Article pubs.acs.org/JPCA
Simple Recipes for Separating Excited-State Absorption and Cascading Signals by Polarization-Sensitive Measurements Maxim F. Gelin* and Wolfgang Domcke Department of Chemistry, Technische Universität München, D-85747 Garching, Germany ABSTRACT: The dependence of four-wave mixing and six-wave mixing signals on the polarization of the laser pulses is analyzed. Assuming that the dipole moments of the electronic transitions are not all parallel, we show that the excited-state absorption signal can be separated from the total pump−probe signal by two measurements with different polarizations of the pump and probe pulses. We show, furthermore, that cascading (third-order) signals can be separated from the fifth-order signal by two polarization-sensitive six-wave mixing measurements. We provide simple explicit formulas that express the excited-state absorption and cascading contributions, respectively, in terms of polarization-sensitive signals.
1. INTRODUCTION Consider an optical pump−probe (PP) experiment with linearly polarized laser pulses performed on an ensemble of chromophores in the gas phase or in an isotropic condensed phase. In polarization-sensitive measurements, the standard observable is the so-called anisotropy1 r=
responses and pathways as compared to polarization-insensitive detection of signals and provide more detailed information on the material system under study. 1,6−11 While several comprehensive theoretical studies of polarization and anisotropy effects in NWM signals exist,11−16 the potential of polarization spectroscopy is not fully exploited yet. The present paper proposes two novel and simple applications of this technique. (i) The signal of PP experiments is a superposition of stimulated emission (SE), ground-state bleach (GSB), and excited-state absorption (ESA) contributions. Theoretically, it is not difficult to consider all relevant Liouville pathways and calculate the contributions from the SE, GSB, and ESA separately.6 Experimentally, the SE, GSB, and ESA are superimposed, and the interpretation of the PP signal is often complicated by their overlap. The ESA can be spectrally separated provided the corresponding spectral region is a priori known (see, e.g., refs 5 and 17). We demonstrate that performing two polarization-sensitive PP measurements, for example, I∥̅ and I⊥̅ , allows the separation of the ESA from the total PP signal without a priori information on the system, provided the dipole moments of the electronic transitions are not parallel. (ii) Cascading is a phenomenon in which lower-order processes contribute to a certain higher-order process, where molecule #2 reabsorbs light emitted by molecule #1.18,19 Cascading obeys the same phase-matching condition as the original high-order process. It is thus impossible to get rid of cascading via phase matching or phase cycling. Cascading is a problem in the fifth-order off-resonant Raman spectroscopy18,19
I ̅ − I⊥̅ I ̅ + 2I⊥̅
(1)
(we use overbars to denote orientational ensemble averaging). Here, I∥̅ is the PP intensity measured with the pump and the probe pulses polarized in the same direction, while I⊥̅ is the PP intensity measured with mutually perpendicular polarizations of the pump and probe pulses. If the chromophore can be modeled as an electronic two-level system with a transition dipole moment vector μ and if rotation−vibration coupling can be neglected, the anisotropy is proportional to the orientational correlation function 2 r(t ) = P2(dd(t )) (2) 5 Here, d ∥ μ is the unit vector (|d| = 1), which determines the direction of the transition dipole moment, P2(x) = (3x2 − 1)/2 is the second-order Legendre polynomial, and t is the time delay between the pulses. The anisotropy (eq 2) can be used to monitor reorientation of chromophores in the gas phase2 or in a condensed phase.1 If several electronic states of the chromophore can simultaneously be excited and probed with optical pulses, and if the corresponding transition dipole moments have different orientations in the molecular frame, then r(t) monitors coherences between the coupled electronic states3,4 as well as the dynamics in high-lying electronic states.5 Clearly, polarization-sensitive four-wave mixing (4WM) measurements offer an additional selectivity over the measured © 2013 American Chemical Society
Received: September 21, 2013 Revised: October 21, 2013 Published: October 21, 2013 11509
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and stimulated Raman spectroscopy.20 In 6WM 3D IR spectroscopy, on the other hand, cascading contaminates the fifth-order signals only slightly, if at all, because the signals scale linearly with the concentration of the species under study.21,22 In optical 6WM 3D spectroscopy,23−25 cascading contributes to the fifth-order signals but does not overwhelm them. In the experiments reported in ref 25 for example, the cascading contribution was estimated to be around 10% of the signal. It was suggested that polarization-sensitive detection26−28 in combination with other methods29−33 can significantly reduce the cascading contributions to the fifth-order off-resonant Raman signals (see ref 34 for a review). We show that two polarization-sensitive measurements permit the exact separation of the cascading (third-order) contributions from the fifthorder optical 6WM responses. Within the main body of the paper, we consider a chromophore with the electronic ground state |g⟩, the lowest bright excited electronic state |e(1)⟩, and a high-lying electronic state |e(2)⟩. The consideration of multiple optically bright lowlying and high-lying electronic states is deferred to Appendices A and B, respectively.
