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4. РАЗВИТИЕ МАТЕМАТИЧЕСКИХ ТЕОРИЙ И МЕТОДОВ ДЛЯ КОМПЬЮТЕРНЫХ ПРИЛОЖЕНИЙ
ELECTRONIC STRUCTURES OF MOLECULAR COMPLEXES WITH FULLERENE C60: COMPUTER MODELING
D.V. Lopatin, E.S. Chirkin, K.A. Kostushina, K.A. Litvinov, V.V. Ruzov
Center for computation security, Tambov State University, Russia
Introduction. In recent years fullerene-based materials have brought up steadily increasing attention both in academic and industrial researches. It is of great interest to use fullerene and fullerite not only by itself but also as modified derivatives, that enhance the properties of fullerenes and extend the application possibility. Recent developments suggest that fullerene-based materials could be successfully used in a wide range of areas such as IT devices, solar cells, clinical diagnostics, pharmaceuticals, environmental and energy industries. It seems interesting to study the electron-optical properties of photoactive fullerene C6o-based molecular complexes characterized by a high quantum efficiency of charge transfer and long-lived charge separation [7; 8]. In present paper we report results of computer simulation of electronic structure of the molecular complexes fullerene C6o and organic donors: TMPDA (N,N,N',N'-
tetramethyl-p-phenylenediamine)), Bz4BTPE (tetrabenzo( 1,2-bis[4H-thiopyran-4-ylidene]ethene)), LCV (Leuco Crystal Violet), LMG (Leucomalachite Green).
Methods. Initial data preparation and intermediate transformations were carried out using original software. Optimization of geometry of complexes was determined in several ways. For initial calculations we used a method of molecular mechanics Universal Force Field (UFF) [8]. UFF method is realized in software packages Gaussian 03 [3] or ArgusLab [14]. It allows one to refine configuration quickly and, thus, to reduce total calculation time. The other approaches are semi-empirical method PM3 (Parametric Method 3) [13] with various parameterization in three quantum-chemical packages PC-GAMESS [6] or Gaussian 03. Density functional theory (DFT) calculations were performed using the Gaussian
03. Electronic structure were calculated B3LYP (hybrid functional - Becke s three-parameter
formulation [1] and gradient corrected correlation functional - Lee, Yang and Parr [11]) with the 6-311++g(2d, 2f) basis set. Tight SCF convergence criteria (10-6-10-8 a.u.) were used for all calculations.
Results. The optimized structures of TMPDAC60, Bz4BTPEC60, LMGQ0 and LCV^C60 are shown in figure 1. Modeling results for isolated molecules correspond to the X-ray diffraction data for fullerene C60 based molecular complexes with volumetric substitutes indicating that donor molecules are bent in such compounds [12]. The bend of donor molecule skeleton provides its more dense conformity to the spherical C60 molecule that increases the number of energetically favorable van-der-Waals contacts. Each donor molecules forms several types shortened van-der-Waals contacts with adjacent C60 spheres (see fig.1 and table 1). These distances are corresponding to the X-ray diffraction analysis of real crystals [9; 10]. It is worth mentioning that the data on structure LCVC60 are received for the first time and absent in Cambridge Crystallographic Data Centre [2].
Computer modeling of C60, Bz4BTPE-C60, LMGC60, LCVC60 and TMPDAC60 molecules electronic structure based on non-empirical DFT (B3LYP/6-311++g(2d, 2f)) calculations allowed to define molecular orbitals energy E and destiny of states (DOS) spectrum. Figure 2 shows calculated spectrum for complex near Fermi level. According to figure 2 all complexes have energy spectrum typical for semiconductors with band-gap AE=1,265-1,731 eV. For the donor isolated molecules AE=2,9-4,7 eV that considerably exceeds (on 1,2-3,2 eV) the same parameter for the molecular complex. The HOMO-LUMO gap for investigated complexes is less than for fullerene C60 molecule. Data of researches of optical properties real crystals [2; 4; 5; 9; 10] confirms results of modeling (see Table 2).
