No Access Submitted: 16 November 2020 Accepted: 10 February 2021 Published Online: 09 March 2021
J. Chem. Phys. 154, 104112 (2021);
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  • Ruth H. Tichauer
  • Johannes Feist
  • Gerrit Groenhof
Coupling molecules to the confined light modes of an optical cavity is showing great promise for manipulating chemical reactions. However, to fully exploit this principle and use cavities as a new tool for controlling chemistry, a complete understanding of the effects of strong light–matter coupling on molecular dynamics and reactivity is required. While quantum chemistry can provide atomistic insight into the reactivity of uncoupled molecules, the possibilities to also explore strongly coupled systems are still rather limited due to the challenges associated with an accurate description of the cavity in such calculations. Despite recent progress in introducing strong coupling effects into quantum chemistry calculations, applications are mostly restricted to single or simplified molecules in ideal lossless cavities that support a single light mode only. However, even if commonly used planar mirror micro-cavities are characterized by a fundamental mode with a frequency determined by the distance between the mirrors, the cavity energy also depends on the wave vector of the incident light rays. To account for this dependency, called cavity dispersion, in atomistic simulations of molecules in optical cavities, we have extended our multi-scale molecular dynamics model for strongly coupled molecular ensembles to include multiple confined light modes. To validate the new model, we have performed simulations of up to 512 Rhodamine molecules in red-detuned Fabry–Pérot cavities. The results of our simulations suggest that after resonant excitation into the upper polariton at a fixed wave vector, or incidence angle, the coupled cavity-molecule system rapidly decays into dark states that lack dispersion. Slower relaxation from the dark state manifold into both the upper and lower bright polaritons causes observable photo-luminescence from the molecule–cavity system along the two polariton dispersion branches that ultimately evolves toward the bottom of the lower polariton branch, in line with experimental observations. We anticipate that the more realistic cavity description in our approach will help to better understand and predict how cavities can modify molecular properties.
The authors thank D. Morozov and J. J. Toppari for commenting on this manuscript and many fruitful discussions. This work was supported by the Academy of Finland (Grant No. 323996 to G.G.) as well as the European Research Council (Grant No. ERC-2016-StG-714870 to J.F.) and the Spanish Ministry for Science, Innovation, and Universities—AEI (Grant No. RTI2018-099737-B-I00 to J.F.). We thank the Center for Scientific Computing (CSC-IT Center for Science) for generous computational resources.
  1. 1. J. A. Hutchison, T. Schwartz, C. Genet, E. Devaux, and T. W. Ebbesen, “Modifying chemical landscapes by coupling to vacuum fields,” Angew. Chem., Int. Ed. 51, 1592–1596 (2012)., Google ScholarCrossref, ISI
  2. 2. A. Thomas, J. George, A. Shalabney, M. Dryzhakov, S. J. Varma, J. Moran, T. Chervy, X. Zhong, E. Devaux, C. Genet, J. A. Hutchison, and T. W. Ebbesen, “Ground-state chemical reactivity under vibrational coupling to the vacuum electromagnetic field,” Angew. Chem., Int. Ed. 55, 11462–11466 (2016)., Google ScholarCrossref
  3. 3. K. Stranius, M. Herzog, and K. Börjesson, “Selective manipulation of electronically excited states through strong light-matter interactions,” Nat. Commun. 9, 2273 (2018)., Google ScholarCrossref
  4. 4. B. Munkhbat, M. Wersäll, D. G. Baranov, T. J. Antosiewicz, and T. Shegai, “Suppression of photo-oxidation of organic chromophores by strong coupling to plasmonic nanoantennas,” Sci. Adv. 4, eaas9552 (2018)., Google ScholarCrossref
