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arXiv:2405.17089 · Journal of Chemical Theory and Computation

An Improved Penalty-Based Excited-State Variational Monte Carlo Approach with Deep-Learning Ansatzes

P. Bernát Szabó, Zeno Schätzle, Michael Entwistle, Frank Noé

Published Aug 30, 2024• 7 citations
arXivHTMLPDF

Abstract

, 274 (2023)] and demonstrate that the accuracy of the updated method is competitive with other available excited-state VMC approaches. A theoretical comparison of the computational aspects of these algorithms is presented, where several benefits of the penalty-based method are identified. Our main contributions include an automatic mechanism for tuning the scale of the penalty terms, an updated form of the overlap penalty with proven convergence properties, and a new term that penalizes the spin of the wave function, enabling the selective computation of states with a given spin. With these improvements, along with the use of the latest self-attention-based ansatz, the penalty-based method achieves a mean absolute error below 1 kcal/mol for the vertical excitation energies of a set of 26 atoms and molecules, without relying on variance matching schemes. Considering excited states along the dissociation of the carbon dimer, the accuracy of the penalty-based method is on par with that of natural-excited-state (NES) VMC, while also providing results for additional sections of the potential energy surface, which were inaccessible with the NES method. Additionally, the accuracy of the penalty-based method is improved for a conical intersection of ethylene, with the predicted angle of the intersection agreeing well with both NES-VMC and multireference configuration interaction.

DOI
10.1021/acs.jctc.4c00678

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, 274 (2023)] and demonstrate that the accuracy of the updated method is competitive with other available excited-state VMC approaches. A theoretical comparison of the computational aspects of these algorithms is presented, where several benefits of the penalty-based method are identified. Our main contributions include an automatic mechanism for tuning the scale of the penalty terms, an updated form of the overlap penalty with proven convergence properties, and a new term that penalizes the spin of the wave function, enabling the selective computation of states with a given spin. With these improvements, along with the use of the latest self-attention-based ansatz, the penalty-based method achieves a mean absolute error below 1 kcal/mol for the vertical excitation energies of a set of 26 atoms and molecules, without relying on variance matching schemes. Considering excited states along the dissociation of the carbon dimer, the accuracy of the penalty-based method is on par with that of natural-excited-state (NES) VMC, while also providing results for additional sections of the potential energy surface, which were inaccessible with the NES method. Additionally, the accuracy of the penalty-based method is improved for a conical intersection of ethylene, with the predicted angle of the intersection agreeing well with both NES-VMC and multireference configuration interaction.
We present a simple and efficient wave function ansatz for the treatment of excited charge-transfer states in real-space quantum Monte Carlo methods. Using the recently introduced variation-after-response method [E. Neuscamman, J. Chem. Phys. 145, 081103 (2016)], this ansatz allows a crucial orbital optimization step to be performed beyond a configuration interaction singles expansion, while only requiring calculation of two Slater determinant objects. We demonstrate this ansatz for the illustrative example of the stretched LiF molecule, for a range of excited states of formaldehyde, and finally for the more challenging ethylene-tetrafluoroethylene molecule.
Describing the electronic structure of molecules using computational methods is of central importance in many areas of chemical research and industry. To this day, the variational quantum Monte Carlo (VMC) algorithm, which utilizes the variational principle of quantum mechanics to optimize an ansatz towards the true electronic wave function, is one of the lesser employed of such computational methods. While it is generally applicable, and provides direct access to the wave function, its accuracy has been limited by insufficiently expressive ansatzes. This barrier was recently lifted with the introduction of deep-learning-based ansatzes, providing unprecedented flexibility and corresponding accuracy, at the cost of increased computational requirements. In this thesis, our implementation of the VMC algorithm with deep-learning ansatzes is described, along with a number of developments facilitating the computation of electronic excited states, extraction of various observables, and characterization of potential energy surfaces, at a reduced computational cost. The method is implemented as open-source software, employing a common framework to encompass most ansatzes present in the literature. Utilizing the direct wave function access granted by VMC, an approach is developed to extract one-electron reduced densities, that are free from Gaussian basis set effects. Significant advances in the methodology of computing electronic excited states via the ladder-of-states approach are made, including an improved form of the overlap penalty term with an automatically determined prefactor, and a new loss term with which the total spin of the solution can be selected. The efficiency of computing excited potential energy surfaces are enhanced by optimizing a single ansatz for a range of molecular configurations. To enable such transferable training in the presence of state crossings, a dynamic, geometry-wise ordering in the ladder of states is introduced. Geometry-optimization-based tasks are identified as natural fits for such transferable ansatzes, and a transferability-native approach for extracting the necessary information from VMC data is devised. Finally, transferable training is employed to simultaneously model different chemical species, resulting in a foundation model predicting bond breaking at a cost-accuracy ratio competitive with mature multi-reference methods. The work presented here contributes significantly to the development of a practically useful deep-learning-based VMC method. The described approaches have the potential to become tools for a wide community of computational chemists, as a source of accurate data, describing strong correlation in both ground and excited states.
Abstract The ground and excited state calculations at key geometries, such as the Frank–Condon (FC) and the conical intersection (CI) geometries, are essential for understanding photophysical properties. To compute these geometries on noisy intermediate-scale quantum devices, we proposed a strategy that combined a chemistry-inspired spin-restricted ansatz and a new excited state calculation method called the variational quantum eigensolver under automatically-adjusted constraints (VQE/AC). Unlike the conventional excited state calculation method, called the variational quantum deflation, the VQE/AC does not require the pre-determination of constraint weights and has the potential to describe smooth potential energy surfaces. To validate this strategy, we performed the excited state calculations at the FC and CI geometries of ethylene and phenol blue at the complete active space self-consistent field (CASSCF) level of theory, and found that the energy errors were at most 2 kcal mol −1 even on the ibm_kawasaki device.