The CO tilting (tau) and bending (beta) potential energy surface of carbon monoxyheme has been investigated with local density functional calculations. The calculations indicate that tau and beta are strongly coupled and that simultaneous, in-phase displacements along these coordinates represent a low-energy pathway across the surface. Calculations on two small model complexes indicate that strong tau-beta coupling also occurs in these systems. Accordingly, this feature appears to be a general characteristic of the Fe-CO unit in a square-planar coordination geometry. In-phase tau-beta co deformations (tau + beta) of as much as 25 degrees can take place with the expenditure of relatively small amounts of energy (2 kcal/mol or less). However, very large distortions of 45-60 degrees are energetically demanding and unreasonable. The calculations also rule out the possibility that the coordination geometry of the proximal histidine is the major determinant of the CO orientation. Both a full vibrational analysis on a small model complex and a limited analysis on a tetraatomic model yield calculated frequencies and isotope shifts for the Fe-CO unit in excellent agreement with those observed fur carbon monoxyhemes. Collectively, our calculated tau-beta potential energy surface provides a plausible explanation for the wide variation in CO orientations reported for carbon monoxymyoglobin and also account for the unusual vibrational characteristics of the Fe-CO unit.