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Validation of semiempirical PM6 method for the prediction of molecular properties of polycyclic aromatic hydrocarbons and fullerenes
Chemical Physics Letters 460 (2008) 151–154
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Validation of semiempirical PM6 method for the prediction of molecular properties of polycyclic aromatic hydrocarbons and fullerenes Andrea Alparone, Vito Librando *, Zelica Minniti Research Centre for Analysis, Monitoring and Minimization Methods of Environmental Risk and Department of Chemistry, University of Catania, viale A. Doria 8, Catania 95125, Italy
a r t i c l e
i n f o
Article history: Received 4 March 2008 In final form 9 May 2008 Available online 20 May 2008
a b s t r a c t Electronic polarizability (a) is a property involved in environmental mechanisms through intermolecular interactions. Recent semiempirical PM6 method has been employed to determine a values of a series of 40 polycyclic aromatic hydrocarbons (PAHs) and of some fullerenes. PM6 results are superior to those obtained with AM1 and PM3 levels, reproducing experimental a values of some fullerenes and PAHs within 6%, and high-level correlated CCSD/Sadlej-pVTZ a values of some oligoacenes within 2–7 a.u. (2%). Present results suggest that PM6 method may be suitable for predicting electronic polarizabilities of sizable PAHs, fullerenes and nanotubes for which ab initio calculations are impracticable so far. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Polycyclic aromatic hydrocarbons (PAHs) are of noticeable environmental impact being widespread and recalcitrant contaminants, usually produced by incomplete combustion processes [1]. From the toxicological point of view PAHs are potentially mutagenic and carcinogenic species [2]. They have also been detected in the interstellar media [3]. Their electronic dipole polarizabilities (a) have been employed in quantitative-structure property relationships (QSPRs) studies for prediction of some physicochemical parameters useful for environmental studies such as boiling point, octanol/water partition constants, gas and liquid chromatographic retention indices [4,5]. Electronic a values of some alkylated PAHs have been recently related to their biodegradation rate coefficients [6]. Fullerenes and nanotubes are carbonaceous materials little soluble in water, showing a remarkable tendency to aggregate in stable colloidal solutions, becoming potential vehicles of environmental pollutants and organic solvents [7,8]. There are also some indications showing that fullerene water suspensions exhibit a significant antibacterial activity [9]. For remediation strategies of contaminated sites, these materials might be especially useful to adsorb hydrophobic organic compounds [7,8]. In this regard, electronic dipole polarizability, through both dispersive and inductive forces, may play a fundamental role. The main goal of this study was to test the ability of the semiempirical PM6 method [10], recently implemented in MOPAC 2007 program [11], in determining a values of large molecular systems. To this purpose we focused our attention on a series of 40 polycyclic aromatic hydrocarbons (PAHs) ranging in size from Azulene (C10H8) to Circumovalene (C66H20), theoretically characterized * Corresponding author. Fax: +39 95 580138. E-mail address: [email protected] (V. Librando). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.05.028
by Malloci et al. [12] and Marques et al. [13] and on C60, C70, C84, C180 and C240 fullerenes. Electronic dipole polarizability of PAHs and fullerenes was the object of numerous experimental and theoretical works [13–30]. As well documented in the literature both PAHs and fullerenes are of great scientific interest for applications in the fields of organic conductors and nanomaterials [31,32]. 2. Computational methods Geometries of PAHs and fullerenes were here optimized at the PM6 level [10]. For PAHs polarizability computations were also carried out on the B3LYP/6-31+G* geometry taken from Ref. [12]. Static electronic aii (i = x, y, z) components were calculated at AM1, PM3 and PM6 levels as second-order derivatives of energy (E) with respect to electric field strength components (Fi), through an analytic procedure described in technical details in Ref. [33]:
EðFÞ ¼ Eð0Þ
X
li F i 1=2
i
1=24
X
X ij
cijkl F i F j F k F l
aij F i F j 1=6
X
bijk F i F j F k
ijk
ð1Þ
ijkl
aij ¼
" # @ 2 EðFÞ @F i @F j
ð2Þ
F!0
