## Saturday, April 15, 2017

### Finding the function that is its own derivative

I saw this "derivation" some years ago but now I can't find it.  If anyone knows the source please let me know.

Let's say we want to find a function $f(x)$ for which
$$\frac{d}{dx} f(x) = f^\prime (x) = f(x)$$
Well, how about $f(x) = x$?
$$f(x) = x \implies f^\prime (x) = 1$$
No, because $f^\prime (x) \ne x$. OK, how about $f(x) = 1+x$?
$$f(x) = 1+x \implies f^\prime (x) = 1$$
That get's me a little closer.  I get the "$1$" back, but I need something whose derivative will give me back the $x$:
$$f(x) = 1+x+\tfrac{1}{2}x^2 \implies f^\prime (x) = 1 + x$$
Now I need something whose derivative will me back the $\tfrac{1}{2}x^2$:
$$f(x) = 1+x+\tfrac{1}{2}x^2 + \tfrac{1}{2 \cdot 3}x^3 \implies f^\prime (x) = 1 + x + \tfrac{1}{2}x^2$$
OK, so if I use infinitely many terms then this function fits the bill
$$f(x) = 1+x+\tfrac{1}{2}x^2 + \tfrac{1}{2 \cdot 3}x^3 + \cdots \tfrac{1}{n!}x^n \cdots \implies f^\prime (x) = 1 + x + \tfrac{1}{2}x^2 + \cdots \tfrac{1}{(n-1)!}x^{n-1} \cdots$$
Can I write $f(x)$ in some compact form?  Well, $f(0) = 1$ and $f(1)$ will give me some number, which I'll call $e$.
$$f(1) = 1+1+\tfrac{1}{2} + \tfrac{1}{2 \cdot 3} + \cdots = e$$
You only need a few terms before $e$ has converged to the first two decimal places (2.717).

For $x$ = 2 you need a few more terms to get the same precision, but the number (7.382) is roughly 2.717 x 2.717, an agreement that quickly gets better with a few more terms
$$f(2) = 1+2+\tfrac{1}{2}4 + \tfrac{1}{2 \cdot 3}8 + \cdots = e^2$$
So
$$f(x) = e^x = 1+x+\tfrac{1}{2}x^2 + \tfrac{1}{2 \cdot 3}x^3 + \cdots \tfrac{1}{n!}x^n \cdots$$
and
$$\frac{d}{dx} e^x = e^x$$

### Where does the ln come from in S = k ln(W) ? - Take 2

Some years ago I wrote this post. Now I want to come at it from a different angle.

A closed system spontaneously goes towards the state with maximum multiplicity, $W$. For a system with $N$ molecules with energies $\varepsilon_1, \varepsilon_2, \ldots$ we therefore want to find the values of $N_i$ that maximises $W(N_1, N_2, \ldots)$.

This is easier to do for $\ln W$ than $W$, which is fine because $W$ is a maximum when $\ln W$ is a maximum, and this happens when
$$\frac{N_i}{N}= p_i = \frac{e^{-\beta \varepsilon_i}}{q}$$
$\beta$ can be found by comparison to experiment.  For example, the energy of an ideal monatomic gas with $N_A$ particles is
$$U^{\mathrm{Trans}} = N_A \langle \varepsilon^{\mathrm{Trans}} \rangle = N_A\sum_i p_i \varepsilon_i = \frac{3N_A}{2\beta} = \tfrac{3}{2}RT \implies \beta = \frac{1}{kT}$$
where $R$ is determined by measuring the temperature increase due to adding a known amount of energy to the system.

So far we have used $\ln W$ instead of $W$ for convenience, but is there something special about $\ln W$? Yes, the change in $\ln W$ has can be expressed quite simply
$$d \ln W = \beta \sum_i \varepsilon_i dN_i = N \beta \sum_i \varepsilon_i dp_i = \frac{dU}{kT}$$
So change in internal energy $U$ due to a redistribution of molecules among energy levels is equal to the change in $\ln W$ (as opposed to $W$) multiplied by $kT$
$$dU = Td\left( k \ln W \right) = TdS$$
The final question is whether there is something special about $\ln = \log_e$ as opposed to say $\log_a$ where $a \ne e$? Well, $\log_a W$ is a maximum when
$$\frac{N_i}{N}= p_i = \frac{a^{-\beta \varepsilon_i}}{q}$$
There is an extra term in the derivation but that cancels out in the end.  So no change there.

