Molecular-Level Understanding of the Ro-vibrational Spectra of N$_2$O in Gaseous, Supercritical and Liquid SF$_6$ and Xe

The transition between the gas-, supercritical-, and liquid-phase behaviour is a fascinating topic which still lacks molecular-level understanding. Recent ultrafast two-dimensional infrared spectroscopy experiments suggested that the vibrational spectroscopy of N$_2$O embedded in xenon and SF$_6$ as solvents provides an avenue to characterize the transitions between different phases as the concentration (or density) of the solvent increases. The present work demonstrates that classical molecular dynamics simulations together with accurate interaction potentials allows to (semi-)quantitatively describe the transition in rotational vibrational infrared spectra from the P-/R-branch lineshape for the stretch vibrations of N$_2$O at low solvent densities to the Q-branch-like lineshapes at high densities. The results are interpreted within the classical theory of rigid-body rotation in more/less constraining environments at high/low solvent densities or based on phenomenological models for the orientational relaxation of rotational motion. It is concluded that classical MD simulations provide a powerful approach to characterize and interpret the ultrafast motion of solutes in low to high density solvents at a molecular level.


Introduction
Solvent-solute interactions and the coupled dynamics between solute molecules embedded in a solvent are central for understanding processes ranging from rotational and vibrational energy relaxation to chemical reactivity in solution. 1,2 Vibrational spectroscopy is a particularly suitable technique to follow the structural dynamics of "hot" solutes in their electronic ground state interacting with a solvent environment. Experimentally, 1d-and 2d-infrared spectroscopies provide measures of the strength and time scale of solvent-solute interactions that couple to the resonant rovibrational excitation. 3 These effects can also be probed directly by molecular dynamics (MD) simulations. 4 The comparison of computations and experiments is a sensitive test for the quality of the intermolecular interaction potentials and provide a molecular-level understanding of energy transfer mechanisms. Furthermore, the entire structural dynamics at molecular-level detail is contained in the time dependent motion of all solution species involved from the MD trajectories and available for further analysis.
The understanding of solute equilibration in solvents including high density gases and supercritical fluids (SCFs) is also important from a more practical perspective. For example, controlling the outcome of combustion reactions which are often performed in the supercritical regime requires knowledge of energy transfer rates and mechanisms in high temperature and pressure solutions. 5,6 For reactions, it has been recognized that characterizing and eventually tuning the physico-chemical properties of the solvent can be as important as determining the best catalyst. 6 Hence, gaining molecular-level insight into the properties of solute-solvent dynamics is central not only for understanding fundamental solution interactions but also for industrial processes where solvents such as ionic, supercritical, or eutectic liquids are employed. On the other hand, the possibility to specifically manipulate dynamical properties in solvent system have been already successfully exploited in a wide range of applications. 7,8 Linear and nonlinear optical and in particular infrared (IR) spectroscopy is a powerful means to characterize the structural and dynamical properties of condensed-phase systems. As an example, recent spectroscopic experiments in the Terahertz and infrared region combined with MD simulations provided an atomistically resolved picture of the structural properties of an eutectic mixture. 9 More broadly speaking, the structural and dynamical properties of solutions can and have been studied at a molecular level using two-dimensional IR (2DIR) spectroscopy through vibrational energy transfer. [10][11][12][13][14][15][16][17][18] The energy transfer rate for exchange of vibrational energy is expected to follow a 6th-power, distance dependent law, 17 similar to NOESY in NMR spectroscopy, 19,20 or Förster energy transfer between electronic chromophores. 21 As an example, the presence of cross-peaks in a 2D spectrum has been directly related to the formation of aggregated structures. 11 However, interpretation and more in-depth understanding of the solvent structure requires additional information that can be obtained for example from MD simulations.
Recent 2DIR experiments on gas and supercritical phase solutions have shown how rotational energy returns to equilibrium following rovibrational excitation. [22][23][24] The dynamics of N 2 O as the spectroscopic probe surrounded by xenon atoms and SF 6 molecules has provided valuable information about density-dependent change in the solvent structure and energy transfer dynamics as the fluid approaches and passes through the near-critical point density region.
The 1D and 2D spectra of the N 2 O asymmetric stretch (ν 3 ) in Xe and SF 6 exhibit a significant dependence on solvent density. 23 At low density, corresponding to SF 6 and Xe in the gas phase, the FTIR (1D) band shape of the asymmetric stretch vibration is that of gas-phase N 2 O with clearly resolved P-and R-band structure whereas at high solvent density of the liquid Xe or SF 6 solvent only a Q-branch-like absorption feature peaked at the pure vibrational transition frequency was observed. Because the solvent density ρ can be changed in a continuous fashion between gas and liquid densities, along a near-critical isotherm (T ∼ 1.01T c ) it is also possible to probe the intermediate, super-critical regime of the solvent. 2DIR spectral shapes as a function of waiting time and solvent density exhibit perfectly anti-correlated features that report on the J−scrambling or rotational energy relaxation rates. [22][23][24] Given the molecular-level detail provided by quantitative MD simulations, the present work focuses on changes in the IR spectroscopy of N 2 O embedded in SF 6  for densities corresponding to those used in the recent 1D and 2D experiments were carried out.
The current work is structured as follows. First, the Methods are presented. Next, the quality of the interaction potentials is discussed. Then, the density-dependent FTIR spectra are compared with experiments, the vibrational frequency fluctuation correlation functions are characterized and the organization of the solvent is analyzed for xenon and SF 6 as the solvents. Finally, the findings are discussed in a broader context.

