From the journal Digital Discovery Peer review history

13-Aug-2022

Dear Dr Walsh:

Manuscript ID: DD-PER-05-2022-000050
TITLE: Free energy predictions for crystal stability and synthesisability

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Dr Kedar Hippalgaonkar
Associate Editor, Digital Discovery
Royal Society of Chemistry

************

Reviewer 1

The authors discussed recent research in free energy descriptions for crystals and their applications in the field of data-driven approaches. This manuscript is well-organized and provides fundamental insights and is probably publishable after addressing the following issues.

-In the abstract, the authors mentioned “We critically discuss some of the techniques and descriptors, including data-driven machine learning approaches.”. However, it seems detailed discussions are missing. The authors should provide that information with tables and figures.

-The database including free energy information for crystals is available such as the phonon database at Kyoto University (http://phonondb.mtl.kyoto-u.ac.jp/), materials project, Jarvis-NIST, and so on. The authors should provide more detailed discussions on how they are constructed and further utilized for related fields.

Reviewer 2

Please see the attached document for my comments to the authors.

Reviewer 3

This article attempts to provide a perspective about the Free energy predictions for the purpose of assessing stability of solid phases and their synthesizability. This is, of course, a very important topic, but I do not think the manuscript represents a thorough and fair picture of the present state of the matter. In particular regarding the synthesizability part of this perspective piece.

First, the article reads as another attempt to reduce synthesizability solely to thermodynamic arguments (minimization principles of the free energy or some other relevant thermodynamic potential). There are also kinetic arguments that are as important (probably even more important than the thermodynamic ones), that are barely touched upon, despite the promise from the abstract: “Avenues are highlighted that deserve further attention including thermodynamic and kinetic factors…” .

Second, a good fraction of the introduction repeats the arguments from the previous works about the proverbial “thermodynamic scale of metastability” (Ref. 2) and the “amorphous limit” (Ref. 3). Both of these are, in my view, highly misleading and inaccurate. First, the definition of metastable structures is wrong in these works. Metastable are not all structures above the ground state, but the structures that LIVE sufficiently long at conditions, at which they should not exist. Also, the estimate of median energy of 15 meV/atom above the convex hull falls within the error bar of the calculations of the heats of reactions that the authors themselves say to be 24 meV/atom. While they did perform some sensitivity tests, one simply cannot make rigorous claims about anything happening within the error bars. In addition, if one performs just a simple back-of-the-envelope exercise by taking the volume difference between diamond and graphite for example and multiplies it by pressure of 100 GPa (not unheard of these days) one concludes that energies of ~1.6 eV/atom become accessible in high-pressure experiments, much higher than 15 meV/atom or 67 meV/atom or 0.1 eV/atom or whatever other “hand-wavy” scale. Again, metastability is about which states that were lowest in enthalpy at a given pressure continue living after the pressure is released and we are back to discussing kinetics (Bell-Polanyi principle and whether it holds for solids in addition to molecules, etc.). The amorphous limit makes even less sense, as there isn’t one, unique amorphous state. The microscopic details of the amorphous states depend highly on the processing conditions. For example, different quenching rates will produce glasses with different mechanical (and other) properties including their total energy. Which of these represents the limit, and why would that one be the limit is not clear?

Third, while I generally agree with the statement from the bottom of page 6: “We posit that if a material is locally stable, there is a non-zero probability of it being synthesized…” there is a body of work showing that the probabilities of various locally stable materials to be synthesized are not all equal. There are locally stable states that are more probable than other, and this ranking has been shown to relate to the sizes of the attraction basins of the corresponding local minima (see for example DOI: 10.1063/5.0049453 and references therein). These arguments are completely absent from the current manuscript.

Dear Dr Hippalgaonkar,

The three reviewers provided a series of very constructive comments to further enhance our perspective. The increased coverage of machine learning methods makes this even more relevant for the readership of Digital Discovery. We hope you like it!

A formal response is uploaded.

Yours sincerely,
Kasper Tolborg and Aron Walsh (on behalf of all authors)

This text has been copied from the PDF response to reviewers and does not include any figures, images or special characters:

Dear Dr Hippalgaonkar,

We hereby enclose our point-by-point response to the reviewer comments for our manuscript entitled “Free energy predictions for crystal stability and synthesisability”. The referee comments are marked with red, our response in black, and any changes to the manuscript are highlighted in yellow.

Yours sincerely,
Kasper Tolborg and Aron Walsh (on behalf of all authors)

Referee: 1

The authors discussed recent research in free energy descriptions for crystals and their applications in the field of data-driven approaches. This manuscript is well-organized and provides fundamental insights and is probably publishable after addressing the following issues.

We thank the referee for the positive comment and will address the points below.

-In the abstract, the authors mentioned “We critically discuss some of the techniques and descriptors, including data-driven machine learning approaches.”. However, it seems detailed discussions are missing. The authors should provide that information with tables and figures.

