V.V. Leonov – Ph.D.(Biol.), Head the Electrochemical Research Department of the Laboratory «Physico-Chemical Mechanics»,  Institute of Mechanics Ufa Scientific Center of RAS

E-mail: ivi9090@mail.ru

O.A. Denisova – Dr.Sc.(Phys.-Math.), Associate Professor, Professor, 

Department of Physics, Ufa State Petroleum Technological University

E-mail: denisovaolga@bk.ru

The practical focus of applied chemistry and chemical technology determines the need to develop reliable performance criteria for technological processes, assess the reactivity of the initial and intermediate reactive components of condensed systems, the stability of the final products of chemical reactions and intermediates of chemical transformations of individual and complex atomic-molecular statistical masses. The urgent need for predictive assessments of the quality of technical solutions being developed for innovative chemistry trends is directly related to the information capabilities of instrumental analysis methods and control of technological environment parameters. One of these trends is represented by complex modeling of the sequence of individual stages of technological operations on the basis of currently existing ideas about the mechanism of chemical interactions. The formal-mathematical methodological approach allows one to find stable formal connections between the restructuring of the electronic shells of individual and complex chemical compounds with the movement of macroscopic volumes of matter (mass transfer). In turn, the thermodynamic approach of chemical technology determines the macrokinetics of the technological process. Formal mathematical relationships of quantum chemistry, atomic-molecular statistics, and chemical thermodynamics contributed to the creation of computer chemistry with a relatively high efficiency of formal predictive trends and the final results of the development of external effects on condensed matter. The purpose of the proposed message is the sequence of formulation and solution of boundary value problems of macroscopic electrodynamics in the boundary conditions of the theory of chemical interaction of components of condensed systems. Evaluation through comparisons of the Fourier components for the decomposition of the charge density, electron density and atomic form factor lead to an unambiguous expression of the relationship by the real part of the dielectric constant of the medium. Within the boundaries of the field of existence of the electromagnetic field, the conversion of the levels of organization of condensed matter determines the unity of the structure of material continua and carriers of the chemical bond phenomenon at all integration limits. The uniqueness of the final result in writing joint solutions of the equations of hydrodynamics, quantum mechanics, and macroscopic electrodynamics indicates the reality of a material carrier of bonds – a self-consistent stationary electromagnetic field of the system, whose properties determine the chemical transformations of the reacting substances. The formation of bonds is accompanied by the effects of the appearance of a third-party EMF, the measurement of which is justified by the quantum theory of macroscopic measurements.

Chemical interactions in condensed matter (chemical reactions) are accompanied by rupture and the formation of «chemical bonds», which are manifested in a change in the state of N outer-sphere (valence electrons of atomic-molecular systems in the frequency range · the strength of the quantum oscillator fk of the finite volume of the medium (dispersion of dielectric constant). Macroscopic electrodynamic chemical bonding theory is not positioned in condensed matter physics and physicochemistry According to Bohr’s principle, the reality of quantum of the effects consists in their macroscopic manifestation (additional correspondence). Therefore, the final electromagnetic nature of the binding is obvious (quantum exchange effects manifest themselves in the form of a measurable Coulomb integral). Non-trivial trends are associated with the quantum measurement theory, within which the conditions for the quantitative estimation of the quantum limits of electricity and magnetism.

According to the ideas about the basic fundamental interactions, only the electromagnetic forces of the microworld manifest themselves in macroscopic phenomena. The authors provide a rationale for the continuum theory of chemical bonding from the correspondence principle, the reality of which is expressed by changing the macroscopic electromagnetic field of the material of the material medium.

The consequences of the integral theorems of vector analysis are a powerful means of application in the formulation and solution of many problems of the discrete and continuum nature of the condensed state of matter. In this communication, the quantum level of mutual conversion of the exchange and Coulomb integrals of chemical bonds is considered sequentially within the boundaries of the overlapping electrodynamics of material media. The transformation of the expressions of vector theorems allows for the direct measurement of the bond strength from the formal approach of electrostatics.

The quantum nature of the mechanism of chemical bonding is universally recognized and confirmed by the options of mechanical and mathematical constructions from the simplest separation models – electron attachments, to the translating functions of Hilbert spaces of topological sets in their vector and operator representations. The conversion of the exchange integral into the electromagnetic field of coupling is a statistical character of the influence function (Green's function G0x0) of the self-adjoint operator L and is directly related to the fundamental physicochemical constants of the discreteness of the quantity of matter.

