194
S. V. Vasylyuk et al.
this work, we confine ourselves to a smaller basis in calculations of relatively long
molecules. In our calculations, we had used the HYPERCHEM 7.0 program package.
Calculations of ions 2–4 had shown a significant electron density alternation of
carbon atoms in polymethine π-electronic collective system, and our calculations
had shown an alternation phase in cations, as established in previous papers [3–11],
which is the opposite of the alternation of electron density in anions. The alternation
amplitude was decreased gradually from center of the polymethine to its boundaries;
therefore, the charges form a wave package described by the hyperbolic soliton
function [12]. To analyze the dependence of charges and the localization of soliton
waves from the topology of polymethine molecules, one could use electronic density
q μ but much more functional difference of their values of charge q μ on neighboring
atoms (1) that are calculated by the following formula:
Dq m = (−1)
μ
(q μ − q μ−1 ).
(1)
Similarly, instead of the length of the bands, it is more convenient to analyze the
amplitude of their alternation:
DL v = (−1)
v
(L v − L v−1 ),
(2)
where the value L ν is the distance between two carbon atoms of ν-bond number.
Scalar parameters are often used: |q μ | and |L ν |.
Consequently, this special type of the “crystalline lattice” configuration of polymer
π- electron system of polymethine dye that is defined by (2.18) could be reflected as
“metallic lattice” in the polymer as confirmed current value in (2.20) [7] that permits
the current presence in deficiency of the external electric field.
Figure 2 shows the graph |q μ | = f(μ) for ions 2–4 with a relatively long polymethine chain (n = 15), which significantly exceeds the size of soliton waves. As
can be seen, the charge wave |q μ | is autolocalized in the middle of the conjugate
system, separating from its edges. True, as you can see from Fig. 2a, the calculations
do not give a zero value of the amplitude of the alternation, and a certain constant
value (≈0,17), which is connected with the nonequivalence of the polarization of the
links of C and H onto even in addition to odd location in the polymethine chain with
opposite sign charges. Figure 2b shows a graph of alternating lengths C–C bonds
obtained in optimization of molecular geometry (with precision up to 0.001 Å). As
can be seen, the graph |l ν | = f(μ) describes the typical shock wave or the tip. At
the edges of the polymethine chain, the value of the alternating amplitude reaches a
constant value, which is close to the value of the alternation in the unaligned neutral
polyenes [11].
We will think about a soliton as a charge or bond length distribution like single
wave, where its size should not connect with the dimension of collective the π-system
and not rely on it. In the case of conjugate systems with a chain length shorter than
a soliton wave, only a part of the charge or topological wave is projected onto a
molecule [11]. Now let us consider the effect of the nature of the terminal group in
the mono-substituted polymethine ion 2. As the model finite residues, groups were
used, the main element of which is an atom with a non-allocated electron pair (NEP),
S. V. Vasylyuk et al.
this work, we confine ourselves to a smaller basis in calculations of relatively long
molecules. In our calculations, we had used the HYPERCHEM 7.0 program package.
Calculations of ions 2–4 had shown a significant electron density alternation of
carbon atoms in polymethine π-electronic collective system, and our calculations
had shown an alternation phase in cations, as established in previous papers [3–11],
which is the opposite of the alternation of electron density in anions. The alternation
amplitude was decreased gradually from center of the polymethine to its boundaries;
therefore, the charges form a wave package described by the hyperbolic soliton
function [12]. To analyze the dependence of charges and the localization of soliton
waves from the topology of polymethine molecules, one could use electronic density
q μ but much more functional difference of their values of charge q μ on neighboring
atoms (1) that are calculated by the following formula:
Dq m = (−1)
μ
(q μ − q μ−1 ).
(1)
Similarly, instead of the length of the bands, it is more convenient to analyze the
amplitude of their alternation:
DL v = (−1)
v
(L v − L v−1 ),
(2)
where the value L ν is the distance between two carbon atoms of ν-bond number.
Scalar parameters are often used: |q μ | and |L ν |.
Consequently, this special type of the “crystalline lattice” configuration of polymer
π- electron system of polymethine dye that is defined by (2.18) could be reflected as
“metallic lattice” in the polymer as confirmed current value in (2.20) [7] that permits
the current presence in deficiency of the external electric field.
Figure 2 shows the graph |q μ | = f(μ) for ions 2–4 with a relatively long polymethine chain (n = 15), which significantly exceeds the size of soliton waves. As
can be seen, the charge wave |q μ | is autolocalized in the middle of the conjugate
system, separating from its edges. True, as you can see from Fig. 2a, the calculations
do not give a zero value of the amplitude of the alternation, and a certain constant
value (≈0,17), which is connected with the nonequivalence of the polarization of the
links of C and H onto even in addition to odd location in the polymethine chain with
opposite sign charges. Figure 2b shows a graph of alternating lengths C–C bonds
obtained in optimization of molecular geometry (with precision up to 0.001 Å). As
can be seen, the graph |l ν | = f(μ) describes the typical shock wave or the tip. At
the edges of the polymethine chain, the value of the alternating amplitude reaches a
constant value, which is close to the value of the alternation in the unaligned neutral
polyenes [11].
We will think about a soliton as a charge or bond length distribution like single
wave, where its size should not connect with the dimension of collective the π-system
and not rely on it. In the case of conjugate systems with a chain length shorter than
a soliton wave, only a part of the charge or topological wave is projected onto a
molecule [11]. Now let us consider the effect of the nature of the terminal group in
the mono-substituted polymethine ion 2. As the model finite residues, groups were
used, the main element of which is an atom with a non-allocated electron pair (NEP),