1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 FULLERENES, NANOTUBES, AND CARBON NANOSTRUCTURES Vol. 12, No. 1, pp. 513 519, 2004 Calculation of Ionization Energy and Electron Affinity of Molecule of Hydro- and Fluorinefullerenes C 60 H(F) n (0 n 60) S. K. Nasibullaev, 1, * G. D. Davletbaeva, 1 Y. V. Vasil ev, 2,3 and I. S. Nasibullayev 2 1 Bashkir State University, Ufa, Russia 2 Institute of Physics of Molecules and Crystals, Ufa Research Center of RAS, Ufa, Russia 3 Bashkir State Agriculture University, Ufa, Russia ABSTRACT Vertical and adiabatic electron affinities (EA) and ionization energies (IE) of C 60 H(F) n (0 n 60) have been determined using semiempirical calculations with AM1 Hamiltonian. Comparison of the thermo-chemical characteristics of the fluorinated and hydrogenated fullerene positive and negative ions has been carried out on the basis of these calculations. Key Words: Electron affinity; Ionization energy; C 60 H(F) n ; Semiempirical calculation; Hydrofullerene; Fluorine fullerene. *Correspondence: S. K. Nasibullaev, Bashkir State University, Ufa, Russia; Fax: (3472) 28 6278; E-mail: nsk@anrb.ru. DOI: 10.1081/FST-120027212 Copyright # 2004 by Marcel Dekker, Inc. 513 1536-383X (Print); 1536-4046 (Online) www.dekker.com Q1 Q2
514 Nasibullaev et al. 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 INTRODUCTION Hydrogenated and fluorinated fullerenes have been a subject of extensive investigation over the last decade with a particular emphasis on the search of different isomeric structures with either the same [1,2] or different [3] hydrogen and fluorine content. Although charged species of these compounds are the most experimentally studied fullerene derivatives, particularly by mass spectrometry, their theoretical examination is rather rare. Indeed, along with a great number of possible isomers that needed to be included, this study is even more time consuming than that of the corresponding neutral molecules because of the open-shell structure of anion- and cation-radicals. Precise quantitative calculations of the charged species can be achieved by applying sophisticated ab initio or density functional methods using a basis set with the necessary polarization and diffusion functions that take into account effects of electron correlation and are known to be particularly important in open-shell systems like anions or cations. The accuracy of semiempirical calculations of open-shell systems is certainly worse because initially these methods are parameterized using characteristics of neutral molecules. Nevertheless, semiempirical calculations are much less time consuming and normally give reasonably good qualitative predictions while considering relative changes within a set of similar molecular systems. The main aim of the present work is the theoretical consideration of positive and negative ions of hydrogenated and fluorinated fullerenes C 60 H(F) n with n ranging from 2 to 60 on the base of semiempirical calculations with AM1 Hamiltonian. The parallel between fluorination and hydrogenation of fullerenes was already manifested in the literature [4] and here the comparative analysis of their positive and negative ions characteristics will be given. RESULTS OF CALCULATIONS AND DISCUSSION At the present, it is unrealistic to calculate all possible isomeric structures of C 60 H(F) n even using semiempirical methods because of their enormous number. For this reason, the calculations were restricted to the isomeric species containing only three-fold axes and lower. This restriction appears reasonable since up to now the vast majority of experimentally isolated C 60 H(F) n species belong to this class of molecules. The only exceptions were C 60 H(F) 60 molecules that were chosen of I h structure. It should be emphasized, however, that different hydrogenation/fluorination reactions can result in production of different isomers of the same elemental composition and what is the major isomer for a particular reaction is often an unresolved problem. To make the comparison of analogous charged species of F- and H-substituted fullerenes
