New Strategies in Modeling Electronic Structures and Properties …
149
Table 2 15 lowest-lying IH-FSCCSD vertical excitation energies of the NUN molecule (r U−N =
1.739 Å). Excitation energies are given in eV [151]
Ω
Character (from DC)
DC
DC(G) X2C/AMF X2C/MMF X2C(G)/MMF
2 g
52% σ 1/2u φ 5/2u + 26%
π 1/2u φ 5/2u
0.956
0.923
0.936
0.957
0.927
3 g
50% σ 1/2u φ 5/2u + 24%
π 1/2u φ 5/2u
1.103
1.068
1.083
1.103
1.072
1 g
45% σ 1/2u δ 3/2u + 20%
π 1/2u δ 3/2u
1.134
1.094
1.106
1.134
1.098
2 g
30% σ 1/2u δ 3/2u + 15%
π 1/2u δ 3/2u
1.398
1.355
1.374
1.398
1.358
4 g
49% σ 1/2u φ 7/2u + 23%
π 1/2u φ 7/2u + 16% σ 1/2u φ
7/2u
1.699
1.645
1.680
1.698
1.646
3 g
43% σ 1/2u δ 5/2u + 20%
π 1/2u δ 5/2u
1.757
1.704
1.739
1.757
1.705
3 g
38% σ 1/2u φ 7/2u + 22%
π 1/2u φ 7/2u
2.076
2.028
2.059
2.076
2.029
2 g
33% σ 1/2u δ 5/2u + 17%
π 1/2u δ 5/2u
2.519
2.476
2.502
2.519
2.478
1 u
40% σ 1/2u δ 3/2g + 24%
π 1/2u δ 3/2g
2.669
2.696
2.680
2.669
2.696
0 +
u
41% σ 1/2u σ 1/2g + 30%
π 1/2u σ 1/2g
2.709
2.757
2.740
2.709
2.755
1 u
41% π 3/2u σ
1/2g + 29%
π
3/2u σ
1/2g
2.711
2.759
2.743
2.711
2.757
1 g
80% π 3/2u φ 5/2u
2.711
2.675
2.690
2.711
2.679
2 u
34% σ 1/2u δ 3/2g + 24%
π 1/2u δ 3/2g
2.749
2.767
2.758
2.749
2.768
4 g
84% π 3/2u φ 5/2u
2.844
2.808
2.823
2.844
2.811
2 u
73% σ 1/2g φ 5/2u
2.895
2.857
2.875
2.895
2.860
different relativistic Hamiltonians is presented in Table 2 [151]. DC denotes the standard Dirac–Coulomb Hamiltonian, DC(G) is the DC Hamiltonian augmented with
the Gaunt operator at the SCF level, X2C/AMF and MMF correspond to the X2C
Hamiltonian with the atomic and molecular mean field approximations to spin–orbit
coupling, and X2C(G) is again the X2C Hamiltonian augmented with the Gaunt operator at the SCF level. Based on the data presented in Table 2, we can conclude that
NUN possesses significant multi-reference character and a rather complex electronic
spectrum [151]. Furthermore, including the Gaunt operator in the Hamiltonian has
only negligible effect on the electronic spectra of NUN, while the X2C Hamiltonian
represents a computationally cheaper alternative to the full DC Hamiltonian. Specifically, the spin–orbit electronic spectrum calculated within X2C/MMF is almost
identical to the DC spectrum.
149
Table 2 15 lowest-lying IH-FSCCSD vertical excitation energies of the NUN molecule (r U−N =
1.739 Å). Excitation energies are given in eV [151]
Ω
Character (from DC)
DC
DC(G) X2C/AMF X2C/MMF X2C(G)/MMF
2 g
52% σ 1/2u φ 5/2u + 26%
π 1/2u φ 5/2u
0.956
0.923
0.936
0.957
0.927
3 g
50% σ 1/2u φ 5/2u + 24%
π 1/2u φ 5/2u
1.103
1.068
1.083
1.103
1.072
1 g
45% σ 1/2u δ 3/2u + 20%
π 1/2u δ 3/2u
1.134
1.094
1.106
1.134
1.098
2 g
30% σ 1/2u δ 3/2u + 15%
π 1/2u δ 3/2u
1.398
1.355
1.374
1.398
1.358
4 g
49% σ 1/2u φ 7/2u + 23%
π 1/2u φ 7/2u + 16% σ 1/2u φ
7/2u
1.699
1.645
1.680
1.698
1.646
3 g
43% σ 1/2u δ 5/2u + 20%
π 1/2u δ 5/2u
1.757
1.704
1.739
1.757
1.705
3 g
38% σ 1/2u φ 7/2u + 22%
π 1/2u φ 7/2u
2.076
2.028
2.059
2.076
2.029
2 g
33% σ 1/2u δ 5/2u + 17%
π 1/2u δ 5/2u
2.519
2.476
2.502
2.519
2.478
1 u
40% σ 1/2u δ 3/2g + 24%
π 1/2u δ 3/2g
2.669
2.696
2.680
2.669
2.696
0 +
u
41% σ 1/2u σ 1/2g + 30%
π 1/2u σ 1/2g
2.709
2.757
2.740
2.709
2.755
1 u
41% π 3/2u σ
1/2g + 29%
π
3/2u σ
1/2g
2.711
2.759
2.743
2.711
2.757
1 g
80% π 3/2u φ 5/2u
2.711
2.675
2.690
2.711
2.679
2 u
34% σ 1/2u δ 3/2g + 24%
π 1/2u δ 3/2g
2.749
2.767
2.758
2.749
2.768
4 g
84% π 3/2u φ 5/2u
2.844
2.808
2.823
2.844
2.811
2 u
73% σ 1/2g φ 5/2u
2.895
2.857
2.875
2.895
2.860
different relativistic Hamiltonians is presented in Table 2 [151]. DC denotes the standard Dirac–Coulomb Hamiltonian, DC(G) is the DC Hamiltonian augmented with
the Gaunt operator at the SCF level, X2C/AMF and MMF correspond to the X2C
Hamiltonian with the atomic and molecular mean field approximations to spin–orbit
coupling, and X2C(G) is again the X2C Hamiltonian augmented with the Gaunt operator at the SCF level. Based on the data presented in Table 2, we can conclude that
NUN possesses significant multi-reference character and a rather complex electronic
spectrum [151]. Furthermore, including the Gaunt operator in the Hamiltonian has
only negligible effect on the electronic spectra of NUN, while the X2C Hamiltonian
represents a computationally cheaper alternative to the full DC Hamiltonian. Specifically, the spin–orbit electronic spectrum calculated within X2C/MMF is almost
identical to the DC spectrum.