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We present efficient algorithms for using selected configuration interaction (sCI) trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC). These advances, geared toward optimizing computational performance for longer configuration interaction expansions, allow us to use up to a million configurations in the trial state for ph-AFQMC. In one example, we found the cost of ph-AFQMC per sample to increase only by a factor of about 3 for a calculation with 10 4 configurations compared to that with a single one, demonstrating the tiny computational overhead due to a longer expansion. This favorable scaling allows us to study the systematic convergence of the phaseless bias in auxiliary field quantum Monte Carlo calculations with an increasing number of configurations and provides a means to gauge the accuracy of ph-AFQMC with other trial states. We also show how the scalability issues of sCI trial states for large system sizes could be mitigated by restricting them to a moderately sized orbital active space and leveraging the near-cancellation of out of active space phaseless errors. 

We present electronic spectra containing the Q x and Q y absorption bands of singly and doubly deprotonated protoporphyrin IX, prepared as mass selected ions in vacuo at cryogenic temperatures, revealing vibronic structure in both bands. We assign the vibronic progression of the Q x band using a Frank–Condon–Herzberg–Teller simulation based on time-dependent density functional theory, comparing the observed bands with those calculated for porphine. A comparison of the electronic spectra of the two charge states allows investigation of the electronic Stark effect with an electric field strength beyond the capabilities of typical laboratory setups. We analyze the differences in the electronic spectra of the two charge states using n-electron valence perturbation theory (NEVPT2) and simulated charge distributions.