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Novel series of giant polycyclic aromatic hydrocarbons: electronic structure and aromaticity
Chemical Physics Letters 385 (2004) 512–518 www.elsevier.com/locate/cplett
Novel series of giant polycyclic aromatic hydrocarbons: electronic structure and aromaticity Bal azs Hajgat o, Koichi Ohno
*
Department of Chemistry, Graduate School of Science, Tohoku University, Aramaki, Aoba-ku, Sendai 980-8578, Japan Received 6 November 2003; in final form 2 January 2004 Published online:
Abstract We present a theoretical study on a novel series of Polycyclic Aromatic Hydrocarbons (PAHs) having hollow sites focusing particularly on electronic structures and spectroscopic aspects using molecular orbital and DFT levels of theory. We have found in the case of a new series of PAHs that the UV–Vis absorption spectra of some PAHs show blue shifts as the number of electrons increases in the p-system. Unusual behaviors of giant PAHs are discussed in connection with aromaticity. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Polycyclic Aromatic Hydrocarbons (PAHs) consist of two or more condensed aromatic rings. They occur in nature mostly in traces in different matrices and their origin is both anthropogenic and natural. PAHs have long been in the focus of both theoretical and experimental researches due to their importance in several fields of science. PAHs form for example an important group of extremely hazardous environmental pollutants and some of them are highly cancerous [1]. Numerous different PAHs are present in petroleum samples, and they are also produced in the burning of mineral oil derivates [2]. Large PAHs are frequently used as model compounds for graphite sheets and glassy carbon materials [3]. PAHs exist not only in the Earth but are commonly accepted as being ubiquitous in the interstellar medium [4] and presumably responsible for some of the Diffuse Interstellar Bands and Unidentified Emission Bands in the mid–IR range [5]. Several different sizes of PAHs have been synthesized and recently some giant ones have been made to contain 114 [6] and 222 [7] carbon atoms. The solubility of large PAHs drastically decreases with their size and the giant ones are completely insoluble, hence structure elucida*
Corresponding author. Fax: +81-22-217-6580. E-mail address: [email protected] (K. Ohno).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.01.029
tion methods are rather limited [6,7]. There are several papers on the theoretical study of the electronic structure and electronic spectra of different PAHs, together with their positive and negative radicals, which range from semi-empirical [8–10] to ab initio [11–13] methods including DFT levels of theory [14,15]. In their early work, Stein and Brown [8] have shown that the HOMO– LUMO gaps of the edge structure of large condensed PAHs have a higher influence over the overall systemsize. They have also shown that in a series of growing PAHs with the same edge structure, the HOMO– LUMO gap is progressively decreasing as the size of the PAHs increases to the limiting value of zero. Hiruta et al. [10] have shown that the zigzag phenes at the ground state have less mobile p-electrons than the linear acenes because they have a tendency to localize in a particular portion of the molecular framework. Dias and other workers [16] by using molecular graph theory have shown that there exist large conjugated systems with a significant non-zero limiting band-gap. All those investigated systems were constructed of hexagonal rings without hollow sites. The only exception is kekulene that has been widely investigated especially concerning with its superaromaticity [17–21]. Some earlier papers suggest that kekulene is superaromatic, although new techniques and more extended investigations negate the possibility of superaromaticity and verify the fact of high aromaticity.
B. Hajgato, K. Ohno / Chemical Physics Letters 385 (2004) 512–518
In this Letter, we systematically investigated some large to giant PAHs that were constructed entirely from condensed hexagon rings, which possess hollow sites. The investigation was made to especially focus on electronic spectroscopy as a useful elucidation tool of giant PAHs. We have also addressed the recurring question of aromaticity in a bit more detail in the case of some of our investigated compounds.
2. Computational methods
1
513
2
3 4
5
6
7 8
All calculations were carried out using GA U S S I A N 98 [22] and MO/8E [23,24] program packages. Since the calculated electronic spectra is not so sensitive for the geometries used [14,15] and some earlier works successfully used semi-empirical INDO/S at the geometry of AM1 in predicting excited states [9], we also decided to use semi-empirical methods for geometry optimizations. However we experienced in some cases serious geometry convergence problems using MNDO, AM1, and PM3 methods, so we have chosen the CNDO method for geometry optimizations. In accordance with other authors [14,15] we performed time-dependent density functional theory using Becke exchange [25] and Lee et al. correlation [26] functionals in conjunction with 3-21G and 6-31G basis sets to calculate excited states. In addition, we also calculated ZINDO, and MO/8E excited states. Aromatic stabilizations were estimated using Isodesmic Bond Separation Energies (IBSE) [27] and Homodesmotic Stabilization Energies (HSE) [27]. Resonance energy calculations were performed using the NBO [28] analysis at the BLYP/6-31G level of theory. Nucleus-Independent Chemical Shifts (NICS(1) [29,30]) were calculated using the GIAO-SCF/6-31G level of theory.
9
11
10
14
12 13
15
16
Fig. 1. Hexagonal structures of PAHs investigated. PAH-Series Type I: 1, 5 and 2, 6, 9 and 3, 7, 10, 12. PAH-Series Type II: 1, 4, 8, 14, 15, 16.
