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We extend the spin-adapted density matrix renormalization group (DMRG)algorithm of McCulloch and Gulacsi [Europhys. Lett.57, 852 (2002)] to quantumchemical Hamiltonians. This involves two key modifications to thenon-spin-adapted DMRG algorithm: the use of a quasi-density matrix to ensurethat the renormalised DMRG states are eigenvalues of $S^2$ , and the use of theWigner-Eckart theorem to greatly reduce the overall storage and computationalcost. We argue that the advantages of the spin-adapted DMRG algorithm aregreatest for low spin states. Consequently, we also implement thesinglet-embedding strategy of Nishino et al [Phys. Rev. E61, 3199 (2000)] whichallows us to target high spin states as a component of a mixed system which isoverall held in a singlet state. We evaluate our algorithm on benchmarkcalculations on the Fe$_2$S$_2$ and Cr$_2$ transition metal systems. Bycalculating the full spin ladder of Fe$_2$S$_2$ , we show that the spin-adaptedDMRG algorithm can target very closely spaced spin states. In addition, ourcalculations of Cr$_2$ demonstrate that the spin-adapted algorithm requiresonly roughly half the number of renormalised DMRG states as thenon-spin-adapted algorithm to obtain the same accuracy in the energy, thusyielding up to an order of magnitude increase in computational efficiency.

A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry