At Nature Chemistry we all love Density Functional Theory and we all love polls – so what could be better than a poll on DFT? Marcel Swart, Matthias Bickelhaupt, and Miquel Duran have, for the last five years, been running a poll to find out which functionals the computational chemistry community like or dislike. The results of the the 2014 poll are now out and we have a guest post from the three of them to explain a little more about it.

I’m sure we’ll be seeing this as a question on Family Fortunes/Family Feud soon: “We asked 100 people to name …. a popular density functional”

Gavin

(Senior Editor, Nature Chemistry)

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Since 2010 we have been organizing an annual online popularity poll for density functionals where we probe the preferences of the computational chemistry community for their preferred Density Functional Theory (DFT) functionals. It all started with a presentation by Matthias Bickelhaupt (Feb. 2009) that showed the values of various chemical properties calculated using quite a number of different density functionals. Miquel Duran suggested, essentially, ‘averaging’ a number of these values but with appropriate weightings applied that reflected how ‘good’ the employed functionals were. Thus obtaining a ‘consensus’ density functional result. This could then act as a measure of how well the computational chemistry community is doing if compared to state-of-the-art reference data.

In order to get the weightings needed for this procedure, we have held annual online polls where people could indicate their preferences for a number of density functionals. The polls were announced on the Computational Chemistry List (CCL; a mailing list where people can ask for advice about any aspect of computational chemistry), on Twitter, Facebook, blogs, and so on, in order to get the maximum number of participants. The aims of this poll were: (i) to probe the ‘preference of the community’, that is, setting up a ranking of preferred DFT methods; and (ii) provide a compilation of the ‘de facto quality’ that this implies for the ‘average DFT computation’.

The DFT poll has led to, what some might deem to be, a polarization of the field, with some people clearly in favor (e.g. Steven Bachrach, Gernot Frenking, John Perdew, Henry Rzepa), and others clearly against. Especially this year there has been a vivid debate on the CCL mailing list in the days after the poll was announced (CCL June 1^st entries, CCL June 2^nd entries, CCL June 3^rd entries). This may, or may not, be related to the fact that in 2013 we had to disqualify one functional that had fallen victim to a blatant attempt to bias the outcome of the poll. This has not happened again this year (because we switched to another survey provider).

In order to stress the motivation for holding the poll, we as organizers felt we needed to add a statement as well, since we “are simply monitoring what happens in the field of DFT and comment on how the choice of the community differs from (or agrees with) reliable reference data. In that way, we do exactly what should be done, namely ‘drive science through evidence and logic’ or maybe even ‘drive science back to evidence and logic’ (because, against all basic principles of science, the community often just follows blindly a fashion)”. And as one message nicely described: “Yes, it is not scientifically sound, epistemologically correct, platonically unsullied. But at least it is fun. We should appreciate fun in chemistry”.

The nice part of the popularity poll is that it opens the field to newbies, who through the poll have a better understanding of which are the most popular functionals within the field  — which can serve as a good starting point for those looking for the best functionals for their given problems. For instance, the rise of the wB97X-D functional is nicely reflected in this year’s results (moving upwards to 4^th place after PBE, PBE0 and B3LYP), as was the fact that the winner of the first editions (PBE0) was largely unknown to many people. The years after the first edition (in which it ‘won’), the number of PBE0 citations has increased considerably, by at least 60% (see Figure 1) for the three PBE0 papers (there is the original paper by Perdew and co-workers where they describe the rationale for using 25% Hartree-Fock exchange; and there are two separate papers that introduce the functional as being PBE0, by Ernzerhof and Scuseria, or by Adamo and Barone).

Figure 1. Normalized number of citations for PBE0 papers, before (2006-2010) and after (2011-2013) the first news-item of the DFT poll (100 = average number of citations for 2008-2010 for each of the three papers separately).{credit}Courtesy of Marcel Swart{/credit}

Given that this is the fifth edition, we asked several researchers in the field (in Sept. 2014) whether they were in favor or against the DFT poll.

Steven Bachrach: “Please feel free to quote me from the Wiley Interdisciplinary Reviews article [“It would be nice if we could somehow again reach some consensus regarding a uniform standard computational method that experts and non-experts could rely upon for most situations. A challenge I make here to the computational community is to try to reach an accord on establishing a standard methodology. Perhaps a conference could be called where leaders propose their best methods and after discussion, a vote yields a recommendation for the greater user community”] and from CCL [“I also think the poll has value in discerning trends, especially new functionals to appear on the list and ones that have fallen down or off”].

John Perdew: “The DFT popularity poll is somewhat like citation analysis: It measures (but in a different way) how well a functional has been received by a set of readers and users.  There are many reasons why some functionals are received better than others: accuracy, reliability, wide applicability, computational efficiency, well-founded construction, availability in standard codes, reputation of the functional and its authors, historical priority, novelty, and even hype.  The poll has to be seen as measuring all these things, and perhaps more. To the extent that the polled scientists use rational criteria, the results of the poll can point other scientists toward good or interesting functionals”.

