The conceptual formalism to understand the properties and function of chlorophylls in the gas and solution phases as well as in protein matrices is reviewed. This formalism is then applied to interpret modern high-resolution spectroscopic data, resulting from methods such as differential fluorescence line-narrowing spectroscopy and selective fluorescence excitation spectroscopy, which resolve individual vibrational transitions within the inhomogeneously broadened emission and absorption spectra of chlorophyll-a, bacteriochlorophyll-a, and pheophytin-a. Density functional theory and ab initio quantum chemical calculations are applied to interpret this data and fill in missing information needed to understand photosynthetic processes. The focus is placed on recognizing environmental and thermal effects, as well as the roles of Duschinsky rotation and non-adiabatic coupling in controlling the spectra. A critical feature of chlorophyll spectroscopy is determined to be absorption-emission asymmetry. Its ramifications for chlorophyll’s function in photosystems are expected to be significant, as most current models for understanding their function assume that absorption and emission are symmetric, i.e. in the absence of relaxation processes, molecules coherently re-emit the light that they absorbed to enact exciton transport. The effect of the Duschinsky rotation is that after vibrational excitation during the electronic transition chlorophylls mostly emit light at different energies to what they absorb, while the effect of non-adiabatic coupling is that the polarization of the light is changed.
1. Blankenship, R. E. Molecular Mechanisms of Photosynthesis. Blackwell Science, Oxford, 2002.
https://doi.org/10.1002/9780470758472
2. Grimm, B., Porra, R. J., Rüdiger, W. and Scheer, H. (eds). Chlorophylls and Bacteriochlorophylls. Biochemistry, Biophysics, Functions and Applications. Springer, Dordrecht, 2006.
https://doi.org/10.1007/1-4020-4516-6
3. Gurinovich, G., Sevchenko, A. and Solov’ev, K. Spectroscopy of chlorophyll and related compounds. U. S. Atomic Energy Commission Translation Series, 1971.
4. May, V. and Kühn, O. Charge and Energy Transfer Dynamics in Molecular Systems. Wiley–VCH, Berlin, 2000.
5. van Amerongen, H., Valkunas, L. and van Grondelle, R. Photosynthetic Excitons. World Scientific, Singapore, 2000.
https://doi.org/10.1142/3609
6. Duysens, L. N. M. Transfer of excitation energy in photosynthesis. PhD thesis. State University of Utrecht, Netherlands, 1952.
7. Seely, G. R. Energy transfer in a model of the photosynthetic unit of green plants. J. Theor. Biol., 1973, 40(1), 189–199.
https://doi.org/10.1016/0022-5193(73)90171-9
8. Bloembergen, N., Purcell, E. M. and Pound, R. V. Relaxation effects in nuclear magnetic resonance absorption. Phys. Rev., 1948, 73, 679–712.
https://doi.org/10.1103/PhysRev.73.679
9. Förster, T. Zwischenmolekulare Energiewanderung und Fluoreszenz. Ann. Phys., 1948, 437(2), 55–75.
https://doi.org/10.1002/andp.19484370105
10. Renge, I. and Mauring, K. Spectral shift mechanisms of chlorophylls in liquids and proteins. Spectrochim. Acta A Mol. Biomol. Spectrosc., 2013, 102, 301–313.
https://doi.org/10.1016/j.saa.2012.10.034
11. Krawczyk, S. The effects of hydrogen bonding and coordination interaction in visible absorption and vibrational spectra of chlorophyll a. Biochim. Biophys. Acta, 1989, 976, 140–149.
https://doi.org/10.1016/S0005-2728(89)80223-3
12. Freiberg, A. and Trinkunas, G. Unraveling the hidden nature of antenna excitations. In Photosynthesis in Silico: Understanding Complexity from Molecules to Ecosystems (Laisk, A., Nedbal, L., Govindjee, eds). Springer, Dordrecht, 2009, 55–82.
https://doi.org/10.1007/978-1-4020-9237-4_4
13. Jang, S. J. and Mennucci, B. Delocalized excitons in natural light-harvesting complexes. Rev. Mod. Phys., 2018, 90(3), 035003.
https://doi.org/10.1103/RevModPhys.90.035003
14. Song, K. S. and Williams, R. T. Self-Trapped Excitons. Springer, Berlin, Heidelberg, New York, 1992.
https://doi.org/10.1007/978-3-642-97432-8
15. Reimers, J. R., Biczysko, M., Bruce, D., Coker, D. F., Frankcombe, T. J., Hashimoto, H. et al. Challenges facing an understanding of the nature of low-energy excited states in photosynthesis. Biochim. Biophys. Acta Bioenerg., 2016, 1857(9), 1627–1640.
https://doi.org/10.1016/j.bbabio.2016.06.010
16. Cupellini, L., Caprasecca, S., Guido, C. A., Müh, F., Renger, T. and Mennucci, B. Coupling to charge transfer states is the key to modulate the optical bands for efficient light harvesting in purple bacteria. J. Phys. Chem. Lett., 2018, 9(23), 6892–6899.
https://doi.org/10.1021/acs.jpclett.8b03233
17. Shafizadeh, N., Ha-Thi, M. H., Soep, B., Gaveau, M. A., Piuzzi, F. and Pothier, C. Spectral characterization in a supersonic beam of neutral chlorophyll aevaporated from spinach leaves. J. Chem. Phys., 2011, 135, 114303.
