Abstract The recent many‐body expanded full configuration interaction (MBE‐FCI) method is reviewed by critically assessing its advantages and drawbacks in the context of contemporary near‐exact electronic structure theory. Besides providing a succinct summary of the history of MBE‐FCI to date within a generalized and unified theoretical setting, its finer algorithmic details are discussed alongside our optimized computational implementation of the theory. A selected few of the most recent applications of MBE‐FCI are revisited, before we close by outlining its future research directions as well as its place among modern near‐exact wave function‐based methods. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods
Abstract The recent many‐body expanded full configuration interaction (MBE‐FCI) method is reviewed by critically assessing its advantages and drawbacks in the context of contemporary near‐exact electronic structure theory. Besides providing a succinct summary of the history of MBE‐FCI to date within a generalized and unified theoretical setting, its finer algorithmic details are discussed alongside our optimized computational implementation of the theory. A selected few of the most recent applications of MBE‐FCI are revisited, before we close by outlining its future research directions as well as its place among modern near‐exact wave function‐based methods. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods
Facilitated by a rigorous partitioning of a molecular system's orbital basis into two fundamental subspaces-a reference and an expansion space, both with orbitals of unspecified occupancy-we generalize our recently introduced many-body expanded full configuration interaction (MBE-FCI) method to allow for electron-rich model and molecular systems dominated by both weak and strong correlation to be addressed. By employing minimal or even empty reference spaces, we show through calculations on the one-dimensional Hubbard model with up to 46 lattice sites, the chromium dimer, and the benzene molecule how near-exact results may be obtained in an entirely unbiased manner for chemical and physical problems of not only academic but also applied chemical interest. Given the massive parallelism and overall accuracy of the resulting method, we argue that generalized MBE-FCI theory possesses an immense potential to yield near-exact correlation energies for molecular systems of unprecedented size, composition, and complexity in the years to come.
We present a wide-reaching revamp of the generalized many-body expanded full configuration interaction (MBE-FCI) method. First, we outline how to automatize the selection of reference active spaces, whereby the inherent bias introduced through a manual identification is reduced, also within the context of traditional complete active space methods. Second, we allow for the use of compact orbital clusters as expansion objects, which works to circumvent the unfavorable scaling with the number of orbitals included in the space complementary to the reference orbitals. Finally, we present a new algorithm for ensuring that many-body expansions can be efficiently terminated while conservatively accounting for resulting errors. These developments are all tested on a variety of molecular systems and different orbital representations to illustrate the abilities of our algorithm to produce correlation energies within predetermined error bounds, significantly broadening the overall applicability of the MBE-FCI method.
Full configuration interaction quantum Monte Carlo for accurate 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 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 6Li.
Full Configuration Interaction Quantum Monte Carlo for Accurate Ab Initio Nuclear Structure Calculations
We introduce novel full configuration interaction quantum Monte Carlo (FCIQMC) as an accurate many-body solver for 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 4He, 8Be, 12C and 16O 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.
The auxiliary‐field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time‐independent Schrödinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed remarkable growth, especially as a tool for electronic structure computations in real materials. The method has demonstrated excellent accuracy across a variety of correlated electron systems. Taking the form of stochastic evolution in a manifold of nonorthogonal Slater determinants, the method resembles an ensemble of density‐functional theory (DFT) calculations in the presence of fluctuating external potentials. Its computational cost scales as a low‐power of system size, similar to the corresponding independent‐electron calculations. Highly efficient and intrinsically parallel, AFQMC is able to take full advantage of contemporary high‐performance computing platforms and numerical libraries. In this review, we provide a self‐contained introduction to the exact and constrained variants of AFQMC, with emphasis on its applications to the electronic structure of molecular systems. Representative results are presented, and theoretical foundations and implementation details of the method are discussed. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Computational Materials Science Computer and Information Science > Computer Algorithms and Programming
We present three modifications to our recently introduced fast randomized iteration method for full configuration interaction (FCI-FRI) and investigate their effects on the method’s performance for Ne, H 2 O, and N 2 . The initiator approximation, originally developed for full configuration interaction quantum Monte Carlo, significantly reduces statistical error in FCI-FRI when few samples are used in compression operations, enabling its application to larger chemical systems. The semistochastic extension, which involves exactly preserving a fixed subset of elements in each compression, improves statistical efficiency in some cases but reduces it in others. We also developed a new approach to sampling excitations that yields consistent improvements in statistical efficiency and reductions in computational cost. We discuss possible strategies based on our findings for improving the performance of stochastic quantum chemistry methods more generally.