About of possibilty of using hybrid method DFT B3LYP for calculation of molecular structures of macropolyazacyclic complexes of 3d-elements Текст научной статьи по специальности «Химические науки»

O. V. Mikhailov, D. V. Chachkov ABOUT OF POSSIBILTY OF USING HYBRID METHOD DFT B3LYP FOR CALCULATION OF MOLECULAR STRUCTURES OF MACROPOLYAZACYCLIC COMPLEXES OF 3J-ELEMENTS

Ключевые слова: молекулярная структура, DFTB3LYP, фталоцианин 3ё-метстла.

С использованием метода DFT B3LYP 6-31G(d) и программы Gaussian09 осуществлен расчет геометрических параметров моле-кулярных структур комплексов M(II) с макроциклическим лигандом - фталоцианином (M = ион 3d-элемента). Представлены длины связей и углы между различными атомами в каждом из вышеуказанных комплексов. Результаты расчета сопоставлены с наиболее современными литературными структурными данными указанных комплексов. Отмечено хорошее согласие между рассчитанными и литературными данными, свидетельст-вующее о надежности данного метода для расчета структурных параметров макроциклических металлохелатов, для комплексов Mn(II), Fe(II), Co(II), Ni(II) и Cu(II), для которых имеются литературные данные.

Keywords: molecular structure, DFTB3LYP, 3d-metal(II) phthalocyanine.

By using DFT B3LYP method with 6-31G(d) basic set and Gaussian09 program, a calculation of geometric parameters of molecular structure of M(II) complexes with macrocyclic ligand - phthalocyanine has been carried out (M = 3d-element ion). The bond lengths and angles between various atoms in each of above-mentioned complexes have been presented. Results of calculation have been compared with the most modern available in the literature structural data for the compound indicated. The good consent between the calculated and literary data testifying to capacity of the given method for calculation of structural parameters of macrocyclic metalchelates, has been noted for Mn(II), Fe(II), Co(II), Ni(II) and Cu(II) complexes for which there is literature data.

INTRODUCTION

The macrocyclic chelates of M(II) ions of various 3d-elements with phthalocyanines of type (I)

are known for a long time u their space structures were repeatedly investigated by various researchers. In this connection, non-empirical (ab initio) quantum-chemical calculation of metalcomplexes of the given type, gets a sufficient urgency. It would allow receive, on the one hand, independent objective data about their structural parameters, on the other hand, would give the chance to compare these parameters with corresponding experimental data and to state an estimation of capacity of either calculation method to forecasting of structures of such chelate complexes. The importance of such researches becomes especially great for those complexes for which, for some reasons, X-ray diffraction researches are impossible. The present paper is devoted to discussion of results of quantum-chemical calculation of molecular structure parameters of simplest phthalocyanine complexes, namely Mn(II),

Fe(II), Co(II), Ni(II) and Cu(II) chelates with non-substituted phthalocyanine, with using one of most popular version, namely by DFT B3LYP functional density method.

Method

As before in our works [1-3], B3LYP 6-31G(d) method, which is hybrid DFT method using Becke function (1988) including Slater exchange, by beginning with amendment including density gradient, and correlation function of Lee, Yang and Parr, which includes local and non-local therms [4,5], was used by us for calculations. The energy values E were calculated according to equation E = V + <hP> + 1/2<PJ(P)> + EX[P] + EC[P] where V is nuclearic energy of repulsion, <hP> - one-electronic (kinetic + potential) energy, 1/2<PJ(P)> - energy of electrons repulsion, EX[P] - exchange function; EC[P] - correlation function. 6-31G(d) basic set where each inner atom orbital (AO) is described by six functions of Gauss type (GTO), valence 2s AO- by three GTO, valence p-AO - by one GTO, with addition of polarization cf-GTO to each ^-function, was used. Conformity of the found stationary points to energy minima in all cases was proved by calculation of the second derivatives of energy on co-ordinates of atoms. Every of equilibrium structures corresponding to points of a minimum on surfaces of potential energy, had only material values of frequencies. Any limitation in symmetry of complexes calculated is not imposed. All quantum-chemical calculations were made with using Gaussian09 program [6] and have been carried out with using supercomputer MVS-100000K by productivity 10 TFLOPS. Supercomputer MVS-100000K consists of 64 units (blocks) connected Gigabit Ethernet and Infiniband. Each unit consists of two four-nuclear Xeon E5450 processors with cycle frequency 3 GHz and has volume of operative memory 8 Gb.

