Quantum Chemistry using the Density Matrix Renormalisation Group

We [1] have shown recently that DMRG can be used in quantum chemistry to obtain the "full-CI" ground state energy for medium sized molecule using the following Hamiltonian

Where the first term describes the core Hamiltonian and the second term the electron-electron repulsion expressed within second quantisation formalism.

DMRG, which is less familiar to chemists, is briefly described in a language which is more familiar for them. Since its invention in 1992 by S.White, DMRG has become one of the most widely used method for investigating the ground state and low-energy properties of strongly interacting quantum lattice systems such as Heisenberg, t-J, and Hubbard models. The method is an iterative numerical procedure for diagonalizing the system Hamiltonian on a finite lattice. It can treat much larger systems than exact diagonalisation even when efficient algorithm such as Lanczos or Davidsson are used, since it does not directly treat the full Hilbert space of the system. In fact, the basic idea of the renormalisation group is to integrate out unimportant degree of freedom progressively using a renormalisation group transformation. It can be shown that this procedure can be made optimal in a certain sense by using density matrix projection, very much alike the use of natural orbitals in a full CI treatment.

Moreover, we show that the same approach can also be used to calculate the magnetic properties of molecular magnets. Values for the exchange coupling constants will be obtained in calculating the energy difference between the lowest lying multiplets with different spin.