Frozen Natural Orbitals for the State-Averaged Driven Similarity Renormalization Group

We present a reduced-cost implementation of the state-averaged
driven similarity renormalization group (SA-DSRG) based on the frozen
natural orbital (FNO) approach. The natural orbitals (NOs) are obtained
by diagonalizing the one-body reduced density matrix from SA-DSRG
second-order perturbation theory (SA-DSRG-PT2). We consider three
criteria to truncate the virtual NOs for the subsequent electron correlation
treatment beyond SA-DSRG-PT2. An additive second-order correction
is applied to the SA-DSRG Hamiltonian to reintroduce correlation effects
from the discarded orbitals. The FNO SA-DSRG method is benchmarked
on 35 small organic molecules in the QUEST database. When keeping
98–99% of the cumulative occupation numbers, the mean absolute
error in the vertical transition energies due to FNO is less than
0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times
compared to the conventional SA-DSRG implementation for nickel carbonyl
with a quadruple-ζ basis set. The FNO approach enables nonperturbative
SA-DSRG computations on chloroiron corrole [FeCl(C19H11N4)] with more than 1000 basis functions, surpassing
the current limit of a conventional implementation.