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 Ionization Energy and Electron Affinity of Hydro- and Fluorinefullerenes 515 more meaningful, the most stable isomers have been selected for each particular n to determine common trends. This comparison will thus reflect a general trend even if some isomeric species of fluorinated or hydrogenated fullerenes with a particular n will slightly deviate. At the first step of the calculations, the more stable isomers of neutral C 60 H(F) n have thus been selected (Table 1) and then corresponding negative and positive ions have been calculated (Table 2). In both cases, the full geometry optimization has been carried out. The quality of calculations of the neutral species was checked by comparison with available literature data. [2,3] The agreement has been found to be very good for the same isomers in Refs. [2,3] and in the present work. To facilitate rationalization of the results of calculations in Tables 1 and 2, a Schlegel diagram is depicted in Fig. 1, where each carbon atoms on the Table 1. Point group symmetries, heat of formations (HOF), and energies of highest occupied molecular orbital (HOMO) and lowest occupied molecular orbital (LUMO) of C 60 H(F) n neutral molecules. n Symmetry HOF (kcal/mol) C 60 H n HOMO LUMO HOF (kcal/mol) C 60 F n HOMO LUMO 0 I h 973.34 29.6 22.9 2 C 2v 931.19 29.3 22.8 864.81 29.6 23.1 4 C 1 888.95 29.1 22.6 755.87 29.6 23.1 6 C s 840.31 29.1 22.3 639.73 29.8 22.9 8 C s 812.03 28.9 22.3 538.73 29.8 23.2 10 C 2 771.78 28.9 22.2 428.44 210.1 23.2 12 C s 731.83 28.8 22.1 318.36 210.2 23.3 14 C 2 692.15 28.7 21.9 208.40 210.3 23.3 16 C s 652.06 28.5 21.7 97.74 210.3 23.3 18 C 3v 595.71 28.6 20.7 210.74 210.7 22.6 20 C s 572.11 28.2 21.3 2123.53 210.3 23.2 22 C s 532.61 28.2 20.9 2233.05 210.6 23.1 24 C 1 495.67 28.2 20.8 2340.10 210.7 23.2 26 C s 458.24 28.2 20.7 2448.47 210.8 23.2 28 C 1 424.55 28.4 20.3 2547.09 211.3 23.1 30 C 1 395.39 28.3 20.3 2646.84 211.4 23.2 32 C 1 365.58 28.4 20.1 2748.02 211.6 23.2 34 C 1 336.70 28.3 0.1 2847.29 211.7 23.1 36 S 6 292.07 28.6 0.7 2950.85 212.5 22.8 48 D 3 226.11 28.4 1.5 21345.95 213.2 23.1 60 I h 334.97 29.7 3.0 21409.22 213.9 22.0 T1 T2 F1
516 Nasibullaev et al. 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 Table 2. Heat of formations (HOF), election affinities (EA, corresponds to neutral molecule), Ionization energies (IE, corresponds to neutral molecule) of C 60 H(F) n negative and positive ions. Negative ions Positive ions C60Hn C60Fn C60Hn C60Fn HOF (kcal/mol) EA HOF (kcal/mol) EA HOF (kcal/mol) IE HOF (kcal/mol) IE n 0 879.49 4.1 (2.65) 1166.98 8.4 (7.64) 2 836.73 4.1 (2.68) 764.82 4.3 (2.91) 1116.53 8.0 (7.28) 1056.80 8.3 (7.57) 4 794.25 4.1 (2.69) 657.37 4.3 (2.85) 1065.63 7.7 (6.90) 945.33 8.2 (7.46) 6 747.98 4.0 (2.58) 540.51 4.3 (2.88) 1013.89 7.5 (6.77) 838.60 8.6 (7.87) 8 724.36 3.8 (2.38) 435.05 4.5 (3.08) 989.78 7.7 (6.95) 735.82 8.5 (7.79) 10 686.84 3.7 (2.26) 323.71 4.5 (3.12) 946.76 7.6 (6.83) 625.83 8.6 (7.80) 12 656.15 3.3 (1.86) 212.08 4.6 (3.19) 904.22 7.5 (6.72) 520.37 8.8 (8.00) 14 619.72 3.1 (1.72) 107.71 4.4 (2.95) 860.34 7.3 (6.54) 414.98 9.0 (8.20) 16 580.14 3.1 (1.70) 25.26 4.5 (3.05) 820.02 7.3 (6.53) 304.27 9.0 (8.20) 18 543.50 2.3 (0.85) 2106.5 4.2 (2.82) 757.94 7.0 (6.23) 211.66 9.6 (8.87) 20 506.51 2.8 (1.43) 2221.23 4.2 (2.82) 735.94 7.1 (6.35) 84.65 9.0 (8.27) 22 472.60 2.6 (1.18) 2339.93 4.6 (3.21) 693.41 7.0 (6.22) 223.77 9.1 (8.32) 24 442.11 2.3 (0.90) 2445.30 4.6 (3.14) 653.72 6.9 (6.10) 2125.29 9.3 (8.56) 26 412.94 2.0 (0.54) 2550.62 4.4 (3.01) 619.50 7.0 (6.24) 2225.02 9.7 (8.93) 28 389.05 1.5 (0.12) 2645.02 4.2 (2.83) 591.66 7.2 (6.49) 2312.61 10.2 (9.41) 30 363.07 1.4 (20.02) 2745.37 4.3 (2.85) 562.91 7.3 (6.51) 2410.29 10.3 (9.50) 32 337.18 1.2 (20.19) 2846.16 4.3 (2.84) 532.54 7.2 (6.48) 2507.08 10.4 (9.69) 34 311.36 1.1 (20.32) 2935.52 3.8 (2.41) 502.77 7.2 (6.44) 2616.05 10.0 (9.27) 36 282.51 0.4 (21.02) 21040.67 3.9 (2.49) 469.00 7.7 (6.89) 2705.83 10.6 (9.8) 48 263.11 21.6 (23.02) 21451.76 4.6 (3.17) 396.52 7.4 (6.63) 21022.78 14.0 (13.26) 60 384.40 22.1 (23.56) 21486.26 3.3 (1.92) 542.19 9.0 (8.23) 21118.32 12.6 (11.86)
