Theor Chem Acc (2015) 134:118
1 3
and TD-HF performance as for smaller molecules.
Figures 5 and 6 present 1 A
and 1 A
excitation energies
for H 2 O (the basis set is taken from Ref. [ 30 ]) as functions of the length, R , of one of the OH bonds. Around
the ground-state equilibrium geometry ( R = 1.8 a.u.)
all three linear response methods: TD-APSG, TD-GVB,
and TD-HF yield similar values of excitation energies,
which are in a substantial error (more than 1 eV) with
respect to the CCSD counterparts. When the bond is
stretched, the TD-APSG and TD-GVB approaches are
more reliable than TD-HF in reproducing excitations
which involve transitions from bonding or antibonding orbitals describing the breaking OH bond. This is
understandable taking into account that both the APSG
and GVB-PP methods are capable of describing bond
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
1
2
3
4
5
6
7
CCSD
TD-APSG
TD-GVB
TD-HF
LiH,
1 +
[eV]
R [a.u.]
Fig. 3 Potential energy curves of the fi rst two 1 Σ + excited states
for the dissociating LiH molecule. Solid lines : CCSD, dotted lines :
TD-APSG, dashed lines : TD-GVB, and dashed-dotted lines : TD-HF
results
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
1
2
3
4
5
6
7
CCSD
TD-APSG
TD-GVB
TD-HF
LiH,
1
[eV]
R [a.u.]
Fig. 4 Potential energy curves of the fi rst two 1 Π excited states for
the dissociating LiH molecule. Solid lines: CCSD, dotted lines: TDAPSG, dashed lines: TD-GVB, and dashed-dotted lines: TD-HF
results
2
3
4
5
6
2
3
4
5
6
7
8
9
10
11
12
13
CCSD
TD-APSG
TD-GVB
TD-HF
H 2 O,
1
A'
[eV]
R [a.u.]
Fig. 5 Potential energy curves of the fi rst two 1 A excited states for
H 2 O molecule with one dissociating OH bond. Solid lines : CCSD,
dotted lines : TD-APSG, dashed lines : TD-GVB, and dashed-dotted
lines : TD-HF results
2
3
4
5
6
0
1
2
3
4
5
6
7
8
9
10
11
CCSD
TD-APSG
TD-GVB
TD-HF
H 2 O,
1
A''
[eV]
R [a.u.]
Fig. 6 Potential energy curves of the fi rst two 1 A excited states for
H 2 O molecule with one dissociating OH bond. Solid lines : CCSD,
dotted lines : TD-APSG, dashed lines : TD-GVB, and dashed-dotted
lines : TD-HF results
224
Reprinted from the journal
1 3
and TD-HF performance as for smaller molecules.
Figures 5 and 6 present 1 A
and 1 A
excitation energies
for H 2 O (the basis set is taken from Ref. [ 30 ]) as functions of the length, R , of one of the OH bonds. Around
the ground-state equilibrium geometry ( R = 1.8 a.u.)
all three linear response methods: TD-APSG, TD-GVB,
and TD-HF yield similar values of excitation energies,
which are in a substantial error (more than 1 eV) with
respect to the CCSD counterparts. When the bond is
stretched, the TD-APSG and TD-GVB approaches are
more reliable than TD-HF in reproducing excitations
which involve transitions from bonding or antibonding orbitals describing the breaking OH bond. This is
understandable taking into account that both the APSG
and GVB-PP methods are capable of describing bond
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
1
2
3
4
5
6
7
CCSD
TD-APSG
TD-GVB
TD-HF
LiH,
1 +
[eV]
R [a.u.]
Fig. 3 Potential energy curves of the fi rst two 1 Σ + excited states
for the dissociating LiH molecule. Solid lines : CCSD, dotted lines :
TD-APSG, dashed lines : TD-GVB, and dashed-dotted lines : TD-HF
results
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
1
2
3
4
5
6
7
CCSD
TD-APSG
TD-GVB
TD-HF
LiH,
1
[eV]
R [a.u.]
Fig. 4 Potential energy curves of the fi rst two 1 Π excited states for
the dissociating LiH molecule. Solid lines: CCSD, dotted lines: TDAPSG, dashed lines: TD-GVB, and dashed-dotted lines: TD-HF
results
2
3
4
5
6
2
3
4
5
6
7
8
9
10
11
12
13
CCSD
TD-APSG
TD-GVB
TD-HF
H 2 O,
1
A'
[eV]
R [a.u.]
Fig. 5 Potential energy curves of the fi rst two 1 A excited states for
H 2 O molecule with one dissociating OH bond. Solid lines : CCSD,
dotted lines : TD-APSG, dashed lines : TD-GVB, and dashed-dotted
lines : TD-HF results
2
3
4
5
6
0
1
2
3
4
5
6
7
8
9
10
11
CCSD
TD-APSG
TD-GVB
TD-HF
H 2 O,
1
A''
[eV]
R [a.u.]
Fig. 6 Potential energy curves of the fi rst two 1 A excited states for
H 2 O molecule with one dissociating OH bond. Solid lines : CCSD,
dotted lines : TD-APSG, dashed lines : TD-GVB, and dashed-dotted
lines : TD-HF results
224
Reprinted from the journal