102
M. Senami et al.
Table 1 Parity-violating energy of H 2 X 2 and contributions from heavy atom X are summarized.
The dihedral angle is chosen to be 45 ◦ or −45 ◦ , which have the same value with opposite sign. HF
means Hartree-Fock with Dirac-Coulomb Hamiltonian
Molecule Method
Basis set for X
|M
X
PV
| [a.u.]
|E PV | [a.u.]
Reference
H 2 O 2
HF
dyall.ae2z
3.3401 × 10 −6 3.8853 × 10 −19
This study
dyall.ae3z
5.1839 × 10
−6
6.0300 × 10
−19
This study
dyall.ae3z
−
6.051 × 10 −19
[10]
dyall.ae4z
−
6.376 × 10
−19
[10]
cc-pVDZ+3p
[22]
5.801 × 10 −6
−
[9]
25s25p5d [8]
6.057 × 10
−6
−
[9]
aug-cc-pVDZ
[22]
3.729 × 10 −6
−
[8]
aug-cc-pVTZ
[22]
4.239 × 10
−6
−
[8]
aug-cc-pVQZ
[22]
4.687 × 10 −6
−
[8]
25s25p5d
6.057 × 10
−6
−
[8]
CISD
cc-pVDZ+3p
5.410 × 10 −6
−
[9]
CCSD
dyall.ae3z
−
5.323 × 10 −19
[10]
dyall.ae4z
−
5.583 × 10 −19
[10]
cc-pVDZ+3p
5.299 × 10 −6
−
[9]
H 2 S 2
HF
dyall.ae2z
7.0563 × 10 −5 1.6416 × 10 −17
This study
cc-pCVTZ [22]
−
1.825826 ×
10
−17
[10]
cc-pVDZ+3p
8.916 × 10 −5
−
[9]
25s25p5d
9.581 × 10
−5
−
[8]
CCSD
cc-pCVTZ [22]
−
1.82103 × 10 −17 [10]
cc-pVDZ+3p
9.283 × 10
−5
−
[9]
H 2 Se 2
HF
dyall.ae2z
2.3917 × 10
−3
1.6334 × 10
−15
This study
25s25p5d
3.586 × 10 −3
−
[8]
CCSD
dyall.cv3z [23]
−
2.115 × 10
−15
[10]
H 2 Te 2
HF
dyall.ae2z
2.3842 × 10 −2 2.7769 × 10 −14
This study
25s25p5d
3.149 × 10 −2
−
[8]
CCSD
dyall.cv3z
−
3.289 × 10 −14
[10]
is consistent with our previous results [6]. The nonzero M
O
PV
means the existence of
the zeta force around oxygen nuclei, since the chirality density is proportional to the
zeta potential and the zeta potential is the potential for the zeta force. Hence this
result is consistent with the existence of the parity-violating energy.
In Fig. 4, the integrated chirality density as a function of the dihedral angle is
shown for (a) H 2 O 2 , (b) H 2 S 2 , (c) H 2 Se 2 , and (d) H 2 Te 2 molecules. Our result of
M. Senami et al.
Table 1 Parity-violating energy of H 2 X 2 and contributions from heavy atom X are summarized.
The dihedral angle is chosen to be 45 ◦ or −45 ◦ , which have the same value with opposite sign. HF
means Hartree-Fock with Dirac-Coulomb Hamiltonian
Molecule Method
Basis set for X
|M
X
PV
| [a.u.]
|E PV | [a.u.]
Reference
H 2 O 2
HF
dyall.ae2z
3.3401 × 10 −6 3.8853 × 10 −19
This study
dyall.ae3z
5.1839 × 10
−6
6.0300 × 10
−19
This study
dyall.ae3z
−
6.051 × 10 −19
[10]
dyall.ae4z
−
6.376 × 10
−19
[10]
cc-pVDZ+3p
[22]
5.801 × 10 −6
−
[9]
25s25p5d [8]
6.057 × 10
−6
−
[9]
aug-cc-pVDZ
[22]
3.729 × 10 −6
−
[8]
aug-cc-pVTZ
[22]
4.239 × 10
−6
−
[8]
aug-cc-pVQZ
[22]
4.687 × 10 −6
−
[8]
25s25p5d
6.057 × 10
−6
−
[8]
CISD
cc-pVDZ+3p
5.410 × 10 −6
−
[9]
CCSD
dyall.ae3z
−
5.323 × 10 −19
[10]
dyall.ae4z
−
5.583 × 10 −19
[10]
cc-pVDZ+3p
5.299 × 10 −6
−
[9]
H 2 S 2
HF
dyall.ae2z
7.0563 × 10 −5 1.6416 × 10 −17
This study
cc-pCVTZ [22]
−
1.825826 ×
10
−17
[10]
cc-pVDZ+3p
8.916 × 10 −5
−
[9]
25s25p5d
9.581 × 10
−5
−
[8]
CCSD
cc-pCVTZ [22]
−
1.82103 × 10 −17 [10]
cc-pVDZ+3p
9.283 × 10
−5
−
[9]
H 2 Se 2
HF
dyall.ae2z
2.3917 × 10
−3
1.6334 × 10
−15
This study
25s25p5d
3.586 × 10 −3
−
[8]
CCSD
dyall.cv3z [23]
−
2.115 × 10
−15
[10]
H 2 Te 2
HF
dyall.ae2z
2.3842 × 10 −2 2.7769 × 10 −14
This study
25s25p5d
3.149 × 10 −2
−
[8]
CCSD
dyall.cv3z
−
3.289 × 10 −14
[10]
is consistent with our previous results [6]. The nonzero M
O
PV
means the existence of
the zeta force around oxygen nuclei, since the chirality density is proportional to the
zeta potential and the zeta potential is the potential for the zeta force. Hence this
result is consistent with the existence of the parity-violating energy.
In Fig. 4, the integrated chirality density as a function of the dihedral angle is
shown for (a) H 2 O 2 , (b) H 2 S 2 , (c) H 2 Se 2 , and (d) H 2 Te 2 molecules. Our result of