**4.2. CH**3**I low-***n* **Rydberg states in Ar, Kr and Xe**

## *4.2.1. CH*3*I absorption*

20 Will-be-set-by-IN-TECH

shows that the 6*s* Rydberg state broadens and shifts to higher energies more quickly than does the 6*s*� state. Since both transitions are excited from the same ground state (implying that the ground state intermolecular potential parameters remain unchanged), Δ*re* must decrease and *ε*(*e*) increase in order to simulate the Xe 6*s*� Rydberg state in argon correctly. These general trends proved helpful when determining the intermolecular potential parameters for new

Messing, *et al.* [25, 26] concluded that the argon induced energy shift is density dependent and temperature independent. However, both our experimental absorption spectra and the line shape simulations show a distinct temperature dependence near the argon critical point. To test the sensitivity of the perturber critical point effect, we extracted the perturber dependent shift Δ(*ρAr*) of the simulated primary Xe 6*s* transition in supercritical argon near the critical density along three different isotherms (i.e., *Tr* = 1.01, 1.06 and 1.11, where *Tr* = *T*/*Tc* with *Tc* = −122.3◦C). These data are shown in Fig. 10a and clearly indicate that the critical effect is extremely sensitive to temperature and can be easily missed if the temperature of the system

**Figure 10.** (a) The calculated argon induced shift Δ(*ρAr*) doped into supercritical argon plotted as a function of reduced argon number density at a reduced temperature *Tr* = 1.01 (◦), 1.06 (•) and 1.11 (). (b) The local densities (*ρ*local = *g*max *ρ*bulk) of the first argon solvent shell around a central Xe atom plotted as a function of reduced argon number density at a reduced temperature *Tr* � 1.01 (◦), 1.06 (•) and 1.11

If we return to the line shape equation [i.e., eq. (29)], we observe that the two-body interaction term *A*1(*t*) and the three-body interaction term *A*2(*t*) depend on the difference between the excited state and ground state intermolecular potentials and on the perturber/dopant radial distribution function. Since the potential difference will not depend dramatically on temperature, the critical point effect must be dominated by changes in the perturber/dopant radial distribution function *g*PD(*r*). In Fig. 10b, we plot the local density of the first solvent shell as a function of the bulk reduced argon number density on the same three isotherms. The *Tr* = 1.01 isotherm shows a much larger density deviation near the critical density in comparison to the other two isotherms. Thus, the argon induced blue shift is caused by the first perturber shell shielding the cationic core from the optical election. This increase in shielding decreases the binding energy of the electron, thereby increasing the excitation

systems.

energy.

is not maintained close to the critical isotherm.

(). The solid lines are provided as visual aid.

The CH3I 6*s* and 6*s*� Rydberg states doped into supercritical argon, krypton and xenon were investigated both experimentally and theoretically [38, 40] from low perturber number density to the density of the triple point liquid, at both non-critical temperatures and on an isotherm near (i.e., +0.5◦C) the critical isotherm of the perturber. The CH3I 6*s* and 6*s*� Rydberg states show perturber-induced energy shifts and broadening similar to that observed for the Xe low-*n* Rydberg states in supercritical argon. The peak positions of the absorption spectra shift to the red slightly and then strongly to the blue as a function of perturber number densities. This is similar to the behavior for CH3I in dense rare gases observed by Messing, *et al.* [27, 28]. Unlike Xe, which forms heterogenous dimers in argon, the CH3I/perturber interactions are weaker. Thus, CH3I does not possess blue satellite bands caused by dimer or excimer formation. However, CH3I does possess a strong vibrational transition on the blue side of the adiabatic transition. Fig. 4 shows the absorption of both the 6*s* and 6*s*� Rydberg states of CH3I and clearly illustrates the vibrational state, which represents the CH3 group deformation vibrational band *ν*2. The solid lines in Figs. 11 - 13 represent selected photoabsorption spectra for the CH3I 6*s* Rydberg transition doped into supercrtical argon, krypton and xenon, while similar plots for the CH3I 6*s*� transition are not shown for brevity. Experimental spectra of CH3I in Xe at number densities between 5.0 <sup>×</sup> 1021 cm−<sup>3</sup> and 7.0 <sup>×</sup> 1021 cm−<sup>3</sup> could not be obtained, because of the large density deviation induced by small temperature fluctuations (<sup>≈</sup> 2.0 <sup>×</sup> 1021 cm−<sup>3</sup> for a 0.001◦C temperature change) in this density region.

