On the spin and symmetry adaptation of the density matrix renormalization group method.

We present a spin-adapted density matrix renormalization group (DMRG) algorithm designed to target spin and spatial symmetry states that can be difficult to obtain while using a non-spin-adapted algorithm. The algorithmic modifications that have to be introduced into the usual density matrix renormalization group scheme in order to spin adapt it are discussed, and it is demonstrated that the introduced modifications do not change the overall scaling of the method. The new approach is tested on HNCO, a model system, that has a singlet-triplet curve crossing between states of the same symmetry. The advantages of the spin-adapted DMRG scheme are discussed, and it is concluded that the spin-adapted DMRG method converges better in almost all cases and gives more parallel curves to the full configuration interaction result than the non-spin-adapted method. It is shown that the spin-adapted DMRG energies can be lower than the ones obtained from the non-spin-adapted scheme. Such a counterintuitive result is explained by noting that the spin-adapted method is not a special case of the non-spin-adapted one; consequently, the spin-adapted result is not an upper bound for the non-spin-adapted energy.