108
P. R. P. Barreto et al.
theory and the exchange corrections E
(nj)
exch arise from the use of a global antisymmetrizer to force the correct permutation symmetry of the dimer wave function in
each order, hence the name “symmetry adaptation”. In this way, the interaction energy
given by SAPT can be written as:
E S APT = E elst + E exch + E ind + E disp
(3)
Using higher-order SAPT, as SAPT2+3, the electrostatic part is given by:
E elst = E
(10)
elst + E
(12)
elst,resp + E
(13)
elst,resp
(4)
The superscript defines the order in V, while the subscript, resp, means that orbital
relaxation effects are included. The exchange part is given by:
E exch = E
(10)
exch + E
(11)
exch + E
(12)
exch
(5)
The induction part is formulated as:
E ind = E
(20)
ind,r + E
(30)
ind,r + E
(22)
ind + E
(20)
exch−ind,r + E
(22)
exch−ind − δ
(2)
H P + δ
(3)
H H
(6)
The δ
(2)
H F and δ
(3)
H F terms take into account higher-order induction effects, not
included in MP2 correlation. Finally, the dispersion energy is given by:
E disp = E
(20)
disp + E
(21)
disp + E
(30)
disp + E
(20)
exch−disp + E
(30)
exch−disp + E
(30)
ind−disp
+ E
(30)
exch−ind−disp + CC D
(7)
where CC D is an improved version of the CCD (couple-cluster doubles) treatment
of dispersion [20, 21].
3 Results and Discussion
In Table 1, we report the structural properties of the optimized geometry of propylene
oxide, calculated at various levels of theory and compared with reference data. The
CBS-QB3 method [22] presents overall the best agreement with reference data, for
both distances and angles. Thus, the geometry optimized by CBS-QB3 is chosen for
the calculation of the interaction potentials of the leading configurations as a function
of the distance and for the analysis of the contributions to the intermolecular forces.
Potential energy profiles of the leading configurations of propylene oxide–He have
been already presented and discussed in Ref. [6], where they have been compared
with the Pirani potential function, also known as Improved Lennard-Jones. Here, we
use a fifth order Rydberg potential function, as discussed in Sect. 2.2 for the three
systems. The single point energies of propylene oxide with the He, Ne and Ar are
P. R. P. Barreto et al.
theory and the exchange corrections E
(nj)
exch arise from the use of a global antisymmetrizer to force the correct permutation symmetry of the dimer wave function in
each order, hence the name “symmetry adaptation”. In this way, the interaction energy
given by SAPT can be written as:
E S APT = E elst + E exch + E ind + E disp
(3)
Using higher-order SAPT, as SAPT2+3, the electrostatic part is given by:
E elst = E
(10)
elst + E
(12)
elst,resp + E
(13)
elst,resp
(4)
The superscript defines the order in V, while the subscript, resp, means that orbital
relaxation effects are included. The exchange part is given by:
E exch = E
(10)
exch + E
(11)
exch + E
(12)
exch
(5)
The induction part is formulated as:
E ind = E
(20)
ind,r + E
(30)
ind,r + E
(22)
ind + E
(20)
exch−ind,r + E
(22)
exch−ind − δ
(2)
H P + δ
(3)
H H
(6)
The δ
(2)
H F and δ
(3)
H F terms take into account higher-order induction effects, not
included in MP2 correlation. Finally, the dispersion energy is given by:
E disp = E
(20)
disp + E
(21)
disp + E
(30)
disp + E
(20)
exch−disp + E
(30)
exch−disp + E
(30)
ind−disp
+ E
(30)
exch−ind−disp + CC D
(7)
where CC D is an improved version of the CCD (couple-cluster doubles) treatment
of dispersion [20, 21].
3 Results and Discussion
In Table 1, we report the structural properties of the optimized geometry of propylene
oxide, calculated at various levels of theory and compared with reference data. The
CBS-QB3 method [22] presents overall the best agreement with reference data, for
both distances and angles. Thus, the geometry optimized by CBS-QB3 is chosen for
the calculation of the interaction potentials of the leading configurations as a function
of the distance and for the analysis of the contributions to the intermolecular forces.
Potential energy profiles of the leading configurations of propylene oxide–He have
been already presented and discussed in Ref. [6], where they have been compared
with the Pirani potential function, also known as Improved Lennard-Jones. Here, we
use a fifth order Rydberg potential function, as discussed in Sect. 2.2 for the three
systems. The single point energies of propylene oxide with the He, Ne and Ar are