Photolysis of Methylcobalamin: Identification of the Relevant Excited

Department of Theoretical Chemistry, Institute of Chemistry, University of Silesia, Szkolna 9, PL-40 006 Katowice, Poland, Institute of Physical and T...
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2007, 111, 2419-2422 Published on Web 02/20/2007

Photolysis of Methylcobalamin: Identification of the Relevant Excited States Involved in Co-C Bond Scission Maria Jaworska,† Piotr Lodowski,† Tadeusz Andrunio´ w,‡ and Pawel M. Kozlowski*,§ Department of Theoretical Chemistry, Institute of Chemistry, UniVersity of Silesia, Szkolna 9, PL-40 006 Katowice, Poland, Institute of Physical and Theoretical Chemistry, Department of Chemistry, Wroclaw UniVersity of Technology, 50-370 Wroclaw, Poland, and Department of Chemistry, UniVersity of LouisVille, LouisVille, Kentucky 40292 ReceiVed: December 14, 2006; In Final Form: January 30, 2007

The relevant excited states involved in the photolysis of methylcobalamin (MeCbl) have been examined by means of time-dependent density functional theory (TD-DFT). The low-lying singlet and triplet excited states have been calculated along the Co-C bond at the TD-DFT/BP86/6-31g(d) level of theory in order to investigate the dissociation process of MeCbl. These calculations have shown that the photodissociation is mediated by the repulsive 3(σCo-C f σ*Co-C) triplet state. The key metastable photoproduct involved in Co-C bond photolysis was identified as an S1 state having predominantly dCo f π*corrin metal-ligand charge transfer (MLCT) character.

The relatively weak cobalt-carbon bond in B12 cofactors (Figure 1) can be photochemically cleaved to generate the cob(II)alamin and alkyl radical pair. These are the same products (at least formally) that are formed in enzyme-catalyzed homolysis;1 thus, the photolytic scission of the Co-C bond has been extensively studied in order to address mechanistic issues related to B12 enzymatic catalysis. Various experimental techniques have been applied to investigate the photochemistry of B12 cofactors and their analogues such as laser-flash2 and continuous wave (CW) photolysis,3 kinetic magnetic field effect (MFE),4 chemically induced dynamic electron polarization (CIDEP),5 and chemically induced dynamic nuclear polarization (CIDNP).6 The time-resolved spectroscopic studies of Sension and co-workers7-14 provided the detailed photolysis mechanism for methyl-, ethyl-, n-propyl-, and adenosylcobalamin in different solvents. The results obtained for methylcobalamin (MeCbl) show that its photolysis depends on the excitation wavelength.9 The excitation at 400 nm results in ∼25% bond photolysis with the formation of cob(II)alamin and methyl radical, while the remaining molecules form a metastable photoproduct with a spectrum characteristic for cob(III)alamin species with weakly bound axial ligand.7,9 This intermediate has a lifetime of about 1 ns in water and 2.4 ns in ethylene glycol.13 Its structure has been interpreted in terms of the fivecoordinate cob(III)alamin-mehyl anion ion pair, or alternatively as a localized metal-ligand charge transfer (MLCT) state.11 The metastable photoproduct undergoes photolysis in about 12%, and the remaining part converts to the ground state. At the excitation with 520 nm, only the formation of the metastable * Author to whom correspondence should be addressed. Phone: (502) 852-6609. Fax: (502) 852-8149. E-mail: [email protected]. † University of Silesia. ‡ Wroclaw University of Technology. § University of Louisville.

10.1021/jp0685840 CCC: $37.00

Figure 1. Molecular structure of B12 cofactors (left panel) where R ) Me for MeCbl and R ) Ado for AdoCbl (R1 ) CH2CONH2, R2 ) CH2CH2CONH2, R3 ) (CH2)2CONHCH2CH(CH3)OPO3-). Right panel: structural model of MeCbl employed in the present study denoted as Im-[CoIII(corrin)]-Me+.