https://doi.org/10.1063/1.3637048
18. Kjær, C., Gruber, E., Nielsen, S. B. and Andersen, L. H. Color tuning of chlorophyll a and b pigments revealed from gas-phase spectroscopy. Phys. Chem. Chem. Phys., 2020, 22, 20331–20336.
https://doi.org/10.1039/D0CP03210G
19. Sild, O. and Haller, K. (eds). Zero-Phonon Lines and Spectral Hole Burning in Spectroscopy and Photochemistry. Springer, Berlin, Heidelberg, 1988.
https://doi.org/10.1007/978-3-642-73638-4
20. Osad’ko, I. S. Selective Spectroscopy of Single Molecules. Springer, Berlin, Heidelberg, 2003.
https://doi.org/10.1007/978-3-662-05248-8
21. Barkai, E., Jung, Y. J. and Silbey, R. Theory of single-molecule spectroscopy: beyond the ensemble average. Annu. Rev. Phys. Chem., 2004, 55, 457–507.
https://doi.org/10.1146/annurev.physchem.55.111803.143246
22. Rebane, K. K. Impurity Spectra of Solids. Plenum Press, New York, 1970.
23. Szabo, A. Laser-induced fluorescence-line narrowing in ruby. Phys. Rev. Lett., 1970, 25(14), 924–926.
https://doi.org/10.1103/PhysRevLett.25.924
24. Gorokhovskii, A. A., Kaarli, R. K. and Rebane, L. A. Hole burning in the contour of a pure electronic line in a Shpol’skii system. JETP Lett., 1974, 20(7), 474–479.
25. Kharlamov, B. M., Personov, R. I. and Bykovskaya, L. A. Stable ‛gap’ in absorption spectra of solid solutions of organic molecules by laser irradiation. Opt. Commun., 1974, 12(2), 191–193.
https://doi.org/10.1016/0030-4018(74)90388-5
26. Rebane, K. K. and Avarmaa, R. A. Sharp line vibronic spectra of chlorophyll and its derivatives in solid solutions. Chem. Phys., 1982, 68(1–2), 191–200.
https://doi.org/10.1016/0301-0104(82)85094-5
27. Rebane, K. K. Purely electronic zero–phonon line as the foundation for high resolution matrix spectroscopy, single impurity molecule spectroscopy, persistent spectral hole burning. J. Lumin., 2002, 100(1–4), 219–232.
https://doi.org/10.1016/S0022-2313(02)00455-6
28. Jaaniso, R. V. and Avarmaa, R. A. Measurement of the inhomogeneous distribution function and homogeneous spectra of an impurity molecule in a glassy matrix. J. Appl. Spectrosc., 1986, 44(4), 365–370.
https://doi.org/10.1007/BF00661051
29. Fünfschilling, J., Glatz, D. and Zschokke-Gränacher, I. Hole-burning spectroscopy as a tool to eliminate inhomogeneous broadening. J. Lumin., 1986, 36, 85–92.
https://doi.org/10.1016/0022-2313(86)90056-6
30. Rätsep, M. and Freiberg, A. Resonant emission from the B870 exciton state and electron–phonon coupling in the LH2 antenna chromoprotein. Chem. Phys. Lett., 2003, 377(3–4), 371–376.
https://doi.org/10.1016/S0009-2614(03)01193-X
31. Rätsep, M. and Freiberg, A. Electron–phonon and vibronic couplings in the FMO bacteriochlorophyll a antenna complex studied by difference fluorescence line narrowing. J. Lumin., 2007, 127(1), 251–259.
https://doi.org/10.1016/j.jlumin.2007.02.053
32. Pieper, J., Artene, P., Rätsep, M., Pajusalu, M. and Freiberg, A. Evaluation of electron–phonon coupling and spectral densities of pigment–protein complexes by line-narrowed optical spectroscopy. J. Phys. Chem. B, 2018, 122(40), 9289–9301.
https://doi.org/10.1021/acs.jpcb.8b05220
33. Osad’ko, I. S. Determination of electron-phonon coupling from structured optical spectra of impurity centers. Sov. Phys. Usp., 1979, 22(5), 311.
https://doi.org/10.1070/PU1979v022n05ABEH005496
34. Gooijer, C., Ariese, F. and Hofstraat, J. W. (eds). Shpol’skii Spectroscopy and Other Site-Selective Methods. John Wiley & Sons, New York, NY, 2000.
35. Orrit, M., Bernard, J. and Personov, R. I. High-resolution spectroscopy of organic molecules in solids: from fluorescence line narrowing and hole burning to single molecule spectroscopy. J. Phys. Chem., 1993, 97(40), 10256–10268.
https://doi.org/10.1021/j100142a003
36. Jankowiak, R., Reppert, M., Zazubovich, V., Pieper, J. and Reinot, T. Site selective and single complex laser-based spectroscopies: A window on excited state electronic structure, excitation energy transfer, and electron-phonon coupling of selected photosynthetic complexes. Chem. Rev., 2011, 111(8), 4546–4598.
https://doi.org/10.1021/cr100234j
37. Naumov, A. V., Gorshelev, A. A., Vainer, Y. G., Kador, L. and Köhler, J. Impurity spectroscopy at its ultimate limit: relation between bulk spectrum, inhomogeneous broadening, and local disorder by spectroscopy of (nearly) all individual dopant molecules in solids. Phys. Chem. Chem. Phys., 2011, 13(5), 1734–1742.
