arXiv subjects

Paul M. Zimmerman

Publications and source records attributed to Paul M. Zimmerman.

12 recordsLinked to original sources

arXiv2026

XC100: A Wavefunction-Derived Exchange-Correlation Energy Dataset for Atomic and Molecular Species

A workflow is introduced for constructing accurate, wavefunction-derived Kohn-Sham (KS) exchange-correlation (XC) energies across atomic and molecular species. Correlated total energies and densities are obtained from configuration interaction wave functions in a polarized triple-zeta basis, cc-pVTZ, and each wavefunction density is then mapped onto a KS determinant. A composite correction adds valence and core basis functions (cc-pVQZ and cc-pCVTZ), plus a two-point Riemann extrapolation to approach the complete-basis-set limit. The workflow is applied to 100 closed-shell atomic and molecular species composed of main group elements to form the XC100 data set. The resulting KS densities closely reproduce the correlated densities, with a median L2/Ne difference of 1.42 X 10^{-5}, while the composite corrections recover substantial correlation energy beyond the cc-pVTZ reference. Comparison with conventional and machine-learned density functional approximations gives insight into the quality of Exc across different types of models for XC. In all, this paper's workflow demonstrates a practical route for generating XC reference data for the assessment and development of density functionals.

physics.chem-ph↗

arXiv2026

Exchange-Correlation Potentials and Energies from Inverse Generalized Kohn-Sham Calculations

The Kohn-Sham (KS) formulation of density functional theory (DFT) is a map from the many-electron problem to an effective single-electron problem that is governed by a local multiplicative potential. The generalized-Kohn-Sham (GKS) formalism extends it to permit any single-electron operator---nonlocal, local non-multiplicative, local multiplicative, or any combination of them. Doing so expands the scope and ease of modeling the exchange-correlation (XC) functional in DFT, which encodes the complicated many-electron interactions into a mean-field of the electron density. However, unlike KS theory, development of XC functionals in GKS theory has been hindered by the absence of corresponding exact XC potentials and energies. We present the exact XC potentials and energies for atoms and molecules by solving the inverse GKS problem, using highly accurate correlated \textit{ab initio} densities. Our approach is validated across weakly and strongly correlated systems. We further examine a common, yet untested, assumption that KS and GKS correlation potentials and energies are similar, finding instead that they differ substantially in strongly correlated systems. Overall, this work offers a powerful tool to model next-generation of XC functionals within the GKS formalism of DFT.

physics.chem-ph↗

arXiv2025

Taming the Virtual Space for Incremental Full Configuration Interaction

Incremental full configuration interaction (iFCI) closely approximates the FCI limit with polynomial cost through a many-body expansion of the correlation energy, providing highly accurate total energies within a given basis set. To extend iFCI beyond previous basis set limitations, this work introduces a novel natural orbital screening approach, iNO-FCI. By consideration of the importance of virtual orbital selection in the convergence of iFCI, iNO-FCI maximizes the consistency between orbitals selected for each correlated body. iNO-FCI employs a principle of cancellation of errors and ensures that the same set of virtual NOs are used for interdependent terms. This strategy significantly reduces computational cost without compromises in precision. Computational savings of up to 95 percent are demonstrated, allowing access to larger basis sets that were previously computationally prohibitive. iNO-FCI is herein introduced and benchmarked for several difficult test cases involving double-bond dissociation, biradical systems, conjugated $π$ systems, and the spin gap of a Cu-based transition metal complex.

physics.chem-ph↗

arXiv2025

Exchange-Correlation Potentials and Energy Densities through Orbital Averaging and Aufbau Integration

Exchange-correlation potentials vxc and energy densities exc are derived for integer and fractional electron counts using an orbital-averaged Kohn-Sham inversion procedure. The reference densities for inversion come from full configuration interaction in a Slater orbital basis. The orbital-averaged potentials accurately capture key features of vxc, including the asymptotic negative one over r decay and the step discontinuity associated with integer electron transitions for the series of atoms He through Ne. Exchange-correlation energy densities exc are produced through an aufbau path integral. The energy densities reach good agreement with total Exc values. By providing full configuration interaction-derived Kohn-Sham quantities, including vxc, exc, and step contributions, this workflow can be instrumental in the development of improved XC functionals that bridge wavefunction-level accuracy with the computational efficiency of density functional theory.

physics.chem-ph↗

arXiv2024

Learning local and semi-local density functionals from exact exchange-correlation potentials and energies