  5. 5. A. Thomas, L. Lethuillier-Karl, K. Nagarajan, R. M. A. Vergauwe, J. George, T. Chervy, A. Shalabney, E. Devaux, J. Moran, and T. W. Ebbesen, “Tilting a ground-state reactivity landscape by vibrational strong coupling,” Science 363, 615–619 (2019)., Google ScholarCrossref
  6. 6. J. Lather, P. Bhatt, A. Thomas, T. W. Ebbesen, and J. George, “Cavity catalysis by cooperative vibrational strong coupling of reactant and solvent molecules,” Angew. Chem., Int. Ed. 58, 10635–10638 (2019)., Google ScholarCrossref
  7. 7. R. M. A. Vergauwe, A. Thomas, K. Nagarajan, A. Shalabney, J. George, T. Chervy, M. Seidel, E. Devaux, V. Torbeev, and T. W. Ebbesen, “Cavity catalysis by cooperative vibrational strong coupling of reactant and solvent molecules,” Angew. Chem., Int. Ed. 58, 15324–15328 (2019)., Google ScholarCrossref
  8. 8. H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: Coherence in context,” Science 298, 1372–1377 (2002)., Google ScholarCrossref
  9. 9. P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: A review,” Rep. Prog. Phys. 78, 013901 (2015)., Google ScholarCrossref, ISI
  10. 10. T. W. Ebbesen, “Hybrid light-matter states in a molecular and material science perspective,” Acc. Chem. Res. 49, 2403–2412 (2016)., Google ScholarCrossref, ISI
  11. 11. J. Feist, J. Galego, and F. J. Garcia-Vidal, “Polaritonic chemistry with organic molecules,” ACS Photonics 5, 205–216 (2018)., Google ScholarCrossref
  12. 12. A. Armitage, M. S. Skolnick, V. N. Astratov, D. M. Whittaker, G. Panzarini, L. C. Andreani, T. A. Fisher, J. S. Roberts, A. V. Kavokin, M. A. Kaliteevski, and M. R. Vladimirova, “Optically induced splitting of bright excitonic states in coupled quantum microcavities,” Phys. Rev. B 57, 14877–14881 (1998)., Google ScholarCrossref
  13. 13. J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks, K. Mackay, R. H. Friend, P. L. Burns, and A. B. Holmes, “Light-emitting diodes based on conjugated polymers,” Nature 347, 539–541 (1990)., Google ScholarCrossref, ISI
  14. 14. D. G. Lidzey, D. D. C. Bradley, S. J. Martin, and M. A. Pate, “Pixelated multicolor microcavity displays,” IEEE J. Sel. Top. Quantum Electron. 4, 113–118 (1998)., Google ScholarCrossref
  15. 15. D. G. Lidzey, D. D. C. Bradley, M. S. Skolnick, T. Virgili, S. Walker, and D. M. Whittaker, “Strong exciton-photon coupling in an organic semiconductor microcavity,” Nature 395, 53–55 (1998)., Google ScholarCrossref
  16. 16. D. G. Lidzey, T. Virgili, D. D. C. Bradley, M. S. Skolnick, S. Walker, and D. M. Whittaker, “Observation of strong exciton-photon coupling in semiconductor microcavities containing organic dyes and J-aggregates,” Opt. Mater. 12, 243–247 (1999)., Google ScholarCrossref
  17. 17. D. G. Lidzey, D. D. C. Bradley, T. Virgili, A. Armitage, M. S. Skolnick, and S. Walker, “Room temperature polariton emission from strongly coupled organic semiconductor microcavities,” Phys. Rev. Lett. 82, 3316–3319 (1999)., Google ScholarCrossref
  18. 18. D. G. Lidzey, D. Bradley, A. Armitage, S. Walker, and M. Skolnick, “Photon-mediated hybridization of Frenkel excitons in organic semiconductor microcavities,” Science 288, 1620–1623 (2000)., Google ScholarCrossref
  19. 19. D. Lidzey, A. Fox, M. Rahn, M. Skolnick, V. Agranovich, and S. Walker, “Experimental study of light emission from strongly coupled organic semiconductor microcavities following nonresonant laser excitation,” Phys. Rev. B 65, 195312-1–195312-10 (2002)., Google ScholarCrossref
  20. 20. J.-H. Song, Y. He, A. Nurmikko, J. Tischler, and V. Bulovic, “Exciton-polariton dynamics in a transparent organic semiconductor microcavity,” Phys. Rev. B 69, 235330 (2004)., Google ScholarCrossref
  21. 21. G. Lodden and R. Holmes, “Electrical excitation of microcavity polaritons by radiative pumping from a weakly coupled organic semiconductor,” Phys. Rev. B 82, 125317 (2010)., Google ScholarCrossref