Henry Rzepa: “I still think the context of any vote cast is absolutely crucial. Perhaps what the community needs to develop is a public set of conformance test sets of molecules, one for each type of property?”

Andreas Savin: “I must shamefully confess that I do not know about the DFT popularity poll.” (after having received more information): “I will not participate, as this poll is intended for people who apply DFT, and I do little in this direction, but I find it interesting. I am amused to see that B3LYP is not as popular as generally believed, and LDA has such a high rank. How does it compare to the number of citations?”

Gustavo Scuseria: “I am not in favor or against the poll. It is interesting though that we need a contest to determine what is popular and useful. A cacophony of functionals have mushroomed in recent years, and I am very much afraid that uncontrolled approximations and rampant empiricism have taken over DFT”.

An interesting addition was brought forward in the discussions this year by Henry Rzepa (June 1, 2014), who suggested that, in the future, the poll should be extended to enable participants to explain why they like or dislike a given functional. This is a new interesting feature that will be added to next year’s edition: for each functional the participants can indicate for a number of properties whether they love using the functional, or rather dislike it. Rzepa proposed a number of properties (reaction barriers, normal mode analysis, NMR shieldings, etc.), which will be fine-tuned before the polling season opens again on June 1 2015!

Marcel Swart, Matthias Bickelhaupt, and Miquel Duran

The July issue of Nature Chemistry features a paper from Stephen Meech, Ben Feringa and co-workers that looks at the ultrafast dynamics of a unidirectional molecular motor. Such motors work through a two step process and enough is known about the thermally-driven second step to be able to improve its efficiency through molecular design, but not so much is known about the light-driven first step, the power stroke. After the Meech and Feringa paper, however, we know quite a bit more!

The paper is also discussed in the issue in a News and Views article from R. J. Dwayne Miller. Professor Miller got so excited with the topic that he wrote more than we were able to publish (!) so we said that we would put his unabridged introduction on here. So it’s like ‘News and Views: The directors cut’.

We can only put the unpublished intro up here, so if after reading this you want to hear the end of the story, the full News and Views article is here, and the original Article from Meech, Feringa and colleagues is here.

Gavin Armstrong

Senior Editor, Nature Chemistry

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Light-driven molecular motors: What are the quantum limits to work at the molecular level?

The motor has been the ‘engine of science’ for over two centuries, enabling humans to do more work than possible given our limited anatomy. In a way, the motor gave us superpowers. A single person operating a machine powered by some form of motor or engine can do many orders of magnitude more work than prior to its inception. Some of the modern day marvels of engineering such as spacecraft enable us to do effectively astronomically more work to literally go into the heavens.

Based on the enormous importance of motors in driving the industrial revolution, it is natural to wonder what the fundamental limits are to the amount of work that a motor can do. It was precisely this question that led to the one of the greatest achievements in science: the formulation of the thermodynamics [1]. Here it has to be appreciated that the steam engine was developed through a serious of successive steps that can be traced back to key developments dating back to Savery’s first patent (1798) to engineering improvements by Newcomen and further improvements in efficiency with the development of the condenser by James Watts.  Each key step led to an increase in output power and efficiency even at a time in which we did not know the origins of the very energy that drove it [1].  It was natural to wonder how much work could be extracted from motors as each advance seemed to bring ever increasing amounts of work to bear on a problem.  Careful measurements by Joule established that energy can appear within a system as heat or work and that this energy was unconditionally conserved. These observations led to the first law of thermodynamics [2] and ruled out the possibility of perpetual motion machines ‘of the first kind’.

There were, however, still interesting conundrums regarding the apparent paradox of coupling engines or motors with different efficiencies together, which lead to the possibility that one might be able to extract energy from the surroundings without requiring an energy source. These considerations led Carnot to posit one of the most brilliant examples of logic ever exercised in his reduction of the maximum amount of work that can be extracted from a system, an engine this case, in thermal contact with its surroundings. This formulation led Clapyeron to the Second Law of Thermodynamics and elimination of the possibility of perpetual motion machines ‘of the second kind’ [2,3].

The connection of entropy to microscopic principles with Boltzmann’s derivation for the entropy and Nernst’s formulation of the Third Law of Thermodynamics put the connection with entropy and extractable work on a quantitative basis [3]. In parallel, the genius of Gibbs led to the formulation of the free energy state function that encompassed both enthalpic and entropic driving terms for a particular process, and enabled the prediction of the maximum amount of work that can be extracted from a system [3].

From these historical reference points, one can see that the motor as a conceptual construct has truly been an engine for advancement of science. The initial motivation was to maximize efficiency and to scale up motors to do ever increasing amounts of work. What about the opposite limit? How small can we make a motor?  The ultimate limit of course is to construct a motor on the molecular level. Are there different scaling relationships in terms of efficiency as we go to the molecular level?

At this point we should recognize that living systems long ago mastered the ability to make molecular motors, for the transport of proteins, motility, transport of charge etc. The protein assemblies that carry out various functions for the cell are marvels of molecular engineering. It is only recently that we have developed the tools to monitor the functions of these assemblies.