Ionization Energy and Electron Affinity of Hydro- and Fluorinefullerenes 517 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 Figure 1. Schlegel diagram of C 60. The numbers correspond to the positions of carbon atoms where addition of H- or F-atom occurs. fullerene cage has been assigned to a particular number. Addition of hydrogen or fluorine atoms to the numbered carbon atoms results in different isomers of C 60 H(F) n, which are the following: n ¼ 2: 1,2;4: 1, 2, 30, 36; 6: 1, 4, 14, 17, 18, 23; 8: 14, 23, 26, 32, 37, 40, 46, 49; 10: 14, 23, 26, 32, 37, 40, 45, 46, 49, 54; 12: 14, 23, 26, 32, 37, 39, 40, 45, 46, 48, 49, 54; 14: 14, 23, 26, 29, 32, 35, 37, 39, 40, 45, 46, 48, 49, 54; 16: 14, 15, 23, 24, 26, 29, 32, 35, 37, 39, 40, 45, 46, 48, 49, 54; 18: 1, 2, 5, 15, 16, 21, 22, 28, 29, 34, 37, 40, 41, 50, 52, 53, 57, 60; 20: 1, 2, 3, 4, 7, 10, 13, 15, 16, 19, 22, 24, 29, 30, 35, 36, 39, 41, 48, 50; 22: 1, 2, 3, 4, 7, 10, 13, 15, 16, 19, 22, 24, 29, 30, 35, 36, 39, 41, 42, 48, 50, 51; 24: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 45, 54, 55, 56, 57, 60; 26: 1, 2, 3, 4, 7, 10, 13, 15, 16, 19, 22, 24, 29, 30, 35, 36, 37, 38, 39, 41, 42, 46, 47, 48, 50, 51; 28: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 41, 43, 45, 50, 52, 54, 55, 56, 57, 60; 30: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 32, 41, 43, 45, 50, 52, 54, 55, 56, 57, 60; 32: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 30,
518 Nasibullaev et al. 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 32, 36, 41, 43, 45, 50, 52, 54, 55, 56, 57, 60; 34: 1, 2, 3, 4, 7, 9, 10, 13, 15, 16, 18, 19, 22, 24, 25, 27, 29, 30, 31, 33, 35, 36, 37, 39, 41, 42, 44, 46, 48, 50, 51, 53, 58, 59; 36: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 25, 27, 29, 32, 34, 36, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54; 48:1,2,3, 4, 5, 6, 7, 9, 11, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 49, 51, 53, 55, 56, 57, 58, 59. In the frame of Koopmans theorem, the energies of HOMOs and LUMOs (Table 1) are related to the vertical IE and to the vertical EA, respectively. They can be compared with corresponding experimental values determined by photoelectron spectroscopy and electron transmission spectroscopy. The IE and EA values that are present in Table 2 have been determined using the following formulas (1) and (2): EA ¼ E (0) E ( ) (1) Figure 2. Electron affinity (a) and IE (b) of hydrogenated (B) and fluorinated (O) fullerenes C 60 H(F) n as functions of the hydrogen/fluorine content, n.
253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 Ionization Energy and Electron Affinity of Hydro- and Fluorinefullerenes 519 where E (0) and E (2) are the total energies of neutral molecule and negative ion, respectively IE ¼ E (þ) E (0) (2) where E (þ) is the total energy of positive ion. The EA and IE magnitudes determined from formulas (1) and (2) correspond to the adiabatic EA and to the adiabatic IE, respectively. 0 Normalized to the known C 60 EA¼2.64 ev and IE ¼ 7.64 ev these values for C 60 H(F) n are given in parentheses. The obvious tendencies are clearly seen from the calculations (Fig. 2): the EA in the case of fluorinated fullerenes varies only slightly, whereas that of hydrogenated fullerenes decreases with increasing hydrogen content at the fast rate, reaching near to zero value for n ¼ 28 or 30 and turning to the steady negative magnitudes at higher n. The situation is exactly reverse for ionization energies where they again go in the opposite directions as the number of substitutions increases and the IEs variation of fluorinated fullerenes is clearly much more dramatic. ACKNOWLEDGMENTS The work has been supported by the Russian Foundation for Basic Research (grant 01-02-16561) and INTAS (grant YSF 01/1-188). REFERENCES 1. Nossal, J.; Saini, R.K.; Sadana, A.K.; Bettinger, H.F.; Alemany, L.B.; Scuseria, G.E.; Billups, W.E.; Saunders, M.; Khong, A.; Weisemann, R. Formation, isolation, spectroscopic properties, and calculated properties of some isomers of C 60 H 36. J. Am. Chem. Soc. 2001, 123 (35), 8482 8495. 2. Clare, B.W.; Kepert, D.L. The structures of C 60 F 36 and new possible structures for C 60 H 36. J. Mol. Struct. (Theochem). 1999, 466, 177 186. 3. Clare, B.W.; Kepert, D.L. Early stages in the addition to C 60 to form C 60 X n, X ¼ H, F, Cl, Br, CH 3,C 4 H 9. J. Mol. Struct. (Theochem). 2003, 621, 211 231. 4. Boltalina, O.V.; Buhl, M.; Khong, A.; Sauders, M.; Street, J.M.; Taylor, R. The 3 He NMR spectra of C 60 F 18 and C 60 F 36 ; the parallel between hydrogenation and fluorination. J. Chem. Soc. Perkin. Trans. 2. 1999, 1, 1475 1480. F2 Q3