3. Results and discussion The hexagon structures of the PAHs investigated are shown in Fig. 1. To generate a new series of molecules we chose the widely investigated kekulene as a base molecule because of the cavity. There are two different ways to generate a new series of PAHs based on kekulene. One involves increasing the size of the super-ring and condensing additional benzene rings to the periphery and inside the cavity (Series Type I, for example 2, 6, 9 and 3, 7, 10, 12). It is important to keep the shape of the molecules similar because this will strongly affect the excited states [8]. Another one is to condense the superrings making dimer, trimers and other oligomers (Series Type II, for example 1, 4, 8, 14, 15, 16). Since tendencies will be different in the case of Series Types I and II, we will discuss them separately. For conciseness, we will dispense with detailing geometrical parameters due to
this being beyond the scope of this Letter. The stationary points were not characterized by harmonic vibrational frequency analysis because all the structures have expected symmetries both in experiment and theory (D6h for 1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, D2h for 4, and C2v for 8). 3.1. Reliability of calculated excited states Generally all the methods used give almost perfect excitation energies for small to moderate sized PAHs, but in the case of large and giant sized PAHs the picture is not so clear. Since we do not have experimental electronic spectra for series type I nor series type II structures we evaluated the quality of our calculations. The molecules 11 and 13 are included for testing purposes because they are the largest PAHs with available
514
B. Hajgato, K. Ohno / Chemical Physics Letters 385 (2004) 512–518
experimental electronic spectra. The calculated electronic transitions, oscillator strengths, and available experimental results (for 1 [31], 11 [6], and 13 [7]) are listed in Table 1. The term Bright State was used in case of the largest oscillator strengths. In the case of ZINDO calculations the size of the used CI space was increased systematically until the excitation energies did not change considerably (less than 1%). Table 1 contains the ZINDO results using 200 200 (200 electrons in 200 orbitals) CI space except for 15 and 16 where the used CI space size was 400 400. The semi-empirical MO/8 and ZINDO results generally give the same results and the MO/8 excitation energies are smaller except for the large PAHs 6, 7, 8 and 14. Most likely, these latter exceptions would also give smaller energies if we had used a larger 10 10 CI space in the MO/8 calculations (but this needs a serious program alteration). The BLYP/631G data in Table 1 are generally smaller than semiempirical data, except for the cases 6 and 7. The differences between BLYP/3-21G and BLYP/6-31G results are less than 1% but are generally in the range of 0.01–0.02 eV. Thus for PAHs the time dependent BLYP S0 –S1 excitation energies are not so basis-set dependent and this is in good agreement with previous papers [14,15]. The errors of excited state calculations of PAHs using TD BLYP method were estimated to be about 0.3–0.4 eV [14,15], and it has been found in a recent paper [32] that in the case of large p-systems, TDDFT calculations unsystematically underestimate the S0 –S1 transition energies and the underestimation increases with system size. The differences from the octacene extrapolated experimental S0 –S1 excitation energy [32] are +0.10, +0.27 and )0.85 eV using MO/8, ZINDO
(100 100), and BLYP/6-31G levels of theory, respectively. We can say that the DFT results give a lower limit and the semi-empirical methods give an upper limit on the excitation energies. 3.1.1. Excited states of Series Type I Excitation energies of Series Type I (2, 3, 6, 7, 9, 10, 12) are given in Fig. 2. In the case of all S0 –S1 excitations the main configurations are p(HOMO)–p*(LUMO) types. The largest difference in S0 –S1 excitation energy between semi-empirical and DFT occurred in the case of 3, being more than 1 eV. Since in the case of octacene the S0 –S1 excitation energy underestimated by 0.85 eV using BLYP/6-31G method, we believe that the experimental results would be closer to the semi-empirical results. Three different methods show the same tendency but normally in the case of a series of PAHs, the excitation energies progressively decrease with an increase in the number of electrons in the p-system (practically equivalent to the number of carbon atoms). Interestingly, within this series there are unusual blue shifts from 6 to 9 and from 7 to 10. 3.1.2. Excited states of Series Type II Excitation energies of Series Type II (1, 4, 8, 14, 15, 16) are given in Fig. 3. Here the main configurations are again p(HOMO)–p*(LUMO) types in the S0 –S1 excitations. This picture however is not as clear as that of Series Type I because three different methods give three different tendencies in the S0 –S1 transition energies. Taking into consideration that when the system size increases the small CI space makes the MO/8 excitation energy larger and the TDDFT energies get much more
Table 1 S0 –S1 and Bright State (BS) excitation energies (in eV) and oscillator strengths (f , in a.u.) MO8/E
ZINDO
BLYP/6-31G
S0 –S1
BS
f
S0 –S1
BS
1 2 3
2.81 2.72 2.62
3.75 3.23 2.97
3.28 3.63 3.21
3.02 2.87 2.75
3.96 3.67 3.33
3.33 4.50 6.82
2.54 2.06 1.58
4 5 6
2.99 2.19 1.04
3.66 3.09 2.12
3.81 2.93 5.02
3.01 2.31 1.02
3.84 3.22 2.17
5.56 2.68 4.23
2.31 2.03 1.08
7 8 9
0.63 3.13 1.77
1.70 3.78 2.46
8.37 3.56 4.15
0.57 3.01 1.90
1.77 3.95 2.67
7.15 4.02 3.45
0.70 2.23 1.45
10 11 12
1.86 2.34 1.47
2.28 3.17 2.01
6.09 4.07 5.21
2.00 2.40 1.62
2.56 3.24 2.24
5.21 3.72 4.26
1.23 2.08 1.06
13 14 15 16
1.63 3.34
2.17 3.51
8.27 6.07
1.70 3.02 3.00 3.01
2.32 3.77 3.55 3.59
6.84 16.0 23.8 31.0
1.19 2.12
f
S0 –S1
BS
2.51
Experimental f
0.85
S0 –S1
BS
2.73
3.80
2.82 1.62
B. Hajgato, K. Ohno / Chemical Physics Letters 385 (2004) 512–518
515
4.00 3
Excitation Energies in eV
3.50 3.00
10 2.50
12
2.00
7
2
1.50 9 1.00
MO/8 Bright State MO/8 S 0 -S 1 ZINDO Bright State ZINDO S 0 -S 1 BLYP S 0 -S 1
6
0.50 0.00 70
90
92 110 130 Number of Carbon Atoms
150
Fig. 2. S0 –S1 and Bright State excitation energies (in eV) of PAH-Series Type I.