We agree with the referee that the submitted version of the manuscript was mainly focussed on ab initio methods for assessing stability, whereas a detailed discussion of the data-driven approaches to phase stability, which are starting to emerge, is more superficial. We have added a new section in “IV Thermodynamic potential” titled “Machine learning and data-driven approaches” where we now address and discuss those issues.

-The database including free energy information for crystals is available such as the phonon database at Kyoto University (http://phonondb.mtl.kyoto-u.ac.jp/), materials project, JarvisNIST, and so on. The authors should provide more detailed discussions on how they are constructed and further utilized for related fields.

As the referee suggests there are now several databases available with information about (harmonic) phonon dispersions and the corresponding free energy for a range of materials. Interestingly, these free energies are still not widely used in materials design and screening processes, perhaps due to the limited number of materials for which these data are available compared to those with athermal internal energies available.

We agree with the referee that it is worthwhile to point the reader to these databases, since they have a large potential for use in materials screening studies. Furthermore, there are a few studies using these data sets to build machine learning models to predict free energies, which links up well with the previous comment from the referee.

We now mention these databases in the harmonic free energies section, and we have included discussion on how they are used in combination with machine learning in the section mentioned above. These are highlighted in the track changes manuscript on Pages 4 and 6.

Referee: 2

In this perspective, the authors highlight the need for free energy predictions to assess new crystal structure stability and synthesizability. Athermal thermodynamic stability predictions based on internal/total energy are insufficient to computationally discover new structures that are metastable at higher temperatures or stabilized by anharmonic effects. The perspective summarizes methods for free energy calculations and discusses synthesizability in the context of local and global stability.

This is a timely perspective that should be published in Digital Discovery. The authors have done an excellent job of presenting the concepts in a pedagogical way that will be useful for nonexperts, while also discussing the more advanced topics on anharmonic phonon effects and entropy contributions to free energy that are beyond vibrational entropy. The article covers a lot of ground and is quite comprehensive. As such, I have only a few comments for the authors.

We thank the referee for their positive feedback.

1. The perspective highlights the need for free energy calculations to predict stability, but offers little guidance on how to tackle the computational expense of such calculations, especially in the context of large-scale materials discovery efforts. Methods such as machine learning fitted force fields are suitable for exploring a single (or few closely related) material system and lack transferability.

We agree with the referee that the focus of the manuscript is on the methods for calculating stability, and less on how we can overcome the computational expenses and use the methods in large-scale materials discovery.

As discussed in our response to Referee 1, we have now included a section describing the availability of databases with calculated (harmonic) phonon dispersions and the potential use of data-driven approaches to predict stability – both methods learning from these databases and methods learning from other available data, e.g. experimental thermochemical data. Application of these databases and models thereof will significantly decrease the computational expense for including thermal effects in materials discovery efforts.

Regarding machine learned force fields (MLFF), we only mention those in the context of thermodynamic integration. Here, they have great promise since the main use is accurate stability prediction for a single material, e.g. in relation to polymorph stability, and transferability is less of an issue. Thus, the focus of MLFF is less related to materials discovery and more to accurate predictions, once a few candidates have been identified using simpler and less computationally expensive methods.

2. A synthetic chemist may argue that crystal structures that can be straightforwardly stabilized through traditional solid-state synthetic procedures have a higher probability of synthesizability “success” compared to metastable structures that can be only accessed with special procedures requiring additional resources (time, labor). As the authors have noted, it will take motivated experts with resources to pursue structures that are predicted to be metastable.

We agree with the referee on this point. However, we believe that we quite clearly state this on page 7, where we mention that traditional solid-state synthesis will give the thermodynamic ground state. Therefore, the methods presented can be useful for identifying if a specific set of thermodynamic conditions will allow for synthesis of a specific material, and determination of the local stability at ambient conditions will suggest if the material can be quenched to ambient conditions as well.

Referee: 3

This article attempts to provide a perspective about the Free energy predictions for the purpose of assessing stability of solid phases and their synthesizability. This is, of course, a very important topic, but I do not think the manuscript represents a thorough and fair picture of the present state of the matter. In particular regarding the synthesizability part of this perspective piece.

We thank the referee for their constructive criticism, and we will take their points into account as explained below.

First, the article reads as another attempt to reduce synthesizability solely to thermodynamic arguments (minimization principles of the free energy or some other relevant thermodynamic potential). There are also kinetic arguments that are as important (probably even more important than the thermodynamic ones), that are barely touched upon, despite the promise from the abstract: “Avenues are highlighted that deserve further attention including thermodynamic and kinetic factors…” .

We agree with the referee that kinetic factors are important for synthesisability. However, thermodynamics in the way, we present it here, is a good starting point for understanding synthesisability. Thermodynamics, in particular local and global stability metrics, provides the basis for identifying which phases may be (meta)stable at a certain set of conditions. Thus, based on local stability criteria, several phases can already be ruled out as nonsynthesisable, and we can identify certain phases that will only exist at certain conditions.