What about $\beta$?  There are two changes.  The previous derivation of $U^{\mathrm{Trans}}$ relied on this relation (I'll drop the "Trans" label for the moment)
$$\varepsilon_i e^{-\beta \varepsilon_i} = - \frac{d }{d \beta} e^{-\beta \varepsilon_i} \implies \langle \varepsilon \rangle = - \frac{1}{q} \frac{dq}{d\beta}$$
which now becomes
$$\varepsilon_i a^{-\beta \varepsilon_i} = - \frac{1}{\ln(a)} \frac{d }{d \beta} a^{-\beta \varepsilon_i} \implies \langle \varepsilon \rangle = - \frac{1}{q \ln(a)} \frac{dq}{d\beta}$$
While $q$ has an extra $\ln (a)$ term, the derivative wrt $\beta$ is still the same and
$$U^{\mathrm{Trans}} = N_A \langle \varepsilon^{\mathrm{Trans}} \rangle = N_A\sum_i p_i \varepsilon_i = \frac{3N_A}{2 \ln (a) \beta} = \tfrac{3}{2}RT \implies \beta = \frac{1}{\ln (a) kT}$$
So, $S = k \log_e W$ is special in the sense that the proportionality constant $k$ is the experimentally measured ideal gas constant divided by Avogadro's number.  In any other base we have to write either $S = k \ln (a) \log_a W$ where $k = R/N_A$ or $S = k^\prime \log_a W$ where $k^\prime = \ln(a)R/N_A$

Clearly, $S = k \log_e W$ is the most natural choice, and this is because $e$ is the (only) value of $a$ for which
$$\frac{d}{dx} a^x = a^x$$
In fact that is one way to define what $e$ actually is.

## Tuesday, February 28, 2017

### Biotechnology and drug-design: My latest paper explained without the jargon

Our latest paper has just appeared in the open access journal Chemical Science. It's ultimately related to biotechnology and drug design so first some background.

Background
Most biotechnology and medicine involves proteins in some way. Many diseases involve mutations that alter the function of proteins, most drugs are molecules that bind to proteins and inhibit their actions, and a large part of industrial biotechnology involves making new types of proteins such as enzymes. Like with everything else, it is easier to deal with proteins of you know what they look like but protein structure determination can be very difficult and we don't know what many important proteins actually look like.

The most popular way of determining protein structure is a technique called x-ray crystallography where you basically take an x-ray of a crystal made from the protein. Unfortunately, it can be very difficult or impossible to grow crystals of some proteins and if you can't get the protein to crystallise you can't use x-ray crystallography to find the structure.  The other main way for determining protein structure is a technique called NMR spectroscopy where you basically take an MRI of a solution containing the protein. The advantage is that there is no need for crystallisation, but the disadvantage it that it is difficult to extract enough information from the "NMR-MRI" go get a good structure.

The "NMR-MRI" of a protein actually provides a unique fingerprint of each protein so in principle all one has to do is generate a lot of possible structures of a protein, compute the NMR fingerprint for each, and compare to the measured fingerprint. The structure with the best fingerprint match should be the correct protein structure.  The questions are how to best generate the structure and how to best predict the NMR fingerprint using the structure.

The New Study
In 2015 we published a new method for predicting NMR fingerprints and in the paper that just got published we combined it with a method for generating a lot of protein structures. We started with known x-ray structures and generated millions of relatively small variations of the structure and found the structure with the best match.  We started from a known structure to answer the question: what is the best match we can hope for? The answer is: not perfect but good enough.  Now that we know this the next step will be to start with a structure we know is wrong and see if the program can find the right structure.  Also, our NMR fingerprint method does not generate fingerprints for all parts of the protein so we need to improve the model as well.