  22. 22. D. M. Coles, P. Michetti, C. Clark, W. C. Tsoi, A. M. Adawi, J.-S. Kim, and D. G. Lidzey, “Vibrationally assisted polariton-relaxation processes in strongly coupled organic-semiconductor microcavities,” Adv. Funct. Mater. 21, 3691–3696 (2011)., Google ScholarCrossref
  23. 23. V. M. Agranovich, M. Litinskaia, and D. G. Lidzey, “Cavity polaritons in microcavities containing disordered organic semiconductors,” Phys. Rev. B 67, 085311 (2003)., Google ScholarCrossref
  24. 24. V. M. Agranovich and G. C. La Rocca, “Electronic excitations in organic microcavities with strong light-matter coupling,” Solid State Commun. 135, 544–553 (2005)., Google ScholarCrossref
  25. 25. V. Agranovich and Y. Gartstein, “Nature and dynamics of low-energy exciton polaritons in semiconductor microcavities,” Phys. Rev. B 75, 075302 (2007)., Google ScholarCrossref
  26. 26. M. Litinskaya, “Propagation and localization of polaritons in disordered organic microcavities,” Phys. Lett. A 372, 3898–3903 (2008)., Google ScholarCrossref
  27. 27. D. M. Coles, P. Michetti, C. Clark, A. M. Adawi, and D. G. Lidzey, “Temperature dependence of the upper-branch polariton population in an organic semiconductor microcavity,” Phys. Rev. B 84, 205214 (2011)., Google ScholarCrossref
  28. 28. M. Litinskaya, P. Reineker, and V. M. Agranovich, “Fast polariton relaxation in strongly coupled organic microcavities,” J. Lumin. 110, 364–372 (2004)., Google ScholarCrossref
  29. 29. P. Michetti and G. C. La Rocca, “Polariton states in disordered organic microcavities,” Phys. Rev. B 71, 115320 (2005)., Google ScholarCrossref
  30. 30. P. Michetti and G. C. La Rocca, “Simulation of J-aggregate microcavity photoluminescence,” Phys. Rev. B 77, 195301 (2008)., Google ScholarCrossref
  31. 31. P. Michetti and G. C. La Rocca, “Exciton-phonon scattering and photoexcitation dynamics in J-aggregate microcavities,” Phys. Rev. B 79, 35325 (2009)., Google ScholarCrossref
  32. 32. P. Michetti and G. C. La Rocca, “Polariton-polariton scattering in organic microcavities at high excitation densities,” Phys. Rev. B 82, 115327 (2010)., Google ScholarCrossref
  33. 33. M. Litinskaya and P. Reineker, “Balance between incoming and outgoing cavity polaritons in a disordered organic microcavity,” J. Lumin. 122-123, 418–420 (2007)., Google ScholarCrossref
  34. 34. J. d. Pino, J. Feist, and F. J. Garcia-Vidal, “Quantum theory of collective strong coupling of molecular vibrations with a microcavity mode,” New J. Phys. 17, 053040 (2015)., Google ScholarCrossref
  35. 35. K. B. Arnardottir, A. J. Moilanen, A. Strashko, P. Törmä, and J. Keeling, “Multimode organic polariton lasing,” Phys. Rev. Lett. 125, 233603 (2020). Google Scholar
  36. 36. H. L. Luk, J. Feist, J. J. Toppari, and G. Groenhof, “Multiscale molecular dynamics simulations of polaritonic chemistry,” J. Chem. Theory Comput. 13, 4324–4335 (2017)., Google ScholarCrossref, ISI
  37. 37. J. del Pino, F. A. Y. N. Schröder, A. W. Chin, J. Feist, and F. J. Garcia-Vidal, “Tensor network simulation of non-Markovian dynamics in organic polaritons,” Phys. Rev. Lett. 121, 227401 (2018)., Google ScholarCrossref, ISI
  38. 38. G. Groenhof, C. Climent, J. Feist, D. Morozov, and J. J. Toppari, “Tracking polariton relaxation with multiscale molecular dynamics simulations,” J. Chem. Phys. Lett. 10, 5476–5483 (2019)., Google ScholarCrossref
  39. 39. O. Vendrell, “Collective Jahn-Teller interactions through light-matter coupling in a cavity,” Phys. Rev. Lett. 121, 253001 (2018)., Google ScholarCrossref
  40. 40. F. Herrera and F. C. Spano, “Dark vibronic polaritons and the spectroscopy of organic microcavities,” Phys. Rev. Lett. 118, 223601 (2017)., Google ScholarCrossref, ISI
  41. 41. F. Herrera and F. C. Spano, “Absorption and photoluminescence in organic cavity QED,” Phys. Rev. A 95, 053867 (2017)., Google ScholarCrossref, ISI