Results and discussions

According to data of our quantum-chemical calculation, the molecular structures of complexes considered are the same type and all they are strongly coplanar. The examples of molecular structures of M(II) complexes with phthalocyanine obtained as a result of quantum-chemical calculations, have been shown on the figs. 1-3.

Fig. 1 - The space structure of Fe(II) complex with phthalocyanine

Fig. 2 - The space structure of Ni(II) complex with phthalocyanine

Fig. 3 - The space structure of Cu(II) complex with phthalocyanine

The data concerning of details of molecular structures of coordination compounds considered here, have been presented in the table 1. As may be seen from them, the data calculated theoretically and observed experimentally, in the most cases are extremely nearly or even practically coincide with each other, the divergence between them practically in all cases is in limits +5%. This distinction, by

the way, is less than disorder degree in the literary given values of parameters of the molecular structures observed for the same connection in publications of different authors. The told especially concerns valence and torsion angles which, according to different authors, differ sometimes rather strongly. It should be noted especially in this connection that average values of these parameters are in even more good harmony with theoretically ones calculated by us with using DFT B3LYP 6-31G(d) method than ones resulted in table 1, which are taken from concrete publishing works.

As may be seen from the table 1, according to data of our calculation, chelate junction MN4 in the each of macrotetracyclic complexes considered by us, is ideal plane; the sum of valence (MNM) angles as well as non-valence (NNN) angles in the each of them are exactly 360°. All they angles are quite the same and equal to 90.0°; besides, it is typical that, the M-N bond lengths in Mn(II) and Cu(II) chelates are differ from each other, in the remaining complexes they are quite the same. In the each of complexes considered, all cycles contained in them - metalcycles containing M, N and C atoms as well as cycles containing N and C atoms, and ones containing only C atoms, are practically ideal plane; the sum of inner angles in all 5-numbered cycles are 540°, in the all 6-numbered ones, 720°.

Table 1 - Bonds lengths, plane and torsion angles in the M(II) phthalocyanine complexes. The bold font in brackets specifies experimental values, regular font, calculated by method DFT B3LYP 6-31G (d)

M Mn Fe Co Ni Cu

1 2 3 4 5 6

M-N bond lengths, pm

(M1N1) 195.9 (193.9) 193.8 (192.7) 189.6 (191.0) 190.4 (183.0) 196.0 (195.3)

(M1N2) 193.7 (193.8) 193.8 (192.6) 189.6 (191.0) 190.4 (183.1) 195.0 (195.0)

(M1N3) 195.9 (193.9) 193.8 (192.7) 189.6 (191.0) 190.4 (183.0) 196.0 (195.3)

(M1N4) 193.7 (193.8) 193.8 (192.6) 189.6 (191.0) 190.4 (183.1) 195.0 (195.0)

C-N bond lengths, pm

(N1C3) 138.5 (138.9) 138.0 (138.1) 138.8 (138.4) 138.1 (137.9) 137.5 (138.8)

(N1C4) 138.5 (139.7) 138.1 (137.5) 138.8 (137.1) 138.1 (139.0) 137.6 (138.9)

(N2C1) 139.5 (139.1) 138.1 (137.5) 138.8 (137.1) 138.1 (137.1) 138.3 (137.9)

(N2C2) 139.5 (139.2) 138.0 (138.2) 138.8 (138.4) 138.0 (137.7) 138.3 (138.1)