4.50 1
Excitation Energies in eV
4.00
4
8 14 16
15 3.50
MO/8 Bright State MO/8 S 0 -S 1 ZINDO Bright State ZINDO S 0 -S 1 BLYP S 0 -S 1
3.00 2.50 2.00 1.50 0
100
200 300 400 Number of Carbon Atoms
500
Fig. 3. S0 –S1 and Bright State excitation energies (in eV) of PAH-Series Type II.
underestimated, we suggest that the S0 –S1 transition energies in Series Type II do not change significantly or otherwise become slightly red shifted. Normally increasing the size of the PAH gives a much deeper color, but in the PAH-Series Type II the color does not noticeably change. Even the PAH 16 was predicted to have a light or pale color despite it containing 468 carbon atoms. In addition, the origin of fluctuations in the Bright States probably arises from the different periphery of the investigated systems. 3.1.3. Aromaticity of Series Type I All the investigated PAHs were expected to be aromatic so the different degree of aromaticity will correlate with the observed special properties. There are several theoretical ways to analyze aromaticity. Here, we chose three different methods, by using NICS values, NBO resonance energies (RE), and by using classical IBSE and HSE. The NICS(1) values are collected in Table 2 and the corresponding ring numberings are given in Fig. 3. The IBSE, HSE and NBO RE energies are
collected in Table 3, where all the energies were normalized to six carbon atoms (benzene units). NBO RE analyses have not been performed for larger PAHs since the increased size gives increased difficulties in choosing the desired Kekule structures and essentially the same values can be more easily obtained using IBSE and HSE. Investigating the NICS values, it is clear that 6 and 7 are more aromatic than the other compounds and their cavity also shows high aromatic character. In terms of the definition of superaromaticity by Schleyer and co-worker [20], these compounds can be denoted as superaromatic. The ÔcornerÕ rings (phenanthrene middlering type) of all investigated PAHs are less aromatic than the other rings, similar to the zigzag phenes [10]. It is also interesting that by condensing a circumference of benzene rings to a ÔrepleteÕ PAH (5, 9, 12) the less aromatic rings become more aromatic and vice-versa, except in the outer layer where the aromaticity of the rings are increasing as their distance from the ÔcornerÕ rings increases. On the other hand there are no outstanding
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B. Hajgato, K. Ohno / Chemical Physics Letters 385 (2004) 512–518
Table 2 above the plane of the molecule) NICS(1) values (1 A Molecules
Ring 1
Ring 2
Ring 3
Ring 4
Ring 5
Ring 6
Ring 7
Ring 8
Ring 9
– – –
)7.11 – –
)12.78 – –
– )4.19 –
– )12.28 –
– – )2.66
– – )10.95
– – )14.00
1 2 3
3.57 1.87 1.09
4 5 6
3.87 )17.45 )15.59
)12.64 )7.74 –
)6.87 )8.30 )19.50
)12.67 )17.53 )13.11
)7.09 – )3.33
)11.57 – )20.69
)3.36 – –
)10.22 – –
– – –
7 8 8
)16.57 4.06 )11.43a
–
– )12.59 )12.60a
– )6.92 )6.85a
)30.90 )11.48 )12.62a
)17.66 )3.23 )6.85a
3.26 )10.19 )12.64a
)18.88 )3.39 )7.08a
)23.37 )10.47 )11.50a
9 10 12
)5.60 6.54 )19.68
)15.42 – )9.42
)14.06 )4.50 )9.75
)5.02 )13.78 )19.52
)2.91 )16.35 )18.66
)15.99 )4.87 )7.79
– )0.48 1.27
– )10.16 )10.97
– )16.35 )18.95
a
3.91 )6.94a
Corresponding ring numbers are given in Fig. 4. NICS(1) value of benzene is )12.05. Add 10 to the ring number.
