considered in previous Sect. 3.1. The symmetry properties of CH 4 and N 2 molecules (see Appendix B) allow us to simplify significantly general formulae obtained
above.
In this book the Cartesian coordinate system shown in Fig. 3.6a is used for
description of the complex. The origin of the coordinate system is placed on the
carbon atom of the methane molecule. The vector R connects the carbon atom with
the center of N 2 bond. It has the components (R, 0, 0). The rotation of the methane
(A) and the nitrogen (B) molecules in this coordinate system is determined by Euler
angles v A ; h A ; u A ; h B and u B , accordingly. The initial position of the molecules in
the CH 4 –N 2 complex presented in Fig. 3.6a corresponds to the Euler angles v A ¼
h A ¼ u A ¼ h B ¼u B ¼ 0 . In this figure the coordinates of nitrogen atoms are (R,
0, ± r NN =2) and the CH 4 molecule has the standard orientation: the carbon atom is
at the origin (0, 0, 0) and hydrogen atoms have the coordinates (c, c, c), (c, −c, −c),
(−c, −c, c) and (−c, c, −c), where c = r CH =
ffiffi ffi
3
p
. In the present study the geometries
of the monomers CH 4 and N 2 were optimized at the CCSD(T)/aug-cc-pVTZ level
of theory. The equilibrium bond lengths for the CH 4 and N 2 molecules were found
to be r CH = 2.0596 a 0 and r NN = 2.0864 a 0 , accordingly. During the calculations
the monomers were kept rigid with geometric parameters mentioned above.
Ab initio calculations of the dipole moment components were carried out at the
CCSD(T) level with the BSSE correction.
The mostly discussed in works [7, 61–64] configurations of the CH 4 –N 2 complex, including the most stable configuration, are presented at Fig. 3.6b. The
geometric parameters (Euler angles v A ; h A ; u A ; h B and u B ) for these configurations
along with equilibrium distance R e and interaction energy DEðR e Þ are given in
Table 3.2. The ab initio calculations of the dipole moment components μ α for these
configurations at the MP2 and CCSD(T) levels of theory are presented at Fig. 3.7.
(a)
(b)
Fig. 3.6 a Coordinate system for the initial geometry; b General geometries of the CH 4 –N 2
complex (Reprinted with permission from Ref. [64]. Copyright 2010 American Institute of
Physics)
3.2 Dipole Moment of van der Waals Complexes
31
above.
In this book the Cartesian coordinate system shown in Fig. 3.6a is used for
description of the complex. The origin of the coordinate system is placed on the
carbon atom of the methane molecule. The vector R connects the carbon atom with
the center of N 2 bond. It has the components (R, 0, 0). The rotation of the methane
(A) and the nitrogen (B) molecules in this coordinate system is determined by Euler
angles v A ; h A ; u A ; h B and u B , accordingly. The initial position of the molecules in
the CH 4 –N 2 complex presented in Fig. 3.6a corresponds to the Euler angles v A ¼
h A ¼ u A ¼ h B ¼u B ¼ 0 . In this figure the coordinates of nitrogen atoms are (R,
0, ± r NN =2) and the CH 4 molecule has the standard orientation: the carbon atom is
at the origin (0, 0, 0) and hydrogen atoms have the coordinates (c, c, c), (c, −c, −c),
(−c, −c, c) and (−c, c, −c), where c = r CH =
ffiffi ffi
3
p
. In the present study the geometries
of the monomers CH 4 and N 2 were optimized at the CCSD(T)/aug-cc-pVTZ level
of theory. The equilibrium bond lengths for the CH 4 and N 2 molecules were found
to be r CH = 2.0596 a 0 and r NN = 2.0864 a 0 , accordingly. During the calculations
the monomers were kept rigid with geometric parameters mentioned above.
Ab initio calculations of the dipole moment components were carried out at the
CCSD(T) level with the BSSE correction.
The mostly discussed in works [7, 61–64] configurations of the CH 4 –N 2 complex, including the most stable configuration, are presented at Fig. 3.6b. The
geometric parameters (Euler angles v A ; h A ; u A ; h B and u B ) for these configurations
along with equilibrium distance R e and interaction energy DEðR e Þ are given in
Table 3.2. The ab initio calculations of the dipole moment components μ α for these
configurations at the MP2 and CCSD(T) levels of theory are presented at Fig. 3.7.
(a)
(b)
Fig. 3.6 a Coordinate system for the initial geometry; b General geometries of the CH 4 –N 2
complex (Reprinted with permission from Ref. [64]. Copyright 2010 American Institute of
Physics)
3.2 Dipole Moment of van der Waals Complexes
31