arXiv subjects

John Kozlowski

Publications and source records attributed to John Kozlowski.

6 recordsLinked to original sources

arXiv2023

Generalized Gradient Approximation Made Thermal

Using the methodology of conditional-probability density functional theory, and several mild assumptions, we calculate the temperature-dependence of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA). This numerically-defined thermal GGA reduces to the local approximation in the uniform limit and PBE at zero temperature, and can be fit reasonably accurately (within 8%) assuming the temperature-dependent enhancement is independent of the gradient. This locally thermal PBE satisfies both the coordinate-scaled correlation inequality and the concavity condition, which we prove for finite temperatures. The temperature dependence differs markedly from existing thermal GGA's.

physics.chem-ph↗

arXiv2023

Exact Conditions for Ensemble Density Functional Theory

Ensemble density functional theory (EDFT) is a promising alternative to time-dependent density functional theory for computing electronic excitation energies. Using coordinate scaling, we prove several fundamental exact conditions in EDFT and illustrate them on the exact singlet bi-ensemble of the Hubbard dimer. Several approximations violate these conditions, and some ground-state conditions from quantum chemistry do not generalize to EDFT. The strong-correlation limit is derived for the dimer, revealing weight-dependent derivative discontinuities in EDFT.

cond-mat.str-el↗

arXiv2023

Seven Useful Questions in Density Functional Theory

We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and why progress toward resolving them would help those doing computations using density functional theory. Subjects covered include the magnitude of the kinetic energy in Hartree-Fock calculations, the shape of adiabatic connection curves, using the constrained search with input densities, densities of states, the semiclassical expansion of energies, the tightness of Lieb-Oxford bounds, and how we decide the accuracy of an approximate density.

math-ph↗

arXiv2022

Large scale quantum chemistry with Tensor Processing Units

We demonstrate the use of Google's cloud-based Tensor Processing Units (TPUs) to accelerate and scale up conventional (cubic-scaling) density functional theory (DFT) calculations. Utilizing 512 TPU cores, we accomplish the largest such DFT computation to date, with 247848 orbitals, corresponding to a cluster of 10327 water molecules with 103270 electrons, all treated explicitly. Our work thus paves the way towards accessible and systematic use of conventional DFT, free of any system-specific constraints, at unprecedented scales.

physics.comp-ph↗

arXiv2022

Lies My Teacher Told Me About Density Functional Theory: Seeing Through Them with the Hubbard Dimer

Most realistic calculations of moderately correlated materials begin with a ground-state density functional theory (DFT) calculation. While Kohn-Sham DFT is used in about 40,000 scientific papers each year, the fundamental underpinnings are not widely appreciated. In this chapter, we analyze the inherent characteristics of DFT in their simplest form, using the asymmetric Hubbard dimer as an illustrative model. We begin by working through the core tenets of DFT, explaining what the exact ground-state density functional yields and does not yield. Given the relative simplicity of the system, almost all properties of the exact exchange-correlation functional are readily visualized and plotted. Key concepts include the Kohn-Sham scheme, the behavior of the XC potential as correlations become very strong, the derivative discontinuity and the difference between KS gaps and true charge gaps, and how to extract optical excitations using time-dependent DFT. By the end of this text and accompanying exercises, the reader will improve their ability to both explain and visualize the concepts of DFT, as well as better understand where others may go wrong.

cond-mat.str-el↗

arXiv2019

Density functional analysis: The theory of density-corrected DFT

Density-corrected density functional theory (DC-DFT) is enjoying substantial success in improving semilocal DFT calculations in a wide variety of chemical problems. This paper provides the formal theoretical framework and assumptions for the analysis of any functional minimization with an approximate functional. We generalize DC-DFT to allow comparison of any two functionals, not just comparison with the exact functional. We introduce a linear interpolation between any two approximations, and use the results to analyze global hybrid density functionals. We define the basins of density-space in which this analysis should apply, and give quantitative criteria for when DC-DFT should apply. We also discuss the effects of strong correlation on density-driven error, utilizing the restricted HF Hubbard dimer as an illustrative example.

physics.chem-ph↗