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Density functional theory study of the canthaxanthin and other carotenoid radical cations
Chemical Physics Letters 366 (2002) 73–81 www.elsevier.com/locate/cplett
Density functional theory study of the canthaxanthin and other carotenoid radical cations Jing-Dong Guo, Yi Luo 1, Fahmi Himo
*
Theoretical Chemistry, Stockholm University, Royal Institute of Technology, SCFAB, Stockholm SE-106 91, Sweden Received 7 August 2002; in final form 18 September 2002
Abstract B3LYP hybrid density functional theory method is employed to study the five carotenoid radical cations of canthaxanthin (1), 70 ,70 -dimethyl-70 -apo-b-carotene (2), 80 -apo-b-carotene-80 -al hydrazone (3), 70 ,70 -dicyano-70 -apo-bcarotene (4), and 80 -apo-b-carotene-80 -al (5). The radicals are characterized by means of their geometries, spin populations, and isotropic hyperfine coupling constants. It is shown that for all the systems, the unpaired spin is delocalized over the whole p-conjugated system in an odd-alternant pattern. As a result of this, the hyperfine coupling constants are rather low. The radical cations of 1, 2, and 3, have very similar properties to the unsubstituted b-carotene radical, while the dicyano- and aldehyde-substitutions result in significantly different electronic structures. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Carotenoids are ubiquitous in plants, animals and bacteria [1]. They play a vital role in the photosynthetic process and also in human health by acting as biological antioxidants, protecting cells and tissues from the damaging effects of radicals and singlet oxygen [2]. Some other health benefits of carotenoids are, e.g., inhibition of the development of certain types of cancers [3] and enhancement of immune system function [4].
*
Corresponding author. Fax: +46-8-347817. E-mail addresses: [email protected] (Y. Luo), himo@ theochem.kth.se (F. Himo). 1 Also corresponding author.
The carotene cofactor in photosystem II (PSII) can act as an alternate electron donor under conditions where the primary electron donor pathway is inhibited, and the carotene radical cation has indeed been detected in PSII reaction center using a variety of spectroscopic methods [5–16]. There is hence a fundamental interest in understanding the properties of carotenoid radical cations. Kispert and co-workers have in a large number of studies extensively examined various properties of several carotenoid radicals generated in vitro using different techniques [17–28]. Despite the importance of this class of molecules, very little quantum chemical theoretical work has been done to study their properties. The size of molecules (up to 100 atoms) has been one
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 1 5 4 1 - 5
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J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81
of the key obstacles, and has limited the study of them to some semi-empirical calculations [29]. Very recently, we studied the b-carotene radical cation using the B3LYP density functional theory (DFT) method [30]. These high-level calculations gave a quite different picture of the carotene radical cation from that reported previously. The spin was shown to be delocalized to a much higher extent, resulting in relatively low methyl hyperfine couplings, the highest in the order of 8 MHz. The results were in excellent agreement with recent electron paramagnetic resonance (EPR) measurements of the carotene radical in solution and in PSII. It was also concluded that semi-empirical methods used in previous studies are not accurate enough to reproduce the data [30]. In the present study, we use the same B3LYPdensity functional method [31] to characterize five other members of the carotenoid radical cation family in terms of their geometries and spin and hyperfine properties. The molecules are: canthaxanthin (1), 70 ,70 -dimethyl-70 -apo-b-carotene (2), 80 -apo-b-carotene-80 -al hydrazone (3), 70 ,70 -dicyano-70 -apo-b-carotene (4), and 80 -apo-b-carotene80 -al (5), as displayed in Fig. 1. These were chosen to illustrate different donor–acceptor substituent effects on the properties of the carotenoids. Furthermore, they have been studied experimentally and there exist hyperfine parameters for some of them.
2. Computational details All the calculations reported in the present study were carried out using the density functional theory (DFT) functional B3LYP [31], as implemented in the GA U S S I A N 98 program package [32]. The geometries were optimized with the double zeta plus polarization basis set 6-31G(d,p), with no symmetry constraints. The hyperfine coupling constants were calculated at the same level of theory, which was demonstrated to be adequate in the previous study [30]. The spin densities reported are calculated using standard Mulliken population analysis.
