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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>로그인</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 로그아웃한 편집자를 위한 문서 <a href="/wiki/%EB%8F%84%EC%9B%80%EB%A7%90:%EC%86%8C%EA%B0%9C" aria-label="편집에 관해 더 알아보기"><span>더 알아보기</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EA%B8%B0%EC%97%AC" title="이 IP 주소의 편집 목록 [y]" accesskey="y"><span>기여</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EC%82%AC%EC%9A%A9%EC%9E%90%ED%86%A0%EB%A1%A0" title="현재 사용하는 IP 주소에 대한 토론 문서 [n]" accesskey="n"><span>토론</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="사이트"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="목차" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">목차</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">숨기기</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">처음 위치</div> </a> </li> <li id="toc-개요" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#개요"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>개요</span> </div> </a> <ul id="toc-개요-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-평면파_바탕_함수_집합" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#평면파_바탕_함수_집합"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>평면파 바탕 함수 집합</span> </div> </a> <ul id="toc-평면파_바탕_함수_집합-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-같이_보기" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#같이_보기"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>같이 보기</span> </div> </a> <ul id="toc-같이_보기-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-각주" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#각주"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>각주</span> </div> </a> <ul id="toc-각주-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="목차" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="목차 토글" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">목차 토글</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">바탕 함수 집합</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="다른 언어로 문서를 방문합니다. 10개 언어로 읽을 수 있습니다" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-10" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">10개 언어</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Basissatz_(Chemie)" title="Basissatz (Chemie) – 독일어" lang="de" hreflang="de" data-title="Basissatz (Chemie)" data-language-autonym="Deutsch" data-language-local-name="독일어" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Basis_set_(chemistry)" title="Basis set (chemistry) – 영어" lang="en" hreflang="en" data-title="Basis set (chemistry)" data-language-autonym="English" data-language-local-name="영어" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Base_(chimie_quantique)" title="Base (chimie quantique) – 프랑스어" lang="fr" hreflang="fr" data-title="Base (chimie quantique)" data-language-autonym="Français" data-language-local-name="프랑스어" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Basis_set_(kimia)" title="Basis set (kimia) – 인도네시아어" lang="id" hreflang="id" data-title="Basis set (kimia)" data-language-autonym="Bahasa Indonesia" data-language-local-name="인도네시아어" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%9F%BA%E5%BA%95%E9%96%A2%E6%95%B0%E7%B3%BB_(%E5%8C%96%E5%AD%A6)" title="基底関数系 (化学) – 일본어" lang="ja" hreflang="ja" data-title="基底関数系 (化学)" data-language-autonym="日本語" data-language-local-name="일본어" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Base_(qu%C3%ADmica_qu%C3%A2ntica)" title="Base (química quântica) – 포르투갈어" lang="pt" hreflang="pt" data-title="Base (química quântica)" data-language-autonym="Português" data-language-local-name="포르투갈어" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%B0%D0%B7%D0%B8%D1%81%D0%BD%D1%8B%D0%B9_%D0%BD%D0%B0%D0%B1%D0%BE%D1%80" title="Базисный