In the case of large fullerenes (C84 C180 and C240) we employed a numerical finite-field approach using a Fi value of 0.001 V Å1 (conversion factors for electric field strength in V Å1 to a.u., S.I. and e.s.u. are: 1 V Å1 = 0.19447 101 Ehe1a01 = 1010 V m1 = 3.33573 105 statvolt cm1). For C70 analytic and numerical aii values were computed to be within 0.7 a.u. with a percentage difference of 0.1%. Frequency-dependent aii values were estimated
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A. Alparone et al. / Chemical Physics Letters 460 (2008) 151–154
within the 0–0.08 a.u. energy range. Polarizability is usually expressed as orientationally averaged value, which is defined by
hai ¼ 1=3ðaxx þ ayy þ azz Þ
lected in Table 1. On the whole PM3 and AM1 methods underestimate PM6 data by 11–28% and 8–24%, respectively. As can be appreciated from the data reported in the Table and also from Fig. 1, PM6 reproduces satisfactorily well the experimental hai values of 2 [14], 6 [15], 7–9 [16], 11 [16], 12 [16], 15 [16] PAHs within 0–12 a.u. (0.0–5.1%), the corresponding deviations obtained using the TDDFT data of Marques et al. [13] being 4–15 a.u. (2.0–9.0%). Least-mean squared fitting procedure between observed and calculated hai data leads to the following linear relationships:
ð3Þ
All computations were performed with the MOPAC 2007 package [11]. 3. Results and discussion 3.1. Polarizabilities of PAHs
haiexp: ¼ 1:28haiPM3 þ 8:74 ðr2 ¼ 0:98Þ; haiexp: ¼ 1:22haiAM1 þ 7:55 ðr2 ¼ 0:99Þ;
Table 1 reports hai values of PAHs computed at the semiempirical AM1, PM3 and PM6 levels. The Table also includes some experimental [14–16] as well as theoretical data recently obtained at the time-dependent density functional theory (TDDFT) [13] and CCSD/ Sadlej-pVTZ [17] levels. Due to a much more effective parametrization scheme, PM6 reproduces reference heats of formation for a set of 3188 compounds better than the widely employed PM3 and AM1 semiempirical methods [10]. As a consequence, PM6 a values are expected to be of superior quality to those obtained with the PM3 and AM1 levels. It is confirmed by examination of data col-
haiexp: ¼ 1:08haiPM6==PM6 9:53 ðr2 ¼ 0:99Þ; haiexp: ¼ 1:05haiPM6 6:52 ðr 2 ¼ 0:99Þ; haiexp: ¼ 1:00haiTDDFT 9:60 ðr2 ¼ 0:99Þ: Note that PM6 hai values are in reasonable agreement with the TDDFT hai data [13], the following relationship being obtained: haiTDDFT = 1.16 haiPM6 23.78 (r2 = 0.985). Additionally PM6 hai values of 2, 7, 10, 20, 24 oligoacenes agree with the recent data
Table 1 Static electronic average dipole polarizabilities (a.u.) of 1-40 PAHs Label
Compound (formula)
PM3a
AM1a
PM6a
PM6//PM6b
TDDFTa,c
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
Azulene (C10H8) Naphthalene (C10H8) Acenaphthylene (C12H8) Biphenylene (C12H8) Acenaphthene (C12H10) Fluorene (C13H10) Anthracene (C14H10) Phenanthrene (C14H10) Pyrene (C16H10) Tetracene (C18H12) Chrysene (C18H12) Triphenylene (C18H12) Benzo[a]anthracene (C18H12) Corannulene (C20H10) Perylene (C20H12) Benzo[a]pyrene (C20H12) Benzo[e]pyrene (C20H12) Anthanthrene (C22H12) Benzo[g,h,i]perylene (C22H12) Pentacene (C22H14) Coronene (C24H12) Dibenzo[b,def]chrysene (C24H14) Dibenzo[cd,lm]perylene (C26H14) Hexacene (C26H16) Bisanthene (C28H14) Benzo[a]coronene (C28H14) Dibenzo[bc,kl]coronene (C30H14) Dibenzo[bc,ef]coronene (C30H14) Terrylene (C30H16) Ovalene (C32H14) Tetrabenzocoronene (C36H16) Circumbiphenyl (C38H16) Circumanthracene (C40H16) Quaterrylene (C40H20) Circumpyrene (C42H16) Hexabenzocoronene (C42H18) Dicoronylene (C48H20) Pentarylene (C50H24) Circumcoronene (C54H18) Circumovalene (C66H20)
100 85 103 104 100 110 135 126 151 194 173 154 178 176 196 205 188 237 212 262 234 268 303 338 325 282 382 328 347 342 498 410 477 539 487 443 558 767 643 840
104 89 108 109 106 115 141 132 157 203 180 171 185 182 204 213 196 246 221 273 242 278 314 351 337 292 395 339 361 354 515 424 492 558 502 458 577 794 659 870
128 117 139 139 138 150 175 166 195 242 221 213 226 224 252 258 240 295 266 319 287 330 375 403 408 344 469 401 439 409 635 482 569 687 576 525 653 1012 722 942
124 116 138 139 138 150 172 165 193 236 218 213 223 223 247 254 238 285 263 307 284 318 357 382 385 339 436 388 415 401 558 473 543 617 550 522 633 848 706 891
133 123 145 152 143 159 189 182 205 264 239 231 246 244 262 277 260 304 282 353 318 355 384 454 402 386 459 431 484 453 565 538 612 799 631 590 770 1196 840 1099
a b c d e f g
Calculations are carried out on the B3LYP/6-31+G* geometries taken from Ref. [12]. Calculations are carried out on the PM6 geometries. Ref. [13]. Ref. [17]. Ref. [14]. Ref. [15]. Ref. [16].