https://doi.org/10.1039/C0CP01689F
38. Naumov, A. V. Low-temperature spectroscopy of organic molecules in solid matrices: from the Shpol’skii effect to laser luminescent spectromicroscopy for all effectively emitting single molecules. Phys.-Uspekhi, 2013, 56(6), 605–622.
https://doi.org/10.3367/UFNe.0183.201306f.0633
39. Purchase, R. and Völker, S. Spectral hole burning: examples from photosynthesis. Photosynth. Res., 2009, 101, 245–266.
https://doi.org/10.1007/s11120-009-9484-5
40. Freiberg, A. and Garab, G. Basic optical spectroscopy for light harvesting. In Light Harvesting in Photosynthesis (Groce, R., van Grondelle, R., van Amerongen, H. and van Stokkum, I., eds). CRC Press, Boca Raton, 2018, 381–426.
https://doi.org/10.1201/9781351242899-17
41. Renge, I., Mauring, K. and Avarmaa, R. High-resolution optical spectra in vivo: Photoactive protochlorophyllide in etiolated leaves at 5 K. Biochem. Biophys. Acta, 1984, 766, 501–504.
https://doi.org/10.1016/0005-2728(84)90266-4
42. Avarmaa, R. A. and Rebane, K. K. High-resolution optical spectra of chlorophyll molecules. Spectrochim. Acta A Mol. Biomol. Spectrosc., 1985, 41(12), 1365–1380.
https://doi.org/10.1016/0584-8539(85)80189-6
43. Renge, I., Mauring, K. and Avarmaa, R. A. Site-selection optical spectra of bacteriochlorophyll and bacteriopheophytin in frozen solutions. J. Lumin., 1987, 37, 207–214.
https://doi.org/10.1016/0022-2313(87)90161-X
44. Avarmaa, R. A. and Rebane, K. K. Zero-phonon lines in spectra of chlorophyll-type molecules in low-temperature solid matrices. Sov. Phys. Usp., 1988, 154(3), 433–458.
https://doi.org/10.3367/UFNr.0154.198803c.0433
45. Gouterman, M. and Stryer, L. Fluorescence polarization of some porphyrins. J. Chem. Phys., 1962, 37, 2260–2266.
https://doi.org/10.1063/1.1732996
46. Houssier, C. and Sauer, K. Circular dichroism and magnetic circular dichroism of the chlorophyll and protochlorophyll pigments. J. Am. Chem. Soc., 1970, 92(4), 779–791.
https://doi.org/10.1021/ja00707a007
47. Deroche, M. E. and Briantais, J. M. Absorption spectra of chlorophyll forms, β-carotene and lutein in freeze–dried chloroplasts. Photochem. Photobiol., 1974, 19(3), 233–240.
https://doi.org/10.1111/j.1751-1097.1974.tb06504.x
48. Fragata, M. U., Nordén, B. and Kurucsev, T. Linear dichroism (250–700 nm) of chlorophyll a and pheophytin a oriented in a lamellar phase of glycerylmonooctanoate/H2O. Characterization of electronic transitions. Photochem. Photobiol., 1988, 47(1), 133–143.
https://doi.org/10.1111/j.1751-1097.1988.tb02703.x
49. Umetsu, M., Wang, Z.-Y., Kobayashi, M. and Nozawa, T. Interaction of photosynthetic pigments with various organic solvents: Magnetic circular dichroism approach and application to chlorosomes. Biochem. Biophys. Acta Bioenerg., 1999, 1410(1), 19–31.
https://doi.org/10.1016/S0005-2728(98)00170-4
50. Reimers, J. R., Cai, Z.–L., Kobayashi, R., Rätsep, M., Freiberg, A. and Krausz, E. The role of high-level calculations in the assignment of the Q-band spectra of chlorophyll. AIP Conf. Proc., 2014, 1618(18), 18–22.
https://doi.org/10.1063/1.4897663
51. Bauman, D. and Wrobel, D. Dichroism and polarized fluorescence of chlorophyll a, chlorophyll c and bacteriochlorophyll a dissolved in liquid crystals.Biophys. Chem., 1980, 12(1), 83–91.
https://doi.org/10.1016/0301-4622(80)80042-1
52. Song, Y., Schubert, A., Maret, E., Burdick, R. K., Dunietz, B. D., Geva, E. and Ogilvie, J. P. Vibronic structure of photosynthetic pigments probed by polarized two-dimensional electronic spectroscopy and ab initio calculations. Chem. Sci., 2019, 10(35), 8143–8153.
https://doi.org/10.1039/C9SC02329A
53. Sundholm, D. Density functional theory calculations of the visible spectrum of chlorophyll a. Chem. Phys. Lett., 1999, 302(5–6), 480–484.
https://doi.org/10.1016/S0009-2614(99)00194-3
54. Jusélius, J. and Sundholm, D. The aromatic pathways of porphins, chlorins and bacteriochlorins. Phys. Chem. Chem. Phys., 2000, 2(10), 2145–2151.
https://doi.org/10.1039/b000260g
55. Pajusalu, M., Kunz, R., Rätsep, M., Timpmann, K., Köhler, J. and Freiberg, A. Unified analysis of ensemble and single–complex optical spectral data from light-harvesting complex-2 chromoproteins for gaining deeper insight into bacterial photosynthesis. Phys. Rev. E, 2015, 92(5), 052709.
