維材料</keyword><keyword>第一性原理計算</keyword><keyword>表面生長理論</keyword><keyword>二維藍磷</keyword><keyword>異質(zhì)結(jié)</keyword><keyword>自旋半金屬</keyword><keyword>分子軌道</keyword><keyword>超晶格</keyword><keyword>拓撲絕緣體</keyword></keywords><dates><year>2019</year></dates><publisher>中國科學技術(shù)大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[44]： i??ψr Ηψr在這兩個式子中，Η和ψ分別為哈密頓算符和波函數(shù)，Ε是本征能量，r為空間坐標，t為時間坐標，ψ為r和t的函數(shù)。當我們的研究對象為多粒子體系時，其薛定諤方程為公式2.2。于是Η可以拆解為三項，即 Η=Η第一項，Ηe為電子項，Ter表示電子動能，V Ηe=第二項，Ηn為原子核項，Tnr表示原子核動能，Vnr Ηn=第三項，Ηe?n Ηe?定態(tài)薛定諤方程相對而言復雜度較低，但是含時薛定諤方程包含了多粒子系統(tǒng)間復雜的相互作用，要想其有實際用途，我們必須要借助在物理模型上的合理近似簡化計算。1.2波恩-奧本海默近似（Born-OppenheimerApproximation）波恩-奧本海默近似也成為絕熱近似，它的提出基于一個物理學事實，即原子核的質(zhì)量一般要比電子質(zhì)量大3~4個數(shù)量級ADDINEN.CITE<EndNote><Cite><Author>余海山</Author><Year>2020</Year><RecNum>22</RecNum><DisplayText><styleface="superscript">[43]</style></DisplayText><record><rec-number>22</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621672199">22</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>余海山</author></authors><tertiary-authors><author>江俊,</author></tertiary-authors></contributors><titles><title>結(jié)合第一性原理計算和機器學習的材料理論研究</title></titles><keywords><keyword>密度泛函理論</keyword><keyword>機器學習</keyword><keyword>硼烯</keyword><keyword>化學改性</keyword><keyword>帶隙</keyword><keyword>解離能</keyword></keywords><dates><year>2020</year></dates><publisher>中國科學技術(shù)大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[43]，其運動速度比電子運動速度慢很多。在這個近似中，假定電子運動時原子核固定于瞬間位置ADDINEN.CITE<EndNote><Cite><Author>柳楊璐</Author><Year>2018</Year><RecNum>2</RecNum><DisplayText><styleface="superscript">[3]</style></DisplayText><record><rec-number>2</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621310840">2</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>柳楊璐</author></authors><tertiary-authors><author>潘復生,</author></tertiary-authors></contributors><titles><title>Mg-Al和Mg-Y合金的第一性原理計算及實驗研究</title></titles><keywords><keyword>鎂合金</keyword><keyword>合金元素</keyword><keyword>臨界剪切應力</keyword><keyword>力學性能</keyword><keyword>變形機制</keyword></keywords><dates><year>2018</year></dates><publisher>重慶大學</publisher><work-type>碩士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[3]，原子核運動時電子能夠迅速響應，也即將核和電子的運動分開，這可以幫助我們將多粒子求解問題轉(zhuǎn)變?yōu)槎嚯娮忧蠼鈫栴}，此時哈密頓算符可以簡化為 Η=Η這個近似方法的確降低了計算求解的難度，但是也具有一定的使用局限性。當研究體系的電子態(tài)出現(xiàn)交叉或接近時ADDINEN.CITE<EndNote><Cite><Author>張靜</Author><Year>2020</Year><RecNum>26</RecNum><DisplayText><styleface="superscript">[50]</style></DisplayText><record><rec-number>26</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621689716">26</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>張靜</author></authors><tertiary-authors><author>王春明,</author><author>于元烈,</author></tertiary-authors></contributors><titles><title>六方氮化硼納米片表面改性與性能研究的第一性原理計算</title></titles><keywords><keyword>密度泛函理論</keyword><keyword>六方氮化硼納米片</keyword><keyword>表面改性</keyword><keyword>性能調(diào)控</keyword><keyword>微納機電系統(tǒng)</keyword></keywords><dates><year>2020</year></dates><publisher>山東大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[50]，波恩-奧本海默近似無法應用。此外，電子間的相互庫倫作用非常復雜，且這仍然是一個量子多體問題，研究體系電子數(shù)目龐大復雜。因此求解過程的復雜度仍不理想，求解時間很長，方程需要進一步簡化。1.3Hartree-Fock近似波恩-奧本海默近似幫助我們將多粒子體系簡化為多電子體系，我們需要繼續(xù)簡化電子相關(guān)方程。這一步中，計算的難點就是每個電子受到的力都與其他電子狀態(tài)密切相關(guān)，因此我們急需簡化多電子相互作用的問題。1928年，根據(jù)Hartree忽略Pauli原理的建議，單電子近似被提出ADDINEN.CITE<EndNote><Cite><Author>張靜</Author><Year>2020</Year><RecNum>26</RecNum><DisplayText><styleface="superscript">[50]</style></DisplayText><record><rec-number>26</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621689716">26</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>張靜</author></authors><tertiary-authors><author>王春明,</author><author>于元烈,</author></tertiary-authors></contributors><titles><title>六方氮化硼納米片表面改性與性能研究的第一性原理計算</title></titles><keywords><keyword>密度泛函理論</keyword><keyword>六方氮化硼納米片</keyword><keyword>表面改性</keyword><keyword>性能調(diào)控</keyword><keyword>微納機電系統(tǒng)</keyword></keywords><dates><year>2020</year></dates><publisher>山東大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[50]，也稱為Hartree-Fock近似。