Normal Mode Analysis in Zeolites: Toward an Efficient Calculation of Adsorption Entropies

An efficient procedure for normal-mode analysis of extended systems, such as zeolites, is developed and illustrated for the physisorption and chemisorption of n-octane and isobutene in H-ZSM-22 and H-FAU using periodic DFT calculations employing the Vienna Ab Initio Simulation Package. Physisorption and chemisorption entropies resulting from partial Hessian vibrational analysis (PHVA) differ at most 10 J mol−1 K−1 from those resulting from full Hessian vibrational analysis, even for PHVA schemes in which only a very limited number of atoms are considered free. To acquire a well-conditioned Hessian, much tighter optimization criteria than commonly used for electronic energy calculations in zeolites are required, i.e., at least an energy cutoff of 400 eV, maximum force of 0.02 eV/Å, and self-consistent field loop convergence criteria of 10−8 eV. For loosely bonded complexes the mobile adsorbate method is applied, in which frequency contributions originating from translational or rotational motions of the adsorbate are removed from the total partition function and replaced by free translational and/or rotational contributions. The frequencies corresponding with these translational and rotational modes can be selected unambiguously based on a mobile block Hessian−PHVA calculation, allowing the prediction of physisorption entropies within an accuracy of 10−15 J mol−1 K−1 as compared to experimental values. The approach presented in this study is useful for studies on other extended catalytic systems.