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RHF and UHF wave functions (Read 6371 times)
Gerrit-Jan Linker
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RHF and UHF wave functions
20.02.08 at 12:46:36
 
RHF and UHF wave functions
 
Quantum mechanics calculations use either of two forms of the wave function: Restricted Hartree-Fock (RHF) or Unrestricted Hartree-Fock (UHF).  
 
Use the RHF wave function for singlet electronic states, such as the ground states of stable organic molecules. Spin orbitals are grouped in pairs for an RHF calculation. Each member of the pair differs in its spin function (one alpha and one beta), but both must share the same space function. For N electron s, N/2 different molecular orbitals (space function s) are doubly occupied, with one alpha (spin up) and one beta (spin down) electron forming a pair.  
 
A restricted Hartree-Fock description means that spin-up and spin-down electrons occupy the same spatial orbitals ψj—there is no allowance for different spatial orbitals for different electron spins.  
 
An unrestricted Hartree-Fock description (UHF) means that spin-up and spin-down electrons occupy different spatial orbitals. There is therefore more variational freedom and that is unphysical. Spin contamination can occur. Care should be taken therefore with UHF.
 
UHF wavefunctions are eigenfunctions of Sz but not of S2:
Szψ0 = ½(Nα - Nί0
RHF wavefunctions are eigenfunctions of both Sz and of S2.
 
See also:
Spin contamination
http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1261474180/0
ROHF
http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1285938955/0#0
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« Last Edit: 08.02.11 at 22:18:26 by Gerrit-Jan Linker »  

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