# studying of the phenomenon of internal rotation in n-alkilnyh radicals. Rotation of the groups containing free valency.

Exact potential functions of internal rotation in radicals in the literature practically are not known, therefore their studying represents certain interest. Tentative estimations show, that rotation of the endgroups containing radiyokalnyj the centre, is characterised by low energy barriers.

It is supposed, that it is connected with very diffuse distribution of electronic density and, sootvetyostvenno, with small work on its deformation. Experimentally to find values baryoerov on PPE, the approached dependence V (φ) and resulted inertia moment Irмолекул it is possible on microwave spectrums and-or by means of electronic diffraction [457, 259]. However for radicals, for a variety of causes, such measurements are extremely complicated, and for them as the basic tool of research of internal rotation serve kvantovoyomehanicheskie calculations. Similar calculations of a high level in the big bases are till now very much resursoemkimi and for considered radicals were not made. On boyolee low level in small bases geometrical parametres, bayorery and potential functions etilnogo and propilnogo radicals [375, 458 ÷ 475], and also a barrier in n-butyl [459] have been calculated. ^postavlenie the received data for C_{3}H

_{7}со spectrum EPR has allowed to assume value of a barrier in propyl as 1.67 [473] and 1.72 [474] кДжхмоль

^{-1}. The barrier size in C

_{2}H

_{5}из IK a spectrum is estimated as 0.24 [375] and 0.20 [472] кДжхмоль

^{-1}.

Kvantovomehanichesky studying of internal rotation _{of group C*H2vokrug} of communication C-C* in ^C^H ^^ C^H has been made on an example of connections C_{3}H_{7} ÷ C_{7}H_{15}. Steady conformstions and their relative values full elektronno-nuclear energy (global and local minima (V_{min}) are defined and energy barriers between them V_{glob}, V_{loc}), Irи dependences V (φ), see Drawings 4.6 and 4.7. C_{2}H_{5}принадлежит to point group of symmetry Cs, other n-alkyls to C_{1}, thus in an equilibrium state gloyobalnogo a minimum chain carbons form a nonplanar skeleton. n-alkilnye radicals C_{3}H_{7} ÷ C_{7}H_{15}представляют itself optical isomerides of position of water sorts of group C*H_{2} (Drawing 4.6) where plane H-C*-H is inclined to communication C-C* under angle 7.1 °. Transferring from one conformstion of the basic condition to another is carried out by group turn H - C*-H round communication C-C* of two-sided angle C-C-C*-H on 56 °.

In all connections the conformstions answering local miniyomumu (figure 5 in Drawing 4.7), global and local to maxima - transitive soyostojanijam (TS, figures 4, 6, 1 in Drawing 4.7), and also to a condition with covered raspoloyozheniem atoms of hydrogen (figure 3 in Drawing 4.7) have been studied. It is necessary to notice, that position TS in С_{и}Н_{2и+1}, n> 2, corresponding V_{glob} (4 in Drawing 4.7), does not coincide with covered poyolozheniem atoms (V_{ec} - figure 3 in Drawing 4.7).

_{4}Н

_{9}in conformstion TS (V

_{g}ι

_{ob}) dvuyogrannyj the angle and (С-С-С*-Н) = 68.3 °, and in V

_{c}он has other value and (С-С-С*-Н) = 56.4 °. For for all covered positions - Veclи Vloc (Drawing 4.7 see) - grouping of kernels With - С*Н

_{2}flat and (С-С*-Н

_{2}) = 0 °, i.e. The moment of inversion of fragment С*Н

_{2}does not coincide with V

_{gιob}, and occurs at V

_{c}и V

_{ιoc}.Симметричное an arrangement of atoms С*Н

_{2}in С

_{и}Н

_{2и+1}, n> 2 {figure 5 in Drawing 4.7, angle and (С-С-С*-Н) = 85.8 °, plane Н-С*-Н is inclined to communication С-С* under angle 8.1 °, close to equilibrium}, is a local minimum with the smallest size of a barrier and does not represent any stable state.

Consideration of potential functions has shown, that dependence V (φ) for С2Н5 differs from those for the others n-alkilnyh radicals, therefore it approksimiyorovalas separately. V (φ) in С2Н5 it is well described 6-fold kosinusoidoj (4.208) with V_{g}ι_{ob} = 0.233 kdzh/MOLE (V_{g}ι_{ob} = V_{6}, Table 4.93).

For С_{и}Н_{2и+1}, n> 2, the description of rotation of group S*N_{2} round communication С-С* has demanded bolyoshego quantity of members of some the Fourier, than (4.208). It is connected with presence and alternation of maxima different in size (Drawing 4.7, Table 4.93). The similar curve for С_{3}Н_{7} has been received in calculation UHF/3-21G, but in more rough model [475].