CCSD/Sadlej-pVTZd
Exp.
119
117e
178
146f 180g 167g 201g
247 233g 221g
251g
325
410
153
A. Alparone et al. / Chemical Physics Letters 460 (2008) 151–154 Table 2 Static electronic average dipole polarizabilities (a.u.) of C60, C70 and C84 Fullerene (symmetry) a
AM1 PM3a PM6a HF/6-31G*b HF/6-31+Gc HF/6-31G+sdd DD-CRPAe DFT/LDFf DFT/LB94g DFT/LDAg DFT/LDA-RPAh DFT/LDAi INDO-TDCPHFj PBE/[5s4p4d]k Exp.l Exp.m
Fig. 1. Relationships between experimental and computed hai data of 2, 6–9, 11, 12, 15 PAHs. See Table 1 for reference label.
obtained at the correlated CCSD/Sadlej-pVTZ level of theory [17], the differences being within 2–7 a.u. (1.7–2.0%), which are substantially inferior to those obtained by the TDDFT calculations [13], being 4–44 a.u. (3.4–10.7%). As widely documented in the literature, commonly used DFT methods are in trouble when dealing with (hyper)polarizability computations of extended p-conjugated systems [34]. Note also that, hai (Hexacene)/hai (naphthalene) ratios obtained at the AM1, PM3, PM6 and PM6//PM6 levels are 3.94, 3.98, 3.44 and 3.29, respectively, to be compared with the corresponding CCSD/Sadlej-pVTZ and TDDFT ratios of 3.45 and 3.69, respectively. The effect of geometry can be crucial for the electric properties [35–37]. On the whole, when passing from B3LYP/631+G* to PM6 structure, hai value reduces, the largest variation being found for Pentarylene (20%). This finding is in some consistency with a decrease of the volume by ca. 3 Å3 and simultaneously an increase of the eLUMO eHOMO energy difference by ca. 0.4 eV. The origin of the decrease in the electronic dipole polarizability can be principally ascribed to the increase of the carbon–carbon bond length alternation (defined as the difference between single and double bond lengths), which reduces p-conjugation effects and electron mobility [35–38].
C60 (Ih)
C70 (D5h)
C84 (D2)
428 434 530 (544) 442 507 532 579 526 544 557 559 558 558 559 516 ± 54 533
530 536 645 (675)
646 652 772
606
738
694 688 ± 94 634
a This work. The PM6 geometry is used. Value in parentheses refers to dynamic datum at the Nd:YAG laser radiation energy of 0.04282 a.u. b Ref. [23]. c Ref. [21]. d Ref. [19]. e Ref. [22]. f Ref. [26]. g Ref. [20]. h Ref. [24]. i Ref. [25]. j Ref. [18]. k Ref. [27]. l Ref. [29]. m Ref. [30].