Table 1
Structural data
Molecule/ cluster Van-der-Waals contacts d; l; a, b, c,a, fi, y (triclinic cell), nm
Type Range, nm
TMPDA*C60 C(TMPDA)..C(C60) 0,2962-0,3112; 0,301 ref.[11] d=1,254
C(CH3)..C(C60) 0,2849
H(CH3)..C(C60) 0,2635; 0,263 ref.[11]
N(TMPDA)..C(C60) 0,3185
Bz4BTPE*C60 C(C9SH4)..C(C60) 0,3130-0,3594; 0,340-0,353 ref.[12] d=1,236
H(C6H4)..C(C60) 0,2809-0,3102
S(C9SH4)..C(C60) 0,3577 0,357 ref.[12]
LMG*C60 C(LMG)..C(C60) 0,3196-0,3410 0,322-0,341 ref.[11] -
H(CH3)..C(C60) 0,2664
N(LMG)..C(C60) 0,2996; 0,299-0,320 ref.[11]
LCV*C60 C(LCV)..C(C60) 0,3244-0,3395 -
C(CH3)..C(C60) 0,2832
H(CH3)..C(C60) 0,2623
N(LCV)..C(C60) 0,3060
LMG*C60 3D cluster UFF only C(C60)..C(C60) 0,2842-0,3493; 0,300-0,338 ref.[11] d= 1,535; a=1,2896; b=1,3647; c=1,5503; a=77,76°; fi=67,44°; y=72,39°; l=(0,9658; 0,9721; 0,9770);
C(LMG)..C(C60) 0,3208-0,3410; 0,322-0,341 ref.[11]
H(CH3)..C(C60) 0,2686
N(LMG)..C(C60) 0,2984; 0,2986; 0,299-0,320 ref.[11] RSA ref. [11]: a=1,2908; b=1,3661; c=1,5501; a=77,69°; fi=67,52°; y=72,34°; l=(0,963; 0,968; 0,975);
LCV*C60 3D cluster UFF only C(C60)..C(C60) 0,2838-0,3498 d=1,590; a=1,3831; b=1,3559; c=1,5648; a=77,21°; fi=66,64°; y=71,80°; l=(0,9816; 0,9709; 0,9955);
C(LCV)..C(C60) 0,3216-0,3413
C(CH3)..C(C60) 0,2803-0,2896
H(CH3)..C(C60) 0,2662
N(LCV)..C(C60) 0,2863-0,3055
Table 2
Energy of optical transitions, eV
Energy, eV \ Ref. (method)
Bz4 BTPE-C6q
1,55-1,77 1,96 2,16 2,29 3,72 4,81 [12] absorption [12] photoconductivity
2,00 2,21 2,63 3,57
1,73 1,85 2,75 2,73 3.74 3.75 4,81 4,74 DFT/B3LYP
TMPDA-C60
1,26 2,1 2,7 [11] absorption
2,29 2,72 2,96 [14] photoconductivity
1,26 2,10 2,50 2,74 2,83 2,90 DFT/B3LYP
LCV^C60
1,7 2,1 2,7 3,5 [11] absorption
1,49 1,71 [15] photoconductivity
1,49 1,67 1,75 2,23 2,84 3,45 DFT/B3LYP
LMG-C60
1,48 | 2,38 | 3,36 | 4,85 | DFT/B3LYP
Figure 1. Visualization of modeling results for molecular complexes TMPDAC60, Bz4BTPE C60, LMGC60 and LCVC6,
Figure 2. DOS spectrum of molecular complexes TMPDAC60, Bz4BTPEC60, LMGC60 and LCVC6,
Comparison of C60, TMPDA-C60, LMGC60, LCV^C60 and Bz4BTPEC60 energy spectrum in UV-Vis range indicates that molecular complexes have more fine electronic structure than the isolated fullerenes C60 and the donor molecules. Displacement and increase in
number of lines in the spectrum of molecular complexes in comparison with the spectrum of individual C60 and the donor molecules take place.
Main causes of distinctions in spectrum of complexes and the isolated molecules connected
with significant increase in number of optical transitions and their shift in the molecular complex forming process. There are two reasons of such changes. The first, distortion of C60 skeleton geometry in complexes leads to the
symmetry reduction that effects on selection rules and the intermolecular excitation energy (shift and splitting of valence and unoccupied levels being degenerated for C60 with Ih-symmetry).
Figure 3. Calculated distribution of electron density from HOMO and LUMO orbital of complexes. HOMO-n and LUMO+n molecular orbitals provided the intermolecular interaction in the complex. Various intensive of gray correspond to the different phases of wave function
The second, in the complexes molecular orbitals are formed due to the n-electrons of phenyl fragments of Bz4BTPE, LMG, LCV donors (or benzene ring of TMPDA) in contrast to individual molecules. Electrons of phenyl rings carbon atoms participate in valence orbitals forming process due to rings
considerable deviation from the initial position in individual donor molecule (figure 1). As a result of donor molecule skeleton bend takes place more dense contact with spherical C60 molecule. It leads to appearance of additional transitions between nearby molecular orbitals of C60 and donor molecules.
The electron density of TMPDA-C60,
LMGC60, LCVC60 and Bz4BTPE^0 complexes are shown in figure 3. The electron density from HOMO is almost completely localized on the donors, and LUMO localized on fullerene spheres (although there is a slight contribution in HOMO from fullerene electrons and LUMO from donor electrons). The overlapping proceeds through quite energy molecular orbitals separated by about 0,2 eV from the HOMO and LUMO level.
Conclusions. Electronic structure of complexes was investigated by B3LYP/6-
311++g(2d, 2f) method. The optimized
structures are shown bend of donor molecule skeleton provides its more dense conformity to the spherical C60 molecule that increases the number of energetically favorable van-der-Waals contacts. All complexes have energy spectrum typical for semiconductors with band-gap 1,265-1,731 eV. Energy spectrum of such type molecular complex was shown fine electronic structure. Displacement and increase in number of lines in the spectrum of molecular complexes in comparison with the spectrum of individual C60 and the donor molecules take place.
Acknowledgements. The work was supported by the Russian foundation for basic research (grant 10-02-00763a).
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