product is observed, without prompt photolysis.9 It again branches between photolysis (14%) and reversion to the ground state. While photophysical properties of B12 cofactors and their analogues have been extensively investigated experimentally, the mechanism of the Co-C bond scission has not yet been analyzed at the molecular level employing methods of computational chemistry. Herein, we investigate the photolysis of MeCbl by means of time-dependent density functional theory (TD-DFT)15,16 as implemented in the Gaussian 0317 suite of programs for electronic structure calculations. For this objective, we use the model complex Im-[CoIII(corrin)]-Me+, which was demonstrated previously to be sufficient to describe the spectroscopic properties of MeCbl.18-20 The model complex contains the actual corrin ring as the equatorial ligand and imidazole (Im) as the axial base (Figure 1). It was shown in previous DFT calculations that replacement of the dimethyl© 2007 American Chemical Society

2420 J. Phys. Chem. B, Vol. 111, No. 10, 2007 benzimidazole (DBI) base by imidazole has only a minor influence on the calculated properties.21 As a starting point, we optimized the ground-state geometry of the model complex with DFT (Supporting Information Table S1). The application of the appropriate level of theory is essential for correct prediction of the Co-C strength and axial bond lengths. Recent studies have demonstrated that the commonly used B3LYP functional sigificanly underestimates the dissociation energy of the Co-C bond while the nonhybrid BP86 functional provides results very consistent with experiment.22,23 In the present work, we follow these recent developments and use the BP86/6-31G(d) (5d components) level of theory to investigate the electronically excited states of Im-[CoIII(corrin)]-Me+ (Figure 1). The optimized Co-C bond length of 1.968 Å is in good agreement with the corresponding distance of 1.979(4) Å in the crystal strucure of MeCbl.24 The Co-C bond dissociation energy (BDE) is predicted to be 37.0 kcal/ mol, upon inclusion of the zero point vibrational energy (ZPE) correction, which is consistent with experimental values of 37 ( 3 kcal/mol based on thermolysis25 and 36 ( 4 kcal/mol employing calorimetric measurments,26 respectively. Since the structure does not include the negative phosphate-containing side chain (Figure 1), the model is a singly positive charged species while the corrin ligand has a formal charge of -1. The cobalt-methyl bond is often considered as being ionic;27 in such a case, cobalt is formally the Co(+3) cation and methyl the CH3- anion. When this bond is considered as a covalent bond (which is supported by DFT calculated atomic charges), it may be described as Co(+2) bonded to the •CH3 radical. The calculated Mulliken charge on cobalt is 0.538, much smaller than the formal oxidation state +2. The total corrin charge is 0.255, which points to a large ligand-to-metal charge donation. This donation occurs through the corrin nitrogen atom lone pairs, which form a σ bond with the unoccupied dxy orbital of cobalt. The methyl carbon atom bears a negative charge, but the total charge of the methyl group is close to zero which indicates that the cobalt-methyl bond is strongly covalent. There is also a charge donation from imidazole to cobalt, which is reflected in the imidazole positive charge. The simulated electronic absorption spectrum of Im-[CoIII(corrin)]-Me+, based on the 30 lowest singlet excited states, is shown in Figure 2. It was computed at the optimized groundstate equilibrium geometry with the TD-DFT method employing the BP86 functional and the 6-31G(d) basis. The low energy part of the electronic spectrum of cobalamins is commonly referred as the R/β band. In the experimental spectrum of MeCbl, there are several peaks found in the R/β band, which have been interpreted as a vibrational progression of two distinct electronic transitions.13 The lowest energy transition (S1) is present in the calculated spectrum at 566 nm, and it has a very small oscillator strength. It comes from HOMO-2 f LUMO and HOMO-1 f LUMO excitations which are of dCo f π*corrin and πcorrin f π*corrin character.28 In the calculated spectrum, there are two transitions of significant oscillator strengths at 528 and 499 nm (S2 and S3), which can be assigned to the R/β band. The transition at 528 nm comes from HOMO f LUMO excitation and has mixed dCo f π*corrin and πcorrin f π*corrin character.28. There is one more calculated transition in the R/β region, at 479 nm, of the dCo f π*corrin type. The higher energy part of the spectrum, up to 400 nm, belongs to the so-called D/E region in cobalamins which has a lower intensity than the R/β band. Two electronic transitions in the MeCbl spectrum have been assigned on the basis of Gaussian deconvolution,19 and we attributed them to the calculated transitions at 427 and

Letters

Figure 2. Simulated absorption spectrum of MeCbl based on the 30 lowest singlet excited states computed at the optimized ground-state equilibrium geometry of Im-[CoIII(corrin)]-Me+ employing the TDDFT/BP86/6-31G(d) level of theory. Arrows indicate laser excitations at 520 and 400 nm, respectively. Electronic excitations with zero oscillator strengths are depicted by filled circles.