(N3C7) 138.5 (138.9) 138.0 (138.1) 138.8 (137.0) 138.1 (137.9) 137.5 (138.8)

(N3C8) 138.5 (139.7) 138.1 (137.5) 138.8 (138.7) 138.1 (139.0) 137.6 (138.9)

(N4C5) 139.5 (139.1) 138.1 (137.5) 138.8 (138.0) 138.0 (139.5) 138.3 (137.9)

(N4C6) 139.5 (139.2) 138.0 (138.2) 138.8 (138.0) 138.1 (137.7) 138.3 (138.1)

(N5C2) 131.2 (131.4) 132.2 (132.1) 131.9 (131.9) 131.8 (136.8) 130.9 (135.4)

(N5C3) 133.1 (132.5) 132.2 (132.2) 131.9 (132.6) 131.8 (137.7) 135.0 (137.1)

(N6C6) 131.2 (131.4) 132.2 (132.1) 131.9 (131.9) 131.8 (136.8) 130.9 (135.4)

(N6C7) 133.1 (132.5) 132.2 (132.2) 131.9 (132.6) 131.8 (137.7) 135.0 (137.1)

(N7C4) 133.1 (132.4) 132.2 (132.0) 131.9 (132.3) 131.8 (138.0) 134.9 (134.4)

(N7C5) 131.2 (132.8) 132.2 (132.4) 131.9 (132.5) 131.8 (137.3) 130.8 (134.9)

(N8C1) 131.2 (132.8) 132.2 (132.4) 131.9 (132.3) 131.8 (137.3) 130.8 (134.9)

(N8C8) 133.1 (132.4) 132.2 (132.0) 131.9 (132.5) 131.8 (138.0) 134.9 (134.4)

Continued table 1

1 2 3 4 5 6

C-C bond lengths, pm

(C9C10) 141.2 (140.8) 140.4 (139.0) 139.9 (139.2) 140.0 (138.3) 141.2 (140.7)

(C11C12) 140.3 (140.7) 140.4 (139.3) 139.9 (139.8) 140.0 (138.9) 139.9 (140.7)

(C13C14) 141.2 (140.8) 140.4 (139.0) 139.9 (139.2) 140.0 (138.3) 141.2 (140.7)

(C15C16) 140.3 (140.7) 140.4 (139.3) 139.9 (139.8) 140.0 (138.9) 139.9 (140.7)

(C9C17) 140.1 (139.2) 139.6 (139.5) 139.2 (139.3) 139.6 (139.4) 139.7 (137.9)

(C17C25) 138.8 (139.4) 139.3 (138.7) 139.8 (139.4) 139.3 (139.2) 139.4 (137.2)

(C25C26) 141.5 (140.9) 140.9 (139.4) 140.4 (139.1) 140.9 (140.7) 141.0 (141.2)

(C26C18) 138.8 (139.6) 139.3 (139.7) 139.8 (139.4) 139.3 (139.5) 139.4 (137.9)

(C18C10) 140.1 (140.0) 139.6 (139.4) 139.2 (139.0) 139.6 (138.5) 139.7 (137.9)

C-H bond lengths, pm

(C17H1) 108.5 (109.5) 108.5 108.5 (95.3) 108.5 108.6 (102.8)

(C25H9) 108.7 (107.8) 108.7 108.6 (95.8) 108.7 108.7 (102.3)

(C26H10) 108.7 (109.4) 108.7 108.6 (96.3) 108.7 108.7 (102.5)

(C18H2) 108.5 (108.0) 108.5 108.5 (95.1) 108.5 108.6 (102.8)

ZNMN valence angles, grad

(N1M1N4) 90.0 (91.3) 90.0 (90.9) 90.0 (90.0) 90.0 (89.3) 90.0 (89.0)

(N4M1N3) 90.0 (88.7) 90.0 (89.1) 90.0 (90.0) 90.0 (90.7) 90.0 (91.0)

