Frequencies and Normal Modes of Vibration of Benz[a]anthracene Radical Ions

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1 Frequencies and Normal Modes of Vibration of Benz[a]anthracene Radical Ions Rehab M. Kubba, Raghida I. Al-ani, and Muthana Shanshal Department of Chemistry, College of Science, University of Baghdad, Jadiriya, Baghdad, Iraq Reprint requests to Prof. M. S.; Z. Naturforsch. 60a, (2005); received September 7, 2004 MINDO/3-FORCES calculations were carried out for the radical ions of benz[a]anthracene. Both ions exhibit C s symmetry with C-C bond alternation in all four rings. The obtained equilibrium geometry was applied for the calculation of all 3N 6 vibration frequencies of each ion, and for the analysis of their normal coordinates. The so calculated frequencies of the radical cation were close to the experimental frequencies and those of the ab initio calculations. They fall in the ranges νchstr. ( cm 1 ), νccstr. ( cm 1 ), δch ( cm 1 ). Interesting correlations could be obtained for the frequencies of similar vibrations, e. g. ν sym CHstr. > ν asym CHstr. Exception is the frequency of vibration of CH α in ring A for the radical cation and the same bond in ring D for the radical anion. The vibration frequencies for the CH bonds depend on the σ-electron densities of the corresponding carbon atoms, i. e. νch.+ str. > νchstr. > νch. str., where σ ρ C.+ > σ ρ C > σ ρ C.. For the C-C stretching vibrations the relation ν(c-c)str.>ν(c-c). str. > ν(c-c).+ str. holds, with the exception of the C β -C β bond, for which the relation ν(c-c)str. > ν(c-c).+ str. > ν(c-c). str. is found. As for the in-plane and out of-plane deformations, the following general correlations δ(ch) > δ(ch). > δ(ch).+ and γ(cc) > γ(cc). > γ(cc).+. Key words: Benz[a]anthracene; Vibrations; Ions. 1. Introduction The chemistry of polyaromatic hydrocarbons (PAHs) is gaining increasing importance due to their carcinogenic properties and their presence in interstellar spaces [1]. They could become potential starting materials for petrochemical industries, being a significant component of the heavy fractions of earth oils [2]. For these reasons considerable efforts were made to study their chemical and physical properties [1], e. g. IR spectroscopic studies which were done for their radical cations too. Benz[a]anthracene, Fig. 1, is a prominent member of the PAH family, for which IR spectroscopic studies were done. Measurements were done for its radical cation in the isolated matrix [3], as well as ab initio theoretical studies [4]. However a complete normal coordinate analysis on the symmetry and the valence basis of all its 3N 6 vibration modes is still missing. In a former paper [5] we described MINDO/3- FORCES SCF-MO treatments for the evaluation of the vibration frequencies and IR absorption intensities of different organic molecules. The method yielded frequencies that were very close to the experimental and ab initio calculated frequencies. In addition to these results, it was possible to assign all the vibration modes both symmetrically and according to their valence nature. The valence assignment could be done considering the calculated atomic partial participation (APP) values [6] and the graphical pictures of all vibration modes as drawn applying the DRAW.MOL routine [7] (Figure 2) / 05 / $ c 2005 Verlag der Zeitschrift für Naturforschung, Tübingen

