  We construct a tensor model for nematic phases of bent-core molecules from
molecular theory. The form of free energy is determined by molecular symmetry,
which includes the couplings and derivatives of a vector and two second-order
tensors, with the coefficients determined by molecular parameters. We use the
model to study the nematic phases resulted from the hard-core potential. Unlike
most macroscopic models, we are able to obtain the phase diagram about the
molecular parameters, but not merely some phenomenological coefficients. The
tensor model is applicable to other molecules with the same symmetry, which we
demonstrate by studying the phase diagram of star molecules.
