  We present two efficient and intruder-free methods for treating dynamic
correlation on top of general multi-configuration reference wave
functions---including such as obtained by the density matrix renormalization
group (DMRG) with large active spaces. The new methods are the second order
variant of the recently proposed multi-reference linearized coupled cluster
method (MRLCC) [S. Sharma, A. Alavi, J. Chem. Phys. 143, 102815 (2015)], and of
N-electron valence perturbation theory (NEVPT2), with expected accuracies
similar to MRCI+Q and (at least) CASPT2, respectively. Great efficiency gains
are realized by representing the first-order wave function with a combination
of internal contraction (IC) and matrix product state perturbation theory
(MPSPT). With this combination, only third order reduced density matrices
(RDMs) are required. Thus, we obviate the need for calculating (or estimating)
RDMs of fourth or higher order; these had so far posed a severe bottleneck for
dynamic correlation treatments involving the large active spaces accessible to
DMRG. Using several benchmark systems, including first and second row
containing small molecules, Cr$_2$, pentacene and oxo-Mn(Salen), we shown that
active spaces containing at least 30 orbitals can be treated using this method.
On a single node, MRLCC2 and NEVPT2 calculations can be performed with over 550
and 1100 virtual orbitals, respectively. We also critically examine the errors
incurred due to the three sources of errors introduced in the present
implementation - calculating second order instead of third order energy
corrections, use of internal contraction and approximations made in the
reference wavefunction due to DMRG.
