arXiv subjects

Kyle R. Bryenton

Publications and source records attributed to Kyle R. Bryenton.

7 recordsLinked to original sources

arXiv2026

Performance of a minimally empirical local-hybrid density functional for molecular chemistry

Delocalisation error has been argued to be the greatest outstanding challenge in density-functional theory (DFT). One of the most promising routes to minimise this error is development of local hybrid functionals, in which the fraction of exact-exchange mixing is position dependent. However, existing local hybrids capable of good thermochemical accuracy are often highly empirical, and tend to have complicated functional forms that involve some combination of range separation, calibration functions, power-series expansions, or even neural networks. In this work, we explore the limits of what can be achieved with a minimally empirical local hybrid functional form that avoids such complexities. The ``LHnz'' functional is proposed, which uses dispersionless exchange and a local mixing fraction dependent on the correlation length and effective exchange--correlation hole normalisations. With only three empirical parameters, LHnz is shown to outperform all existing global hybrid functionals for the GMTKN55 molecular-thermochemistry benchmark with no large outliers.

physics.chem-ph↗

arXiv2026

Consistent GMTKN55 and molecular-crystal accuracy using minimally empirical DFT with XDM(Z) dispersion

Density-functional theory (DFT) has become the workhorse of modern computational chemistry, with dispersion corrections such as the exchange-hole dipole moment (XDM) model playing a key role in high-accuracy modelling of large-scale systems. All previous production implementations of XDM have used the two-parameter Becke--Johnson damping function based on atomic radii. Here, we introduce and implement a new XDM variant that uses a one-parameter damping function based on atomic numbers, recently proposed by Becke. Both this new Z damping and the canonical BJ-damping variants of XDM are benchmarked on the comprehensive GMTKN55 database using minimally empirical generalised-gradient-approximation, global hybrid, and range-separated hybrid functionals. This marks the first time that the XDM (and many-body dispersion, MBD) corrections have been tested on the GMTKN55 set. Using the new WTMAD-4 metric, an outlier analysis is performed for all new data, as well as for top-ranking functionals from the literature at each rung, providing insight into both performance and consistency across the dataset. We also extended our analysis to the DM21 and Skala machine-learned functionals that have garnered recent attention. To test Z damping's transferability to the solid state, four benchmarks involving molecular crystals are also considered. Across these molecular and solid-state benchmarks, the revPBE0 and B86bPBE0 hybrid functionals, paired with the Z-damped XDM variant, show excellent performance.

physics.chem-ph↗

arXiv2026

The effects of dispersion damping and three-body interactions for accurate layered-material exfoliation energies

Accurate predictions of exfoliation energies and lattice constants of layered materials hinge on a correct description of London dispersion physics. Modern a posteriori dispersion corrections in density-functional theory (DFT), such as the exchange-hole dipole moment (XDM) model, capture the proper asymptotic behaviour at long range while making use of damping functions to prevent unphysical divergence at short range. In the united-atom limit, the dispersion energy is damped to a finite, non-zero value by both the canonical Becke--Johnson (BJ) damping function and the new Z-damping function. XDM(BJ) has previously demonstrated exceptional accuracy for modelling layered materials, such as in the LM26 benchmark, which includes graphite, hexagonal boron nitride, lead(II) oxide, and transition-metal dichalcogenides. This work presents the first assessment of XDM(Z) on the same benchmark. We also show that inclusion of three-body interactions via the Axilrod--Teller--Muto (ATM) term further improves the computed exfoliation energies for both XDM(BJ) and XDM(Z), yielding the best performance achieved on LM26 using semi-local functionals to date, relative to reference data from the random-phase approximation.

cond-mat.mtrl-sci↗

arXiv2026

Roadmap on Advancements of the FHI-aims Software Package

Electronic-structure theory is the foundation of the description of materials including multiscale modeling of their properties and functions. Obviously, without sufficient accuracy at the base, reliable predictions are unlikely at any level that follows. The software package FHI-aims has proven to be a game changer for accurate free-energy calculations because of its scalability, numerical precision, and its efficient handling of density functional theory (DFT) with hybrid functionals and van der Waals interactions. It treats molecules, clusters, and extended systems (solids and liquids) on an equal footing. Besides DFT, FHI-aims also includes quantum-chemistry methods, descriptions for excited states and vibrations, and calculations of various types of transport. Recent advancements address the integration of FHI-aims into an increasing number of workflows and various artificial intelligence (AI) methods. This Roadmap describes the state-of-the-art of FHI-aims and advancements that are currently ongoing or planned.

cond-mat.mtrl-sci↗

arXiv2025

WTMAD-4: A Fair Weighting Scheme for GMTKN55

The GMTKN55 data set is a collection of standard benchmarks used in molecular quantum chemistry that spans small- and large-molecule thermochemistry, reaction barriers, and non-covalent interactions. Herein, we identify a flaw in the weighted mean absolute deviation (WTMAD) definitions commonly used to quantify performance of various electronic-structure methods for the GMTKN55 set, which under-weight some of its component benchmarks by orders of magnitude. A new WTMAD-4 metric is proposed, based on typical errors observed for a set of ten minimally empirical dispersion-corrected density-functional approximations (DFAs), ensuring fair treatment across all benchmarks. The performance of 115 DFAs is then reassessed using WTMAD-4 and we highlight a literature example where a DFA parametrised by minimising WTMAD-2 underperforms for benchmarks marginalised by that metric.

physics.chem-ph↗

arXiv2018

The $d$-dimensional softcore Coulomb potential and the generalized confluent Heun equation

An analysis of the generalized confluent Heun equation $(α_2r^2+α_1r)\,y''+(β_2r^2+β_1r+β_0)\,y'-(\varepsilon_1r+\varepsilon_0)\,y=0$ in $d$-dimensional space, where $\{α_i, β_i, \varepsilon_i\}$ are real parameters, is presented. With the aid of these general results, the quasi exact solvability of the Schrödinger eigenproblem generated by the softcore Coulomb potential $V(r)=-e^2Z/(r+b),\, b>0$, is explicitly resolved. Necessary and sufficient conditions for polynomial solvability are given. A three-term recurrence relation is provided to generate the coefficients of polynomial solutions explicitly. We prove that these polynomial solutions are sources of finite sequences of orthogonal polynomials. Properties such as recurrence relations, Christoffel-Darboux formulas, and the moments of the weight function are discussed. We also reveal a factorization property of these polynomials which permits the construction of other interesting related sequences of orthogonal polynomials.

math-ph↗

arXiv2018

A Note on the Generalized and Universal Associated Legendre Equations

A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated Legendre Equations are examined and established. The hypergeometric solutions, presented in this work, will promote future investigations of their mathematical properties and applications to problems in theoretical physics.

math-ph↗