Two-dimensional IR-Raman spectroscopy of vibrational polaritons: Role of dipole surfaces

Abstract

Nonlinear spectroscopy provides a unique perspective to understand time-resolved molecular dynamics under vibrational strong coupling (VSC). Herein, equilibrium-nonequilibrium cavity molecular dynamics simulations are performed to compute the two-dimensional (2D) infrared-infrared-Raman (IIR) spectroscopy of liquid water under VSC. In conventional computational chemistry practices, accurate molecular spectra are often constructed by using an advanced molecular dipole or polarizability model to post-process molecular dynamics trajectories evolved under a computationally efficient potential. By contrast, this work highlights the necessity of employing a consistent dipole surface model in both CavMD simulations and spectroscopic post-processing. While utilizing inconsistent dipole models only mildly influences the linear polariton spectrum, it severely distorts 2D spectra in wide frequency regions. With a consistent dipole-induced-dipole model, compared to the outside-cavity molecular 2D-IIR spectrum, the cavity 2D-IIR spectrum splits the OH stretch band to a pair of polariton branches along only the IR (not Raman) axis, while fading molecular signals at other frequency regions. This work provides the foundation for employing direct CavMD simulations to construct 2D spectra of realistic molecules under VSC.

Figures (8)

• Figure 1: Scheme of the equilibrium-nonequilibrium MD approach for calculating the 2D-IIR response function defined in Eq. \ref{['eq:rfcm']}. Along the propagation of an equilibrium MD trajectory (black arrow), positive or negative delta pulse is applied at equilibrium molecular configurations (black nodes) to induce nonequilibrium molecular trajectories (yellow arrows). These nonequilibrium trajectories are used to evaluate the nonequilibrium polarizabilities $\bm{\Pi}^{+}(t_2)$ and $\bm{\Pi}^{-}(t_2)$, whereas the time derivatives of the dipole vector $\dot{\boldsymbol{\mu}}$ are evaluated along the negative time ($-t_1$) propagation of the equilibrium trajectory.
• Figure 2: General workflow for evaluating linear and nonlinear spectra with direct equilibrium-nonequilibrium MD or CavMD simulations. See Sec. \ref{['sec:simulation_details']} for the detailed description.
• Figure 3: Simulated linear IR spectra of liquid water by evaluating molecular dipole autocorrelation functions. In each panel, the outside-cavity spectrum (black) is compared against that under VSC with the effective light-matter coupling strength $\widetilde{\varepsilon}=4 \times 10^{-4}$ a.u. (red) or $7 \times 10^{-4}$ a.u. (orange). For CavMD propagation and spectroscopic calculations, both the fixed point-charge (PC) or the DID dipole model are employed: (a) PC in both CavMD propagation and spectroscopic calculations; (b) DID in both CavMD propagation and spectroscopic calculations; (c) DID in CavMD propagation and PC in spectroscopic calculations; (d) PC in CavMD propagation and DID in spectroscopic calculations. Each blue arrow indicates a weak middle peak between the LP and UP, arising from the inconsistency in the dipole models employed in CavMD simulations versus spectroscopic calculations. For parameters, the cavity frequency is set to $\omega_{\rm{c}} = 3550$ cm$^{-1}$, and the explicitly simulated water system contains $N_{\rm{simu}}=64$ molecules.
• Figure 4: Simulated linear cavity IR spectra for liquid water under VSC. The CavMD propagation employs the (a) fixed point-charge model or (b) DID dipole model. In each panel, the linear cavity IR spectra is plotted according to Eq. \ref{['eq:IR_cavity_linear']} under two effective coupling strengths: $\widetilde{\varepsilon}=4 \times 10^{-4}$ a.u. (red) and $7 \times 10^{-4}$ a.u. (orange). Beneath each cavity lineshape, a horizontal baseline (dotted gray) guides the visualization. All simulation parameters remain the same as those in Fig. \ref{['fig:1d-ir']}.
• Figure 5: Simulated linear Raman spectra for liquid water inside versus outside the cavity. Both the isotropic (top panel) and anisotropic (bottom panel) Raman spectra are plotted. The CavMD propagation employs the (a,c) fixed point-charge (PC) model or (b,d) DID dipole model, while the spectroscopic post-processing always uses the DID model. In each part, the outside-cavity spectrum (black) is compared against that under VSC when the effective coupling strength is set to $\widetilde{\varepsilon}=4 \times 10^{-4}$ a.u. (red) or $7 \times 10^{-4}$ a.u. (orange). All simulation parameters remain the same as those in Fig. \ref{['fig:1d-ir']}. For the linshapes inside the cavity, blue arrows indicate the weak contributions from the LP and UP states, as only $N_{\rm{simu}}=64$H2O molecules are explicitly simulated.