2 R. M. Kubba et al. Vibration of Benz[a]anthracene Radical Ions 159 a b Fig. 1. Benz[a]anthracene molecule, (a) IUPAC and (b) nomenclature used in this text. Table 1. MINDO/3-FORCES calculated geometric structures of benz[a]anthracene radical cation, radical anion and neutral molecule; lengths in Å, angles in deg. Fig. 2. DRAW.MOL plotted graphical pictures of two vibration modes of the benz[a]anthracene radical cation. 2. Results and Discussion Both radical ions of benz[a]anthracene are planar and of C s symmetry, according to the MINDO/3- FORCES calculated geometric structures (Table 1). Both ions posses two irreducible representations, E and σ h. Table 1 includes the MINDO/3-FORCES calculated geometry for the neutral molecule too. The calculated geometric structures were applied for the calculation of the vibration frequencies and APP values for all vibration modes of the two radical ions. Table 2 shows the so obtained frequencies for the radical cation of benz[a]anthracene. The ordering of the modes follows the Herzberg convention [8]. Table 3 includes the calculated IR absorption intensities for each mode of the ion. Generally the frequency values of the cation compare well with the experimental values of Allemen- Lengths Cation Neutral Anion molecule [9] C 1 -C C 2 -C C 3 -C C 4 -C C 5 -C C 5 -C C 6 -C C 7 -C C 7 -C C 8 -C C 8 -C C 9 -C C 10 -C C 11 -C C 12 -C C 12 -C C 1 -C C 1 -C C 1 -C C 3 -C C 5 -C C 1 -H C 2 -H C 3 -H C 4 -H C 5 -H C 6 -H C 7 -H C 8 -H C 9 -H C 10 -H C 11 -H C 12 -H dola and Hudgins [3] and the theoretical values of Langhoff [4]. The present treatment enables calculating and assigning all 3N 6 vibration modes at once. The knowledge of the valence form of each vibration,

3 160 R. M. Kubba et al. Vibration of Benz[a]anthracene Radical Ions Table 1 (continued). Angles Cation Neutral Anion molecule [9] C 1 C 2 C C 2 C 3 C C 3 C 4 C C 2 C 5 C C 5 C 6 C C 3 C 7 C C 5 C 8 C C 8 C 9 C C 1 C 1 C C 2 C 1 C C 4 C 2 C C 1 C 2 C C 6 C 3 C C 7 C 3 C C 3 C 4 C C 1 C 4 C C 7 C 5 C C 8 C 5 C C 5 C 6 C C 11 C 6 C C 6 C 12 C H 1 C 1 C H 2 C 2 C H 3 C 3 C H 4 C 4 C H 5 C 5 C H 6 C 6 C H 7 C 7 C H 8 C 8 C H 9 C 9 C H 10 C 10 C H 11 C 11 C H 11 C 11 C H 12 C 12 C as provided by the APP values and DRAW.MOL pictures, Fig. 3 allows a correlative comparison of the modes and consequently the force constants and bond strengths within the molecule. As for the benz[a]anthracene anion no experimental IR data are known in the literature. However, since such an anion can be formed as intermediate in chemical reactions, it is interesting to study its vibrations theoretically. For this reason we carried out a similar treatment for the molecule s anion as was done for its cation. Table 4 includes the calculated vibration frequencies and IR absorption intensities for the benz[a]anthracene anion The C-H Stretching Vibrations For each ion and neutral molecule 57 C-H stretching modes are calculated. Inspection of their frequencies Fig. 3. Graphical pictures of some vibration modes of the benz[a]anthracene radical cation as drawn through the DRAW.MOL routine. reveals that for both ions the following relation holds: ν sym CHstr. > ν asym CHstr. Exceptions are for the cation: ν asym CH α str.(ring D) > ν sym CH α str. (ring D), and for the anion: ν asym CH α str. (ring A) > ν sym CH α str. (ring A). The νchstr. frequency increases on going from the radical cation to the neutral and the radical anion: νch.+ str. > νchstr. > νchstr.. As explained in [10] the introduction of a positive charge to the molecule causes an increase, that of a negative charge a decrease in the σ-electron density of the carbon atoms of the PAH molecules. In fact, the