https://doi.org/10.1103/PhysRevE.92.052709
56. Gouterman, M. Spectra of porphyrins. J. Mol. Spectrosc., 1961, 6, 138–163.
https://doi.org/10.1016/0022-2852(61)90236-3
57. Gouterman, M., Wagnière, G. H. and Snyder, L. C. Spectra of porphyrins: Part II. Four orbital model. J. Mol. Spectrosc., 1963, 11, 108–127.
https://doi.org/10.1016/0022-2852(63)90011-0
58. Huang, K. and Rhys, A. Theory of light absorption and non-radiative transitions in F-centres. Proc. Math. Phys. Eng. Sci., 1950, 204(1078), 406–423.
https://doi.org/10.1098/rspa.1950.0184
59. de Jong, M., Seijo, L., Meijerink, A. and Rabouw, F. T. Resolving the ambiguity in the relation between Stokes shift and Huang–Rhys parameter. Phys. Chem. Chem. Phys., 2015, 17(26), 16959–16969.
https://doi.org/10.1039/C5CP02093J
60. Fulton, R. L. and Gouterman, M. Vibronic coupling. I. Mathematical treatment for two electronic states. J. Chem. Phys., 1961, 35, 1059–1071.
https://doi.org/10.1063/1.1701181
61. Piepho, S. B. and Schatz, P. Group Theory in Spectroscopy with Applications to Magnetic Circular Dichroism. Wiley, New York, NY, 1983.
62. Fischer, G. Vibronic Coupling: the Interaction between the Electronic and Nuclear Motions. Academic Press, London, Orlando, 1984.
63. Reimers, J. R., Cai, Z.–L., Kobayashi, K., Rätsep, M., Freiberg, A. and Krausz, E. Assignment of the Q-bands of the chlorophylls: coherence loss via Qx-Qymixing. Sci. Rep., 2013, 3, 2761.
https://doi.org/10.1038/srep02761
64. Duschinsky, F. On the interpretation of electronic spectra of polyatomic molecules. Acta Physicochim. USSR, 1937, 7, 551.
65. Davydov, A. S. Theory of Molecular Excitons. Plenum Press, New York, NY, 1971.
https://doi.org/10.1007/978-1-4899-5169-4
66. Linnanto, J. and Korppi–Tommola, J. Quantum chemical simulation of excited states of chlorophylls, bacteriochlorophylls and their complexes. Phys. Chem. Chem. Phys., 2006, 8(6), 663–687.
https://doi.org/10.1039/B513086G
67. Rätsep, M., Cai, Z.-L., Reimers, J. R. and Freiberg, A. Demonstration and interpretation of significant asymmetry in the low-resolution and high-resolution Qy fluorescence and absorption spectra of bacteriochlorophyll a. J. Chem. Phys., 2011, 134(2), 024506.
https://doi.org/10.1063/1.3518685
68. Cogdell, R. J., Gall, A. and Köhler, J. The architecture and function of the light-harvesting apparatus of purple bacteria: from single molecules to in vivo membranes. Q. Rev. Biophys., 2006, 39(3), 227324.
https://doi.org/10.1017/S0033583506004434
69. Parr, R. G., Craig, D. P. and Ross, I. G. Molecular orbital calculations of the lower excited electronic levels of benzene, configuration interaction included.J. Chem. Phys., 1950, 18(12), 1561–1563.
https://doi.org/10.1063/1.1747540
70. Norden, B., Fragata, M. and Kurucsev, T. X- and Y-polarized spectra of chlorophyll a and pheophytin a in the red region: resolution enhancement and Gaussian deconvolution. Aust. J. Chem., 1992, 45(10), 1559–1570.
https://doi.org/10.1071/CH9921559
71. van Zandvoort, M. A. M. J., Wróbel, D., Lettinga, P., van Ginkel, G. and Levine, Y. K. The orientation of the transition dipole moments of chlorophyll aand pheophytin a in their molecular frame. Photochem. Photobiol., 1995, 62(2), 299–308.
https://doi.org/10.1111/j.1751-1097.1995.tb05272.x
72. Kleima, F. J., Hofmann, E., Gobets, B., van Stokkum, I. H. M., van Grondelle, R., Diederichs, K. and van Amerongen, H. Förster excitation energy transfer in peridinin-chlorophyll-a-protein. Biophys. J., 2000, 78(1), 344353.
https://doi.org/10.1016/S0006-3495(00)76597-0
73. Simonetto, R., Crimi, M., Sandonà, D., Croce, R., Cinque, G., Breton, J. and Bassi, R. Orientation of chlorophyll transition moments in the higher-plant light-harvesting complex CP29. Biochem., 1999, 38(40), 12974–12983.
https://doi.org/10.1021/bi991140s
74. Cai, Z.-L., Sendt, K. and Reimers, J. R. Failure of density-functional theory and time-dependent density-functional theory for large extended π systems. J. Chem. Phys., 2002, 117(12), 5543–5549.
https://doi.org/10.1063/1.1501131
75. Cai, Z.-L., Crossley, M. J., Reimers, J. R., Kobayashi, R. and Amos, R. D. Density functional theory for charge transfer: The nature of the N-bands of porphyrins and chlorophylls revealed through CAM-B3LYP, CASPT2, and SAC-CI calculations. J. Phys. Chem. B, 2006, 110(31), 15624–15632.
https://doi.org/10.1021/jp063376t
76. Sponer, H. and Teller, E. Electronic spectra of polyatomic molecules. Rev. Mod. Phys., 1941, 13(2), 75.
https://doi.org/10.1103/RevModPhys.13.75
77. Longuet-Higgins, H. C. Some recent developments in the theory of molecular energy levels. Adv. Spectrosc., 1961, 2, 429–472.