Search of optimum representation V (φ) has demanded consideration various apyoproksimatsy. As initial were numbers (4.209) ÷ (4.214) with to = 6, 12, 15, 20 are taken,

266

Role of a test molecule played butilnyj radical С4Н9. It has appeared, that the choice of an initial configuration essentially influences on nevjazku Δ

(Vcalc - settlement relative energy, Vapprox - ordinates of potential function, n - number of points on Ш1Э), therefore for minimisation v quality of initial conformstion with φ = 0 consistently got over various structures - with the covered position of atoms V_{ec} ι, TS, global and local minima (in Drawing 4.7 they are designated tsifyorami). In other words, in different approximatings of function V (φ) to reaction co-ordinate φ = 0 there corresponded the different conformstions, differing two-sided angle S-S-S*-N. I.e. to each structure of a radical, which was taken over for initial (the first point on a drawing V (φ)), there corresponded angle φ = 0, and change of initial conformstion simply result ined to shift of potential function along an axis of abscisses. For each number (4.209) ÷ (4.214) and each sum with k = 6, 12, 15, 20 it has been made six decomposition, corresponding to the same co-ordinate of reaction φ = 0, but with different reference values of angle and (С-æ-С*-) (Drawing 4.7, figures 1,2, 4-7). Thus, for С_{4}Н_{9} 144 calculations have been manufactured.

The statistical analysis has shown, that the most exact description V (φ) in С4Н9 (the least is nonviscous) is reached with a number (4.209) if for φ = 0 to take a condition, otvechayojushchee TS (V_{glob}, figure 4 in Drawing 4.7). At a variation of number of summands in (4.209) poyolucheno, that, since k = 15, according to Fisher's criterion of [329] distinctions in dispersions with a considerable quantity kстатистически neznachimy. As a result, the best approximating V (φ) for С_{п}Н_{2п+1}, n> 2, is (4.209) with k = 15. Similar representation V (φ) contains 31 summand that assumes corresponding number of points (calculations). It not always vozyomozhno, therefore has been manufactured search of decomposition V (φ) with smaller quantity of points V_{ca}ι_{c}так that the size pri model coarsening remained in permissible limits. The declared requirement is answered with other initial conformstion, also TS (Vιoc, figure 1 in Drawing 4.7), reduction kдо 12 and zanulenie factors before sine, i.e. a number (4.213). At such decomposition V (φ) it is nonviscous increases least. Use of some (4.209) for the chosen initial conformstion does not yield improvement, since factors

Before sine (V_{j}) are smallest and accuracy do not influence. Other representations (other initial conformstion and a decomposition kind) or reduction of quantity of summands privoyodjat to artefacts: or to disappearance Vmin, or to occurrence additional minimuyomovi maxima. V_{glob}, V_{loc}, V_{min}, V_{ecl}радикалов are shown in Table 4.93, factors V (φ), answering to Drawing 4.7 and to the equation (4.213), are yielded in Table 4.94.

Barriers Vglobв studied n-alkilnyh radicals do not exceed 1.5 kdzh/MOLE (Table 4.93), hence, round communication C-C* at T = 298 To and more heats it is possible to consider rotation free. At low temperatures (Vl_{oc} 2, at rotation _{of group S*N2dvuYogrannogo} of angle S-S-S*-N round communication С-С* (Tables 4.93 and 4.94 see also). By arrows and figures are noted: 1 - a local maximum Vl_{oc} - the covered position of atoms With and N two-sided angle S-S-S*-N; 2, 7 - global minima V_{min} (optical isomerides) - osyonovnoe a condition (Drawing 4.6); 3 - V_{ec}l, the covered position of atoms Н2 and Н1 two-cut angle N2-S-S*-N1; 4 - global maximum V_{g}l_{o}bпри value of angle S-S-S*-N equal 68.3 ° and 5 - local minimum V_{min}при value of angle S-S-S*-N equal 85.8 °. Position (5) corresponds to point group of symmetry Cs.

Drawing 4.8.

And

Distribution of electronic density of not coupled electron for conformstion of a global minimum (Drawing 4.6, figure 2 in Drawing 4.7) in a plane which are passing through kernel С* and perpendicularly communications S-S *; in a plane coinciding with a plane of kernels Н-С*-Н. And the density is designated by continuous isolines, β - dotted. Figures 2 and 5 about contours correspond to an isosurface 0.001 a.e./bor^{3}, 2 - and density, 15 - β density. Construction is made by means of program MolDen [222].

Drawing 4.9.

And

Distribution of electronic density of not coupled electron for conformstion of a global maximum (figure 4 in Drawing 4.7) in a plane which are passing through kernel С* and perpendicularly communications S-S *; in a plane coinciding with a plane of kernels Н-С*-N and the density is designated by continuous isolines, β - dotted. Figures 2 and 29 okoyolo contours correspond to an isosurface 0.001 a.e./bor^{3}, 2 - and density, 29 - plotyonost. Construction is made by means of program MolDen [222].

Drawing 4.10.

Dependence V (φ) for n-butyl (solid line) and generalised potential function V_{cp} (φ) (points) for С_{п}Н_{2и}+_{1}, n> 4 (Table 4.93).

4.8.3.3.

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