Table 3 Stoichiometry, Isodesmic Bond-Separation Energies (IBSE), Homodesmotic Stabilization Energies (HSE) and NBO Resonance Energies (NBO RE) Stoichiometry C Benzene
ZINDO H
BLYP/6-31G
IBSE
HSE
IBSE
HSE
NBO RE
6
6
355.8
215.6
322.0
110.7
1450.4
1 2 3
48 72 96
24 36 48
365.0 350.5 339.9
131.4 117.0 106.4
415.5 412.0 407.6
99.6 96.1 91.7
1785.7 1750.6
4 5 6
82 54 90
38 18 30
372.3 401.4 381.8
131.9 136.8 117.1
422.4 481.6 466.3
98.9 130.8 115.5
1964.5 1918.0
7 8 9
126 116 96
42 52 24
372.3 374.9 408.8
107.7 131.7 128.6
463.6 425.2 502.4
112.9 98.5 134.2
1969.5
10 11 12
144 78 150
36 30 30
402.7 408.7 414.5
122.5 153.7 125.0
494.2 458.8 515.4
126.0 118.8 136.8
13 14 15 16
222 204 360 468
42 84 144 180
436.6 382.5 384.6 387.4
145.1 132.5 132.4 132.3
520.1 431.9
139.1 97.6
Energy units in kJ/mol.
values in the IBSE, HSE and NBO RE energy sets. The changes are smooth and progressive, and all systems are highly aromatic (but no superaromatic species). Combining the results of the two fundamentally different explanations of aromaticity, the following conclusion can be made. The investigated systems are overall highly aromatic but there are aromatic and slightly less aromatic rings (benzenoid structure). The p-systems of the individual rings are more or less separated from each other, and thus the p-electrons cannot flow through the system with complete freedom (being more localized). It is in good accordance with the chemical graph theories [33–35], which assign the major origin of aromaticity of
small (4n þ 2)-membered conjugated circuits. In the case of 6 and 7 the cavities have annulenoid structure so the p-electrons can flow in larger circuits. The annulenoid structure of the cavity is also supported by the bond length equalization. (The standard deviations of the calculated carbon–carbon bond lengths in the cavity are 0.026, 0.021, 0.025, 0.028 and 0.023 in 1, 6, 10, 2 and 7, respectively.) Considering that in the case of a widely delocalized p-system the excitation energies are lower, the blue shifts calculated within this series are just a consequence of a previous very large red shift. In NBO RE analysis there are many different kinds of localizations (Kekule structures). The NBO RE is the
B. Hajgato, K. Ohno / Chemical Physics Letters 385 (2004) 512–518
5 6 7 4
8
3 7 8 9 5 6 3 4 2 1
517
Lastly, the oscillator strengths of the Bright States of 14, 15, and 16 are intriguing, and a more in depth investigation would be interesting from an astronomical point of view.
1 2
4. Conclusion
3 1
4 5
9 6 7 8 19 11 12 18 2 13 17 16 15 14 Fig. 4. Ring numbering for NICS calculations.
energy difference between the non-localized and the NBO localized Kekule structures. Clearly not all of the Kekule structures have been calculated, but some of the important basic types of localized structures were analyzed and shown to possess different energies. In Table 3 the energy of the lowest calculated Kekule structures was used. 3.1.4. Aromaticity of Series Type II The NICS(1) values are collated in Table 2 and the corresponding ring numbers are given in Fig. 4. The IBSE and HSE values in Table 3 were normalized to six carbon atoms (benzene units). The NICS values show that in the case of 4 and 8 the alternating high and low aromatic rings become less aromatic as they get closer to the least aromatic adjoining (triple condensed) benzene ring. In this series, the IBSE values increase while the HSE values decrease or remain uniform. This shows that even though delocalization increases, aromaticity still decreases or remains the same because the IBSE and HSE values encompass many different types of stabilization energies (for example cyclization, delocalization and aromatization) and the HSE values contain relatively more contributions from aromatic stabilization energy. Combining the results of two fundamentally different explanations of aromaticity the following conclusion can be made. The investigated systems are overall highly aromatic but contain both aromatic and slightly less aromatic rings. The p-systems of the individual rings are more or less separated from each other by the adjoining benzene rings, and hence the complete freeflowing of p-electrons occurs only between triple condensed rings. Since with an increase in system size the area between the adjacent rings does not increase, the S0 – S1 transition energies will only change marginally.
In the present study we have found a new series of giant PAHs that in some cases show blue shift with extended sizes. The analysis of the aromaticity of these systems give us an easy explanation of the blue shifts. All investigated systems are highly aromatic and contain aromatic and slightly aromatic rings. Interestingly, compounds 6 and 7 have annulenoid type aromatic cavity, which means widely delocalized p-electrons. The blue shift within Series Type I apparently is the direct consequence of a previous extreme red shift. In the case of Series Type II, the triple condensed rings somehow block aromatic conjugation over the whole system and the infinite layer is expected to have high excitation energies with slight coloring.