78. Ballhausen, C. J. and Hansen, A. E. Electronic spectra. Annu. Rev. Phys. Chem., 1972, 23, 15–38.
https://doi.org/10.1146/annurev.pc.23.100172.000311
79. Azumi, T. and Matsuzaki, K. What does the term “vibronic coupling” mean? Photochem. Photobiol., 1977, 25(3), 315–326.
https://doi.org/10.1111/j.1751-1097.1977.tb06918.x
80. Lax, M. The Franck–Condon principle and its application to crystals. J. Chem. Phys., 1952, 20, 1752.
https://doi.org/10.1063/1.1700283
81. Markham, J. J. Interaction of normal modes with electron traps. Rev. Mod. Phys., 1959, 31(4), 956–989.
https://doi.org/10.1103/RevModPhys.31.956
82. McCumber, D. E. Theory of vibrational structure in optical spectra of impurities in solids. I. Singlets. J. Math. Phys., 1964, 5(2), 221–230.
https://doi.org/10.1063/1.1704112
83. Holstein, T. Studies of polaron motion: Part I. The molecular-crystal model. Ann. Phys., 1959, 8(3), 325342.
https://doi.org/10.1016/0003-4916(59)90002-8
84. Dexter, D. L. A theory of sensitized luminescence in solids. J. Chem. Phys., 1953, 21(5), 836–850.
https://doi.org/10.1063/1.1699044
85. Reimers, J. R. A practical method for the use of curvilinear coordinates in calculations of normal-mode-projected displacements and Duschinsky rotation matrices for large molecules. J. Chem. Phys., 2001, 115, 9103–9109.
https://doi.org/10.1063/1.1412875
86. Frisch, M. J., Trucks, G. W., Schlegel, H. B., Scuseria, G. E., Robb, M. A., Cheeseman, J. R. et al. Gaussian 16, Revision C.01. Gaussian Inc., Wallingford CT, 2016.
87. Wales, D. J. A microscopic basis for the global appearance of energy landscapes. Science, 2001, 293, 2067–2070.
https://doi.org/10.1126/science.1062565
88. Saunders, P. T. An Introduction to Catastrophe Theory. Cambridge University Press, 1980.
https://doi.org/10.1017/CBO9781139171533
89. Reimers, J. R., McKemmish, L. K., McKenzie, R. H. and Hush, N. S. Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: the general importance of all three Born–Oppenheimer breakdown corrections. Phys. Chem. Chem. Phys., 2015, 17(38), 24641–24665.
https://doi.org/10.1039/C5CP02238J
90. Born, M. and Oppenheimer, R. Zur Quantentheorie der Molekeln. Ann. Phys., 1927, 389, 457–484.
https://doi.org/10.1002/andp.19273892002
91. Hush, N. S. Adiabatic rate processes at electrodes. I. Energy-charge relationships. J. Chem. Phys., 1958, 28(5), 962–972.
https://doi.org/10.1063/1.1744305
92. Levich, V. G. and Dogonadze, R. R. Theory of rediationless electron transitions between ions in solution. Dokl. Akad. Nauk SSSR Ser. Fiz. Khim., 1959, 124, 123–126.
93. Levich, V. G. and Dogonadze, R. R. Adiabatic theory for electron-transfer processes in solution. Dokl. Akad. Nauk SSSR., 1960, 133, 158–161.
94. Frank-Kamenetskiĭ, M. D. and Lukashin, A. V. Electron-vibrational interactions in polyatomic molecules. Sov. Phys. Usp., 1975, 18(6), 391–409.
https://doi.org/10.1070/PU1975v018n06ABEH001963
95. Reimers, J. R. and Watts, R. O. The structure and vibrational spectra of small clusters of water molecules. Chem. Phys., 1984, 85(1), 83–112.
https://doi.org/10.1016/S0301-0104(84)85175-7
96. Wilson, E. B., Decius, J. G., Cross, P. G. and Lagemann, R. T. Molecular vibrations. Am. J. Phys., 1955, 23.
https://doi.org/10.1119/1.1934101
97. Reimers, J. R., and Watts, R. O. A local mode potential function for the water molecule. Mol. Phys., 1984, 52(2), 357–381.
https://doi.org/10.1080/00268978400101271
98. Condon, E. U. Nuclear motions associated with electron transitions in diatomic molecules. Phys. Rev., 1928, 32(6), 858–872.
https://doi.org/10.1103/PhysRev.32.858
99. Herzberg, G. and Teller, E. Schwingungsstruktur der Elektronenübergänge bei mehratomigen Molekülen. Z. Phys. Chem., 1933, 21B, 410–446.
https://doi.org/10.1515/zpch-1933-2136
100. Small, G. J. Herzberg–Teller vibronic coupling and the Duschinsky effect. J. Chem. Phys., 1971, 54(8), 3300–3306.
https://doi.org/10.1063/1.1675343
101. Chappell, P. J. and Ross, I. G. Vibronic coupling by out-of-plane modes in pyridine, pyrazine and quinoxaline. Chem. Phys. Lett., 1976, 43, 440–445.