набор – 러시아어" lang="ru" hreflang="ru" data-title="Базисный набор" data-language-autonym="Русский" data-language-local-name="러시아어" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Temel_seti_(kimya)" title="Temel seti (kimya) – 터키어" lang="tr" hreflang="tr" data-title="Temel seti (kimya)" data-language-autonym="Türkçe" data-language-local-name="터키어" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D0%B0%D0%B7%D0%B8%D1%81%D0%BD%D0%B8%D0%B9_%D0%BD%D0%B0%D0%B1%D1%96%D1%80" title="Базисний набір – 우크라이나어" lang="uk" hreflang="uk" data-title="Базисний набір" data-language-autonym="Українська" data-language-local-name="우크라이나어" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%9F%BA%E7%BB%84" title="基组 – 중국어" lang="zh" hreflang="zh" data-title="基组" data-language-autonym="中文" data-language-local-name="중국어" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q2664086#sitelinks-wikipedia" title="언어 간 링크 편집" class="wbc-editpage">링크 편집</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="이름공간"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected 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class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="보기"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%EB%B0%94%ED%83%95_%ED%95%A8%EC%88%98_%EC%A7%91%ED%95%A9"><span>읽기</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%EB%B0%94%ED%83%95_%ED%95%A8%EC%88%98_%EC%A7%91%ED%95%A9&action=edit" title="이 문서의 원본 코드를 편집 [e]" accesskey="e"><span>편집</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a 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<b>바탕 함수 집합</b>(-函數集合) 또는 <b>기저 함수 집합</b>(基底函數集合, basis set)은 <a href="/wiki/%EA%B3%84%EC%82%B0%ED%99%94%ED%95%99" title="계산화학">계산화학</a>과 <a href="/wiki/%EC%9D%B4%EB%A1%A0%ED%99%94%ED%95%99" title="이론화학">이론화학</a>에서 사용하는 <a href="/wiki/%ED%95%A8%EC%88%98" title="함수">함수</a> 종류다. <a href="/wiki/%EA%B3%84%EC%82%B0%ED%99%94%ED%95%99" title="계산화학">계산화학</a>과 <a href="/wiki/%EC%9D%B4%EB%A1%A0%ED%99%94%ED%95%99" title="이론화학">이론화학</a>에서는 전자의 <a href="/wiki/%ED%8C%8C%EB%8F%99_%ED%95%A8%EC%88%98" title="파동 함수">파동 함수</a>를 주로 연구하는데, 여기에서 <a href="/wiki/%ED%8C%8C%EB%8F%99_%ED%95%A8%EC%88%98" title="파동 함수">파동 함수</a>를 표현할 때 사용하는 함수 종류들을 바탕 함수 집합이라고 한다. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="개요"><span id=".EA.B0.9C.EC.9A.94"></span>개요</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%B0%94%ED%83%95_%ED%95%A8%EC%88%98_%EC%A7%91%ED%95%A9&action=edit&section=1" title="부분 편집: 개요"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>계산화학에서 바탕 함수 집합을 사용하지 않고도 파동 함수를 표현할 수는 있지만, 대부분 바탕 함수 집합을 사용한다.<sup id="cite_ref-Chelikowsky_1994_1-0" class="reference"><a href="#cite_note-Chelikowsky_1994-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>. 그 이유는 계산화학에서 <a href="/wiki/%EC%9B%90%EC%9E%90_%EA%B6%A4%EB%8F%84_%ED%95%A8%EC%88%98_%EC%84%A0%ED%98%95_%EA%B2%B0%ED%95%A9" title="원자 궤도 함수 선형 결합">원자 궤도 함수 선형 결합</a>을 사용하기 때문이다. 원자 궤도 선형 결합은 슈뢰딩거 방정식을 풀기 위해 사용되는 계산이다. 원자 궤도 함수 선형 결합의 이론에 의하면 모든 파동함수는 정해진 함수의 <a href="/wiki/%EC%84%A0%ED%98%95_%EA%B2%B0%ED%95%A9" title="선형 결합">선형 결합</a>으로 나타낼 수 있다. </p><p>초기에는 원자들의 파동함수를 함수 선형 결합으로 표현했고. 분자의 파동함수를 원자 파동함수의 선형 결합으로 표현했다. </p><p>대부분의 바탕 함수는 원자 궤도 함수와 비슷한 함수이다. </p> <div class="mw-heading mw-heading2"><h2 id="평면파_바탕_함수_집합"><span id=".ED.8F.89.EB.A9.B4.ED.8C.8C_.EB.B0.94.ED.83.95_.ED.95.A8.EC.88.98_.EC.A7.91.ED.95.A9"></span>평면파 바탕 함수 집합</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%B0%94%ED%83%95_%ED%95%A8%EC%88%98_%EC%A7%91%ED%95%A9&action=edit&section=2" title="부분 편집: 평면파 바탕 함수 집합"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>궤도 함수를 평면파의 선형 결합으로 나타내는 것도 가능하다. 