(N3M1N2) 90.0 (91.3) 90.0 (90.9) 90.0 (90.0) 90.0 (89.3) 90.0 (89.0)

(N2M1N1) 90.0 (88.7) 90.0 (89.1) 90.0 (90.0) 90.0 (90.7) 90.0 (91.0)

VAS 360.0 (360.0) 360.0 (360.0) 360.0 (360.0) 360.0 (360.0) 360.0 (360.0)

ZNNN non-valence angles, grad

(N1N4N3) 90.7 (90.5) 90.0 (90.0) 90.0 (90.0) 90.0 (90.2) 90.2 (90.1)

(N4N3N2) 89.3 (89.5) 90.0 (90.0) 90.0 (90.0) 90.0 (89.8) 89.8 (89.9)

(N3N2N1) 90.7 (90.5) 90.0 (90.0) 90.0 (90.0) 90.0 (90.2) 90.2 (90.1)

(N2N1N4) 89.3 (89.5) 90.0 (90.0) 90.0 (90.0) 90.0 (89.8) 89.8 (89.9)

NVAS 360.0 (360.0) 360.0 (360.0) 360.0 (360.0) 360.0 (360.0) 360.0 (360.0)

Valence angles in the 6-numbered cycle (M1N1C4N7C5N4), grad

(N4M1N4) 90.0 (91.3) 90.0 (90.9) 90.0 (90.0) 90.0 (89.3) 90.0 (89.0)

(M1N4C5) 126.2 (125.2) 126.3 (125.4) 127.0 (127.8) 126.7 (130.4) 125.9 (127.5)

(N4C5N7) 127.5 (127.9) 127.5 (128.0) 127.6 (126.2) 127.7 (126.9) 128.5 (127.2)

(C5N7C4) 123.1 (122.7) 122.5 (122.2) 120.8 (121.1) 121.2 (116.0) 122.1 (122.0)

(N7C4N1) 127.2 (127.7) 127.5 (127.9) 127.6 (128.4) 127.7 (126.9) 127.6 (126.5)

(C4N1M1) 125.9 (125.2) 126.2 (125.5) 127.0 (125.8) 126.7 (130.5) 125.9 (127.8)

VAS1 719.9 (720.0) 720.0 (719.9) 720.0 (719.3) 720.0 (720.0) 720.0 (720.0)

Valence angles in the 5-numbered cycle (C3N1C4C9C10), grad

(C3N1C4) 108.2 (107.5) 107.6 (107.3) 106.1 (107.3) 106.5 (99.9) 108.0 (106.1)

The end of the tablel

1 2 3 4 5 6

(N1C4C9) 109.2 (109.5) 109.8 (110.0) 110.6 (109.3) 110.5 (115.9) 109.6 (111.4)

(C4C9C10) 106.7 (106.6) 106.4 (106.6) 106.3 (106.2) 106.3 (102.6) 106.4 (106.5)

(C9C10C3) 106.7 (107.0) 106.4 (106.5) 106.3 (106.5) 106.3 (106.5) 106.4 (105.5)

(C10C3N1) 109.2 (109.3) 109.8 (109.6) 110.6 (108.2) 110.4 (115.1) 109.6 (110.4)

VAS2 540.0 (539.9) 540.0 (540.0) 539.9 (537.5) 540.0 (540.0) 540.0 (539.9)

Valence angles in the 6-numbered cycle (C9C10C18C26C25C17), grad

(C9C10C18) 121.0 (120.8) 121.2 (121.4) 121.4 (119.6) 121.4 (119.9) 121.0 (120.0)

(C10C18C26) 117.7 (117.5) 117.6 (117.0) 117.5 (119.2) 117.4 (120.9) 117.8 (118.0)

(C18C26C25) 121.3 (121.3) 121.2 (121.2) 121.1 (119.4) 121.2 (119.0) 121.2 (120.7)

(C26C25C17) 121.3 (121.3) 121.2 (121.8) 121.1 (120.0) 121.2 (119.9) 121.2 (119.7)

