Skip to main content
SpringerLink
Log in

Reliability and performances of real-time time-dependent auxiliary density functional theory

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

We recently adapted the Auxiliary DFT framework as implemented in deMon2k to the simulation of time-dependent problems via the Runge and Gross equations. Our implementation of the so-called Real-Time-Time-Dependent ADFT (RT-TD-ADFT) fully benefits from the algorithms available in deMon2k to carry out variational density fitting, notably the MINRES algorithm recently proposed for self-consistent-field calculations. We test here MINRES for the first time in the context of RT-TD-ADFT. We report extensive benchmarks calculations to assess the reliability of the ADFT framework. These encompass the construction of absorption spectra in the gas phase and in solvent, the calculation of electronic stopping power curves, the irradiation of zeolites by swift ions and the investigation of charge migrations with attosecond time resolution. All our results are very encouraging. We show that even small auxiliary basis sets are sufficient to obtain results almost undisguisable from those obtained with large and flexible auxiliary bases. Overall, we establish the reliability of RT-TD-ADFT to simulate electronics dynamics in large or very large molecular systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Andrade X, Strubbe D, De Giovannini U, Larsen AH, Oliveira MJT, Alberdi-Rodriguez J, Varas A, Theophilou I, Helbig N, Verstraete MJ, Stella L, Nogueira F, Aspuru-Guzik A, Castro A, Marques MAL, Rubio A (2015) Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems. Phys Chem Chem Phys 17:31371–31396. https://doi.org/10.1039/C5CP00351B

    Article  CAS  PubMed  Google Scholar 

  2. Wopperer P, Dinh PM, Reinhard PG, Suraud E (2015) Electrons as probes of dynamics in molecules and clusters: a contribution from time dependent density functional theory. Phys Rep 562:1–68. https://doi.org/10.1016/j.physrep.2014.07.003

    Article  CAS  Google Scholar 

  3. Runge E, Gross EKU (1984) Density-functional theory for time-dependent systems. Phys Rev Lett 52:997–1000. https://doi.org/10.1103/PhysRevLett.52.997

    Article  CAS  Google Scholar 

  4. Casida ME (1995) Time-dependent density functional response theory for molecules. In: Recent advances in density functional methods. World Scientific, pp 155–192

  5. Yabana K, Bertsch GF (1996) Time-dependent local-density approximation in real time. Phys Rev B 54:4484–4487. https://doi.org/10.1103/PhysRevB.54.4484

    Article  CAS  Google Scholar 

  6. Calvayrac F, Reinhard PG, Suraud E (1995) Nonlinear plasmon response in highly excited metallic clusters. Phys Rev B 52:R17056–R17059. https://doi.org/10.1103/PhysRevB.52.R17056

    Article  CAS  Google Scholar 

  7. Schleife A, Draeger EW, Anisimov VM, Correa AA, Kanai Y (2014) Quantum dynamics simulation of electrons in materials on high-performance computers. Comput Sci Eng 16:54–60. https://doi.org/10.1109/MCSE.2014.55

    Article  Google Scholar 

  8. Tavernelli I, Röhrig UF, Rothlisberger U (2005) Molecular dynamics in electronically excited states using time-dependent density functional theory. Mol Phys 103:963–981. https://doi.org/10.1080/00268970512331339378

    Article  CAS  Google Scholar 

  9. Li X, Smith SM, Markevitch AN, Romanov DA, Levis RJ, Schlegel HB (2005) A time-dependent Hartree-Fock approach for studying the electronic optical response of molecules in intense fields. Phys Chem Chem Phys 7:233–239. https://doi.org/10.1039/b415849k

    Article  CAS  PubMed  Google Scholar 

  10. Lopata K, Govind N (2011) Modeling fast electron dynamics with real-time time-dependent density functional theory: application to small molecules and chromophores. J Chem Theor Comput 7:1344–1355. https://doi.org/10.1021/ct200137z

    Article  CAS  Google Scholar 

  11. Maliyov I, Crocombette J-P, Bruneval F (2018) Electronic stopping power from time-dependent density-functional theory in Gaussian basis. Eur Phys J B 91:172. https://doi.org/10.1140/epjb/e2018-90289-y

    Article  CAS  Google Scholar 

  12. Nguyen TS, Parkhill J (2015) Nonadiabatic dynamics for electrons at second-order: real-time TDDFT and OSCF2. J Chem Theor Comput 11:2918–2924. https://doi.org/10.1021/acs.jctc.5b00262

    Article  CAS  Google Scholar 

  13. Li X, Govind N, Isborn C, DePrince AE, Lopata K (2020) Real-time time-dependent electronic structure theory. Chem Rev 120:9951–9993. https://doi.org/10.1021/acs.chemrev.0c00223

    Article  CAS  PubMed  Google Scholar 

  14. Valiev M, Bylaska EJ, Govind N, Kowalski K, Straatsma TP, Van Dam HJJ, Wang D, Nieplocha J, Apra E, Windus TL, de Jong WA (2010) NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations. Comput Phys Commun 181:1477–1489. https://doi.org/10.1016/j.cpc.2010.04.018

