How to define HOMO-LUMO gap in open shell system ?

From: "Ding Xunlei" <dxl=at=ustc.edu.cn>
Organization: University of Science and Technology of China
Subject: How to define HOMO-LUMO gap in open shell system ?
Date: Tue, 28 Jun 2005 08:34:00 +0800

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
 ______________________________________________