Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes

In earlier work [J. Chem. Phys. 144, 064102 (2016)], we introduced a time-dependent formulation of the second-order N-electron valence perturbation theory (t-NEVPT2) which (i) had a lower computational scaling than the usual internally-contracted perturbation formulation, and (ii) yielded the fully uncontracted NEVPT2 energy. Here, we present a combination of t-NEVPT2 with a matrix product state (MPS) reference wavefunction (t-MPS-NEVPT2) that allows to compute uncontracted dynamic correlation energies for large active spaces and basis sets, using the time-dependent density matrix renormalization group (td-DMRG) algorithm. In addition, we report a low-scaling MPS-based implementation of strongly-contracted NEVPT2 (sc-MPS-NEVPT2) that avoids computation of the four-particle reduced density matrix. We use these new methods to compute the dissociation energy of the chromium dimer and to study the low-lying excited states in all-trans polyenes (C$_4$H$_6$ to C$_{24}$H$_{26}$), incorporating dynamic correlation for reference wavefunctions with up to 24 active electrons and orbitals.