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Yang J, Gelin MF, Chen L, Šanda F, Thyrhaug E, Hauer J. Two-dimensional fluorescence excitation spectroscopy: A novel technique for monitoring excited-state photophysics of molecular species with high time and frequency resolution. J Chem Phys 2023; 159:074201. [PMID: 37581414 DOI: 10.1063/5.0156297] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 07/27/2023] [Indexed: 08/16/2023] Open
Abstract
We propose a novel UV/Vis femtosecond spectroscopic technique, two-dimensional fluorescence-excitation (2D-FLEX) spectroscopy, which combines spectral resolution during the excitation process with exclusive monitoring of the excited-state system dynamics at high time and frequency resolution. We discuss the experimental feasibility and realizability of 2D-FLEX, develop the necessary theoretical framework, and demonstrate the high information content of this technique by simulating the 2D-FLEX spectra of a model four-level system and the Fenna-Matthews-Olson antenna complex. We show that the evolution of 2D-FLEX spectra with population time directly monitors energy transfer dynamics and can thus yield direct qualitative insight into the investigated system. This makes 2D-FLEX a highly efficient instrument for real-time monitoring of photophysical processes in polyatomic molecules and molecular aggregates.
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Affiliation(s)
- Jianmin Yang
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Maxim F Gelin
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
| | | | - František Šanda
- Institute of Physics, Faculty of Mathematics and Physics, Charles University, 12116 Prague, Czech Republic
| | - Erling Thyrhaug
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
| | - Jürgen Hauer
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
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2
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Zhang Z, Peng T, Nie X, Agarwal GS, Scully MO. Entangled photons enabled time-frequency-resolved coherent Raman spectroscopy and applications to electronic coherences at femtosecond scale. LIGHT, SCIENCE & APPLICATIONS 2022; 11:274. [PMID: 36104344 PMCID: PMC9474554 DOI: 10.1038/s41377-022-00953-y] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/26/2022] [Revised: 07/02/2022] [Accepted: 08/07/2022] [Indexed: 06/15/2023]
Abstract
Quantum entanglement has emerged as a great resource for spectroscopy and its importance in two-photon spectrum and microscopy has been demonstrated. Current studies focus on the two-photon absorption, whereas the Raman spectroscopy with quantum entanglement still remains elusive, with outstanding issues of temporal and spectral resolutions. Here we study the new capabilities provided by entangled photons in coherent Raman spectroscopy. An ultrafast frequency-resolved Raman spectroscopy with entangled photons is developed for condensed-phase molecules, to probe the electronic and vibrational coherences. Using quantum correlation between the photons, the signal shows the capability of both temporal and spectral resolutions not accessible by either classical pulses or the fields without entanglement. We develop a microscopic theory for this Raman spectroscopy, revealing the electronic coherence dynamics even at timescale of 50fs. This suggests new paradigms of optical signals and spectroscopy, with potential to push detection below standard quantum limit.
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Affiliation(s)
- Zhedong Zhang
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong SAR, China.
- City University of Hong Kong, Shenzhen Research Institute, Shenzhen, Guangdong, 518057, China.
- Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX, 77843, USA.
| | - Tao Peng
- Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX, 77843, USA
| | - Xiaoyu Nie
- School of Physics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China
| | - Girish S Agarwal
- Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX, 77843, USA
- Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX, 77843, USA
| | - Marlan O Scully
- Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX, 77843, USA
- Baylor University, Waco, TX, 76704, USA
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3
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Freixas VM, Keefer D, Tretiak S, Fernandez-Alberti S, Mukamel S. Ultrafast coherent photoexcited dynamics in a trimeric dendrimer probed by X-ray stimulated-Raman signals. Chem Sci 2022; 13:6373-6384. [PMID: 35733898 PMCID: PMC9159119 DOI: 10.1039/d2sc00601d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 04/11/2022] [Indexed: 12/14/2022] Open
Abstract
The photoinduced ultrafast coherent inter-chromophore energy redistribution in a triarylamine trimer is explored using nonadiabatic excited state molecular dynamics followed by simulations of X-ray Raman signals. The nitrogencentered system ensures strong interchromophore interactions and, thus, the presence of coherences. Nevertheless, the multitude of non-deterministic photoinduced pathways during the ultrafast inter-branch migration of the excitation results in random confinement on some branches and, therefore, spatial exciton scrambling and loss of phase information at long times. We show that the vibronic coherence dynamics evolving into the incoherent scrambling mechanism on ultrafast 50 fs timescale, is accurately probed by the TRUECARS X-ray stimulated Raman signal. In combination with previous results, where the technique has revealed long-lived coherences in a rigid heterodimer, the signal is most valuable for detecting ultrafast molecular coherences or their absence. We demonstrate that X-ray Raman spectroscopy is a useful tool in the chemical design of functional molecular building blocks. The photoinduced ultrafast coherent inter-chromophore energy redistribution in a triarylamine trimer is explored using nonadiabatic excited state molecular dynamics followed by simulations of X-ray Raman signals.![]()
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Affiliation(s)
- Victor M Freixas
- Departamento de Ciencia y Tecnologia, Universidad Nacional de Quilmes/CONICET B1876BXD Bernal Argentina
| | - Daniel Keefer
- Department of Chemistry and Physics and Astronomy, University of California Irvine California 92697-2025 USA
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory Los Alamos New Mexico 87545 USA
| | | | - Shaul Mukamel
- Department of Chemistry and Physics and Astronomy, University of California Irvine California 92697-2025 USA
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4
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Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems. J Biol Phys 2022; 48:1-36. [PMID: 34822073 PMCID: PMC8866630 DOI: 10.1007/s10867-021-09586-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Accepted: 09/07/2021] [Indexed: 10/19/2022] Open
Abstract
We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.