obtained by Zope [27] at PBE/[5s4p4d] level (with a total number of 2870 basis functions for C70) within 29–49 a.u. (5–7%), giving almost similar hai (C84)/hai(C70) = 1.20, hai(C84)/hai(C60) = 1.46, hai (C70)/hai(C60) = 1.22 ratios. Static PM6 hai values of the sizable fullerenes C180, C240 are computed to be 1905 and 2601 a.u., which are comparable to the values of 1784 and 2662 a.u., respectively, previously obtained by Shanker and Applequist [28], using atom monopole–dipole interaction method. In Fig. 2 are shown dispersion curves of hai(x; x) for C60 and C70 obtained in the 0.00– 0.08 a.u. energy range at the PM6 level of calculation. Note that
3.2. Polarizabilities of fullerenes In Table 2 are listed hai values of C60, C70 and C84 computed at the AM1, PM3 and PM6 levels on the PM6 optimized geometries, together with experimental and high-level theoretical data for comparison. PM6 geometry of C60 (rC–C = 1.469 Å, rC@C = 1.385 Å) is in reasonable agreement with the experimental one (rC–C = 1.450 ± 0.015 Å, rC@C = 1.400 ± 0.015 Å) determined from solidstate 13C NMR measurements [39]. It is worth to note that PM6 hai values of C60 and C70 are in reasonable agreement with experimental estimates [29,30], the differences being within 3–14 a.u. (0.6–2.7%) and 11–43 a.u. (1.7–6.2%), respectively. As can be seen from data reported in the Table, PM6 hai values of C60, C70 and C84 agree with previous ab initio and DFT data [19–27]. In line with the results found for PAHs, PM6 hai data are of better-quality than those obtained at the PM3 and AM1 levels, the differences being within 96–126 a.u. (16–19%). It is interesting to note that PM6 calculations reproduce the HF/6-31+G hai values for C60, C70 of Jonsson et al. [21] within 23–39 a.u. (5–6%), and those recently
Fig. 2. Frequency-dependent hai (x; x) values of C60 and C70 as a function of x. PM6//PM6 results.
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A. Alparone et al. / Chemical Physics Letters 460 (2008) 151–154
for C70 at the energy value of 0.06 a.u., which is near the observed lowest excitation energy at 0.0975 a.u. [40], hai(x; x) value suffers of resonance phenomena. The frequency dependence of hai(x; x) can be expressed as a truncated even-order power series expansion of x [41]:
C60 : haiðx; xÞ ¼ 530½1 þ 13x2 þ 1020x4 C70 : haiðx; xÞ ¼ 645½1 þ 19x2 þ 5382x4 Frequency dispersion effects evaluated at the experimental Nd:YAG laser radiation energy of 0.04282 a.u. (k = 1064 nm) increase the static PM6 hai value of C60 and C70 by 2.7% and 4.6%, respectively, in line with a dispersion correction for C60 of 2.3%, estimated from DFT/LB94 results [20]. 4. Conclusions Owing to its relatively low computational cost and reasonable accuracy, PM6 is a potentially valid alternative method for predicting electronic polarizabilities of very extended PAHs, fullerene and nanotube systems, for which ab initio methods are prohibitive to date. Use of PM6 level of calculation might be especially attractive in characterizing electrical properties of organic macromolecules and nanomaterial as well as in development of more reliable molecular descriptors for QSPRs applications. Acknowledgements This work was carried out in the framework of the RIC action of the Project No. 1999/IT.16.1.PO.011/3.13/7.2.4/339 PROT. 238, ‘‘Formazione per la ricerca nel campo della bonifica dei siti contaminati” POR Sicilia 2000–2006, Asse: III Misura: 3.13. References [1] M. Howsman, K.C. Jones, in: A.H. Neilson (Ed.), The Handbook of Environmental Chemistry, vol. 3.1, Springer-Verlag, 1998, pp. 137–174. [2] R.G. Harvey, in: Polycyclic Aromatic Hydrocarbons: Chemistry and Carcinogenicity, Cambridge University Press, Cambridge, UK, 1991. [3] L.J. Allamandola, Top. Curr. Chem. 153 (1990) 1.
