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УДК: 547.62:544.183.26
V. A. Bab kin, A. V. Ignatov, N. G. Lebedev, R.G. Fedunov, E. S. Titova, V. T. Fomichev, G. E. Zaikov
QUANTUM-CHEMICAL CALCULATION OF PYRENE BY METHOD MNDO
IN FRAME OF MOLECULAR NONLINEAR MODEL OF GRAPHENE
Keywords: quantum-chemical calculation, method MNDO, pyrene, graphene, acid force.
Quantum-chemical calculation of the molecular model of pyrene has been first performed. Pyrene structure is considered as a molecular model of a new class of carbon materials - graphene by method MNDO. Optimized geometric and electronic structure of this compound is obtained. Acid power ofpyrene is theoretically evaluated (pKa = 33). It is established that pyrene pertains to class of very weak acids (pKa> 14).
Ключевые слова: квантово-химический расчет, метод MNDO, пирен, графен, кислотная сила.
Впервые выполнен квантово-химический расчет молекулы пирена методом MNDO в рамках нелинейной модели графена с оптимизацией геометрии по всем параметрам стандартным градиентным методом Получено оптимизированное геометрическое и электронное строение этого соединения. Теоретически оценена его кислотная сила (рКа=33). Установлено, что пирен относится к классу очень слабыхН-кислот (pKa>14).
Aim and Background
Graphenes were discovered by Geim A.K. and Novoselov K.S. in 2004 [1-2]. Quantum-chemical calculations of the simplest molecular systems that can serve as models of graphenes are not executed. This structure may consist of 2, 3 , 4 , 5, etc. six-membered rings of carbon atoms. Quantum-chemical calculations of such structures may contribute to a deeper understanding of the physicochemical properties of graphene.
Knowing the structure of the above models, the charge distribution on atoms, bond lengths and valence angles is needed for the further research graphenes. The aim of this work is the quantum-chemical calculation of the electronic structure and geometrical characteristics of pyrene, which obviously is a nonlinear molecular model of graphene consisting of six hexagons, by semiempirical method MNDO [7] at the nanoscale with geometry optimization of all parameters of the standard gradient method built into the PC GAMESS [8], theoretical evaluation of its acid power. Pyrene molecule has a planar structure and contains four six-membered rings composed of carbon atoms (hexagons).
The MacMolPlt program was used to visualize the models of studied molecule [9]. Calculation of pyrene molecules is made in the ground state, for which M = 2S + 1 = 1 since the sum of the molecular spin S =E 0 (all electrons are paired, where M- multiplicity and S - total spin of test compound).
Methodical Part
Optimized geometric and electronic structure, total energy and electronic energy of pyrene have been obtained by method MNDO. The calculation results are shown on fig. and in tabl. Charges on carbon atoms by Mulliken unevenly distributed on the structure. On the "outside" atom C a charge is minimal (tabl. Charges on atoms C (2) and C (22) are equal to -0.06). The remaining carbon atoms are slightly larger charge distributed symmetrically about the center of symmetry of the molecule. These molecules contain carbon bonds:
2-n-bonds, 5-g- bonds and 12-sesquialteral bonds. The accuracy of the performed quantum calculations doesn't raise doubts because the length of the carbon bonds pyrene (1.36-1.46 A) obtained in this study coincide with the bond lengths of the same compound in [2, 14] (1.36-1.49 A) . There is a coincidence of lengths C-H bonds (1.084 A and 1,09 A, respectively) [3, 15], and the valence angles are close to 120°. This corresponds to the calculations of valence angles, for example benzene [3]. The universal factor of acidity was calculated by formula [10]:
рКа = 42.11 - 147.18 qm
(1)
(where qmax + - a maximum positive charge on atom of the hydrogen, pKa - universal factor of acidity). The formula has been used successfully, for example, [12, 13]. According to the formula (1) find the value of the acid power of pyrene molecules pKa = 33 (qmaxH+ = +0.06 table 1). The results correspond to the known ranges of the acid strength of various molecular systems [14]:
1. very strong acid pKa < 0
2. strong acid 0 < pKa < 4,5
3. medium strong acid 4,5 < pKa < 9
4. weak acids 9 < pKa < 14
5. very weak acids pKa > 14,
Pyrene pertain to the class of very weak H-acids (pKa (benzene) = 37 [16]).