The experimental absorption of CH3I low-*n* Rydberg transitions shows that as the perturber number density increases, the *ν*<sup>2</sup> vibrational band broadens and shifts until it merges with the adiabatic transition. Therefore, determining the perturber induced shift Δ(*ρ*P) of the adiabatic transition from a simple moment analysis of the spectra presented in Figs. 11 - 13 is not possible, and we must perform an accurate line shape analysis of these data in order to extract Δ(*ρ*P) and investigate the perturber critical effect. However, some qualitative information can be gleaned from Figs. 11 - 13. First, the rate of the broadening and the rate of shift for both the adiabatic transition band and the *ν*<sup>2</sup> vibrational transition band differ dramatically for different perturbers. However, although not shown, the CH3I 6*s* and 6*s*� transitions have almost the same perturber induced shift, which differs from the behavior observed for the Xe in Ar system previously presented.

#### *4.2.2. Discussion*

Although CH3I in the rare gases does not form dimers or excimers, the accurate simulation of the low-*n* Rydberg transitions must include both the adiabatic transition, given by eq. (26) and denoted *a* in Fig. 4, as well as one quantum of the CH3 deformation vibrational transition *ν*<sup>2</sup> in the excited state, given by eq. (27) and denoted *b* in Fig. 4. For all of the simulations presented here, we again chose eq. (41) for the ground-state perturber/perturber intermolecular interactions. All of the ground-state dopant/perturber interactions, on the other hand, were approximated with eq. (43). The excited-state dopant/ground state perturber interactions were again modeled using eq. (44). All intermolecular potential parameters except the Ar/Ar, Kr/Kr, Xe/Xe, CH3I/Ar, and CH3I/Kr ground state potential parameters were adjusted by hand to give the best simulated line shape in comparison to our experimental absorption spectra. (The Ar/Ar, Kr/Kr, Xe/Xe, CH3I/Ar, and CH3I/Kr ground-state potential parameters used are in accord with those employed in our earlier studies of the quasi-free electron energy in rare gas perturbers [12].) Appendix A gives the values for all intermolecular potential parameters used in the line shape simulations presented here. The relative intensities of the simulated bands were fixed by comparison to the absorption spectra of CH3I at perturber number densities where all bands (i.e., the adiabatic and vibrational transitions) could be clearly identified. Experimentally, at low perturber number densities the ratio of the vibrational band intensity to the adiabatic transition intensity is 0.22 for both the CH3I 6*s* and 6*s*� Rydberg states in all three perturbers.

**Figure 11.** Selected photoabsorption spectra (—, relative units) and simulated line shapes (··· ) for the CH3I 6*s* Rydberg transition in argon at (a) non-critical temperatures and (b) on an isotherm (−121.8◦C) near the critical isotherm. The data are offset vertically by the argon number density *ρ*Ar. The transition energy is *E*<sup>0</sup> = 6.154 eV for the unperturbed CH3I 6*s* Rydberg transition. The variation between experiment and simulation is caused by other vibrational transitions and by perturber-dependent lifetime broadening not modeled here.