400 nm of the D/E band. These transitions have dCo, πcorrin f dCo, π*corrin character.28 The other transitions calculated in this region at 413, 388, and 382 nm with small oscillator strengths are of similar type, though excitations at 388 and 382 nm have transitions from dCo, π corrin f σ*Co-C. At shorter wavelengths, in the intense γ band of MeCbl, three electronic transitions are inferred from the Gaussian deconvolution19 of the experimental spectrum. The experimental one at 378 nm can be assigned to the calculated transition at 353 nm with an oscillator strength of 0.0216. The calculated transitions with large oscillator strengths at 330 and 324 nm can be attributed to the experimental transition at 336 nm. They involve excitations of dCo, πcorrin f π*corrin, σ*Co-C character.28 The calculated transition at 318 nm with a large oscillator strength can be ascribed to the experimental one at 316 nm, and it is of dCo, πcorrin, σCo-C f π*corrin type. It can be noted that in the calculated transitions at 364, 353, and 339 nm there is a significant participation of excitations having σCo-C f σ*Co-C character. In addition, a manifold of triplet excited states was also calculated. They were not included in the simulated spectrum (Figure 2) because they have been obtained from the singlet ground-state wavefunction and have a zero transition dipole moment (Supporting Information Table S4). Three of them lie energetically below the first singlet excited state (S1, 566 nm). The lowest triplet state at 758 nm (T1) is a HOMO f LUMO transition, and the next two transitions (T2 and T3) are transitions from HOMO-1 f LUMO and HOMO-2 f LUMO located at 655 and 594 nm, respectively.28 To simulate the dissociation process of MeCbl, we repeatedly elongated the cobalt-carbon bond with a step of 0.05 Å, reoptimized the ground-state geometry at each point, and calculated the vertical excitation energies using the BP86/631G(d) level of theory. At each optimized point, the energies of 10 singlet and 15 triplet excited states have been computed. The resulting potential curves are displayed in Figure 3. A similar approach has been applied to study dissociation of CO or O2 from heme where singlet-singlet vertical excitation energies were computed via TD-DFT along the iron-ligand coordinate.29-31 The calculated S1-S4 singlet excited states belong to the R/β band, while the S5-S10 singlet states belong to the D/E band

Letters

Figure 3. Potential energy curves of the lowest-excited singlet (red) and triplet (blue) states of the Im-[CoIII(corrin)]-Me+ model complex along the Co-C bond stretch computed at TD-DFT/BP86/6-31g(d).

(Figure 3). The photolysis process is initiated either with excitation by light of 520 nm near the maximum of the R/β band or 400 nm near the upper limit of D/E just below the γ band (Figure 2). The low-lying S1-S4 states have nonrepulsive character and S2-S3 cross at ∼2.5 Å. According to TD-DFT calculations, the S4 and S5 states display an avoided crossing at ∼2.3 Å.32 The higher states S5-S10 display multiple crossings, even at small cobalt-methyl distances. The low-lying electronically excited states possess bound character, and therefore, the mechanism of photolysis which directly involves singlet excited states leading to the methyl radical and excited cob(II)alamin cannot be considered as being valid. In addition, the singlet state with 1(σCo-C f σ*Co-C) character does not participate in the photolysis process. There are two reasons for that. The first is that a state possessing such a character is energetically very high. Indeed, none of the 30 calculated singlet states have a dominant contribution from 1(σCo-C f σ*Co-C) excitation. Furthermore, such a state would not dissociate to cob(II)alamin and •CH3 but rather to the ionic fragments. On the other hand, the triplet state which has 3(σCo-C f σ*Co-C) character can make such a correlation. This state has a repulsive character and in the dissociation limit gives the proper products, cob(II)alamin and •CH3. Such a state, denoted with a black line and labeled as 3(σ f σ*) in Figure 3, was obtained by connecting triplet transitions with significant contributions of excitations from occupied orbitals of σCo-C character to unoccupied orbitals of σ*Co-C nature. The dissociative 3(σCo-C f σ*Co-C) state becomes the lowest energy excited state above 2.35 Å cobaltcarbon distance and also displays an avoided crossing with the T1 state which arises from the HOMO f LUMO (dCo,

