Applying Quantum Monte Carlo, Chinese team efficiently and accurately calculates molecular atomic structures

Stochastic methods, namely Quantum Monte Carlo (QMC) methods, have been competitors of deterministic methods in pursuing the ground truth of molecular many-body electronic wave functions. In particular, Diffusion Monte Carlo (DMC) - a method based on ground state projection - is capable of handling dynamic correlations and achieving molecular subchemical accuracy. It has grown considerably in the past decades and has become one of the preferred methods when accurate ground-state energies of molecules and materials are needed.

 

Recently, byte-hopping and a team from Peking University applied a neural network-based experimental wave function in fixed-node DMC, which can accurately calculate various atomic and molecular systems with different electronic properties. The method compares favorably with state-of-the-art neural network methods using Variational Monte Carlo (VMC) in terms of accuracy and efficiency.

 

 

It has been shown that machine learning techniques such as neural networks can provide powerful support for describing the electronic structure of molecular systems and provide a powerful method for reconstructing many-body wave functions. "FermiNet" (FermiNet) is one of the noteworthy examples, showing promising results for small molecules that are usually composed of less than 30 electrons.

 

This time, the experimental team integrated the FermiNet neural network wave function into the DMC. This approach exploits the precise experimental wave function of FermiNet and the efficient ground-state projection of DMC to achieve unprecedented accuracy in the computation of a series of systems.

 

This FermiNet-based DMC method is called FermiNet-DMC. compared with FermiNet-VMC, FermiNet-DMC is able to achieve lower variational ground state energy at lower computational cost.

 

 

Computational framework. a) A brief overview of variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) from the eigenstate composition point of view is given. The atomic orbitals represent the different eigenstates and the bar chart indicates the weight of each eigenstate in the state decomposition. Top: a randomly initialized state. Middle: output states of the VMC. b) Left: neural network resolution of the wave function; right: one-dimensional projection of the multi-electron wave function and its nodal surface. c) Left: parallel diffusion Monte Carlo process on the GPU; right: amplification of the stochastic dynamics of each walker, containing the configuration of all electrons in the system, while the nodal structure is fixed. d) Three key steps of the diffusion Monte Carlo.

 

The experimental team then tested atoms as well as molecules, including N2, cyclobutadiene, water dimer, benzene, and benzene dimer.

 

Accuracy and efficiency of FermiNet-DMC on single atoms

 

Calculations for N2, cyclobutadiene and water dimer

 

Calculations for benzene

 

Calculated energy for benzene dimers and extrapolation based on the VMC-DMC linear relationship

 

FermiNet-DMC enables accurate ab initio calculations for various systems, obtaining 16 atoms for the ground state, N2 along the bonding curve, 2 cyclobutadiene conformations, 10 hydrogen-bonded water dimers, benzene monomers and dimers.FermiNet-DMC performs consistently well.

 

The combination of neural network with DMC provides a powerful solution compared to VMC: it allows to achieve more accurate results with a simpler network and better efficiency. In the large systems tested, FermiNet-DMC can achieve improvements in efficiency of 1 or 2 orders of magnitude to reach the same level of accuracy as FermiNet-VMC, which can become increasingly important when dealing with larger molecules.

 

Even for small systems, FermiNet-DMC should still be preferred because it can achieve comparable or even better accuracy with a smaller network and fewer computational resources than FermiNet-VMC. Thus, this work eliminates the negative concerns from VMC to DMC with neural network wave function theorems.

 

Moreover, the DMC approach can be further integrated with other powerful molecular neural networks, solid periodic neural networks, and neural networks with effective core potential - which has the potential to catalyze a paradigm shift in the application of stochastic electronic structure methods.