arXiv subjects

Janus J. Eriksen

Publications and source records attributed to Janus J. Eriksen.

At least 19 recordsLinked to original sources

arXiv2026

Solvation Lies Within: Simulating Condensed-Phase Properties from Local Electronic Structures

In transitions between different environmental settings, a molecular system inevitably undergoes a range of detectable changes, and the ability to accurately simulate such responses, e.g., in the form of shifts to molecular energies, remains an important challenge across physical chemistry. Based on an exact decomposition of total energies from Kohn--Sham density functional theory in a basis of spatially localized molecular orbitals, the present work outlines a robust protocol for sampling the effect of solvation within homogeneous condensed phases by focusing on perturbations to local electronic structures only. We report chemically intuitive results for binding energies of water, ethanol, and acetonitrile that all display fast convergence with respect to the bulk size. Results stay largely invariant with respect to the choice of basis set while reflecting differences in density functional approximations, and our protocol thus allows for a physically sound and efficient estimation of general effects related to bulk solvation.

physics.chem-ph↗

arXiv2025

A Reusable Library for Second-Order Orbital Optimization Using the Trust Region Method

We present a reusable, open-source software implementation of the second-order trust region algorithm in the new OpenTrustRegion library. We apply the implementation to the general-purpose optimization of molecular orbitals in various contexts within electronic-structure theory. Our permissibly licensed implementation can be included in any software package, be it free and open-source, academically licensed closed-source, or commercial. Detailing the implementation in OpenTrustRegion, we present a review of the theory behind trust region-based methods alongside various extensions. We demonstrate the robustness and efficiency of our optimization library with extensive benchmarks for self-consistent field calculations, orbital localization, as well as orbital symmetrization tasks, featuring challenging and pathological systems.

physics.chem-ph↗

arXiv2024

Atomic Decompositions of Periodic Electronic-Structure Simulations

We present a new theory for partitioning simulations of periodic and solid-state systems into physically sound atomic contributions at the level of Kohn-Sham density functional theory. Our theory is based on spatially localized linear combinations of crystalline Gaussian-type orbitals and, as such, capable of exposing local features within periodic electronic structures in a more intuitive and robust manner than alternatives based on the spatial distribution of atomic basis functions alone. Early decomposed cohesive energies of both molecular polymers and different crystalline polymorphs demonstrate how the atomic properties yielded by our theory convincingly align with the expected charge polarization in these systems, also whenever partial charges and Madelung energies may lend themselves somewhat ambiguous to interpretation.

physics.chem-ph↗

arXiv2024

Transferability of Atom-Based Neural Networks

Machine-learning models in chemistry - when based on descriptors of atoms embedded within molecules - face essential challenges in transferring the quality of predictions of local electronic structures and their associated properties across chemical compound space. In the present work, we make use of adversarial validation to elucidate certain intrinsic complications related to machine inferences of unseen chemistry. On this basis, we employ invariant and equivariant neural networks - both trained either exclusively on total molecular energies or a combination of these and data from atomic partitioning schemes - to evaluate how such models scale performance-wise between datasets of fundamentally different functionality and composition. We find the inference of local electronic properties to improve significantly when training models on augmented data that appropriately expose local functional features. However, molecular datasets for training purposes must themselves be sufficiently comprehensive and rich in composition to warrant any generalizations to larger systems, and even then, transferability can still only genuinely manifest if the body of atomic energies available for training purposes exposes the uniqueness of different functional moieties within molecules. We demonstrate this point by comparing machine models trained on atomic partitioning schemes based on the spatial locality of either native atomic or molecular orbitals.

physics.chem-ph↗

arXiv2024

Exploiting Non-Abelian Point-Group Symmetry to Estimate the Exact Ground-State Correlation Energy of Benzene in a Polarized Split-Valence Triple-Zeta Basis Set

Local electronic-structure methods in quantum chemistry operate on the ability to compress electron correlations more efficiently in a basis of spatially localized molecular orbitals than in a parent set of canonical orbitals. However, many typical choices of localized orbitals tend to be related by selected, near-exact symmetry operations whenever a molecule belongs to a point group, a feature which remains largely unexploited in most local correlation methods. The present Letter demonstrates how to leverage a recent unitary protocol for enforcing symmetry properties among localized orbitals to yield a high-accuracy estimate of the exact ground-state correlation energy of benzene ($D_{6h}$) in correlation-consistent polarized basis sets of both double- and triple-$ζ$ quality. Through an initial application to many-body expanded full configuration interaction (MBE-FCI) theory, we show how molecular point-group symmetry can lead to computational savings that are inversely proportional to the order of the point group in a manner generally applicable to the acceleration of modern local correlation methods.