J. Phys. Chem. B, Vol. 111, No. 10, 2007 2421 πcorrin f π*corrin) excitation. At the equilibrium geometry, the 3(σ Co-C f σ*Co-C) state is quite high in energy. The energy of this state drops rapidly above 2.4 Å, which might be indicative that at longer Co-CH3 bond distances this state is not properly described with one-determinant approximation. However, this distance is actually shorter than 2.65 Å at which the instability in the ground-state wave occurs and above which the UHF type description is required. Importantly, the photochemical events occur at much shorter distances, where 3(σCo-C f σ*Co-C) behaves properly. The presence of avoided crossing between T1 and 3(σCo-C f σ*Co-C) does not preclude the existence of a conical intersection between these two states along some other coordinate, such as a change in geometry of the corrin ring. The answer for this question requires a multireference wavefunction and analysis of excited-state potential energy surfaces using energy derivatives.32 At the excitation with 520 nm, no prompt photolysis is observed; instead, a long-lived (∼1 ns) metastable product is formed, with the electronic spectrum similar to cob(III)alamin species, with a weakly bound axial ligand.9 Subsequently, this product in part (∼12%) undergoes photolysis, and the remaining part reverts to the ground state. On the basis of TD-DFT calculations, the following mechanism may be proposed: the excitation at 520 nm leads to the excited state in the R/β band, presumably S2 or S3, because of large oscillator strengths. The S1-S4 states are very close in energy, and fast transition to the lowest one, that is, S1, is possible. From this state, the photodissociation may occur through intersystem crossing (ISC) with the dissociative 3(σCo-C f σ*Co-C) state. The conversion back to the ground state can take place by a radiationless transition from S1 (most probably through a conical intersection involving some energy barrier). The reversion from 3(σCo-C f σ*Co-C) to T1 and radiationless transition from the lowest triplet state to the ground state can also be considered. Crossing of the two states, S1 and dissociative 3(σCo-C f σ*Co-C), involves a small energy barrier, which may be an explanation for the long living time of the metastable state. From this point of view, the S1 state would be a likely candidate for a long-lived transient detected in the photolysis of MeCbl. The excitation at 400 nm leads in part (∼25%) to a prompt photolysis and in remaining part to the formation of the longlived metastable state.7,9 Figure 3 shows that S5-S10 crosses with the 3(σCo-C f σ*Co-C) state practically without any energy barrier. This explains the prompt photolysis at excitation to the high part of the D/E spectrum. Alternatively, the consecutive transitions from an excited state in this region to the lowest energy singlet (S1) are possible, which again leads to a longlived transient product. One should note that, according to magnetic measurements made by Grissom and co-workers on a model complex,6 the lowest triplet state from which photolysis occurs should be excluded as a possible metastable photoproduct. Since the singlet states are energetically close, such transitions are very likely and they can be very fast. It is possible that there are intersections between these states along some other coordinate than the Co-C distance, for example, corrin distortion, which would make such an internal conversion process very efficient. The metastable state was characterized as being similar to cob(III)alamin with the weakly bound axial ligand on the basis of its electronic spectrum.7 The S1 state has mixed dCo f π*corrin and πcorrin f π*corrin character. The dCo f π*corrin character of this state may result in a diminished electron density on the cobalt atom. Although the minimum on the energy curve of this state appears at a Co-CH3 distance not very different than