https://doi.org/10.1016/0009-2614(76)80595-7
102. Albrecht, A. C. “Forbidden” character in allowed electronic transitions. J. Chem. Phys., 1960, 33, 156–169.
https://doi.org/10.1063/1.1731071
103. Ziegler, L. and Albrecht, A. C. Vibronic calculations in benzene by CNDO/S. J. Chem. Phys., 1974, 60, 3558–3561.
https://doi.org/10.1063/1.1681573
104. Craig, D. P. and Small, G. J. Totally symmetric vibronic perturbations and the phenanthrene 3400Å spectrum. J. Chem. Phys., 1969, 50, 3827–3834.
https://doi.org/10.1063/1.1671634
105. Piepho, S. B., Krausz, E. R. and Schatz, P. N. Vibronic coupling model for calculation of mixed valence absorption profiles. J. Am. Chem. Soc., 1978, 100, 2996–3005.
https://doi.org/10.1021/ja00478a011
106. Chappell, P. J., Fischer, G., Reimers, J. R. and Ross, I. G. Electronic spectrum of 1,5-naphthyridine: theoretical treatment of vibronic coupling. J. Mol. Spectrosc., 1981, 87(2), 316–330.
https://doi.org/10.1016/0022-2852(81)90405-7
107. Fisher, G. Vibronic Coupling. Academic Press, London, 1984.
108. London, F. Zur Theorie nicht adiabatisch verlaufender chemischer Prozesse. Z. Phys., 1932, 74, 143174.
https://doi.org/10.1007/BF01342370
109. Shuler, K. E. Adiabatic correlation rules for reactions involving polyatomic intermediate complexes and their application to the formation of OH (2 ∑+) in the H2 - O2 flame. J. Chem. Phys., 1953, 21(4), 624–632.
https://doi.org/10.1063/1.1698979
110. Ross, I. G. Vibrational electronic coupling and a closer look at a severe case. Isr. J. Chem., 1975, 14, 118–123.
https://doi.org/10.1002/ijch.197500051
111. Piepho, S. B., Krausz, E. R. and Schatz, P. N. Vibronic coupling model for calculation of mixed valence absorption profiles. J. Am. Chem. Soc., 1978, 100, 2996–3005.
https://doi.org/10.1021/ja00478a011
112. Piepho, S. B. and Schatz, P. N. Group Theory in Spectroscopy: with Applications to Magnetic Circular Dichroism. Wiley, New York, NY, 1983.
113. Holstein, T. Studies of polaron motion: Part II. The “small” polaron. Ann. Phys., 1959, 8, 343–389.
https://doi.org/10.1016/0003-4916(59)90003-X
114. Hush, N. S. Inequivalent XPS binding energies in symmetrical delocalized mixed-valence complexes. Chem. Phys., 1975, 10, 361–366.
https://doi.org/10.1016/0301-0104(75)87049-2
115. Öpik, U. and Pryce, M. H. L. Studies of the Jahn-Teller effect. I. A survey of the static problem. Proc. Math. Phys. Eng. Sci.,1957, 238(1215), 425–447.
https://doi.org/10.1098/rspa.1957.0010
116. Pekar, S. and Deigen, M. Quantum states and optical transitions of electron in a polaron and at a color center of a crystal. Zh. Eksp. Teor. Fiz., 1948, 18(6), 481–486.
117. Rätsep, M., Pajusalu, M. and Freiberg, A. Wavelength-dependent electron-phonon coupling in impurity glasses. Chem. Phys. Lett. 2009, 479(1), 140–143.
https://doi.org/10.1016/j.cplett.2009.07.094
118. Ingold, C. K. and Leeke, F. M. Electronic spectra of polyatomic molecules. Vibrations of the 1B2ustate of benzene. Nature, 1946, 157, 46–47.
https://doi.org/10.1038/157046a0
119. Azumi, T. and Matsuzaki, K. What does the term vibronic coupling mean? Photochem. Photobiol., 1977, 25, 315–326.
https://doi.org/10.1111/j.1751-1097.1977.tb06918.x
120. Ballhausen, C. J. and Hansen, A. E. Electronic spectra. Annu. Rev. Phys. Chem., 1972, 23, 15–38.
https://doi.org/10.1146/annurev.pc.23.100172.000311
121. Freiberg, A., Rätsep, M., Timpmann, K. and Trinkunas, G. Excitonic polarons in quasi-one-dimensional LH1 and LH2 bacteriochlorophyll a antenna aggregates from photosynthetic bacteria: A wavelength-dependent selective spectroscopy study. Chem. Phys., 2009, 357(1), 102–112.
https://doi.org/10.1016/j.chemphys.2008.10.043
122. Rätsep, M., Linnanto, J. M., Muru, R., Biczysko, M., Reimers, J. R. and Freiberg, A. Absorption-emission symmetry breaking and the different origins of vibrational structures of the 1Qy and 1Qx electronic transitions of pheophytin a. J. Chem. Phys., 2019, 151, 165102.
https://doi.org/10.1063/1.5116265
123. Zazubovich, V., Tibe, I. and Small, G. J. Bacteriochlorophyll a Frank-Condon factors for the S0-S1(Qy) transition. J. Phys. Chem. B, 2001, 105(49), 12410–12417.