physics.chem-ph↗

arXiv2024

MBE-CASSCF Approach for the Accurate Treatment of Large Active Spaces

We present a novel implementation of the complete active space self-consistent field (CASSCF) method that makes use of the many-body expanded full configuration interaction (MBE-FCI) method to incrementally approximate electronic structures within large active spaces. On the basis of a hybrid first-order algorithm employing both Super-CI and quasi-Newton strategies for the optimization of molecular orbitals, we demonstrate both computational efficacy and high accuracy of the resulting MBE-CASSCF method. We assess the performance of our implementation on a set of established numerical tests before applying MBE-CASSCF in the investigation of the triplet-quintet spin gap of iron(II) porphyrin with active spaces as large as 50 electrons in 50 orbitals.

physics.chem-ph↗

arXiv2024

Error Control and Automatic Detection of Reference Active Spaces in Many-Body Expanded Full Configuration Interaction

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.

physics.chem-ph↗

arXiv2023

Properties of Local Electronic Structures

The simulation of intrinsic contributions to molecular properties holds the potential to allow for chemistry to be directly inferred from changes to electronic structures at the atomic level. In the present study, we demonstrate how such local properties can be readily derived from suitable molecular orbitals to yield effective fingerprints of various types of atoms in organic molecules. In contrast, corresponding inferences from schemes that instead make use of individual atomic orbitals for this purpose are generally found to fail in expressing much uniqueness in atomic environments. By further studying the extent to which entire chemical reactions may be decomposed into meaningful and continuously evolving atomic contributions, schemes based on molecular rather than atomic orbitals are once again found to be the more consistent, even allowing for intricate differences between seemingly uniform nucleophilic substitutions to be probed.

physics.chem-ph↗

arXiv2023

Symmetrization of Localized Molecular Orbitals

We present a novel algorithm for (i) detecting approximate symmetries inherently present among spatially localized molecular orbitals and (ii) enforcing these in numerically exact manners by means of unitary optimization techniques. The vast potential of our algorithm to compress a full set of molecular orbitals into only a minimal set of symmetry-unique orbitals is demonstrated, starting from localized bases of either Pipek-Mezey or Foster-Boys orbitals. Comparisons of results based on either of these two localization procedures indicate that Foster-Boys molecular orbitals can be spanned by a smaller number of symmetry-unique orbitals on average, making these outstanding candidates for the exploitation of general, (non-)Abelian point-group symmetries in a range of local correlation methods. As an illustration of said compressibility, our algorithm is capable of identifying a mere 14 symmetry-unique orbitals for the buckminsterfullerene in the highly symmetric $I_h$ molecular point group, corresponding to only $1.7\%$ of its total 840 molecular orbitals in a standard double-$ζ$ basis set. The present work thus marks an important advancement in the exploitation of point-group symmetry within local correlation methods, for which the appropriate adaption of symmetry uniqueness among orbitals has the potential to yield unprecedented speed-ups.

physics.chem-ph↗

arXiv2023

Decomposing Chemical Space: Applications to the Machine Learning of Atomic Energies

We apply a number of atomic decomposition schemes across the standard QM7 dataset -- a small model set of organic molecules at equilibrium geometry -- to inspect the possible emergence of trends among contributions to atomization energies from distinct elements embedded within molecules. Specifically, a recent decomposition scheme of ours based on spatially localized molecular orbitals is compared to alternatives that instead partition molecular energies on account of which nuclei individual atomic orbitals are centred on. We find these partitioning schemes to expose the composition of chemical compound space in very dissimilar ways in terms of the grouping, binning, and heterogeneity of discrete atomic contributions, e.g., those associated with hydrogens bonded to different heavy atoms. Furthermore, unphysical dependencies on the one-electron basis set are found for some, but not all of these schemes. The relevance and importance of these compositional factors for training tailored neural network models based on atomic energies are next assessed. We identify both limitations and possible advantages with respect to contemporary machine learning models and discuss the design of potential counterparts based on atoms and the intrinsic energies of these as the principal decomposition units.

