 
Summary: Ab initio statistical mechanics of surface adsorption and desorption. II.
Nuclear quantum effects
D. Alfè1,2,a
and M. J. Gillan2
1
Department of Earth Sciences, UCL, Gower St., London WC1E 6BT, United Kingdom
2
London Centre for Nanotechnology and Thomas Young Centre, UCL, Gordon St., London WC1H 0AH,
United Kingdom and Department of Physics, UCL, Gower St., London WC1E 6BT, United Kingdom
Received 26 April 2010; accepted 28 June 2010; published online 22 July 2010
We show how the pathintegral formulation of quantum statistical mechanics can be used to
construct practical 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 generalize the techniques
developed recently for classical nuclei. We present practical calculations based on density functional
theory with a generalizedgradient exchangecorrelation functional for the case of H2O on the MgO
001 surface at low coverage. We note that the very high vibrational frequencies of the H2O
molecule would normally require very large numbers of time slices beads in pathintegral
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
