High pressure is used with hole burning and absorption spectroscopies at low temperatures to study the pressure dependence of the B800--+B850 energy transfer rate in the LH2 complex of Rhodobacter sphaeroides and to assess the extent to which pressure can be used to identify and characterize states associated with strongly coupled chlorophyll molecules. Pressure tuning of the B800-B850 gap from ,-~ 750 cm-1 at 0.1 MPa to ,,~ 900 cm-1 at 680 MPa has no measurable effect on the 2 ps energy transfer rate of the B800-B850 complex at 4.2 K. An explanation for this resilience against pressure, which is supported by earlier hole burning studies, is provided. It is based on weak coupling nonadiabatic transfer theory and takes into account the inhomogeneous width of the B800-B850 energy gap, the large homogeneous width of the B850 band from exciton level structure and the Franck-Condon factors of acceptor protein phonons and intramolecular BChl a modes. The model yields reasonable agreement with the 4.2 K energy transfer rate and is consistent with its weak temperature dependence. It is assumed that it is the C9-ring exciton levels which lie within the B850 band that are the key acceptor levels, meaning that BChl a modes are essential to the energy transfer process. These ring exciton levels derive from the strongly allowed lowest energy component of the basic B850 dimer. However, the analysis of B850s linear pressure shift suggests that another F6rster pathway may also be important. It is one that involves the ring exciton levels derived from the weakly allowed upper component of the B850 dimer which we estimate to be quasi-degenerate with B800. In the second part of the paper, which is concerned with strong BChl monomer-monomer interactions of dimers, we report that the pressure shifts of B875 (LH2), the primary donor absorption bands of bacterial RC (P870 of Rb. sphaeroides and P960 of Rhodopseudomonas viridis) and B 1015 (LH complex of Rps. viridis) are equal and large in value (,,~ -0.4 cm°l/MPa at 4.2 K) relative to those of isolated monomers in polymers and proteins (< -0.1 cm°l/MPa). The shift rate for B850 at 4.2 K is -0.28 cm-l/MPa. A model is presented which appears to be capable of providing a unified explanation for the pressure shifts.Abbreviations: B800-BChl antenna band absorbing (at room temperature) at 800 nm (B850, B875, B 1015 are defined similarly) CD -circular dichroism; FC factor-Franck-Condon factor; FMO complex-Fenna-MatthewsOlson complex; L-S theory-Laird-Skinner theory; LH 1 -core light-harvesting complex of the BChl antenna complexes; LH2-peripheral light-harvesting complex of the BChl antenna complexes; NPHB -non-photochemical hole burning; P960-absorption band of special pair of Rhodopseudomonas viridis absorbing at 960 nm (room temperature). P870 of Rhodobacter sphaeroides is defined similarly; QM/MM results -quantum mechanical/molecular mechanical results; RC-reaction center; ZPH-zero phonon hole 278