MOLPRO

20 THE CI PROGRAM 163
***,BH singlet Sigma and Delta states
r=2.1
geometry={b;h,b,r}
{hf;occ,3;wf,6,1;}
{multi;
occ,3,1,1;frozen,1;wf,6,1;state,3;lquant,0,2,0;wf,6,4;lquant,2;
tran,lz;
expec2,lzlz;}
! Sigma states -- energies -25.20509620 -24.94085861
{ci;occ,3,1,1;core,1;wf,6,1;state,2,1,3;}
! Delta states -- energies -24.98625171
{ci;occ,3,1,1;core,1;wf,6,1;state,1,2;}
! Delta state -- xy component
{ci;occ,3,1,1;core,1;wf,6,4;}
http:
//www.molpro.net/info/current/examples/bh_mrci_sigma_delta.com
20.7 Cluster corrections for multi-state MRCI
In the following, we assume that
Ψ (n)
Ψ (n)
ref
= ∑
R
C (0)
Rn Φ R (46)
mrci
= ∑C Rn Φ R + Ψ c (47)
R
are the normalized reference and MRCI wave functions for state n, respectively. C (0)
R are the
coefficients of the reference configurations in the initial reference functions and C Rn are the
relaxed coefficients of these configurations in the final MRCI wave function. Ψ c is the remainder
of the MRCI wave function, which is orthogonal to all reference configurations Φ R .
The corresponding energies are defined as
E (n)
ref
= 〈Ψ (n)
ref |Ĥ|Ψ(n) ref
〉, (48)
E (n)
mrci
= 〈Ψ (n)
mrci |Ĥ|Ψ(n) mrci
〉. (49)
The standard Davidson corrected correlation energies are defined as
E n D = E (n)
corr · 1 − c2 n
c 2 n
(50)
where c n is the coefficient of the (fixed) reference function in the MRCI wave function:
c n
= 〈Ψ (n)
ref |Ψ(n)
mrci 〉 = ∑
R
C (0)
Rn C Rn, (51)
and the correlation energies are
E (n)
corr
= E (n)
mrci − E(n) ref . (52)
In the vicinity of avoided crossings this correction may give unreasonable results since the reference
function may get a small overlap with the MRCI wave function. One way to avoid this