physics.chem-ph↗

arXiv2022

Electronic Excitations Through the Prism of Mean-Field Decomposition Techniques

The potential of mean-field decomposition techniques in interpreting electronic transitions in molecules is explored, particularly, the usefulness of these for offering computational signatures of different classes of such excitations. When viewed as a conceptual lens for this purpose, decomposed results are presented for ground- and excited-state energies and dipole moments of selected prototypical organic dyes, and the discrete nature of these properties as well as how they change upon transitioning from one state to another is analyzed without recourse to a discussion based on the involved molecular orbitals. On the basis of results obtained both with and without an account of continuum solvation, our work is further intended to shed new light on practical and pathological differences in between various functional approximations in orbital-optimized Kohn-Sham density functional theory for excited states, equipping practitioners and developers in the field with new probes and possible validation tools.

physics.chem-ph↗

arXiv2021

Decomposed Mean-Field Simulations of Local Properties in Condensed Phases

The present work demonstrates a robust protocol for probing localized electronic structure in condensed-phase systems, operating in terms of a recently proposed theory for decomposing the results of Kohn-Sham density functional theory in a basis of spatially localized molecular orbitals [Eriksen, J. Chem. Phys. 153, 214109 (2020)]. In an initial application to liquid, ambient water and the assessment of the solvation energy and the embedded dipole moment of H$_2$O in solution, we find that both properties are amplified on average -- in accordance with expectation -- and that correlations are indeed observed to exist between them. However, the simulated solvent-induced shift to the dipole moment of water is found to be significantly dampened with respect to typical literature values. The local nature of our methodology has further allowed us to evaluate the convergence of bulk properties with respect to the extent of the underlying one-electron basis set, ranging from single-$ζ$ to full (augmented) quadruple-$ζ$ quality. Albeit a pilot example, our work paves the way towards future studies of local effects and defects in more complex phases, e.g., liquid mixtures and even solid-state crystals.

physics.chem-ph↗

arXiv2021

Incremental Treatments of the Full Configuration Interaction Problem

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.

physics.chem-ph↗

arXiv2020

The Shape of Full Configuration Interaction to Come

We present a perspective on what the future holds for full configuration interaction (FCI) theory, with an emphasis on conceptual rather than technical details. Upon revisiting the early history of FCI, a number of its key contemporary approximations are compared on as equal a footing as possible, using a recent blind challenge on the benzene molecule as a testbed [Eriksen et al., J. Phys. Chem. Lett., 11, 8922 (2020)]. In the process, we review the scope of applications for which FCI continues to prove indispensable, and the required traits in terms of robustness, efficacy, and reliability its modern approximations must satisfy are discussed. We close by conveying a number of general observations on the merits offered by the state-of-the-art alongside some of the challenges still faced to this day. While the field has altogether seen immense progress over the years - the past decade, in particular - it remains clear that our community as a whole has a substantial way to go in enhancing the overall applicability of near-exact electronic structure theory for systems of general composition and increasing size.

physics.chem-ph↗

arXiv2020

Mean-Field Density Matrix Decompositions

We introduce new and robust decompositions of mean-field Hartree-Fock (HF) and Kohn-Sham density functional theory (KS-DFT) relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning 1-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regards to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure-property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.

physics.chem-ph↗

arXiv2020

Ground and Excited State First-Order Properties in Many-Body Expanded Full Configuration Interaction Theory

The recently proposed many-body expanded full configuration interaction (MBE-FCI) method is extended to excited states and static first-order properties different from total, ground state correlation energies. Results are presented for excitation energies and (transition) dipole moments of two prototypical, heteronuclear diatomics---LiH and MgO---in augmented correlation consistent basis sets of up to quadruple-$ζ$ quality. Given that MBE-FCI properties are evaluated without recourse to a sampled wave function and the storage of corresponding reduced density matrices, the memory overhead associated with the calculation of general first-order properties only scales with the dimension of the desired property. In combination with the demonstrated performance, the present developments are bound to admit a wide range of future applications by means of many-body expanded treatments of electron correlation.

physics.chem-ph↗

arXiv2020

The Ground State Electronic Energy of Benzene

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$ζ$ quality. As a broad international endeavour, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around $-863$ m$E_{\text{H}}$. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 m$E_{\text{H}}$), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

physics.chem-ph↗

arXiv2019

Generalized Many-Body Expanded Full Configuration Interaction Theory

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 a 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.

physics.chem-ph↗