Valence bonds are the basic entities in many chemical compounds. In a linear array of atoms translational invariance tells us the bonds have to be superposed. These superposed bond variables are shown to satisfy a closed algebra. We use a natural parameter in the algebra to truncate it. This allows us to transform the Hamiltonian of electrons into the Hamiltonian of bonds. Comparing the solutions, we establish the validity of the truncation procedure. The quantum bonds are obtained by superposing valence bonds with arbitrary phases. We demonstrate that these quantum valence bonds satisfy an extended algebra that admits truncation. The electron Hamiltonian is recast in terms of the quantum bonds and solved.