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Register a new userAb initio statistical mechanics of surface adsorption and desorption: II. Nuclear quantum effects
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We show how the path-integral formulation of quantum statistical mechanics can be used to construct practical {em ab initio} techniques for computing the chemical potential of molecules adsorbed on surfaces, with full inclusion of quantum nuclear effects. The techniques we describe are based on the computation of the potential of mean force on a chosen molecule, and generalise the techniques developed recently for classical nuclei. We present practical calculations based on density functional theory with a generalised-gradient exchange-correlation functional for the case of H$_2$O on the MgO~(001) surface at low coverage. We note that the very high vibrational frequencies of the H$_2$O molecule would normally require very large numbers of time slices (beads) in path-integral calculations, but we show that this requirement can be dramatically reduced by employing the idea of thermodynamic integration with respect to the number of beads. The validity and correctness of our path-integral calculations on the H$_2$O/MgO~(001) system are demonstrated by supporting calculations on a set of simple model systems for which quantum contributions to the free energy are known exactly from analytic arguments.
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We present a general computational scheme based on molecular dynamics (m.d.) simulation for calculating the chemical potential of adsorbed molecules in thermal equilibrium on the surface of a material. The scheme is based on the calculation of the mean force in m.d. simulations in which the height of a chosen molecule above the surface is constrained, and subsequent integration of the mean force to obtain the potential of mean force and hence the chemical potential. The scheme is valid at any coverage and temperature, so that in principle it allows the calculation of the chemical potential as a function of coverage and temperature. It avoids all statistical mechanical approximations, except for the use of classical statistical mechanics for the nuclei, and assumes nothing in advance about the adsorption sites. From the chemical potential, the absolute desorption rate of the molecules can be computed, provided the equilibration rate on the surface is faster than the desorption rate. We apply the theory by {em ab initio} m.d. simulation to the case of H$_2$O on MgO (001) in the low-coverage limit, using the Perdew-Burke-Ernzerhof (PBE) form of exchange-correlation. The calculations yield an {em ab initio} value of the Polanyi-Wigner frequency prefactor, which is more than two orders of magnitude greater than the value of $10^{13}$ s$^{-1}$ often assumed in the past. Provisional comparison with experiment suggests that the PBE adsorption energy may be too low, but the extension of the calculations to higher coverages is needed before firm conclusions can be drawn. The possibility of including quantum nuclear effects by using path-integral simulations is noted.
The adsorption and diffusion of H atoms on beta-PtO2(001) surface have been studied using first-principles calculations. The chemisorbed H atoms are found to bind preferentially on the top sites of O atoms due to the much larger adsorption energies with comparison to adsorption atop Pt atoms. The calculated energy barriers along the optimal diffusion paths are comparable with that of H diffusion on Pt(111). Within the WKB approximation, the nuclear quantum effects (NQEs) along the diffusion paths are investigated. It turns out that the NQEs are significant for the surface diffusion of H at room temperature and play a dominant role in cryogenic conditions.
First-principles calculations using density functional theory based on norm-conserving pseudopotentials have been performed to investigate the Cs adsorption on the Si(001) surface for 0.5 and 1 ML coverages. We found that the saturation coverage corresponds to 1 ML adsorption with two Cs atoms occupying the double layer model sites. While the 0.5 ML covered surface is of metallic nature, we found that 1 ML of Cs adsorption corresponds to saturation coverage and leads to a semiconducting surface. The results for the electronic behavior and surface work function suggest that adsorption of Cs takes place via polarized covalent bonding.
The electronic and structural properties of (i) boron doped graphene sheets, and (ii) the chemisorption processes of hydrogen adatoms on the boron doped graphene sheets have been examined by {it ab initio} total energy calculations.
We introduced a method to obtain the continuum description of the elastic properties of mono- layer h-BN through ab initio density functional theory. This thermodynamically rigorous contin- uum description of the elastic response is formulated by expanding the elastic strain energy density in a Taylor series in strain truncated after the fifth-order term. we obtained a total of fourteen nonzero independent elastic constants for the up to tenth-order tensor. We predicted the pressure dependent second-order elastic moduli. This continuum formulation is suitable for incorporation into the finite element method.
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