Potential-energy surfaces of adsorbates on periodic substrates: Application of the Morse theory

We employ the Morse theory of critical points (extrema and saddle points) of functions on compact manifolds to analyze the potential-energy surface of adsorbates on periodic crystalline surfaces. Formulation of the theory for this case is very simple and allows one, e.g., to check completeness or consistency of a proposed potential-energy surface topology. For highly symmetric adsorption or surface-diffusion systems and/or when some additional information on the potential energy is available, the theory can be predictive. For example, if the most stable adsorption position for a symmetric adsorbate is the bridge site on bcc or fcc(001) surfaces, or on fcc(111) and hcp(0001) ones, the saddle points of the potential energy will appear away from top and hollow sites. Application of the Morse theory is illustrated on examples of known adsorption systems.