Potential Energy Surfaces for Noble Gas (Ar, Kr, Xe, Rn)–Propylene Oxide Systems: Analytical Formulation and Binding
Abstract
:1. Introduction
2. Potential Energy Surfaces
2.1. The Improved Lennard-Jones Potential
2.2. Ab Initio Calculations
3. Results and Discussion
4. Final Remarks and Conclusions
- (1)
- The adopted method represents the intermolecular potential by an analytic formulation that makes use of few parameters, all having a well-defined physical meaning. This physically grounded restriction, at variance with most interpolation procedures, ensures the reliability of the interaction in the whole space of the relative configurations;
- (2)
- The present method allows a direct evaluation of the long-range dispersion coefficient C6, that controls the capture character of the long-range forces;
- (3)
- All systems present five minima very close in energy. Therefore, the collision dynamics is likely to be determined from their overall contribution, as well as from the possibility of adiabatic inter-conversion between them, hindered by the energy barriers that increase with the noble gas mass, and as the R distance decreases;
- (4)
- For each system, the location of the minimum energy changes as the intermolecular distance varies, that is the most stable configuration at long range, can substantially differ from that exhibited at intermediate and short range. An important consequence is that a system, formed by the trapping long-range anisotropic attractive forces, can be channeled during the relaxation of its internal degrees of freedom via fast non-adiabatic cooling, in configurations that can differ from that of the PES global minimum;
- (5)
- The dissociation energy of Ar−propylene oxide and Kr−propylene oxide, estimated by Blanco et al. [25], is consistent with the well depth and geometries of the minima determined in the present work. Moreover, considerations made at the previous point 4 can also applied to this point;
- (6)
- The analytical formulation of the PES allows the calculation of physical, dynamical, and spectroscopic properties of the systems, which selectively depend on the weak anisotropic forces, effective both at long and intermediate range of separation distances;
- (7)
- The same method can be applied, after parameters scaling for the change in polarizability, to the description of simple diatomic molecule-propylene oxide systems, when the diatom (as H2, N2 and O2), with rotational levels following a Boltzmann distribution at room and higher temperature, rotates sufficiently faster than propylene oxide. Therefore, under such conditions, the diatom, which during the collision behaves as a pseudo-atom, interacts with propylene oxide with intermolecular forces basically of van der Waals nature. In particular, N2 and O2 would behave like Ar, as they show a similar isotropic polarizability component, while the polarizability of H2 suggests for this molecule an intermediate behavior between Ne and Ar. However, the anisotropic character of the intermolecular forces emerges at low temperature, which is when only slowly rotating diatoms are interacting with the propylene oxide. In this case, the complete potential formulation must also include the anisotropic contribution of the electrostatic components, as those arising from permanent molecular electric multipole interactions. The method can also be extended to more complex systems of interest for their chiral properties, like propylene oxide dimers.
- (8)
- These potential energy surfaces can be used to evaluate and investigate possible collision alignment processes, basic for chiral discrimination in gaseous streams and vortices occurring in no equilibrium atmosphere environments [40];
- (9)
- Finally, it is also worth pointing out that this methodology can be profitably used to preliminarily address the search of ab-initio stationary points in multidimensional surfaces for weakly bound systems. This might be a difficult task, as they require a higher level of theory than bound systems, and may present many minima, particularly when some of them are shallow and can easily escape a grid search. The ab-initio calculation of transition states may be even more elusive. A preliminary detailed search on the present PES is reliable and much faster and allows identification of confined regions where minima or transition state points are located, strongly reducing the number of points to be evaluated quantum mechanically. Moreover, its formulation permits both forces and force constants to be obtained analytically, speeding up their calculation in molecular dynamics simulations, where these quantities play a crucial role, therefore alleviating the related computational burden.
