Coupled cluster (original) (raw)
Metoda vázaných klastrů nebo spřažených klastrů (CC, z angl. Coupled Cluster) je jedna z ab initio metod pro odhad elektronové korelační energie. Tato metoda byla vytvořena v padesátých letech 20. století původně pro potřeby jaderné fyziky. Po jejím přeformulování Jiřím Čížkem se stala více využívanou pro elektronovou korelaci v atomech a molekulách.
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| dbo:abstract | Metoda vázaných klastrů nebo spřažených klastrů (CC, z angl. Coupled Cluster) je jedna z ab initio metod pro odhad elektronové korelační energie. Tato metoda byla vytvořena v padesátých letech 20. století původně pro potřeby jaderné fyziky. Po jejím přeformulování Jiřím Čížkem se stala více využívanou pro elektronovou korelaci v atomech a molekulách. (cs) Coupled Cluster (CC) bezeichnet eine Methode zur Lösung der Schrödinger-Gleichung, die besonders in der Quantenchemie als eine von vielen post-Hartee-Fock ab initio Methoden verwendet wird. Es handelt sich um ein der Configuration Interaction ähnliches Verfahren. Die Vielteilchen-Wellenfunktion wird dabei in eine Basis aus Slater-Determinanten entwickelt, wodurch die Schrödinger-Gleichung auf ein Matrix-Eigenwertproblem reduziert wird. Die (teilweise) Diagonalisierung dieser Matrix liefert dann die Eigenzustände des quantenmechanischen Systems. Da die Genauigkeit z. B. der Hartree-Fock (HF) Lösungen in der Regel nicht ausreichend ist muss im Anschluss an z. B. eine HF-Rechnung eine korrelierte Rechnung durchgeführt werden, wobei die vorher berechneten unbesetzten Orbitale zum Einsatz kommen. Die Methode stammte ursprünglich aus der Kernphysik und wurde dort in den 1950er Jahren von Fritz Coester und Hermann Kümmel eingeführt. In den 1960er Jahren wurde sie von (später zusammen mit ) für Elektronenkorrelationen in Atomen und Molekülen formuliert und fand weite Verbreitung in der Quantenchemie. Für die Coupled Cluster Methode (CCM) erhielten Kümmel und Raymond Bishop 2005 die Feenberg-Medaille. (de) Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used in nuclear physics. Coupled cluster essentially takes the basic Hartree–Fock molecular orbital method and constructs multi-electron wavefunctions using the exponential cluster operator to account for electron correlation. Some of the most accurate calculations for small to medium-sized molecules use this method. The method was initially developed by and in the 1950s for studying nuclear-physics phenomena, but became more frequently used when in 1966 Jiří Čížek (and later together with Josef Paldus) reformulated the method for electron correlation in atoms and molecules. It is now one of the most prevalent methods in quantum chemistry that includes electronic correlation. CC theory is simply the perturbative variant of the many-electron theory (MET) of Oktay Sinanoğlu, which is the exact (and variational) solution of the many-electron problem, so it was also called "coupled-pair MET (CPMET)". J. Čížek used the correlation function of MET and used Goldstone-type perturbation theory to get the energy expression, while original MET was completely variational. Čížek first developed the linear CPMET and then generalized it to full CPMET in the same work in 1966. He then also performed an application of it on the benzene molecule with Sinanoğlu in the same year. Because MET is somewhat difficult to perform computationally, CC is simpler and thus, in today's computational chemistry, CC is the best variant of MET and gives highly accurate results in comparison to experiments. (en) La méthode du cluster couplé, ou théorie du cluster couplé (expression souvent abrégée en « cluster couplé », en anglais coupled cluster) est une technique numérique de description des . Son utilisation la plus répandue est comme méthode ab initio de chimie quantique post-Hartree-Fock en chimie numérique. Il est basé sur la méthode d'orbitale moléculaire Hartree-Fock et lui ajoute un terme de correction afin de prendre en compte la corrélation électronique. Certains des calculs les plus précis pour des molécules de petite ou de taille moyenne utilisent cette méthode. La méthode fut développée initialement par et dans les années 1950 afin d'étudier les phénomènes de physique nucléaire, mais devint plus fréquemment utilisée après que et eurent reformulé la méthode pour l'adapter à la corrélation électronique dans les atomes et molécules dans les années 1960. Elle constitue à ce jour une des méthodes les plus répandues en chimie quantique incluant la corrélation électronique. (fr) Il metodo Coupled Cluster (CC) è una tecnica di calcolo utilizzata per descrivere sistemi a molte particelle. Il suo uso principale è nell'ambito dei metodi computazionali post-Hartree-Fock ab initio in chimica quantistica. Come tutti i metodi post-Hartree-Fock, il metodo CC introduce un fattore correttivo all'orbitale molecolare in modo da tenere conto