Potential Energy Surfaces
The intramolecular potential energy surface (PES) of N 2 O in its electronic ground state ( 1 A ) is provided by a machine-learned representation using the reproducing kernel Hilbert space (RKHS) method. 28,29 Reference energies at the CCSD(T)-F12/aug-cc-pVQZ level of theory were determined on a grid of Jacobi coordinates (R, r, θ) with r the N-N separation, R the distance between the center of mass of the diatom and the oxygen atom, and θ the angle between the two distance vectors. The grid in r contained 15 points between 1.6 a 0 and 3.1 a 0 , 15 points between 1.8 a 0 and 4.75 a 0 for R, and a 10-point Gauss-Legendre quadrature between 0 • and 90 • for θ. All calculations were carried out using the MOLPRO package. 30 The total energy is represented by a 3D kernel as [2,6] (R, R )k [2,6] (r, r )k [2] (z, z ) (1) and the total PES is represented as . For more details the reader is referred to the literature. 28 Reciprocal power decay kernels k 2,6 (x, x ) = 1 14 were used for the radial dimensions (R and r). Here, x > and x < are the larger and smaller values of x and x , respectively. For large separations such kernels approach zero according to ∝ 1 x n (here n = 6) which gives the correct long-range behavior for neutral atom-diatom type interactions. For the angular coordinate a Taylor spline kernel k [2] and z > and z < are again the larger and smaller values of z and z , defined similarly to x > and x > .
Intramolecular and intermolecular force field parameters for SF 6 are those from the work of Samios et al.. 31 Intermolecular interactions are based on Lennard-Jones potentials only and the parameters are optimized such that MD simulations of pure SF 6 reproduce the experimentally observed P V T state points for liquid and gas SF 6 , as well as the states of liquid-vapor coexistence below and supercritical fluid above the critical temperature T c , respectively. For xenon the parametrization for a Lennard-Jones potential from Aziz et al.
was used that reproduces dilute gas macroscopic properties such as virial coefficient, viscosity and thermal conductivity over a wide temperature range but not specifically supercritical fluid properties. 32 As discussed further below, the critical concentration for xenon as determined from simulations (see Figure S1) was found to be 5. 19  wave function methods such as CCSD. 42,43 In addition, the corrections due to BSSE are of a similar magnitude as the error in fitting the van der Waals parameters. Therefore, it was decided to not correct the interaction energies for BSSE. Then, the vdW parameters for each atom i of N 2 O were optimized to match the interaction energy predicted by CHARMM with the reference interaction energies from electronic structure calculations for the respective dimer conformations. The optimized vdW parameters are given in Table S2.

Molecular Dynamics Simulations
Molecular dynamics simulations were performed with the CHARMM program package. 44 Each system (N 2 O in Xe and N 2 O in SF 6 at given temperature and solvent concentration) was initially heated and equilibrated for 100 ps each, followed by 10 ns production simulations in the N V T ensemble using a time step of 1 fs for the leapfrog integration scheme.
A quantum correction factor Q(ω) = tanh (β ω/2) was applied to the results of the Fourier transform. 45 This procedure yields lineshapes but not absolute intensities. For direct compar-ison, individual spectra are thus multiplied with a suitable scaling factor to bring intensities of all spectra on comparable scales.
The response of the solute on the solvent structure and dynamics was evaluated by deter- The normalized vibrational frequency-frequency correlation function (FFCF) ν as (t) · ν as (0) / ν as (0) · ν as (0) was computed for the time series of the asymmetric stretch frequency ν as gathered from the QNM analyses. The amplitude A, lifetimes τ i and offset ∆ of a bi-exponential Radial distribution functions g(r) for solvent-solvent and solvent-solute pairs were determined from the average number of molecules dn r of type B within the shell in the range of r − ∆r/2 < r ≤ r + ∆r/2 around molecules of type A.
Here, ρ local is the local density of compound B around compound A within a range that is half the simulation box edge length and the shell width was ∆r = 0.1Å. The average coordination number N (r ) of compounds B within range r around compound A can be obtained from g(r) according to