즉, 평면파만으로 바탕 함수 집합을 구성할 수 있다. 평면파는 <a href="/wiki/%EB%B8%94%EB%A1%9C%ED%9D%90_%ED%8C%8C" title="블로흐 파">블로흐 정리</a>의 해가 되며, 주기성이 명확히 드러나므로 주기적 경계 조건이 있는 문제를 다루기에 좋으며, 따라서 단순한 구조가 반복되는 거대한 구조를 계산하기에 적합하다. 반면, 한 개의 원자를 실용적으로 정확하게 나타내는 데에도 바탕 함수 수백 개를 선형 결합해야 하기 때문에, 원자나 작은 분자 계산에서는 평면파보다는 원자 궤도 함수와 같이 국소적인 함수가 더 적합하다.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="같이_보기"><span id=".EA.B0.99.EC.9D.B4_.EB.B3.B4.EA.B8.B0"></span>같이 보기</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%B0%94%ED%83%95_%ED%95%A8%EC%88%98_%EC%A7%91%ED%95%A9&action=edit&section=3" title="부분 편집: 같이 보기"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%EA%B0%81%EC%9A%B4%EB%8F%99%EB%9F%89" title="각운동량">각운동량</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="각주"><span id=".EA.B0.81.EC.A3.BC"></span>각주</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%B0%94%ED%83%95_%ED%95%A8%EC%88%98_%EC%A7%91%ED%95%A9&action=edit&section=4" title="부분 편집: 각주"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r35556958">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Chelikowsky_1994-1"><span class="mw-cite-backlink"><a href="#cite_ref-Chelikowsky_1994_1-0">↑</a></span> <span class="reference-text"><cite class="citation journal">James R. Chelikowsky, N. Troullier, and Y. Saad (1994). “Finite-difference-pseudopotential method: Electronic structure calculations without a basis”. 《<a href="/w/index.php?title=Physical_Review_Letters.&action=edit&redlink=1" class="new" title="Physical Review Letters. (없는 문서)">Physical Review Letters.</a>》 <b>72</b> (8): 1240. <a href="/wiki/%EB%94%94%EC%A7%80%ED%84%B8_%EA%B0%9D%EC%B2%B4_%EC%8B%9D%EB%B3%84%EC%9E%90" title="디지털 객체 식별자">doi</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRevLett.72.1240">10.1103/PhysRevLett.72.1240</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters.&rft.atitle=Finite-difference-pseudopotential+method%3A+Electronic+structure+calculations+without+a+basis&rft.volume=72&rft.issue=8&rft.pages=1240&rft.date=1994&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.72.1240&rft.au=James+R.+Chelikowsky%2C+N.+Troullier%2C+and+Y.+Saad&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EB%B0%94%ED%83%95+%ED%95%A8%EC%88%98+%EC%A7%91%ED%95%A9" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33"> CS1 관리 - 여러 이름 (<a href="/wiki/%EB%B6%84%EB%A5%98:CS1_%EA%B4%80%EB%A6%AC_-_%EC%97%AC%EB%9F%AC_%EC%9D%B4%EB%A6%84" title="분류:CS1 관리 - 여러 이름">링크</a>)</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><cite class="citation book">Lee, June Gunn (2016년 12월 1일). <a rel="nofollow" class="external text" href="https://www.crcpress.com/Computational-Materials-Science-An-Introduction-Second-Edition/Lee/p/book/9781498749732">《Computational Materials Science: An Introduction》 [전산재료과학개론]</a>. CRC Press. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/9781498749732" title="특수:책찾기/9781498749732"><bdi>9781498749732</bdi></a><span class="reference-accessdate">. 2018년 2월 27일에 확인함</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+Materials+Science%3A+An+Introduction&rft.pub=CRC+Press&rft.date=2016-12-01&rft.isbn=9781498749732&rft.aulast=Lee&rft.aufirst=June+Gunn&rft_id=https%3A%2F%2Fwww.crcpress.com%2FComputational-Materials-Science-An-Introduction-Second-Edition%2FLee%2Fp%2Fbook%2F9781498749732&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EB%B0%94%ED%83%95+%ED%95%A8%EC%88%98+%EC%A7%91%ED%95%A9" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div></div> <p><br /> </p> <table class="notice metadata plainlinks stub" 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