anisotropic contribution (the second term in the parentheses). The latter depends on the mutual orientations of the polarization vectors (ξs) and the transition dipole moment vectors (ξd). A. Chromophore Exhibiting ESA. Consider a chromophore with the electronic ground state |g⟩, the lowest bright excited electronic state |e(1)⟩, and a high-lying electronic state |e(2)⟩. We assume that the energy gap between the states |g⟩ and |e(1)⟩ and the states |e(1)⟩ and |e(2)⟩ is in resonance with the laser fields involved, so that radiative transitions between |g⟩ and |e(1)⟩ and between |e(1)⟩ and |e(2)⟩ are possible, d1 and d2 being the unit vectors along the corresponding transition dipole moments. 1. Temporally Separated Pulses. Assuming temporally wellseparated pulses and neglecting molecular reorientation, we can write the PP signal as I = (s1d1)2 (s 2d1)2 A + (s1d1)2 (s 2d 2)2 B
The quantities A and B are orientationally isotropic. They depend on the carrier frequencies, durations, and the time delay of the pulses, as well as on properties of the chromophore. A is the contribution to the PP signal arising from transitions between the electronic ground state |g⟩ and the lowest bright excited electronic state |e(1)⟩ (it involves only d1). B arises from the transition between |g⟩ and |e(1)⟩ and further between |e(1)⟩ and the high-lying electronic state |e(2)⟩. It is the ESA contribution, which involves both d1 and d2. The orientational averaging in eq 6 can be performed according to eq 4, yielding
2. POLARIZATION-SENSITIVE 4WM SIGNALS The part of the Hamiltonian describing the interaction of a molecule with an external laser field in the optical regime is written in the dipole approximation as the product of the field amplitude and the electronic transition dipole moment operator, HF(t) = −E(t)μ. We assume that the field is linearly polarized, E(t) = sE(t), s being the unit vector of the field polarization and E(t) being the time-dependent electric field. The transition dipole moment in the molecular frame can be written as μ = dμ̂, where μ̂ is an operator acting on the electronic and vibrational degrees of freedom. HF(t) is thus the product of an orientation-dependent factor, sd, and a rotationally isotropic part HF(t ) = −(sd)E(t )μ ̂
I̅ =
1⎛ 4 s d⎞ ⎜1 + ξξ ⎟ ⎠ 9⎝ 5 ξ d = P2(d1d 2)
(7)
where ξ and ξ are defined by eq 5. We can evaluate the PP intensity at parallel pulse polarizations (s1 ∥ s2, ξs = 1) I̅ =
(3)
d
1 1⎛ 4 ⎞ A + ⎜1 + ξ d ⎟B ⎝ 5 9 5 ⎠
(8)
and at perpendicular pulse polarizations (s1 ⊥ s2, ξ = −1/2) s
I⊥̅ =
1 1⎛ 2 ⎞ A + ⎜1 − ξ d ⎟ B ⎝ 15 9 5 ⎠
(9)
Hence, the contributions A and B can be expressed through I∥̅ and I⊥̅ as follows A=
B=
d d 3 (5 − 2ξ )I ̅ − (5 + 4ξ )I⊥̅ 2 1 − ξd
(10)
9 3I⊥̅ − I ̅ 2 1 − ξd
(11)
