Raman Spectroscopy of Fullerene-60

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International Journal of Emerging Technology and Advanced Engineering

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Raman Spectroscopy of Fullerene-60

Rashid Nizam

1

, Mirza Mohd Sehban

2

, Shabina Parveen

3

1,2_{Department of Physics, IFTM University, Moradabad, India}

3_{Department of Botany Pt. L. M. S. Govt. Autonomous P. G. College, Rishikesh, India}

Abstract: - The C60 has point group which is the irreducible

representations. These are the 174 vibrational degrees of freedom. From the theoretical based calculations it is known fact that invariably overestimate frequencies by 10-30% so the intensities may vary significantly in error. Hence the calculated frequencies for C60 have been scaled by 0.855

uniformly across the range. The Raman active modes of C60

have Ag and Hg symmetry (corresponding to the basis

functions for all symmetrical quadratic forms while the anti-symmetric F1g does not contribute to the Raman scattering)

among its irreducible representation. It may be seen that there are 10 Raman active modes. The comparison of observed experimental values of those calculated here for C60

is summarized in the table.

Keywords:-- Ab initio method, Raman spectrum and C60

I. INTRODUCTION

Smalley, Kroto and co-workers [l] found new carbon cage molecules CN, called “Buckminster fullerenes” or simply “fullerenes”. This has directed to a new class of carbon-based solids which exhibit a wide variety of unusual physical and chemical properties [2, 3]. Research on the solid state properties of the novel molecular solids based on the nearly spherical C60 molecules. This could be syntheses (C60) easily possible with the electric arc method [4] in gram quantities.

It was clearly from the research that pristine solid C60 is a Vander Waals bonded molecular solid. The electronic and vibrational of C60 properties are strongly connected to the properties of the molecule itself and this C60 has the appearance of a soccer ball. The icosahedral (Ih) symmetry

of C60 is the isolated molecule that follows 120 point group operations for the 60 carbon atoms. Solid C60 exhibits an orientational ordering temperature T ≈ 260 K, above which the C60 molecules spin freely about their lattice positions in an f. c.c. structure [3, 5-9].

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II. MODEL DETAILS

Figure 1 shows pure fullerene with 60 carbon atoms

The 60 carbon atoms used to form the model a fullerene (C60) and the location of these carbon atoms are at the vertices of truncated icosahedrons. These all carbon sites are equivalent and is given in figure.1. It is found that located at the corners of the 20 hexagonal and 12 pentagonal faces of the truncated icosahedrons. These faces are very high and this leads to a dramatic simplification of the vibrational and electronic states The average nearest-neighbor carbon-carbon (C-C) distance in C60 is 1.44 Å which is almost identical to that in graphite (1.42 A). Each carbon atom is trigonally bonded to other three carbon atoms in a sp2-derived bonding configuration in C60 structure. A regular (C60) truncated icosahedron has 90 edges of equal lengths, 60 equivalent vertices, 20 hexagonal faces, and 12 additional pentagonal faces to form a closed shell fullerene.

III. CALCULATION

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Thus the theory of vibrational spectra (Raman and Infrared spectra) is based upon the nuclear Schrodinger Equation given below in its time-independent form within the Born-Oppenheimer approximation in which electronic and nuclear degrees of freedom are decoupled.

( ( ) ( )_⃗

( )) | 〉

| 〉 ( )

Here ( ) ( )is the kinetic energy operator for the

nuclei, ⃗ ( ) is the potential energy for the nuclei which

is a function of the nuclear coordinates R, Etot is the total

nuclear energy of the system, | 〉 is the total wave function and is the Laplace operator. These help to find out the Raman tensor with three elements of fullerene a1≠ a2 ≠ a3.

To find the Raman intensity one would integrate and average over all possible orientations of the crystal. Taking help of Euler’s angles [57, 58]:

∫ | | ( ) ∫ 〈( ) ( ) ( )〉 ( )

Integrating and rearranging one gets:

( )

Where

( )

Calculation Results of C60 Raman Spectrum

The variables used in the present work for calculation of Raman spectrum are: the rotational constants in x, y and z axes in the fullerenes are 0.09, 0.09 and 0.09 (GHz) respectively. C60 has 300 symmetry adapted basis functions, 900 primitive gaussians, 300 cartesian basis functions, 180 alpha electrons and 180 beta electrons with the nuclear repulsion energy of 8844.27 Hartree. Optimization of C60 is done before proceeding with the calculation of Raman spectrum. The results of calculations of Raman Spectrum for C60 are displayed in Figure 2 (b) and in Table 1. Figure 2 (a) shows results of experiment of [10].

The numerical results of C60 Raman spectrum are summarized below:

1)The same parameters of Raman spectrum for C60 have been used in the present calculations that are used for optimization of C60.