Acknowledgements This research was partially supported by the Ministry of Education, Science, Sports and Culture, a Grant-inAid for the COE project, Giant Molecules and Complex Systems, 2003.
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Novel series of giant polycyclic aromatic hydrocarbons: electronic structure and aromaticity Bal azs Hajgat o, Koichi Ohno
*
Department of Chemistry, Graduate School of Science, Tohoku University, Aramaki, Aoba-ku, Sendai 980-8578, Japan Received 6 November 2003; in final form 2 January 2004 Published online:
Abstract We present a theoretical study on a novel series of Polycyclic Aromatic Hydrocarbons (PAHs) having hollow sites focusing particularly on electronic structures and spectroscopic aspects using molecular orbital and DFT levels of theory. We have found in the case of a new series of PAHs that the UV–Vis absorption spectra of some PAHs show blue shifts as the number of electrons increases in the p-system. Unusual behaviors of giant PAHs are discussed in connection with aromaticity. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Polycyclic Aromatic Hydrocarbons (PAHs) consist of two or more condensed aromatic rings. They occur in nature mostly in traces in different matrices and their origin is both anthropogenic and natural. PAHs have long been in the focus of both theoretical and experimental researches due to their importance in several fields of science. PAHs form for example an important group of extremely hazardous environmental pollutants and some of them are highly cancerous [1]. Numerous different PAHs are present in petroleum samples, and they are also produced in the burning of mineral oil derivates [2]. Large PAHs are frequently used as model compounds for graphite sheets and glassy carbon materials [3]. PAHs exist not only in the Earth but are commonly accepted as being ubiquitous in the interstellar medium [4] and presumably responsible for some of the Diffuse Interstellar Bands and Unidentified Emission Bands in the mid–IR range [5]. Several different sizes of PAHs have been synthesized and recently some giant ones have been made to contain 114 [6] and 222 [7] carbon atoms. The solubility of large PAHs drastically decreases with their size and the giant ones are completely insoluble, hence structure elucida*
Corresponding author. Fax: +81-22-217-6580. E-mail address: [email protected] (K. Ohno).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.01.029
tion methods are rather limited [6,7]. There are several papers on the theoretical study of the electronic structure and electronic spectra of different PAHs, together with their positive and negative radicals, which range from semi-empirical [8–10] to ab initio [11–13] methods including DFT levels of theory [14,15]. In their early work, Stein and Brown [8] have shown that the HOMO– LUMO gaps of the edge structure of large condensed PAHs have a higher influence over the overall systemsize. They have also shown that in a series of growing PAHs with the same edge structure, the HOMO– LUMO gap is progressively decreasing as the size of the PAHs increases to the limiting value of zero. Hiruta et al. [10] have shown that the zigzag phenes at the ground state have less mobile p-electrons than the linear acenes because they have a tendency to localize in a particular portion of the molecular framework. Dias and other workers [16] by using molecular graph theory have shown that there exist large conjugated systems with a significant non-zero limiting band-gap. All those investigated systems were constructed of hexagonal rings without hollow sites. The only exception is kekulene that has been widely investigated especially concerning with its superaromaticity [17–21]. Some earlier papers suggest that kekulene is superaromatic, although new techniques and more extended investigations negate the possibility of superaromaticity and verify the fact of high aromaticity.
B. Hajgato, K. Ohno / Chemical Physics Letters 385 (2004) 512–518
In this Letter, we systematically investigated some large to giant PAHs that were constructed entirely from condensed hexagon rings, which possess hollow sites. The investigation was made to especially focus on electronic spectroscopy as a useful elucidation tool of giant PAHs. We have also addressed the recurring question of aromaticity in a bit more detail in the case of some of our investigated compounds.
2. Computational methods
1
513
2
3 4
5
6
7 8
All calculations were carried out using GA U S S I A N 98 [22] and MO/8E [23,24] program packages. Since the calculated electronic spectra is not so sensitive for the geometries used [14,15] and some earlier works successfully used semi-empirical INDO/S at the geometry of AM1 in predicting excited states [9], we also decided to use semi-empirical methods for geometry optimizations. However we experienced in some cases serious geometry convergence problems using MNDO, AM1, and PM3 methods, so we have chosen the CNDO method for geometry optimizations. In accordance with other authors [14,15] we performed time-dependent density functional theory using Becke exchange [25] and Lee et al. correlation [26] functionals in conjunction with 3-21G and 6-31G basis sets to calculate excited states. In addition, we also calculated ZINDO, and MO/8E excited states. Aromatic stabilizations were estimated using Isodesmic Bond Separation Energies (IBSE) [27] and Homodesmotic Stabilization Energies (HSE) [27]. Resonance energy calculations were performed using the NBO [28] analysis at the BLYP/6-31G level of theory. Nucleus-Independent Chemical Shifts (NICS(1) [29,30]) were calculated using the GIAO-SCF/6-31G level of theory.
9
11
10
14
12 13
15
16
Fig. 1. Hexagonal structures of PAHs investigated. PAH-Series Type I: 1, 5 and 2, 6, 9 and 3, 7, 10, 12. PAH-Series Type II: 1, 4, 8, 14, 15, 16.