3. Results and discussion 3.1. Geometry As in the case of the all-trans b-carotene radical cation [30], the cyclohexene ring groups of the carotenoid radicals studied here were found to adopt two orientations relative to the polyene chain. The first has a \C5–C6–C7–C8 dihedral angle of around 30° and the other a dihedral angles of around 170°. The energy difference between these two minima is very small, on the order of a few tenths of a kcal/mol, favoring the former. For the properties under consideration, the two minima yield very similar results. Selected optimized geometric parameters of the molecules are listed in Table 1, and the bond lengths of the polyene chain are graphically displayed in Figs. 2 and 3. As seen from Fig. 2, the canthaxanthin radical cation 1 shows very similar geometric properties as the unsubstituted b-carotene 6 calculated previously [30]. The molecule is strongly conjugated, with the difference between single and double bonds being smaller at the middle of the polyene chain than towards the sides. For example, the central C14–C15 bond has the same length as the ), and is only 0.006 A shorter C15–C150 (1.397 A than the C13–C14 bond (1.403 A). Closer to the head groups, the difference between the C6–C7 (1.459 vs. 1.365 A ). and C7–C8 bonds is 0.094 A The degree of conjugation in a molecule can be evaluated by means of the bond length alternation (BLA) parameter, defined as the total length difference between single bonds and double bonds. We have calculated the BLA parameter in two ways, from C5 to the central C15 (called BLA5–15 ), and from C5 to C80 at the other end of the molecule (called BLA5–80 ). As seen from Table 1, the canthaxanthin radical cation has slightly larger BLA parameters than the b-carotene (0.20 vs. for BLA5–15 and 0.29 vs. 0.23 A for 0.17 A BLA5–80 ), indicating a slightly lower degree of conjugation in the former compared to the latter. Interestingly, the two electron-donating substitutions in 2 (dimethyl) and 3 (hydrazone) show smaller difference from the unsubstituted b-carotene compared to the canthaxanthin molecule (see
J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81
75
Fig. 1. Numbering schemes and B3LYP/6-31G(d,p) calculated spin density distributions of the carotenoid radical cations. The b-carotene calculated previously [30] is included for comparison.
Table 1 and Fig. 3). Both the BLA5–15 and BLA5–80 parameters are almost identical in 2 and 3 to those of 6. Large effects are, however, seen for the electron-withdrawing substitutions in 4 (dicyano) and 5 (aldehyde). As seen from Fig. 3, the largest changes occur, as expected, close to the substituents. The introduction of the triple bonds in the dicyano-substituted carotene 4 has an overall effect of increasing the conjugation of the molecule, as
seen from the BLA5–15 and BLA5–80 parameters, which decrease relative to b-carotene. The aldehyde-substitution 5, on the other hand, exhibits an interesting feature. The BLA5–15 is smaller than the corresponding parameter in the unsubstituted ), while the BLA5–80 is b-carotene (0.12 vs. 0.17 A ). This indicates a much larger (0.33 vs. 0.23 A greater fluctuation closer to the aldehyde functionality, a fact clearly visible in Fig. 3.
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Table 1 and (°)) of the carotenoid radical cations optimized at the B3LYP/6-31G(d,p) level Selected geometric parameters (A 1
2
3
4
5
6a
C4–C5 C5–C6 C6–C7 C7–C8 C8–C9 C9–C10 C10–C11 C11–C12 C12–C13 C13–C14 C14–C15 C15–C150 C150 –C140 C140 –C130 C130 –C120 C120 –C110 C110 –C100 C100 –C90 C90 –C80 C80 –C70 C70 –C60 C60 –C50 C50 –C40 C4–O4 ðC40 –O40 Þ C80 –X
1.501 1.371 1.459 1.365 1.438 1.389 1.410 1.387 1.414 1.403 1.397 1.397 1.397 1.403 1.414 1.387 1.410 1.389 1.438 1.365 1.459 1.371 1.501 1.223
1.511 1.370 1.454 1.371 1.432 1.394 1.405 1.391 1.409 1.407 1.393 1.400 1.393 1.407 1.410 1.389 1.408 1.392 1.441 1.368 1.515/1.510
1.511 1.369 1.455 1.370 1.433 1.393 1.406 1.391 1.409 1.407 1.393 1.400 1.393 1.407 1.409 1.391 1.405 1.391 1.428
1.508 1.375 1.446 1.377 1.426 1.399 1.400 1.395 1.405 1.411 1.392 1.400 1.395 1.405 1.415 1.385 1.414 1.388 1.436 1.376 1.430/1.432
1.509 1.375 1.446 1.377 1.426 1.400 1.400 1.394 1.407 1.408 1.396 1.395 1.402 1.395 1.428 1.373 1.429 1.366 1.483
1.511 1.369 1.455 1.370 1.433 1.392 1.406 1.390 1.410 1.407 1.394 1.399 1.394 1.407 1.410 1.390 1.406 1.392 1.433 1.370 1.455 1.369 1.511
\C5–C6–C7 \C5–C6–C7–C8
122.7 38.1
123.0 33.1
123.0 34.1
123.1 30.0
123.3 28.8
123.0 34.3
BLA5–15 b BLA5–80 c
0.203 0.286
0.160 0.224
0.166 0.212
0.112 0.194
0.121 0.334
0.170 0.225
1.309
1.216
a
From Ref. [30]. Bond length alternation from C5 to C15. c Bond length alternation from C5 to C80 . b
3.2. Spin distribution The b-carotene radical was previously shown to exhibit an odd-alternant spin pattern, with positive spins alternating with smaller negative spins [30]. This general pattern is preserved in the canthaxanthin and the other substituted radical cations (calculated spin densities are displayed in Fig. 1). The largest spin densities on the polyene chain of the canthaxanthin radical cation are found at positions 7,70 (0.18), 9,90 (0.18), 11,110 (0.15) and 13,130 (0.10), very similar to the b-carotene spins. Also here, there is a significant spin delocalization onto the double bonds of the ring headgroups. The C5 and C6 centers carry respectively, 0.10 and
)0.06 of the unpaired spin, and the oxygens possess 0.03 each. The two electron-donating substitutions in 2 and 3 introduce very little modification to the spin population pattern on the polyene chain. Although the hydrazone moiety of 3 has as much as 0.24 of the unpaired spin, the spin of the rest of the molecule looks very similar to both b-carotene and canthaxanthin. As is the case for geometry, the largest changes in the spin distribution are seen for the electronwithdrawing substitutions in 4 and 5. In the cases of 1, 2, 3, and 6 it is observed that the carbon centers between the C14 and C140 centers have small spins (
J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81
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Fig. 2. Bond lengths of canthaxanthin compared to b-carotene (from [30]).