Validation of the Interaction Potentials
First, the quality of the intramolecular PES for N 2 O is discussed, followed by a description of the van der Waals parameters for the N 2 O solute fit to the ab initio reference calculations.
The RKHS model provides a full-dimensional, intramolecular PES for N 2 O which was originally developed for investigating the N+NO collision reaction dynamics. 29   The critical concentration at which transition to a supercritical fluid occurs is another relevant property for the present work. Earlier work showed that this transition can be correlated with a pronounced increase in the local solvent reorganization lifetime τ ρ . 52,53 The quantity τ ρ is the integral over the local-density autocorrelation function τ ρ = ∞ 0 C ρ (t)dt and characterizes the time required for the local environment around a reference particle, e.g. the solute N 2 O in the present case, to change substantially. Hence, τ ρ can also be considered a local-density reorganization time. 53 Figures S1 and S2 report the local solvent reorganization lifetimes τ ρ for pure xenon and SF 6 , respectively, from MD simulations. The solvent environments are defined by cutoff radii which correspond approximately to the first and second minima of the solvent-solvent RDF, see Figure S4. For SF 6 the force field was parameterized 31 to reproduce the experimentally measured critical density with corresponding concentration c crit (SF 6 ) = 5.06 M at the critical temperature. 33,34 The present simulations yield a peak for τ ρ at c(SF 6 ) = 5.02 M, in close agreement with the experimental critical concentration at the critical temperature and the concentration with the local peak in τ 2 in Figure 4D. For xenon, however, the parametrization of the PES 32 did not include phase transition properties to the supercritical regime. Figure   S1 shows that the maximum in τ ρ occurs at c(Xe) = 5.19 M. This compares with a critical concentration of 8.45 M at T c from experiment. 33,34 Infrared Spectroscopy The computed IR spectra for the N 2 O asymmetric (ν as ) stretch in xenon and SF 6 solution as a function of solvent density for near critical isotherms allows comparison between experimental and simulation results. The present work focuses mainly on the change of the IR line shape at different solvent concentrations especially the P-, Q-, and R-branch structure, see Figures 2 and 3. The P-and R-branches are the IR spectral features at lower and higher wavenumber from the pure vibrational transition frequency for the excitation of mode ν. The ν as , ν s , and ν δ band shapes arise due to conservation of angular momentum during a vibrational excitation upon photon absorption. 49 The Q-branch is the absorption band feature at the transition frequency. In addition to the asymmetric stretch ν as (∼ 2220 cm −1 , symmetry A 1 /Σ + ), the symmetric stretch ν s (∼ 1305 cm −1 , A 1 /Σ + ) and the bending vibration ν δ (∼ 615 cm −1 , E 1 /Π) fundamentals from MD simulations are reported and analyzed as a function of solvent density.
From a quantum mechanical perspective, the rotational structure of an IR-active vibrational mode for a linear molecule (such as N 2 O) in the gas phase leads to P-and R-branches.
Selection rules dictate the change of the rotational and vibrational quantum states, j and ν, satisfying ∆ν = ±1 and ∆j = ±1 for vibrational modes of A 1 /Σ + symmetry, and ∆j = 0, ±1 for vibrational modes of E 1 /Π symmetry, respectively. For N 2 O, the asymmetric ν as and symmetric stretch ν s are vibrational modes with parallel vibrational transition dipole moment to the bond axis and of A 1 /Σ + representation, and the bending mode ν δ with perpendicular vibrational transition dipole moment of E 1 /Π representation. These rotational selection rules are only strictly valid in the absence of perturbations (exact free rotor) and break down with increasing deviation from a free rotor model which, for example, can be due to embedding the rotor into a solvent of different density which is a means to tune the strength of the perturbation. As a consequence of the perturbation a Q-branch-like spectral feature emerges for parallel bands and becomes dominant with a band maximum at the wavenumber of the corresponding pure vibrational transition energy at sufficiently high solvent density. To make all spectra comparable, the amplitudes are scaled by the factor indicated at the center left for each range and density. In panel C the line shape frequency bands are shifted in frequency ω to maximize the overlap with the experimental IR signal (dashed black lines, at 291 K for gas, SCF, and at 287 K for liquid xenon) at the corresponding density for the N 2 O asymmetric stretch vibration. The frequency shift is also given in the bottom left corner, and an average shift is applied for densities without experimental reference spectra.
