Kieron Burke’s research while affiliated with University of California, Irvine and other places

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Publications (366)


Extending Density-Corrected Density Functional Theory to Large Molecular Systems
  • Article

January 2025

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10 Reads

The Journal of Physical Chemistry Letters

Youngsam Kim

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Mingyu Sim

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Minhyeok Lee

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[...]

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Extending Density-Corrected Density Functional Theory to Large Molecular Systems

October 2024

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11 Reads

Practical density-corrected density functional theory (DC-DFT) calculations rely on Hartree-Fock (HF) densities, which can be computationally expensive for systems with over a hundred atoms. We extend the applicability of HF-DFT using the dual-basis method, where the density matrix from a smaller basis set is used to estimate the HF solution on a larger basis set. Benchmarks on many systems, including the GMTKN55 database for main-group chemistry, and the L7 and S6L datasets for large molecular systems demonstrate the efficacy of our approach. We apply the dual-basis method to both DNA and HIV systems, and compare with the literature. A careful reparameterisation of HF-r2SCAN-DC4 eliminates the negative s8 coefficient, with no loss of performance.


Exchange-Correlation Energy from Green’s Functions

August 2024

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54 Reads

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2 Citations

Physical Review Letters

Density-functional theory (DFT) calculations yield useful ground-state energies and densities, while Green’s function techniques (such as GW) are mostly used to produce spectral functions. From the Galitskii-Migdal formula, we extract the exchange correlation of DFT directly from a Green’s function. This spectral representation provides an alternative to the fluctuation-dissipation theorem of DFT, identifying distinct single-particle and many-particle contributions. Results are illustrated on the uniform electron gas and the two-site Hubbard model.



Orbital-free potential functionals with submillihartree errors for single-well slabs

May 2024

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6 Reads

Using principles of asymptotic analysis, we derive the exact leading corrections to the Thomas-Fermi kinetic energy approximation for Kohn-Sham electrons for slabs. This asymptotic expansion approximation includes crucial quantum oscillations missed by standard semilocal density functionals. Because these account for the derivative discontinuity, chemical accuracy is achieved at fourth order. The implications for both orbital-free electronic structure and exchange-correlation approximations are discussed.


Correcting dispersion corrections with density-corrected DFT

May 2024

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14 Reads

Almost all empirical parameterizations of dispersion corrections in DFT use only energy errors, thereby mixing functional and density-driven errors. We introduce density and dispersion-corrected DFT (D2C-DFT), a dual-calibration approach that accounts for density delocalization errors when parametrizing dispersion interactions. We simply exclude density-sensitive reactions from the training data. We find a significant reduction in both errors and variation among several semilocal functionals and their global hybrids when tailored dispersion corrections are employed with Hartree-Fock densities.


Exact conditions for ensemble density functional theory

May 2024

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9 Reads

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6 Citations

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.


Exchange energy per electron vs nuclear charge Z for neutral atoms up to Z = 120, exactly (black), within LDA (blue), and with PBE (red). The leading-order term in the large-Z expansion, Dirac exchange applied to the TF density, is shown with a violet dotted-dashed line.
Asymptotic residual of exchange. It shows what is left over of the exchange energy/particle when the leading term in the asymptotic expansion for exchange −(9/11)0.2699Z2/3 is removed. The OEP data from opmks, the LDA, B88 exchange, and PBE are shown. The line at zero gives the Thomas–Fermi limit of the exchange energy. The vertical lines show the location of each atom with a filled s² valence shell (He and the alkali earths).
Difference with LDA or beyond-LDA exchange energy per electron. The details are the same as in Figs. 1 and 2.
Beyond-LDA exchange energies per electron. OEP is the optimized effective potential; the other three curves are fits to various asymptotic models as described in the text. OEP data used to make the fits are highlighted in red.
Extrapolation of beyond-LDA exchange energies per electron to the Z → ∞ limit for OEP data and several common GGAs. The y axis intercept yields the coefficient ΔBX. PBEsol is included as a proxy for the gradient expansion. The black line is the semi-theoretical result of Ref. 21, while the other straight lines are fit to DFT models for Z > 259. Green dots are calculated theoretical limits of each model and the OEP.

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Investigations of the exchange energy of neutral atoms in the large-Z limit
  • Article
  • Publisher preview available

January 2024

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38 Reads

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3 Citations

The non-relativistic large-Z expansion of the exchange energy of neutral atoms provides an important input to modern non-empirical density functional approximations. Recent works report results of fitting the terms beyond the dominant term, given by the local density approximation (LDA), leading to an anomalous Z ln Z term that cannot be predicted from naïve scaling arguments. Here, we provide much more detailed data analysis of the mostly smooth asymptotic trend describing the difference between exact and LDA exchange energy, the nature of oscillations across rows of the Periodic Table, and the behavior of the LDA contribution itself. Special emphasis is given to the successes and difficulties in reproducing the exchange energy and its asymptotics with existing density functional approximations.

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The difference between molecules and materials: Reassessing the role of exact conditions in density functional theory

December 2023

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163 Reads

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11 Citations

Exact conditions have long been used to guide the construction of density functional approximations. However, hundreds of empirical-based approximations tailored for chemistry are in use, of which many neglect these conditions in their design. We analyze well-known conditions and revive several obscure ones. Two crucial distinctions are drawn: that between necessary and sufficient conditions and that between all electronic densities and the subset of realistic Coulombic ground states. Simple search algorithms find that many empirical approximations satisfy many exact conditions for realistic densities and non-empirical approximations satisfy even more conditions than those enforced in their construction. The role of exact conditions in developing approximations is revisited.



