Theory of rotationally resolved two-dimensional infrared spectroscopy including polarization dependence and rotational coherence dynamics

Abstract

Two-dimensional infrared (2DIR) spectroscopy is widely used to study molecular dynamics but it is typically restricted to optically thick samples and modest spectral resolution. The recently proposed technique of cavity-enhanced 2D spectroscopy using frequency combs and developments in multi-comb spectroscopy can lift these restrictions, demonstrating the need for rigorous and quantitative treatment of rotationally-resolved, polarization-dependent third-order response of gas-phase samples. This article provides such description using density-matrix, time-dependent perturbation theory and angular momentum algebra techniques. We describe the band and branch structure of 2D spectra, decompose the molecular response into polarization-dependence classes, use this decomposition to derive and explain special polarization conditions and relate the liquid-phase polarization conditions to gas-phase ones. Furthermore, we discuss the rotational coherence dynamics during waiting time.

Controlling rotationally-resolved two-dimensional infrared spectra with polarization

“…In this short Letter, we focus on these novel features. Our theory, described more fully in a longer companion paper [31] with an accompanying software package [32], is completely general and can be used to simulate RR2DIR spectra under a range of conditions.…”

“…where the sum is over all experimentally relevant third-order excitation pathways. N is the concentration of the active molecule, E (t) i are the integrated pulse envelopes, and S (3) is the third-order pathway amplitude [31]. I (t 1 ,t 2 ,t 3 ) encapsulates molecular dynamics between excitations.…”

“…I (t 1 ,t 2 ,t 3 ) encapsulates molecular dynamics between excitations. Under a simplified model of gas-phase 2D line shapes, individual resonances are represented by complex 2D Lorentzian profiles [31,35] that mix absorptive and dispersive parts of the response.…”

“…1a), this effect is seen as a faint, diffuse background signal caused by long tails of dispersive line shapes. Moreover, the positive branches are partially negative and vice versa, depending on the degree of imbalance for the specific branch and on the phases accumulated via waiting time, Ω 2 t 2 , of the contributing RC pathways, with Ω 2 determined by the rotational energy difference between the bra and ket of the coherences [31]. The effect on individual resonances is shown in Fig.…”

“…( 3) can be derived using spherical tensor operator techniques [38,39], as demonstrated by Williams et al [22][23][24][25][26] and Vaccaro et al [27][28][29]. The key result is the separation of all rovibrational third-order pathways into 7 classes with regards to their dependence on the polarization angles [31]. The amplitude of each pathway is proportional to an expression depending only on the beam polarizations, ε ε ε = (θ 1 , θ 2 , θ 3 , θ 4 ), and on the rotational angular momentum of involved states, J J J = (J i , J j , J k , J l ), given by [29,31]:…”