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Gelin MF, Borrelli R. Simulation of Nonlinear Femtosecond Signals at Finite Temperature via a Thermo Field Dynamics-Tensor Train Method: General Theory and Application to Time- and Frequency-Resolved Fluorescence of the Fenna-Matthews-Olson Complex. J Chem Theory Comput 2021; 17:4316-4331. [PMID: 34076412 DOI: 10.1021/acs.jctc.1c00158] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Addressing needs of contemporary nonlinear femtosecond optical spectroscopy, we have developed a fully quantum, numerically accurate wave function-based approach for the calculation of third-order spectroscopic signals of polyatomic molecules and molecular aggregates at finite temperature. The systems are described by multimode nonadiabatic vibronic-coupling Hamiltonians, in which diagonal terms are treated in harmonic approximation, while off-diagonal interstate couplings are assumed to be coordinate independent. The approach is based on the Thermo Field Dynamics (TFD) representation of quantum mechanics and tensor-train (TT) machinery for efficient numerical simulation of quantum evolution of systems with many degrees of freedom. The developed TFD-TT approach is applied to the calculation of time- and frequency-resolved fluorescence spectra of the Fenna-Matthews-Olson (FMO) antenna complex at room temperature taking into account finite time-frequency resolution in fluorescence detection, orientational averaging, and static disorder.
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Affiliation(s)
- Maxim F Gelin
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
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6
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Zerah Harush E, Dubi Y. Do photosynthetic complexes use quantum coherence to increase their efficiency? Probably not. SCIENCE ADVANCES 2021; 7:7/8/eabc4631. [PMID: 33597236 PMCID: PMC7888942 DOI: 10.1126/sciadv.abc4631] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/26/2020] [Accepted: 12/31/2020] [Indexed: 06/12/2023]
Abstract
Answering the titular question has become a central motivation in the field of quantum biology, ever since the idea was raised following a series of experiments demonstrating wave-like behavior in photosynthetic complexes. Here, we report a direct evaluation of the effect of quantum coherence on the efficiency of three natural complexes. An open quantum systems approach allows us to simultaneously identify their level of "quantumness" and efficiency, under natural physiological conditions. We show that these systems reside in a mixed quantum-classical regime, characterized by dephasing-assisted transport. Yet, we find that the change in efficiency at this regime is minute at best, implying that the presence of quantum coherence does not play a substantial role in enhancing efficiency. However, in this regime, efficiency is independent of any structural parameters, suggesting that evolution may have driven natural complexes to their parameter regime to "design" their structure for other uses.
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Affiliation(s)
- Elinor Zerah Harush
- Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
- Ilse-Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| | - Yonatan Dubi
- Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.
