An improved penalty-based excited-state variational Monte Carlo approach with deep-learning ansatzes

Abstract

We introduce several improvements to the penalty-based variational quantum Monte Carlo (VMC) algorithm for computing electronic excited states of Entwistle $\text{et al.}$ [M. T. Entwistle $\text{et al.}$, Nat. Commun. $\text{14}$, 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 larger sections of the potential energy surface. Additionally, the accuracy of the original 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 multi-reference configuration interaction.

arXiv comment18 pages, 7 figures

References in corpus (19)

• Recent developments in the PySCF program package
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Symmetries and many-body excited states with neural-network quantum states
• A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Medium Size Molecules
• Energy and variance optimization of many body wave functions
• QUESTDB: a database of highly-accurate excitation energies for the electronic structure community
• Excited states using semistochastic heat-bath configuration interaction
• Ab-initio quantum chemistry with neural-network wavefunctions
• A New Generation of Effective Core Potentials for Correlated Calculations
• New generation of effective core potentials from correlated calculations: 3d transition metal series
• Mapping The Ultrafast Flow Of Harvested Solar Energy In Living Photosynthetic Cells
• A Mountaineering Strategy to Excited States: Highly-Accurate Oscillator Strengths and Dipole Moments of Small Molecules
• A new generation of effective core potentials from correlated calculations: 4s and 4p main group elements and first row additions
• Excited states in variational Monte Carlo using a penalty method
• A Self-Attention Ansatz for Ab-initio Quantum Chemistry
• DeepQMC: an open-source software suite for variational optimization of deep-learning molecular wave functions
• Calculate electronic excited states using neural networks with effective core potential
• Penalty and auxiliary wave function methods for electronic Excitation in neural network variational Monte Carlo

Cited by in corpus (3)

• Analyzing Atomic Interactions in Molecules as Learned by Neural Networks
• Deep quantum Monte Carlo approach for polaritonic chemistry
• Expressivity of determinantal ansatzes for neural network wave functions