Equations 10 and 11 become singular if d1 ∥ d2. In this case, ξd = 1, I∥̅ = 3I⊥̅ , and a discrimination between A and B is not possible. If the orientations of d1 and d2 are different, eqs 10 and 11 are well-defined. For example, d1 ⊥ d2 yields ξd = −1/2. The anisotropy (eq 1) can be expressed in terms of A and B as follows
(4)
where ξ s = P2(s1s 2)
⎞ 1⎛ 4 s⎞ 1⎛ 4 ⎜1 + ξ ⎟A + ⎜1 + ξ sξ d⎟B ⎠ 9⎝ 5 ⎠ 9⎝ 5 s
The 4WM signal can be decomposed into a sum of so-called Liouville pathways.6 Each pathway involves four consecutive electronic transitions and yields the product of four orientationdependent factors. If molecular reorientation can be neglected on the time scale of the (femtosecond) experiment, the product of these four factors determines the orientational dependence of the signal. Let us consider a PP signal with temporally well-separated pulses (probe follows pump). We denote the polarizations of the pump and probe pulses as s1 and s2 and formally introduce d1 and d2 as the unit vectors along the transition dipole moments responsible for the interaction with the pump and probe pulses (d1 = d2 is included, of course, as a special case). Because the si are defined in the laboratory frame and the di are defined in the molecular frame, we have to perform an averaging over all possible orientations of the molecular frame with respect to the laboratory frame. The result reads11,13−15 (s1d1)2 (s 2d 2)2 =
(6)
r= (5)
(1 − ξ d)B ⎞ 2⎛ ⎜1 − ⎟ 5⎝ A+B ⎠
(12)
The deviation of r from the standard value of 2/5 is due to the ESA (cf. ref 3).
Equation 4 shows that the averaging yields an isotropic contribution (the first term in the parentheses) and an 11510
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2. Effect of Pulse Overlap. Consider the PP signal for a system with three electronic states (|g⟩, |e(1)⟩, |e(2)⟩), but now allow for pulse overlap. The PP intensity can be written as
expression can be used for working out a general theory of polarization effects in 6WM experiments. In the present work, we restrict ourselves to the separation of the fifth-order contributions from the so-called cascading contributions in optical 6WM signals (see refs 23−25 for recent measurements of 3D electronic signals). A 6WM signal in the PP-like configuration24,25 and with temporally well-separated pulses can be expressed as
I = (s1d1)2 (s 2d1)2 A + (s1d1)2 (s 2d 2)2 B + (s1d1)(s1d 2)(s 2d1)(s 2d 2)C
(13)
where we have assumed that the chromophore interacts first with the pump pulse. As before, A is the contribution of the transition betwen the ground state and the lowest excited electronic state (including the so-called coherent artifact). B is the ESA signal. C arises from the pulse sequence pump− probe−pump−probe involving the three electronic states and vanishes for temporally separated pulses. Orientational averaging of eq 13 as described, for example, in ref 11 yields ⎞ 1⎛ 4 s⎞ 1⎛ 4 ⎜1 + ξ ⎟A + ⎜1 + ξ sξ d⎟B ⎠ 9⎝ 5 ⎠ 9⎝ 5 ⎛ ⎞ 1 2 d s d s ⎜1 + 2ξ + 2ξ + + ξ ξ ⎟C ⎠ 27 ⎝ 5
