Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2506.03304

MC-PDFT Nuclear Gradients and L-PDFT Energies with Meta and Hybrid Meta On-Top Functionals for Ground- and Excited-State Geometry Optimization and Vertical Excitation Energies

Matthew R. Hennefarth·Younghwan Kim·Bhavnesh Jangid·Jacob Wardzala·Matthew R. Hermes·Donald G. Truhlar·Laura Gagliardi
View original source ↗Read source document ↗Export metadata ↓

Abstract

Multiconfiguration pair-density functional theory (MC-PDFT) is a post-MCSCF multireference electronic-structure method that explicitly models strong electron correlation, and linearized pair-density functional theory (L-PDFT) is a recently developed multi-state extension that can accurately model conical intersections and locally-avoided crossings. Because MC-PDFT and L-PDFT rely on an on-top energy functional, their accuracy depends on the quality of the on-top functional used. Recent work has introduced translated meta-gradient-approximation (meta-GA) on-top functionals, and specifically the MC23 hybrid meta-GA on-top functional, which is the first on-top functional specifically optimized for MC-PDFT. Here we report the derivation and implementation of analytic nuclear gradients for MC-PDFT calculations using meta-GA and hybrid meta-GA on-top functionals. This development also enables analytic nuclear gradients for the widely successful tPBE0 hybrid on-top functional. Because MC-PDFT nuclear-gradient calculations involve the derivative of the on-top functional, this development also enables the use of meta-GA on-top functionals in L-PDFT single-point energy calculations. We use the new capabilities to test MC23 for ground-state geometries, excited-state geometries, and vertical excitation energies of s-trans-butadiene and benzophenone as well as to test MC23, another hybrid meta-GA, and seven other meta-GA on-top functionals for 441 vertical excitation energies. We find MC23 performs the best of all nine meta and hybrid meta functionals for vertical excitation energies and is comparable in accuracy to tPBE0 and to the NEVPT2 multireference wave function method. Additionally, we directly compare our MC-PDFT vertical excitation results to previously computed TD-DFT values and find that MC-PDFT outperforms even the best performing Kohn-Sham density functional.

Explore related subjects

physics.chem-phquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Matthew R. Hennefarth, Younghwan Kim, Bhavnesh Jangid, Jacob Wardzala, Matthew R. Hermes, Donald G. Truhlar, Laura Gagliardi. 2025-08-21. MC-PDFT Nuclear Gradients and L-PDFT Energies with Meta and Hybrid Meta On-Top Functionals for Ground- and Excited-State Geometry Optimization and Vertical Excitation Energies. https://doi.org/10.1021/acs.jctc.5c00899

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Global approximations to the error function of real argument for vectorized computation

The error function of real argument can be approximated to a given uniform relative accuracy by a single closed-form expression for the whole variable range either in terms of addition, multiplication, division, and square root operations only, or also using the exponential function. The coefficients have been tabulated for up to 128-bit precision. Tests of a computer code implementation using the standard single- and double-precision floating-point arithmetic show good performance and vectorizability. Approximations to the complementary error function have also been found, including those where only additions, multiplications, and one division are needed to reach a uniform absolute accuracy.

physics.chem-ph↗
arXiv2026

From Heuristics to Machine Learning: The Performance Ceiling for Single-Ion Magnets and Its Electronic Origin

Machine learning (ML) is expected to speed up the discovery of single-ion magnets (SIMs), but does the structural information available before synthesis allow such predictions? For 1215 lanthanide complexes from the SIMDAVIS 1.2.1 database we compared three increasing levels of structural description: tabular features of the coordination site, continuous symmetry measures of the coordination polyhedron, and the complete 3D arrangement of atoms. All three converge to an accuracy near 76%, only slightly above the 71% of the single rule "predict SIM for Dy3+". To explain the failures, we combined multireference ab initio calculations with an inspection of the structures behind the high-confidence errors. The SIMs missed by the geometric models are field-induced relaxers whose ground Kramers doublets are prone to tunnelling, a property invisible to geometric descriptors. Many false positives contain several lanthanide centers or radicals, so their relaxation is collective and outside the single-ion picture. The electronic-structure and connectivity information needed to identify SIMs is therefore not accessible to geometric methods alone. Geometric models remain useful: restricting the screening to compounds with high prediction confidence raises the accuracy to 88% while retaining 48% of the dataset. Building on the analysis of the failures, we propose a strategy that combines simple filters for nuclearity and for radicals with ligand-field descriptors from ab initio calculations.

physics.chem-ph↗
arXiv2026

Composition-Dependent Self-Diffusion Coefficients in Liquid Mixtures from Hybrid Machine Learning

Self-diffusion coefficients are key descriptors of molecular mobility, yet experimental data remain scarce, highlighting the need for reliable prediction methods. In previous work, we introduced the hybrid Enhanced Stokes-Einstein (ESE) model, which advanced the state of the art in the physically consistent prediction of self-diffusion coefficients of solutes at infinite dilution in pure solvents by integrating the Stokes-Einstein equation with machine learning (ML). Here, we extend this approach to concentration-dependent self-diffusion coefficients and multicomponent solvents with HADES. This hybrid architecture leverages a deep-set neural network to connect pure-component and mixture prediction within a single framework. HADES predicts self-diffusion coefficients in liquid mixtures with any number of components at any composition and temperature. The only required inputs are SMILES-encoded molecular structures of the components and the pure-component viscosities, making the method broadly applicable. Trained and evaluated on a comprehensive dataset of 2526 data points for 600 systems, HADES significantly outperforms benchmark prediction methods. The trained model and its source code are fully disclosed, and the application is available via an interactive website https://ml-prop.mv.rptu.de/.

physics.chem-ph↗