  We describe how to efficiently construct the quantum chemical Hamiltonian
operator in matrix product form. We present its implementation as a density
matrix renormalization group (DMRG) algorithm for quantum chemical applications
in a purely matrix product based framework. Existing implementations of DMRG
for quantum chemistry are based on the traditional formulation of the method,
which was developed from a viewpoint of Hilbert space decimation and attained a
higher performance compared to straightforward implementations of matrix
product based DMRG. The latter variationally optimizes a class of ansatz states
known as matrix product states (MPS), where operators are correspondingly
represented as matrix product operators (MPO). The MPO construction scheme
presented here eliminates the previous performance disadvantages while
retaining the additional flexibility provided by a matrix product approach; for
example, the specification of expectation values becomes an input parameter. In
this way, MPOs for different symmetries - abelian and non-abelian - and
different relativistic and non-relativistic models may be solved by an
otherwise unmodified program.
