This paper considers a functional modeling of a head-related transfer function (HRTF) where the spatial-portion is constrained to be expanded using spherical harmonics and the frequency-portion is expanded in terms of standard closed-form orthonormal functions, which may be user selected. We derive an objective evaluation metric to compare the relative energy efficiencies of candidate functional models using empirical HRTF database measurements and robust estimation techniques. Among four sets of closed-form orthonormal functions the complex exponentials are identified as the most efficient to represent the frequency-portion in the spherical harmonics-based HRTF functional model. The proposed model is evaluated across three HRTF data sets: 1) CIPIC database, 2) the MIT KEMAR (Knowles Electronics Mannequin for Acoustics Research) database, and 3) the ANU KEMAR database.