[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]
J. Kang, C. Cao, Z. Li, J. Chromatogr. A 799 (1998) 361. F.A.L. Ribeiro, M.M.C. Ferreira, J. Mol. Struct. (Theochem.) 663 (2003) 109. V. Librando, A. Alparone, Environ. Sci. Technol. 41 (2007) 1646. W. Chen, L. Duan, D. Zhu, Environ. Sci. Technol. 41 (2007) 8295. L.K. Duncan, J.R. Jinschek, P.J. Vikesland, Environ. Sci. Technol. 42 (2008) 173. D.Y. Lyon, L.K. Adams, J.C. Falkner, P.J.J. Alvarez, Environ. Sci. Technol. 40 (2006) 4360. J.J.P. Stewart, J. Mol. Model. 13 (2007) 1173. J.J.P. Stewart, MOPAC 2007, Stewart Computational Chemistry, Colorado Springs, CO, USA,. G. Malloci, C. Joblin, G. Mulas, Chem. Phys. 332 (2007) 353.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Validation of semiempirical PM6 method for the prediction of molecular properties of polycyclic aromatic hydrocarbons and fullerenes Andrea Alparone, Vito Librando *, Zelica Minniti Research Centre for Analysis, Monitoring and Minimization Methods of Environmental Risk and Department of Chemistry, University of Catania, viale A. Doria 8, Catania 95125, Italy
a r t i c l e
i n f o
Article history: Received 4 March 2008 In final form 9 May 2008 Available online 20 May 2008
a b s t r a c t Electronic polarizability (a) is a property involved in environmental mechanisms through intermolecular interactions. Recent semiempirical PM6 method has been employed to determine a values of a series of 40 polycyclic aromatic hydrocarbons (PAHs) and of some fullerenes. PM6 results are superior to those obtained with AM1 and PM3 levels, reproducing experimental a values of some fullerenes and PAHs within 6%, and high-level correlated CCSD/Sadlej-pVTZ a values of some oligoacenes within 2–7 a.u. (2%). Present results suggest that PM6 method may be suitable for predicting electronic polarizabilities of sizable PAHs, fullerenes and nanotubes for which ab initio calculations are impracticable so far. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Polycyclic aromatic hydrocarbons (PAHs) are of noticeable environmental impact being widespread and recalcitrant contaminants, usually produced by incomplete combustion processes [1]. From the toxicological point of view PAHs are potentially mutagenic and carcinogenic species [2]. They have also been detected in the interstellar media [3]. Their electronic dipole polarizabilities (a) have been employed in quantitative-structure property relationships (QSPRs) studies for prediction of some physicochemical parameters useful for environmental studies such as boiling point, octanol/water partition constants, gas and liquid chromatographic retention indices [4,5]. Electronic a values of some alkylated PAHs have been recently related to their biodegradation rate coefficients [6]. Fullerenes and nanotubes are carbonaceous materials little soluble in water, showing a remarkable tendency to aggregate in stable colloidal solutions, becoming potential vehicles of environmental pollutants and organic solvents [7,8]. There are also some indications showing that fullerene water suspensions exhibit a significant antibacterial activity [9]. For remediation strategies of contaminated sites, these materials might be especially useful to adsorb hydrophobic organic compounds [7,8]. In this regard, electronic dipole polarizability, through both dispersive and inductive forces, may play a fundamental role. The main goal of this study was to test the ability of the semiempirical PM6 method [10], recently implemented in MOPAC 2007 program [11], in determining a values of large molecular systems. To this purpose we focused our attention on a series of 40 polycyclic aromatic hydrocarbons (PAHs) ranging in size from Azulene (C10H8) to Circumovalene (C66H20), theoretically characterized * Corresponding author. Fax: +39 95 580138. E-mail address: [email protected] (V. Librando). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.05.028