Finding accurate exchange-correlation (XC) functionals remains the defining challenge in density functional theory (DFT). Despite 40 years of active development, the desired chemical accuracy is still elusive with existing functionals. We present a data-driven pathway to learn the XC functionals by utilizing the exact density, XC energy, and XC potential. While the exact densities are obtained from accurate configuration interaction (CI), the exact XC energies and XC potentials are obtained via inverse DFT calculations on the CI densities. We demonstrate how simple neural network (NN) based local density approximation (LDA) and generalized gradient approximation (GGA), trained on just five atoms and two molecules, provide remarkable improvement in total energies, densities, atomization energies, and barrier heights for hundreds of molecules outside the training set. Particularly, the NN-based GGA functional attains similar accuracy as the higher rung SCAN meta-GGA, highlighting the promise of using the XC potential in modeling XC functionals. We expect this approach to pave the way for systematic learning of increasingly accurate and sophisticated XC functionals.

physics.chem-ph↗

arXiv2024

Accelerating inverse Kohn-Sham calculations using reduced density matrices

The Ryabinkin-Kohut-Staroverov (RKS) and Kanungo-Zimmerman-Gavini (KZG) methods offer two approaches to find exchange-correlation (XC) potentials from ground state densities. The RKS method utilizes the one- and two-particle reduced density matrices to alleviate any numerical artifacts stemming from a finite basis (e.g., Gaussian- or Slater-type orbitals). The KZG approach relies solely on the density to find the XC potential, by combining a systematically convergent finite-element basis with appropriate asymptotic correction on the target density. The RKS method, being designed for a finite basis, offers computational efficiency. The KZG method, using a complete basis, provides higher accuracy. In this work, we combine both the methods to simultaneously afford accuracy and efficiency. In particular, we use the RKS solution as initial guess to the KZG method to attain a significant $3-11\times$ speedup. This work also presents a direct comparison of the XC potentials from the RKS and the KZG method and their relative accuracy on various weakly and strongly correlated molecules, using their ground state solutions from accurate configuration interaction calculations solved in a Slater orbital basis.

physics.chem-ph↗

arXiv2024

Examining the Impact of Local Condition Violations on Energy Computations in DFT

This work introduces Extent of Violation Indices (EVIs), a novel metric for quantifying how well exchange-correlation functionals adhere to local conditions. Applying EVIs to a diverse set of molecules for GGA functionals reveals widespread violations, particularly for semi-empirical functionals. We leverage EVIs to explore potential connections between these violations and errors in chemical properties. While no correlation is observed for atomization energies, a link emerges between EVIs and total energies. Similarly, the analysis of reaction energies suggests weak positive correlations for specific conditions, but definitive conclusions about error cancellation require advancements in both functional accuracy and our understanding of cancellation mechanisms. Overall, this study highlights EVIs as a powerful tool for analyzing functional behavior and adherence to local conditions, paving the way for future research to fully elucidate the impact of violations on energy errors.

physics.chem-ph↗

arXiv2023

Exact and model exchange-correlation potentials for open-shell systems

The conventional approaches to the inverse density functional theory problem typically assume non-degeneracy of the Kohn-Sham (KS) eigenvalues, greatly hindering their use in open-shell systems. We present a generalization of the inverse density functional theory problem that can seamlessly admit degenerate KS eigenvalues. Additionally, we allow for fractional occupancy of the Kohn-Sham orbitals to also handle non-interacting ensemble-v-representable densities, as opposed to just non-interacting pure-v-representable densities. We present the exact exchange-correlation (XC) potentials for six open-shell systems -- four atoms (Li, C, N, and O) and two molecules (CN and $\text{CH}_2$) -- using accurate ground-state densities from configuration interaction calculations. We compare these exact XC potentials with model XC potentials obtained using non-local (B3LYP, SCAN0) and local/semi-local (SCAN, PBE, PW92) XC functionals. Although the relative errors in the densities obtained from these DFT functionals are of $\mathcal{O}(10^{-3}-10^{-2})$, the relative errors in the model XC potentials remain substantially large -- $\mathcal{O}(10^{-1}-10^0)$.