I ̅ = (s1d1)2 (s 2d 2)2 (s3d 3)2 Z + (s1d1)2 (s 2d 2)2 A × (s 2d 2)2 (s3d 3)2 B + (s1d1)2 (s3d 3)2 C(s 2d 2)2 (s3d 3)2 D (22)
Here, Z corresponds to the fifth-order signal, A and B represent the so-called sequential cascade, while C and D describe the socalled parallel cascade.18,19 We consider a system with the ground electronic state |g⟩ and the lowest bright excited electronic state |e(1)⟩ (d1 = d2 = d3, ξd = 1) and assume, for simplicity, that the polarizations of the second and third pulses are the same (s2 = s3, ξs23 = 1, ξs123 = ξs12). Making use of eqs 19−21, we obtain
I̅ =
(14)
The above equation can alternatively be written as
I̅ =
1 I ̅ = (X + ξ sY ) 9 X=A+B+
(16)
We cannot separate the three contributions A, B, C by performing three different polarization measurements because I ̅ is linear in ξs. However, we can express X, Y, and r in terms of I∥̅ and I⊥̅ Y X = 3(I ̅ + 2I⊥̅ ) Y = 6(I ̅ − I⊥̅ ) r= (5X )
AB + CD = ∥
(17)
1 (1 − ξ d)(2B − C) 9
I̅ =
3. POLARIZATION-SENSITIVE 6WM SIGNALS The orientational averaging is based on the identity15 1 ⎛ 4 s d 4 d ⎜1 + ξ12ξ12 + ξ23s ξ23 ⎝ 27 5 5 4 s d 16 s d ⎞ + ξ31ξ31 + ξ123ξ123⎟ ⎠ 5 35
ξ(t ) = P2(d1(0)d1(t ))
s ξ123 = P2(s123)
ξ d(t ) = P2(d1(0)d 2(t ))
If molecular reorientation can be neglected, we recover eq 7 because ξ(0) = 1 and ξd(0) = ξd. In general, the expressions for ξ(t) and ξd(t) are quite complicated (see, e.g., refs 35 and 36 and references therein). If we assume that molecular reorientation is isotropic and can be described as that of a spherical top, then ξd(t) = ξ(t)ξd. For example, isotropic rotational diffusion corresponds to ξ(t) = exp(−6Dt), where D is the rotational diffusion coefficient. The contributions A and B can be expressed in terms of I∥̅ and I⊥̅ , ξ(t) and ξd(t)
(20) 2
(26)
(27) (19)
Here
2
⎞ ⎞ 1⎛ 4 s 1⎛ 4 ⎜1 + ξ ξ(t )⎟A + ⎜1 + ξ sξ d(t )⎟B ⎠ ⎠ 9⎝ 5 9⎝ 5
where t is the time delay between the pump and probe pulses. Here, we have introduced the orientational correlation functions11,13−15
(s1d1)2 (s 2d 2)2 (s3d 3)2 =
2 s123
(25)
⊥
4. EFFECT OF CHROMOPHORE REORIENTATION If the chromophore undergoes rotational motion on the time scale of the PP experiment, eq 7 is replaced by
(18)
yields the contribution involving the high-lying electronic state | e(2)⟩.
ξijs = P2(sisj)
75 (5I⊥̅ − I ̅ ) 2
Therefore, I ̅ − 3I ̅ yields the signal that is not contaminated by cascading. The quantity 5I⊥̅ − I∥̅ , on the other hand, can be called the “cascading witness”. If measurements for three different polarizations si are performed, the parallel (AB) and sequential (CD) cascades can be extracted separately.