by Malloci et al. [12] and Marques et al. [13] and on C60, C70, C84, C180 and C240 fullerenes. Electronic dipole polarizability of PAHs and fullerenes was the object of numerous experimental and theoretical works [13–30]. As well documented in the literature both PAHs and fullerenes are of great scientific interest for applications in the fields of organic conductors and nanomaterials [31,32]. 2. Computational methods Geometries of PAHs and fullerenes were here optimized at the PM6 level [10]. For PAHs polarizability computations were also carried out on the B3LYP/6-31+G* geometry taken from Ref. [12]. Static electronic aii (i = x, y, z) components were calculated at AM1, PM3 and PM6 levels as second-order derivatives of energy (E) with respect to electric field strength components (Fi), through an analytic procedure described in technical details in Ref. [33]:
EðFÞ ¼ Eð0Þ
X
li F i 1=2
i
1=24
X
X ij
cijkl F i F j F k F l
aij F i F j 1=6
X
bijk F i F j F k
ijk
ð1Þ
ijkl
aij ¼
" # @ 2 EðFÞ @F i @F j
ð2Þ
F!0
In the case of large fullerenes (C84 C180 and C240) we employed a numerical finite-field approach using a Fi value of 0.001 V Å1 (conversion factors for electric field strength in V Å1 to a.u., S.I. and e.s.u. are: 1 V Å1 = 0.19447 101 Ehe1a01 = 1010 V m1 = 3.33573 105 statvolt cm1). For C70 analytic and numerical aii values were computed to be within 0.7 a.u. with a percentage difference of 0.1%. Frequency-dependent aii values were estimated
152
A. Alparone et al. / Chemical Physics Letters 460 (2008) 151–154
within the 0–0.08 a.u. energy range. Polarizability is usually expressed as orientationally averaged value, which is defined by
hai ¼ 1=3ðaxx þ ayy þ azz Þ
lected in Table 1. On the whole PM3 and AM1 methods underestimate PM6 data by 11–28% and 8–24%, respectively. As can be appreciated from the data reported in the Table and also from Fig. 1, PM6 reproduces satisfactorily well the experimental hai values of 2 [14], 6 [15], 7–9 [16], 11 [16], 12 [16], 15 [16] PAHs within 0–12 a.u. (0.0–5.1%), the corresponding deviations obtained using the TDDFT data of Marques et al. [13] being 4–15 a.u. (2.0–9.0%). Least-mean squared fitting procedure between observed and calculated hai data leads to the following linear relationships:
ð3Þ
All computations were performed with the MOPAC 2007 package [11]. 3. Results and discussion 3.1. Polarizabilities of PAHs
haiexp: ¼ 1:28haiPM3 þ 8:74 ðr2 ¼ 0:98Þ; haiexp: ¼ 1:22haiAM1 þ 7:55 ðr2 ¼ 0:99Þ;
Table 1 reports hai values of PAHs computed at the semiempirical AM1, PM3 and PM6 levels. The Table also includes some experimental [14–16] as well as theoretical data recently obtained at the time-dependent density functional theory (TDDFT) [13] and CCSD/ Sadlej-pVTZ [17] levels. Due to a much more effective parametrization scheme, PM6 reproduces reference heats of formation for a set of 3188 compounds better than the widely employed PM3 and AM1 semiempirical methods [10]. As a consequence, PM6 a values are expected to be of superior quality to those obtained with the PM3 and AM1 levels. It is confirmed by examination of data col-
haiexp: ¼ 1:08haiPM6==PM6 9:53 ðr2 ¼ 0:99Þ; haiexp: ¼ 1:05haiPM6 6:52 ðr 2 ¼ 0:99Þ; haiexp: ¼ 1:00haiTDDFT 9:60 ðr2 ¼ 0:99Þ: Note that PM6 hai values are in reasonable agreement with the TDDFT hai data [13], the following relationship being obtained: haiTDDFT = 1.16 haiPM6 23.78 (r2 = 0.985). Additionally PM6 hai values of 2, 7, 10, 20, 24 oligoacenes agree with the recent data
Table 1 Static electronic average dipole polarizabilities (a.u.) of 1-40 PAHs Label
Compound (formula)
PM3a
AM1a
PM6a
PM6//PM6b
TDDFTa,c