4 R. M. Kubba et al. Vibration of Benz[a]anthracene Radical Ions 161 Table 2. Calculated vibration frequencies and IR absorption intensities of the benz[a]anthracene radical cation. Frequency in cm 1 Frequency in cm 1 This work Others This work Others Symmetry and description Scaled Calcd. [4] Exptl. [3] Symmetry and description Scaled Calcd. [4] Exptl. [3] A ν 44 ring(δ CCC)+ δ CH α & δ CH α 883 ν 1 CH β str ν 45 ring(δ C α C β C β ) 860 ν 2 CH β str ν 46 ring(δ C α C β C β ) 851 ν 3 CH β str ν 47 ring(δ CCC) 832 ν 4 CH β str ν 48 ring(δ CCC) 738 ν 5 CH α str ν 49 ring(δ CCC) 654 ν 6 CH α str ν 50 ring(δ CCC) 611 ν 7 CH α str ν 51 ring(δ CCC) 577 ν 8 CH α str ν 52 ring(δ CCC) ν 9 CH α str ν 53 ring(δ CCC) 496 ν 10 CH α str ν 54 ring(δ CCC) 454 ν 11 CH α str ν 55 ring(δ CCC) 371 ν 12 CH α str ν 56 ring(δ CCC) 310 ν 13 (C β -C α )str ν 57 ring(δ CCC) 166 ν 14 C β -C α )str Out of-plane ν 15 (C α -C α )str. + (C β -C β )str. + (C r -C r )str A ν 16 (C β -C β )str. + (C r -C α )str ν 58 γch β + γch α 984 ν 17 (C α -C α )str. + (C a -C b )str ν 59 γch β + γch α 981 ν 18 (C a -C α )str. + (C b -C α )str ν 60 γch α + γch β 980 ν 19 (C r -C α )str. + (C b -C α )str ν 61 γch β + γch α 974 ν 20 (C b -C α )str. + (C r -C α )str ν 62 γch α + γch β 963 ν 21 (C α -C α )str ν 63 γch α + γch α 950 ν 22 (C a -C a )str ν 64 γch α 941 ν 23 ring(cc)str ν 65 γch α + γch β 921 ν 24 (C β -C α )str. + (C α -C r )str ν 66 γch α + γch α ν 25 (C r -C r )str. + (C b -C α )str ν 67 γch α + γch α 867 ν 26 (C b -C b )str. + (C a -C α )str. + (C r -C α )str ν 68 γ(c a -C a )+γ(c b -C b )+γch α ν 27 ring(cc)str. (ring A & B) ν 69 γch β + γch α ν 28 ring(ccc)str ν 70 γch β + γch α 791 ν 29 ring(ccc)str ν 71 γ(c r -C r )+γch α + γch α ν 30 δ CH α + δ CH α +(C β -C β )&(C α -C α )str ν 72 γ(c b -C b )+γ(c a -C a ) 649 ν 31 δ CH α + δ CH α +(C α -C a )str ν 73 γ(c a -C a )+γ(c b -C b )+γch α 548 ν 32 δ CH α + δ CH α + ring(δ CCC) ν 74 γ(c β -C β )+γch β 518 ν 33 δ CH α + ring(δ CCC) 1174 ν 75 γ(c β -C β )+γch β 506 ν 34 δ CH α + δ CH α + δ CH α + ring(ccc)str ν 76 γ(c r -C r )+γch α + γch α 483 ν 35 δ CH α + δ CH α + δ CH α + ring(δ CCC) 1129 ν 77 ring(γccc)+ γch α ν 36 δ CH α + δ CH β + δ CH α 1177 ν 78 ring(γccc)+ γch α 382 ν 37 δ CH β + δ CH α 1164 ν 79 γ(c α -C α ) 264 ν 38 δ CH β + δ CH α 1161 ν 80 γ(c α -C b ) 249 ν 39 δ CH α + δ CH β + ring(δ CCC) ν 81 ring(γccc) 180 ν 40 δ CH β + δ CH α ν 82 ring(γccc) 136 ν 41 δ CH β + δ CH α 1150 ν 83 γ(c α -C β )+γ(c α -C b )&γ(c β -C β ) 60 ν 42 δ CH β + δ CH α + δ CH α 1142 ν 84 γ(c α -C α )+ γ(c α -C β ) 58 ν 43 ring(δ CCC)+ δ CH α + δ CH α 1010 Scaling factors: (CHstr.); 0.96 (ring (CC)str.); 1.00 (ring (CCC)str.); 1.06 (δch); 1.08 (ring(δccc); 1.11 (γch); 1.11 (γccc); 1.03 (γcc). Special scaling factors were used for vibration modes with overlaps of different types of motion; 1.06 [ring (CCC)str. + δch]; 1.11 (γccc + γch) or (γcc + γch); 1.03 (γch+ γcc). calculation of the σ-electron densities at the carbon atoms (ρ 2s + ρ 2px + ρ 2py ) yields the following correlation for all atoms: σ ρ C.+ > σ ρ C > σ ρ C.. Figure 4 shows the correlation curve between the C-H stretching frequencies and the calculated σ-electron densities for the corresponding carbon atoms The C-C Stretching Vibrations Totally seventeen such vibration modes (Nc-1) were calculated. For these bonds also different vibration frequencies and consequently force constants may be detected. The order of magnitudes of the C-C vibration frequencies follows the relation ν asym (C β C α )str. > ν asym (C β C α )str., ring D ring A and for the rings: Ring D: ν asym (C β C α )str. > ν sym (C β C β )str. > ν sym (C a C a )str.

