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This study evaluates the precision of widely recognized quantum chemical methodologies, CCSD(T), DLPNO−CCSD(T), and localized ph-AFQMC, for determining the thermochemistry of main group elements. DLPNO−CCSD- (T) and localized ph-AFQMC, which o(er greater scalability compared to canonical CCSD(T), have emerged over the past decade as pivotal in producing precise benchmark chemical data. Our investigation includes closed-shell, neutral molecules, focusing on their heat of formation and atomization energy sourced from four specific small molecule data sets. First, we selected molecules from the G2 and G3 data sets, noted for their reliable experimental heat of formation data. Additionally, we incorporate molecules from the W4−11 and W4−17 sets, which provide high-level theoretical reference values for atomization energy at 0 K. Our findings reveal that both DLPNO−CCSD(T) and ph-AFQMC methods are capable of achieving a root-mean-square deviation of less than 1 kcal/mol across the combined data set, aligning with the threshold for chemical accuracy. Moreover, we make e(orts to confine the maximum deviations within 2 kcal/mol, a degree of precision that significantly broadens the applicability of these methods in fields such as biology and materials science. 

In this work we demonstrate that accurate ground state wave functions may be constructed for polarons in a fully ab initio setting across the wide range of couplings associated with both the large and small polaron limits. We present a single general unitary transformation approach which encompasses an ab initio version of the Lee-Low-Pines theory at weak coupling and the coherent state Landau-Pekar framework at strong coupling while interpolating between these limits in general cases. We show that perturbation theory around these limits may be performed in a facile manner to assess the accuracy of the approach, as well as provide an independent route to the ab initio properties of polarons. We test these ideas on the case of LiF, where the electron-polaron is expected to be large and relatively weakly coupled, while the hole-polaron is expected to be a strongly coupled small polaron. 

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently. 

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.