Fourth-order quantum master equation and its Markovian bath limitSix major theories of quantum dissipative dynamics are compared: Redfield theory, the Gaussian phase space ansatz of Yan and Mukamel, the master equations of Agarwal, Caldeira-Leggett/ Oppenheim-Romero-Rochin, and Louisell/Lax, and the semigroup theory of Lindblad. The time evolving density operator from each theory is transformed into a Wigner phase space distribution, and classical-quantum correspondence is investigated via comparison with the phase space distribution of the classical Fokker-Planck ͑FP͒ equation. Although the comparison is for the specific case of Markovian dynamics of the damped harmonic oscillator with no pure dephasing, certain inferences can be drawn about general systems. The following are our major conclusions: ͑1͒ The harmonic oscillator master equation derived from Redfield theory, in the limit of a classical bath, is identical to the Agarwal master equation. ͑2͒ Following Agarwal, the Agarwal master equation can be transformed to phase space, and differs from the classical FP equation only by a zero point energy in the diffusion coefficient. This analytic solution supports Gaussian solutions with the following properties: the differential equations for the first moments in p and q and all but one of the second moments (q 2 and pq but not p 2 ) are identical to the classical equations. Moreover, the distribution evolves to the thermal state of the bare quantum system at long times. ͑3͒ The Gaussian phase space ansatz of Yan and Mukamel ͑YM͒, applied to single surface oscillator dynamics, reduces to the analytical Gaussian solutions of the Agarwal phase space master equation. It follows that the YM ansatz is also a solution to the Redfield master equation. ͑4͒ The Agarwal/ Redfield master equation has a structure identical to that of the master equation of Caldeira-Leggett/ Oppenheim-Romero-Rochin, but the two are equivalent only in the high temperature limit. ͑5͒ The Louisell/Lax HO master equation differs from the Agarwal/Redfield form by making a rotating wave approximation ͑RWA͒, i.e., keeping terms of the form â â † ,â † â and neglecting terms of the form â † â † ,â â . When transformed into phase space, the neglect of these terms eliminates the modulation in time of the energy dissipation, modulation which is present in the classical solution. This neglect leads to a position-dependent frictional force which violates the principle of translational invariance. ͑6͒ The Agarwal/Redfield ͑AR͒ equations of motion are shown to violate the semigroup form of Lindblad required for complete positivity. Considering the triad of properties: complete positivity, translational invariance and asymptotic approach to thermal equilibrium, AR sacrifices the first while Lindblad's form must sacrifice either the second or the third. This implies that for certain initial states Redfield theory can violate simple positivity; however, for a wide range of initial Gaussians, the solution of the AR equations does maintain simple positivity, and...

Adsorption of CO 2 and N 2 , both as single components and as binary mixtures, in three zeolites with identical chemical composition but differing pore structures (silicalite, ITQ-3, and ITQ-7) was studied using atomistic simulations. These three zeolites preferentially adsorb CO 2 over N 2 during both single-component and mixture adsorption. The CO 2 /N 2 selectivities observed in the three siliceous zeolites vary strongly as the adsorbent's crystal structure changes, with the selectivity in ITQ-3 being the largest. Our studies indicate that the different electric fields present inside zeolites with different crystal structures but identical chemical composition play an important role in the observed adsorption capacities and selectivities. The accuracy of the ideal absorbed solution theory in predicting the behavior of CO 2 /N 2 mixtures in silica zeolites based on single component adsorption data was also tested; this theory performs quite accurately for these adsorbed mixtures.

Among other zeolites, sodium-substituted zeolite Na-RHO exhibits a phenomenon known as "trapdoor" adsorption, with extra-framework cations acting as gates to small windows in the zeolite structures. While carbon dioxide can diffuse through these gates, methane and other guests cannot, leading to strong potential for gas separation. This effect has been attributed in the literature to specific cation-guest interactions which would allow to CO2 to pull the trapdoor open. We investigate here the gating phenomenon using ab initio molecular dynamics simulations combined with free energy methods. Our findings invalidate this previously-proposed mechanism, showing that presence of CO2 does not significantly affect the motion of the gating cation. We put forward and demonstrate an alternative mechanism, showing that the thermal motion of the cations are of large amplitude and that CO2 is able to squeeze while the gate is open, while nonpolar guests such as methane cannot. This brings an image of the mechanism that is closer to swinging doors than trapdoors. ACKNOWLEDGMENTWe thank Fabien Trousselet, Rodolphe Vuilleumier, Anne Boutin, and Marie-Laure Bocquet for stimulating discussions. We acknowledge access to HPC platforms provided by a GENCI grant (x2016087069).