WORKSHOP
"The determination of Hubbard parameters: progress, pitfalls, and prospects"
22 - 26 September 2025, Gandia (Spain)

Density-functional theory (DFT) [1,2] serves as a fundamental tool in physics, chemistry, and materials science. In practice, it is used with approximate exchange-correlation functionals such as e.g. local density approximation (LDA) and generalized gradient approximation (GGA) which, however, suffer from large self-interaction errors in transition-metal and rare-earth compounds containing partially filled d and f electrons (leading to their overdelocalization). To address this issue, many other more advanced functionals have been developed (e.g. hybrids, meta-GGA, to name a few), among which DFT with the on-site Hubbard U correction (DFT+U) [3-6] stands out as particularly attractive option due to a good compromise between the computational cost and accuracy. Historically, DFT+U was devised by combining DFT with the Hubbard model [3], with the U correction assumed to treat strong correlations, though subsequently it was realized that it actually cures self-interactions [7,8]. Furthermore, more recently DFT+U has been reevaluated as a means to restore the flat-plane condition of the functional [9,10]. 

Despite the significant successes of DFT+U, a critical challenge remains - the determination of the U parameter, which is not known a priori. Approaches to determining U can be classified into two categories: i) empirical calibration based on experimental data, and ii) first-principles calculations. The former approach relies on experimental information, which may not always be available and detracts from the fully ab initio nature of the DFT+U method. Conversely, the latter approach holds great appeal as it requires no input from experiments, with various theories proposed for defining and computing U. Notable among these are constrained DFT [11], linear-response theory [12,13], constrained random phase approximation [14], and Hartree-Fock-based methods [15,16]. In recent years, machine learning methods have also gained popularity for determining U based on experimental data or other advanced functionals such as hybrids [17,18]. Additionally, the calculation of other parameters, such as inter-site V [19-21] and Hund's J [22], has garnered increased attention. However, each of these theories and techniques features distinct definitions of Hubbard parameters, leading to variations in their values. Consequently, a broad range of Hubbard parameter values exists in the literature, often resulting in contradictory outcomes of DFT+U calculations compared to both other studies and experimental data.

Therefore, it is imperative to address these discrepancies and establish a common framework for understanding the physical and theoretical foundations of Hubbard parameters. This workshop aims to bring together experts in the field of DFT+U to comprehensively survey and compare diverse methods for determining Hubbard parameters. By identifying similarities, differences, advantages, and limitations, the workshop seeks to facilitate a deeper understanding of these parameters and develop strategies and best practices to achieve consistency and reliability in their determination.

The anticipated outcomes of the workshop are substantial and wide-ranging. Participants will gain an enhanced understanding of the various methods for computing Hubbard parameters, enabling informed decision-making and driving scientific advancements in materials design and characterization. By comparing different approaches, commonalities and divergences will be identified, fostering consensus and encouraging the development of standardized protocols for determining Hubbard parameters.

References

[1] P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964).

[2] W. Kohn, L. Sham, Phys. Rev. 140, A1133 (1965).

[3] V. Anisimov, J. Zaanen, O. Andersen, Phys. Rev. B 44, 943 (1991).

[4] V. Anisimov, F. Aryasetiawan, A. Lichtenstein, J. Phys.: Condens. Matter 9, 767 (1997).

[5] S. Dudarev, G. Botton, S. Savrasov, C. Humphreys, A. Sutton, Phys. Rev. B 57, 1505 (1998).

[6] B. Himmetoglu, A. Floris, S. de Gironcoli, M. Cococcioni, Int. J. Quantum Chem. 114, 14 (2013).

[7] H. Kulik, N. Marzari, The Journal of Chemical Physics 129, 134314 (2008).

[8] A. Cohen, P. Mori-Sánchez, W. Yang, Science 321, 792 (2008).

[9] A. Bajaj, J. Janet, H. Kulik, The Journal of Chemical Physics 147, 191101 (2017).

[10] A. Burgess, E. Linscott, D. O'Regan, Phys. Rev. B 107, L121115 (2023).

[11] O. Gunnarsson, O. Andersen, O. Jepsen, J. Zaanen, Phys. Rev. B 39, 1708 (1989).

[12] M. Cococcioni, S. de Gironcoli, Phys. Rev. B 71, 035105 (2005).

[13] I. Timrov, N. Marzari, M. Cococcioni, Phys. Rev. B 98, 085127 (2018).

[14] F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, A. Lichtenstein, Phys. Rev. B 70, 195104 (2004).

[15] N. Mosey, E. Carter, Phys. Rev. B 76, 155123 (2007).

[16] L. Agapito, S. Curtarolo, M. Buongiorno Nardelli, Phys. Rev. X 5, 011006 (2015).

[17] M. Yu, S. Yang, C. Wu, N. Marom, npj. Comput. Mater. 6, 180 (2020).

[18] P. Tavadze, R. Boucher, G. Avendaño-Franco, K. Kocan, S. Singh, V. Dovale-Farelo, W. Ibarra-Hernández, M. Johnson, D. Mebane, A. Romero, npj. Comput. Mater. 7, 182 (2021).

[19] V. Leiria Campo Jr, M. Cococcioni, J. Phys.: Condens. Matter. 22, 055602 (2010).

[20] N. Tancogne-Dejean, A. Rubio, Phys. Rev. B 102, 155117 (2020).

[21] S. Lee, Y. Son, Phys. Rev. Research 2, 043410 (2020).

[22] E. Linscott, D. Cole, M. Payne, D. O'Regan, Phys. Rev. B 98, 235157 (2018).

 OBJECTIVES

• To comprehensively survey and compare diverse methods employed to compute Hubbard U, including but not limited to linear-response theory (LRT), constrained random phase approximation (cRPA), Hartree-Fock based methods, and emerging machine learning approaches.

• To identify the underlying similarities, differences, advantages, and limitations of each method from a fundamental standpoint.

• To establish a common framework for understanding the physical and theoretical foundations of onsite Hubbard U, inter-site Hubbard V, and onsite Hund's J.

• To propose strategies and best practices for achieving consistency and reliability in the computation of Hubbard parameters, thereby reducing the spread of data arising from methodological variations.

OUTCOMES AND IMPACT

• Enhanced understanding: Participants will gain a comprehensive understanding of the various methods for computing Hubbard U, facilitating informed decision-making and promoting scientific advancements in materials design and characterization.

• Methodological convergence: By comparing different approaches, we will identify commonalities and divergences, thereby fostering consensus and encouraging the development of standardized protocols for determining Hubbard parameters.

• Research collaboration: The workshop will cultivate a network of researchers, fostering collaborations that extend beyond the event itself and leading to future joint projects and publications.

• Community building: This workshop will contribute to building a strong and interconnected community of researchers working in the field of DFT+U, facilitating continued knowledge exchange and collaboration in the years to come.

SPONSORS