當一個電子運動時，將其他粒子對它的作用視為一個平均等效勢場ADDINEN.CITE<EndNote><Cite><Author>曾犟</Author><Year>2019</Year><RecNum>23</RecNum><DisplayText><styleface="superscript">[44]</style></DisplayText><record><rec-number>23</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621681296">23</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>曾犟</author></authors><tertiary-authors><author>張振宇,</author></tertiary-authors></contributors><titles><title>二維材料的生長機理與功能性設(shè)計的第一性原理研究</title></titles><keywords><keyword>二維材料</keyword><keyword>第一性原理計算</keyword><keyword>表面生長理論</keyword><keyword>二維藍磷</keyword><keyword>異質(zhì)結(jié)</keyword><keyword>自旋半金屬</keyword><keyword>分子軌道</keyword><keyword>超晶格</keyword><keyword>拓撲絕緣體</keyword></keywords><dates><year>2019</year></dates><publisher>中國科學技術(shù)大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[44]，忽略了電子之間的相互碰撞和作用，這樣一來，每個電子的運動都是在其他粒子形成的勢場中進行獨立運動，這個勢場中包含了電子與原子核之間的庫倫相互作用、電子之間的庫倫相互作用和電子之間的交互作用。整個體系的波函數(shù)則變?yōu)閱坞娮硬ê瘮?shù)的乘積ADDINEN.CITE<EndNote><Cite><Author>張靜</Author><Year>2020</Year><RecNum>26</RecNum><DisplayText><styleface="superscript">[50]</style></DisplayText><record><rec-number>26</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621689716">26</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>張靜</author></authors><tertiary-authors><author>王春明,</author><author>于元烈,</author></tertiary-authors></contributors><titles><title>六方氮化硼納米片表面改性與性能研究的第一性原理計算</title></titles><keywords><keyword>密度泛函理論</keyword><keyword>六方氮化硼納米片</keyword><keyword>表面改性</keyword><keyword>性能調(diào)控</keyword><keyword>微納機電系統(tǒng)</keyword></keywords><dates><year>2020</year></dates><publisher>山東大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[50]，即 ψr1這能夠幫助我們解決多電子體系中Η的求解時多粒子多中心導致的積分問題ADDINEN.CITE<EndNote><Cite><Author>曾犟</Author><Year>2019</Year><RecNum>23</RecNum><DisplayText><styleface="superscript">[44]</style></DisplayText><record><rec-number>23</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621681296">23</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>曾犟</author></authors><tertiary-authors><author>張振宇,</author></tertiary-authors></contributors><titles><title>二維材料的生長機理與功能性設(shè)計的第一性原理研究</title></titles><keywords><keyword>二維材料</keyword><keyword>第一性原理計算</keyword><keyword>表面生長理論</keyword><keyword>二維藍磷</keyword><keyword>異質(zhì)結(jié)</keyword><keyword>自旋半金屬</keyword><keyword>分子軌道</keyword><keyword>超晶格</keyword><keyword>拓撲絕緣體</keyword></keywords><dates><year>2019</year></dates><publisher>中國科學技術(shù)大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[44]，龐大復雜的方程求解也可以簡化為多個關(guān)聯(lián)的單電子方程的求解。隨后，在Hartre的基礎(chǔ)上，F(xiàn)ock考慮將Pauli原理與之結(jié)合，認為電子屬于費米子，因此其波函數(shù)具有反對稱性質(zhì)，并提出一種合理的自洽場完善Hartree-Fock近似，以便求解多個單電子方程。通過Slater行列式表示單電子波函數(shù)的乘積ADDINEN.CITE<EndNote><Cite><Author>張靜</Author><Year>2020</Year><RecNum>26</RecNum><DisplayText><styleface="superscript">[50]</style></DisplayText><record><rec-number>26</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621689716">26</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>張靜</author></authors><tertiary-authors><author>王春明,</author><author>于元烈,</author></tertiary-authors></contributors><titles><title>六方氮化硼納米片表面改性與性能研究的第一性原理計算</title></titles><keywords><keyword>密度泛函理論</keyword><keyword>六方氮化硼納米片</keyword><keyword>表面改性</keyword><keyword>性能調(diào)控</keyword><keyword>微納機電系統(tǒng)</keyword></keywords><dates><year>2020</year></dates><publisher>山東大學</publisher><work-type>博士</work-type><urls></urls><remote-database-provider>Cnki</remote-database-provider></record></Cite></EndNote>[50]，即 ψ1,2,?,N=其中，ψni是第n個能級的單電子的波函數(shù)，坐標里含有第i電子的位置和自旋態(tài)。Hartree-Fock近似考慮了相同自旋電子間的交換作用，這充分體現(xiàn)出了電子波函數(shù)的交換反對稱性質(zhì)ADDINEN.CITE<EndNote><Cite><Author>曾犟</Author><Year>2019</Year><RecNum>23</RecNum><DisplayText><styleface="superscript">[44]</style></DisplayText><record><rec-number>23</rec-number><foreign-keys><keyapp="EN"db-id="rdze5zzau99z5cevfr0vv054ex0pwe9wsptr"timestamp="1621681296">23</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>曾犟</author></authors><tertiary-authors><author>張振宇,</author></tertiary-authors></contributors><titles><title>二維材料的生長機理與功能性設(shè)計的第一性原理研究</title></titles><keywords><keyword>二維材料<