## Monday, February 13, 2017

### What are the most important reactions in drug synthesis and stability?

Synthesis
1. Aromatic electrophilic substitution of heteroaromatics
2. Suzuki coupling of heteroaryl halides
3. Diels-Alder reaction (of what)?
4. Michael reaction (of what)?
5. Friedel-Crafts alkylation (of what)?
6. Nazarov cyclization reaction (of what)?
7. ...

Stability (Probably solvolysis and oxidative degradation, but can we be more specific)
1. Autooxidation of C-H bonds?
2. Ester hydrolysis?
3. ..

## Sunday, February 5, 2017

### Preprints and the speed of publishing

When I talk about preprints with colleagues some of them say "Oh, what's the rush?" or "Publishing is so fast these days. Why, my last paper was online 6 weeks after submission don't you know" and then go on to clean their pipe with a thoughtful smile or get up to stoke the coal fire.

I'm currently writing a couple of proposals and as I was updating the reference list on one of them when I noticed that two preprints I cited apparently still haven't been "published" by a journal.  One of them first appeared on arXiv on October 7th and the other October 27th.

Both papers are important to the proposal in the sense that they changed my thinking on what is possible and I think the proposal would be less ambitious if I hadn't read them. So I am very happy these authors chose to deposit them as preprints.  I wish more people would do this and I wish fewer journals/journal editors would stand in the way of them doing so.

## Saturday, January 28, 2017

### Drug design: My latest paper explained without the jargon

Our latest paper has just appeared in the Journal of Physical Chemistry A.  If you don't have access to this journal you can find a free version of an earlier draft here. It's ultimately related to making better drugs so first some background.

Background
Designing new drugs currently involves a lot of trial-and-error, so you have to pay a lot of smart scientists a lot of money for a long time to design new drugs - a cost that is ultimately passed on to you and I as consumers.  There are many, many reasons why drug design is so difficult. One of them is that we often don't know fundamental properties of drug-candidates such as the charge of the molecule at a given pH. Obviously, it is hard to figure out whether or how a drug-candidate interact with the body if you don't even know whether it is postive, negative or neutral.

It is not too difficult to measure the charge at a given pH, but modern day drug design involves the screening of hundreds of thousands of molecules and it is simply not feasible to measure them all. Besides, you have to make the molecules to do the measurement, which may be a waster of time if it turn out to have the wrong charge. There are several computer programs that can predict the charge at a given pH very quickly but they have been known to fail quite badly from time to time.  The main problem it that these programs rely on a database of experimental data and if the molecule of interest doesn't resemble anything in the database this approach will fail.

Last year we developed a "new" method for predicting the charge of a molecule that relies less on experimental data but it fast enough to be of practical use in drug design. We showed that the basic approach works reasonably well for small prototypical molecules and we even tested one drug-like molecule where one of the commercial programs fail and show that our new method performs better (but not great).

The New Study
We test the method on 48 drug molecules and show that it works reasonably well.  It is not quite as accurate as the methods that rely on experimental data, but this is probably because many of the molecules we test are in the databases that the programs use.  But we felt we had to test these molecules first because they are some of the first molecules other users will try to test the method. The next step is to test the method on molecules where some of the existing methods perform poorly. We also have to think about how best to make this method available to researchers who are acutually doing the drug design.

## Saturday, January 21, 2017

### Prediction of the Regioselectivity of Electrophilic Aromatic Substitution Reactions of Heteroaromatic Systems Using Semi-Empirical Quantum Chemical Methods

Art Winter tweeted this paper by Morten Jørgensen and co-workers last year and I decided to see if semi-empirical methods could help here.  The paper uses Chemdraws chemical shift predictor to predict where a bromine atom will be added to a heteroaromatic molecules using electrophilic aromatic substitution reactions. They tested this on 132 different compounds and achieved an 80% success rate, which is very good.

Googling a bit let me to this paper by Wang and Streitwieser where they show a correlation between the rate of electrophilic aromatic substitution reactions and the lowest proton affinity of the protonated species.  This suggests that the protonated carbon with the lowest proton affinity (or pKa if solvent is included) should be the reacting carbon.  So I tested this using semiempirical QM methods for these 132 compounds.  When I say "I" I should say that +Jimmy Charnley Kromann ran many of the calculations and Monika Kruszyk provided most of the structures as Chemdraw files, which I could convert to SMILES strings using OpenBabel. These are preliminary results and may contain errors.

