Chlorophyll (chl) is involved in two ways in photosynthetic organisms firstly as a light gathering pigment and second in electron transfer once the light is captured. It is unique in this role.
In the first case, that of gathering light there are pigment protein complexes containing many chl (100's) and work in such a way that energy absorbed in one molecule is transferred among the others until it reaches the reaction centre where electron transfer starts. The feature that makes chl good for the energy transfer bit is that it has a large overlap in energy (equivalently wavelength) between its fluorescence spectrum and the absorption spectrum. This allows very efficient energy transfer between pigments, each step taking only picoseconds. Chlorophyll is among the best if not the best molecules known to do this.
(In some cases carotenoids may assist this energy capture process and in some antenna called phycobilisomes linear tetrapyrroles augment chl (they extend the wavelength range when the organism normally grows in low light conditions) but in these cases there are also chl pigment-protein complexes.)
The second role is that after energy is absorbed it is funnelled to a Reaction Centre. This is done by the energy transfer steps described above but slight changes in the chl environment change its energy levels slightly so that spatially the energy moves towards the reaction centre where electron transfer begins. The electron produced ultimately reduces carbon dioxide to carbohydrate and is replaced by dragging an electron of a water molecule, this is done in the protein in a sequence of complex steps called the dark reactions.
Returning to the Reaction Centre, this consists of a pair of slightly offset face-to-face chl molecules (the Special Pair) that act as an energy trap and from here an electron is transferred in a couple of picoseconds to a nearby chl then to a pheophytin (a chl less the Mg atom) then to quinone then to an Fe atom all within a nanosecond. The crystal structures are all known and the photophysics of species involved also measured. The structure of these Reaction Centres can be found on the web.
The important property here is that the special pair of chl molecules has the right redox potential to donate an electron to a nearby chl and this the correct potential to transfer the electron to the pheophytin at the same time preserving as much energy as possible and preventing the electron from returning, i.e. making sure it goes down hill in energy but only slightly and thus preserving as much of the initial photon energy as possible. The special pair does not fluoresce to any appreciable extent and so does not loose energy this way.
Chlorophyll has a unique set of properties, excellent ability to transfer energy among other chl with out being quenched until it reaches the reaction centre where the special pair uses this energy to transfer an electron to nearby molecules and start the chemistry leading to reducing carbon dioxide using water as a fuel. All the variant of photosynthesis, algae, plants, bacteria work in essentially the same way, the bacteria have one photosystem, the plants two (PS1, PS2) that work together.
(You should be able to find lost pictures of xray structures of pigment protein complexes on the web but if not I can post some later)