Fig. 1 - Geometric and electronic structure of pyrene. (Е0= -210836 kJ/mol, Ee,= -1300907 kJ/mol)
H+
Table 1 - Optimized bond lengths, valence corners and charges on atoms of pyrene
Bond lengths R, A Valence angle Grad
C(1)-C(2) 1.44 C(3)-C(2)-C(1) 120
C(1)-C(10) 1.46 C(13)-C(10)-C(1) 122
C(2)-C(3) 1.44 C(4)-C(3)-C(2) 119
C(3)-C(4) 1.41 C(10)-C(1)-C(2) 118
C(3)-C(16) 1.46 C(17)-C(11)-C(2) 120
C(4)-C(5) 1.40 C(5)-C(4)-C(3) 121
C(5)-C(6) 1.40 C(11)-C(2)-C(3) 120
C(6)-C(1) 1.41 C(6)-C(5)-C(4) 121
H(7)-C(4) 1.09 C(16)-C(3)-C(4) 123
H(8)-C(5) 1.09 C(1)-C(6)-C(5) 121
H(9)-C(6) 1.09 C(2)-C(1)-C(6) 119
с(10)-С(13) 1.36 C(10)-C(1)-C(6) 123
C(11)-C(2) 1.46 C(3)-C(4)-H(7) 120
C(12)-C(11) 1.44 C(4)-C(5)-H(8) 120
C(12)-C(20) 1.41 C(5)-C(6)-H(9) 119
C(13)-C(12) 1.46 C(12)-C(13)-C(10) 122
H(14)-C(13) 1.09 С(1)-С(2)-С(11) 120
H(15)-C(10) 1.09 С(18)-С(17)-С(11) 118
C(16)-C(18) 1.36 С(20)-С(12)-С(11) 119
С(17)-С(11) 1.44 С(2)-С(11)-С(12) 120
С(18)-С(17) 1.46 С(22)-С(20)-С(12) 121
H(19)-C(16) 1.09 С(2)-С(12)-С(13) 118
C(20)-C(22) 1.40 С(20)-С(12)-С(13) 123
C(21)-C(17) 1.41 С( 10)-С( 13)-H( 14) 120
C(22)-C(21) 1.40 C(1)-C(10)-H(15) 118
H(23)-C(20) 1.09 С(2)-С(3)-С(16) 118
H(24)-C(22) 1.09 С( 16)-С( 18)-С( 17) 122
H(25)-C(21) 1.09 С( 12)-С( 11 )-С( 17) 120
H(26)-C(18) 1.09 С(3)-С(16)-С(18) 122
С(21 )-С( 17)-С( 18) 123
С( 18)-С( 16)-H( 19) 120
С(21 )-С(22)-С(20) 121
С( 11 )-С( 17)-С(21 ) 119
С( 17)-С(21)-С(22) 121
С( 12)-C(20)-H(23) 120
C(20)-C(22)-H(24) 120
C(22)-C(21)-H(25) 119
С( 17)-С( 18)-H(26) 118
Conclusion
Quantum-chemical calculation of molecule pyrene by method MNDO was executed for the first time. Optimized geometric and electronic structure of this compound was received. Acid power of pyrene was theoretically evaluated (pKa=33). This compound pertains to class of very weak ^acids (pKa> 14).
Presented results of quantum-chemical calculations (optimized length of C- and H-bonds, valence corners and atomic charges, etc.) indicate that this structure may be regarded as a molecular model of a new class of carbon materials - nonlinear graphene [11]. These data may contribute to a deeper understanding of the physicochemical processes occurring in graphene at the nanoscale.
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© V. A. Babkin - Doctor of Chemical Sciences, professor, Head of Science department of Volgograd State Architecture Building University, Sebryakov's, Branch. [email protected]; A.V. Ignatov - 4th year student of class "S41-d"of Volgograd State Architecture Building University, Sebryakov's Branch, [email protected]; N. G. Lebedev - Doctor of Physico-mathematical Sciences, professor. Cathedra "Theoretical physics and wave processes. PhysTech of VolSU, [email protected]; R. G. Fedunov — Candidate of Physico-mathematical Sciences, professor of "Theoretical Physics and Wave Processes" department of Volgograd State [email protected]; E. S. Titova - Candidate of Chemical Sciences, professor of department "Organic Chemistry" of Volgograd State Technical University, [email protected]; V. T. Fomichev — Doctor of Engineering Sciences, professor of department "Applied Chemistry" of Volgograd State Architecture Building University, [email protected]; G. E. Zaikov -Doctor of Chemical Sciences, professor of TPM department of KNRTU, Honored scientist of Russian Federation. Institute of Biochemical Physics, [email protected].
© В. А. Бабкин — д-р хим. наук, проф., нач. научн. отдела Себряковского филиала Волгоградского госуд. ун-та, [email protected]; А. В. Игнатов — студ. гр. С-41д того же вуза, [email protected]; Н. Г. Лебедев — д-р физ.-мат. наук, проф., каф. «Теоретической физики и волновых процессов» ФизТех при ВолГУ, [email protected]; Р. Г. Федунов — канд. физ.-мат. наук, доц. каф. «Теоретической физики и волновых процессов», Волгоградский госуд. ун-тет, [email protected]; Е. С Титова — к.х.н. доц. каф.ы «Органическая химия» Волгоградского госуд. технич. ун-та, [email protected]; В. Т. Фомичёв — д.т.н., проф., зав. каф. «Прикладная химия», Волгоградского госуд. архитектурно-строительного ун-та, [email protected]; Г. Е. Заиков — д-р хим. наук, проф. кафедры ТПМ КНИТУ, заслуженный деятель РФ. Институт биохимической физики, РАН, [email protected].