The reactions for the 132 compounds are not all run in the same solvent, so I first tested gas phase, chloroform (i.e. dielectric 4.8) and DMF (dimethylformamide, dielectric 37) using PM3 and COSMO in MOPAC. I chose PM3/COSMO because that gave the best results in a previous pKa study. The most representative choice of solvent seems to be chloroform, where PM3/COSMO predicted the correct bromination site in 95% of the cases, i.e. it fails for 7 cases. Gas phase and DMF fails for 14 and 8 cases, so it's important to include solvent, but the value of the dielectric constant is not all that important.  Using chloroform as a solvent, I then tested AM1,  PM6, PM6-DH+, PM7 and DFTB3/SMD (using GAMESS for the last one), which resulted in 12, 12, 12, 9, and 13 wrong predictions. One of the compounds includes an Si atom, which the DFTB3 parameter set I used couldn't handle so the 13 wrong predictions is out of 131 compounds.  Anyway, PM3/COSMO/chloroform works best.

In some cases the lowest pKa value is quite close to some of the other pKa values, so I took an approach similar to that of Jørgensen and co-workers: if the correct bromination site is included in the set of atoms with pKa values within 0.74 pH units (corresponding to 1 kcal/mol at room temperature) then I counted it as correct.  For PM3/COSMO/chloroform this occurred 10 times. In 9 cases the set included 2 atoms and in 1 case, 3 atoms.  In one of the 9 cases (15) there are only two possible bromination sites, so this case is not a successful prediction and PM3/COSMO/chloroform actually gets 8 wrong. However, in all other cases there are more possibilities than those predicted. Furthermore, in all but 2 of thes 10 cases the atom with the lowest pKa is the "correct" atom.

Bromination, or more generally, halogenation is often a first step towards adding an aryl group, usually using a Suzuki reaction.  Often there is more than one halogen of the same type so there is also interest in predicting where the aryl group will go.  I tried the PM3/COSMO/chloroform approach on the six molecules in this paper by Houk and co-workers. Computing pKa's of the halogenated carbon atoms let to correct predictions in 4 of the 6 cases, while computing proton affinities of the carbon atoms in the non-halogenated parent compounds let to correct predictions in 2 of the 6 cases. The former approach seems promising but needs to be tested on a much larger set of molecules.

Next step is to write this up and get the set-up and analysis code in such a shape that we can distribute it. I've also started thinking about how to make the approach more generally available and usable for non-experts. A grant proposal is also in the works, so if we're successful that should definitely be possible to achieve.

## Monday, January 16, 2017

### Open access chemistry publishing options in 2017

I just noticed that my go-to journal increased its APC again.*  Now there's a flat fee of $1095 so I am re-evaluating my options for impact neutral OA publishing. I don't think PeerJ is greedy, so I think the most likely explanation is be that their old model was not sustainable. I now feel I have been a bit to hard on some other OA publishers (e.g. here and here, but not here). While price and impact-neutrality is the main consideration, open peer review is a nice bonus that I became accustomed to from PeerJ. In my experience it makes for much better reviews and keeps the tone civil. Impact neutral journals$0. Royal Society Open Science still has an APC waiver and open peer review. (The RSC manages "the journal’s chemistry section by commissioning articles and overseeing the peer-review process")

€750. Research Ideas and Outcomes (disclaimer: I am subject editor), open peer review.

$1000 F1000Research. Open peer review$1095 PeerJ. Open peer review.

$1350 Cogent Chemistry. Has a "pay what you can" policy. Closed peer review. HT +Stephan P. A. Sauer$1495 PLoS ONE. Closed peer review.

$1675 Scientific Reports. Closed peer review$2000 ACS Omega. Price for CC-BY by ACS member ($140/year). Closed peer review. So it looks like Royal Society Open Science is the next thing for me to try, as long as the APC waiver is in place. Free or reasonably priced journals that judge perceived impact$0 Chemical Science Closed peer review

$0 Beilstein Journal of Organic Chemistry. Closed peer review. HT +Wendy Patterson$0 Beilstein Journal of Nanotechnology. Closed peer review. HT +Wendy Patterson

$500 ACS Central Science Price for CC-BY by ACS member ($140/year). Closed peer review.