3. Results and discussion The hexagon structures of the PAHs investigated are shown in Fig. 1. To generate a new series of molecules we chose the widely investigated kekulene as a base molecule because of the cavity. There are two different ways to generate a new series of PAHs based on kekulene. One involves increasing the size of the super-ring and condensing additional benzene rings to the periphery and inside the cavity (Series Type I, for example 2, 6, 9 and 3, 7, 10, 12). It is important to keep the shape of the molecules similar because this will strongly affect the excited states [8]. Another one is to condense the superrings making dimer, trimers and other oligomers (Series Type II, for example 1, 4, 8, 14, 15, 16). Since tendencies will be different in the case of Series Types I and II, we will discuss them separately. For conciseness, we will dispense with detailing geometrical parameters due to
this being beyond the scope of this Letter. The stationary points were not characterized by harmonic vibrational frequency analysis because all the structures have expected symmetries both in experiment and theory (D6h for 1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, D2h for 4, and C2v for 8). 3.1. Reliability of calculated excited states Generally all the methods used give almost perfect excitation energies for small to moderate sized PAHs, but in the case of large and giant sized PAHs the picture is not so clear. Since we do not have experimental electronic spectra for series type I nor series type II structures we evaluated the quality of our calculations. The molecules 11 and 13 are included for testing purposes because they are the largest PAHs with available
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experimental electronic spectra. The calculated electronic transitions, oscillator strengths, and available experimental results (for 1 [31], 11 [6], and 13 [7]) are listed in Table 1. The term Bright State was used in case of the largest oscillator strengths. In the case of ZINDO calculations the size of the used CI space was increased systematically until the excitation energies did not change considerably (less than 1%). Table 1 contains the ZINDO results using 200 200 (200 electrons in 200 orbitals) CI space except for 15 and 16 where the used CI space size was 400 400. The semi-empirical MO/8 and ZINDO results generally give the same results and the MO/8 excitation energies are smaller except for the large PAHs 6, 7, 8 and 14. Most likely, these latter exceptions would also give smaller energies if we had used a larger 10 10 CI space in the MO/8 calculations (but this needs a serious program alteration). The BLYP/631G data in Table 1 are generally smaller than semiempirical data, except for the cases 6 and 7. The differences between BLYP/3-21G and BLYP/6-31G results are less than 1% but are generally in the range of 0.01–0.02 eV. Thus for PAHs the time dependent BLYP S0 –S1 excitation energies are not so basis-set dependent and this is in good agreement with previous papers [14,15]. The errors of excited state calculations of PAHs using TD BLYP method were estimated to be about 0.3–0.4 eV [14,15], and it has been found in a recent paper [32] that in the case of large p-systems, TDDFT calculations unsystematically underestimate the S0 –S1 transition energies and the underestimation increases with system size. The differences from the octacene extrapolated experimental S0 –S1 excitation energy [32] are +0.10, +0.27 and )0.85 eV using MO/8, ZINDO
(100 100), and BLYP/6-31G levels of theory, respectively. We can say that the DFT results give a lower limit and the semi-empirical methods give an upper limit on the excitation energies. 3.1.1. Excited states of Series Type I Excitation energies of Series Type I (2, 3, 6, 7, 9, 10, 12) are given in Fig. 2. In the case of all S0 –S1 excitations the main configurations are p(HOMO)–p*(LUMO) types. The largest difference in S0 –S1 excitation energy between semi-empirical and DFT occurred in the case of 3, being more than 1 eV. Since in the case of octacene the S0 –S1 excitation energy underestimated by 0.85 eV using BLYP/6-31G method, we believe that the experimental results would be closer to the semi-empirical results. Three different methods show the same tendency but normally in the case of a series of PAHs, the excitation energies progressively decrease with an increase in the number of electrons in the p-system (practically equivalent to the number of carbon atoms). Interestingly, within this series there are unusual blue shifts from 6 to 9 and from 7 to 10. 3.1.2. Excited states of Series Type II Excitation energies of Series Type II (1, 4, 8, 14, 15, 16) are given in Fig. 3. Here the main configurations are again p(HOMO)–p*(LUMO) types in the S0 –S1 excitations. This picture however is not as clear as that of Series Type I because three different methods give three different tendencies in the S0 –S1 transition energies. Taking into consideration that when the system size increases the small CI space makes the MO/8 excitation energy larger and the TDDFT energies get much more
Table 1 S0 –S1 and Bright State (BS) excitation energies (in eV) and oscillator strengths (f , in a.u.) MO8/E
ZINDO
BLYP/6-31G
S0 –S1
BS
f
S0 –S1
BS
1 2 3
2.81 2.72 2.62
3.75 3.23 2.97
3.28 3.63 3.21
3.02 2.87 2.75
3.96 3.67 3.33
3.33 4.50 6.82
2.54 2.06 1.58
4 5 6
2.99 2.19 1.04
3.66 3.09 2.12
3.81 2.93 5.02
3.01 2.31 1.02
3.84 3.22 2.17
5.56 2.68 4.23
2.31 2.03 1.08
7 8 9
0.63 3.13 1.77
1.70 3.78 2.46
8.37 3.56 4.15
0.57 3.01 1.90
1.77 3.95 2.67
7.15 4.02 3.45
0.70 2.23 1.45
10 11 12
1.86 2.34 1.47
2.28 3.17 2.01
6.09 4.07 5.21
2.00 2.40 1.62
2.56 3.24 2.24
5.21 3.72 4.26
1.23 2.08 1.06
13 14 15 16
1.63 3.34
2.17 3.51
8.27 6.07
1.70 3.02 3.00 3.01
2.32 3.77 3.55 3.59
6.84 16.0 23.8 31.0
1.19 2.12
f
S0 –S1
BS
2.51
Experimental f
0.85
S0 –S1
BS
2.73
3.80
2.82 1.62
B. Hajgato, K. Ohno / Chemical Physics Letters 385 (2004) 512–518
515
4.00 3
Excitation Energies in eV
3.50 3.00
10 2.50
12
2.00
7
2
1.50 9 1.00
MO/8 Bright State MO/8 S 0 -S 1 ZINDO Bright State ZINDO S 0 -S 1 BLYP S 0 -S 1
6
0.50 0.00 70
90
92 110 130 Number of Carbon Atoms
150
Fig. 2. S0 –S1 and Bright State excitation energies (in eV) of PAH-Series Type I.