Local stability in principle shows the existence of a barrier for conversion, which means that any locally stable material will have a finite lifetime. This, of course, does not guarantee that the material will be stable on “practical” timescales. We discuss these aspects in the last two paragraphs of section “V Synthesisablity” with reference to, e.g., enhanced sampling methods that can be used to probe complex potential energy surfaces and therefore the barriers for interconversion from a metastable to a lower energy phase. We also note the difficulties in determining pathways between two crystal structures when they are not connected by sub-group relations on Page 8.

Second, a good fraction of the introduction repeats the arguments from the previous works about the proverbial “thermodynamic scale of metastability” (Ref. 2) and the “amorphous limit” (Ref. 3). Both of these are, in my view, highly misleading and inaccurate. First, the definition of metastable structures is wrong in these works. Metastable are not all structures above the ground state, but the structures that LIVE sufficiently long at conditions, at which they should not exist. Also, the estimate of median energy of 15 meV/atom above the convex hull falls within the error bar of the calculations of the heats of reactions that the authors themselves say to be 24 meV/atom. While they did perform some sensitivity tests, one simply cannot make rigorous claims about anything happening within the error bars. In addition, if one performs just a simple back-of-the-envelope exercise by taking the volume difference between diamond and graphite for example and multiplies it by pressure of 100 GPa (not unheard of these days) one concludes that energies of ~1.6 eV/atom become accessible in high-pressure experiments, much higher than 15 meV/atom or 67 meV/atom or 0.1 eV/atom or whatever other “hand-wavy” scale. Again, metastability is about which states that were lowest in enthalpy at a given pressure continue living after the pressure is released and we are back to discussing kinetics (Bell-Polanyi principle and whether it holds for solids in addition to molecules, etc.). The amorphous limit makes even less sense, as there isn’t one, unique amorphous state. The microscopic details of the amorphous states depend highly on the processing conditions. For example, different quenching rates will produce glasses with different mechanical (and other) properties including their total energy. Which of these represents the limit, and why would that one be the limit is not clear?

This comment is related to the arguments from two different published articles, which we use as part of the introduction for the present perspective. Overall, we agree with the referee that the use of “metastability” in these references is inaccurate/incomplete, which was part of our motivation for writing a critical perspective. An important contribution from our perspective is to give a more rigorous definition of metastability.

The definition of metastability in ref. 2 is unfortunate in that it suggests that all observed phases with an energy above the convex hull (constructed at 0 K) are metastable. This is of course not correct as some of these phases are only observed at thermodynamic conditions where they are actually the global minimum, but would not be possible to stabilise at 0 K and ambient pressure.

In the perspective, we therefore suggest a different definition of metastability, in which the thermodynamic conditions are taken into account. We write the following: “[…] we can define metastable materials more generally as materials that are locally stable, but globally unstable at a given set of conditions.“ Whether the material will be kinetically stable for long enough timescales is unknown solely from thermodynamics, as we also address in the response to the previous comment.

We also agree with the referee that the “hand-wavy” scales mentioned in the manuscript are exactly “hand-wavy”. Thus, they are not well suited for a rigorous definition of metastability – as we also detail in the perspective – but they may still serve a purpose in materials discovery efforts, since they will filter out many unrealistic candidates. As any approximate method, this will of course lead to some false negative being filtered out, which could have been accessible at, e.g., very high pressure, and retained to ambient conditions.

As the referee points out, it is also true that there is not one unique amorphous state, and therefore the scale using the amorphous state as an upper limit for athermal energies may seem unjustified. However, the authors in ref. 3 clearly state that their amorphous state is the lowest energy amorphous state they encounter in their sampling, and the limit is thus well-defined in a variational sense. Whether this limit makes sense or not as an upper bound for possible metastability will be a matter of empirical testing, and the results in ref. 3 suggest that the limit is indeed useful, in the sense that no false negatives are produced from the method. It should be mentioned that several non-observed materials fall within the amorphous limit, but again, the metric should not be considered a rigorous definition, and furthermore, it is not clear if the materials are not observed because it is not possible to obtain them, or because it would require very tedious synthetic procedures that have not yet been attempted.

Third, while I generally agree with the statement from the bottom of page 6: “We posit that if a material is locally stable, there is a non-zero probability of it being synthesized…” there is a body of work showing that the probabilities of various locally stable materials to be synthesized are not all equal. There are locally stable states that are more probable than other, and this ranking has been shown to relate to the sizes of the attraction basins of the corresponding local minima (see for example DOI: 10.1063/5.0049453 and references therein). These arguments are completely absent from the current manuscript.

We thank the referee for pointing this out, and we have now included a discussion on these methods in the section on Synthesisability on page 7-8 starting with “Another approach that […]”.

06-Sep-2022

Dear Dr Walsh:

Manuscript ID: DD-PER-05-2022-000050.R1
TITLE: Free energy predictions for crystal stability and synthesisability

Thank you for submitting your revised manuscript to Digital Discovery. I am pleased to accept your manuscript for publication in its current form. I have copied any final comments from the reviewer(s) below.

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Associate Editor, Digital Discovery
Royal Society of Chemistry

Reviewer 2

The authors have addressed my comments. I recommend publication of this manuscript in its current form.

Reviewer 3

The authors have addressed all my concerns and I recommend publication.