The dotted lines in Figs.11 - 13 present the simulated line shapes (dotted lines) of the low-*n* CH3I Rydberg transitions in the atomic perturbers at non-critical temperatures and on an isotherm near the critical isotherm of the perturber. As was true for Xe in Ar, the simulated spectra closely match the experimental spectra for all densities. Both the simulated and experimental line shapes show a slight red shift at low perturber number densities, followed by a strong blue shift at high perturber densities. Given the accuracy of the simulated line shapes, simulated spectra for CH3I in Xe in the region where experimental data were unobtainable are also presented in Fig. 13. We should note here that we were able to model the CH3I 6*s* and 6*s*� Rydberg states in Ar using the same set of intermolecular potential parameters for both states. This behavior was also observed for the CH3I 6*s* and 6*s*� Rydberg states in Kr. With identical potential parameters, the perturber induced shift Δ(*ρ*P) will be the same for the 6*s* and 6*s*� states. The independence of Δ(*ρ*P) on the dopant cationic core state is different from that observed for Xe low-*n* Rydberg states in Ar and will be discussed in more detail below. The accurate line shape simulations allow Δ(*ρ*P) for the adiabatic transitions to be extracted using eq. (21).

As with Xe in Ar, the accurate line shape simulations allow a moment analysis to be performed on the CH3I low-*n* adiabatic Rydberg transition to obtain the perturber induced shift Δ(*ρ*P)

22 Will-be-set-by-IN-TECH

our experimental absorption spectra. (The Ar/Ar, Kr/Kr, Xe/Xe, CH3I/Ar, and CH3I/Kr ground-state potential parameters used are in accord with those employed in our earlier studies of the quasi-free electron energy in rare gas perturbers [12].) Appendix A gives the values for all intermolecular potential parameters used in the line shape simulations presented here. The relative intensities of the simulated bands were fixed by comparison to the absorption spectra of CH3I at perturber number densities where all bands (i.e., the adiabatic and vibrational transitions) could be clearly identified. Experimentally, at low perturber number densities the ratio of the vibrational band intensity to the adiabatic transition intensity

**Figure 11.** Selected photoabsorption spectra (—, relative units) and simulated line shapes (··· ) for the CH3I 6*s* Rydberg transition in argon at (a) non-critical temperatures and (b) on an isotherm (−121.8◦C) near the critical isotherm. The data are offset vertically by the argon number density *ρ*Ar. The transition energy is *E*<sup>0</sup> = 6.154 eV for the unperturbed CH3I 6*s* Rydberg transition. The variation between experiment and simulation is caused by other vibrational transitions and by perturber-dependent

The dotted lines in Figs.11 - 13 present the simulated line shapes (dotted lines) of the low-*n* CH3I Rydberg transitions in the atomic perturbers at non-critical temperatures and on an isotherm near the critical isotherm of the perturber. As was true for Xe in Ar, the simulated spectra closely match the experimental spectra for all densities. Both the simulated and experimental line shapes show a slight red shift at low perturber number densities, followed by a strong blue shift at high perturber densities. Given the accuracy of the simulated line shapes, simulated spectra for CH3I in Xe in the region where experimental data were unobtainable are also presented in Fig. 13. We should note here that we were able to model the CH3I 6*s* and 6*s*� Rydberg states in Ar using the same set of intermolecular potential parameters for both states. This behavior was also observed for the CH3I 6*s* and 6*s*� Rydberg states in Kr. With identical potential parameters, the perturber induced shift Δ(*ρ*P) will be the same for the 6*s* and 6*s*� states. The independence of Δ(*ρ*P) on the dopant cationic core state is different from that observed for Xe low-*n* Rydberg states in Ar and will be discussed in more detail below. The accurate line shape simulations allow Δ(*ρ*P) for the adiabatic transitions to be extracted

As with Xe in Ar, the accurate line shape simulations allow a moment analysis to be performed on the CH3I low-*n* adiabatic Rydberg transition to obtain the perturber induced shift Δ(*ρ*P)

is 0.22 for both the CH3I 6*s* and 6*s*� Rydberg states in all three perturbers.

lifetime broadening not modeled here.

using eq. (21).