Macroscopic atomic-molecular systems possess the properties of continuous media (bodies) and do not reveal pronounced quantumstatistical features of the microworld. At the same time, the hierarchy of levels of the condensed state is real and manifests itself in differences in the characteristic relaxation times as continuum features (effects) of the structure of matter. According to the concepts of condensed matter physics, the slowest relaxation processes with the effect of sound dispersion are determined by chemical reactions and slow transfer of energy to the vibrational degrees of freedom of the molecule. That is, the formation of a chemical bond is accompanied by fluctuations in the sound spectrum of the density of the medium and is recorded in a macroscopic experiment. 

The reality of the condensed state of the reaction medium determines the possibility of a hydrodynamic approach. The use of limit theorems of vector and tensor analysis in joint boundary value problems in the sense of Cauchy–Feynman (transitional solutions) characterizes the consideration of equations of motion outside the framework of model constraints of a particular topology. The real self-similar properties of the one-coordinate x-solutions of the equations of hydrodynamics are directly justified by the physical meaning of the charge-mass ratios of the amount of medium substance. The obtained relations reflect the estimate of the displacement of the minimum attached mass mik (amount of substance) in the processes of rupture-formation of a chemical bond. The moment of forces M during the rotation of the molecule in the medium determines the calculation of the binding energy from the equations of rotational motion with an angle δθ,, significantly simplifying the measurement technique in a real experiment. The conservation of velocity circulation, according to Thomson's theorem, allows one to calculate the drag force of a medium when one molecule moves in a stationary force field. The potential motion of a molecule follows from a number of considerations and the shape of the field does not depend on the real geometry of the moving particle due to its physical smallness. The binding energy as a variation of the work of creating (breaking) the bond is equal to the change in the free energy of the system. The expression is equivalent to the chemical potential, the physical meaning is represented by the electrodynamic integro-differential relations established earlier for the processes of matter transfer in condensed matter. By definition, the expression for the field is identically equal to the circulation of the intensity vector with the physical meaning of the EMF. From the considerations of the quantum theory of measurements, there follows the unambiguous possibility of the measurability of such an emf when exposed to an LC-circuit. The equality of dimension E2 of the dimension of pressure determines the electrodynamic macroscopic expression for the virtual process of converting the energy of the exchange interaction of a chemical bond (exchange integral) into electromagnetic form (Coulomb integral).

A theoretical estimate of the two limits of fundamental interactions is related to the radius of the electron and the fine structure constant. Due to some overlap between the boundaries of the interaction of structural fields, the quantum effects of the macroscopic state lose their relevance at a distance of about two orders of the radius of the shells of external sphere electrons (the quantum limit of the macroscopic manifestation of the Bohr principle of correspondence). Obviously, the zone of conversion of the properties of the microstate into the macroscopic properties of one or another material continuum is represented by a transition layer r of the influence of the basic structure ρ the configuration of several external (valence) electrons. The traditional consideration of the dispersion of dielectric constant in the aspect of the electromagnetic theory of radiation largely determines non-trivial approaches to the phenomenon of chemical bonding. Its representation in the form of a standing electromagnetic wave determines the appropriateness of the dispersion application to the field in material media when the Fourier component of the charge density is expanded in the Fourier integral. A nonlinear system of equations allows an exact solution in the form of a plane monochromatic wave.

The relationship is estimated as the braking force eE in the case of wave resistance with a direction opposite to the velocity vector v (for plane motion q with components of the wave vector k). The total field strength E allows us to calculate the energy loss of a moving molecule as the work of the inverse braking force. A significant contribution to the braking integral is made by the average value of the frequency of motion of atomic electrons (bond strength) ln. The connection is due to the influence of the entire electron charge of the atom (atomic form factor) F(r) on the braking force of the minimum amount of a substance (single molecule) by the total volume of the condensed medium.

