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| '''Restricted open-shell Hartree–Fock''' ('''ROHF''') is a variant of [[Hartree–Fock]] theory for [[open shell]] molecules. It uses doubly occupied [[molecular orbitals]] as far as possible and then singly occupied orbitals for the unpaired electrons. This is the simple picture for open shell molecules but it is difficult to implement. | | Jayson Berryhill is how I'm known as and my wife doesn't like it at all. Distributing manufacturing is where my primary income comes from and it's something I really appreciate. Alaska is exactly where I've always been residing. The preferred pastime for him and his online psychic ([http://fashionlinked.com/index.php?do=/profile-13453/info/ fashionlinked.com]) free psychic - [http://alles-herunterladen.de/excellent-advice-for-picking-the-ideal-hobby/ simply click the next website page], children is fashion and he'll be beginning some thing else along with it.<br><br>my webpage :: [http://www.010-5260-5333.com/index.php?document_srl=1880&mid=board_ALMP66 phone psychic readings] |
| The foundations of the ROHF method were first formulated by Roothaan in a celebrated paper <ref> | |
| {{cite journal
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| | last = Roothaan|first= C. C. J.
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| | year = 1960
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| | title = Self-consistent field theory for open shells of electronic systems
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| | journal = Rev. Mod. Phys.
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| | volume = 32
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| | issue = 2
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| | pages = 179–185
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| | doi = 10.1103/RevModPhys.32.179|bibcode = 1960RvMP...32..179R }}
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| </ref> and then extended by various authors, see e.g.<ref>
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| {{cite book
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| | isbn = 978-0-387-08535-7
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| | year = 1978
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| | first1 = R. |last1=Carbó|first2=J. M.|last2= Riera
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| | volume =5
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| | publisher = Springer
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| |doi=10.1007/978-3-642-93075-1_1
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| |title=A General SCF Theory
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| |series=Lecture Notes in Chemistry |pages=1–4
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| |chapter=Historical Review }}
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| </ref><ref>
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| {{cite book
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| | first = R.|last= McWeeny
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| | title = Methods of Molecular Quantum Mechanics
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| | edition = 2nd
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| | year =1992
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| | publisher = Academic Press
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| | isbn = 978-0-470-01187-4
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| }}</ref><ref>
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| {{cite book
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| | editor-first = K. D. |editor-last=Sen
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| | first = B. N.|last= Plakhutin
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| | title = Reviews of Modern Quantum Chemistry
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| | publisher = Word Scientific
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| | pages = 16–42
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| | volume = 1
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| | year = 2002
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| | isbn = 978-981-02-4889-5
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| }}
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| </ref> for in-depth discussions.
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| As with restricted Hartree–Fock theory for closed shell molecules, it leads to [[Roothaan equations]] written in the form of a [[generalized eigenvalue problem]]
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| :<math>\mathbf{F} \mathbf{C} = \mathbf{S} \mathbf{C} \mathbf{\epsilon}</math>
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| Where F is the so-called [[Fock matrix]] (which is a function of C), C is a matrix of coefficients, S is the [[overlap matrix]] of the basis functions, and <math>\epsilon</math> is the (diagonal, by convention) matrix of orbital energies. Unlike restricted Hartree–Fock theory for closed shell molecules, the form of the Fock matrix is not unique. Different so-called canonicalisations can be used leading to different orbitals and different orbital energies, but the same total wavefunction, total energy, and other observables.
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| In contrast to [[unrestricted Hartree–Fock]] (UHF), the ROHF wave function is a satisfactory eigenfunction of the total spin operator - <math>\mathbf{S}^2</math> (i.e. no [[Spin contamination]]).
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| Developing [[post-Hartree–Fock]] methods based on a ROHF wave function is inherently more difficult than using a UHF wave function, due to the lack of a unique set of molecular
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| orbitals.<ref>{{cite journal | last1 = Glaesemann | first1 = Kurt R. | last2 = Schmidt | first2 = Michael W. | title = On the Ordering of Orbital Energies in High-Spin ROHF† | journal = The Journal of Physical Chemistry A | volume = 114 | issue =33 | pages = 8772–8777 | year = 2010 | pmid = 20443582 | doi = 10.1021/jp101758y}}
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| </ref>
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| However, different choices of reference orbitals have shown to provide similar results,<ref>
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| {{cite book
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| | first = F.|last= Jensen
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| | title = Introduction to Computational Chemistry
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| | edition = 2nd
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| | publisher = Wiley
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| | year = 2007
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| | isbn = 978-0-471-98425-2
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| }}</ref> and thus many different [[post-Hartree–Fock]] methods have been implemented in a variety of electronic structure packages.
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| Many (but not all) of these post-Hartree–Fock methods are completely [[Invariant (mathematics)|invariant]] with respect to orbital choice (assuming that no orbitals are "frozen" and
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| thus not correlated).<ref>{{cite journal | doi=10.1063/1.471951 | title=On the energy invariance of open-shell perturbation theory with respect to unitary transformations of molecular orbitals | year=1996 | last1=Crawford | first1=T. Daniel | last2=Schaefer | first2=Henry F. | last3=Lee | first3=Timothy J. | journal=The Journal of Chemical Physics | volume=105 | issue = 3 | pages=1060|bibcode = 1996JChPh.105.1060C }}</ref>
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| The ZAPT2 version of [[Møller–Plesset perturbation theory]] specifies the choice of orbitals.
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| ==References== | |
| <references/>
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| {{DEFAULTSORT:Restricted Open-Shell Hartree-Fock}}
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| [[Category:Electronic structure methods]]
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| {{Chem-stub}}
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| {{Quantum-stub}}
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