Article pubs.acs.org/JPCA
Triply Resonant Sum Frequency Spectroscopy: Combining Advantages of Resonance Raman and 2D-IR Erin S. Boyle,* Nathan A. Neff-Mallon, and John C. Wright Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, United States S Supporting Information *
ABSTRACT: This article describes the new multidimensional spectroscopy technique triply resonant sum frequency spectroscopy, a four-wave mixing technique sharing advantages of both 2D-IR and resonance Raman experiments. In this technique, lasers with three independent frequencies interact coherently within a sample and generate an output frequency at their triple summation. The output intensity depends on coupled electronic and vibrational resonances in the sample. We use an organic dye as a model system to demonstrate fully resonant, fully coherent multidimensional spectroscopy using two independently tunable mid-infrared vibrational interactions and one visible electronic interaction. When the pulses are time ordered, the method has a single coherence pathway, eliminating interference between pathways. Fundamental vibrational transitions appear on one axis and overtones and combinations bands on the other, allowing anharmonicities of the modes to be determined easily and conveying molecular coupling information. The experiments demonstrate coupling between seven vibrational ring modes and an electronic state, the resolution of a Fermi resonance, detection of low concentrations, elimination of excitation pulse scattering and fluorescence, background suppression of solvent and co-solutes, and observation of coherence dephasing dynamics. The electronic resonance enhancements used in this methodology are similar to the enhancements responsible for resonance Raman spectroscopy and can be considered resonance 2D-IR spectroscopy.
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INTRODUCTION Coherent multidimensional spectroscopy (CMDS) is an emerging field that is the optical analogue to multidimensional NMR.1−6 Its experiments provide similar advantages, improved resolution of electronic and vibrational resonances, line narrowing of inhomogeneously broadened systems, and direct measurement of coupling between interacting quantum states. It has proven particularly valuable in characterizing the structure and/or ultrafast dynamics of a wide range of systems including peptides and proteins,7−12 quantum confined nanostructures,13−15 J-aggregates,16,17 water,18 and other molecular systems.19−21 CMDS experiments employ pulsed, coherent excitation fields to generate time-dependent multiple quantum coherences (MQCs) within a chemical system. Coupled pairs of MQC states form output coherences that launch coherent, directional light fields at their frequency differences for the duration of the coherence. The direction of an output beam is defined by the phase and multiplicity of the interactions of the excitation pulses because the output polarization obeys conservation of momentum. The output beam intensity depends on the phase matching between the vector sum of the excitation pulses and the wave vector of the output beam but also relies upon the existence of coupling between the modes. This coupling depends on molecular structure.1,22 The most widely used CMDS techniques are time domain methods that are based on ultrafast excitation pulses and stimulated photon echo coherence pathways that are either © 2013 American Chemical Society
fully coherent or involve intermediate populations. They include two-dimensional infrared spectroscopy (2D-IR)7,10,23 and two-dimensional electronic spectroscopy (2D-ES).13,14,24 The phase oscillations of each coherence are resolved by heterodyning the output with a local oscillator, scanning the time delays between pulses, and Fourier transforming the signals to the frequency domain. Although the multiplex advantage of this approach makes it efficient, it is spectrally limited in the range of accessible quantum states by the bandwidth of the excitation pulses. 2D-IR is further limited in the accessible vibrational modes by the efficiency of infrared detectors and the inherently low transition moment of most vibrational transitions. The latter is especially problematic when the transitions of interest overlap with stronger transitions from solvent or co-solute modes. An alternative CMDS strategy is to perform mixed frequency−time domain experiments. In these experiments, pulses are designed to have spectral and temporal widths that match the sample dephasing times. With this design, each pulse has the spectral width to excite single modes and the temporal width to define the time ordering of the interactions. Frequencies are scanned to obtain spectral information, and pulse delay times are changed to measure coherent and incoherent dynamics. Mixed frequency−time domain CMDS Received: September 19, 2013 Revised: October 22, 2013 Published: October 25, 2013 12401
dx.doi.org/10.1021/jp409377a | J. Phys. Chem. A 2013, 117, 12401−12408