Again, the quantity 3I⊥̅ − I ̅ =
(23)
It is seen that the fifth-order term Z and the cascading contribution AB + CD exhibit different orientational anisotropies. These two contributions can therefore be separated by two polarization-sensitive measurements. In terms of the signals I∥̅ (s1 ∥ s2, ξs12 = 1) and I⊥̅ (s1 ⊥ s2, ξs12 = −1/2), we have 35 Z= (I ̅ − 3I⊥̅ ) (24) 2
(15)
1 (1 + 2ξ d)C 3 ⎛2 4 4 2 d⎞ Y = A + ξ dB + ⎜ + ξ ⎟C ⎝3 5 5 15 ⎠
8 ⎞ 1 ⎛ 4 s⎞ 1 ⎛⎜ ⎜1 + 1 + ξ12s ⎟Z + ξ12⎟(AB + CD) 15 ⎝ 7 ⎠ 45 ⎝ 5 ⎠
2
= 3(s1s 2)(s 2s3)(s3s1) − (s1s 2) − (s 2s3) − (s3s1) + 1 (21)
The expressions for ξd are obtained from those for ξs by s → d. Equation 19 reveals five contributions that can be separated by performing several polarization-sensitive experiments. This 11511
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B=
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d d 3 (5 − 2ξ (t ))I ̅ − (5 + 4ξ (t ))I⊥̅ 2 ξ(t ) − ξ d(t )
3 (5 + 4ξ(t ))I⊥̅ − (5 − 2ξ(t ))I ̅ 2 ξ(t ) − ξ d(t )
|g⟩ and |eB⟩, while * and + involve the transitions betwen |g⟩ and |eA⟩ as well as between |g⟩ and |eB⟩. Orientational averaging of eq A1 yields
(28)
I̅ = (29)
(A2)
where ξAB = P2(dAdB). Mathematically, eq A2 is equivalent to eq 7 under the substitution A → ( + ) , B → * + + , and ξd → ξAB. Therefore, we can separate the contribution ( + ) and the cross contribution, * + + , by performing I∥̅ and I⊥̅ measurements, as is specified in eqs 10 and 11. Again, 3I⊥̅ − I∥̅ is proportional to the cross contribution, * + + . Generalization to more than two electronic states is straightforward.
The other results of the present work can be generalized accordingly.
5. CONCLUSION We have shown that the ESA contribution can be separated from the total PP signal by two polarization-sensitive measurements if the transition dipole moments of the two electronic transitions (from the electronic ground state to the lowest bright excited electronic state and from lowest bright excited electronic state to a high-lying electronic state) are not parallel. Analogously, the (third-order) cascading contributions can be separated from the fifth-order contribution in optical 6WM experiments by polarization-sensitive detection. In both cases, the quantity 3I⊥̅ − I∥̅ is of particular significance. For PP experiments, it yields the ESA contribution. For 6WM experiments, it delivers the fifth-order cascading-free contribution. These results are universal because no a priori information on the molecular Hamiltonian and transition dipole moments is necessary. These results apply if the chromophore rotation is slow compared to the time scale of the PP or 6WM experiment. If molecular reorientation cannot be neglected, the generalized expressions involve orientational correlation functions. In the present paper, we restricted our considerations to resonantly excited electronic transitions. The results are applicable to IR spectroscopy as well because the derivations are of purely geometrical character (see refs 10 and 12 for a general discussion of polarization effects in IR 6WM). The results can also be generalized toward nonresonant Raman spectroscopies. In the latter case, the key quantity is the polarizability tensor α. If the geometrical factors sα(0)s can be factored out of the signal intensities (that is, if the polarizability tensor can be written as α = α(0)α̂ , where the tensor α(0) is independent of nuclear coordinates and α̂ is a scalar coordinatedependent operator), off-resonant signals can be treated analogously to resonant optical signals. If, furthermore, α(0) = α∥dd + α⊥(1 − dd), where d is a unit vector fixed in the molecular frame (for a symmetric top, e.g., d specifies the figure axis), the derivations require minor modifications. For linear rotors and oblate tops (α∥ ≫ α⊥), no modifications are needed.
