  We develop a generalization of the singlet sector valence bond basis
projection algorithm of Sandvik, Beach, and Evertz (A. W. Sandvik, Phys. Rev.
Lett. 95, 207203 (2005); K. S. D. Beach and A. W. Sandvik, Nucl. Phys. B750,
142 (2006); A. W. Sandvik and H. G. Evertz, arXiv:0807.0682, unpublished.) to
cases in which the ground state of an antiferromagnetic Hamiltonian has total
spin $S_{tot} = 1/2$ in a finite size system. We explain how various ground
state expectation values may be calculated by generalizations of the estimators
developed in the singlet case, and illustrate the power of the method by
calculating the ground state spin texture and bond energies in a $L \times L$
Heisenberg antiferromagnet with $L$ odd and free boundaries.