1. Stromberg A.G., Semchenko D.P. Fizicheskaya khimiya. M.: Vysshaya shkola. 2001. 527 s. (In Russian).
2. Kafarov V.V., Dorokhov I.N., Koltsova E.M. Sistemnyi analiz protsessov khimicheskoi tekhnologii. M.: Nauka. 1989. 367 s. (In Russian).
3. Prokhorov V.A. Osnovy avtomatizatsii analiticheskogo kontrolya khimicheskikh proizvodstv. M.: KHimiya. 1984. 320 s. (In Russian).
4. Gibbs Dzh.V. Termodinamika. Statisticheskaya mekhanika. M.: Nauka. 1982. 584 s. (In Russian).
5. Gladyshev G.P. Termodinamika i makrokinetika prirodnykh ierarkhicheskikh protsessov. M.: Nauka. 1988. 289 s. (In Russian).
6. Bochkov G.N., Efremov G.F. K mikroskopicheskomu obosnovaniyu nelineinoi fluktuatsionnoi termodinamiki. Termodinamika neobratimykh protsessov. M.: Nauka. 1992. S. 2−30. (In Russian).
7. Pertsev V.T., Golovinskii P.A. Struktura dvoinogo sloya vblizi fraktalnoi poverkhnosti. Izvestiya VUZov. «PND». 2000. T. 8. № 3. S. 31−36. (In Russian).
8. Feinman R., Leiton R., Sends M. Feinmanovskie lektsii po fizike. Zadachi i uprazhneniya s otvetami i resheniyami. M.: Nauka. 1978. 543 s. (In Russian).
9. Sobolev S.L. Uravneniya matematicheskoi fiziki. M.: Nauka. 1992. 432 s. (In Russian).
10. Bronshtein I.N., Semendyaev K.A. Spravochnik po matematike dlya inzhenerov i uchashchikhsya vtuzov. M.: Nauka. 1986. 544 s. (In Russian).
11. Kamke E. Spravochnik po obyknovennym differentsialnym uravneniyam. M.: Nauka. 1976. 704 s. (In Russian).
12. Korn G., Korn T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov. M.: Nauka. 1977. 832 s. (In Russian).
13. Boum A. Kvantovaya mekhanika: osnovy i prilozheniya. Per. s angl. M.: Mir. 1990. 720 s. (In Russian).
14. Stepanov N.F. Kvantovaya mekhanika i kvantovaya khimiya. M.: Mir. 2001. 519 s. (In Russian).
15. Vorontsov Yu.I. Teoriya i metody makroskopicheskikh izmerenii. Pod red. V.B. Braginskogo. M.: Nauka. 1989. 280 s. (In Russian).
16. Rabinovich M.I., Trubetskov D.I. Vvedenie v teoriyu kolebanii i voln. M.: Nauka. 1992. 456 s. (In Russian).
17. Salem R.R. Teoreticheskaya elektrokhimiya. M.: Vuzovskaya kniga. 2001. 328 s. (In Russian).
18. Yavorskii B.M., Detlaf A.A. Spravochnik po fizike. M.: Nauka. 1980. 512 s. (In Russian).
19. Rid R., Prausnits Dzh., Shervud T. Svoistva gazov i zhidkostei: Spravochnoe posobie. Per. s angl.. Pod red. B.I. Sokolova. Izd. 3-e, pererab. i dop. L.: KHimiya. 1982. 592 s. (In Russian).
20. Gurvich L.V., Karachevtsev G.V., Kondratev V.N. Energii razryva khimicheskikh svyazei. Potentsialy ionizatsii i srodstvo k elektronu. M.: Nauka. 1974. 351 s. (In Russian).
21. Dobosh D. Elektrokhimicheskie konstanty. Spravochnik dlya elektrokhimikov. M.: Mir. 1980. 365 s. (In Russian).
22. Leonov V.V. Elektrodinamika fenomenov fizikokhimii kondensirovannykh sred. Kraevye zadachi i perekhodnye resheniya. Kurs lektsii. Saarbrücken (Germaniya): LAP Lambert Academic Publishing. 2014. 144 s. (In Russian).
23. Landau L.D., Lifshits E.M. Mekhanika. M.: Nauka. 2002. 512 s. (In Russian).
24. Landau L.D., Lifshits E.M. Elektrodinamika sploshnykh sred. M.: Nauka. 2005. 632 s. (In Russian).
25. Landau L.D., Lifshits E.M. Teoriya polya. M.: Nauka. 2004. 512 s. (In Russian).
26. Landau L.D., Lifshits E.M. Statisticheskaya fizika. Ch. 1. M.: Nauka. 2008. 584 s. (In Russian).
27. Dolomatov M.Yu., Mukaeva G.R. Sposob opredeleniya potentsialov ionizatsii i srodstva k elektronu atomov i molekul metodom elektronnoi spektroskopii. Zhurnal prikladnoi spektroskopii. 1992. T. 56. № 4. S. 570−574. (In Russian).
