Geometry optimization of large molecules with quantum Monte Carlo
Final Report Abstract
We developed methods for Quantum Monte Carlo (QMC) simulations by (1) reducing the bias for the computation of excited states and their properties and improving the efficiency of QMC calculations by reducing (2) the scaling with the atomic number Z and (3) the scaling with the number of particles N. (1) The choice of the wave function affects the accuracy of the final results, however, constructing wave functions for multiple electronic states can be biased because they are described with varying accuracy. We developed an automatic approach which constructs compact wave functions while monitoring and matching at the same time the accuracy of each electronic state in order to obtain a balanced description. (2) The core electrons lead to a double penalty for the computational cost of QMC simulations. They require very small time steps as they move in a small area close to the nuclei and they contribute to most of the variance. This leads to a very unfavourable scaling with the atomic number Z and, therefore, empirical effective core potentials are widely used. They are computationally cheap but the associated error cannot be easily judged. We developed an improved estimator which almost completely removes the numerical cost of the core electrons by exploiting that core regions located at different atoms are physically independent. This approach allows us to adjust the simulation optimally to the different scales which are encountered and sample the core electrons with many small steps and the valence electrons with few large ones. This approach reduces the scaling with Z. (3) We were able to generalize the core subsampling approach to a framework for Monte Carlo simulations by partitioning the system into fragments and subsampling each fragment. For extensive observables this reduces the numerical scaling with the number of particles N by O(N ) to O(N^2 ). This approach is exact and does not introduce any approximations. We demonstrated that this approach is even useful for metallic systems far from the separability limit. Additionally, the framework provides a useful tool for analysing the correlation between fragments.
Publications
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Journal of Chemical Theory and Computation 2019, 15, 4896–4906
Dash, M.; Feldt, J.; Moroni, S.; Scemama, A.; Filippi, C.
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Quantum Chemistry and Dynamics of Excited States; John Wiley & Sons, Ltd: 2020, pp 247–275
Feldt, J.; Filippi, C.
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Journal of Chemical Theory and Computation 2021, 17, 1380–1389
Feldt, J.; Assaraf, R.