delle singole forze repulsive elettrone-elettrone; tale fattore è rappresentato da un operatore esponenziale. Alcuni dei calcoli più accurati, relativamente a dimensioni molecolari che variano da piccole a medie, utilizzano questo metodo. Il Coupled Cluster fu inizialmente sviluppato da e negli anni cinquanta per lo studio di fenomeni fisico nucleari, ma e nel decennio successivo riformularono il metodo per renderlo applicabile per i calcoli di chimica quantistica relativamente ad atomi e molecole. Attualmente rappresenta uno dei più importanti metodi computazionali che tengono conto della correlazione elettronica. È importante notare che il Coupled Cluster è applicabile a tutti i sistemi fermionici, che nel nostro caso sono rappresentati da sistemi di elettroni. (it) 結合クラスター法（けつごうクラスターほう、クラスター展開法、CC法：Coupled Cluster）は多体系を記述するために使われる数値手法である。最もよく使われるのは、量子化学（計算化学）におけるポスト-ハートリー-フォック第一原理計算がある。CC法は、ハートリーフォック分子軌道法を基本にして、電子相関を考慮する指数関数クラスター演算子を使って多電子波動関数を構成する。CC法を用いて、小さい分子や中程度の大きさの分子について最も正確な計算を行うことができる。 (ja) Зв'язані кластери (англ. Coupled cluster, CC) — числовий метод, що використовується для квантового розрахунку систем багатьох частинок. Найчастіше його використовуються в обчислювальній хімії для ab initio розрахунку кореляційної енергії після методу Хартрі-Фока, але він також використовується в ядерній фізиці. (uk) 耦合簇方法（coupled cluster, CC）是量子化學中對的其中一種高精確計算方法。它从哈特里－福克分子轨道出发，通过指数形式的耦合算符运算得到真实体系的波函数。一些小分子和中等大小的分子精度最高的计算结果是通过 CC 方法得到的。 (zh) |
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| rdfs:comment | Metoda vázaných klastrů nebo spřažených klastrů (CC, z angl. Coupled Cluster) je jedna z ab initio metod pro odhad elektronové korelační energie. Tato metoda byla vytvořena v padesátých letech 20. století původně pro potřeby jaderné fyziky. Po jejím přeformulování Jiřím Čížkem se stala více využívanou pro elektronovou korelaci v atomech a molekulách. (cs) 結合クラスター法（けつごうクラスターほう、クラスター展開法、CC法：Coupled Cluster）は多体系を記述するために使われる数値手法である。最もよく使われるのは、量子化学（計算化学）におけるポスト-ハートリー-フォック第一原理計算がある。CC法は、ハートリーフォック分子軌道法を基本にして、電子相関を考慮する指数関数クラスター演算子を使って多電子波動関数を構成する。CC法を用いて、小さい分子や中程度の大きさの分子について最も正確な計算を行うことができる。 (ja) Зв'язані кластери (англ. Coupled cluster, CC) — числовий метод, що використовується для квантового розрахунку систем багатьох частинок. Найчастіше його використовуються в обчислювальній хімії для ab initio розрахунку кореляційної енергії після методу Хартрі-Фока, але він також використовується в ядерній фізиці. (uk) 耦合簇方法（coupled cluster, CC）是量子化學中對的其中一種高精確計算方法。它从哈特里－福克分子轨道出发，通过指数形式的耦合算符运算得到真实体系的波函数。一些小分子和中等大小的分子精度最高的计算结果是通过 CC 方法得到的。 (zh) Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used in nuclear physics. Coupled cluster essentially takes the basic Hartree–Fock molecular orbital method and constructs multi-electron wavefunctions using the exponential cluster operator to account for electron correlation. Some of the most accurate calculations for small to medium-sized molecules use this method. (en) Coupled Cluster (CC) bezeichnet eine Methode zur Lösung der Schrödinger-Gleichung, die besonders in der Quantenchemie als eine von vielen post-Hartee-Fock ab initio Methoden verwendet wird. Es handelt sich um ein der Configuration Interaction ähnliches Verfahren. Die Vielteilchen-Wellenfunktion wird dabei in eine Basis aus Slater-Determinanten entwickelt, wodurch die Schrödinger-Gleichung auf ein Matrix-Eigenwertproblem reduziert wird. Die (teilweise) Diagonalisierung dieser Matrix liefert dann die Eigenzustände des quantenmechanischen Systems. (de) La méthode du cluster couplé, ou théorie du cluster couplé (expression souvent abrégée en « cluster couplé », en anglais coupled cluster) est une technique numérique de description des . Son utilisation la plus répandue est comme méthode ab initio de chimie quantique post-Hartree-Fock en chimie numérique. Il est basé sur la méthode d'orbitale moléculaire Hartree-Fock et lui ajoute un terme de correction afin de prendre en compte la corrélation électronique. Certains des calculs les plus précis pour des molécules de petite ou de taille moyenne utilisent cette méthode. (fr) Il metodo Coupled Cluster (CC) è una tecnica di calcolo utilizzata per descrivere sistemi a molte particelle. Il suo uso principale è nell'ambito dei metodi computazionali post-Hartree-Fock ab initio in chimica quantistica. Come tutti i metodi post-Hartree-Fock, il metodo CC introduce un fattore correttivo all'orbitale molecolare in modo da tenere conto delle singole forze repulsive elettrone-elettrone; tale fattore è rappresentato da un operatore esponenziale. Alcuni dei calcoli più accurati, relativamente a dimensioni molecolari che variano da piccole a medie, utilizzano questo metodo. (it) |
| rdfs:label | Metoda vázaných klastrů (cs) Coupled Cluster (de) Coupled cluster (en) Méthode du cluster couplé (fr) Metodo Coupled Cluster (it) 結合クラスター法 (ja) Зв'язані кластери (uk) 耦合簇方法 (zh) |
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