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
Azulene (C10H8) Naphthalene (C10H8) Acenaphthylene (C12H8) Biphenylene (C12H8) Acenaphthene (C12H10) Fluorene (C13H10) Anthracene (C14H10) Phenanthrene (C14H10) Pyrene (C16H10) Tetracene (C18H12) Chrysene (C18H12) Triphenylene (C18H12) Benzo[a]anthracene (C18H12) Corannulene (C20H10) Perylene (C20H12) Benzo[a]pyrene (C20H12) Benzo[e]pyrene (C20H12) Anthanthrene (C22H12) Benzo[g,h,i]perylene (C22H12) Pentacene (C22H14) Coronene (C24H12) Dibenzo[b,def]chrysene (C24H14) Dibenzo[cd,lm]perylene (C26H14) Hexacene (C26H16) Bisanthene (C28H14) Benzo[a]coronene (C28H14) Dibenzo[bc,kl]coronene (C30H14) Dibenzo[bc,ef]coronene (C30H14) Terrylene (C30H16) Ovalene (C32H14) Tetrabenzocoronene (C36H16) Circumbiphenyl (C38H16) Circumanthracene (C40H16) Quaterrylene (C40H20) Circumpyrene (C42H16) Hexabenzocoronene (C42H18) Dicoronylene (C48H20) Pentarylene (C50H24) Circumcoronene (C54H18) Circumovalene (C66H20)
100 85 103 104 100 110 135 126 151 194 173 154 178 176 196 205 188 237 212 262 234 268 303 338 325 282 382 328 347 342 498 410 477 539 487 443 558 767 643 840
104 89 108 109 106 115 141 132 157 203 180 171 185 182 204 213 196 246 221 273 242 278 314 351 337 292 395 339 361 354 515 424 492 558 502 458 577 794 659 870
128 117 139 139 138 150 175 166 195 242 221 213 226 224 252 258 240 295 266 319 287 330 375 403 408 344 469 401 439 409 635 482 569 687 576 525 653 1012 722 942
124 116 138 139 138 150 172 165 193 236 218 213 223 223 247 254 238 285 263 307 284 318 357 382 385 339 436 388 415 401 558 473 543 617 550 522 633 848 706 891
133 123 145 152 143 159 189 182 205 264 239 231 246 244 262 277 260 304 282 353 318 355 384 454 402 386 459 431 484 453 565 538 612 799 631 590 770 1196 840 1099
a b c d e f g
Calculations are carried out on the B3LYP/6-31+G* geometries taken from Ref. [12]. Calculations are carried out on the PM6 geometries. Ref. [13]. Ref. [17]. Ref. [14]. Ref. [15]. Ref. [16].
CCSD/Sadlej-pVTZd
Exp.
119
117e
178
146f 180g 167g 201g
247 233g 221g
251g
325
410
153
A. Alparone et al. / Chemical Physics Letters 460 (2008) 151–154 Table 2 Static electronic average dipole polarizabilities (a.u.) of C60, C70 and C84 Fullerene (symmetry) a
AM1 PM3a PM6a HF/6-31G*b HF/6-31+Gc HF/6-31G+sdd DD-CRPAe DFT/LDFf DFT/LB94g DFT/LDAg DFT/LDA-RPAh DFT/LDAi INDO-TDCPHFj PBE/[5s4p4d]k Exp.l Exp.m
Fig. 1. Relationships between experimental and computed hai data of 2, 6–9, 11, 12, 15 PAHs. See Table 1 for reference label.
obtained at the correlated CCSD/Sadlej-pVTZ level of theory [17], the differences being within 2–7 a.u. (1.7–2.0%), which are substantially inferior to those obtained by the TDDFT calculations [13], being 4–44 a.u. (3.4–10.7%). As widely documented in the literature, commonly used DFT methods are in trouble when dealing with (hyper)polarizability computations of extended p-conjugated systems [34]. Note also that, hai (Hexacene)/hai (naphthalene) ratios obtained at the AM1, PM3, PM6 and PM6//PM6 levels are 3.94, 3.98, 3.44 and 3.29, respectively, to be compared with the corresponding CCSD/Sadlej-pVTZ and TDDFT ratios of 3.45 and 3.69, respectively. The effect of geometry can be crucial for the electric properties [35–37]. On the whole, when passing from B3LYP/631+G* to PM6 structure, hai value reduces, the largest variation being found for Pentarylene (20%). This finding is in some consistency with a decrease of the volume by ca. 3 Å3 and simultaneously an increase of the eLUMO eHOMO energy difference by ca. 0.4 eV. The origin of the decrease in the electronic dipole polarizability can be principally ascribed to the increase of the carbon–carbon bond length alternation (defined as the difference between single and double bond lengths), which reduces p-conjugation effects and electron mobility [35–38].
