carried out with the correlation-consistent aug-cc-pVTZ basis set. For the evaluation of binding energy in the CBS limit, the aug-cc-pVQZ basis set was also used.
In order to correct the energy for the basis set incompleteness error (BSIE), the
energy was extrapolated to the CBS limit using the schemes of Martin (2.3.11) and
Helgaker (2.3.12). The dipole moment of the ethylene dimer was calculated by the
finite-field method described by Cohen and Roothaan [1] using Eq. (3.1.1) which
provides enough accuracy for the system under consideration (the errors do not
exceed 2 × 10
−5 ea 0 ). The experimental ground state geometry (averaged over
zero-point vibrations) of ethylene molecule was used for all calculations: the bond
lengths and angles of ethylene molecule r CC = 2.5303 a 0 , r CH = 2.0504 a 0 ,
∠HCC = 121.085° and ∠HCH = 117.83° were taken from Ref. [108]. The coordinate system of C 2 H 4 –C 2 H 4 complex is shown in Fig. 3.12.
The long-range analytical approximation used for the description of dipole
moment of the ethylene dimer, following the Sect. 3.1.2, gives the induction and
dispersion contributions through the order R
−7 as (here, the exchange interactions
are not considered)
Table 3.5 Molecular properties for C 2 H 4 molecule
Property
[100]
a
Lit.
Property
[100]
a
Lit.
Θ xx
−2.47
−2.42
b
C xx,xx
72.19
51.93
d
Θ yy
1.25
1.23
b
C xx,yy
−19.88
−10.65
d
Θ zz
1.22
1.19
b
C xx,zz
−52.31
−41.27
d
Φ xxxx
18.90
18.42
b
C xy,xy
45.35
29.24
d
Φ yyyy
−17.02
−16.27
b
C xz,xz
75.40
58.71
d
Φ zzzz
−15.89
−15.51
b
C yy,yy
75.82
51.47
d
α xx
22.05
22.41
c
C yy,zz
−55.95
−40.82
d
α yy
24.96
25.21
c
C yz,yz
118.68
101.00
d
α zz
34.24
34.24
c
C zz,zz
108.26
82.09
d
E x,xxx
−65.27
−80.67
d
B xx,xx
−733.70
–
E y,yyy
−92.39
−81.01
d
B xx,yy
314.70
–
E z,zzz
71.29
88.90
d
B xx,zz
419.00
–
E x,xyy
−8.81
−8.11
d
B xy,xy
−399.39
–
E x,xzz
74.08
88.78
d
B xz,xz
−574.40
–
E z,zxx
−78.43
−62.24
d
B yy,yy
−394.06
–
E z,zyy
7.14
−26.63
d
B yy,zz
188.14
–
E y,yxx
−75.09
−88.80
d
B yz,yz
−591.64
–
E y,yzz
167.48
169.82
d
B zz,zz
−579.30
–
a Calculated at the CCSD(T)/aug-cc-pVTZ level of theory using approach described in Ref. [105]
b
Reference [106];
c Reference [107];
d
Reference [96]
40
3 Interaction-induced Dipole Moment
In order to correct the energy for the basis set incompleteness error (BSIE), the
energy was extrapolated to the CBS limit using the schemes of Martin (2.3.11) and
Helgaker (2.3.12). The dipole moment of the ethylene dimer was calculated by the
finite-field method described by Cohen and Roothaan [1] using Eq. (3.1.1) which
provides enough accuracy for the system under consideration (the errors do not
exceed 2 × 10
−5 ea 0 ). The experimental ground state geometry (averaged over
zero-point vibrations) of ethylene molecule was used for all calculations: the bond
lengths and angles of ethylene molecule r CC = 2.5303 a 0 , r CH = 2.0504 a 0 ,
∠HCC = 121.085° and ∠HCH = 117.83° were taken from Ref. [108]. The coordinate system of C 2 H 4 –C 2 H 4 complex is shown in Fig. 3.12.
The long-range analytical approximation used for the description of dipole
moment of the ethylene dimer, following the Sect. 3.1.2, gives the induction and
dispersion contributions through the order R
−7 as (here, the exchange interactions
are not considered)
Table 3.5 Molecular properties for C 2 H 4 molecule
Property
[100]
a
Lit.
Property
[100]
a
Lit.
Θ xx
−2.47
−2.42
b
C xx,xx
72.19
51.93
d
Θ yy
1.25
1.23
b
C xx,yy
−19.88
−10.65
d
Θ zz
1.22
1.19
b
C xx,zz
−52.31
−41.27
d
Φ xxxx
18.90
18.42
b
C xy,xy
45.35
29.24
d
Φ yyyy
−17.02
−16.27
b
C xz,xz
75.40
58.71
d
Φ zzzz
−15.89
−15.51
b
C yy,yy
75.82
51.47
d
α xx
22.05
22.41
c
C yy,zz
−55.95
−40.82
d
α yy
24.96
25.21
c
C yz,yz
118.68
101.00
d
α zz
34.24
34.24
c
C zz,zz
108.26
82.09
d
E x,xxx
−65.27
−80.67
d
B xx,xx
−733.70
–
E y,yyy
−92.39
−81.01
d
B xx,yy
314.70
–
E z,zzz
71.29
88.90
d
B xx,zz
419.00
–
E x,xyy
−8.81
−8.11
d
B xy,xy
−399.39
–
E x,xzz
74.08
88.78
d
B xz,xz
−574.40
–
E z,zxx
−78.43
−62.24
d
B yy,yy
−394.06
–
E z,zyy
7.14
−26.63
d
B yy,zz
188.14
–
E y,yxx
−75.09
−88.80
d
B yz,yz
−591.64
–
E y,yzz
167.48
169.82
d
B zz,zz
−579.30
–
a Calculated at the CCSD(T)/aug-cc-pVTZ level of theory using approach described in Ref. [105]
b
Reference [106];
c Reference [107];
d
Reference [96]
40
3 Interaction-induced Dipole Moment