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An analytic expression for the surface dipole barrier as a function of the barrier height is derived in the jellium step-potential approximation of a metal. This is solved self-consistently assuming the barrier height to be a sum of the exchange, correlation, and surface-dipole-barrier contributions. It is next employed in a nonself-consistent calculation for the surface dipole barrier and work function by application of the Budd-Vannimenus (BV) theorem to this model problem. On comparison with the results of Lang and Kohn, the results for the work function obtained by use of the BV theorem are observed to be generally superior to those determined self-consistently. Finally, the application of the BV theorem together with self-consistency is indicated for a model in which the local exchange-correlation approximation is also not required.
Sahni et al. (Wed,) studied this question.