Indeed, the results of ab initio calculations have shown that these invariants for
different most stable configurations of the CH 4 –N 2 complex change by less than
0.1 % [49]. The calculated values of the invariants A
2 and B
2 of the complex are
presented in Table 5.3. Note, that at R ¼ 1 the invariants A
2 and B
2 are fully
determined by b abc of the CH 4 molecule because for N 2 the hyperpolarizability b abc
is equal to zero.
6
8
10
12
14
16
18
20
-2
0
2
4
6
8
10
(a.u.)
R (a 0 )
xxx
CCSD(T)
xyy
CCSD(T)
yyy
CCSD(T)
xxx
analytic
xyy
analytic
yyy
analytic
1
2
3
6
8
10
12
14
16
18
20
-2
0
2
4
6
8
xxx
CCSD(T)
xyy
CCSD(T)
yyy
CCSD(T)
xxx
analytic
xyy
analytic
yyy
analytic
(a.u.)
R (a 0 )
1
2
3
6
8
10
12
14
16
18
20
-2
0
2
4
6
xxx
CCSD(T)
xyy
CCSD(T)
xzz
CCSD(T)
xxx
analytic
xyy
analytic
xzz
analytic
(a.u.)
R (a 0 )
1
2
3
6
8
10
12
14
16
18
20
0
2
4
6
8
xxx
CCSD(T)
xyy
CCSD(T)
xzz
CCSD(T)
xxx
analytic
xyy
analytic
xzz
analytic
(a.u.)
R (a 0 )
1
2
3
6
8
1 0
1 2
1 4
1 6
1 8
2 0
-2
-1
0
1
2
3
4
5
3
4
6
1
2
R (a 0 )
(a.u.)
xxx
analytic
xxy
analytic
xyy
analytic
yyy
analytic
xzz
analytic
yzz
analytic
xxx
CCSD(T)
xxy
CCSD(T)
xyy
CCSD(T)
yyy
CCSD(T)
xzz
CCSD(T)
yzz
CCSD(T)
6
8
10
12
14
16
18
20
-4
-2
0
2
4
6
xxx
CCSD(T)
xxy
CCSD(T)
xyy
CCSD(T)
yyy
CCSD(T)
xzz
CCSD(T)
yzz
CCSD(T)
5
3
4
6
1
2
R (a 0 )
(a.u.)
xxx
analytic
xxy
analytic
xyy
analytic
yyy
analytic
xzz
analytic
yzz
analytic
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 5.1 Induced first hyperpolarizability tensor components for six configurations of the CH 4 –N 2
complex
5.2 First Hyperpolarizabilitiy of the CH 4 –N 2 van der Waals Complex
89