(C25C17C9) 117.7 (117.3) 117.6 (116.9) 117.5 (119.7) 117.4 (119.9) 117.8 (118.5)

(C17C9C10) 121.0 (121.8) 121.2 (121.7) 121.4 (119.6) 121.4 (120.4) 121.0 (120.8)

VAS3 720.0 (720.0) 720.0 (720.0) 720.0 (717.5) 720.0 (720.0) 720.0 (720.0)

Selected torsion angles

(M1N1C4N3) 0.0 (1.1) 0.0 (0.0) 0.0 (11.0) 0.0 (0.0) 0.0 (2.7)

(N1C4C9C17) 180.0 (176.9) 180.0 (178.8) 180.0 (175.8) 180.0 (180.0) 180.0 (172.9)

(N1C3C10C18) 180.0 (177.3) 180.0 (178.6) 180.0 (157.8) 180.0 (180.0) 180.0 (180.0)

(N7C4C9C17) 0.0 (1.9) 0.0 (0.0) 0.0 (3.4) 0.0 (0.0) 0.0 (0.0)

(N5C3C10C18) 0.0 (3.5) 0.0 (1.9) 0.0 (2.6) 0.0 (0.0) 0.0 (0.0)

(H1C17C9C10) 180.0 (178.9) 180.0 180.0 (165.0) 180.0 180.0 (178.5)

(H9C26C18C10) 180.0 (178.9) 180.0 180.0 (153.4) 180.0 180.0 (180.0)

(H2C18C10C9) 180.0 (179.4) 180.0 180.0 (180.0) 180.0 180.0 (180.0)

(C9C4N1M1) 180.0 (177.6) 180.0 (178.1) 180.0 (168.1) 180.0 (180.0) 180.0 (176.5)

(C10C3N1M1) 180.0 (177.5) 180.0 (177.9) 180.0 (159.9) 180.0 (180.0) 180.0 (176.3)

(H1C17C9C4) 0.0 (3.3) 0.0 0.0 (4.6) 0.0 0.0 (0.0)

(H2C18C10C3) 0.0 (2.1) 0.0 0.0 (7.0) 0.0 0.0 (0.0)

It is obviously extremely, that in the each of these complexes, all torsion angles are either 0o or 180o; this circumstance is most well-defined evidence that all these coordination compounds have strongly coplanar structure. It should be noticed in this connection that, according to data of our calculation, electric dipole moments of each of chelates considered here, are equal to 0.0 Debye units; this value is in full harmony with experimental data.

The data of quantum-chemical calculation of values of standard thermodynamic parameters of macrotetracyclic compounds under examination have been presented in the table 2. As may be seen from it, the AH°f,298 and AG0f,298 values for all complexes under examination are positive and, moreover, they are extremely considerable (as a rule, more than 1000 kJ/mole).

Table 2 - Standard thermodynamical parameters of formation of M(II) phthalocyanine complexes

AH f, 298, kJ/mole S0f, 298, J/mole-К AG0f, 298, kJ/mole

Mn 98б.7 1053.4 1219.S

Fe 101S.1 1054.0 1249.7

Co 10бб.7 1059.4 1297.5

Ni 9б8.3 1057.3 1199.7

Cu 98б.7 1075.S 1213.7

Acknowledgements

The Russian Foundation of Basic Researches (RFBR) is acknowledgement for financial support of given work (grant N 09-03-97001). Also, authors are grateful Kazan Branch of Joint Supercomputer Center of Russian Academy of Sciences where all quantum-chemical calculations were carried out.

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© О. В. Михайлов - д-р хим. наук, проф. каф. аналитической химии, сертификации и менеджмента качества КНИТУ, ovm@kstu.ru; Д. В. Чачков - канд. хим. наук, ст. науч. сотр. Казанского филиала Межведомственного Суперкомпьютерного Центра РАН, chachkov@kstu.ru.