Citations (52)


... For example, in [21], the authors calculated the photoemission spectra coupling the one-body Green's function with the three-body one, and applied their approach to the Hubbard dimer. In [22] Crisostomo and coworkers put forward an original approach to extract the exchangecorrelation energy of DFT from the Galitskii-Migdal formula, which is based on many-body Green's functions, and test it both on the Hubbard dimer and the HEG. Finally, in [23], the authors investigated the performance of the GW approximation for the challenging case of very simple multireference systems, where strong electronic correlation plays a crucial role. ...

Reference:

Potential energy surfaces from many-body functionals: Analytical benchmarks and conserving many-body approximations
Exchange-Correlation Energy from Green’s Functions
  • Citing Article
  • August 2024

Physical Review Letters

... Furthermore, the parallel-displaced benzene dimer 65 is included in this set of complexes, making it an interesting modeling challenge. Such a dataset has been pivotal towards benchmarking [66][67][68][69][70][71][72][73][74] DFAs in DFT as well as lower-level approximations to wave-function methods 56,[75][76][77][78][79][80] and even machine-learning models. 81,82 In this work, we leverage the latest developments in DMC to compute interaction energies for the entire S66 dataset. ...

Correcting Dispersion Corrections with Density-Corrected DFT
  • Citing Article
  • August 2024

Journal of Chemical Theory and Computation

... From a practical perspective, our work is motivated by the growing interest in reduced density matrix methods for targeting excited states using a distinctive ensemble variational principle [7,8]. Specifically, we demonstrate that solving the spin-symmetry-adapted ensemble N -representability problem provides a compact and rigorous characterization of the yet-unknown domain of universal interaction functionals in the rapidly evolving field of ensemble density functional theory (EDFT) [9][10][11][12][13][14][15][16][17][18][19] and ensemble one-particle reduced density matrix functional theory (w-RDMFT) [20][21][22][23]. In this context, our work addresses a critical gap, providing a foundational cornerstone for the advancement of these ensemble-based methodologies. ...

Exact conditions for ensemble density functional theory
  • Citing Article
  • May 2024

... where the relation between N and M was given above in (6). Note that while the F M , G M are obtained here for any M ≥ 1, the F N , G N are obtained only for the specific values of N corresponding to filled shells (the full dependence in N ≥ 1 may be much more complex [31,45] and is out of reach at present). Note that Q(z 1 , z 2 ) contains the information both about the direct term and the exchange term, hence we will obtain F M and G M from a single calculation of Q(z 1 , z 2 ). ...

Investigations of the exchange energy of neutral atoms in the large-Z limit

... Non-empirically designed DFAs are constructed to satisfy some exact conditions, which are known analytical properties of the exact functional (Section II). For example, the correlation energy E C non-positivity condition states that the correlation energy cannot be positive, i.e., E c [n] ≤ 0 [28]. Furthermore, so-called norms are imposed on DFAs by requiring that they reproduce correctly some known physical systems, e.g. a hydrogen or a helium atom for which exact results are available. ...

The difference between molecules and materials: Reassessing the role of exact conditions in density functional theory
  • Citing Article
  • December 2023

... The latter arises in "abnormal" systems 22 , where the density is particularly sensitive to changes in v xc (r), giving rise to large errors in the density, which are only further exacerbated by the self-consistent cycle. In such instances, the use of the Hartree-Fock (HF) density in a non-self-consistent manner can give improved total energies such as in water clusters [28][29][30][31][32] . ...

Density-Corrected Density Functional Theory for Open Shells: How to Deal with Spin Contamination
  • Citing Article
  • October 2023

The Journal of Physical Chemistry Letters

... Since this expectation value of the coupling is also the integrand in the adiabatic connection, Eq. (37), it is interesting to compare this plot to other DFT settings, where an unproven conjecture says that such adiabatic-connection curves must always be convex, see e.g. [67,Section 3]. While this conjecture was formulated for usual particle interactions, it clearly does not hold in case of the quantum Rabi model as shown in Fig. 9 (top panel). ...

Seven useful questions in density functional theory

Letters in Mathematical Physics

... Moreover, by including interaction effects in a non-perturbative way this MB Weyl appraoch has further been extended to systems of experimental relevance in cold atom physics, such as interacting bosons in traps, demonstrating for instance that systems with very few up to many particles share the same underlying spectral features [76]. We believe that such underlying MB scaling laws have much in common with related semiclassical scalings in recent generalizations of Thomas-Fermi theory [80]. ...

SEMICLASSICS: THE HIDDEN THEORY BEHIND THE SUCCESS OF DFT
  • Citing Chapter
  • February 2023

Lecture Notes Series

... Interestingly, the meta-GGA or hybrid levels of theory do not consistently perform better. For example, the overbinding of dispersion-corrected SCAN for water has already been noted before.81 From this cluster benchmark, the most appropriate reference level of theory appears to be rPBE-D3(BJ), with an error of 2.4 kJ/mol on the framework−water interaction of −103.52 kJ/mol and a mean error on the water−water interactions of −0.87 kJ/mol per molecule. ...

Extending density functional theory with near chemical accuracy beyond pure water