5 162 R. M. Kubba et al. Vibration of Benz[a]anthracene Radical Ions Table 3. Calculated IR absorption intensities of the benz[a]anthracene radical cation. Symmetry and Intensity in Km/mol Symmetry and Intensity in Km/mol description This work Calcd. [4] description This work Calcd. [4] In-plane ν 43 ring(δ CCC) + δ CH α + δ CH α 2.96 A ν 44 ring(δ CCC) + δ CH α & δ CH α ν 1 CH β str ν 45 ring(δ C α C β C β ) 5.05 ν 2 CH β str ν 46 ring(δ C α C β C β ) 0.06 ν 3 CH β str ν 47 ring(δ CCC) 0.81 ν 4 CH β str ν 48 ring(δ CCC) 0.08 ν 5 CH α str ν 49 ring(δ CCC) 0.16 ν 6 CH α str ν 50 ring(δ CCC) 0.13 ν 7 CH α str ν 51 ring(δ CCC) 0.69 ν 8 CH α str ν 52 ring(δ CCC) ν 9 CH α str ν 53 ring(δ CCC) 0.51 ν 10 CH α str ν 54 ring(δ CCC) 0.04 ν 11 CH α str ν 55 ring(δ CCC) 0.19 ν 12 CH α str ν 56 ring(δ CCC) 1.17 ν 13 (C β -C α )str ν 57 ring(δ CCC) 0.23 ν 14 (C β -C α )str Out of-plane ν 15 (C α -C α )str. + (C β -C β )str. + (C r -C r )str A ν 16 (C β -C β )str. + (C r -C α )str ν 58 γch β + γch α 0.06 ν 17 (C α -C α )str. + (C a -C b )str ν 59 γch β + γch α 0.47 ν 18 (C a -C α )str. + (C b -C α )str ν 60 γch α + γch β 0.16 ν 19 (C r -C α )str. + (C b -C α )str ν 61 γch β + γch α 0.14 ν 20 (C b -C α )str. + (C r -C α )str ν 62 γch α + γch β 0.00 ν 21 (C α -C α )str ν 63 γch α + γch α + ring(γccc) 0.03 ν 22 (C a -C a )str ν 64 γch α 0.31 ν 23 ring(ccc)str ν 65 γch α + γch β 0.10 ν 24 (C β -C α )str. + (C α -C r )str ν 66 γch α + γch α ν 25 (C r -C r )str. + (C b -C α )str ν 67 γch α + γch α 1.19 ν 26 (C b -C b )str. + (C a -C α )str. + (C r C α )str ν 68 γ(c a -C a )+γ(c b -C b )+γch α ν 27 ring(cc)str ν 69 γch β + γch α ν 28 ring(cc)str. (ring A + B) ν 70 γch β + γch α 0.11 ν 29 ring(ccc)str ν 71 γ(c r -C r )+γch α + γch α ν 30 δ CH α + δ CH α +(C β -C β )&(C α C α )str ν 72 γ(c b -C b )+γ(c a -C a ) 0.29 ν 31 δ CH α + δ CH α +(C α -Ca)str ν 73 γ(c a -C a )+γ(c b -C b )+γch α 0.32 ν 32 δ CH α + δ CH α + ring(δ CCC) ν 74 γ(c β -C β )+γch β 0.13 ν 33 δ CH α + ring(δ CCC) ν 75 γ(c β -C β )+γch β 0.10 ν 34 δ CH α + δ CH α + δ CH α 0.56 ν 76 γ(c r -C r )+γch α + γch α 1.65 ν 35 δ CH α + δ CH α + δ CH α + ring(δ CCC) ν 77 ring(γccc)+ γch α ν 36 δ CH α + δ CH β + δ CH α 0.12 ν 78 ring(γccc)+ γch α 0.59 ν 37 δ CH β + δ CH α ν 79 γ(c α -C α ) 0.09 ν 38 δ CH β + δ CH α ν 80 γ(c α -C b ) 0.20 ν 39 δ CH α + δ CH β + ring(δ CCC) ν 81 ring(γccc) 0.27 ν 40 δ CH β + δ CH α 7.68 ν 82 ring(γccc) 0.12 ν 41 δ CH β + δ CH α 4.83 ν 83 γ(c α -C β )+γ(c α -C b )&γ(c β -C β ) 0.12 ν 42 δ CH β + δ CH α + δ CH α 6.02 ν 84 γ(c α -C α )+γ(c α -C β ) 0.09 Ring C: ν sym (C α C α )str. > ν sym (C α C a )str. > ν sym (C α C α )str. > ν sym (C a C a )str. > ν sym (C b C b )str., Ring B: ν sym (C α C r )str. > ν sym (C α C b )str. > ν sym (C r C r )str. > ν sym (C b C b )str., Ring A: ν asym (C β C α )str. > ν sym (C β C β )str. > ν sym (C r C r )str.. As for the middle bonds, the following relation applies: ν sym (C a C a )str. > ν sym (C r C r )str. > ν sym (C b C b )str.. Comparing the frequencies of the C-C bonds of the three differently charged species one finds the general relation ν(c-c)str. > ν(c-c). str. > ν(c-c).+ str. with the exception of the C β -C β bond, for which the radical cation shows a higher frequency than the radical anion, i. e. ν(c-c)str. > ν(c-c).+ str. > ν(c-c). str..

6 R. M. Kubba et al. Vibration of Benz[a]anthracene Radical Ions 163 Table 4. Calculated vibration frequencies and IR absorption intensities of benz[a]anthracene radical anion. Symmetry Frequency Intensity Symmetry Frequency Intensity and in cm 1 in Km/mol and in cm 1 in Km/mol description Scaled Calcd. description Scaled Calcd. A Out of-plane ν 27 ring(ccc)str. + δ CH β A ν 28 ring(ccc)str. + δ CH α & δ CH α ν 58 γch β + γch α ν 29 ring(ccc)str ν 59 γch β + γch α ν 30 δ CH α + ring(c-c)str ν 60 γch α + γch β ν 31 δ CH α + δ CH α ν 61 γch α + γch β ν 32 δ CH α + δ CH α + ring(c-c)str ν 62 γch α ν 33 δ CH α + δ CH α & δ CH α + ring(δ CCC) ν 63 γch α + γch β ν 34 δ CH α + δ CH α + ring(δ CCC) ν 64 γch α + γch β ν 35 δ CH α + δ CH β ν 65 γch α + γ(c a -C b ) ν 36 δ CH α + δ CH β ν 66 γch α + γch β + ring(γccc) ν 37 δ CH β + δ CH α ν 67 γ(c a -C b )+γch α ν 38 δ CH α + δ CH β + ring(δ CCC) ν 68 γch α + γch β + γch α ν 39 δ CH β ν 69 γch β + γ(c b -C b ) ν 40 δ CH β + δ CH α ν 70 γch α + γch α & γch β ν 41 δ CH β + δ CH α + ring(δ CCC) ν 71 γ(c r -C r )+γch α ν 42 ring(c-c)str. + δ CH α + δ CH α ν 72 γ(c a -C a )+γ(c b -C b )+γch α ν 43 ring(δ CCC)+ δ CH α + δ CH α ν 73 γ(c a -C a )+γ(c b -C b )+γch α ν 44 ring(δ CCC)+ δ CH α ν 74 γ(c β -C β ) ν 45 ring(δ C α C β C β ) ν 75 γ(c β -C β )+γch β ν 46 ring(δ C α C β C β ) ν 76 γ(c r -C r )+γch α ν 47 ring(δ CCC) ν 77 ring(γccc)+ γch α ν 48 ring(δ CCC) ν 78 γ(c α -C α )+γ(c α -C b ) ν 49 ring(δ CCC) ν 79 ring(γccc) ν 50 ring(δ CCC) ν 80 γ(c α -C α ) ν 51 ring(δ CCC) ν 81 ring(γccc) ν 52 ring(δ CCC) ν 82 ring(γccc) ν 53 ring(δ CCC) ν 83 ring(γccc) ν 54 ring(δ CCC) ν 84 ring(γccc) ν 55 ring(δ CCC) ν 56 ring(δ CCC) ν 57 ring(δ CCC) Fig. 4. Graphical correlation of the calculated σ-ρ C at different carbon atoms with the corresponding C-H vibration frequencies ν for each carbon atom in benz[a]anthracene radical ions and the neutral molecule.