https://doi.org/10.1021/jp012804m
124. Reimers, J. R., Rätsep, M. and Freiberg, A. Asymmetry in the Qy fluorescence and absorption spectra of chlorophyll a pertaining to exciton dynamics.Frontiers in Chemistry, 2020, 8, 588289.
https://doi.org/10.3389/fchem.2020.588289
125. Rätsep, M., Linnanto, J. and Freiberg, A. Mirror symmetry and vibrational structure in optical spectra of chlorophyll a. J. Chem. Phys., 2009, 130(19), 194501.
https://doi.org/10.1063/1.3125183
126. McKemmish, L. K., McKenzie, R. H., Hush, N. S. and Reimers, J. R. Quantum entanglement between electronic and vibrational degrees of freedom in molecules. J. Chem. Phys., 2011, 135(24), 244110.
https://doi.org/10.1063/1.3671386
127. McKemmish, L., McKenzie, R. H., Hush, N. S. and Reimers, J. R. Electron-vibration entanglement in the Born–Oppenheimer description of chemical reactions and spectroscopy. Phys. Chem. Chem. Phys., 2015, 17(38), 24666–24682.
https://doi.org/10.1039/C5CP02239H
128. Reimers, J. R. and Hush, N. S. Electron transfer and energy transfer through bridged systems. I. Formalism. Chem. Phys., 1989, 134(2–3), 323–354.
https://doi.org/10.1016/0301-0104(89)87167-8
129. Shi, Y., Liu, J.-Y. and Han, K.-L. Investigation of the internal conversion time of the chlorophyll a from S3, S2 to S1. Chem. Phys. Lett., 2005, 410, 260–263.
https://doi.org/10.1016/j.cplett.2005.05.017
130. Paschenko, V. Z., Gorokhov, V. V., Korvatovskiy, B. N., Bocharov, E. A., Knox, P. P., Sarkisov, O. M. et al. The rate of Qx→Qy relaxation in bacteriochlorophylls of reaction centers from Rhodobacter sphaeroides determined by kinetics of the ultrafast carotenoid bandshift. Biochim. Biophys. Acta Bioenerg., 2012, 1817, 1399–1406.
https://doi.org/10.1016/j.bbabio.2012.02.006
131. Visser, H. M., Somsen, O. J. G., van Mourik, F., Lin, S., van Stokkum, I. H. M. and van Grondelle, R. Direct observation of sub-picosecond equilibration of excitation energy in the light-harvesting antenna of Rhodospirillum rubrum. Biophys. J., 1995, 69, 1083–1099.
https://doi.org/10.1016/S0006-3495(95)79982-9
132. Ganago, A. O., Parker, E. P., Laible, P. D., Albrecht, A. C. and Owens, T. G. Femtosecond dynamics of population and coherence of the S2 singlet excited state of bacteriochlorophyll (the Qx absorption band) in vivo and in vitro. Laser Phys., 1995, 5, 693–698.
133. Causgrove, T. P., Yang, S. and Struve, W. S. Polarized pump-probe spectroscopy of exciton transport in bacteriochlorophyll a-protein from Prosthecochloris aestuarii. J. Phys. Chem., 1988, 92, 6790–6795.
https://doi.org/10.1021/j100334a058
134. Chai, J.-D. and Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. Phys. Chem. Chem. Phys., 2008, 10(44), 6615–6620.
https://doi.org/10.1039/b810189b
135. Sirohiwal, A., Berraud-Pache, R., Neese, F., Izsák, R. and Pantazis, D. A. Accurate computation of the absorption spectrum of chlorophyll a with pair natural orbital coupled cluster methods. J. Phys. Chem. B, 2020, 124(40), 8761–8771.
https://doi.org/10.1021/acs.jpcb.0c05761
136. Santoro, F., Lami, A., Improta, R. and Barone, V. Effective method to compute vibrationally resolved optical spectra of large molecules at finite temperature in the gas phase and in solution. J. Chem. Phys., 2007, 126(18), 184102.
https://doi.org/10.1063/1.2721539
137. Santoro, F., Lami, A., Improta, R., Bloino, J. and Barone, V. Effective method for the computation of optical spectra of large molecules at finite temperature including the Duschinsky and Herzberg–Teller effect: The Qx band of porphyrin as a case study. J. Chem. Phys., 2008, 128(22), 224311.
https://doi.org/10.1063/1.2929846
138. Cerezo, J., Aranda, D., Avila Ferrer, F. J., Prampolini, G. and Santoro, F. Adiabatic-molecular dynamics generalized vertical Hessian approach: A mixed quantum classical method to compute electronic spectra of flexible molecules in the condensed phase. J. Chem. Theory Comput., 2020, 16(2), 1215–1231.
https://doi.org/10.1021/acs.jctc.9b01009
139. Santoro, F. and Jacquemin, D. Going beyond the vertical approximation with time-dependent density functional theory. WIREs Comput. Mol. Sci., 2016, 6(5), 460–486.
https://doi.org/10.1002/wcms.1260
140. Götze, J. P., Anders, F., Petry, S., Witte, J. F. and Lokstein, H. Spectral characterization of the main pigments in the plant photosynthetic apparatus by theory and experiment. Chem. Phys., 2022, 559, 111517.
https://doi.org/10.1016/j.chemphys.2022.111517
141. Kundu, S., Roy, P. P., Fleming, G. R. and Makri, N. Franck–Condon and Herzberg–Teller signatures in molecular absorption and emission spectra. J. Phys. Chem. B, 2022, 126(15), 2899–2911.