- Ilse-Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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7
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Freixas VM, Tretiak S, Makhov DV, Shalashilin DV, Fernandez-Alberti S. Vibronic Quantum Beating between Electronic Excited States in a Heterodimer. J Phys Chem B 2020; 124:3992-4001. [DOI: 10.1021/acs.jpcb.0c01685] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- V. M. Freixas
- Departamento de Ciencia y Tecnologia, Universidad Nacional de Quilmes/CONICET, B1876BXD Bernal, Argentina
| | - S. Tretiak
- Theoretical Division, Center for Nonlinear Studies (CNLS), and Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - D. V. Makhov
- School of Chemistry, University of Leeds, Leeds LS2 9JT, U.K
- School of Mathematics, University of Bristol, Bristol BS8 1TW, U.K
| | | | - S. Fernandez-Alberti
- Departamento de Ciencia y Tecnologia, Universidad Nacional de Quilmes/CONICET, B1876BXD Bernal, Argentina
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8
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Zhang Z, Wang K, Yi Z, Zubairy MS, Scully MO, Mukamel S. Polariton-Assisted Cooperativity of Molecules in Microcavities Monitored by Two-Dimensional Infrared Spectroscopy. J Phys Chem Lett 2019; 10:4448-4454. [PMID: 31304758 DOI: 10.1021/acs.jpclett.9b00979] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Molecular polaritons created by the strong coupling between matter and field in microcavities enable the control of molecular dynamical processes and optical response. Multidimensional infrared spectroscopy is proposed for monitoring the polariton-assisted cooperative properties. The response of molecules to local fluctuations is incorporated and the full dynamics is monitored through the time- and frequency-resolved multidimensional signal. The cooperativity against solvent-induced disorder and its connection to the localization of the vibrational excitations are predicted. New insights are provided for recent 2DIR experiments on vibrational polaritons.
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Affiliation(s)
- Zhedong Zhang
- Institute for Quantum Science and Engineering , Texas A&M University , College Station , Texas 77843 , United States
| | - Kai Wang
- Institute for Quantum Science and Engineering , Texas A&M University , College Station , Texas 77843 , United States
| | - Zhenhuan Yi
- Institute for Quantum Science and Engineering , Texas A&M University , College Station , Texas 77843 , United States
| | - M Suhail Zubairy
- Institute for Quantum Science and Engineering , Texas A&M University , College Station , Texas 77843 , United States
| | - Marlan O Scully
- Institute for Quantum Science and Engineering , Texas A&M University , College Station , Texas 77843 , United States
- Quantum Optics Laboratory , Baylor Research and Innovation Collaborative , Waco , Texas 76704 , United States
- Department of Mechanical and Aerospace Engineering , Princeton University , Princeton , New Jersey 08544 , United States
| | - Shaul Mukamel
- Department of Chemistry, Department of Physics and Astronomy , University of California Irvine , Irvine , California 92697 , United States
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9
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Zhang Z, Agarwal GS, Scully MO. Quantum Fluctuations in the Fröhlich Condensate of Molecular Vibrations Driven Far From Equilibrium. PHYSICAL REVIEW LETTERS 2019; 122:158101. [PMID: 31050540 DOI: 10.1103/physrevlett.122.158101] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2018] [Revised: 03/07/2019] [Indexed: 05/28/2023]
Abstract
Fröhlich discovered the remarkable condensation of polar vibrations into the lowest frequency mode when the system is pumped externally. For a full understanding of the Fröhlich condensate one needs to go beyond the mean field level to describe critical behavior as well as quantum fluctuations. The energy redistribution among vibrational modes with nonlinearity included is shown to be essential for realizing the condensate and the phonon-number distribution, revealing the transition from quasithermal to super-Poissonian statistics with the pump. We further study the spectroscopic properties of the Fröhlich condensate, which are especially revealed by the narrow linewidth. This gives the long-lived coherence and the collective motion of the condensate. Finally, we show that the proteins such as bovine serum albumin and lysozyme are most likely the candidates for observing such collective modes in THz regime by means of Raman or infrared spectroscopy.
