Chemistry Reference
In-Depth Information
Table 8
Comparison of Vertical Excitation Energies for First 12 Excited States of N
2
Calculated Using Different Methods for SCF Step
Excitation Energy (eV)
BARE KS
a
ALDA
a
ALDA
b
LB94
c
OEP
d
Expt
e
State
Excitation
Singlet ! Singlet Transitions
w
1
u
1
p
u
! 1
p
g
9.63
10.20
10.27
9.82
10.66
10.27
a
01
P
u
1
p
u
!
1
p
g
9.63
9.63
9.68
9.18
10.09
9.92
a
1
g
3
s
g
!
1
p
g
8.16
9.04
9.23
8.68
9.76
9.31
a
001
P
g
3
s
g
!
4
s
g
—
—
10.48
—
12.47
12.20
o
1
u
2
s
u
!
1
p
g
—
—
13.87
—
14.32
13.63
c
1
u
1
p
u
!
4
s
g
—
—
11.85
—
13.07
12.90
Singlet
!
Triplet Transitions
C
3
u
2
s
u
!
1
p
g
11.21
10.36
10.44
10.06
11.05
11.19
B
03
P
u
1
p
u
!
1
p
g
9.63
9.63
9.68
9.18
10.09
9.67
W
3
u
1
p
u
!
1
p
g
9.63
8.80
8.91
8.32
9.34
8.88
B
3
g
3
s
g
!
1
p
g
8.16
7.50
7.62
7.14
8.12
8.04
A
3
P
u
1
p
u
!
1
p
g
9.63
7.84
8.07
7.29
8.51
7.74
E
3
P
g
3
s
g
!
4
s
g
—
—
10.33
12.32
11.96
12.00
Mean Absolute Error
(0.61)
(0.27)
0.54
(0.63)
0.34
a
Using the Sadlej basis set. From Ref. 222.
b
Basis set free. From Ref. 221.
c
From Ref. 223.
d
Using KLI approximation. From Ref. 221.
e
Computed in Ref. 224 from the spectroscopic constants of Huber and Herzberg.
225
behavior as mentioned eariler. When comparing the basis set calculation with
the basis set free calculation, the occupied orbitals are found to be in good
agreement. However, for the unoccupied states that are unbounded in LDA,
basis sets cannot describe these states correctly, giving a positive energy value
that can vary greatly from one basis set to another.
For the LDA results calculated with the Sadlej basis set, the bare KS tran-
sition frequencies between these levels are shown in Table 8. Note that they
are in rough agreement with the experimental values and that they lie in
between the singlet-singlet and singlet-triplet transitions.
226
The ALDA XC
kernel
f
ACDA
XC
then shifts the KS transitions toward their correct values. Also
given in Table 8 are the mean absolute errors for each method; errors in par-
entheses are calculated for the lowest eight transitions only. For the eight low-
est transitions LDA does remarkably well, the mean absolute error (MAE)
being 0.27 eV for the Sadlej basis set. For higher transitions LDA fails drasti-
cally, the MAE increasing to 0.54 eV when the next four transitions are
included. This increase in the MAE is attributed to a cancellation of errors
that lead to good frequencies for the lower transitions.
221
Because LDA binds
