Abstract
The effect of anharmonicity on the energy relaxation of excited state has been studied by means of a dissipative oscillator. The present study also sheds light on the recent femtosecond stimulated Raman spectroscopy results of Kovalenko et al. (J. Chem. Phys. 139 011101 2013) on optical cooling of trans-stilbene. It has been shown that anharmonicity plays a crucial role in explaining the time-dependent frequency shift as well as the time evolution of bandwidth of \(\nu _{C=C}\) mode of trans-stilbene in excited state, found in experiment.
Graphical abstract
The effect of anharmonicity on the energy relaxation of a vibrationally excited state is presented in this paper. The paper also suggest that at initial stage IVR plays a key role in changing the effective temperature of optically excited molecule.
Similar content being viewed by others
References
Pigliucci A, Duvanel G, Daku L M L and Vauthey E 2007 Investigation of the Influence of Solute-Solvent Interactions on the Vibrational Energy Relaxation Dynamics of Large Molecules in Liquids J. Phys. Chem. A 111 6135
Heitz R, Veit M, Ledentsov N N, Hoffmann A, Bimberg D, Ustinov V M, Kopev P S and Alferov Z I 1997 Energy relaxation by multiphonon processes in InAs/GaAs quantum dots Phys. Rev. B 56 10435
Morisaki H, Koretsune T, Hotta C, Takeya J, Kimura T and Wakabayashi Y 2014 Large surface relaxation in the organic semiconductor tetracene Nat. Commun. 5 5400
Ishizaki A and Fleming G R 2012 Quantum coherence in photosynthetic light harvesting Annu. Rev. Condens. Matter Phys. 3 333
von Lintig J, Kiser P D, Golczak M and Palczewski K 2010 The biochemical and structural basis for trans-to-cis isomerization of retinoids in the chemistry of vision Trends Biochem. Sci. 35 400
Kukura P, McCamant D W, Yoon S, Wandschneider D B and Mathies R A 2005 Structural observation of the primary isomerization in vision with femtosecond-stimulated Raman Science 310 1006
Kumar P and Pollak E 2014 Energy relaxation of a dissipative quantum oscillator J. Chem. Phys. 141 234509
Pollak E, Shao J and Zhang D H 2008 Effects of initial correlations on the dynamics of dissipative systems Phys. Rev. E 77 021107
Levine A M, Shapiro M and Pollak E 1988 Hamiltonian theory for vibrational dephasing rates of small molecules in liquids J. Chem. Phys. 88 1959
Rips I and Pollak E 1990 Quantum Kramers model: Solution of the turnover problem Phys. Rev. A 41 5366
Waldeck D H 1991 Photoisomerization dynamics of stilbenes Chem. Rev. 91 415
Hochstrasser R M 1980 Picosecond processes in the isomerism of stilbenes Pure Appl. Chem. 52 2683
Saltiel J and Charlton J 1980 Organic Chemistry: A Series of Monographs Vol. 42 (New York: Elsevier) p. 25
Meyer A, Schroeder J and Troe J 1999 Photoisomerization of trans-stilbene in moderately compressed gases: Pressure-dependent effective barriers J. Phys. Chem. A 103 10528
Sundström V and Gillbro T 1984 Dynamics of the isomerization of trans-stilbene in n-alcohols studied by ultraviolet picosecond absorption recovery Chem. Phys. Lett. 109 538
Courtney S and Fleming G 1985 Photoisomerization of stilbene in low viscosity solvents: comparison of isolated and solvated molecules J. Chem. Phys. 83 215
Balk M W and Fleming G R 1986 Unimolecular reactions in isolated and collisional systems: Is the transition-state rate an upper limit for the isomerization of stilbene? J. Phys. Chem. 90 3975
Gershinsky G and Pollak E 1997 Unimolecular reactions in the gas and liquid phases: A possible resolution to the puzzles of the trans-stilbene isomerization J. Chem. Phys. 107 812