these centers are larger. For 4 and 5 this low spin region is moved two double bonds toward the cyclohexene ring, to between the C10 and C13 centers. Another effect of the electron-withdrawing substitutions is the increased spin polarization in the radicals. That is, the absolute magnitudes of both the positive and the negative spins increase. These effects are displayed graphically in Fig. 4. 3.3. Hyperfine coupling constants The spin density distributions described above are directly reflected in the hyperfine coupling constants. The proton hyperfine couplings of carotenoid radical cations can be divided into two classes, methyl proton couplings and a-proton couplings. In frozen solution, methyl protons give rise to intense and narrow ENDOR lines, while a-protons give rise to broadened lines, which normally escape detection. The B3LYP/6-31G(d,p) calculated isotropic methyl hyperfine couplings are
given in Table 2 and the a-proton couplings in Table 3. Canthaxanthin has six methyl groups in three distinct positions (5, 9, and 13). The magnitudes of the hyperfine couplings of these are expected to follow the trend: Aiso ð9Þ > Aiso ð13Þ Aiso ð5Þ, since the spin densities at these positions show this trend. Indeed the largest calculated isotropic methyl coupling was found on the 9,90 positions, with a magnitude of 9.5 MHz. The Aiso ð13Þ and Aiso ð5Þ couplings are smaller and almost equal, with magnitudes of 5.8 and 5.7 MHz, respectively. These values are quite close to the b-carotene methyl couplings, which were previously calculated to 8.5, 5.1, and 6.8 MHz, for the Aiso ð9Þ, Aiso ð13Þ, and Aiso ð5Þ, respectively [30]. ENDOR experiments by Kispert and co-workers found the three methyl hyperfine coupling constants to be ca. 2, 8, and 13 MHz [18,20,28]. These were assigned to positions 5, 9, and 13, respectively, based on RHF-INDO/SP calculations,
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Fig. 3. Bond lengths of molecules 2–5.
which gave couplings very close to the experimental values. This assignment suggests higher spin concentration in the middle polyene chain than toward the sides of the molecule, in sharp contrast to our results presented above. We found the spin concentration in the middle of the chain to be smaller than at the ends (see Fig. 1). Considering that the DFT calculations presented here are more accurate than the semi-empirical RHFINDO/SP calculations, a fact that was further established previously for the b-carotene radical [30], the results here show that the experimental couplings are misassigned. This conclusion is also valid for radicals 4 and 5, for which the same approach was used to assign the experimental hyperfine couplings (see Table 2). Apart from the obvious loss of the H4 proton couplings, the 1 H couplings of canthaxanthin are very similar to those of the b-carotene (see Table 3). The largest isotropic polyene chain a-proton
hyperfine couplings are found at 7,70 positions ()12.4 MHz) and 11,110 positions ()9.9 MHz), reflecting the high spin population at these centers (0.18 and 0.16, respectively). The other a-protons have smaller hfcÕs, lower than 5 MHz (see Table 3). The dimethyl- and hydrazone-substitutions affect the hyperfine pattern very modestly compared to b-carotene. The largest changes in 2, are the two new methyl hyperfine couplings introduced (13.1 and 13.6 MHz), and in 3 the two protons of the NNH2 -substituent ()9.1 and )9.4 MHz). In 4 and 5, on the other hand, the different spin patterns compared to b-carotene result in quite different hyperfine patterns also (Tables 2 and 3). The increased spin polarization of the dicyanoand aldehyde-substituted carotenoids (see above) gives increased magnitudes of the hyperfine coupling constants of these molecules. The largest methyl hyperfine coupling is no longer found at 9,90 positions. Instead, the largest couplings are
J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81
79
Fig. 4. Spin populations of molecules 4 and 6.
Table 2 Averaged isotropic hyperfine coupling constants (MHz) for methyl protons Molecular position
1a
C5 –Cb H3 C9 –Cb H3 C13 –Cb H3 C130 –Cb H3 C90 –Cb H3 C50 –Cb H3 C70 –Cb H3
5.7 9.5 5.8 5.8 9.5 5.7
(2.6) (8.6) (13.0) (13.0) (8.6) (2.6)
2
3
4b
5c
6d
7.3 8.6 4.8 6.0 11.1
6.9 8.5 4.9 5.6 9.4
8.6 (4.3) 6.3 (11.3) 3.3 (6.9) 11.3 (15.6) 13.2 (4.5)
9.8 (4.7) 7.2 (11.1) 0.9 (7.1) 11.1 (14.0) 10.8 (2.6)
6.8 8.5 5.1 5.1 8.5 6.8
13.1/13.6
Available experimental values are in parenthesis. a Experimental values from Ref. [28]. b Experimental values from Ref. [21]. c Experimental values from Ref. [19]. d From Ref. [30].
