Eirik Fadum Kjønstad

Phaseless auxiliary-field quantum Monte Carlo (AFQMC) has in several cases been found to perform well on strongly correlated systems, including compounds containing transition-metal elements. Here, we benchmark the method for three iron–sulfur clusters ([2Fe-2S], [4Fe-4S], and the FeMo cofactor) using a hierarchy of systematically improved trial states derived from coupled cluster (CC) theory, including up to quadruple excitations relative to the Hartree–Fock (HF) reference, as well as multi-Slater trial states derived from unrestricted density matrix renormalization group wave functions. Our results reveal for these systems that, as the symmetry-broken trial is improved beyond the mean-field level, the phaseless AFQMC energy can become less accurate, and in some cases even less accurate than the underlying trial projected energy itself, displaying an inverted energy pattern that is only corrected once the trial fidelity is sufficiently high. For [2Fe-2S], we show that a decreased accuracy in the AFQMC energy can coincide with a simultaneous improvement in the trial state and the walker ensemble, as measured by their fidelity relative to the exact ground state, a behavior which is allowed by the nonvariational nature of the phaseless AFQMC energy estimator. We further find that this is not solely due to the use of spin-unrestricted trial states, as the inversion persists in [2Fe-2S] when we explicitly break the symmetry of the Hamiltonian by applying a fictitious local spin-Zeeman field. Instead, we find that the energy inversion is related to the choice of measurement trial in the estimator, where using a high-order CC trial state for measurements may introduce errors that are suppressed when the measurement wave function is restricted to lower excitation subspaces. In particular, measuring the energy with the mean-field reference while guiding the walkers with a CC trial removes the inverted pattern and improves the overall accuracy across the iron–sulfur clusters, with a possible exception for [4Fe-4S] where energies with a CCSDT guide may be less accurate than those guided by CCSD for some broken-symmetry families. Taken together, our findings suggest that the relatively accurate energies obtained with an HF trial state in these systems arise from favorable error cancellation, warranting significant caution about the reliability of phaseless AFQMC with such trials for strongly correlated transition-metal systems of this kind.

We extend the use of coupled cluster (CC) trial states in the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method beyond single and double excitations to include both triple and quadruple excitations. With this AFQMC/CC hierarchy, we are able to systematically benchmark the method’s performance on molecular systems as the quality of the trial is improved. Our results show that the phaseless AFQMC energy improves systematically and is typically significantly more accurate than the energy of the underlying trial state. However, the relative improvement compared to the trial CC energy decreases as we ascend the CC hierarchy. As the CC wave function is usually further approximated when used as an AFQMC trial, we also explore the relationship between the components of the CC wave function and the resulting AFQMC/CC error. Our results suggest that improving the representation of the CC wave function in the AFQMC trial does not always lower the bias even when it increases the fidelity of the trial with the exact ground state.

The eT program is an open-source electronic structure program with an emphasis on performance and modularity. As its name suggests, the program features extensive coupled cluster capabilities, performing well compared to other electronic structure programs and, in some cases, outperforming commercial alternatives. However, eT is more than a coupled cluster program; other models based on wave function theory (such as full and reduced-space configuration interaction and a variety of self-consistent field models) and density functional theory are supported. The second major release of the program, eT 2.0, has specialized functionality for strong light–matter coupling conditions. In addition, it includes a wide range of optimizations and algorithmic improvements, as well as new capabilities for exploring potential energy surfaces and for modeling experiments in the ultraviolet and X-ray regimes. Molecular gradients are now available at the coupled cluster level, and high-accuracy spectroscopic simulations are available at reduced computational cost within the multilevel coupled cluster and multiscale frameworks. We present the modifications to the program since its first major release, eT 1.0, highlighting some notable new features and demonstrating the performance of the new version relative to the first release and to other established electronic structure programs.

