Using a solution of Maxwell's equations in the three-dimensional frequency domain, femtosecond two-dimensional Fourier transform (2DFT) spectra that include distortions due to phase matching, absorption, dispersion, and noncollinear excitation and detection of the signal are calculated for Bloch, Kubo, and Brownian oscillator relaxation models. For sample solutions longer than a wavelength, the resonant propagation distortions are larger than resonant local field distortions by a factor of approximately L/lambda, where L is the sample thickness and lambda is the optical wavelength. For the square boxcars geometry, the phase-matching distortion is usually least important, and depends on the dimensionless parameter, L sin(2)(beta)Deltaomega/(nc), where beta is the half angle between beams, n is the refractive index, c is the speed of light, and Deltaomega is the width of the spectrum. Directional filtering distortions depend on the dimensionless parameter, [(Deltaomega)w(0) sin(beta)/c](2), where w(0) is the beam waist at the focus. Qualitatively, the directional filter discriminates against off diagonal amplitude. Resonant absorption and dispersion can distort 2D spectra by 10% (20%) at a peak optical density of 0.1 (0.2). Complicated distortions of the 2DFT peak shape due to absorption and dispersion can be corrected to within 10% (15%) by simple operations that require knowledge only of the linear optical properties of the sample and the distorted two-dimensional spectrum measured at a peak optical density of up to 0.5 (1).

The laser-induced fluorescence (LIF) excitation spectrum of cyclohexoxy radical has been measured for the first time. The dominant vibrational progression is consistent with computations, at CIS/6-31+G(d), of the C−O stretch frequency of the axial conformer of cyclohexoxy radical. LIF intensity was used as a probe in direct kinetic studies of the reaction of cyclohexoxy radicals with O2. The Arrhenius expression obtained was k O2 = (5.8 ± 2.3) × 10-12 exp[(−14.3 ± 0.8) kJ/mol/RT] cm3 molecule-1 s-1 (225−302 K), independent of pressure in the range 50−125 Torr. The room temperature rate constant for this reaction is a factor of 2 higher than the commonly recommended value, but the observed activation energy is 9 times larger than the recommended value of 1.6 kJ/mol. Combining our results with the ratio of rate constants, k O2/k scission, measured in chamber experiments, we obtained an Arrhenius expression for k scission, the rate constant for β C−C scission of cyclohexoxy radical. However, the resulting Arrhenius preexponential factor of 4.5 × 1015 s-1 is unreasonably high compared with the value of ∼2 × 1013 s-1 obtained in our RRKM/Master Equation calculations as well as in calculations and experiments reported for other alkoxy radicals. The apparent discrepancy is resolved by examining the uncertainties in the values of k scission and the limited temperature range spanned by the relative rate experiments. A part of the discrepancy might also be explained by the observation that the O2 rate constant measured here is only for a single conformer of cyclohexoxy radical, whereas the relative rate experiments represent some averaging over both conformers.

Four-level two-dimensional (2D) Fourier transform relaxation spectra are simulated with response functions for a chromophore pair in the exponential relaxation (optical Bloch model) limit. The parameters in this study are chosen to model coupled carbonyl stretching vibrations. As long as coherence persists, every peak in the real 2D spectra has a partially mixed absorptive/dispersive ("phase-twisted") shape because the nonlinear signals are not symmetric with respect to interchange of the first two pulses. This asymmetry in 2D relaxation spectra arises from coherence between singly excited states and a red shift of the doubly excited state. Coherence between the singly excited states causes oscillation of the 2D spectra and the associated spectrally resolved pump-probe (SRPP) transients at the quantum beat frequency. Projecting the phase-twisted nature of the 2D peaks onto the detection frequency axis, the SRPP peaks are also asymmetric about their maximum when not at maximum or minimum amplitude. Three-dimensional Fourier transform (3DFT) methods are used to simulate absorption/dispersion and beam geometry distortions of the multilevel 2D spectra with cross peaks. The distortions can be understood by consideration of their effects on individual coherence pathways that contribute to peaks in the 2D spectra. The beam geometry distortion explains some unequal cross peak amplitudes previously observed experimentally by Khalil et al. (J. Chem. Phys. 2004, 121, 362). A representation of 2D spectra that reduces beam geometry distortion is presented. If the transformation to correct for beam geometry distortion is combined with the transformations that correct absorptive/dispersive propagation distortions (J. Chem. Phys. 2007, 126, 044511), the recovered 2D spectrum matches the ideal 2D spectrum after all coherence is destroyed. In the presence of coherence, the new representation reduces the error in the distorted 2D spectrum by a factor of 4 for practical 2D-IR experimental conditions.

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