of ab initio methods is that they do not use any empirical parameters. We can
schematic distinguish the following law of increasing accuracy using a middle size
basis set for single reference methods:
HF\MP2 ffi CCSD\SAPT CCSDðTÞ % CCSDðTÞ À F12\CCSDT. . .;
where the conventional denotes are used for methods: HF—Hartree-Fock (or
Self-Consistent Field (SCF)); MP2—second-order Møller-Plesset Perturbation
theory; SAPT—Symmetry-Adapted Perturbation Theory; CCSD and CCSDT—
Coupled Cluster theory with a full use of single (S), double (D) and triple
(T) electron excitations; CCSD(T)—Coupled Cluster theory with a full use of
single (S), double (D) and perturbative treatment of triple excitations. In 2007 a new
explicitly correlated CCSD(T)-F12 approximation was presented and tested in Ref.
[12]. This method proved to be more accurate and faster than conventional CCSD
(T) method with the same basis set [12]. The considered methods (except HF) take
into account the electron correlations which play an important role in van der Waals
interactions, thus these methods could be successfully applied for solving problems
of weakly-bound complexes. For example, CCSD(T) method allows to account for
99 % of correlation energy and at present it is one of the most popular methods
applied to small molecules. However, it is difficult to apply this method for systems
with a large number of particles due to big computational time and limited computational resources. For large molecular complexes the different variations of the
density functional theory (DFT) or time dependent density functional theory
(TDDFT) can be applied. The accuracy of these methods depends on the fortunate
choose of exchange-correlation functionals. Recently, Wu et al. [13] have carried
out the assessment of density functional methods in calculating the electric polarizability of 145 medium-size (3–14 atomic) organic molecules. They have found
that at least three functionals among 34 considered should be used. They are
devided into three groups: 1) one of M11 and M06-2X; 2) one of ωB97 and
LC-τHTCH; 3) one of HISS and LC-ωPBE.
At last, it should be noted that a lot of semiempirical model potentials applied for
both short and long separations are widely used now to solve different problems of
physics and chemistry. A rather complete review of those one can find in the book
of I. Kaplan [2].
2.3 Interaction Energy
2.3.1 Long-Range Distances
For the long-range intermolecular separations the perturbation theory can be
applied. Within the perturbation theory using the interaction operator (2.2.3) one
can obtain the energy of the pair of uncharged molecules A and B perturbed by a
weak general static electric field as [5, 14]:
2.2 Interaction Hamiltonian
9
schematic distinguish the following law of increasing accuracy using a middle size
basis set for single reference methods:
HF\MP2 ffi CCSD\SAPT CCSDðTÞ % CCSDðTÞ À F12\CCSDT. . .;
where the conventional denotes are used for methods: HF—Hartree-Fock (or
Self-Consistent Field (SCF)); MP2—second-order Møller-Plesset Perturbation
theory; SAPT—Symmetry-Adapted Perturbation Theory; CCSD and CCSDT—
Coupled Cluster theory with a full use of single (S), double (D) and triple
(T) electron excitations; CCSD(T)—Coupled Cluster theory with a full use of
single (S), double (D) and perturbative treatment of triple excitations. In 2007 a new
explicitly correlated CCSD(T)-F12 approximation was presented and tested in Ref.
[12]. This method proved to be more accurate and faster than conventional CCSD
(T) method with the same basis set [12]. The considered methods (except HF) take
into account the electron correlations which play an important role in van der Waals
interactions, thus these methods could be successfully applied for solving problems
of weakly-bound complexes. For example, CCSD(T) method allows to account for
99 % of correlation energy and at present it is one of the most popular methods
applied to small molecules. However, it is difficult to apply this method for systems
with a large number of particles due to big computational time and limited computational resources. For large molecular complexes the different variations of the
density functional theory (DFT) or time dependent density functional theory
(TDDFT) can be applied. The accuracy of these methods depends on the fortunate
choose of exchange-correlation functionals. Recently, Wu et al. [13] have carried
out the assessment of density functional methods in calculating the electric polarizability of 145 medium-size (3–14 atomic) organic molecules. They have found
that at least three functionals among 34 considered should be used. They are
devided into three groups: 1) one of M11 and M06-2X; 2) one of ωB97 and
LC-τHTCH; 3) one of HISS and LC-ωPBE.
At last, it should be noted that a lot of semiempirical model potentials applied for
both short and long separations are widely used now to solve different problems of
physics and chemistry. A rather complete review of those one can find in the book
of I. Kaplan [2].
2.3 Interaction Energy
2.3.1 Long-Range Distances
For the long-range intermolecular separations the perturbation theory can be
applied. Within the perturbation theory using the interaction operator (2.2.3) one
can obtain the energy of the pair of uncharged molecules A and B perturbed by a
weak general static electric field as [5, 14]:
2.2 Interaction Hamiltonian
9