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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ε/meV | rm/Å | β | |
---|---|---|---|
CH3-Ar | 9.21 | 4.02 | 7.0 |
C-Ar | 7.19 | 3.79 | 7.0 |
O-Ar | 8.51 | 3.61 | 7.0 |
H-Ar | 3.27 | 3.51 | 8.0 |
ε/meV | rm/Å | β | |
---|---|---|---|
CH3-Kr | 11.78 | 4.11 | 7.0 |
C-Kr | 8.73 | 3.91 | 7.0 |
O-Kr | 9.72 | 3.76 | 7.0 |
H-Kr | 3.59 | 3.69 | 8.0 |
ε/meV | rm/Å | β | |
---|---|---|---|
CH3-Xe | 14.25 | 4.26 | 7.0 |
C-Xe | 9.93 | 4.09 | 7.0 |
O-Xe | 10.19 | 3.97 | 7.0 |
H-Xe | 3.67 | 3.93 | 8.0 |
ε/meV | rm/Å | β | |
---|---|---|---|
CH3-Rn | 16.80 | 4.34 | 7.0 |
C-Rn | 11.37 | 4.19 | 7.0 |
O-Rn | 11.39 | 4.10 | 7.0 |
H-Rn | 3.96 | 4.07 | 8.0 |
Minimum 1 | Minimum 2 | Minimum 3 | Minimum 4 | Minimum 5 | |
---|---|---|---|---|---|
θ | 98.8 (99.8) | 87.6 (81.3) | 49.7 (50.0) | 100.4 (99.4) | 43.1 (30.5) |
ϕ | 22.6 (10.5) | 254.7 (259.1) | 114.8 (106.7) | 156.5 (66.1) | 255.6 (247.4) |
R (Å) | 3.93 (3.83) | 3.74 (3.75) | 4.06 (3.87) | 3.88 (3.67) | 4.24 (4.15) |
V (meV) | −34.6 (−36.8) | −34.1 (−36.0) | −31.8 (−40.2) | −31.7 (−40.3) | −26.9 (−33.0) |
Minimum 1 | Minimum 2 | Minimum 3 | Minimum 4 | Minimum 5 | |
---|---|---|---|---|---|
θ | 99.9 (99.3) | 88.8 (80.8) | 49.9 (49.9) | 101.7 (98.8) | 43.2 (31.5) |
ϕ | 21.2 (12.0) | 254.1 (257.7) | 115.9 (108.7) | 157.9 (157.0) | 254.9 (246.4) |
R (Å) | 4.06 (3.93) | 3.88 (3.81) | 4.21 (3.97) | 4.02 (3.77) | 4.38 (4.28) |
V (meV) | −42.2 (−44.2) | −40.9 (−44.6) | −37.0 (−49.2) | −38.2 (−49.0) | −31.7 (−39.8) |
Minimum 1 | Minimum 2 | Minimum 3 | Minimum 4 | Minimum 5 | |
---|---|---|---|---|---|
θ | 101.2 (98.7) | 90.1 (79.0) | 50.2 (49.9) | 103.1 (97.5) | 41.9 (33.0) |
ϕ | 20.0 (13.2) | 253.4 (256.2) | 117.3 (110.8) | 159.6 (157.0) | 254.0 (244.6) |
R (Å) | 4.25 (4.10) | 4.07 (3.97) | 4.42 (4.12) | 4.21 (3.94) | 4.59 (4.39) |
V (meV) | −48.1 (−53.2) | −46.0 (−55.2) | −40.2 (−60.2) | −43.1 (−59.7) | −34.9 (−49.2) |
Minimum 1 | Minimum 2 | Minimum 3 | Minimum 4 | Minimum 5 | |
---|---|---|---|---|---|
θ | 102.8 (98.6) | 90.8 (79.7) | 50.5 (49.8) | 103.8 (96.9) | 40.8 (33.8) |
ϕ | 19.4 (13.8 | 253.1 (255.1) | 118.1 (112.0) | 160.4 (156.5) | 253.6 (243.2) |
R (Å) | 4.36 (4.15) | 4.18 (4.01) | 4.54 (4.17) | 4.32 (3.99) | 4.72 (4.43) |
V (meV) | −55.1 (−59.9) | −52.6 (−63.7) | −45.1 (−67.6) | −49.4 (−67.1) | −39.5 (−55.2) |
System | |
---|---|
He-C3H6O | 1.65 |
Ne-C3H6O | 3.65 |
Ar-C3H6O | 11.80 |
Kr-C3H6O | 17.43 |
Xe-C3H6O | 25.78 |
Rn-C3H6O | 34.35 |
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Palazzetti, F.; Coletti, C.; Marrone, A.; Pirani, F. Potential Energy Surfaces for Noble Gas (Ar, Kr, Xe, Rn)–Propylene Oxide Systems: Analytical Formulation and Binding. Symmetry 2022, 14, 249. https://doi.org/10.3390/sym14020249
Palazzetti F, Coletti C, Marrone A, Pirani F. Potential Energy Surfaces for Noble Gas (Ar, Kr, Xe, Rn)–Propylene Oxide Systems: Analytical Formulation and Binding. Symmetry. 2022; 14(2):249. https://doi.org/10.3390/sym14020249
Chicago/Turabian StylePalazzetti, Federico, Cecilia Coletti, Alessandro Marrone, and Fernando Pirani. 2022. "Potential Energy Surfaces for Noble Gas (Ar, Kr, Xe, Rn)–Propylene Oxide Systems: Analytical Formulation and Binding" Symmetry 14, no. 2: 249. https://doi.org/10.3390/sym14020249
APA StylePalazzetti, F., Coletti, C., Marrone, A., & Pirani, F. (2022). Potential Energy Surfaces for Noble Gas (Ar, Kr, Xe, Rn)–Propylene Oxide Systems: Analytical Formulation and Binding. Symmetry, 14(2), 249. https://doi.org/10.3390/sym14020249