Calculations of bond energy in cluster aqueous nanostructures

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НАУЧНОЕ ПЕРИОДИЧЕСКОЕ ИЗДАНИЕ «IN SITU» № 1−2/2016 ISSN 2411−7161
ХИМИЧЕСКИЕ НАУКИ
УДК 536. 7+541−539
GA. Korablev*, N.V. Khokhriakov*, G.S. Valiullina*
* - Izhevsk State Agricultural Academy Studencheskaya St. 11, Izhevsk, 426 000, Russia
CALCULATIONS OF BOND ENERGY IN CLUSTER AQUEOUS NANOSTRUCTURES
Abstract
The bond energy in some cluster aqueous structures has been calculated using spatial-energy notions and compared with quantum-mechanical methods. It is demonstrated that the variety and specifics of aqueous solutions are determined by the changes in structural energy characteristics of these cluster compounds.
Based on modified Lagrangian equation for relative movement of two interacting material points the notion of spatial-energy parameter (P-parameter), which is a complex characteristic of important atomic values responsible for interatomic interactions and directly connected with electron density in atom [1].
The value of relative difference of P-parameters of interacting atoms — components of a -coefficient of structural interactions was used as the main quantitative characteristic of structural interactions in condensed media:
P -P,
a = -r-1-^100% (1)
(Pi +P2)/2
The nomogram of dependence of structural interaction degree upon the coefficient a (the same for a wide range of structures) was obtained applying the reliable experimental data. This approach allowed evaluating the degree and direction of structural interactions of phase-formation, isomorphism and solubility in multiple systems, including the molecular ones. In particular, the peculiarities of cluster-formation in the system CaSO4 — H2O were studied [2].
To evaluate the direction and degree of phase-formation processes the following equations were used [1]: 1) To calculate the initial values of Р-parameters:
1 = ^ - -1 = Л + 7^ P =Po/ Г (2, 3, 4)
q2/ rt W, n, P3 '- P0 q2 (M, 3 0
here: Wi — orbital energy of electrons [3]- r — orbital radius of i-orbital [4]- q = Z * /n * - [5, 6]- n — number of electrons of the given orbital, Z * and n * - nucleus effective charge and effective main quantum number. The value P0 will be called spatial-energy parameter (SEP), and — effective P-parameter.
The calculation results by equations [2,3,4] for some elements are given in Table 1, where we can see that for hydrogen atom the values of PE-parameters considerably differ at the distances of orbital (n) and covalent radii ®. The hybridization of valent orbitals of carbon atom were evaluated as an averaged value of P-parameters of 2S2 and 2P2-orbitals.
2) To calculate the value of Ps-parameter in binary and complex structures:
111
— =-±+… (5)
Ps N2P2
where N — number of homogeneous atoms in each subsystem. The results of these calculations for some systems are given in Table 2.
3) To determine the bond energy (E) in binary and more complicated structures:
—. -L… (6)
E PE Pi (N / K) i P2(N / K)2 Here (as applied to cluster systems): Ki and K2 — number of subsystems forming the cluster system- N1 and
_НАУЧНОЕ ПЕРИОДИЧЕСКОЕ ИЗДАНИЕ «IN SITU» № 1−2/2016 ISSN 2411−7161_
N2 — number of homogeneous clusters [7].
Table 1
P-parameters of atoms calculated via the bond energy of electrons
Atom Valent electrons W (eV) n (A) q2 (eVA) Po (eVA) R (A) Pe=Po/R (eV)
H 1S1 13. 595 0. 5295 14. 394 4. 7985 0. 5295 0. 28 9. 0624 17. 137
C 2P1 11. 792 0. 596 35. 395 5. 8680 0. 77 0. 69 7. 6208 8. 5043
2P2 11. 792 0. 596 35. 395 10. 061 0. 77 13. 066
2S1 19. 201 0. 620 37. 240 9. 0209 0. 77 11. 715
2S2 14. 524 0. 77 18. 862
2S2+2P2 24. 585 0. 77 31. 929
& gt-2 (2s2 + 2P2) 15. 964
O 2P1 17. 195 0. 4135 71. 383 4. 663 0. 66 9. 7979
2P2 17. 195 0. 4135 71. 383 11. 858 0. 66 0. 59 17. 967 20. 048
2P4 17. 195 0. 4135 71. 383 20. 338 0. 66 30. 815
Table 2
Structural Ps-parameters
Radical, molecules Р1 (eV) Р2 (eV) Р3 (eV) Р4 (eV) Ps (eV) Orbitals of oxygen atom
OH 17. 967 17. 137 8. 7712 2P2
OH 9. 7979 9. 0624 4. 7080 2P1
H2O 2 X 17. 138 2 X 9. 0624 17. 967 17. 967 11. 788 9. 0226 2P2 2P2
C2H5OH 2 X 15. 964 2 X 9. 0624 9. 7979 9. 0624 3. 7622 2P1
Thus for C6o (OH)io ki = 60, k2=10.
It is assumed that the stable aqueous cluster (H2O) can have the same static number of subsystems (k) as the number of subsystems in the system interacting with it [8]. For example, aqueous cluster of N (H2O)io type interacts with fullerene [C6OH]io.
Apparently, cluster [(C2H5OH)6 — H2O]io can be formed similarly to cluster [C6OH)10, that assumes the structural interaction of subsystems (C2H5OH)60 — (H2O)io. And the interaction of aqueous clusters can be considered as the interaction of subsystems (H2O)60 — N (H2O)60.
