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arXiv:2606.22341

Full Configuration Interaction Quantum Monte Carlo for Accurate $\textit{Ab Initio}$ Nuclear Structure Calculations

Rongzhe Hu, Furong Xu, B. S. Hu, Ali Alavi

Published Jun 21, 2026• 0 citations
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Abstract

We introduce novel full configuration interaction quantum Monte Carlo (FCIQMC) as an accurate many-body solver for $\textit{ab initio}$ nuclear structure calculations. This stochastic approach directly samples the exact wave function in the full configuration space, enabling high-fidelity treatment of high-order many-body correlations in strongly interacting nuclear systems. Using interactions from chiral effective field theory, we have computed ground-state energies and charge radii of $^4$He, $^8$Be, $^{12}$C and $^{16}$O with sub-percent-level many-body uncertainties. These results establish FCIQMC as a stochastic full-configuration-space solver capable of treating systems beyond the reach of the conventional no-core shell model, and as an accurate benchmark for truncated many-body expansion methods.

DOI
10.48550/arxiv.2606.22341

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Full configuration interaction quantum Monte Carlo for accurate ab initio\textit{ab initio}ab initio nuclear structure calculations: algorithms and calculation details
Full configuration interaction quantum Monte Carlo (FCIQMC) is a stochastic many-body solver that has been widely applied to electronic, molecular, and condensed-matter systems. In this work we apply FCIQMC to ab initio\textit{ab initio}ab initio nuclear structure calculations using interactions derived from chiral effective field theory. We describe the algorithm in detail, including imaginary-time propagation, excitation generation, estimator choices, the initiator approximation with adaptive shift correction, and reduced-density-matrix (RDM) sampling. Benchmark calculations in small model spaces, where deterministic full configuration interaction (FCI) results are available, validate the stochastic calculation of energies, radii, and RDM-based pure estimators. For large model spaces, we analyze the residual finite-walker bias through systematic walker-number convergence and infinite-walker extrapolations. We also demonstrate that FCIQMC can be extended beyond ground-state calculations by computing the low-lying spectrum of 6^66Li.
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The initiator full configuration interaction quantum Monte Carlo (i-FCIQMC) method has recently been developed as a highly accurate stochastic electronic structure technique. It has been shown to calculate the exact basis-set ground state energy of small molecules, to within modest stochastic error bars, using tractable computational cost. Here, we use this technique to elucidate an often troublesome series of first-row diatomics consisting of Be2, C2, CN, CO, N2, NO, O2, and F2. Using i-FCIQMC, the dissociation energies of these molecules are obtained almost entirely to within chemical accuracy of experimental results. Furthermore, the i-FCIQMC calculations are performed in a relatively black-box manner, without any a priori knowledge or specification of the wave function. The size consistency of i-FCIQMC is also demonstrated with regards to these diatomics at their more multiconfigurational stretched geometries. The clear and simple i-FCIQMC wave functions obtained for these systems are then compared and investigated to demonstrate the dynamic identification of the dominant determinants contributing to significant static correlation. The appearance and nature of such determinants is shown to provide insight into both the i-FCIQMC algorithm and the diatomics themselves.
By performing a stochastic dynamic in a space of Slater determinants, the full configuration interaction quantum Monte Carlo (FCIQMC) method has been able to obtain energies which are essentially free from systematic error to the basis set correlation energy, within small and systematically improvable error bars. However, the weakly exponential scaling with basis size makes converging the energy with respect to basis set costly and in larger systems, impossible. To ameliorate these basis set issues, here we use perturbation theory to couple the FCIQMC wavefunction to an explicitly correlated strongly orthogonal basis of geminals, following the [2](R12) approach of Valeev et al. The required one- and two-particle density matrices are computed on-the-fly during the FCIQMC dynamic, using a sampling procedure which incurs relatively little additional computation expense. The F12 energy corrections are shown to converge rapidly as a function of sampling, both in imaginary time and number of walkers. Our pilot calculations on the binding curve for the carbon dimer, which exhibits strong correlation effects as well as substantial basis set dependence, demonstrate that the accuracy of the FCIQMC-F12 method surpasses that of all previous FCIQMC calculations, and that the F12 correction improves results equivalent to increasing the quality of the one-electron basis by two cardinal numbers.