Distinguishing different excitation pathways in two-dimensional terahertz-infrared-visible spectroscopy

Abstract

In condensed molecular matter, low-frequency modes (LFMs) associated with specific molecular motions are excited at room temperature and determine essential physical and chemical properties of materials. LFMs, with typical mode energies of up to ∼500 cm−1 (62 meV), contribute significantly to thermodynamic parameters and functions (e.g., heat capacity and entropy) and constitute the basis for room temperature molecular dynamics (e.g., conformational fluctuations and change). LFMs are often analyzed indirectly by the measurement of their effect on specific high-frequency modes (HFMs); the LFM–HFM coupling is reflected in the lineshape, as well as in the spectral and angular diffusion of the HFM. Two-dimensional terahertz-infrared-visible (2D TIRV) spectroscopy allows measuring the LFM–HFM coupling directly and can thereby provide new insights into the strength and nature of the coupling and the character of LFMs. However, the interference between the different signals generated by different excitation pathways can complicate 2D TIRV spectra, preventing a straightforward analysis. Here, we develop an experimental method to distinguish different excitation pathways in 2D TIRV spectroscopy and plot them separately in different quadrants of a 2D spectrum. We validate this method by measuring the spectra of CaF2 and nitrogen gas. For CaF2, only sum-frequency mixing between infrared and terahertz fields generates the signal. In contrast, for N2, only difference-frequency mixing is observed. We then use this method to separate sum- and difference-frequency pathways in the 2D TIRV spectrum of liquid water, verifying the previous interpretation of the lineshape of the 2D TIRV spectrum of water.

Equilibrium–nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy

“…(Ω 1 = 0.5, Ω 2 = 2) and a linear-linear coupling term proportional to λ = 0.1. The lightmatter interaction operators are set to  = q1 , B = Ĉ = q2 , reflecting the terahertzinfrared-Raman pulse sequence, 5,14 in which the first, terahertz pulse interacts only with the low-frequency mode q 1 , while the infrared and off-resonant Raman interactions probe the high-frequency mode q 2 . Figure 4 shows that the two-dimensional spectrum, obtained as the double cosine transform of the two-time response function (see Supplementary Material for further details), exhibits off-diagonal peaks at (Ω 1 , Ω 2 ) and (Ω 1 , Ω 2 ± Ω 1 ), as predicted by the Feynman diagrams of Refs.…”

“…1 Recently, a series of hybrid spectroscopic experiments [2][3][4][5] involving mid-infrared, far-infrared (or terahertz), and visible (Raman) pulses have been developed to study electrical and mechanical anharmonicities, [6][7][8][9] structural heterogeneities of liquids, [10][11][12] and the couplings between intermolecular and intramolecular vibrational modes. 13,14 However, the interpretation of such spectra is still an open question and requires adequate simulation methods. 12,[15][16][17] Several computational methods have been proposed for simulating two-dimensional offresonant Raman and hybrid terhertz-Raman spectra.…”

Simulating two-dimensional correlation spectroscopies with third-order infrared and fifth-order infrared--Raman processes of liquid water

“…Two-dimensional (2D) experiments, in which an additional time correlation is imprinted on the system response, are capable of determining anharmonic coupling among vibrational modes and homogeneous linewidths that are needed to understand the degree of coupling to the bath (i.e., the surrounding molecules with respect to the excited transition). [20][21][22][23][24] Recent developments of experimental techniques have significantly augmented the study of both intermolecular and intramolecular modes in the 0∼4000 cm −1 frequency range through 2D IR, [25][26][27][28][29] 2D THz-Raman spectroscopies, [30][31][32][33] and 2D THz-IR-visible (TIV) spectroscopy, 34,35 which is equivalent to 2D IR-IR-Raman spectroscopy. 36,37 Although 2D IR and 2D THz-Raman experiments provide information about intramolecular and intermolecular degrees of freedom, respectively, neither approach can directly measure the anharmonic coupling between intermolecular and intramolecular modes.…”

Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy

“…1 Recently, a series of hybrid spectroscopic experiments [2][3][4][5] involving mid-infrared, far-infrared (or terahertz), and visible (Raman) pulses have been developed to study electrical and mechanical anharmonicities, [6][7][8][9] structural heterogeneities of liquids, [10][11][12] and the couplings between intermolecular and intramolecular vibrational modes. 13,14 However, the interpretation of such spectra is still an open question and requires adequate simulation methods. 12,15 Several computational methods have been proposed for simulating two-dimensional Raman and hybrid terhertz-Raman spectra.…”