The Journal of Physical Chemistry A
Article
where α(i) a→b is the absorption coefficient of the a → b transition (3) is the Raman cross section of the at the ωi frequency, σ(ν+ν′)→g (ν + ν′) → g transition, and l is the path length. M is a correction factor for absorption and phase-matching changes
can use any combination of electronic and vibrational states.1,2,25−28 Triply resonant sum frequency (TRSF) spectroscopy is a fully coherent four-wave mixing technique that uses the phasematching condition ks⃗ = k1⃗ + k2⃗ + k3⃗ , where the subscripts denote the three excitation frequencies, ω1, ω2, and ω3. The subscripts do not describe the pulse time ordering because any ordering is possible. Unlike other four-wave mixing methods where multiple coherence pathways interfere, defining a TRSF time ordering also defines a unique pathway. For example, 1
2
e−α4l(1 − eΔαl /2) + 4eΔαl /2 sin 2 M=
2
( Δ2αl )
( Δ2kl )
+ (Δkl)2
(3)
where αi are the absorption coefficients at the ith excitation or output frequency, Δα = α4 − (α1 + α2 + α3) and Δk ⃑ is the phase mismatch of the wave vectors. For the TRSF pathway, Δk⃗ ≡ k1⃗ + k2⃗ + k3⃗ − k4⃗ , where ki = (niωi)/c, ni is the index of refraction of the ith frequency, and c is the speed of light. Equation 3 predicts a decrease in signal as the output k4⃑ is absorbed, and saturation of nonlinear gain at the path length where inputs k1⃑ , k 2⃑ , and k 3⃑ have been absorbed. In the limit of negligible absorption, the M factor reduces to the familiar sinc2(Δkl/2) dependence. The TRSF pathway cannot be phase-matched in systems with normal dispersion because the indices of refraction make the k4⃗ output wave vector larger than the k1⃗ + k2⃗ + k3⃗ nonlinear polarization wave vector. Consequently, it has not been used for CMDS experiments. Nevertheless, we observe high-output intensities because the three resonance enhancements are multiplicative and create a high nonlinear gain over a path length shorter than the inverse of their phase mismatch, Δk. This gain (eq 2) results from the transition moments of coupled infrared modes (α1, α2) and the Raman cross section of the resulting overtone or combination band (σ). The high gain reduces the effects of absorption and phase mismatch; therefore, they do not play a role in these experiments. They have been described in a previous publication.26
3
gg → νg → ν′g → eg represents a unique coherence pathway where ω1 excites fundamental vibrational modes, ω2 excites overtone and combination band modes, ω3 excites the final electronic coherence, and the electronic coherence creates a cooperative and coherent resonance Raman transition, returning the system to the ground state. The fundamental vibrational frequencies appear on the ω1 axis, and overtones/ combination bands appear on the ω2 axis. The anharmonic coupling appears as an offset from the diagonal. In this paper, we demonstrate TRSF CMDS using the donor−acceptor styryl ionic dye 2-(6-(p-dimethylaminophenyl)-2,4-neopentylene-1,3,5-hexatrienyl)-3-ethylbenzothiazolium perchlorate), or Styryl 9M, as a model system. The CMDS spectra contain diagonal- and cross peaks involving nearly all of the vibrational transitions observed in FTIR. The output intensities are large because of the triple resonance enhancement involving strong electronic transitions. The method allows detection limits for vibrational transitions that are far below FTIR detection limits. This form of spectroscopy can be considered the resonance IR analogue of resonance Raman. The two vibrational resonances resolve the fundamental and overtone/combination band transitions on separate axes in the 2D spectra. TRSF has a different dependence on coupling than other coherent CMDS methods. The coupling in these experiments is controlled by the displacements of the excited electronic state along different normal-mode coordinates and therefore provides a method that directly correlates vibrational and electronic states. The isolation of a single pathway eliminates coherent interferences such as the bleaching, stimulated emission and excited-state absorption pathways of pump−probe, 2D-IR, and 2D-ES.
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EXPERIMENTAL SECTION Styryl 9M was obtained as LDS821 from Exciton, and its structure is shown in Figure 1. The CMDS experimental system
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THEORY In the steady state, the TRSF output coherence would be given by the density matrix element ρeg =
Figure 1. Structure of styryl 9M (LDS821), from Exciton, Inc.
Ω νgΩν ′ νΩeν′ (1,2) (1,2,3) 8Δ(1) νg Δν ′ g Δeg
used a 1 kHz Ti:Sapphire regenerative amplifier to pump two independently tunable optical parametric amplifiers to create infrared frequencies ω1 and ω2. Residual pump light from one OPA provided the ω3 pulse. The three pulses were focused into the sample using a linear phase-matching geometry where ω1 and ω2 were displaced ±10° from a central ω3 pulse, and the ω4 output was collinear with ω3. The focal region had a spot size