    Article  CAS  Google Scholar 

  15. Dunlap BI, Rösch N, Trickey SB (2010) Variational fitting methods for electronic structure calculations. Mol Phys 108:3167–3180. https://doi.org/10.1080/00268976.2010.518982

    Article  CAS  Google Scholar 

  16. Köster AM, Geudtner G, Álvarez-Ibarra A, Calaminici P, Casida ME, Carmona-Espíndola J, Delesma FA, Delgado-Venegas R, Domínguez VD, Flores-Moreno R, Gamboa GU, Goursot A, Heine Th, Ipatov A, de la Lande A, Janetzko F, Martín del Campo J, Pedroza-Montero, JN, Petterson LGM, Mejía-Rodríguez D, Reveles J, Vásquez-Pérez J, Vela A, Zúñiga-Gutiérrez B, Salahub DR (2020) deMon2k. Mexico City

  17. Wu X, Teuler J-M, Cailliez F, Clavaguéra C, Salahub DR, de la Lande A (2017) Simulating electron dynamics in polarizable environments. J Chem Theory Comput 13:3985–4002. https://doi.org/10.1021/acs.jctc.7b00251

    Article  CAS  PubMed  Google Scholar 

  18. Köster AM, Reveles JU, del Campo JM (2004) Calculation of exchange-correlation potentials with auxiliary function densities. J Chem Phys 121:3417–3424. https://doi.org/10.1063/1.1771638

    Article  CAS  PubMed  Google Scholar 

  19. Mejía-Rodríguez D, Trickey SB (2021) Variational properties of auxiliary density functionals. Theoret Chem Acc 140:37. https://doi.org/10.1007/s00214-021-02731-2

    Article  CAS  Google Scholar 

  20. Calaminici P, Alvarez-Ibarra A, Cruz-Olvera D, Dominguez-Soria V-D, Flores-Moreno R, Gamboa GU, Geudtner G, Goursot A, Mejia-Rodriguez D, Salahub DR, Zuniga-Gutierrez B, Koster A (2016) Auxiliary density functional theory: from molecules to nanostructures. In: Leszczynski J (ed) Handbook of computational chemistry. Springer, Netherlands, Dordrecht, pp 1–67

    Google Scholar 

  21. Alvarez-Ibarra A, Köster AM (2013) Double asymptotic expansion of three-center electronic repulsion integrals. J Chem Phys 139:024102. https://doi.org/10.1063/1.4812183

    Article  CAS  PubMed  Google Scholar 

  22. Pedroza-Montero JN, Morales JL, Geudtner G, Álvarez-Ibarra A, Calaminici P, Köster AM (2020) Variational density fitting with a Krylov subspace method. J Chem Theory Comput 16:2965–2974. https://doi.org/10.1021/acs.jctc.9b01212

    Article  CAS  PubMed  Google Scholar 

  23. Domínguez-Soria VD, Geudtner G, Morales JL, Calaminici P, Köster AM (2009) Robust and efficient density fitting. J Chem Phys 131:124102. https://doi.org/10.1063/1.3216476

    Article  CAS  PubMed  Google Scholar 

  24. Alvarez-Ibarra A, Parise A, Hasnaoui K, de la Lande A (2020) The physical stage of radiolysis of solvated DNA by high-energy-transfer particles: insights from new first principles simulations. Phys Chem Chem Phys 22:7747–7758. https://doi.org/10.1039/D0CP00165A

    Article  CAS  PubMed  Google Scholar 

  25. Li X, Tully JC, Schlegel HB, Frisch MJ (2005) Ab initio ehrenfest dynamics. J Chem Phys 123:084106. https://doi.org/10.1063/1.2008258

    Article  CAS  PubMed  Google Scholar 

  26. Magnus W (1954) On the exponential solution of differential equations for a linear operator. Commun Pure App Math 7:649–673. https://doi.org/10.1002/cpa.3160070404

    Article  Google Scholar 

  27. Köster AM, Flores-Moreno R, Reveles JU (2004) Efficient and reliable numerical integration of exchange-correlation energies and potentials. J Chem Phys 121:681–690

    Article  Google Scholar 

  28. Mintmire JW, Dunlap BI (1982) Fitting the Coulomb potential variationally in linear-combination-of-atomic-orbitals density-functional calculations. Phys Rev A 25:88–95

    Article  CAS  Google Scholar 

  29. Broyden CG (1970) The convergence of a class of double-rank minimization algorithms 1. General considerations. IMA J Appl Math 6:76–90. https://doi.org/10.1093/imamat/6.1.76

    Article  Google Scholar 

  30. Broyden CG (1970) The convergence of a class of double-rank minimization algorithms: 2. The new algorithm. IMA J Appl Math 6:222–231. https://doi.org/10.1093/imamat/6.3.222

    Article  Google Scholar 

  31. Fletcher R (1970) A new approach to variable metric algorithms. Comput J 13:317–322. https://doi.org/10.1093/comjnl/13.3.317

    Article  Google Scholar 

  32. Pedroza-Montero JN, Delesma FA, Morales JL, Calaminici P, Köster AM (2020) Variational fitting of the Fock exchange potential with modified Cholesky decomposition. J Chem Phys 153:134112. https://doi.org/10.1063/5.0020084

