# Workshops

## Improving the Theory in Density Functional Theory

### Organisers

- Attila Cangi
*(Sandia National Laboratories, USA)* - Eberhard K.U. Gross
*(Max Planck Institute of Microstructure Physics, Halle, Germany)* - Kieron Burke
*(University of California, Irvine, USA)*

### Supports

### Description

-Short description

While density functional theory (DFT) is being applied successfully in ever more areas of science [1], the theory behind it [2, 3, 4, 5] is rarely covered at sufficient depth at international conferences which are usually dominated by a plethora of applications in specific fields. The unique aim of this conference is provide an interactive venue for DFT developers for discussing (1) the theoretical developments rather than computational methods or specific applications and (2) the current theoretical challenges DFT is facing. The ultimate goal of this conference is to identify methods and approaches needed to increase the accuracy and efficiency of the current state-of-the-art and hence make DFT systematic and reliably applicable beyond its current scope.

-Target audience

Experts and junior researchers (Ph.D. students and postdocs) who currently work in methods development within DFT and related fields.

-Why CECAM/Psi-k

CECAM has often founded workshops and tutorials on various aspects of electronic structure theory. All of them proved excellent both in terms of quality and attendance. Nonetheless, usually these emphasize specific applications. We intend to complement these by focusing solely on theoretical research very similar to a few previous workshops (How to Speed Up Progress and Reduce Empiricism in Density Functional Theory, 2011, ACAM, Dublin, Ireland; Density Functional Theory: learning from the past, looking to the future, 2013, Magnus-Haus, Berlin, Germany). By offering such a conference, CECAM would actively support high quality research and facilitate the synergy of theory and computation.

-Scientific scope

The balance between low computational cost and useful (but not yet chemical) accuracy has made DFT [6, 7] and its time-dependent formulation [8] (TDDFT) a standard technique in most branches of chemistry and materials science. DFT is useful, in fact, for a dazzling variety of electronic structure problems. Furthermore, it is increasingly applied beyond its traditional scope and validity in order to solve electronic structure problems under extreme conditions [9]. However, DFT has many limitations: it requires too many approximations, it presents failures for fundamental gaps and strongly correlated systems, it is too slow for complex systems. In the following, we give a concise compilation of some these limitations.

Exchange-correlation (XC) functionals in DFT Early approximations such as the local density approximation (LDA), generalized gradient approximations [10, 11, 12, 13], and hybrid functionals[14, 15] have led to a success story. However, further progress in deriving more accurate approximations for a wider scope (such as incorporating long-range van der Waals interactions or curing the self-interaction error) has proved increasingly difficult. This has led to more empiricism in functional construction and, eventually, to a plethora of available approximations. Notwithstanding recent progress in developing more sophisticated approximations such as meta-GGAs [16], non-local functionals for van-der-Waals interactions [17, 18], range-separated hybrids [19], or functionals based on the RPA[20], a clear route for advancing the field does not exist. A striking example of the limitations of the current theory is the metallic KS ground state of strongly correlated Mott insulators. There has been some (limited) progress in the density functional description of strongly correlated lattice models [21, 22, 23, 24, 25], but it is unclear how to turn this insight into a practical density functional scheme for strongly correlated systems. Beyond its traditional scope, DFT has recently been applied to warm dense matter (WDM) [26, 27]. DFT simulations of WDM melt properties and thermal conductivities are crucial for achieving nuclear fusion under laboratory conditions [28]. Furthermore, DFT simulations of WDM can elucidate fundamental questions in planetary sciences, such as the formation processes of planets [29, 30] and the search for exoplanets [31, 32]. The main caveat in these simulations is the lack of XC approximations that properly account for temperature effects [33].

Exchange-correlation functionals in TDDFT TDDFT has been successfully applied in predicting excitation spectra of molecules and solids in the linear response regime. Also more complex time-dependent phenomena, such as matter in strong laser fields [34] and optimal control of electron (spin) dynamics [35] are continuously being explored through TDDFT. As in static DFT, the greatest challenge is the derivation of accurate approximations to the XC kernel [36, 37, 38]. Currently the standard approach is the adiabatic LDA, where the ground-state LDA functional is evaluated on time-dependent densities [39, 40]. Present limitations and further developments are needed in charge transfer excitations [41], double excitations [42], excitons[43], and alternative approximations to the XC kernel from many-body theory[44].

### References

[1] K. Burke, J. Chem. Phys. 136, 150901 (2012).

[2] R. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules, International Series of Monographs on Chemistry, Oxford University Press, USA, ISBN 9780195092769 (1994).

[3] R. Dreizler and E. Gross, Density Functional Theory: An Approach to the Quantum Many-Body Problem, Springer-Verlag, ISBN 0387519939 (1990).

