ENDOR data suggests that the special-pair radical cation P+ from Rhodobacter sphaeroides is 68% localized on P-L while simple interpretations of FTIR difference spectra based primarily on intensity information, but to some extent also bandwidths, suggest near-complete charge localization. We provide a complete a priori spectral simulation of the spectrum of P+ in the range 0-5000 cm(-1), including explicit treatment of the high-resolution vibrational transitions, the low-resolution hole-transfer absorption centered at 2700 cm-1, and the resonance with the SHOMO to HOMO transition at 2200 cm(-1) that resolve the issues concerning the nature of P+. The description of the vibrational aspects of the problem were taken from results of previous density-functional calculations, and a qualitatively realistic large number of vibrational modes (50 antisymmetric and 18-20 symmetric) were included. To facilitate the calculations, a new representation of the vibronic-coupling Hamiltonian for intervalence hole-transfer or electron-transfer problems is introduced, allowing the spectrum to be simulated efficiently using only up to 4x10(9) vibronic basis functions and leading also to new general analytical relationships. Observed spectra are fitted using seven adjustable chemical parameters describing the interactions between the four electronic states involved. The resulting fits provide unique descriptions of the parameters that are insensitive to the source of the observed spectrum or the nature of the symmetric modes used in the model, and all fitted parameters are found to be close in value to those from independent estimates. We determine the electronic coupling, antisymmetric-mode reorganization energy, and redox asymmetry to be J=0.126+/-0.002 eV, lambda=0.139+/-0.003 eV, and E-0=0.069+/-0.002 eV, respectively. Our description forms the basis of understanding for a wide range of other properties observed for Rhodobacter sphaeroides mutants, as well as the properties of the reaction centers from photosystems I, II, etc., facilitating a deeper understanding of the role of the special pair in initiating primary charge separation during photosynthesis. (C) 2003 American Institute of Physics.