found at the methyl groups closer to the substituents. For example, in 4 the methyl groups at positions 130 and 90 have hyperfine coupling constants of 11.3 and 13.2 MHz, much higher than the
methyl at position 9, which has a coupling of 6.3 MHz. Also the a-proton couplings are quite different from the b-carotene ones. For instance, the H150 coupling increases from )3.1 MHz in
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Table 3 B3LYP/6-31G(d,p) calculated 1 H isotropic hyperfine coupling constants (MHz) for the carotenoid radical cations Molecular position
1
H4 H7 H8 H10 H11 H12 H14 H15 H150 H140 H120 H110 H100 H80 H70 HN a
)12.4 4.6 3.4 )9.9 3.0 )1.0 )3.6 )3.6 )1.0 3.0 )9.9 3.4 4.6 )12.4
2
3
4
5
6a
14.5 11.0 )11.8 3.9 2.4 )8.6 1.8 )2.0 )2.4 )4.0 )0.6 3.0 )10.1 3.3 4.1
13.6 10.6 )11.6 3.9 2.6 )8.7 2.1 )1.6 )2.7 )3.4 )0.8 2.9 )9.7 3.3 3.9
17.8 12.9 )10.1 2.4 )0.7 )4.1 )2.3 )7.5 3.8 )10.1 5.9 8.4 )14.9 8.1 6.1
20.4 14.6 )11.5 2.8 )0.7 )5.1 )2.6 )8.2 2.8 )10.7 4.7 6.6 )13.2 5.0 )0.3
13.5 10.5 )11.6 3.9 2.7 )8.9 2.2 )1.3 )3.1 )3.1 )1.3 2.2 )8.9 2.7 3.9 )11.6
)9.4/)9.1
From Ref. [30].
b-carotene to )10.7 in 5, and the H14 coupling increases from )1.3 to )8.2 MHz. 4. Conclusions In the present study, we have characterized five carotenoid radical cations by means of their geometries, spin density distributions, and hyperfine coupling constants, using density functional theory. The calculations show the spin to be delocalized to a much higher extent than previously estimated, resulting in relatively low methyl hyperfine. The canthaxanthin, dimethyl- and hydrazone-substituted carotene radicals have very similar properties to the unsubstituted b-carotene radical. The dicyano- and aldehyde-substitutions, on the other hand, cause some significant changes in the electronic structures. The calculated hyperfine properties presented here provide a better basis for identification of the carotenoid radical cations in e.g., biological systems. Acknowledgements F.H. thanks the Wenner–Gren Foundations for financial support. This work was supported
by the Swedish Research Council (VR) and the Carl Trygger Foundation (CTS). The computing time provided by National Supercomputer Center in Link€ oping (NSC) is gratefully acknowledged.
References [1] H. Pfander, Meth. Enzymol. 213 (1992) 3. [2] (a) P. Di Mascio, S. Kaiser, H. Sies, Arch. Biochem. Biophys. 274 (1989) 532; (b) P. Di Mascio, M.E. Murphy, H. Sies, Am. J. Clin. Nutr. 53 (1991) 194S; (c) D.M. Snodderly, Am. J. Clin. Nutr. 62 (1995) 1448S. [3] H. Nishino, Mutat. Res. 402 (1998) 159. [4] A. Bendich, J. Nutr. 119 (1989) 112. [5] E.A. Dawe, E.J. Land, J. Chem. Soc., Faraday Trans. 71 (1975) 2162. [6] B.R. Velthuys, FEBS Lett. 126 (1981) 272. [7] C.C. Schenck, D. Diner, P. Mathis, K. Satoh, Biochim. Biophys. Acta 689 (1982) 216. [8] P. Mathis, A.W. Rutherford, Biochim. Biophys. Acta 767 (1984) 217. [9] A. Telfer, J. De La Rivas, J. Barber, Biochim. Biophys. Acta 1060 (1991) 106. [10] T. Noguchi, T. Mitsuka, Y. Inoue, FEBS Lett. 356 (1994) 179. [11] J. Hanley, Y. Deligiannakis, A. Pascal, P. Faller, A.W. Rutherford, Biochemsitry 38 (1999) 8189. [12] Y. Deligiannakis, J. Hanley, A.W. Rutherford, J. Am. Chem. Soc. 122 (2000) 400.