[4] E. Engel and R. Dreizler, Density Functional Theory: An Advanced Course, Theoretical and Mathematical Physics, Springer, ISBN 9783642140907 (2011).

[5] C. A. Ullrich, Time-Dependent Density-Functional Theory, Concepts and Applications, Oxford University Press, USA (2012).

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

[7] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).

[8] E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).

[9] F. Graziani, M. P. Desjarlais, R. Redmer, and S. B. Trickey, editors, Frontiers and Challenges in Warm Dense Matter, volume 96 of Lecture Notes in Computational Science and Engineering, Springer International Publishing, ISBN 978-3-319-04911-3 (2014).

[10] D. Langreth and M. Mehl, Phys. Rev. B 28, 1809 (1983).

[11] A. D. Becke, Phys. Rev. A 38, 3098 (1988).

[12] C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988).

[13] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865, ibid. 78, 1396(E) (1997) (1996).

[14] C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 (1999).

[15] P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, J. Phys. Chem. 98, 11623 (1994).[16] J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003).

[17] M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004).

[18] A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. 102, 073005 (2009).

[19] R. Baer, E. Livshits, and U. Salzner, Ann. Rev. Phys. Chem. 61, 85 (2010).

[20] F. Furche and T. van Voorhis, J. Chem. Phys. 122, 164106 (2005).

[21] N. A. Lima, M. F. Silva, L. N. Oliveira, and K. Capelle, Phys. Rev. Lett. 90, 146402 (2003).

[22] S. Abedinpour, M. Polini, G. Xianlong, and M. Tosi, Eur. Phys. J. B 56 (2007).

[23] G. Stefanucci and S. Kurth, Phys. Rev. Lett. 107, 216401 (2011).

[24] J. P. Bergfield, Z.-F. Liu, K. Burke, and C. A. Stafford, Phys. Rev. Lett. 108, 066801 (2012).

[25] D. J. Carrascal and J. Ferrer, Phys. Rev. B 85, 045110 (2012).

[26] M. P. Desjarlais, Phys. Rev. B 68, 064204 (2003).

[27] B. Holst, R. Redmer, and M. P. Desjarlais, Phys. Rev. B 77, 184201 (2008).

[28] S. Atzeni and J. Meyer-ter Vehn, The Physics of Inertial Fusion: Beam-Plasma Interaction,

Hydrodynamics, Hot Dense Matter, Clarendon Press (2004).

[29] N. Nettelmann, A. Becker, B. Holst, and R. Redmer, Astrophys. J. 750, 52 (2012).

[30] N. Nettelmann, R. Helled, J. Fortney, and R. Redmer, Planet. Space Sci. 77, 143 (2013).

[31] N. Nettelmann, J. J. Fortney, U. Kramm, and R. Redmer, Astrophys. J. 733, 2 (2011).

[32] Kramm, U. Kramm, N. Nettelmann, J. J. Fortney, R. Neuhäuser, and R. Redmer, Astronomy & Astrophysics 538, 8 (2012).

[33] A. Pribram-Jones, S. Pittalis, E. Gross, and K. Burke, in F. Graziani, M. P. Desjarlais, R. Redmer, and S. B. Trickey, editors, Frontiers and Challenges in Warm Dense Matter, volume 96 of Lecture Notes in Computational Science and Engineering, pages 25-60, Springer International Publishing, ISBN 978-3-319-04911-3 (2014).

[34] M. Lein and S. Kümmel, Phys. Rev. Lett. 94, 143003 (2005).

[35] K. Yabana, T. Sugiyama, Y. Shinohara, T. Otobe, and G. F. Bertsch, Phys. Rev. B 85, 045134 (2012).

[36] E. K. U. Gross and W. Kohn, Phys. Rev. Lett. 55, 2850 (1985).

[37] G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996).

[38] G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997).

[39] P. Elliott, J. I. Fuks, A. Rubio, and N. T. Maitra, Phys. Rev. Lett. 109, 266404 (2012).

[40] J. D. Ramsden and R. W. Godby, Phys. Rev. Lett. 109, 036402 (2012).

[41] T. Stein, L. Kronik, and R. Baer, J. Am. Chem. Soc. 131, 2818, pMID: 19239266 (2009).

[42] N. T. Maitra, F. Zhang, R. J. Cave, and K. Burke, J. Chem. Phys. 120, 5932 (2004).

[43] S. Sharma, J. K. Dewhurst, A. Sanna, and E. K. U. Gross, Phys. Rev. Lett. 107, 186401 (2011).

[44] L. Reining, V. Olevano, A. Rubio, and G. Onida, Phys. Rev. Lett. 88, 066404 (2002).