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Koopmans' theorem (Read 3948 times)
Gerrit-Jan Linker
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Koopmans' theorem
28.08.09 at 12:36:04
 
Koopmans' theorem
 
IP ≈ -εi      , 1 ≤ i ≤ N
EA ≈ -εa , N+1 ≤ a
 
N is the number of electrons.
 
IP = Ionisation Potential = the amount of energy needed to remove an electron from the molecule
EA = Electron Affinity = the amount of energy needed to remove an electron from the charged negative ion.
 
The IP is equal to -εHOMO of the uncharged molecule.
The EA is equal to -εHOMO of the singly charged molecule.
 
Two errors in the calculation of Koopman's IP's work to (partially) cancel eachother. Orbital relaxation and correlation. Orbitals are not relaxed after extracting the electron. Also correlation effect are not taken into account.  
 
Occupied HF orbital energies are self interaction free:
The electrons in an occupied HF orbital feels the potential of N-1 electrons.
 
Unoccupied HF orbital energies are not self-interaction free:
The electrons in virtual HF orbitals feel the potential of N electrons.
 
Binding energy (Koopmans) BEi(KT)=Ei(N-1)(FO)-EN(HF) = -εi
KT = Koopmans Theorem ; FO = Frozen Orbital ; HF = Hartree Fock
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« Last Edit: 19.02.12 at 00:11:37 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
Linker IT Software
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Gerrit-Jan Linker
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Posts: 75
Delta SCF
Reply #1 - 09.10.09 at 11:57:25
 
Delta SCF
 
Koopman's theorem states that the first ionisation potential IP is appoximately equal to the HF orbital energy of the HOMO: -εHOMO.
 
IP = Ionisation Potential = the amount of energy needed to remove an electron from the molecule.
 
Another way to calculate the first ionisation potential is to do a delta SCF calculation. Obtain the total HF energy for the uncharged molecule. Then ionise it, calculate the total HF energy for the molecule with +1 charge. In this second calculation all the orbitals adopt (relax) to the missing electron. Each electron now moves in an average field of N-1 electrons.
 
IP1 = E(uncharged molecule) - E(+1 charged molecule)
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« Last Edit: 15.10.09 at 15:48:13 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
Linker IT Software
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