4.50 1
Excitation Energies in eV
4.00
4
8 14 16
15 3.50
MO/8 Bright State MO/8 S 0 -S 1 ZINDO Bright State ZINDO S 0 -S 1 BLYP S 0 -S 1
3.00 2.50 2.00 1.50 0
100
200 300 400 Number of Carbon Atoms
500
Fig. 3. S0 –S1 and Bright State excitation energies (in eV) of PAH-Series Type II.
underestimated, we suggest that the S0 –S1 transition energies in Series Type II do not change significantly or otherwise become slightly red shifted. Normally increasing the size of the PAH gives a much deeper color, but in the PAH-Series Type II the color does not noticeably change. Even the PAH 16 was predicted to have a light or pale color despite it containing 468 carbon atoms. In addition, the origin of fluctuations in the Bright States probably arises from the different periphery of the investigated systems. 3.1.3. Aromaticity of Series Type I All the investigated PAHs were expected to be aromatic so the different degree of aromaticity will correlate with the observed special properties. There are several theoretical ways to analyze aromaticity. Here, we chose three different methods, by using NICS values, NBO resonance energies (RE), and by using classical IBSE and HSE. The NICS(1) values are collected in Table 2 and the corresponding ring numberings are given in Fig. 3. The IBSE, HSE and NBO RE energies are
collected in Table 3, where all the energies were normalized to six carbon atoms (benzene units). NBO RE analyses have not been performed for larger PAHs since the increased size gives increased difficulties in choosing the desired Kekule structures and essentially the same values can be more easily obtained using IBSE and HSE. Investigating the NICS values, it is clear that 6 and 7 are more aromatic than the other compounds and their cavity also shows high aromatic character. In terms of the definition of superaromaticity by Schleyer and co-worker [20], these compounds can be denoted as superaromatic. The ÔcornerÕ rings (phenanthrene middlering type) of all investigated PAHs are less aromatic than the other rings, similar to the zigzag phenes [10]. It is also interesting that by condensing a circumference of benzene rings to a ÔrepleteÕ PAH (5, 9, 12) the less aromatic rings become more aromatic and vice-versa, except in the outer layer where the aromaticity of the rings are increasing as their distance from the ÔcornerÕ rings increases. On the other hand there are no outstanding
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B. Hajgato, K. Ohno / Chemical Physics Letters 385 (2004) 512–518
Table 2 above the plane of the molecule) NICS(1) values (1 A Molecules
Ring 1
Ring 2
Ring 3
Ring 4
Ring 5
Ring 6
Ring 7
Ring 8
Ring 9
– – –
)7.11 – –
)12.78 – –
– )4.19 –
– )12.28 –
– – )2.66
– – )10.95
– – )14.00
1 2 3
3.57 1.87 1.09
4 5 6
3.87 )17.45 )15.59
)12.64 )7.74 –
)6.87 )8.30 )19.50
)12.67 )17.53 )13.11
)7.09 – )3.33
)11.57 – )20.69
)3.36 – –
)10.22 – –
– – –
7 8 8
)16.57 4.06 )11.43a
–
– )12.59 )12.60a
– )6.92 )6.85a
)30.90 )11.48 )12.62a
)17.66 )3.23 )6.85a
3.26 )10.19 )12.64a
)18.88 )3.39 )7.08a
)23.37 )10.47 )11.50a
9 10 12
)5.60 6.54 )19.68
)15.42 – )9.42
)14.06 )4.50 )9.75
)5.02 )13.78 )19.52
)2.91 )16.35 )18.66
)15.99 )4.87 )7.79
– )0.48 1.27
– )10.16 )10.97
– )16.35 )18.95
a
3.91 )6.94a
Corresponding ring numbers are given in Fig. 4. NICS(1) value of benzene is )12.05. Add 10 to the ring number.