Appendix B: Chromophore with Multiple High-Lying Bright Excited Electronic States
In polyatomic molecules, the density of high-lying electronic states is generally rather high. As a generalization of the treatment of section 2.A.1, we consider here a chromophore with the electronic ground state |g⟩, the lowest bright excited electronic state |e(1)⟩, and several high-lying excited electronic (1) states |e(2) n ⟩. We assume that the states |g⟩ and |e ⟩ and the (1) (2) states |e ⟩ and |en ⟩ are in resonance with the laser fields, the transitions between |g⟩ and |e(1)⟩ and between |e(1)⟩ and |e(2) n ⟩ are allowed, and d1 and d(n) are the unit vectors of the 2 corresponding transition dipole moments. For this system, the PP intensity reads I = (s1d1)2 (s 2d1)2 A +
I̅ =
2
+ (s1dA) (s 2dB) * + (s1dB) (s 2dA) +
1⎛ 4 s⎞ 1 ⎜1 + ξ ⎟A + ⎝ ⎠ 9 5 9
⎛
∑ ⎜⎝1 + n
4 s d⎞ ξ ξn ⎟Bn ⎠ 5
(B2)
ξdn = P2(d1d(n) 2 ). It is impossible to retrieve all contributions A and Bn to the signal from multiple polarization-sensitive measurements. Because I ̅ is linear in ξs, only two independent measurements yield nontrivial information. Nevertheless, we can separate the total ESA contribution. Defining I∥̅ and I⊥̅ as above, we obtain 3I⊥̅ − I ̅ =
2 9
∑ (1 − ξnd)Bn n
(B3)
It is remarkable that no a priori knowledge about the system Hamiltonian and the transition dipole moments is necessary because 3I⊥̅ − I∥̅ yields the ESA contribution. This quantity can be called a “witness” of the ESA. If, however, some of the d(n) 2 are parallel to d1, their contributions cannot be detected through the ESA witness.
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
I = (s1dA)2 (s 2dA)2 ( + (s1dB)2 (s 2dB)2 ) 2
(B1)
and
Consider the commonly occurring situation where the relevant electronic states are the ground electronic state |g⟩ and two bright low-lying excited (possibly coupled) electronic states, |eA⟩ and |eB⟩, both of which are optically accessible from |g⟩. If we denote the unit vectors of the transition dipole moments between |g⟩ and |eA⟩ and between |g⟩ and |eB⟩ as dA and dB, respectively, and assume temporally well-separated pulses, the PP intensity can be written as
2
∑ (s1d1)2 (s2d(2n))2 Bn n
Appendix A: Chromophore with Two Low-Lying Electronic States but without ESA
2
⎛ ⎛ ⎞ 1 4 ⎞ 1 4 (( + ))⎜1 + ξ s⎟ + (* + +)⎜1 + ξ sξAB⎟ ⎝ ⎝ ⎠ 9 5 ⎠ 9 5
ACKNOWLEDGMENTS This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) through a research grant and the DFGCluster of Excellence “Munich-Centre for Advanced Photonics” (www.munich-photonics.de). We are grateful to Gagik
(A1)
Here, the contribution ( involves the transitions between the states |g⟩ and |eA⟩, ) involves the transitions between the states 11512