7 164 R. M. Kubba et al. Vibration of Benz[a]anthracene Radical Ions 2.3. The In-plane δ CH Vibration Similarly, different frequencies are calculated for the δ CH deformation vibrations of the different CH bonds. As for the radical cation twelve such vibrations were detected (ν = cm 1 ), and in general the symmetric modes have higher frequencies than the asymmetric ones. The frequencies values decrease on going from the neutral molecules to the radical cation, through the radical anion. δ(ch) > δ(ch). > δ(ch) The out of-plane γch Vibration On their turn these vibrations show different frequencies for the different valence positions. For the γch vibration, the frequency of the radical cation is higher than that of the neutral molecule, which is higher than that of the radical anion. Exception is γch α of the ring C. For the γcc vibration the highest frequency belongs to the neutral molecule followed by the radical anion and then the radical cation; i. e. γ(cc) > γ(cc). > γ(cc) Conclusion It was possible, on applying the MINDO/3- FORCES method, to calculate the different vibration frequencies of all 3N 6 vibration modes of the PAH benz[a]anthracene and its radical ions. Minor deviations of the calculated frequencies for the cation from the available experimental and theoretical ab initio values are detected. Both valence and symmetry assignments of the frequencies allow useful comparison between modes of the same valence nature for the three species. Comparing the frequencies for the different charged species some general and interesting correlations between these and the charge of the molecule are found. The results are expected to be of major importance in discussing the bond strengths and reactivity of the species at different sites of the molecule. [1] R. G. Harvey, Polycyclic Hydrocarbons and Carcinogenesis, American Chemical Society, Washington D.C. 1985; R. G. Harvey, Chemistry of the Polycyclic Aromatic Compounds, Verlag Chemie, Weinheim, Germany [2] M. R. Guerin, Polycyclic Hydrocarbons and Cancer, Vol. I, Academic Press Inc., [3] L. J. Allemendola and D. M. Hudgins, J. Phys. Chem. 101, 3472 (1997). [4] S. R. Langhoff, J. Phys. Chem. 100, 2819 (1996). [5] D. H. Abed, S. F. Al Saidi, and M. Shanshal, Chim. Acta Turc. 7, 23 (1995). [6] D. H. Abed, M. B. Mammo, S. F. Al-Saidi, and M. Shanshal, Iraqi J. Sci. 31, 539 (1990). [7] A. Vincent, Molecular Symmetry and Group Theory, John Wiley & Sons, Ltd. London, New York, Sydney [8] G. Herzberg, Molecular Spectra and Molecular Structure, Infrared and Raman Spectra of Polyatomic Molecules, van Nostrand Co, New York [9] R. M. Kubba and M. Shanshal, Z. Naturforsch. 56a, 493 (2001). [10] R. M. Kubba, R. I. Al-ani, and M. Shanshal, Z. Naturforsch. 60a, 165 (2005).