**Figure 12.** Selected photoabsorption spectra (—, relative units) and simulated line shapes (··· ) for the CH3I 6*s* Rydberg transition in krypton at (a) non-critical temperatures and (b) on an isotherm (−63.3◦C) near the critical isotherm. The data are offset vertically by the krypton number density *ρ*Kr. The transition energy is *E*<sup>0</sup> = 6.154 eV for the unperturbed CH3I 6*s* Rydberg transition. The variation between experiment and simulation is caused by other vibrational transitions and by perturber-dependent lifetime broadening not modeled here.

**Figure 13.** Selected photoabsorption spectra (—, relative units) and simulated line shapes (··· ) for the CH3I 6*s* Rydberg transition in xenon at (a) non-critical temperatures and (b) on an isotherm (17.0◦C) near the critical isotherm. The data are offset vertically by the xenon number density *ρ*Xe. The transition energy is *E*<sup>0</sup> = 6.154 eV for the unperturbed CH3I 6*s* Rydberg transition. The variation between experiment and simulation is caused by other vibrational transitions and by perturber-dependent lifetime broadening not modeled here.

from eq.(21). The first moment of the simulated CH3I 6*s* adiabatic transition is plotted as a function of the reduced perturber number density *ρr* in Fig. 14 for the 6*s* transition. (A similar figure for the 6*s*� transition is not shown for brevity.) The first moment of the simulated adiabatic band does not red shift at low perturber density, as was originally stated by Messing, *et al.* [27, 28]. This absence of a red shift is again caused by the blue degradation of the adiabatic transition, which places the average energy (i.e., the first moment) of the band to the high energy side of the absorption maximum. The ground state interaction between CH3I and the perturber is attractive, and therefore the ground state of the dopant is stabilized by the perturber solvent shell. The slight red shift of the absorption maximum observed at low perturber number densities is indicative of the stabilization of the CH3I excited states by the perturber solvent shell. As the density increases, however, perturber molecules begin to shield the optical electron from the CH3I cationic core, thereby increasing the excitation energy of the optical electron. Thus, as the perturber density increases, the energy of the excited state also increases, leading to a blue shift at higher perturber densities.

The 6*s* and 6*s* Rydberg states correspond to an optical electron in the same Rydberg orbital, but with the cation in a different core state: *J* = 3/2 for *s* and *J* = 1/2 for *s* , where *J* is the total angular momentum of the core. In our investigation of Δ(*ρ*P) for Xe in Ar, we found that Δ(*ρ*P) of the 6*s* transition is 0.2 eV larger than that for the 6*s* transition, indicating that the change in the core quadrupole moment affects the dopant/perturber interactions in a dense perturbing medium. However, Δ(*ρ*P) for the CH3I 6*s* and 6*s* Rydberg transitions near the triple point density are identical to within experimental error for the perturbers argon and krypton, and differ only slightly (i.e., 30 meV) for CH3I in xenon. The insensitivity of these CH3I/perturber systems to the change in the CH3I cationic core is probably caused by the large permanent dipole moment of CH3I, which masks the effect of the quadrupole moment. Xenon, however, is extremely sensitive to electric fields because of its large polarizability. Therefore, the slight difference between the xenon induced shifts of the CH3I 6*s* and 6*s* Rydberg transitions may well be caused by small changes in the permanent dipole moment of CH3I influencing changes in the induced dipole or local quadrupoles in the xenon perturber.

A critical point effect on the 6*s* and 6*s* transition energies is also apparent in Fig. 14 for all three perturbers. The CH3I 6*s* adiabatic transition in argon is blue-shifted by 20 meV near the critical temperature and critical density, while those in krypton and xenon are blue-shifted by 30 meV and 15 meV, respectively. Identical results are obtained for the CH3I 6*s* adiabatic transitions in argon and krypton. However, a smaller critical effect of 5 meV is observed for the CH3I 6*s* transition in xenon, which is related to the smaller overall blue shift of the CH3I 6*s* transition in comparison to the 6*s* transition.