£500 RSC Advances. Closed peer review. (Normally £750)

Let me know if I have missed anything.

Last update: 2017.03.05

*I just noticed that the membership model still exists though the price has increased. I already have a premium membership, so this may still be a viable option for me. If you are a single author or have only one co-author this is still the way to go.

## Sunday, January 15, 2017

### Making your computational protocol available to the non-expert

I recently read this paper by Jonathan Goodman and co-workers which I learned about through this highlight by Steven Bachrach.  The DP4 method is a protocol for computing chemical shifts of organic molecules using DFT and comparing the chemical shifts to experimental values.  This paper automates the method, switches to free software packages (NWCHEM instead of Gaussian and TINKER instead of Macromodel), and tests the applicability for drug like molecules.  The python and Java code is made available on Github under the MIT license.

The method is clearly aimed at organic chemists who use NMR to figure out what they made or isolated. Let's say they want to try DP4 to see how well it works on some molecule they are currently working on.

What's needed to get started
1. Access to multicore Linux computer.  The method requires quite many B3LYP/6-31G(d,p) NMR calculations and given the typical size of organic molecules it will probably not be practically possible to even test this method on a desktop computer.  Even if it is, the instructions for PyDP4 assumes you are using Linux to you'd have to somehow deal with that if you, like many, have a Windows machine.

2. Installation. You have to install NWCHEM, Tinker, OpenBabel and configure PyDP4.

3. Coordinates. PyDP4 requires an sdf file as input.  You have to figure out what that is and how to make one.

4. Familiarity with Linux.  All this assumes that you are familiar with Linux. How many synthetic organic chemists are?

If you'll be using DP4 a lot, all of this may be worth doing but perhaps not just to try it?  If you don't have access to a Linux cluster, buying one for the occasional NMR calculation may be hard to justify. If one is convinced/determined enough, the most likely solution would probably be to find and pay an undergrad to do all this using an older computer you were gonna throw out anyway.  Or maybe your department has a shared cluster and a sysadmin who could handle the installation.

Alternative 1: Web server
One alternative is to make DP4 available as a web server, where the user can upload the sdf file and other data.  If one includes a GUI all 4 problems are solved ... for the user.  The problem for the developer is that this could eat up a lot of your own computational resources. One could probably do something smart to only use idle cycles, but the best case scenario (lots of users) also becomes the worst case scenario.  Perhaps there's a way to crowdsource this?

Alternative 2: VM Virtual box
Another alternative is to make DP4 available as a virtual machine (VM).

This mostly solves the installation issue. The main problem here is that the user needs still needs to find a reasonably powerful computer to run this on. The other problem is that the developer needs to test the VM-installation on various operating systems and keep up to date as new ones appear. Perhaps there's a way to crowdsource all this?

Alternative 3: Amazon Web Services or Google Compute Engine
Another alternative is to make DP4 available as a VM image for AWS or GCE.  This mostly solves the CPU and installation issue. The user creates an AWS or GCE account and imports the VM image and then pays Amazon and Google for computer time using a credit card. For reasonably sized molecules the cost would probably be less than $10/molecule as far as I can tell. I don't have any direct experience with AWS or GCE so I don't know how slick the interface can be made. All examples I have seen have involved ssh to the AWS/GCE console, so some Linux knowledge is required. Alternative 4: AWS/GCE-based Web server Another alternative is to combine 2 and 3. The problem here is how to bill the individual user for their CPU-usage. There is probably ways to to this but it's starting to sound like a lot of work to set up and manage. Perhaps by adding a surcharge one could pay someone to handle this on a part-time basis. Perhaps existing companies would be interesting in offering such a service? Licensing issues As far as I can tell the licenses of NWCHEM, TINKER, and OpenBabel allow for all 4 alternatives. The bigger issue A key step in making a computational chemistry-based methods such as DP4 usable to the non-expert is clearly automation and careful testing. Another is using free software (I have access to Gaussian but I am not going to buy Macromodel just to try out DP4!). Kudos to Goodman and co-workers for doing this. But if we want to target the non-experts, I think we should try to go a bit further. One could even imagine something like this in the impact/dissemination section of a proposal: The computational methodology is based on free software packages and the code needed for automatisation and analysis, that is written as part of the proposed work, will be made available on Github under an open source license. Furthermore, Company X will make the approach available on the AWS cloud computing platform, which will allow the non-expert to use the approach without installation or investment in in-house computational resources and greatly increase usage. Company X handles the set-up, billing for on-demand CPU-time, usage-statistics, and provides a rudimentary GUI for the approach for a one-time fee of$2000, which is included in the budget.
Anyway, just some thoughts.  Have I missed other ways of getting a relatively CPU-intensive computational chemistry method in the hands of non-experts?