The geometric phase effect arises from the dependence on the nuclear coordinates in the electronic Hamiltonian, leading to sign changes of the electronic wave functions upon traversal of certain paths in nuclear configuration space. The geometric phase effect can have important consequences for the electronic structure problem, but this fact has largely gone unnoticed. We show how the geometric phase effect can significantly impact the accuracy of approximate electronic structure methods. In particular, we prove that for paths that enclose a conical intersection, any component of the wave function (such as an approximation to it) must vanish exactly, unless the associated conical intersections of the component and the wave function coincide. This has implications for methods that employ intermediate normalization, where the contribution along a reference wave function is fixed. We demonstrate numerically that the failure to account for the phase effect leads to asymptotic discontinuities in the wave function parameters. This results in breakdowns in coupled cluster methods or perturbation theories converging to excited states rather than the ground state. The global nature of the geometric phase effect means that these failures can span extended regions of nuclear configuration space, including regions far away from any conical intersection.

Despite their high accuracy, standard coupled cluster models cannot be used for nonadiabatic molecular dynamics simulations because they yield unphysical complex excitation energies at conical intersections between same symmetry excited states. On the other hand, similarity constrained coupled cluster theory has enabled the application of coupled cluster theory in such dynamics simulations. Here, we present a similarity constrained perturbative doubles (SCC2) model with same symmetry excited-state conical intersections that exhibit correct topography, topology, and real excitation energies. This is achieved while retaining the favorable computational scaling of the standard CC2 model. We illustrate the model for conical intersections in hypofluorous acid and thymine, and compare its performance with other methods. The results demonstrate that conical intersections between excited states can be described correctly and efficiently at the SCC2 level. We therefore expect that the SCC2 model will enable coupled cluster nonadiabatic dynamics simulations for large molecular systems.

Experimental studies have shown that external electromagnetic fields can offer a means to modify molecular structure and reactivity. In this work, we derive and implement analytical molecular gradients at the Hartree-Fock level for both static and quantized electromagnetic fields to explore the field effects on equilibrium geometries. We investigate the equilibrium geometries and field-induced orientations of representative molecules: water, the water dimer, and corannulene. Our analysis reveals distinct field-induced effects: shifts in the equilibrium geometry of water under a combined cavity and static electric field; a reduction in the inversion barrier of corannulene in the presence of quantized or magnetic fields; and orthogonal orientation of the individual water molecules in the water dimer with respect to the quantized field component.

We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and a locally ordered formalism. We provide a pedagogical description of these two conventions as implemented for the quimb library. Using hyperoptimized approximate contraction strategies, we present benchmark fermionic projected entangled pair state simulations of finite Hubbard models defined on the three-dimensional diamond lattice and random regular graphs. Published by the American Physical Society 2025

Minimum energy conical intersections can be used to rationalize photochemical processes. In this Letter, we examine an algorithm to locate these structures that does not require the evaluation of nonadiabatic coupling vectors, showing that it minimizes the energy on hypersurfaces that envelop the intersection seam. By constraining the states to be separated by a small non-zero energy difference, the algorithm ensures that numerical artifacts and convergence problems of coupled cluster theory at conical intersections are not encountered during the optimization. In this way, we demonstrate for various systems that geometries at minimum energy conical intersections with the ground state are well described by the coupled cluster singles and doubles model, suggesting that coupled cluster theory may, in some cases, provide a good description of relaxation to the ground state in nonadiabatic dynamics simulations.

Coupled cluster theory in the standard formulation is unable to correctly describe conical intersections among states of the same symmetry. This limitation has restricted the practical application of an otherwise highly accurate electronic structure model, particularly in nonadiabatic dynamics. Recently, the intersection problem among the excited states was fully characterized and resolved. However, intersections with the ground state remain an open challenge, and addressing this problem is our objective here. We present a generalized coupled cluster framework that correctly accounts for the geometric phase effect and avoids bifurcations of the solutions to the ground state equations. Several applications are presented that demonstrate the correct description of ground state conical intersections. We also propose how the framework can be used for other electronic-structure methods.