Dear Ding,Typically when we refer to "HOMO" we mean "Highest (Doubly) Occupied MO" and the term "SOMO" for "Singly Occupied MO" is used instead for an open-shell system. So I personally don't like the term "HOMO-LUMO gap" in an open-shell system like you describe. Sometimes though people will refer to orbital #1 (with both alpha and beta occupancy) as the HOMO or DOMO, orbital #2 as the SOMO, etc. (I'm also ignoring the extra question of whether you're using ROHF and your alpha and beta orbital energies match up nicely or UHF and the alpha and beta orbitals are of different energy.)
Frequently, people care about HOMO-LUMO gap for optical properties, since for many organic molecules, the strongest optical absorption comes from a HOMO-LUMO optical transition.
So if you care about the optical absorption property of open-shell molecules rather than SOMO-LUMO gap or something like this, then I suggest you do something like a ZINDO (INDO/S) or TDDFT calculation and look at the low-energy optical excitations. These can be done on close-shell or open-shell systems, although there can be multiple strong excitations in an open shell system -- particularly common in pi-conjugated organic molecules.
The accuracy of ZINDO or TDDFT calculations on open-shell systems is a frequent topic of discussion on the list, and you should try to compare computed excitation energies with experimental measurements for your particular system.
Regards, -Geoff -- -Dr. Geoffrey Hutchison <grh25(at)cornell.edu> Cornell University, Department of Chemistry and Chemical Biology Abruqa Group http://abruna.chem.cornell.edu/ On Jun 27, 2005, at 8:34 PM, Ding Xunlei wrote:
Dear Sir/Madam#: A open shell system has the MOs like this: #- #-4 #- #-5 #- #-3 #-x#-2 #-x#- #-x#-1 #-x#- #-x#- #-x#- #-x#- alpha beta MO with "x" has an electron occupation. Then how to define the HOMO-LUMO gap of this system? To define on gap as E_gap=E3-E2 or to define two gaps for alpha and beta as E_gap=E3-E1, and E_gap=E4-E2 ,respectively? Yours sincerely, Ding Xunlei 2005-06-28 ______________________________________________-= This is automatically added to each message by the mailing script =- To send e-mail to subscribers of CCL put the string CCL: on your Subject: lineand send your message to: CHEMISTRY(at)ccl.netSend your subscription/unsubscription requests to: CHEMISTRY- REQUEST(at)ccl.netHOME Page: http://www.ccl.net | Jobs Page: http://www.ccl.net/jobsIf your is mail bouncing from ccl.net domain due to spam filters, pleaseuse the Web based form from CCL Home Page-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+- +-+-+