2)C60 has point group and these irreducible representations for the 174 vibrational degrees of freedom are given as:

Γtot = 2Ag + 3F1g + 4F2g + 6Gg +8Hg+Au + 4F1u + 5F2u + 6Gu + 7Hu

3)The Raman active modes of C60 have Ag and Hg symmetry (corresponding to the basis functions for all symmetrical quadratic forms while the anti-symmetric F1g does not contribute to the Raman scattering) among its irreducible representation. It may be seen from (2) above that there are 10 Raman active modes. 4)Table 1 gives comparison of experimental results of

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Table 1

Comparison of calculated Raman spectra with the experimental data for C60

1. Mode

2. Experimental Results (cm-1)

[ref. 10]

3. Calculated

Results (cm-1) [ref.11]

4. Present Calculation

Results (cm-1)

5. Experimental value/Calculated

Result [ref.11]

6.

Experimental value / Present Calculations

Hg(1) 270 280 257 0.96 1

Hg(2) 431 447 436 0.96 0.98

Ag(1) 493 530 470 0.93 1

Hg(3) 708 769 718 0.92 0.98

Hg(4) 773 820 761 0.94 1

Hg(5) 1099 1205 1094 0.91 1

Hg(6) 1248 1288 1248 0.96 1

Hg(7) 1426 1516 1436 0.94 0.99

Ag(2) 1469 1548 1462 0.94 1

Hg(8) 1573 1610 1633 0.97 0.96

5)It was observed that the theoretical calculation techniques invariably overestimate frequencies by 10-30% [12], and therefore, the calculation results do not compare well. A scaling factor (0.855) is used here for the purpose of comparison of the present results of calculations with the experimental data. The same scaling factor was also used earlier in the case of calculation of the Infrared spectra.

In the present calculations the predicted frequencies shown in column (4) in Table 1 as well as in Figure 2

have been scaled down by a factor of 0.855 uniformly across the range.

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Figure 2 Raman Spectra of (a) C60 experimental data [ref. 10] cm-1 _{(b) present predictions}

IV. CONCLUSION

It is found that the Raman active modes of C60 have Ag and Hg symmetry among its irreducible representation. It is seen that the present results compare well with the experimental data of C60. It is observed that there are 10 Raman active modes. The predicted results are better than the calculation of Beu et al [11] as shown above.

REFERENCE

[1] H. W. Kroto, J. R. Heath. S. C. O’Brien. R. F. Curl and R. E. Smalley nature (London). 318 162 1985.

[2] Acc.. Chem. Res. 25 1992.

[3] M. S. Dresselhaus. G. Dresselhaus and P. C. Eklund. J. Matter. Res., 8 2054. 1993

[4] R. E. Haufler. J. Conceicao. L. P. F. Chibante. Y. Chai. N. E Byrne. S. Flanagan. M. M. Haley. S. C. O’Brien. C. Pan. Z. Xiao. W. E. Billups, M. A. Ciufolini. R. H. Hauge. J. L. Margrave. L. J. Wilson. R. F. Curn and R. E. Smalley. J. Phys. Chem. 94 8634 1990. [5] P. A. Heiney, J. E. Fischer. A. R. McGhie. W. J. Romamnow. A. M.

Denenstein. J. P. McCauley and A. B. Smith, Phys. Rev. Lett., 66 3911 1991.

[6] P. Heiney. J. Phys. Chem. Solids 53 1333 1992.

[7] W. I. F. David. R. M. Ibherson. T. J. S. Dennis. J. P. Hare and K. Prassides. Europhys. Lett. 18 219 1992.

[8] R. Tycko. G. Dabbagh. R. M. Fleming, R. C. Haddon. A. V. Makhija and S. M. Zahurak. Phys. Rev. Lett. 67 1886 1991.

[9] R. D. Johnson, D. S. Bethune and C. S. Yannoni. Acc. Chem. Res. 25 169 1992.

[10] P. Zhou, A. M. Rao, K-A Wang, J. D. Robertson, C. Eloi, M. S. Meier, S. L. Ren, X-X Bi , P. C. Eklund and M. S. Dresselhaus ,“ Photo-assisted structural transition and oxygen diffusion in solid C60

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[11] T. A. Beu, J. Onoe and K. Takeuchi, “Simulation of Raman spectra of C60 and C70 by non-orthogonal tight-binding molecular

dynamics”, Eur. Phys. J. D 10, 391 398, 2000.

[12] J. P. Hare, T. J. Dennis, H. W. Kroto, R. Taylor, A. W. Allaf, S. Balm and D. R. M. Walton, “The infrared spectra of fullerene 60 and 70”, J . Chem. Soc., Chem. Commun., 10.1039/C39910000412, 1991

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