physics.chem-ph↗

arXiv2023

Massively parallel quantum chemistry: PFAS on over 1 million cloud vCPUs

Accurate solutions to the electronic Schrödinger equation can provide valuable insight for electron interactions within molecular systems, accelerating the molecular design and discovery processes in many different applications. However, the availability of such accurate solutions are limited to small molecular systems due to both the extremely high computational complexity and the challenge of operating and executing these workloads on high-performance compute clusters. This work presents a massively scalable cloud-based quantum chemistry platform by implementing a highly parallelizable quantum chemistry method that provides a polynomial-scaling approximation to full configuration interaction (FCI). Our platform orchestrates more than one million virtual CPUs on the cloud to analyze the bond-breaking behaviour of carbon-fluoride bonds of per- and polyfluoroalkyl substances (PFAS) with near-exact accuracy within the chosen basis set. This is the first quantum chemistry calculation utilizing more than one million virtual CPUs on the cloud and is the most accurate electronic structure computation of PFAS bond breaking to date.

physics.chem-ph↗

arXiv2023

Exchange Correlation Potentials from Full Configuration Interaction in a Slater Orbital Basis

Ryabinkin-Kohut-Staroverov (RKS) theory builds a bridge between wave function theory and density functional theory by using quantities from the former to produce accurate exchange-correlation potentials needed by the latter. In this work, the RKS method is developed and tested alongside Slater atomic orbital basis functions for the first time. To evaluate this approach, Full Configuration Interaction computations in the Slater orbitals are employed to give quality input to RKS method, allowing full correlation to be present along with correct nuclei cusps and asymptotic decay of the wavefunction. The RKS method will be shown to be an efficient algorithm to arrive at exchange correlation potentials without unphysical artifacts in moderately-sized basis sets. Furthermore, enforcement of the nuclear cusp conditions will be shown to be vital for the success of the Slater-basis RKS method. Examples of weakly and strongly correlated molecular systems will demonstrate the main features of Slater RKS.

physics.chem-ph↗

arXiv2021

A comparison of exact and model exchange-correlation potentials for molecules

Accurate exchange-correlation (XC) potentials for 3-dimensional systems -- via solution of the \emph{inverse} density functional theory (DFT) problem -- are now available to test the quality of DFT approximations. Herein, the \emph{exact} XC potential for six molecules -- hydrogen molecule at three different bond-lengths, lithium hydride, water, and ortho-benzyne -- are computed using accurate ground-state densities from full configuration interaction (CI) calculations. These potentials are then compared to model XC potentials obtained from DFT calculations with commonly used non-local (B3LYP, HSE06, SCAN0, and M08-HX) and local/semi-local (SCAN, PBE, PW92) XC functionals. While relative errors in the ground-state densities from these models are order $\mathcal{O}(10^{-3}-10^{-2})$, much larger errors in the model XC potentials are found, $\mathcal{O}(10^{-1}-10^0)$, in both the $L_2$ norm of the potential as well as its gradients. These errors are exacerbated in strongly correlated situations, such as the stretched $\text{H}_2$ molecule. Among the model XC functionals under consideration, SCAN0 offers the best quantitative and qualitative agreement with the exact XC potential, underlining the significance of satisfying the exact conditions as well as the incorporation of non-local effects in the construction of XC functionals. Overall, this work indicates that tests against the exact XC potential will provide a promising new direction for building more accurate XC functionals for DFT.

physics.chem-ph↗

arXiv2018

Excited States of Methylene, Polyenes, and Ozone from Heat-Bath Configuration Interaction

The electronically excited states of methylene (CH$_2$), ethylene (C$_2$H$_4$), butadiene (C$_4$H$_6$), hexatriene (C$_6$H$_8$), and ozone (O$_3$) have long proven challenging due to their complex mixtures of static and dynamic correlations. Semistochastic heat-bath configuration interaction (SHCI), which efficiently and systematically approaches the full configuration interaction (FCI) limit, is used to provide close approximations to the FCI energies in these systems. This article presents the largest FCI-level calculation to date -- on hexatriene using a polarized double-zeta basis (ANO-L-pVDZ), which gives rise to a Hilbert space containing more than $10^{38}$ determinants. These calculations give vertical excitation energies of 5.58 and 5.59 eV respectively for the $2^1{\rm A}_{\rm g}$ and $1^1{\rm B}_{\rm u}$ states, showing that they are nearly degenerate. The same excitation energies in butadiene/ANO-L-pVDZ were found to be 6.58 and 6.45 eV. In addition to these benchmarks, our calculations strongly support the presence of a previously hypothesized ring-minimum species of ozone that lies 1.3 eV higher than the open-ring minimum energy structure and is separated from it by a barrier of 1.11 eV.

physics.chem-ph↗