Based on such notions and assumptions the bond energy in corresponding systems was calculated by the equation (6), the results are given in Table 3.
The calculation data obtained by N.V. Khokhriakov based on his quantum-mechanical technique [9] are given here for comparison.
kcal
Both techniques present comparable bond energy values (eV). Transfer multiplier: (i-=0. 4 336 eV).
mol
Besides, the technique of P-parameter allows explaining why the energy value of cluster bonds of water molecule with fullerene C60(OH)i0 two times exceeds the bond energy between the molecule in cluster water (Table 3).
In accordance with the nomogram the structure phase-formation can take place only with the relative difference of their P-parameters below 25%-30%, and the most stable structures are formed at a & lt- (6−7)%.
Table 4 gives the values of coefficient a in systems H-C, H-OH and H-H2O, which are within 0. 44 -7. 09(%).
But in the system H-C for carbon and hydrogen atoms the interactions at the distances of covalent radii were
_НАУЧНОЕ ПЕРИОДИЧЕСКОЕ ИЗДАНИЕ «IN SITU» № 1−2/2016 ISSN 2411−7161_
considered, but for other systems — at the distances of orbital radius.
Thus, the interaction in the system H-C at the distances of covalent radius plays a role of fermentative action, which results in the transition of dimensional characteristics of water molecules from orbital radius to the covalent one, i.e. to the formation of the system Сбо (ОН)ю — N (H2O)10 with bond energy between the main components two times exceeding the one between water molecules themselves.
The broad possibilities of aqueous clusters in changing their spatial-energy characteristics apparently explain all other water properties with its different names: mineral, holly, live, spring, radioactive, etc.
Table 3
Calculations of bond energy — Е (eV)
System Сб0 (OH)l0 (H2O)l0 Ре Е (calculation)
Pi/Kl P2/K2 P3/K3 N3 Equation (6) Quantum-mechanical
C6o (OH)io -- N (H2O)io 15. 964/60 8. 77l2/l0 ll. 788/l0 l 0. l74 0. 176
2 0. l88 0. 209
3 0. l93 0. 218
4 0. l96 0. 212
5 0. l97 0. 204
(H2O)60 -- N (H2O)60 Pl/Kl P2/K2 N2
9. 0226/60 9. 0226/60 l 0. 0768 0. 0863
2 0. l020 0. 1032
3 0. ll28 0. 1101
4 0. l203 0. 1110
5 0. l274 0. 115
(С2Н5ОЩЮ -- (H2O)10 Pl/Kl P2/K2
3. 7622/60 9. 0226/l0 0. 0586 0. 0607
(С2Н5ОЩ0 -- (H2O)60 Pl/Kl P2/K2
3. 7622/l0 9. 0226/60 0. l074 «0,116
Table 4
Spatial-energy interactions in the system H-R, where R= C, (OH), H2O
System Pl (eV) P2(eV) AP a= 100% & lt-P>- Type of spatial bond
H-C l7. l37 l5. 964 7. 09 Covalent
H-OH 9. 0624 8. 77l2 3. 27 Orbital
H-H2O 9. 0624 9. 0226 0. 44 Orbital
Conclusions
1. Structural interactions in the bond H-C at the distances of covalent radius play the role of fermentative action, which results in the transition of dimensional characteristics of water molecules from orbital radius to covalent one, i.e. to the system: C6o (OH)io — N (H2O)io.
2. Broad possibilities of aqueous clusters in the change of their spatial-energy characteristics apparently explain all other unique properties of water with different names: mineral, holly, live, spring, radioactive, etc.
References
1. Korablev G.A. Spatial-Energy Principles of Complex Structures Formation, Leiden, the Netherlands, Brill Academic Publishers and VSP, 2005, 426 pages (Monograph).
2. Korablev G.A., Yakovlev G.I., Kodolov V.I. Some peculiarities of cluster-formation in the system CaSO4-H2O. Chemical physics and mesoscopy, vol. 4, № 2, 2002, p. 188−196.
3. Fischer C.F. Average-Energy of Configuration Hartree-Fock Results for the Atoms Helium to Radon. //Atomic Data,-1972, № 4, p. 301−399.
4. Waber J.T., Cromer D.T. Orbital Radii of Atoms and Ions. //J. Chem. Phys -1965, -V 42, -№ 12, p. 4116−4123.
5. Clementi E., Raimondi D.L. Atomic Screening constants from S.C.F. Functions, 1. //J. Chem. Phys. 1963, v. 38, № 11, p. 2686−2689.
_НАУЧНОЕ ПЕРИОДИЧЕСКОЕ ИЗДАНИЕ «IN SITU» № 1−2/2016 ISSN 2411−7161_
6. Clementi E., Raimondi D.L. Atomic Screening constants from S.C.F. Functions, 2. //J. Chem. Phys. -1967, v. 47, № 4, p. 1300−1307.
7. Korablev G.A., Zaikov G.E. Energy of chemical bond and spatial-energy principles of hybridization of atom orbitals. //J. Applied Polymer Science. USA, 2006, V. 101, n. 3, p. 2101−2107.
8. Hodges M.P., Wales D.J. Glolal minima of protonated Water clusters. Chemlocal Physies Letters, 324, (2000), p. 279−288.
9. Khokhriakov N.V., Melchor Ferrers. Electron properties of contacts in ideal carbon nanotubes. // Chemical physics and mesoscopy. Vol. 4, № 2, 2002, p. 261−263.
© Korablev G.A., Khokhriakov N.V., Valiullina G.S., 2016

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