One of the most remarkable examples of a biological motor is the ATPase motor protein that is involved in motility through the rotation of flagella. It has in fact been possible to directly determine that these motors operate very close to theoretical efficiency limits [4]. The degree of efficiency is all the more remarkable when one recalls that these systems are functioning within stochastic limits. The collisions and exchange of energy of a molecular motor with its surroundings at this scale is orders of magnitude more than the power generated to do work on the surroundings. For example, the collisional exchange of energy of a molecule with the surrounding bath molecules is on the order of KT at a collision rate of 10¹² sec^-1 for a power dissipation rate of nW [5]. In comparison, a typical turnover rate of a motor protein (20kT barrier), involving the conversion of a typical bond energy providing 4×10^-18Joules of energy per molecule, is typically on the millisecond timescale such that only 4×10^-15 Watts are involved in carrying out the work relevant to function [5]. This is more than 5 orders of magnitude less than the power dissipated through stochastic fluctuations within the immediate surroundings of the molecular motor.  Imagine trying to do work under conditions where you are being battered about by random forces that are orders of magnitude more powerful than your feeble attempts to move ahead.

Let us consider the fundamental constraints with respect to making molecular motors. First, thermodynamics is based on microscopic principles related to thermal motion of molecules and atoms. There are no loop holes in the laws of thermodynamics at the nanoscale that enable higher theoretical efficiencies for molecular motors (one, however, can wonder about possible increases in effective efficiency as friction and associated losses become ill-defined).  Within the depiction of Carnot, a molecular motor immersed in its surroundings cannot sustain a temperature differential to harness thermal motion into direction and thus execution of work on the surroundings. Simply put: no work is possible without the input of an energy source into the system.

Second, the structure of the system must involve an asymmetry, much like a ratchet, such that the motions activated by the energy source go into a given direction related to the function of the motor [5,6]. Think about all the engineering that goes into a combustion engine. A typical combustion engine has very rigid walls, stable to high operating temperatures (to maximize operating temperatures and thermal gradients), and pistons with a lubricant to reduce frictional losses, so that the energetic motions of the product gases from combustion lead to unidirectional displacement of the pistons. This displacement is converted into rotary motion to move an object or do work on the surroundings. The efficiencies of modern day gas engines are around 25% with diesel engines running at close to 50% efficiency [5].

In this context, think of the challenges at the molecular level. One has to construct a molecular system in which specific motions of the motor are driven over other loss channels by imposing a highly asymmetric potential to the reaction coordinate coupling the energy source to the motor’s functional motions. The problem is that molecules are not rigid like macroscale engines. Despite the many orders of magnitude smaller size of molecular motors relative to macroscale systems, there are many more uncorrelated, independent degrees of freedom, with motions comparable to the motor’s functionally relevant motions. In scaling the problem, it would be impossible to imagine how rough the ride in a ’molecular car’ would be. Here it has to be appreciated that these other uncorrelated motions act as loss mechanisms in terms of efficiency. The fluctuation and dissipation processes leading to frictional (entropic) losses are comparable to mechanized motions of interest. In this sense, molecular scale frictional losses are actually more of a problem than in a macroscale motor.

One way around this dilemma for molecular motors is to design the process so that the functional motion occurs faster than entropic losses, or in molecular terms ideally faster than intramolecular vibrational energy redistribution (IVR) within the molecular complex, so that all the energy goes into the designed motions.  This would give the highest possible efficiency. Here it has to be appreciated that we are talking about quantum speed limits to molecular reaction dynamics. For slower processes there will be energy losses. As an additional consideration, collisional exchange or intermolecular energy redistribution represents energy losses to the surroundings. This time scale defines the lower limit to the required speed of the “motorized” molecular motions or the time scale involved in barrier crossing for the key power strokes. This problem in optimization requires dynamical information on the relevant motions and the competing pathways for energy dissipation. In this respect, the work of Meech, Feringa and colleagues is significant as it provides the first direct dynamical information on the primary motions of a synthetically designed molecular motor [7].

References

1.      M. Kerker, in Technology and Culture Vol. 2, No. 4 pp. 381-390 (Wayne State Univ. Press, August 1961); https://www.jstor.org/ stable/3100893.

2.      John Hudson, The History of Chemistry (The MacMillan Press, London, 1992), pp. 214-216.

3.      W. J. Moore, 4th Ed Physical Chemistry (Prentice-Hall, Englewood Cliffs, New Jersey, 1972), pp. 77-109.

4.      H. Itoh, A.Takahashi, K. Adachi, H. Noji, R. Yasuda, M. Yoshida, and K. Kinosita, Nature 427, 465-468 (2004); R. Yasuda, H. Noji, K. Kinosita and M. Yoshida, Cell, 1998, 93, 1117–1124.

5.       A. Coskun, M. Banaszak, R. D. Astumian, J. F. Stoddart and B. A. Grzybowski, Chem. Soc. Rev., 2012, 41, 19–30.

6.       R. D. Astumian, Science 276, 917–922 (1997).

7.       J. Conyard, et al. Nature Chem. doi:10.1038/nchem.1343 (2012).

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To find out more read the rest of the News and Views article here, and the original Article from Meech, Feringa and colleagues here