In the low to medium density range, the energy of the absorption maximum for the 6*s* and 6*s* CH3I Rydberg states has a larger red shift in xenon, which is caused by the larger xenon polarizability. The CH3I Rydberg states also broaden more quickly in xenon. This increased broadening is probably due to a combination of increased xenon polarizability and an increase in the probability of collisional de-excitation due to the size of xenon. However, Δ(*ρ*P) is larger for argon than for krypton and xenon. This change is caused by an overall decrease in the total number of perturber atoms within the first solvent shell surrounding the CH3I dopant as the perturber atoms become larger. The variation in the critical point effect, with krypton having a larger effect than argon and xenon, is caused by the strength of the perturber/CH3I interactions in comparison to the perturber/perturber interactions, coupled with the differences in the ground-state and excited-state dopant/perturber interaction potentials. The CH3I/Kr ground state potential well depth is close (i.e., 24 K) to the Kr/Kr potential well depth. This implies that the CH3I/Kr interactions near the krypton critical point will be comparable to the Kr/Kr interactions, thereby leading to a large increase in the local perturber density near the critical point of the perturber, and a larger critical point effect. Similarly, the critical point effect decreases as one goes from krypton to argon to xenon because the difference in well depth for all intermolecular potentials increases.

#### 474 Advanced Aspects of Spectroscopy Atomic and Molecular Low-*<sup>n</sup>* Rydberg States in Near Critical Point Fluids<sup>12</sup> <sup>25</sup> Atomic and Molecular Low-n Rydberg States in Near Critical Point Fluids 475

**Figure 14.** (a) The perturber induced shift Δ(*ρ*P), as approximated by a moment analysis [i.e., eq. (21)], of the simulated primary transition for the CH3I 6*s* Rydberg state as a function of the reduced perturber number density *ρ<sup>r</sup>* for argon, krypton and xenon. (•), simulations obtained at noncritical temperatures; (◦), simulations near the critical isotherm. (b) An expanded view of Δ(*ρ*P) near the perturber critical point. *<sup>ρ</sup><sup>c</sup>* <sup>=</sup> 8.0 <sup>×</sup> 1021 cm−<sup>3</sup> for argon, *<sup>ρ</sup><sup>c</sup>* <sup>=</sup> 6.6 <sup>×</sup> 1021 cm−<sup>3</sup> for krypton and *<sup>ρ</sup><sup>c</sup>* <sup>=</sup> 5.0 <sup>×</sup> 1021 cm−<sup>3</sup> for xenon [12]. The solid lines provide a visual aid. See text for discussion.

#### **5. Conclusion**

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the perturber solvent shell. The slight red shift of the absorption maximum observed at low perturber number densities is indicative of the stabilization of the CH3I excited states by the perturber solvent shell. As the density increases, however, perturber molecules begin to shield the optical electron from the CH3I cationic core, thereby increasing the excitation energy of the optical electron. Thus, as the perturber density increases, the energy of the excited state also

The 6*s* and 6*s* Rydberg states correspond to an optical electron in the same Rydberg orbital,

total angular momentum of the core. In our investigation of Δ(*ρ*P) for Xe in Ar, we found that Δ(*ρ*P) of the 6*s* transition is 0.2 eV larger than that for the 6*s* transition, indicating that the change in the core quadrupole moment affects the dopant/perturber interactions in a dense perturbing medium. However, Δ(*ρ*P) for the CH3I 6*s* and 6*s* Rydberg transitions near the triple point density are identical to within experimental error for the perturbers argon and krypton, and differ only slightly (i.e., 30 meV) for CH3I in xenon. The insensitivity of these CH3I/perturber systems to the change in the CH3I cationic core is probably caused by the large permanent dipole moment of CH3I, which masks the effect of the quadrupole moment. Xenon, however, is extremely sensitive to electric fields because of its large polarizability. Therefore, the slight difference between the xenon induced shifts of the CH3I 6*s* and 6*s* Rydberg transitions may well be caused by small changes in the permanent dipole moment of CH3I influencing changes in the induced dipole or local quadrupoles in the xenon perturber. A critical point effect on the 6*s* and 6*s* transition energies is also apparent in Fig. 14 for all three perturbers. The CH3I 6*s* adiabatic transition in argon is blue-shifted by 20 meV near the critical temperature and critical density, while those in krypton and xenon are blue-shifted by 30 meV and 15 meV, respectively. Identical results are obtained for the CH3I 6*s* adiabatic transitions in argon and krypton. However, a smaller critical effect of 5 meV is observed for the CH3I 6*s* transition in xenon, which is related to the smaller overall blue shift of the CH3I