28. Dolomatov M.Yu., Leonov V.V. Vzaimosvyaz energii aktivatsii vyazkogo techeniya nyutonovskikh uglevodorodnykh sred i integralnykh kharakteristik ikh elektronnykh spektrov pogloshcheniya v vidimoi i UF-oblasti. Izvestiya VUZov. Povolzhskii region. Ser. Fizikomatematicheskaya. 2010. № 4. S. 141−149. (In Russian).
29. Leonov V.V., Denisova O.A. Elektrodinamicheskii selektivnyi filtr kondensirovannykh sred. Naukoemkie tekhnologii. 2017. № 1.
    1. 19−31. (In Russian).
30. Dolomatov M.Yu., Shulyakovskaya D.O., Karabelskaya I.V. Integralnye kharakteristiki spektrov slozhnykh molekulyarnykh sistem i ikh informatsionnye svoistva. Elektrotekhnicheskie i informatsionnye kompleksy i sistemy. 2015. № 3. T. 11. S. 113−120. (In Russian).
31. Denisova O.A. Turbulentnyi rezhim techeniya zhidkikh kristallov pri deistvii garmonicheskogo sdviga. Nauchnoe obozrenie. 2013. № 1.
    1. 34−36. (In Russian).
32. Romanovskii Yu.M., KHurgin Yu.I., Chikishev A.Yu., Tereshko V.M. Klasternaya dinamika belka i ee svyaz s funktsionalnoi aktivnostyu. Termodinamika neobratimykh protsessov. M.: Nauka. 1992. S. 177−184. (In Russian).
33. Tamm I.E. Osnovy teorii elektrichestva. M.: Nauka. 1966. 624 s. (In Russian).
34. Dolomatov M.Yu., Kovaleva E.A. Novyi molekulyarnyi deskriptor dlya prognoza sostoyanii molekulyarnykh sistem. Elektrotekhnicheskie i informatsionnye kompleksy i sistemy. 2015. T. 11. № 2. S. 98−104. (In Russian).
35. Landau L.D., Lifshits E.M. Gidrodinamika. M.: Nauka. 2003. 632 s. (In Russian).
36. Zakharov E.M. Dissipatsiya energii v dvoinom elektricheskom sloe granitsy metall – rastvor elektrolita pri prokhozhdenii postoyannogo elektricheskogo toka. Termodinamika neobratimykh protsessov. M.: Nauka. 1992. S. 185−194. (In Russian).
37. Leonov V.V., Dolomatov M.Yu., Ismagilov T.A. Elektrodinamika protsessov adsorbtsii v kondensirovannykh sredakh. Inzhenernofizicheskii zhurnal. 2013. T. 86. № 1. S. 168−172. (In Russian).
38. Leonov V.V. Elektrodinamika diffuzii v kondensirovannykh fiziko-khimicheskikh sistemakh. Inzhenerno-fizicheskii zhurnal. 2014. T. 87. № 2. S. 265−271. (In Russian).
39. Leonov V.V., Denisova O.A. Elektrodinamika formirovaniya granichnykh poverkhnostei kondensirovannykh sred. Naukoemkie tekhnologii. 2017. № 9. S. 25−40. (In Russian).
40. Rekhviashvili S.Sh. Ob analogii mezhdu termodinamikoi poverkhnosti i elektrostatikoi. Kondensirovannye sredy i mezhfaznye granitsy. 2009. T. 11. № 3. S. 244−248. (In Russian).
41. Leonov V.V., Denisova O.A. Elektrodinamika vyazkogo techeniya kondensirovannykh sred. Naukoemkie tekhnologii. 2016. № 2.
    1. 12−23. (In Russian).
42. Leonov V.V., Denisova O.A. elektrodinamika sdvigovogo deistviya i realizatsiya rezhima turbulentnosti v kondensirovannykh sredakh. Elektrotekhnicheskie i informatsionnye kompleksy i sistemy. 2015. № 2. T. 11. S. 90−97. (In Russian).
43. Leonov V.V., Dolomatov M.Yu. Elektrometricheskoe opredelenie dinamicheskoi vyazkosti nyutonovskikh zhidkostei. Naukoemkie tekhnologii. 2011. № 3. S. 36−43. (In Russian).
44. Leonov V.V., Dolomatov M.Yu., Ismagilov T.A., Ragulin V.V. Makroskopicheskaya elektrodinamika fiziko-khimicheskikh protsessov v mnogokomponentnykh kondensirovannykh sredakh. SPb.: Nedra. 2013. 204 s. (In Russian).
45. Leonov V.V., Denisova O.A. Elektrodinamicheskie sistemnye ogranicheniya kvantovogo predela elektronnoi spektroskopii kondensirovannykh sred. Naukoemkie tekhnologii. 2019. № 3. S. 30−52. DOI: 10.18127/j19998465-201903-04. (In Russian).