2422 J. Phys. Chem. B, Vol. 111, No. 10, 2007 in the ground state, the minimum of S1 is very shallow and the cobalt-methyl bond is weaker in this state. The influence of solvent may also be important here. The photolysis experiments were carried out in polar solvents, as water and ethylene glycol.13 On the other hand, the curves of excited states are drawn for the ground-state optimized geometry and it is possible that the optimal geometry of S1 would be different. On the basis of results of TD-DFT calculations, it may be concluded that the metastable state has a predominantly dCo f π*corrin MLCT character. A large participation of dCo f π*corrin excitations was found in the lowest singlet S1-S4 transitions. This is in line with the mechanism of carboxyhemoglobin photolysis, where participation of the dFe f π*porphyrin state was proposed by Franzen et al.,33 and recently computationally confirmed by Dreuw et al.29 Supporting Information Available: The Cartesian coordinates generated by the study (Table S1), the relevant MOs (Figure S1, Table S2), and TD-DFT results (Tables S3 and S4). This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) See, for example: (a) Dolphin, D., Ed. B12; Wiley-Interscience: New York, 1982. (b) Marzilli, L. G. In Bioinorganic Catalysis; Reedijk, J., Ed.; Marcel Dekker: New York, 1993; pp 227-259. (c) Ludwig, M. L.; Matthews, R. G. Annu. ReV. Biochem. 1997, 66, 269-313. (d) Kra¨utler, B., Arigoni, D., Golding, B. T., Eds. Vitamin B12 and B12 Proteins; WileyVCH: New York, 1998. (e) Banerjee, R. Chemistry and Biochemistry of B12; John Wiley & Sons: New York, 1999. (f) Banerjee, R. Chem. ReV. 2003, 103, 2083-2094. (g) Toraya, T. Chem. ReV. 2003, 103, 2095-2127. (h) Brown, K. L. Chem. ReV. 2005, 105, 2075-2149. (2) (a) Endicott, J. F.; Netzel, T. L. J. Am. Chem. Soc. 1979, 101, 40004002. (b) Chagovetz, A. M.; Grissom, C. B. J. Am. Chem. Soc. 1993, 115, 12152-12157. (c) Lott, W. B.; Chagovetz, A. M.; Grissom, C. B. J. Am. Chem. Soc. 1995, 117, 12194-12201. (d) Chen, E.; Chance, M. R. J. Biol. Chem. 1990, 265, 12987-12994. (e) Endicott, J. F.; Ferraudi, G. J. J. Am. Chem. Soc. 1977, 99, 243-245. (3) Chen, E.; Chance, M. R. Biochemistry 1993, 32, 1480-1487. (4) (a) Grissom, C. B.; Chagovetz, A. M. Z. Phys. Chem. 1993, 182, 181-188. (b) Natarajan, E.; Grissom, C. B. Photochem. Photobiol. 1996, 64, 286-295. (5) (a) Sakaguchi, Y.; Hayashi, H.; I’Haya, Y. J. J. Phys. Chem. 1990, 94, 291-291. (b) Rao, D. N. R.; Symons, M. C. R. J. Chem. Soc., Chem. Commun. 1982, 954-955 (6) Kruppa, A. I.; Taraban, M. B.; Leshina, T. V.; Natarajan, E.; Grissom, C. B. Inorg. Chem. 1997, 36, 758-759. (7) Walker, L. A., II; Jarrett, J. T.; Anderson, N. A.; Pullen, S. H.; Matthews, R. G.; Sension, R. J. J. Am. Chem. Soc. 1998, 120, 3597-3603. (8) Walker, L. A., II; Shiang, J. J.; Anderson, N. A.; Pullen, S. H.; Sension, R. J. J. Am. Chem. Soc. 1998, 120, 7286-7292. (9) Shiang, J. J.; Walker, L. A., II; Anderson, N. A.; Cole, A. G.; Sension, R. J. J. Phys. Chem. B 1999, 103, 10532-10539. (10) Yoder, L. M.; Cole, A. G.; Walker, L. A., II; Sension, R. J. J. Phys. Chem. B 2001, 105, 12180-12188. (11) Cole, A. G.; Yoder, L. M.; Shiang, J. J.; Anderson, N. A., Walker, L. A., II; Banaszak Holl, M. M.; Sension, R. J. J. Am. Chem. Soc. 2002, 124, 434-441. (12) (a) Sension, R. J.; Cole, A. G.; Harris, A. D.; Fox, C. C.; Woodbury, N. W.; Lin, S.; Marsh, E. N. G. J. Am. Chem. Soc. 2004, 126, 1598-1599.