https://doi.org/10.1021/acs.jpcb.2c00846
142. Rätsep, M., Pajusalu, M., Linnanto, J. M. and Freiberg, A. Subtle spectral effects accompanying the assembly of bacteriochlorophylls into cyclic light harvesting complexes revealed by high-resolution fluorescence spectroscopy. J. Chem. Phys., 2014, 141(15), 155102.
https://doi.org/10.1063/1.4897637
143. Pajusalu, M., Rätsep, M., Trinkunas, G. and Freiberg, A. Davydov splitting of excitons in cyclic bacteriochlorophyll a nanoaggregates of bacterial light-harvesting complexes between 4.5 and 263 K. ChemPhysChem., 2011, 12(3), 634–644.
https://doi.org/10.1002/cphc.201000913
144. Freiberg, A., Pajusalu, M. and Rätsep, M. Excitons in intact cells of photosynthetic bacteria. J. Phys. Chem. B, 2013, 117, 11007–11014.
https://doi.org/10.1021/jp3098523
145. Freiberg, A., Rätsep, M. and Timpmann, K. A comparative spectroscopic and kinetic study of photoexcitations in detergent-isolated and membrane-embedded LH2 light-harvesting complexes. Biochem. Biophys. Acta, 2012, 1817(8), 1471–1482.
https://doi.org/10.1016/j.bbabio.2011.11.019
146. Sundström, V., Pullerits, T. and van Grondelle, R. Photosynthetic light-harvesting: Reconciling dynamics and structure of purple bacterial LH2 reveals function of photosynthetic unit. J. Phys. Chem. B, 1999, 103(13), 2327–2346.
https://doi.org/10.1021/jp983722+
147. Hu, X., Ritz, T., Damjanović, A., Autenrieth, F. and Schulten, K. Photosynthetic apparatus of purple bacteria. Q. Rev. Biophys., 2002, 35(1), 1–62.
https://doi.org/10.1017/S0033583501003754
148. Hunter, C. N., Daldal, F., Thurnauer, M. C. and Beatty, J. T. (eds). The Purple Phototrophic Bacteria. Springer, Dordrecht, 2009.
https://doi.org/10.1007/978-1-4020-8815-5
149. Green, B. R. and Parson, W. W. (eds). Ligh-Harvesting Antennas in Photosynthesis. Kluwer Academic Publishers, Dordrecht-Boston-London, 2003.
150. Osad’ko, I. S. Theory of light absorption and emission by organic impurity centers. In Spectroscopy and Excitation Dynamics of Condensed Molecular Systems (Agranovich, V. M. and Hochstrasser, R. M., eds). North–Holland, Amsterdam, 1983, 438–514.
151. Wu, H.-M., Rätsep, M., Lee, I.-J., Cogdell, R. J. and Small, G. J. Exciton level structure and energy disorder of the B850 ring of the LH2 antenna complex. J. Phys. Chem. B, 1997, 101(38), 7654–7663.
https://doi.org/10.1021/jp971514w
152. Freiberg, A., Timpmann, K., Ruus, R. and Woodbury, N. W. Disordered exciton analysis of linear and nonlinear absorption spectra of antenna bacteriochlorophyll aggregates: LH2-only mutant chromatophores of Rhodobacter sphaeroides at 8 K under spectrally selective excitation. J. Phys. Chem. B, 1999, 103(45), 10032–10041.
https://doi.org/10.1021/jp991676n
153. Hochstrasser, R. M. and Whiteman, J. D. Exciton band structure and properties of a real linear chain in a molecular crystal. J. Chem. Phys., 1972, 56, 5945–5958.
https://doi.org/10.1063/1.1677140
154. Hanson, D. M. Effect of the exciton bandwidth on electron-phonon coupling in molecular crystals. Chem. Phys. Lett., 1976, 43, 217–220.
https://doi.org/10.1016/0009-2614(76)85288-8
155. Kell, A., Khmelnitskiy, A., Jassas, M. and Jankowiak, R. Dichotomous disorder versus excitonic splitting of the B800 band of Allochromatium vinosum. J. Phys. Chem. Lett., 2018, 9(14), 4125–4129.
https://doi.org/10.1021/acs.jpclett.8b01584
156. Ostrowski, W. Michael S. Tswett–inventor of column chromatography. Folia Biol., 1968, 16(4), 429–448.
157. Craig, D. P. The Franck–Condon principle and the size of the excited benzene molecule. J. Chem. Soc., 1950, 2146–2151.
https://doi.org/10.1039/JR9500002146
158. Craig, D. P. The role of Eg+ vibrations in the 2600-A benzene band system. J. Chem. Soc., 1950, 59–62.
https://doi.org/10.1039/jr9500000059
159. Cai, Z.-L., Crossley, M. J., Reimers, J. R., Kobayashi, R. and Amos, R. D. Density-functional theory for charge-transfer: the nature of the N-bands of porphyrins and chlorophylls revealed through CAM-B3LYP, CASPT2, and SAC-CI calculations. J. Phys. Chem. B, 2006, 110(31), 15624–15632.
https://doi.org/10.1021/jp063376t
160. Reimers, J. R. and Hush, N. S. A unified description of the electrochemical, charge distribution, and spectroscopic properties of the special-pair radical cation in bacterial photosynthesis. J. Am. Chem. Soc., 2004, 126, 4132–4144.
https://doi.org/10.1021/ja036883m