For N 2 O in xenon the IR band structure of ν as in Figure 2C ranges from resolved P-and R-branch in gaseous xenon up to a single near-Lorentzian-shaped band in liquid xenon in these classical MD simulations. From the simulations, at xenon concentrations higher than 5.19 M, or relative density of ρ * = ρ/ρ c = 0.62, the xenon solvent is a supercritical fluid. In the simulated absorption spectra at this density and above the ν as P-and R-band structure is not resolved and a centrally peaked band at the pure vibrational frequency dominates the band shape. The black dashed lines in Figure 2C are the experimentally determined spectra at the given solvent concentration. [22][23][24] The agreement between experimental and computed N 2 O in Xe absorption band shapes is good and captures the dramatic gas phase-to-condensed phase lineshape change as a function of solvent density. However, the frequency position of the ν as band needs to be blue-shifted by a small frequency shift ω to achieve the best overlap with the experimental IR line shape.
The density dependent shifts are indicated in the panel and range from +6 to +22 cm −1 with no discernible trend. The shift originates from different effects, including insufficient sampling of the amount and distribution of internal energy within the N 2 O solutes vibrational degrees of freedom, remaining small inaccuracies in the intermolecular interactions, neglecting many-body contributions, and slightly underestimating the anharmonicity in the PES along the relevant coordinates. Figure 2B shows the corresponding band shape for ν s of N 2 O in Xe around 1305 cm −1 in comparison to experimentally measured 1291 cm −1 for N 2 O in the gas phase. Similar to ν as , it also displays resolved P-and R-branches at low solvent concentrations and changes into a Q-branch-like dominated structure in supercritical and liquid xenon. The IR band of the N 2 O bending mode ν δ appears at around 615 cm −1 shown in Figure 2A, compared with 589 cm −1 from experiment in the gas phase. 49 At low solvent concentrations the band structure of ν δ from the MD simulations is a sharp Q-branch with weaker P-and R-branch side bands consistent with the quantum mechanical selection rules. The intensity of these bands are no longer evident relative to the central bending feature at higher solvent concentration. The first overtone of the ν δ vibration is also detected between 1220 to 1230 cm −1 in Figure 2B    is also adjusted by a small frequency blue shift ω within the range of +8 to +27 cm −1 to maximize the overlap with the experimental IR line shape.
The line shapes for the ν δ and ν s vibrational modes are shown in Figures 3A and B as a function of SF 6 concentrations. The ν s mode changes from P-/R-branches at low solvent concentrations into a single featured structure in supercritical and liquid SF 6 . The calculated IR band of ν δ around 615 cm −1 exhibits a sharp Q-branch with resolvable weak P-and R-branch satellites only at low SF 6 concentration. The first overtone of the perpendicularly polarized ν δ mode is again detected between 1220 to 1230 cm −1 with low intensity and a band shape as observed for the parallel polarized fundamental ν s and ν as band structures. It is important to note that experimentally decay times on the several 10 fs time scale are difficult to determine with confidence from vibrational FFCFs. Therefore only those longer than that are considered in the following. It is noted that for both ions (CN − and N − 3 ) in water, mentioned above, the longer decay times are 1 ps or longer compared with ∼ 0.5 ps for N 2 O in SF 6 . This is consistent with the fact that ion-water interactions are considerably stronger than N 2 O-SF 6 interactions. Furthermore, the N 2 O-Xe interaction is weakest among all those considered here which leads to the rather short τ 2 value for this system, even relative to SF 6 .

