We extend the recently proposed heat-bath configuration interaction (HCI)method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 12, 3674 (2016)], byintroducing a semistochastic algorithm for performing multireferenceEpstein-Nesbet perturbation theory, in order to completely eliminate the severememory bottleneck of the original method. The proposed algorithm has severalattractive features. First, there is no sign problem that plagues severalquantum Monte Carlo methods. Second, instead of using Metropolis-Hastingssampling, we use the Alias method to directly sample determinants from thereference wavefunction, thus avoiding correlations between consecutive samples.Third, in addition to removing the memory bottleneck, semistochastic HCI (SHCI)is faster than the deterministic variant for many systems if a stochastic errorof 0.1 mHa is acceptable. Fourth, within the SHCI algorithm one can tradememory for a modest increase in computer time. Fifth, the perturbativecalculation is embarrassingly parallel. The SHCI algorithm extends the range ofapplicability of the original algorithm, allowing us to calculate thecorrelation energy of very large active spaces. We demonstrate this byperforming calculations on several first row dimers including F2 with an activespace of (14e, 108o), Mn-Salen cluster with an active space of (28e, 22o), andCr2 dimer with up to a quadruple-zeta basis set with an active space of (12e,190o). For these systems we were able to obtain better than 1 mHa accuracy witha wall time of merely 55 seconds, 37 seconds, and 56 minutes on 1, 1, and 4nodes, respectively.
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