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Ab initio electron-lattice downfolding: potential energy landscapes, anharmonicity, and molecular dynamics in charge density wave materials

by Arne Schobert, Jan Berges, Erik G. C. P. van Loon, Michael A. Sentef, Sergey Brener, Mariana Rossi, Tim O. Wehling

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Submission summary

Authors (as registered SciPost users): Jan Berges · Mariana Rossi · Arne Schobert · Erik van Loon
Submission information
Preprint Link:  (pdf)
Date submitted: 2023-08-08 06:12
Submitted by: Schobert, Arne
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


The interplay of electronic and nuclear degrees of freedom presents an outstanding problem in condensed matter physics and chemistry. Computational challenges arise especially for large systems, long time scales, in nonequilibrium, or in systems with strong correlations. In this work, we show how downfolding approaches facilitate complexity reduction on the electronic side and thereby boost the simulation of electronic properties and nuclear motion - in particular molecular dynamics (MD) simulations. Three different downfolding strategies based on constraining, unscreening, and combinations thereof are benchmarked against full density functional calculations for selected charge density wave (CDW) systems, namely 1H-TaS$_2$, 1T-TiSe$_2$, 1H-NbS$_2$, and a one-dimensional carbon chain. We find that the downfolded models can reproduce potential energy surfaces on supercells accurately and facilitate computational speedup in MD simulations by about five orders of magnitude in comparison to purely ab initio calculations. For monolayer 1H-TaS$_2$ we report classical replica exchange and quantum path integral MD simulations, revealing the impact of thermal and quantum fluctuations on the CDW transition.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2023-10-21 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2303.07261v2, delivered 2023-10-21, doi: 10.21468/SciPost.Report.7981


1. Well-written
2. Excellent implementation
3. Accurate and efficient methodology


More applications regarding the temperature-dependent effect of the CDW on the electronic structure? (and some other minor points in the report)


n this work, Schobert et al performed an interesting study on CDW systems for exploring anharmonic potential energy surfaces accurately and efficiently using downfolded models to DFT and ab initio MD. They studied three different downfolding strategies and considered four different systems (1H-TaS 2 , 1T-TiSe 2 , 1H-NbS 2 , and a carbon chain) to find that the models are very beneficial reducing by a large factor the complexity of ab initio MD electronic structure calculations. The work is very interesting and deserves publication as it indeed offers a route for speeding up path integral simulations of quantum nuclear effects which are rather cumbersome to be applied for extended systems. Below I provide some other points for consideration:

1. Typo p.12: "for the case example of monolayer".

2. p.4 : "since DFT calculations with large supercells are prohibitively expensive" Maybe the authors could quantify further the supercell size and explain why is needed in more detail.

3. Can the authors comment in more detail on the relative comparison of the models with respect to computational efficiency?

4. Eq. (19): (a) Are the atomic scattering amplitudes missing from the equation of the structure factor? How is this relation related to diffuse scattering?
(b) How many scattering wavevectors are used for the sampling? To me it looks to be a coarse grid.
(c) How many configurations are needed to obtain a converged average ?
(d) What is the nature of CDW peaks? Is it quasi-elastic or inelastic?
(e) Can the authors comment whether this term includes contributions to diffuse scattering both from coupled and independent lattice vibrations (one-phonon and multiphonon scattering)?

5. Is there a double definition of N? Does it represent the number of k-points and number of atoms? I think it's better for the authors to make sure that no definitions with the same symbol appear in the text.

6. Let me also suggest a new paper for the EPW code:

7. Can the authors comment if anharmonic temperature-dependent lattice constants C^{DFT} can be used in Models II and III? Will it be more appropriate? More, will it be more beneficial and more consistent if the deformation potential is computed with nonperturbative supercell calculations to electron-phonon coupling (see for example: I am simply sharing thoughts here.

8. Will the first-principles calculations (inputs and outputs) uploaded to a database or the Python codes on open-source platforms?

9. I think the work has some more space to be expanded for example in the calculation of other thermal averages related to the electronic structure.

  • validity: high
  • significance: high
  • originality: high
  • clarity: top
  • formatting: excellent
  • grammar: excellent

Author:  Arne Schobert  on 2024-01-17  [id 4258]

(in reply to Report 2 on 2023-10-21)

The new manuscript has been resubmitted. Please find the "reply.pdf" document below that answers directly to these questions and includes a formal list of changes.



Anonymous Report 1 on 2023-10-15 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2303.07261v2, delivered 2023-10-15, doi: 10.21468/SciPost.Report.7950


1. the approaches here presented and valuable and interesting
2. the results are useful and well supported
3. the paper is clear and convincing


1. no weak point


In this paper the Authors present three different downfolding schemes for approching phonon anharmonicity and phase transitions in compounds with charge-density-waves (CDWs).
They test the validity of these scheme against few selected representative materials, showing their efficiency.
The paper is sound, well written and the results are interesting and useful.
I gladly recommend publication.

Requested changes

1. no requested change

  • validity: high
  • significance: high
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: excellent

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