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Spectroscopy: Observation of Cascading Raman Signals in Acetonitrile. J. Chem. Phys. 2009, 131, 214502−214515. (21) Fulmer, E. C.; Ding, F.; Zanni, M. T. Heterodyned Fifth-Order 2D-IR Spectroscopy of the Azide Ion in an Ionic glass. J. Chem. Phys. 2005, 122, 034302/1−034302/12. (22) Garrett-Roe, S.; Hamm, P. Purely Absorptive Three-Dimensional Infrared Spectroscopy. J. Chem. Phys. 2009, 130, 164510/1− 164510/9. (23) Fidler, A. F.; Harel, E.; Engel, G. S. Dissecting Hidden Couplings Using Fifth-Order Three-Dimensional Electronic Spectroscopy. J. Phys. Chem. Lett. 2010, 1, 2876−2880. (24) Zhang, Z.; Wells, K. L.; Tan, H.-S. Purely Absorptive FifthOrder Three-Dimensional Electronic Spectroscopy. Opt. Lett. 2012, 37, 5058−5060. (25) Zhang, Z.; Wells, K. L.; Seidel, M. T.; Tan, H.-S. Fifth-Order Three-Dimensional Electronic Spectroscopy Using a Pump−Probe Configuration. J. Phys. Chem. B 2013, DOI: 10.1021/jp4046403. (26) Jansen, T. I. C.; Snijders, J. G.; Duppen, K. Interaction Induced Effects in the Nonlinear Raman Response of Liquid CS2: A Finite Field Nonequilibrium Molecular Dynamics Approach. J. Chem. Phys. 2001, 114, 10910−10921. (27) Murry, R. L.; Fourkas, J. T.; Keyes, T. Nonresonant Intermolecular Spectroscopy Beyond the Placzek Approximation. I. Third-Order Spectroscopy. J. Chem. Phys. 1998, 109, 2814−2825. (28) Murry, R. L.; Fourkas, J. T.; Keyes, T. Nonresonant Intermolecular Spectroscopy Beyond the Placzek Approximation. II. Fifth-Order Spectroscopy. J. Chem. Phys. 1998, 109, 7913−7922. (29) Golonzka, O.; Demirdöven, N.; Khalil, M.; Tokmakoff, A. Separation of Cascaded and Direct Fifth-Order Raman Signals Using Phase-Sensitive Intrinsic Heterodyne Detection. J. Chem. Phys. 2000, 113, 9893−9896. (30) Kaufman, L. J.; Blank, D. A.; Fleming, G. R. Polarization Selectivity in Fifth-Order Electronically Nonresonant Raman Scattering from CS2. J. Chem. Phys. 2001, 114, 2312−2331. (31) Kaufman, L. J.; Heo, J.; Ziegler, L. D.; Fleming, G. R. Heterodyne-Detected Fifth-Order Nonresonant Raman Scattering from Room Temperature CS2. Phys. Rev. Lett. 2002, 88, 207402/1− 207402/4. (32) Kubarych, K. J.; Milne, C. J.; Miller, R. J. D. Heterodyne Detected Fifth-Order Raman Response of Liquid CS2: ‘Dutch Cross’ Polarization. Chem. Phys. Lett. 2003, 369, 635−642. (33) Milne, C. J.; Li, Y. L.; Jansen, T. I. C.; Huang, L.; Miller, R. J. D. Fifth-Order Raman Spectroscopy of Liquid Benzene: Experiment and Theory. J. Phys. Chem. B 2006, 110, 19867−19876. (34) Kubarych, K. J.; Milne, C. J.; Miller, R. J. D. Fifth-Order TwoDimensional Raman Spectroscopy: A New Direct Probe of the Liquid State. Int. Rev. Phys. Chem. 2003, 22, 497−532. (35) Burshtein, A. I.; Temkin, S. I. Spectroscopy of Molecular Rotations in Gases and Liquids; Cambridge University Press: Cambridge, U.K., 1994. (36) Gelin, M. F.; Kosov, D. S. Molecular Reorientation in Hydrogen-Bonding Liquids: Through Algebraic ∼ t−3/2 Relaxation Toward Exponential Decay. J. Chem. Phys. 2006, 124, 144514/1− 144514/8.
Gurzadyan, Ma Lin, and Sergy Grebenshchikov for stimulating discussions.
