in the complex show that the exchange contributions into the dipole moment of the
complex CH 4 –N 2 may be obtained in the analytical form.
B. Dipole moment of the most stable configuration of CH 4 –N 2 complex
It is also interesting to consider the dipole moment of the most stable configuration of CH 4 –N 2 complex. In Ref. [63] it was found that the CH 4 –N 2 complex has
a family of such configurations with practically equal interaction energies (the
difference is less than 0.04 cm
−1 ). These configurations can be obtained from the
configuration 4 by rotation of the N 2 molecule by angle τ over the x axis at fixed
equilibrium intermolecular separation R e = 6.8 a 0 . The rotation of nitrogen molecule by angle τ corresponds to its rotation by angle θ B at fixed angle φ B = 90°.
The dipole moment of the complex was obtained for angle τ from 0° to 180° by
15° (13 configurations). For the calculations we have employed Eq. (3.1.2), that
provides enough accuracy for the correct description of small changing in l a ðR; sÞ.
The resulting analytical form for l a ðR; sÞ was found to be as follows (in a.u.)
l x ðR; sÞ ¼ À
27:67779
R 4
À
78:76850
R 5
þ
379:8549
R 6
þ
687:0685
R 7
þ B x ðsÞf ðRÞ;
ð3:2:15Þ
l y ðR; sÞ ¼ À
8:282
R 5 þ
39:795
R 6
2 cos
2 s À 1
À
Á
þ
57:053 cos
4 s þ 610:461 cos
2 s À 326:625
R 7
þ B y s
ð Þf ðRÞ;
ð3:2:16Þ
l z ðR; sÞ ¼ À
16:564
R 5 þ
79:590
R 6 þ
57:053 cos
2 s À 696:041
R 7
sin s cos s þ B z s
ð Þf ðRÞ;
ð3:2:17Þ
where
f ðRÞ ¼ R
3:20238 expðÀ1:53525RÞÁ
ð3:2:18Þ
The fitting parameters B a ðsÞ were obtained from ab initio values of dipole
moments at R e = 6.8 a 0 and can be written as
B x ðsÞ ¼ 0:112522 þ 0:000154 cos
2 s 4 cos
2 s À 3
À
Á 2 ;
ð3:2:19Þ
B y ðsÞ ¼ À0:005913 þ 0:000111 cos
2 s þ 0:022825 cos
4 s À 0:008514 cos
6 s;
ð3:2:20Þ
B z ðsÞ ¼ 0:019364 À 0:007734 cos
2 s
À
Á
sin s cos sÁ
ð 3:2:21Þ
3.2 Dipole Moment of van der Waals Complexes
37
complex CH 4 –N 2 may be obtained in the analytical form.
B. Dipole moment of the most stable configuration of CH 4 –N 2 complex
It is also interesting to consider the dipole moment of the most stable configuration of CH 4 –N 2 complex. In Ref. [63] it was found that the CH 4 –N 2 complex has
a family of such configurations with practically equal interaction energies (the
difference is less than 0.04 cm
−1 ). These configurations can be obtained from the
configuration 4 by rotation of the N 2 molecule by angle τ over the x axis at fixed
equilibrium intermolecular separation R e = 6.8 a 0 . The rotation of nitrogen molecule by angle τ corresponds to its rotation by angle θ B at fixed angle φ B = 90°.
The dipole moment of the complex was obtained for angle τ from 0° to 180° by
15° (13 configurations). For the calculations we have employed Eq. (3.1.2), that
provides enough accuracy for the correct description of small changing in l a ðR; sÞ.
The resulting analytical form for l a ðR; sÞ was found to be as follows (in a.u.)
l x ðR; sÞ ¼ À
27:67779
R 4
À
78:76850
R 5
þ
379:8549
R 6
þ
687:0685
R 7
þ B x ðsÞf ðRÞ;
ð3:2:15Þ
l y ðR; sÞ ¼ À
8:282
R 5 þ
39:795
R 6
2 cos
2 s À 1
À
Á
þ
57:053 cos
4 s þ 610:461 cos
2 s À 326:625
R 7
þ B y s
ð Þf ðRÞ;
ð3:2:16Þ
l z ðR; sÞ ¼ À
16:564
R 5 þ
79:590
R 6 þ
57:053 cos
2 s À 696:041
R 7
sin s cos s þ B z s
ð Þf ðRÞ;
ð3:2:17Þ
where
f ðRÞ ¼ R
3:20238 expðÀ1:53525RÞÁ
ð3:2:18Þ
The fitting parameters B a ðsÞ were obtained from ab initio values of dipole
moments at R e = 6.8 a 0 and can be written as
B x ðsÞ ¼ 0:112522 þ 0:000154 cos
2 s 4 cos
2 s À 3
À
Á 2 ;
ð3:2:19Þ
B y ðsÞ ¼ À0:005913 þ 0:000111 cos
2 s þ 0:022825 cos
4 s À 0:008514 cos
6 s;
ð3:2:20Þ
B z ðsÞ ¼ 0:019364 À 0:007734 cos
2 s
À
Á
sin s cos sÁ
ð 3:2:21Þ
3.2 Dipole Moment of van der Waals Complexes
37