  42. 42. A. Warshel and M. Levitt, “Theoretical studies of enzymatic reactions: Dielectric, electrostatic and steric stabilization of carbonium ion in the reaction of lysozyme,” J. Mol. Biol. 103, 227–249 (1976)., Google ScholarCrossref
  43. 43. E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with to the beam maser,” Proc. IEEE 51, 89–109 (1963)., Google ScholarCrossref
  44. 44. M. Tavis and F. W. Cummings, “Approximate solutions for an N-molecule radiation-field Hamiltonian,” Phys. Rev. 188, 692–695 (1969)., Google ScholarCrossref
  45. 45. A. Sisto, D. R. Glowacki, and T. J. Martinez, “Ab initio nonadiabatic dynamics of multichromophore complexes: A scalable graphical-processing-unit-accelerated exciton framework,” Acc. Chem. Res. 47, 2857–2866 (2014)., Google ScholarCrossref
  46. 46. J. C. Tully, “Molecular dynamics with electronic transitions,” J. Chem. Phys. 93, 1061–1071 (1990)., Google ScholarScitation, ISI
  47. 47. R. Crespo-Otero and M. Barbatti, “Recent advances and perspectives on nonadiabatic mixed quantum-classical dynamics,” Chem. Rev. 118, 7026–7068 (2018)., Google ScholarCrossref
  48. 48. G. Groenhof and J. J. Toppari, “Coherent light harvesting through strong coupling to confined light,” J. Phys. Chem. Lett. 9, 4848–4851 (2018)., Google ScholarCrossref
  49. 49. P. Ehrenfest, “Bemerkung über die angenäherte gültigkeit der klassischen mechanik innerhalb der quantenmechanik,” Z. Phys. 45, 445–457 (1927)., Google ScholarCrossref
  50. 50. G. Granucci, M. Persico, and A. Toniolo, “Direct semiclassical simulation of photochemical processes with semiempirical wave functions,” J. Chem. Phys. 114, 10608–10615 (2001)., Google ScholarScitation, ISI
  51. 51. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003)., Google ScholarCrossref, ISI
  52. 52. T. Schwartz, J. A. Hutchison, J. Léonard, C. Genet, S. Haacke, and T. W. Ebbesen, “Polariton dynamics under strong light-molecule coupling,” ChemPhysChem 14, 125–131 (2013)., Google ScholarCrossref
  53. 53. J. George, S. Wang, T. Chervy, A. Canaguier-Durand, G. Schaeffer, J.-M. Lehn, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Ultra-strong coupling of molecular materials: Spectroscopy and dynamics,” Faraday Discuss. 178, 281–294 (2015)., Google ScholarCrossref
  54. 54. Y. Duan, C. Wu, S. Chowdhury, M. C. Lee, G. Xiong, W. Zhang, R. Yang, P. Cieplak, R. Luo, T. Lee, J. Caldwell, J. Wang, and P. Kollman, “A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations,” J. Comput. Chem. 24, 1999–2012 (2003)., Google ScholarCrossref
  55. 55. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, “Comparison of simple potential functions for simulation liquid water,” J. Chem. Phys. 79, 926–935 (1983)., Google ScholarScitation, ISI
  56. 56. H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak, “Molecular dynamics with coupling to an external bath,” J. Chem. Phys. 81, 3684–3690 (1984)., Google ScholarScitation, ISI
  57. 57. B. Hess, H. Bekker, H. J. C. Berendsen, and J. G. E. M. Fraaije, “LINCS: A linear constraint solver for molecular simulations,” J. Comput. Chem. 18, 1463–1472 (1997).<1463::aid-jcc4>;2-h, Google ScholarCrossref, ISI
  58. 58. S. Miyamoto and P. A. Kollman, “SETTLE: An analytical version of the SHAKE and RATTLE algorithms for rigid water molecules,” J. Comput. Chem. 13, 952–962 (1992)., Google ScholarCrossref
  59. 59. U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen, “A smooth particle mesh Ewald potential,” J. Chem. Phys. 103, 8577–8592 (1995)., Google ScholarScitation, ISI
  60. 60. E. Runge and E. K. U. Gross, “Density-functional theory for time-dependent systems,” Phys. Rev. Lett. 52, 997–1000 (1984)., Google ScholarCrossref, ISI
  61. 61. B. O. Roos, “Theoretical studies of electronically excited states of molecular systems using multiconfigurational perturbation theory,” Acc. Chem. Res. 32, 137–144 (1999)., Google ScholarCrossref
