146
T. A. Zubatiuk et al.
To verify the obtained results, a more rigorous account of electron correlation
using the MP2/aug-cc-pvdz method has been performed. As follows from the data
presented in Table 5.4, the application of the MP2 level does not change the order
of stability of anti conformers of DNTs. Only some increase of differences in energy
between south/anti and north/anti conformers is observed. However, the MP2 method significantly decreases the relative energy of orthogonal (north/syn) conformers
of CMP and AMP (Table 5.4). In the case of CMP this conformer becomes the most
stable, and the energy of this conformer in AMP is lower, compared to the north/
anti conformer. Such stabilization may be caused by differences in energy of deformation of the fragments of these DNTs, calculated at the DFT and MP2 levels of
theory. In particular, it was recently demonstrated [43] that the MP2 method slightly
underestimates the conformational flexibility of the pyrimidine ring in uracil, compared to the more accurate, CCSD(T) data. The value of ring deformation energy
calculated within the density functional theory is slightly higher, compared to the
MP2 data. Similar effects may be expected for other fragments of DNTs. Therefore,
the contribution of these differences in deformation energy may be considerable.
An analysis of the geometrical parameters and relative stability of conformers
discussed above indicates that the application of diffuse functions is required for a
correct description of the molecular structure and energetics of DNTs. An absence
of diffuse functions may lead to the appearance of artificial local minima on the
potential energy surface. A comparison of the molecular structure of DNTs calculated using the 6-31(d) basis set as reported in [19, 20] and the 6-31++G(d,p) basis
(Tables 5.2, 5.3) reveals that an increase in the size of the basis set results in slight
changes in the geometrical parameters of the considered molecules. A decrease of
differences between the O4′–C bond lengths and the degree of pyramidality of the
amino groups are among molecular parameters which changes are observed when
going from the 6-31G(d,p) to the 6-31++ G(d,p) basis set.
5.4 Intramolecular Hydrogen Bonds
in the 2′-deoxyribonucleotide
According to the AIM theory [44], the presence of a hydrogen bond that appears
in topological analysis of the electron density distribution, like any chemical bond,
must correspond to the existence of a bond path between the hydrogen atom and
the acceptor containing bond critical points (BCP). This is the requirement and
first criteria for the existence of any chemical bond. In the case of hydrogen bonds
several additional criteria were developed [45, 46]. Two of them concern properties of the BCP, namely, the value of electron density (ρ) at the BCP should be between 0.002 and 0.035 a.u. and the value of the Laplacian of electron density ∇
2
(ρ)
should be within 0.024–0.139 a.u. Besides that, some useful information about the
stability of hydrogen bonds may be retrieved from the values of bond ellipticity at
the BCP [47] and the distance between the BCP and the ring critical points (RCP)
[48]. RCP is defined as a (3, + 1) critical point and exists whenever a succession
of bond paths closes into a ring. An abnormally high value of ellipticity and the
short distance between BCP and RCP usually indicate locally unstable topology of
T. A. Zubatiuk et al.
To verify the obtained results, a more rigorous account of electron correlation
using the MP2/aug-cc-pvdz method has been performed. As follows from the data
presented in Table 5.4, the application of the MP2 level does not change the order
of stability of anti conformers of DNTs. Only some increase of differences in energy
between south/anti and north/anti conformers is observed. However, the MP2 method significantly decreases the relative energy of orthogonal (north/syn) conformers
of CMP and AMP (Table 5.4). In the case of CMP this conformer becomes the most
stable, and the energy of this conformer in AMP is lower, compared to the north/
anti conformer. Such stabilization may be caused by differences in energy of deformation of the fragments of these DNTs, calculated at the DFT and MP2 levels of
theory. In particular, it was recently demonstrated [43] that the MP2 method slightly
underestimates the conformational flexibility of the pyrimidine ring in uracil, compared to the more accurate, CCSD(T) data. The value of ring deformation energy
calculated within the density functional theory is slightly higher, compared to the
MP2 data. Similar effects may be expected for other fragments of DNTs. Therefore,
the contribution of these differences in deformation energy may be considerable.
An analysis of the geometrical parameters and relative stability of conformers
discussed above indicates that the application of diffuse functions is required for a
correct description of the molecular structure and energetics of DNTs. An absence
of diffuse functions may lead to the appearance of artificial local minima on the
potential energy surface. A comparison of the molecular structure of DNTs calculated using the 6-31(d) basis set as reported in [19, 20] and the 6-31++G(d,p) basis
(Tables 5.2, 5.3) reveals that an increase in the size of the basis set results in slight
changes in the geometrical parameters of the considered molecules. A decrease of
differences between the O4′–C bond lengths and the degree of pyramidality of the
amino groups are among molecular parameters which changes are observed when
going from the 6-31G(d,p) to the 6-31++ G(d,p) basis set.
5.4 Intramolecular Hydrogen Bonds
in the 2′-deoxyribonucleotide
According to the AIM theory [44], the presence of a hydrogen bond that appears
in topological analysis of the electron density distribution, like any chemical bond,
must correspond to the existence of a bond path between the hydrogen atom and
the acceptor containing bond critical points (BCP). This is the requirement and
first criteria for the existence of any chemical bond. In the case of hydrogen bonds
several additional criteria were developed [45, 46]. Two of them concern properties of the BCP, namely, the value of electron density (ρ) at the BCP should be between 0.002 and 0.035 a.u. and the value of the Laplacian of electron density ∇
2
(ρ)
should be within 0.024–0.139 a.u. Besides that, some useful information about the
stability of hydrogen bonds may be retrieved from the values of bond ellipticity at
the BCP [47] and the distance between the BCP and the ring critical points (RCP)
[48]. RCP is defined as a (3, + 1) critical point and exists whenever a succession
of bond paths closes into a ring. An abnormally high value of ellipticity and the
short distance between BCP and RCP usually indicate locally unstable topology of