In the low to medium density range, the energy of the absorption maximum for the 6*s* and 6*s* CH3I Rydberg states has a larger red shift in xenon, which is caused by the larger xenon polarizability. The CH3I Rydberg states also broaden more quickly in xenon. This increased broadening is probably due to a combination of increased xenon polarizability and an increase in the probability of collisional de-excitation due to the size of xenon. However, Δ(*ρ*P) is larger for argon than for krypton and xenon. This change is caused by an overall decrease in the total number of perturber atoms within the first solvent shell surrounding the CH3I dopant as the perturber atoms become larger. The variation in the critical point effect, with krypton having a larger effect than argon and xenon, is caused by the strength of the perturber/CH3I interactions in comparison to the perturber/perturber interactions, coupled with the differences in the ground-state and excited-state dopant/perturber interaction potentials. The CH3I/Kr ground state potential well depth is close (i.e., 24 K) to the Kr/Kr potential well depth. This implies that the CH3I/Kr interactions near the krypton critical point will be comparable to the Kr/Kr interactions, thereby leading to a large increase in the local perturber density near the critical point of the perturber, and a larger critical point effect. Similarly, the critical point effect decreases as one goes from krypton to argon to xenon because

the difference in well depth for all intermolecular potentials increases.

, where *J* is the

but with the cation in a different core state: *J* = 3/2 for *s* and *J* = 1/2 for *s*

increases, leading to a blue shift at higher perturber densities.

6*s* transition in comparison to the 6*s* transition.

In this work, the structure of low-*n* Rydberg states doped into supercritical fluids was investigated in several atomic perturbers. Both the experimental absorption spectra and full line shape simulations over the entire perturber density range at non-critical temperatures and along isotherms near perturber critical isotherms were presented for all dopant/perturber systems. These accurate line shape simulations allowed us to extract the perturber-induced energy shift Δ(*ρ*P) from the simulated primary low-*n* Rydberg transitions. These shifts showed a striking critical point effect in all dopant/perturber systems. Our group also performed similar absorption measurements of atomic and molecular low-*n* Rydberg states in molecular perturbers [39, 40] with similar results. Because of the brevity of this Chapter, the details of these measurements cannot be presented here.

In all of the systems investigated [37–40], the dopant low-*n* Rydberg states are extremely sensitive to the nature of the perturbing fluid. When these states are doped into supercritical fluids, the surrounding perturbers interact with the central dopant causing shifts both in the dopant ground state energy and in the excited state energy. At low perturber number densities, the dopant/perturber interaction stabilizes the dopant ground state and the low-*n* Rydberg state. As the perturber density increases, perturber/dopant interactions lead to the formation of a perturber solvent shell around the dopant core, thereby inducing local perturber density inhomogeneities. This solvent shell begins to shield the optical electron from the cationic core. Therefore, the dense perturber fluid increases the dopant excitation energy, resulting in a blue shift of the abosrption band, which is observed experimentally. The local density of the first perturber solvent shell is almost proportional to the perturber bulk density at non-critical temperatures. However, near the critical isotherm and critical density of the perturber, the dopant/perturber interactions strengthen due to the increased perturber/perturber correlation length. This increased order yields a corresponding increase of the local density in the solvent shell that, in turn, leads to a stronger shielding of the optical electron from the cationic core. Thus, increased blue shifts of the low-*n* absorption bands are observed in all dopant/perturber systems near the critical point of the perturber. The area of this critical effect is demarcated by the turning points that bound the saddle point in the thermodynamic phase diagram of the critical isotherm.