C60 (Ih)
C70 (D5h)
C84 (D2)
428 434 530 (544) 442 507 532 579 526 544 557 559 558 558 559 516 ± 54 533
530 536 645 (675)
646 652 772
606
738
694 688 ± 94 634
a This work. The PM6 geometry is used. Value in parentheses refers to dynamic datum at the Nd:YAG laser radiation energy of 0.04282 a.u. b Ref. [23]. c Ref. [21]. d Ref. [19]. e Ref. [22]. f Ref. [26]. g Ref. [20]. h Ref. [24]. i Ref. [25]. j Ref. [18]. k Ref. [27]. l Ref. [29]. m Ref. [30].
obtained by Zope [27] at PBE/[5s4p4d] level (with a total number of 2870 basis functions for C70) within 29–49 a.u. (5–7%), giving almost similar hai (C84)/hai(C70) = 1.20, hai(C84)/hai(C60) = 1.46, hai (C70)/hai(C60) = 1.22 ratios. Static PM6 hai values of the sizable fullerenes C180, C240 are computed to be 1905 and 2601 a.u., which are comparable to the values of 1784 and 2662 a.u., respectively, previously obtained by Shanker and Applequist [28], using atom monopole–dipole interaction method. In Fig. 2 are shown dispersion curves of hai(x; x) for C60 and C70 obtained in the 0.00– 0.08 a.u. energy range at the PM6 level of calculation. Note that
3.2. Polarizabilities of fullerenes In Table 2 are listed hai values of C60, C70 and C84 computed at the AM1, PM3 and PM6 levels on the PM6 optimized geometries, together with experimental and high-level theoretical data for comparison. PM6 geometry of C60 (rC–C = 1.469 Å, rC@C = 1.385 Å) is in reasonable agreement with the experimental one (rC–C = 1.450 ± 0.015 Å, rC@C = 1.400 ± 0.015 Å) determined from solidstate 13C NMR measurements [39]. It is worth to note that PM6 hai values of C60 and C70 are in reasonable agreement with experimental estimates [29,30], the differences being within 3–14 a.u. (0.6–2.7%) and 11–43 a.u. (1.7–6.2%), respectively. As can be seen from data reported in the Table, PM6 hai values of C60, C70 and C84 agree with previous ab initio and DFT data [19–27]. In line with the results found for PAHs, PM6 hai data are of better-quality than those obtained at the PM3 and AM1 levels, the differences being within 96–126 a.u. (16–19%). It is interesting to note that PM6 calculations reproduce the HF/6-31+G hai values for C60, C70 of Jonsson et al. [21] within 23–39 a.u. (5–6%), and those recently
Fig. 2. Frequency-dependent hai (x; x) values of C60 and C70 as a function of x. PM6//PM6 results.
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for C70 at the energy value of 0.06 a.u., which is near the observed lowest excitation energy at 0.0975 a.u. [40], hai(x; x) value suffers of resonance phenomena. The frequency dependence of hai(x; x) can be expressed as a truncated even-order power series expansion of x [41]:
C60 : haiðx; xÞ ¼ 530½1 þ 13x2 þ 1020x4 C70 : haiðx; xÞ ¼ 645½1 þ 19x2 þ 5382x4 Frequency dispersion effects evaluated at the experimental Nd:YAG laser radiation energy of 0.04282 a.u. (k = 1064 nm) increase the static PM6 hai value of C60 and C70 by 2.7% and 4.6%, respectively, in line with a dispersion correction for C60 of 2.3%, estimated from DFT/LB94 results [20]. 4. Conclusions Owing to its relatively low computational cost and reasonable accuracy, PM6 is a potentially valid alternative method for predicting electronic polarizabilities of very extended PAHs, fullerene and nanotube systems, for which ab initio methods are prohibitive to date. Use of PM6 level of calculation might be especially attractive in characterizing electrical properties of organic macromolecules and nanomaterial as well as in development of more reliable molecular descriptors for QSPRs applications. Acknowledgements This work was carried out in the framework of the RIC action of the Project No. 1999/IT.16.1.PO.011/3.13/7.2.4/339 PROT. 238, ‘‘Formazione per la ricerca nel campo della bonifica dei siti contaminati” POR Sicilia 2000–2006, Asse: III Misura: 3.13. References [1] M. Howsman, K.C. Jones, in: A.H. Neilson (Ed.), The Handbook of Environmental Chemistry, vol. 3.1, Springer-Verlag, 1998, pp. 137–174. [2] R.G. Harvey, in: Polycyclic Aromatic Hydrocarbons: Chemistry and Carcinogenicity, Cambridge University Press, Cambridge, UK, 1991. [3] L.J. Allamandola, Top. Curr. Chem. 153 (1990) 1.
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