Letters (b) Sension, R. J.; Harris, A. D.; Stickrath, A.; Cole, A. G.; Fox, C. C.; Marsh, E. N. G. J. Phys. Chem. B 2005, 109, 18146-18152. (13) Sension, R. J.; Harris, A. D.; Cole, A. G. J. Phys. Chem. B 2005, 109, 21954-21962. (14) Shiang, J. J.; Cole, A. G.; Sension, R. J.; Hang, K.; Weng, Y.; Trommel, J. S.; Marzilli, L. G.; Lian, T., Anderson J. Am. Chem. Soc. 2006, 128, 801-808. (15) Runge, E.; Gross, E. K. U. Phys. ReV. Lett. 1984, 52, 997-1000. (16) (a) Baerends, E. J.; Ricciardi, G.; Rosa, A.; van Gisergen, S. J. A. Coord. Chem. ReV. 2002, 230, 5-27. (b) Dreuw, A.; Head-Gordon, M., Chem. ReV. 2005, 105, 4009-4037. (c) Dreuw, A. ChemPhysChem 2006, 7, 2259-2274. (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (18) (a) Andruniow, T.; Zgierski, M. Z.; Kozlowski, P. M. Chem. Phys. Lett. 2000, 331, 502-508. (b) Andruniow, T.; Zgierski, M. Z.; Kozlowski, P. M. J. Phys. Chem. A 2002, 106, 1365-1373. (19) Stich, T. R.; Brooks, A. J.; Buan, N. R.; Brunold, T. C. J. Am. Chem. Soc. 2003, 125, 5897-5914. (20) Kozlowski, P. M.; Andruniow, T.; Jarzecki, A. A.; Zgierski, M. Z.; Spiro, T. G. Inorg. Chem. 2006, 45, 5585-5590. (21) (a) Jensen, K. P.; Ryde, U. THEOCHEM 2002, 585, 239-255. (b) Kozlowski, P. M.; Zgierski, M. Z. J. Phys. Chem. B 2004, 108, 1416314170. (22) Jensen, K. P.; Ryde, U. J. Phys. Chem. A 2003, 107, 7539-7545. (23) Kuta, J.; Patchkovskii, S.; Zgierski, M. Z.; Kozlowski, P. M. J. Comput. Chem. 2006, 27, 1429-1437. (24) Randaccio, L.; Furlan, M.; Geremia, S.; Slouf, M.; Srnova, I.; Toffoli, D. Inorg. Chem. 2000, 39, 3403-3413. (25) Martin, B. D.; Finke, R. G. J. Am. Chem. Soc. 1992, 114, 585592. (26) Hung, R. R.; Grabowski J. J. J. Am. Chem. Soc. 1999, 121, 13591364. (27) De Ridder, D. J. A.; Zangrando, E.; Bu¨urgi, H.-B. J. Mol. Struct. 1996, 374, 63-83. (28) The data generated by the study are collected in the Supporting Information (Figure S1, Tables S2-S4). (29) (a) Dreuw, A.; Dunietz, B. D.; Head-Gordon, M. J. Am. Chem. Soc. 2003, 124, 12070-12071. (b) Dunietz, B. D.; Dreuw, A.; Head-Gordon, M. J. Phys. Chem. B 2003, 107, 5623-5629. (30) Ohta, T.; Pal, B.; Kitagawa, T. J. Phys. Chem. B 2005, 109, 2111021117. (31) Angelis, F. F.; Carr, R.; Spiro, T. G. J. Am. Chem. Soc. 2003, 125, 15710-15711. (32) The single-reference TD-DFT method is not capable of providing any detailed description when crossing of two curves takes place. The only estimate can be obtained on the basis of energy interpolation. (33) Franzen, S.; Kiger, L.; Poyart, C.; Martin, J.-L. Biophys. J. 2001, 80, 2372-2385.