J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81 [13] P. Faller, A.W. Rutherford, S. Un, J. Phys. Chem. B 104 (2000) 10960. [14] J.S. Vrettos, D.H. Stewart, J.C. de Paula, G.W. Brudvig, J. Phys. Chem. B 103 (1999) 6403. [15] C.A. Tracewell, A. Cua, D.H. Stewart, D.F. Bocian, G.W. Brudvig, Biochemistry 40 (2001) 193. [16] P. Faller, T. Maly, A.W. Rutherford, F. MacMillan, Biochemistry 40 (2001) 320. [17] Piekara-L. Sady, M.M. Khaled, E. Bradford, L.D. Kispert, M. Plato, Chem. Phys. Lett. 186 (1991) 143. [18] Y. Wu, L. Piekara-Sady, L.D. Kispert, Chem. Phys. Lett. 180 (1991) 573. [19] A.S. Jeevarajan, L.D. Kispert, L. Piekara-Sady, Chem. Phys. Lett. 209 (1993) 269. [20] L. Piekara-Sady, A.S. Jeevarajan, L.D. Kispert, Chem. Phys. Lett. 207 (1993) 173. [21] L. Piekara-Sady, A.S. Jeevarajan, L.D. Kispert, E.G. Bradford, M. Plato, J. Chem. Soc., Faraday Trans. 91 (1995) 2881. [22] G. Gao, C.C. Wei, A.S. Jeevarajan, L.D. Kispert, J. Phys. Chem. 100 (1996) 5362.
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[23] J.A. Jeevarajan, C.C. Wei, A.S. Jeevarajan, L.D. Kispert, J. Phys. Chem. 100 (1996) 5637. [24] G. Gao, Y. Deng, L.D. Kispert, J. Phys. Chem. B 102 (1998) 3897. [25] T.A. Konovalova, L.D. Kispert, J. Chem. Soc., Faraday Trans. 94 (1998) 1465. [26] T.A. Konovalova, J. Krzystek, P.J. Bratt, L. Brunel, L.D. Kispert, J. Phys. Chem. B 103 (1999) 5782. [27] Y. Deng, G. Gao, Z. He, L.D. Kispert, J. Phys. Chem. B 104 (2000) 5651. [28] T.A. Konovalova, S.A. Dikanov, M.K. Bowman, L.D. Kispert, J. Phys. Chem. B 105 (2001) 8361. [29] Kispert and co-workers have used INDO and RHFINDO/SP calculations based on AM1 geometries, as in reference 17. [30] F. Himo, J. Phys. Chem. A 105 (2001) 7933. [31] (a) A.D. Becke, Phys. Rev. A 38 (1988) 3098; (b) J. Chem. Phys. 98 (1993) 1372; (c) J. Chem. Phys. 98 (1993) 5648. [32] M.J. Frisch et al., GA U S S I A N 98, Revision A.9, Gaussian, Inc., Pittsburgh PA, 1998.
Density functional theory study of the canthaxanthin and other carotenoid radical cations Jing-Dong Guo, Yi Luo 1, Fahmi Himo
*
Theoretical Chemistry, Stockholm University, Royal Institute of Technology, SCFAB, Stockholm SE-106 91, Sweden Received 7 August 2002; in final form 18 September 2002
Abstract B3LYP hybrid density functional theory method is employed to study the five carotenoid radical cations of canthaxanthin (1), 70 ,70 -dimethyl-70 -apo-b-carotene (2), 80 -apo-b-carotene-80 -al hydrazone (3), 70 ,70 -dicyano-70 -apo-bcarotene (4), and 80 -apo-b-carotene-80 -al (5). The radicals are characterized by means of their geometries, spin populations, and isotropic hyperfine coupling constants. It is shown that for all the systems, the unpaired spin is delocalized over the whole p-conjugated system in an odd-alternant pattern. As a result of this, the hyperfine coupling constants are rather low. The radical cations of 1, 2, and 3, have very similar properties to the unsubstituted b-carotene radical, while the dicyano- and aldehyde-substitutions result in significantly different electronic structures. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Carotenoids are ubiquitous in plants, animals and bacteria [1]. They play a vital role in the photosynthetic process and also in human health by acting as biological antioxidants, protecting cells and tissues from the damaging effects of radicals and singlet oxygen [2]. Some other health benefits of carotenoids are, e.g., inhibition of the development of certain types of cancers [3] and enhancement of immune system function [4].
*
Corresponding author. Fax: +46-8-347817. E-mail addresses: [email protected] (Y. Luo), himo@ theochem.kth.se (F. Himo). 1 Also corresponding author.
The carotene cofactor in photosystem II (PSII) can act as an alternate electron donor under conditions where the primary electron donor pathway is inhibited, and the carotene radical cation has indeed been detected in PSII reaction center using a variety of spectroscopic methods [5–16]. There is hence a fundamental interest in understanding the properties of carotenoid radical cations. Kispert and co-workers have in a large number of studies extensively examined various properties of several carotenoid radicals generated in vitro using different techniques [17–28]. Despite the importance of this class of molecules, very little quantum chemical theoretical work has been done to study their properties. The size of molecules (up to 100 atoms) has been one
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 1 5 4 1 - 5
74
J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81
of the key obstacles, and has limited the study of them to some semi-empirical calculations [29]. Very recently, we studied the b-carotene radical cation using the B3LYP density functional theory (DFT) method [30]. These high-level calculations gave a quite different picture of the carotene radical cation from that reported previously. The spin was shown to be delocalized to a much higher extent, resulting in relatively low methyl hyperfine couplings, the highest in the order of 8 MHz. The results were in excellent agreement with recent electron paramagnetic resonance (EPR) measurements of the carotene radical in solution and in PSII. It was also concluded that semi-empirical methods used in previous studies are not accurate enough to reproduce the data [30]. In the present study, we use the same B3LYPdensity functional method [31] to characterize five other members of the carotenoid radical cation family in terms of their geometries and spin and hyperfine properties. The molecules are: canthaxanthin (1), 70 ,70 -dimethyl-70 -apo-b-carotene (2), 80 -apo-b-carotene-80 -al hydrazone (3), 70 ,70 -dicyano-70 -apo-b-carotene (4), and 80 -apo-b-carotene80 -al (5), as displayed in Fig. 1. These were chosen to illustrate different donor–acceptor substituent effects on the properties of the carotenoids. Furthermore, they have been studied experimentally and there exist hyperfine parameters for some of them.