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Affiliation(s)
- Zhedong Zhang
- Texas A&M University, College Station, Texas 77843, USA
| | | | - Marlan O Scully
- Texas A&M University, College Station, Texas 77843, USA
- Baylor University, Waco, Texas 76704, USA
- Princeton University, Princeton, New Jersey 08544, USA
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10
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Wang YC, Zhao Y. Effect of an underdamped vibration with both diagonal and off-diagonal exciton-phonon interactions on excitation energy transfer. J Comput Chem 2019; 40:1097-1104. [PMID: 30549065 DOI: 10.1002/jcc.25611] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Revised: 08/29/2018] [Accepted: 09/06/2018] [Indexed: 11/08/2022]
Abstract
A numerically exact approach, named as the hierarchical stochastic Schrödinger equation, is employed to investigate the resonant vibration-assisted excitation energy transfer in a dimer system, where an underdamped vibration with both diagonal and off-diagonal exciton-phonon interactions is incorporated. From a large parameter space over the site-energy difference, excitonic coupling, and reorganization energy, it is found that the promotion effect of the underdamped vibration is significant only when the excitonic coupling is smaller than the site-energy difference. Under the circumstance, there is an optimal strength ratio between diagonal and off-diagonal exciton-phonon interactions for the resonant vibration-assisted excitation energy transfer as the site-energy difference is greater than the reorganization energy, whereas in the opposite situation the most efficient energy transfer occurs as the exciton-phonon interaction is totally off-diagonal. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Yu-Chen Wang
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Yi Zhao
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
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11
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Ling F, Li S, Wang Y, Wang P, Zhang B. Vibrational coherence in the composition-selected wavepacket of photoexcited pyrimidine. J Chem Phys 2019; 150:044308. [DOI: 10.1063/1.5083681] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Fengzi Ling
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Shuai Li
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Yanmei Wang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Pengfei Wang
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Bing Zhang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
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12
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Rourk CJ. Ferritin and neuromelanin "quantum dot" array structures in dopamine neurons of the substantia nigra pars compacta and norepinephrine neurons of the locus coeruleus. Biosystems 2018; 171:48-58. [PMID: 30048795 DOI: 10.1016/j.biosystems.2018.07.008] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2018] [Revised: 07/13/2018] [Accepted: 07/22/2018] [Indexed: 01/28/2023]
Abstract
In this review, the author shows that ferritin has documented quantum dot material properties that have been reported in numerous independent studies, and can enable quantum mechanical electron transport over substantial distances. In addition, neuromelanin is a pi-conjugated polymer, and quantum dot/pi-conjugated polymer combinations have been reported in numerous independent studies to facilitate electron transport for solar photovoltaic and other applications. Both ferritin and neuromelanin are present in large quantities in the dopamine neurons of the substantia nigra pars compactaand the norepinephrine neurons of the locus coeruleus. The unique structure of subgroups of these neurons that have a large number of axon branches and synapses may have evolved to take advantage of this electron transport mechanism, if it is present, such as to coordinate conscious action, or for other purposes. Independent clinical and laboratory studies are also reviewed that corroborate this theory of coordinated action in these neuron groups. Research to validate the theory using charge transport measurements, materials characterization, existing fluorescent probe material and reaction time testing is proposed.
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Zhang Z, Saurabh P, Dorfman KE, Debnath A, Mukamel S. Monitoring polariton dynamics in the LHCII photosynthetic antenna in a microcavity by two-photon coincidence counting. J Chem Phys 2018; 148:074302. [DOI: 10.1063/1.5004432] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhedong Zhang
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
| | - Prasoon Saurabh
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
| | - Konstantin E. Dorfman
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Arunangshu Debnath
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
| | - Shaul Mukamel
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
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14
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Fluorescence spectroscopy of vibronic polaritons of molecular aggregates in optical microcavities. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.02.022] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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15
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Zhang Z, Bennett K, Chernyak V, Mukamel S. Utilizing Microcavities To Suppress Third-Order Cascades in Fifth-Order Raman Spectra. J Phys Chem Lett 2017; 8:3387-3391. [PMID: 28671843 DOI: 10.1021/acs.jpclett.7b01129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Nonlinear optical signals in the condensed phase are often accompanied by sequences of lower-order processes, known as cascades, which share the same phase matching and power dependence on the incoming fields and are thus hard to distinguish. The suppression of cascading in order to reveal the desired nonlinear signal has been a major challenge in multidimensional Raman spectroscopy, that is, the χ(5) signal being masked by cascading signals given by a product of two χ(3) processes. Because cascading originates from the exchange of a virtual photon between molecules, it can be manipulated by performing the experiment in an optical microcavity which modifies the density of radiation field modes. Using a quantum electrodynamical (QED) treatment, we demonstrate that the χ(3) cascading contributions can be greatly suppressed. By optimizing the cavity size and the incoming pulse directions, we show that up to ∼99.5% suppression of the cascading signal is possible.
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Affiliation(s)
- Zhedong Zhang
- Department of Chemistry, University of California Irvine , Irvine, California 92697, United States
| | - Kochise Bennett
- Department of Chemistry, University of California Irvine , Irvine, California 92697, United States
| | - Vladimir Chernyak
- Department of Chemistry, Wayne State University , Detroit, Michigan 48202, United States
| | - Shaul Mukamel
- Department of Chemistry, University of California Irvine , Irvine, California 92697, United States
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