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REFERENCES
(1) Lakowicz, J. R. Principles of Fluorescence Spectroscopy, 3rd ed.; Springer Science+Business Media, LLC: New York, 2006. (2) Borisevich, N. A.; Khoroshilov, E. V.; Kryukov, I. V.; Kryukov, P. G.; Sharkov, A. V.; Blokhin, A. P.; Tolstorozhev, G. B. Femtosecond Analysis of Free Molecular Rotation in the Gas Phase. Chem. Phys. Lett. 1992, 191, 225−231. (3) Wynne, K.; Hochstrasser, R. M. Anisotropy as an Ultrafast Probe of Electronic Coherence in Degenerate Systems Exhibiting Raman Scattering, Fluorescence, Transient Absorption and Chemical Reactions. J. Raman Spectrosc. 1995, 26, 561−569. (4) Smith, E. R.; Jonas, D. M. Alignment, Vibronic Level Splitting, and Coherent Coupling Effects on the Pump−Probe Polarization Anisotropy. J. Phys. Chem. A 2011, 115, 4101−4113. (5) Gurzadyan, G. G.; Tran-Thi, T.-H.; Gustavsson, T. TimeResolved Fluorescence Spectroscopy of High-Lying Electronic States of Zn-Tetraphenylporphyrin. J. Chem. Phys. 1998, 108, 385−388. (6) Mukamel, S. Principles of Nonlinear Optical Spectroscopy; Oxford University Press: New York, 1995. (7) Golonzka, O.; Tokmakoff, A. Polarization-Selective Third-Order Spectroscopy of Coupled Vibronic States. J. Chem. Phys. 2001, 115, 297−309. (8) Tan, H.-S.; Piletic, I. R.; Fayer, M. D. Polarization Selective Spectroscopy Experiments: Methodology and Pitfalls. J. Opt. Soc. Am. B 2005, 22, 2009−2017. (9) Peters, W. K.; Smith, E. R.; Jonas, D. M. Femtosecond Pump− Probe Polarization Spectroscopy of Vibronic Dynamics at Conical Intersections and Funnels. In Conical Intersections; Domcke, W., Yarkony, D. R., Köppel, H., Eds.; World Scientific: Singapore, 2011; pp 715−745. (10) Bredenbeck, J.; Helbing, J.; Hamm, P. Transient TwoDimensional Infrared Spectroscopy: Exploring the Polarization Dependence. J. Chem. Phys. 2004, 121, 5943−5957. (11) Hochstrasser, R. M. Two-Dimensional IR-Spectroscopy: Polarization Anisotropy Effects. Chem. Phys. 2001, 266, 273−284. (12) Ding, F.; Fulmer, E. C.; Zanni, M. T. Heterodyned Fifth-Order Two-Dimensional IR Spectroscopy: Third-Quantum States and Polarization Selectivity. J. Chem. Phys. 2005, 123, 094502/1− 094502/13. (13) Tokmakoff, A. Orientational Correlation Functions and Polarization Selectivity for Nonlinear Spectroscopy of Isotropic Media. I. Third Order. J. Chem. Phys. 1996, 105, 1−12. (14) Tokmakoff, A. Orientational Correlation Functions and Polarization Selectivity for Nonlinear Spectroscopy of Isotropic Media. II. Fifth Order. J. Chem. Phys. 1996, 105, 13−21. (15) Blokhin, A. P.; Gelin, M. F.; Kalosha, I. I.; Polubisok, S. A.; Tolkachev, V. A. Polarized Fluorescence of Polyatomic Fragments Produced through Photodissociation of Polyatomic Molecules in the Gas Phase. J. Chem. Phys. 1999, 110, 978−993. (16) Murry, R. L.; Fourkas, J. T. Polarization Selectivity of Nonresonant Spectroscopies in Isotropic Media. J. Chem. Phys. 1997, 107, 9726−9740. (17) Dobryakov, A. L.; Kovalenko, S. A.; Ernsting, N. P. Coherent and Sequential Contributions to Femtosecond Transient Absorption Spectra of a Rhodamine Dye in Solution. J. Chem. Phys. 2005, 123, 044502/1−044502/8. (18) Ulness, D. J.; Kirkwood, J. C.; Albrecht, A. C. Competitive Events in Fifth Order Time Resolved Coherent Raman Scattering: Direct Versus Sequential Processes. J. Chem. Phys. 1998, 108, 3897− 3902. (19) Blank, D. A.; Kaufman, L. J.; Fleming, G. R. Direct Fifth-Order Electronically Nonresonant Raman Scattering from CS2 at Room Temperature. J. Chem. Phys. 2000, 113, 771−778. (20) Wilson, K. C.; Lyons, B.; Mehlenbacher, R.; Sabatini, R.; McCamant, D. W. Two-Dimensional Femtosecond Stimulated Raman 11513
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