2. Computational details All the calculations reported in the present study were carried out using the density functional theory (DFT) functional B3LYP [31], as implemented in the GA U S S I A N 98 program package [32]. The geometries were optimized with the double zeta plus polarization basis set 6-31G(d,p), with no symmetry constraints. The hyperfine coupling constants were calculated at the same level of theory, which was demonstrated to be adequate in the previous study [30]. The spin densities reported are calculated using standard Mulliken population analysis.
3. Results and discussion 3.1. Geometry As in the case of the all-trans b-carotene radical cation [30], the cyclohexene ring groups of the carotenoid radicals studied here were found to adopt two orientations relative to the polyene chain. The first has a \C5–C6–C7–C8 dihedral angle of around 30° and the other a dihedral angles of around 170°. The energy difference between these two minima is very small, on the order of a few tenths of a kcal/mol, favoring the former. For the properties under consideration, the two minima yield very similar results. Selected optimized geometric parameters of the molecules are listed in Table 1, and the bond lengths of the polyene chain are graphically displayed in Figs. 2 and 3. As seen from Fig. 2, the canthaxanthin radical cation 1 shows very similar geometric properties as the unsubstituted b-carotene 6 calculated previously [30]. The molecule is strongly conjugated, with the difference between single and double bonds being smaller at the middle of the polyene chain than towards the sides. For example, the central C14–C15 bond has the same length as the ), and is only 0.006 A shorter C15–C150 (1.397 A than the C13–C14 bond (1.403 A). Closer to the head groups, the difference between the C6–C7 (1.459 vs. 1.365 A ). and C7–C8 bonds is 0.094 A The degree of conjugation in a molecule can be evaluated by means of the bond length alternation (BLA) parameter, defined as the total length difference between single bonds and double bonds. We have calculated the BLA parameter in two ways, from C5 to the central C15 (called BLA5–15 ), and from C5 to C80 at the other end of the molecule (called BLA5–80 ). As seen from Table 1, the canthaxanthin radical cation has slightly larger BLA parameters than the b-carotene (0.20 vs. for BLA5–15 and 0.29 vs. 0.23 A for 0.17 A BLA5–80 ), indicating a slightly lower degree of conjugation in the former compared to the latter. Interestingly, the two electron-donating substitutions in 2 (dimethyl) and 3 (hydrazone) show smaller difference from the unsubstituted b-carotene compared to the canthaxanthin molecule (see
J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81
75
Fig. 1. Numbering schemes and B3LYP/6-31G(d,p) calculated spin density distributions of the carotenoid radical cations. The b-carotene calculated previously [30] is included for comparison.
Table 1 and Fig. 3). Both the BLA5–15 and BLA5–80 parameters are almost identical in 2 and 3 to those of 6. Large effects are, however, seen for the electron-withdrawing substitutions in 4 (dicyano) and 5 (aldehyde). As seen from Fig. 3, the largest changes occur, as expected, close to the substituents. The introduction of the triple bonds in the dicyano-substituted carotene 4 has an overall effect of increasing the conjugation of the molecule, as
seen from the BLA5–15 and BLA5–80 parameters, which decrease relative to b-carotene. The aldehyde-substitution 5, on the other hand, exhibits an interesting feature. The BLA5–15 is smaller than the corresponding parameter in the unsubstituted ), while the BLA5–80 is b-carotene (0.12 vs. 0.17 A ). This indicates a much larger (0.33 vs. 0.23 A greater fluctuation closer to the aldehyde functionality, a fact clearly visible in Fig. 3.