    Article  CAS  PubMed  Google Scholar 

  33. Mejía-Rodríguez D, Köster AM (2014) Robust and efficient variational fitting of Fock exchange. J Chem Phys 141:124114

    Article  Google Scholar 

  34. Delesma FA, Geudtner G, Mejía-Rodríguez D, Calaminici P, Köster AM (2018) Range-separated hybrid functionals with variational fitted exact exchange. J Chem Theor Comput 14:5608–5616. https://doi.org/10.1021/acs.jctc.8b00436

    Article  CAS  Google Scholar 

  35. R Development Core Team (2012) R: a language and environment for statistical computing. R foundation for statistical computing, Vienna, Austria. http://www.R-project.org/

  36. Köster AM (2003) Hermite Gaussian auxiliary functions for the variational fitting of the Coulomb potential in density functional methods. J Chem Phys 118:9943–9951

    Article  Google Scholar 

  37. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868

    Article  CAS  Google Scholar 

  38. Blackford LS, Choi J, Cleary AJ, D’Azevedo EF, Demmel J, Dhillon IS, Dongarra J, Hammarling S, Henry G, Petitet A, Stanley K, Walker DW, Whaley RC (1997) ScaLAPACK: a linear algebra library for message-passing computers. https://www.osti.gov/servlets/purl/468499

  39. Köster AM, del Campo JM, Janetzko F, Zuniga-Gutierrez B (2009) A MinMax self-consistent-field approach for auxiliary density functional theory. J Chem Phys 130:114106. https://doi.org/10.1063/1.3080618

    Article  CAS  PubMed  Google Scholar 

  40. Calaminici P, Janetzko F, Köster AM, Mejia-Olvera R, Zuniga-Gutierrez B (2007) Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems. J Chem Phys 126:044108

    Article  Google Scholar 

  41. Calaminici P, Flores-Moreno R, Köster AM (2005) A density functional study of structures and vibrations of Ta3O and Ta3O−. Comput Lett 1:164–171. https://doi.org/10.1163/157404005776611420

    Article  CAS  Google Scholar 

  42. de la Lande A, Köster AM, Denisov S, Mostafavi M (2021) The mystery of sub-picosecond charge transfer following irradiation of hydrated uridine monophosphate (Under review)

  43. Maliyov I, Crocombette J-P, Bruneval F (2020) Quantitative electronic stopping power from localized basis set. Phys Rev B 101:035136. https://doi.org/10.1103/PhysRevB.101.035136

    Article  CAS  Google Scholar 

  44. Berstis L, Beckham GT, Crowley MF (2015) Electronic coupling through natural amino acids. J Chem Phys 143:225102. https://doi.org/10.1063/1.4936588

    Article  CAS  PubMed  Google Scholar 

  45. Řezáč J, Lévy B, Demachy I, de la Lande A (2012) Robust and efficient constrained DFT molecular dynamics approach for biochemical modeling. J Chem Theor Comput 8:418–427. https://doi.org/10.1021/ct200570u

    Article  CAS  Google Scholar 

  46. Cheng C-L, Evans JS, Van Voorhis T (2006) Simulating molecular conductance using real-time density functional theory. Phys Rev B 74:155112

    Article  Google Scholar 

Download references

Acknowledgements

We are grateful to Fabien Bruneval and Ivan Maliyov for providing us with the structure of the Lithium system, to Tzonka Mineva for the zeolite coordinates and to Laura Berstis for the peptide coordinate. This work was supported by the Agence nationale de la Recherche scientifique (Project RUBI, Number: ANR-19-CE29-0011-01). This work was performed using HPC resources from the GENCI (CINES/IDRIS, Grant No. 2020- A0080806830).

Author information

Authors and Affiliations

  1. Institut de Chimie Physique, CNRS, Université Paris Saclay, Orsay, France

    Rika Tandiana, Carine Clavaguéra & Aurélien de la Lande

  2. Institut du Développement et des Ressources en Informatique Scientifique (IDRIS), High Performance Computing User Support Team, 91403, Orsay, France

    Karim Hasnaoui

  3. Maison de la Simulation, CNRS, Commissariat à l’Energie Atomique Et aux Énergies Alternatives (CEA), Université Paris-Saclay, 91191, Gif-sur-Yvette, France

    Karim Hasnaoui

  4. Programa de Doctorado en Nanociencias y Nanotecnologías, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Mexico City, Mexico

    Jesús Naín Pedroza-Montero

Authors
  1. Rika Tandiana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carine Clavaguéra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Karim Hasnaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jesús Naín Pedroza-Montero
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Aurélien de la Lande
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aurélien de la Lande.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Published as part of the special collection of articles “20th deMon Developers Workshop”.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tandiana, R., Clavaguéra, C., Hasnaoui, K. et al. Reliability and performances of real-time time-dependent auxiliary density functional theory. Theor Chem Acc 140, 126 (2021). https://doi.org/10.1007/s00214-021-02819-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-021-02819-9

Keywords

Search

Navigation