  62. 62. A. A. Granovsky, “Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory,” J. Chem. Phys. 134, 214113 (2011)., Google ScholarScitation, ISI
  63. 63. B. Hess, C. Kutzner, D. van der Spoel, and E. Lindahl, “GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation,” J. Chem. Theory Comput. 4, 435–447 (2008)., Google ScholarCrossref, ISI
  64. 64. I. S. Ufimtsev and T. J. Martínez, “Quantum chemistry on graphical processing units. 3. Analytical energy gradients and first principles molecular dynamics,” J. Chem. Theory Comput. 5, 2619–2628 (2009)., Google ScholarCrossref
  65. 65. A. V. Titov, I. S. Ufimtsev, N. Luehr, and T. J. Martínez, “Generating efficient quantum chemistry codes for novel architectures,” J. Chem. Theory Comput. 9, 213–221 (2013)., Google ScholarCrossref, ISI
  66. 66. G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, and T. Shegai, “Realizing strong light-matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions,” Phys. Rev. Lett. 114, 157401 (2015)., Google ScholarCrossref
  67. 67. D. Melnikau, R. Esteban, D. Savateeva, A. Sánchez-Iglesias, M. Grzelczak, M. K. Schmidt, L. M. Liz-Marzán, J. Aizpurua, and Y. P. Rakovich, “Rabi splitting in photoluminescence spectra of hybrid systems of gold nanorods and J-aggregates,” J. Phys. Chem. Lett. 7, 354–362 (2016)., Google ScholarCrossref
  68. 68. C. A. Delpo, B. Kudisch, K. H. Park, S.-U.-Z. Khan, F. Fassioli, D. Fausti, B. P. Rand, and G. D. Scholes, “Polariton transitions in femtosecond transient absorption studies of ultrastrong light-molecule coupling,” J. Phys. Chem. Lett. 11, 2667–2674 (2020)., Google ScholarCrossref
  69. 69. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, and D. J. Fox, Gaussian 16 Revision C.01, Gaussian, Inc., Wallingford, CT, 2016. Google Scholar
  70. 70. Mathematica, Version 11.3, Wolfram Research, Inc., Champaign, IL, 2018. Google Scholar
  71. 71. P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys. 91, 025005 (2019)., Google ScholarCrossref
  72. 72. J. Flick, H. Appel, M. Ruggenthaler, and A. Rubio, “Cavity Born-Oppenheimer approximation for correlated electron-nuclear-photon systems,” J. Chem. Theory Comput. 13, 1616–1625 (2017)., Google ScholarCrossref
  73. 73. J. Flick, M. Ruggenthaler, H. Appel, and A. Rubio, “Atoms and molecules in cavities: From weak to strong coupling in QED chemistry,” Proc. Natl. Acad. Sci. U. S. A. 114, 3026–3034 (2017)., Google ScholarCrossref
  74. 74. D. M. Coles, R. Grant, D. G. Lidzey, C. Clark, and P. G. Lagoudakis, “Imaging the polariton relaxation bottleneck in strongly coupled organic semiconductor microcavities,” Phys. Rev. B 88, 121303 (2013)., Google ScholarCrossref
  75. 75. K. Georgiou, R. Jayaprakash, A. Askitopoulos, D. M. Coles, P. G. Lagoudakis, and D. G. Lidzey, “Generation of anti-Stokes fluorescence in a strongly coupled organic semiconductor microcavity,” ACS Photonics 5, 4343–4351 (2018)., Google ScholarCrossref
  76. 76. S. Takahashi and K. Watanabe, “Decoupling from a thermal bath via molecular polariton formation,” J. Phys. Chem. Lett. 11, 1349–1356 (2020)., Google ScholarCrossref, ISI
  77. 77. V. Agranovich, H. Benisty, and C. Weisbuch, “Organic and inorganic quantum wells in a microcavity: Frenkel-Wannier-Mott excitons hybridization and energy transformation,” Solid State Commun. 102, 631–636 (1997)., Google ScholarCrossref
  78. 78. S. Kéna-Cohen and S. R. Forrest, “Room-temperature polariton lasing in an organic single-crystal microcavity,” Nat. Photonics 4, 371–375 (2010)., Google ScholarCrossref
  79. 79. K. S. Daskalakis, S. A. Maier, R. Murray, and S. Kéna-Cohen, “Nonlinear interactions in an organic polariton condensate,” Nat. Mater. 13, 271–275 (2014)., Google ScholarCrossref
  80. 80. J. Keeling and S. Kéna-Cohen, “Bose-Einstein condensation of exciton-polaritons in organic microcavities,” Annu. Rev. Phys. Chem. 71, 435–459 (2020)., Google ScholarCrossref
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