Pollak E, Talkner P and Berezhkovskii A 1997 A theory for nonisothermal unimolecular reaction rates J. Chem. Phys. 107 3542
Courtney S H, Balk M W, Philips L A, Webb S P, Yang D, Levy D H and Fleming G R 1988 Unimolecular reactions in isolated and collisional systems: deuterium isotope effect in the photoisomerization of stilbene J. Chem. Phys. 89 6697
Troe J 1985 Quantitative analysis of photoisomerization rates in trans-stilbene and 4-methyl-trans-stilbene Chem. Phys. Lett. 114 241
Nordholm S 1989 Photoisomerization of stilbene-a theoretical study of deuteration shifts and limited internal vibrational redistribution J. Chem. Phys. 137 109
Wadi H and Pollak E 1999 Theory of laser cooling of polyatomic molecules in an electronically excited state J. Chem. Phys. 110 11890
Tatchen J and Pollak E 2008 Ab initio spectroscopy and photoinduced cooling of the trans-stilbene molecule J. Chem. Phys. 128 164303
Hamaguchi H-O 1996 Solvent-induced dynamic polarization and vibrational dephasing of electronically excited molecules Mol. Phys. 89 463
Kovalenko S, Dobryakov A, Pollak E and Ernsting N 2013 Communication: Optical cooling of trans-stilbene J. Chem. Phys. 139 011101
Iwata K and Hamaguchi H-o 1992 Picosecond structural relaxation of S1 trans-stilbene in solution as revealed by time-resolved Raman spectroscopy Chem. Phys. Lett. 196 462
Iwata K, Ozawa R and Hamaguchi H-o 2002 Analysis of the Solvent-and Temperature-Dependent Raman Spectral Changes of S1 trans-Stilbene and the Mechanism of the trans to cis Isomerization: Dynamic Polarization Model of Vibrational Dephasing and the CC Double-Bond Rotation J. Phys. Chem. A 106 3614
Oxtoby D W 1979 Dephasing of molecular vibrations in liquids Adv. Chem. Phys. 40 1
Leitner D M, Levine B, Quenneville J, Martínez T J and Wolynes P G 2003 Quantum energy flow and trans-stilbene photoisomerization: an example of a non-RRKM reaction J. Chem. Phys. A 107 10706
Weston R E and Barker J R 2006 On modeling the pressure-dependent photoisomerization of trans-stilbene by including slow intramolecular vibrational energy redistribution J. Chem. Phys. A 110 7888
Tuckerman M and Berne B 1993 Vibrational relaxation in simple fluids: Comparison of theory and simulation J. Chem. Phys. 98 7301
Dove J and Jones D G 1971 Numerical Calculation of Vibrational Relaxation and Dissociation for a Quantum Anharmonic Oscillator J. Chem. Phys. 55 1531
Ishizaki A and Tanimura Y 2006 Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies J. Chem. Phys. 125 084501
Bader J S and Berne B 1994 Quantum and classical relaxation rates from classical simulations J. Chem. Phys. 100 8359
Bader J S, Berne B, Pollak E and Hänggi P 1996 The energy relaxation of a nonlinear oscillator coupled to a linear bath J. Chem. Phys. 104 1111
Dobryakov A, Ioffe I, Granovsky A, Ernsting N and Kovalenko S 2012 Femtosecond Raman spectra of cis-stilbene and trans-stilbene with isotopomers in solution J. Chem. Phys. 137 244505
Acknowledgements
RK acknowledges DST, Govt. of India for financial assistance. PK acknowledges DST, Govt. of India for the financial support through sanctioned project [No. ECR/2016/000279 ]. We also thank Prof N. Ernsting for sending us experimental data of Figure 5.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kumar, R., Kumar, P. Effect of anharmonicity on energy relaxation of a dissipative quantum oscillator. J Chem Sci 131, 23 (2019). https://doi.org/10.1007/s12039-019-1599-4
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12039-019-1599-4