Vibrational Frequency-Frequency Correlation Function
Given that for the present system the intermolecular interactions are weak and the decay times are rapid it is anticipated that only τ 2 for N 2 O in SF 6 would be amenable to 2DIR experiments. It is also noted that the slope for τ 2 (c) for N 2 O in SF 6 is considerably steeper than for Xe as the solvent. This is most likely also due to the increased solvent-solute interaction strength between N 2 O and SF 6 compared with Xe. The results for τ 2 indicate that interesting dynamical effects, such as critical slowing, can be expected to develop around the critical point of the solvent. It is worthwhile to note that at the critical concentration c(Xe) = 5.19 M for the transition to a SCF the spectroscopy of the asymmetric stretch changes from P-/Rbranches to Q-branch-like ( Figure 2) and the decay time τ 2 from the FFCF of the asymmetric stretch (see Figure 4B)   classical rotor (without damping) has been expressed as

Radial Distribution Functions and Size of the Solvent Shells
which assumes constant angular velocity, an approximation that does not necessarily hold for vibrating molecules. 68 The Fourier transform of φ(t) in equation 6 leads to one Q-branch signal at ω vib for parallel alignment of the rotational axis and vibrational transition dipole vector (cos θ = 1) and two P-and R-branch signals at ω vib − ω rot and ω vib + ω rot for perpendicularly aligned rotational axis and vibrational transition dipole vector (cos θ = 0). For other cases or an unstable rotation axis, signals for all P-, Q-and R-branches arise in the IR spectra. Figure 6 shows computed IR spectra from the Fourier transform of the dipole-dipole correlation function from MD simulations of a single N 2 O molecule with different initial conditions.

For all cases (A-D) intramolecular energy is distributed along all vibrational normal modes
with respect to the thermal energy at 321.9 K. Without any rotational energy assigned the IR spectra in Figure 6A shows no split into P-and R-branches. With rotational energy assigned around rotational axis parallel to the transition dipole vector the IR spectra in Figure 6B shows separation into P-and R-branches by 28 cm −1 for ν as stretch that correlates The damping with characteristic time τ models all sources of the dipole correlation function decay, primarily the solvent density dependence on orientational relaxation due to collisions between N 2 O and the solvent in the present case. With increasing density of the solvent, for example, τ decreases, which leads to loss of knowledge about its rotational motion as well as broadening of the computed IR signals, see Figure 7A. Consequently, the P-/R-features collapse into a single Q-branch-like peak for relaxation decays 0.1 ≤ τ ≤ 0.2 ps which are considerably shorter than the rotational periods.
Alternatively, interaction with a solvent can be modelled from MD simulations with a stochastic thermostat, such as in Langevin dynamics, which applies random forces on the atoms to simulate orientational interactions with the heat bath. For this, 10 ns Langevin simulations with varying coupling strengths γ were run for a single N 2 O molecule in the gas phase using CHARMM and the dipole-dipole correlation function was determined. Figure 7B shows the computed IR spectra. At low coupling strength γ i = 10 −4 ps −1 the IR spectra still yield a split of the asymmetric stretch into P-and R-branches (yellow trace). With increasing friction γ i = 0.01 ps −1 still multiple peaks are visible in the asymmetric stretch absorption lineshape but the spectral Q-branch-like region is getting filled in (pink trace). At yet higher γ i ≥ 0.1 ps −1 (green, red, blue traces) the P-/R-features wash out entirely.
Finally, it is of some interest to discuss the results on the spectroscopy (Figures 2 and 3) and the solvent structure ( Figure 5) from a broader perspective. The interaction between N 2 O and Xe is weaker by about 50 % than that between N 2 O and SF 6 . The type of interaction also differs: pure van der Waals (in the present treatment) for Xe versus van der Waals and electrostatics for SF 6 . It is interesting to note that the transition between the P-/R-and the Q-band-like spectra in Xe occurs at ρ * ∼ 0.6 (∼ 5.2 M) compared with ρ * ∼ 0.2 (∼ 0.9 M) for SF 6 , see Figures 2 and 3. This is consistent with the increased interaction strength for N 2 O-SF 6 as fewer solvent molecules are required to sufficiently perturb the system to illicit the change in the spectroscopy. Similarly, the slope of N (r) vs. concentration can also serve as a qualitative measure for the interaction strength. To stabilize a solvent shell of a certain size a smaller number (lower concentration) of solvent molecules is required if the solvent:solute interaction is sufficiently strong. These qualitative relationships are also reflected in the longer τ 2 values of the FFCFs for N 2 O in SF 6 compared with Xe as the solvent, see Figure   4. For large polyatomic molecules in highly compressible fluids, "attractive" solutes have been found to recruit increased numbers of solvent molecules which leads to local density augmentation. 75 While the amount of augmentation was found to correlate well with the free energy of solvation of the solute from simulations, computations and experiments were reported to follow different correlations.