For fluids with similar compressibilities, the structures of low-*n* dopant Rydberg states in the perturbing fluid show systematic behaviors. At non-critical temperatures, Δ(*ρ*P) is determined by the polarizability and size of the perturbing fluid. The larger the polarizability and, therefore, the larger the size, the smaller the perturber-induced energy shift of the dopant absorption bands. This is caused by the number of atoms that can exist between the optical electron and the dopant cationic core, coupled with the strength of the shielding. The large overall energy shift observed in the dopant low-*n* Rydberg states perturbed by CF4 [39, 40], on the other hand, was caused by the larger compressibility of CF4 in comparison to the other gases in this study [37, 38, 40]. This larger compressibility implies that CF4 is closer together on average at high perturber number densities than are the other perturbers studied, which increases the local density of CF4 and, therefore, increases the blue shift in this perturber.

The critical point effect, on the other hand, is dominated by the similarity of the perturber/ perturber interaction with the dopant/perturber ground state and dopant/perturber excited state interactions, coupled with the overall local density of the system. In krypton, the well depth of the ground state perturber/perturber intermolecular potential and the dopant/ perturber intermolecular potential shows greater similarity in comparison to that in Ar and Xe. Moreover, the excited state CH3I/Kr interaction is slightly stronger than the ground state Kr/Kr interaction. These facts dictate that the largest critical point effect for CH3I in atomic perturbers is in Kr. Similarly, the largest overall critical effect was observed in CH3I/CH4 [39, 40]. This large critical effect is caused by both the ground state and excited state CH3I/CH4 interactions having strengths comparable to the CH4/CH4 interaction. Although the excited state CH3I/CF4 interactions are comparable in strength to the CF4/CF4 interactions, the ground state CH3I/CF4 interactions are not close to those of CF4/CF4. Similarly, the Xe/CF4 ground state interactions are comparable to the ground state CF4/CF4 interactions, but the excited state Xe/ground state CF4 interactions are weaker. Moreover, the bulk critical density in CF4 is small in comparison to the rest of the perturbers investigated here. This results in the CF4 critical effect on Δ(*ρ*P) being the smallest one observed [39, 40].

These data sets also allowed us to generate a consistent set of intermolecular potential parameters for various dopant/perturber systems, which are summarized in Appendix A. Several general trends in these parameters can be observed. For atomic perturbers, the steepness of the exponential-6 intermolecular potential (i.e., *γ*) used to model the dopant excited state/perturber intermolecular interaction decreases with increasing perturber size and polarizability. This trend is reversed in molecular perturbers, were the larger, more compressible CF4 has a steeper repulsive component in comparison to CH4. The excited vibrational states of CH3I always have exponential-6 potentials with a smaller *γ* in comparison to the CH3I adiabatic transition in the same perturbing gas. Moreover, the vibrational states always have an equilibrium collision radius that is identical or larger than the collision radius of the adiabatic transition. The excited state collision radii are always larger than the ground state collision radii, as one would expect. However, the interaction strength of the excited state (as gauged by the well depth) can be stronger or weaker than that for the ground state of the same system. These changing interactions are what dominate the variations observed in the critical effects for each of the dopant/perturber systems investigated here.

An understanding of the structure of low-*n* Rydberg states in supercritical fluids is an important tool in the investigation of solvation effects, since these studies can yield accurate dopant/perturber ground state and excited state intermolecular potentials. We conclude from the present work that the absorption line shapes can be adequately simulated within a simple semi-classical line shape analysis. However, this work focused on highly symmetric perturbers. Future studies should concern more asymmetric perturbers and polar perturbers. Such an extension will require changing the calculation techniques involved in determining the radial distribution functions as well as the type of Fourier transform used to simulate the line shape. Since the excited state is sensitive to the structure of the perturbing fluid, we anticipate that multi-site intermolecular potentials and angular dependent intermolecular potentials will be needed as the perturber complexity increases, in order to model the full line shape accurately.