Table 3 Stoichiometry, Isodesmic Bond-Separation Energies (IBSE), Homodesmotic Stabilization Energies (HSE) and NBO Resonance Energies (NBO RE) Stoichiometry C Benzene
ZINDO H
BLYP/6-31G
IBSE
HSE
IBSE
HSE
NBO RE
6
6
355.8
215.6
322.0
110.7
1450.4
1 2 3
48 72 96
24 36 48
365.0 350.5 339.9
131.4 117.0 106.4
415.5 412.0 407.6
99.6 96.1 91.7
1785.7 1750.6
4 5 6
82 54 90
38 18 30
372.3 401.4 381.8
131.9 136.8 117.1
422.4 481.6 466.3
98.9 130.8 115.5
1964.5 1918.0
7 8 9
126 116 96
42 52 24
372.3 374.9 408.8
107.7 131.7 128.6
463.6 425.2 502.4
112.9 98.5 134.2
1969.5
10 11 12
144 78 150
36 30 30
402.7 408.7 414.5
122.5 153.7 125.0
494.2 458.8 515.4
126.0 118.8 136.8
13 14 15 16
222 204 360 468
42 84 144 180
436.6 382.5 384.6 387.4
145.1 132.5 132.4 132.3
520.1 431.9
139.1 97.6
Energy units in kJ/mol.
values in the IBSE, HSE and NBO RE energy sets. The changes are smooth and progressive, and all systems are highly aromatic (but no superaromatic species). Combining the results of the two fundamentally different explanations of aromaticity, the following conclusion can be made. The investigated systems are overall highly aromatic but there are aromatic and slightly less aromatic rings (benzenoid structure). The p-systems of the individual rings are more or less separated from each other, and thus the p-electrons cannot flow through the system with complete freedom (being more localized). It is in good accordance with the chemical graph theories [33–35], which assign the major origin of aromaticity of
small (4n þ 2)-membered conjugated circuits. In the case of 6 and 7 the cavities have annulenoid structure so the p-electrons can flow in larger circuits. The annulenoid structure of the cavity is also supported by the bond length equalization. (The standard deviations of the calculated carbon–carbon bond lengths in the cavity are 0.026, 0.021, 0.025, 0.028 and 0.023 in 1, 6, 10, 2 and 7, respectively.) Considering that in the case of a widely delocalized p-system the excitation energies are lower, the blue shifts calculated within this series are just a consequence of a previous very large red shift. In NBO RE analysis there are many different kinds of localizations (Kekule structures). The NBO RE is the
B. Hajgato, K. Ohno / Chemical Physics Letters 385 (2004) 512–518
5 6 7 4
8
3 7 8 9 5 6 3 4 2 1
517
Lastly, the oscillator strengths of the Bright States of 14, 15, and 16 are intriguing, and a more in depth investigation would be interesting from an astronomical point of view.
1 2
4. Conclusion
3 1
4 5
9 6 7 8 19 11 12 18 2 13 17 16 15 14 Fig. 4. Ring numbering for NICS calculations.
energy difference between the non-localized and the NBO localized Kekule structures. Clearly not all of the Kekule structures have been calculated, but some of the important basic types of localized structures were analyzed and shown to possess different energies. In Table 3 the energy of the lowest calculated Kekule structures was used. 3.1.4. Aromaticity of Series Type II The NICS(1) values are collated in Table 2 and the corresponding ring numbers are given in Fig. 4. The IBSE and HSE values in Table 3 were normalized to six carbon atoms (benzene units). The NICS values show that in the case of 4 and 8 the alternating high and low aromatic rings become less aromatic as they get closer to the least aromatic adjoining (triple condensed) benzene ring. In this series, the IBSE values increase while the HSE values decrease or remain uniform. This shows that even though delocalization increases, aromaticity still decreases or remains the same because the IBSE and HSE values encompass many different types of stabilization energies (for example cyclization, delocalization and aromatization) and the HSE values contain relatively more contributions from aromatic stabilization energy. Combining the results of two fundamentally different explanations of aromaticity the following conclusion can be made. The investigated systems are overall highly aromatic but contain both aromatic and slightly less aromatic rings. The p-systems of the individual rings are more or less separated from each other by the adjoining benzene rings, and hence the complete freeflowing of p-electrons occurs only between triple condensed rings. Since with an increase in system size the area between the adjacent rings does not increase, the S0 – S1 transition energies will only change marginally.
In the present study we have found a new series of giant PAHs that in some cases show blue shift with extended sizes. The analysis of the aromaticity of these systems give us an easy explanation of the blue shifts. All investigated systems are highly aromatic and contain aromatic and slightly aromatic rings. Interestingly, compounds 6 and 7 have annulenoid type aromatic cavity, which means widely delocalized p-electrons. The blue shift within Series Type I apparently is the direct consequence of a previous extreme red shift. In the case of Series Type II, the triple condensed rings somehow block aromatic conjugation over the whole system and the infinite layer is expected to have high excitation energies with slight coloring.
Acknowledgements This research was partially supported by the Ministry of Education, Science, Sports and Culture, a Grant-inAid for the COE project, Giant Molecules and Complex Systems, 2003.
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