What is the function of Chlorophyll B as an accessory pigment?

Chlorophyll alpha is the most abundant pigment carrying out photosynthesis.
Accessory pigments can include chlorophyll b (also c, d, and e), xanthophylls, and carotenoids (such as beta-carotene). They absorb energy that chlorophyll a does not absorb and pass it to alpha.

Chlorophyll a absorbs well at a wavelength of about 450 nm and again with a higher peak at red 675nm;
Chlorophyll b absorbs most effectively at blue 470 but also at 430 and 640.
 Alpha absorption peaks in the red while beta peaks in the blue.
Xanthophyll absorbs well at 400-530 nm
Beta-carotene absorbs most strongly between 400-500 nm.

Absorption under water is best in the long penetrating red wavelengths. So alpha still absorbs mostly at that end. The other pigments arose to capture the high enegry blue end in shallow water and on land.