Conclusion
In conclusion, the present work establishes that the rotational structure of the asymmetric stretch band is quantitatively described for N 2 O in xenon and is qualitatively captured in SF 6 compared with experiment. Specifically, the change from P-/R-branches in the gas phase environment changes to a Q-branch-like structure, eventually assuming a Lorentzianlike lineshape once the solvent passes through the supercritical fluid to the liquid state.
Transition between the gas-and SCF-like solvent is reflected in a steep increase in the longer correlation time τ 2 in the FFCF for both solvents. As the density of the solvent increases, additional solvent shells appear in g(r). The present work suggests that atomistic simulations together with machine learned and accurate electrostatic interactions yield a quantitative understanding of the spectroscopy and structural dynamics 4 from very low density to the liquid environment with the possibility to characterize transition to the SCF.

Supplementary Material
See supplementary material for additional data and figures referred to in the manuscript that further support the findings of this work.

Local Solvent Reorganization Lifetime
The local solvent reorganization lifetime can be used as a proxy to determine the critical concentration (density) at which transition so a SCF occurs. 5,6 Figure S1: Local solvent reorganization lifetime τ ρ from MD simulations of pure Xenon (600 atoms) at T = 291.2 K. The lifetime is computed following the work by Tucker et al. 5,6 for two cutoff radii r cut = 6.6, 10.5Å for the first and second solvation shells, respectively. These radii correspond to the local minima of the Xe-Xe radial distribution function, see Figure  S4A. The peak in τ ρ as a function of concentration at c(Xe) = 5.19 M compares with an experimentally determined critical concentration of c(Xe) = 8.45 M (dotted vertical line). 7 This difference arises due to the fact that the parametrization of the Xe-Xe interaction potential was carried out exclusively based on reference data from the gas phase. 4 Figure S2: Local solvent reorganization lifetime τ ρ from MD simulations of pure SF 6 (343 molecules) at T = 321.9 K. The lifetime is computed following the work by Tucker et al. 5,6 for two cutoff radii r cut = 8.0, 12.7Å of the first and second solvation shells, respectively. These radii correspond to the local minima of the SF 6 -SF 6 radial distribution function, see Figure S4B. The peak in τ ρ for r cut = 8.0 at c(SF 6 ) = 5.02 M agrees with the experimentally observed 7 critical concentration for SF 6 at c(SF 6 ) = 5.06 M at T = 318.76 K.   Figure S5: IR spectra of N 2 O in xenon at different solvent concentrations frequency ranges of (A) 580-650 cm −1 , (B) 1180-1350 cm −1 and (C) 2120-2310 cm −1 at 291.2 K. The amplitudes are scaled by the factor indicated at the center left for each range and density. The amplitude of the line shape in Panel B are separately scaled for hot band and symmetric stretch on the left and right of the black dashed line, respectively. In the right column, the line shape frequency bands are shifted in frequency ω to maximize the overlap with the experimental IR signal (dashed black lines, at 291 K for gas, SCF, and at 287 K for liquid xenon) at the corresponding density for the N 2 O asymmetric stretch vibration. The frequency shift is also given in the bottom left corner, and an average shift is applied for densities without experimental reference spectra. Figure S6: IR spectra of N 2 O in SF 6 at different solvent concentrations frequency ranges of (A) 580-650 cm −1 , (B) 1180-1350 cm −1 and (C) 2120-2310 cm −1 at 291.2 K. The amplitudes are scaled by the factor indicated at the center left for each range and density. The amplitude of the line shape in Panel B are separately scaled for hot band and symmetric stretch on the left and right of the black dashed line, respectively. In the right column, the line shape frequency bands are shifted in frequency ω to maximize the overlap with the experimental IR signal (dashed black lines, at 322 K for gas, SCF, and at 293 K for liquid SF 6 ) at the corresponding density for the N 2 O asymmetric stretch vibration. The frequency shift is also given in the bottom left corner, and an average shift is applied for densities without experimental reference spectra. Figure S7: Amplitudes (a 1 and a 2 ), decay times (τ 1 and τ 2 ), and asymptotic values (∆) for the bi-exponential fits of the normalized FFCF to the ν as time series from INMs for N 2 O in Xe (A, C, E) and SF 6 (B, D, F) depending on solvent concentration. The experimental 7 critical concentration c crit and from simulations at T c of xenon and SF 6 , are marked by the vertical dashed and dotted line, respectively. It should be noted that the Xe-Xe interactions 4 were not optimized to reproduce the experimentally known T c for pure Xe whereas the model for SF 6 does.