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J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81
Table 1 and (°)) of the carotenoid radical cations optimized at the B3LYP/6-31G(d,p) level Selected geometric parameters (A 1
2
3
4
5
6a
C4–C5 C5–C6 C6–C7 C7–C8 C8–C9 C9–C10 C10–C11 C11–C12 C12–C13 C13–C14 C14–C15 C15–C150 C150 –C140 C140 –C130 C130 –C120 C120 –C110 C110 –C100 C100 –C90 C90 –C80 C80 –C70 C70 –C60 C60 –C50 C50 –C40 C4–O4 ðC40 –O40 Þ C80 –X
1.501 1.371 1.459 1.365 1.438 1.389 1.410 1.387 1.414 1.403 1.397 1.397 1.397 1.403 1.414 1.387 1.410 1.389 1.438 1.365 1.459 1.371 1.501 1.223
1.511 1.370 1.454 1.371 1.432 1.394 1.405 1.391 1.409 1.407 1.393 1.400 1.393 1.407 1.410 1.389 1.408 1.392 1.441 1.368 1.515/1.510
1.511 1.369 1.455 1.370 1.433 1.393 1.406 1.391 1.409 1.407 1.393 1.400 1.393 1.407 1.409 1.391 1.405 1.391 1.428
1.508 1.375 1.446 1.377 1.426 1.399 1.400 1.395 1.405 1.411 1.392 1.400 1.395 1.405 1.415 1.385 1.414 1.388 1.436 1.376 1.430/1.432
1.509 1.375 1.446 1.377 1.426 1.400 1.400 1.394 1.407 1.408 1.396 1.395 1.402 1.395 1.428 1.373 1.429 1.366 1.483
1.511 1.369 1.455 1.370 1.433 1.392 1.406 1.390 1.410 1.407 1.394 1.399 1.394 1.407 1.410 1.390 1.406 1.392 1.433 1.370 1.455 1.369 1.511
\C5–C6–C7 \C5–C6–C7–C8
122.7 38.1
123.0 33.1
123.0 34.1
123.1 30.0
123.3 28.8
123.0 34.3
BLA5–15 b BLA5–80 c
0.203 0.286
0.160 0.224
0.166 0.212
0.112 0.194
0.121 0.334
0.170 0.225
1.309
1.216
a
From Ref. [30]. Bond length alternation from C5 to C15. c Bond length alternation from C5 to C80 . b
3.2. Spin distribution The b-carotene radical was previously shown to exhibit an odd-alternant spin pattern, with positive spins alternating with smaller negative spins [30]. This general pattern is preserved in the canthaxanthin and the other substituted radical cations (calculated spin densities are displayed in Fig. 1). The largest spin densities on the polyene chain of the canthaxanthin radical cation are found at positions 7,70 (0.18), 9,90 (0.18), 11,110 (0.15) and 13,130 (0.10), very similar to the b-carotene spins. Also here, there is a significant spin delocalization onto the double bonds of the ring headgroups. The C5 and C6 centers carry respectively, 0.10 and
)0.06 of the unpaired spin, and the oxygens possess 0.03 each. The two electron-donating substitutions in 2 and 3 introduce very little modification to the spin population pattern on the polyene chain. Although the hydrazone moiety of 3 has as much as 0.24 of the unpaired spin, the spin of the rest of the molecule looks very similar to both b-carotene and canthaxanthin. As is the case for geometry, the largest changes in the spin distribution are seen for the electronwithdrawing substitutions in 4 and 5. In the cases of 1, 2, 3, and 6 it is observed that the carbon centers between the C14 and C140 centers have small spins (
J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81
77
Fig. 2. Bond lengths of canthaxanthin compared to b-carotene (from [30]).
these centers are larger. For 4 and 5 this low spin region is moved two double bonds toward the cyclohexene ring, to between the C10 and C13 centers. Another effect of the electron-withdrawing substitutions is the increased spin polarization in the radicals. That is, the absolute magnitudes of both the positive and the negative spins increase. These effects are displayed graphically in Fig. 4. 3.3. Hyperfine coupling constants The spin density distributions described above are directly reflected in the hyperfine coupling constants. The proton hyperfine couplings of carotenoid radical cations can be divided into two classes, methyl proton couplings and a-proton couplings. In frozen solution, methyl protons give rise to intense and narrow ENDOR lines, while a-protons give rise to broadened lines, which normally escape detection. The B3LYP/6-31G(d,p) calculated isotropic methyl hyperfine couplings are
given in Table 2 and the a-proton couplings in Table 3. Canthaxanthin has six methyl groups in three distinct positions (5, 9, and 13). The magnitudes of the hyperfine couplings of these are expected to follow the trend: Aiso ð9Þ > Aiso ð13Þ Aiso ð5Þ, since the spin densities at these positions show this trend. Indeed the largest calculated isotropic methyl coupling was found on the 9,90 positions, with a magnitude of 9.5 MHz. The Aiso ð13Þ and Aiso ð5Þ couplings are smaller and almost equal, with magnitudes of 5.8 and 5.7 MHz, respectively. These values are quite close to the b-carotene methyl couplings, which were previously calculated to 8.5, 5.1, and 6.8 MHz, for the Aiso ð9Þ, Aiso ð13Þ, and Aiso ð5Þ, respectively [30]. ENDOR experiments by Kispert and co-workers found the three methyl hyperfine coupling constants to be ca. 2, 8, and 13 MHz [18,20,28]. These were assigned to positions 5, 9, and 13, respectively, based on RHF-INDO/SP calculations,
78
J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81
Fig. 3. Bond lengths of molecules 2–5.
