196
S. V. Vasylyuk et al.
Influence of the amino group R = -N(CH 3 ) 2 , as can be seen from Fig. 1, is fundamentally different: the centers and waves of the charge distribution and the bonds
lengths waves are not simply transferred at definite space as of the molecule center
nevertheless almost completely localized on a heteroatom. As it is shown by the calculations of monoamino-substituted molecular ions 3 (R = -N(CH 3 ) 2 ), such a limiting
displacement of solitons on the edge of the conjugate system occurs regardless of the
vinylene groups number n in polymethine π-electronic chain. Obviously, the graphs
in Fig. 2a, b represent only half of each soliton wave. Considerably, the differences in
the influence on the localization and the form of the soliton waves between low- and
high-donor substituents are given more carefully for distilled polymethines 4. As can
be seen from Fig. 2, the simultaneous influence of two oxy groups in polymethine 4
(R = -OCH 3 ) leaves the localization of charge and topological waves in the center of
the molecule unchanged, and also does not change the magnitudes of the maximum
amplitude of the alternation of the electron density (Fig. 2a) and the boundary alignment of the bond lengths (|L ν | = 0) in the middle of the molecule relative to the
unchanged polymethine cation 2. Calculations show that a more significant impact
on charges and bond lengths appears at the ends of the chain, especially in molecules
with a small number of vinyl groups. For illustration, the calculations for conjugated
systems 2–4 with n = 6 are given in Table 1.
As it can be seen, even at insertion of the ending group (dyes 3), the electron
wave density distribution onto the different chromophore ends increases significantly, although there is no significant difference between the hydroxy (R = -OH)
and the amino-substituted (R = -NH 2 ) polymethine dye results. At the end of the
chromophore near the finite group R, the atom charge alteration is more substantial,
so that the charge sign is even changed to a positive carbon atom, which is bound
to a terminal heteroatom, oxygen, or nitrogen. Accordingly, both carbon atoms are
positively charged at both ends of the polymethine chain in the case of dispersed dyes
4. Unlike charges, the length of carbon–carbon bonds at the ends of chromophore
is less sensitive to the introduction of substituents. As it can be seen from the table,
the calculations give a significant decrease in alternating length amplitude of neighboring CH bonds at ending boundaries of the chromophore, bringing it closer to L ν
in the interior the polymethine chains.
In the case of molecules with short polymethine chains that are found to be
physical, the effects of finite groups can become dominant. This can lead to significant
deformation of the soliton-shaped charge waves.
Assuming that the finite groups influence the distribution of the electron density
in the main chromophore primarily due to both σ-inductive and π-mesomeric effects,
then in the theory of perturbations of molecular orbits [13] quantitatively such an
effect can be estimated by changing the Coulomb integral of the terminal atom. At
the same time, the electron density changes for a random μ -s of the polymethine
chain atom: q μ = q
o
μ + π 1,μ h, where h is the correction for the Coulomb integral,
and π 1,μ -the atom–atomic polarizability. For linear conjugate systems 1, when R is
a heteroatom, the parameter π 1,μ can be written analytically [13] as
π 1,μ ≈ (−1)
μ
/[π(2
μ
− 1)].
(3)
S. V. Vasylyuk et al.
Influence of the amino group R = -N(CH 3 ) 2 , as can be seen from Fig. 1, is fundamentally different: the centers and waves of the charge distribution and the bonds
lengths waves are not simply transferred at definite space as of the molecule center
nevertheless almost completely localized on a heteroatom. As it is shown by the calculations of monoamino-substituted molecular ions 3 (R = -N(CH 3 ) 2 ), such a limiting
displacement of solitons on the edge of the conjugate system occurs regardless of the
vinylene groups number n in polymethine π-electronic chain. Obviously, the graphs
in Fig. 2a, b represent only half of each soliton wave. Considerably, the differences in
the influence on the localization and the form of the soliton waves between low- and
high-donor substituents are given more carefully for distilled polymethines 4. As can
be seen from Fig. 2, the simultaneous influence of two oxy groups in polymethine 4
(R = -OCH 3 ) leaves the localization of charge and topological waves in the center of
the molecule unchanged, and also does not change the magnitudes of the maximum
amplitude of the alternation of the electron density (Fig. 2a) and the boundary alignment of the bond lengths (|L ν | = 0) in the middle of the molecule relative to the
unchanged polymethine cation 2. Calculations show that a more significant impact
on charges and bond lengths appears at the ends of the chain, especially in molecules
with a small number of vinyl groups. For illustration, the calculations for conjugated
systems 2–4 with n = 6 are given in Table 1.
As it can be seen, even at insertion of the ending group (dyes 3), the electron
wave density distribution onto the different chromophore ends increases significantly, although there is no significant difference between the hydroxy (R = -OH)
and the amino-substituted (R = -NH 2 ) polymethine dye results. At the end of the
chromophore near the finite group R, the atom charge alteration is more substantial,
so that the charge sign is even changed to a positive carbon atom, which is bound
to a terminal heteroatom, oxygen, or nitrogen. Accordingly, both carbon atoms are
positively charged at both ends of the polymethine chain in the case of dispersed dyes
4. Unlike charges, the length of carbon–carbon bonds at the ends of chromophore
is less sensitive to the introduction of substituents. As it can be seen from the table,
the calculations give a significant decrease in alternating length amplitude of neighboring CH bonds at ending boundaries of the chromophore, bringing it closer to L ν
in the interior the polymethine chains.
In the case of molecules with short polymethine chains that are found to be
physical, the effects of finite groups can become dominant. This can lead to significant
deformation of the soliton-shaped charge waves.
Assuming that the finite groups influence the distribution of the electron density
in the main chromophore primarily due to both σ-inductive and π-mesomeric effects,
then in the theory of perturbations of molecular orbits [13] quantitatively such an
effect can be estimated by changing the Coulomb integral of the terminal atom. At
the same time, the electron density changes for a random μ -s of the polymethine
chain atom: q μ = q
o
μ + π 1,μ h, where h is the correction for the Coulomb integral,
and π 1,μ -the atom–atomic polarizability. For linear conjugate systems 1, when R is
a heteroatom, the parameter π 1,μ can be written analytically [13] as
π 1,μ ≈ (−1)
μ
/[π(2
μ
− 1)].
(3)