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Subject: search.filters.subject.540Start date: 2020Institute: search.filters.UBSInstitut.Max-Planck-Institut für FestkörperforschungAuthor: search.filters.author.Haupt, Jacobus Philip

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    Development of the transcorrelated full configuration interaction quantum Monte Carlo method
    (2025) Haupt, Jacobus Philip; Alavi, Ali (Prof. Dr.)
    The transcorrelated (TC) method is a technique in electronic structure theory that has recently been gaining momentum. In it, a similarity transformation is applied to the electronic Hamiltonian to capture effects of electron correlation, particularly dynamical correlation, by explicit treatment of analytically-known properties of the Hamiltonian near coalescence points. This has already been combined with the full configuration interaction quantum Monte Carlo (FCIQMC) method, an efficient stochastic approach to solving the electronic Schrödinger equation and calculating physical observables. This dissertation further explores these methods, particularly TC. After a recapitulation of the core concepts of wave function and quantum Monte Carlo methods, we introduce the use of flexible Jastrow factors familiar in the variational Monte Carlo (VMC) literature to minimise the variance of the TC-reference energy. This is shown to result in a rapid basis-set convergence, reaching accuracy for which conventional FCIQMC would require much larger basis sets. Moreover, this minimisation procedure is shown to also compactify the wave function, allowing for more efficient sampling in FCIQMC. We next extend the methodology for problems of strongly multireference character, notably using the dissociation of the nitrogen dimer as a stress test. We illustrate the need for a multireference Jastrow-factor ansatz, and hence minimise the variance of a multireference state. This is shown to recover favourable, size-consistent energies while maintaining the rapid basis-set convergence that comes with TC. As a multireference technique (FCIQMC) is used after optimisation, it moreover does not increase the computational scaling of the method to use the conventional (non-TC) form of the same multireference technique as the TC ansatz. Finally, we explore the possibility of constructing simplified Jastrow factors in order to improve or possibly wholly bypass the optimisation procedure so far for the TC method, which can be computationally expensive. We show that parameter-free Jastrow factors can result in poor absolute energies, but favourable relative energies thanks to error cancellation, whereas Jastrow factors optimised for atoms and reused for molecules result in both accurate absolute and relative energies. This opens the possibility of optimising Jastrow factors for atoms across the periodic table and storing them in a database, which can be queried for larger molecules, thereby aiding the scalability of the method.