which gave couplings very close to the experimental values. This assignment suggests higher spin concentration in the middle polyene chain than toward the sides of the molecule, in sharp contrast to our results presented above. We found the spin concentration in the middle of the chain to be smaller than at the ends (see Fig. 1). Considering that the DFT calculations presented here are more accurate than the semi-empirical RHFINDO/SP calculations, a fact that was further established previously for the b-carotene radical [30], the results here show that the experimental couplings are misassigned. This conclusion is also valid for radicals 4 and 5, for which the same approach was used to assign the experimental hyperfine couplings (see Table 2). Apart from the obvious loss of the H4 proton couplings, the 1 H couplings of canthaxanthin are very similar to those of the b-carotene (see Table 3). The largest isotropic polyene chain a-proton
hyperfine couplings are found at 7,70 positions ()12.4 MHz) and 11,110 positions ()9.9 MHz), reflecting the high spin population at these centers (0.18 and 0.16, respectively). The other a-protons have smaller hfcÕs, lower than 5 MHz (see Table 3). The dimethyl- and hydrazone-substitutions affect the hyperfine pattern very modestly compared to b-carotene. The largest changes in 2, are the two new methyl hyperfine couplings introduced (13.1 and 13.6 MHz), and in 3 the two protons of the NNH2 -substituent ()9.1 and )9.4 MHz). In 4 and 5, on the other hand, the different spin patterns compared to b-carotene result in quite different hyperfine patterns also (Tables 2 and 3). The increased spin polarization of the dicyanoand aldehyde-substituted carotenoids (see above) gives increased magnitudes of the hyperfine coupling constants of these molecules. The largest methyl hyperfine coupling is no longer found at 9,90 positions. Instead, the largest couplings are
J.-D. Guo et al. / Chemical Physics Letters 366 (2002) 73–81
79
Fig. 4. Spin populations of molecules 4 and 6.
Table 2 Averaged isotropic hyperfine coupling constants (MHz) for methyl protons Molecular position
1a
C5 –Cb H3 C9 –Cb H3 C13 –Cb H3 C130 –Cb H3 C90 –Cb H3 C50 –Cb H3 C70 –Cb H3
5.7 9.5 5.8 5.8 9.5 5.7
(2.6) (8.6) (13.0) (13.0) (8.6) (2.6)
2
3
4b
5c
6d
7.3 8.6 4.8 6.0 11.1
6.9 8.5 4.9 5.6 9.4
8.6 (4.3) 6.3 (11.3) 3.3 (6.9) 11.3 (15.6) 13.2 (4.5)
9.8 (4.7) 7.2 (11.1) 0.9 (7.1) 11.1 (14.0) 10.8 (2.6)
6.8 8.5 5.1 5.1 8.5 6.8
13.1/13.6
Available experimental values are in parenthesis. a Experimental values from Ref. [28]. b Experimental values from Ref. [21]. c Experimental values from Ref. [19]. d From Ref. [30].
found at the methyl groups closer to the substituents. For example, in 4 the methyl groups at positions 130 and 90 have hyperfine coupling constants of 11.3 and 13.2 MHz, much higher than the
methyl at position 9, which has a coupling of 6.3 MHz. Also the a-proton couplings are quite different from the b-carotene ones. For instance, the H150 coupling increases from )3.1 MHz in
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Table 3 B3LYP/6-31G(d,p) calculated 1 H isotropic hyperfine coupling constants (MHz) for the carotenoid radical cations Molecular position
1
H4 H7 H8 H10 H11 H12 H14 H15 H150 H140 H120 H110 H100 H80 H70 HN a
)12.4 4.6 3.4 )9.9 3.0 )1.0 )3.6 )3.6 )1.0 3.0 )9.9 3.4 4.6 )12.4
2
3
4
5
6a
14.5 11.0 )11.8 3.9 2.4 )8.6 1.8 )2.0 )2.4 )4.0 )0.6 3.0 )10.1 3.3 4.1
13.6 10.6 )11.6 3.9 2.6 )8.7 2.1 )1.6 )2.7 )3.4 )0.8 2.9 )9.7 3.3 3.9
17.8 12.9 )10.1 2.4 )0.7 )4.1 )2.3 )7.5 3.8 )10.1 5.9 8.4 )14.9 8.1 6.1
20.4 14.6 )11.5 2.8 )0.7 )5.1 )2.6 )8.2 2.8 )10.7 4.7 6.6 )13.2 5.0 )0.3
13.5 10.5 )11.6 3.9 2.7 )8.9 2.2 )1.3 )3.1 )3.1 )1.3 2.2 )8.9 2.7 3.9 )11.6
)9.4/)9.1
From Ref. [30].
b-carotene to )10.7 in 5, and the H14 coupling increases from )1.3 to )8.2 MHz. 4. Conclusions In the present study, we have characterized five carotenoid radical cations by means of their geometries, spin density distributions, and hyperfine coupling constants, using density functional theory. The calculations show the spin to be delocalized to a much higher extent than previously estimated, resulting in relatively low methyl hyperfine. The canthaxanthin, dimethyl- and hydrazone-substituted carotene radicals have very similar properties to the unsubstituted b-carotene radical. The dicyano- and aldehyde-substitutions, on the other hand, cause some significant changes in the electronic structures. The calculated hyperfine properties presented here provide a better basis for identification of the carotenoid radical cations in e.g., biological systems. Acknowledgements F.H. thanks the Wenner–Gren Foundations for financial support. This work was supported
by the Swedish Research Council (VR) and the Carl Trygger Foundation (CTS). The computing time provided by National Supercomputer Center in Link€ oping (NSC) is gratefully acknowledged.
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