Theses Doctoral

Developments in Auxiliary Field Quantum Monte Carlo for Molecules

Weber, John Landstrom

This thesis presents a compilation of recent work on benchmarking, applying, and developing Auxiliary Field Quantum Monte Carlo (AFQMC) for use in ab initio simulations of the electronic structure of molecules.

With Chapter 1 I begin with a benchmark of phaseless AFQMC versus experiment in obtaining gas phase ligand dissociation energies of a set of tetrahedral and octahedral transition metal complexes. ph-AFQMC is shown to acquire chemical accuracy through the use of correlated sampling (CS) and CASSCF trial wave functions selected via a black box procedure.

This is followed in Chapter 2 with another gas phase benchmark of ph-AFQMC versus experiment, this time calculating the redox potentials for a set of metallocenes, where we find a mix of correlated sampling and large CASSCF trials necessary to reproduce gas phase experimental values to within 1.7 ± 1.0 kcal/mol. Additionally, the inclusion of QZ ph-AFQMC values, either using UHF or CASSCF trials, was found to be necessary for a few systems, as opposed to using a hybrid approach with alternate methods such as coupled cluster to extrapolate to the basis set limit.

In Chapter 3, having established protocols to obtain decent results on transition metal complexes with known experimental values, I apply ph-AFQMC to successfully predict the activity of a set of new annihilators for optical upconversion. For a set of functionalized anthracene molecules, I report agreement within statistics between ph-AFQMC and a localized approximation to coupled cluster singles doubles and perturbative triples (DLPNO-CCSD(T0)), and develop intuitive guidelines for tuning the excited state energies of anthracene. For a single molecule in an additional set of functionalized benzothiadiazole (BTD) molecules, Ph-BTD, ph-AFQMC and DLPNO-CCSD(T) disagree significantly; subsequent experimental testing validates the ph-AFQMC result.

In Chapter 4 I present an approach based on localized orbitals to reduce the scaling with system size from quartic to cubic for the energy evaluation, the functional bottleneck for the majority of AFQMC calculations. Additionally, I describe the practical implementation of such an algorithm to be run on large GPU clusters. This allows AFQMC to be run for both larger systems and trials at a significantly decreased cost, while still reproducing full AFQMC results within the statistics of the method.

With Chapter 5, I conclude with the development and characterization of a novel constraint, linecut (lc-) AFQMC, which exhbits distinct behavior versus the phaseless constraint. We demonstrate benchmarks for a variety of weakly to strongly correlated molecules for which we have the exact total energies, and observe that lc-AFQMC outperforms ph-AFQMC for the majority of systems studied.

I conclude with the description of a systematic method to remove the linecut constraint, partially removing the bias and re-introducing the fermionic sign problem while still maintaining a practicable signal to noise ratio. This allows for us to recover the exact energy of FeO with a fraction of the cost of converging the trial wave function within ph-AFQMC.


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More About This Work

Academic Units
Chemical Physics
Thesis Advisors
Reichman, David R.
Friesner, Richard A.
Ph.D., Columbia University
Published Here
July 5, 2023