## Saturday, January 7, 2017

### Planned papers for 2017

A year ago I thought I'd probably publish three papers in 2016:

Listed as probable in 2016
1. Benchmarking of PM6 and DFTB3 for barrier heights computed using enzyme active site models.
2. pKa prediction using PM6 - part 1
3. Protein structure refinement using ProCS15 - starting from x-ray structure

and this basically turned out to be correct, as you can see from the links, except that paper number 3 officially is published in 2017 because Chemical Science still uses issues. So I will have to list it as a 2017 paper, meaning I published two papers in 2016.  Not my best year.

Here's the plan for 2017

Accepted
1. Protein structure refinement using a quantum mechanics-based chemical shielding predictor
2. Prediction of pKa values for drug-like molecules using semiempirical quantum chemical methods

Probable
3. Intermolecular Interactions in the Condensed Phase: Evaluation of Semi-empirical Quantum Mechanical Methods
4. Fast Prediction of the Regioselectivity of Electrophilic Aromatic Substitution Reactions of Heteroaromatic Systems Using Semi-Empirical Quantum Chemical Methods
5. Benchmarking cost vs. accuracy for computation of NMR shielding constants by quantum mechanical methods
6. Improved prediction of chemical shifts using machine learning
7. PM6 for all elements in GAMESS, including PCM interface

Probably not in 2017
8. Protonator: an open source program for the rapid prediction of the dominant protonation states of organic molecules in aqueous solution
9. pKa prediction using semi-empirical methods: difficult cases
10. Prediction of C-H pKa values and homolytic bond strengths using semi-empirical methods
11. High throughput transition state determination using semi-empirical methods

### Reviews of Prediction of pKa values for drug-like molecules using semiempirical quantum chemical methods

I have been remiss in posting reviews of my papers. I submitted the paper to Journal of Physical Chemistry A on November 2, 2016, received first round of reviews November 29, and second round of reviews December 12.  The paper was accepted January 5, 2017 and has appeared online.

Round 1

Reviewer: 1

Recommendation: This paper is not recommended because it does not provide new physical insights.

This is an interesting study on very important subject - prediction of pKa for drug-like molecules. Standard free energy of a molecule is determined as the sum of heat of formation/electronic energy and solvation free energy and these terms are obtained by various semiempirical QM (SQM) methods and two continuous solvent models. Author used SQM methods as a black box and compared them on the basis of their performance to predict pKa. This is, however, not justified since the SQM methods used described differently system under study. For example, PM6-DH+ describes well H-bonding and dispersion energy contrary to e.g. PM3 and AM1. Consequently, structures stabilized by H-bonding and dispersion will be described much better by the former method. Further, PM7 was parametrized to cover dispersion in core parametrization, contrary to PM6 (and PM3) where it should be included a posteriori by e.g. DH+ term. Consequently, PM7 should be also better suited than, e.g. PM6. The question arises how good those methods work and here performance of these methods should be compared with some higher-level method like DFT.

Further, SQM methods were in the last 5 years already used for protein - ligand interactions but these papers were not mentioned at all.

On the basis of above-mentioned arguments I cannot recommend the paper for publication in JPC.

Reviewer: 2

Recommendation: This paper is publishable subject to minor revisions noted.  Further review is not needed.

This is simply excellent work on an important topic. The only thing is that the author could put the importance of his work in an even greater perspective. Semi-empirical methods are becoming increasingly important also in materials science and the pKa is of high importance also in this field, as it is a good indicator of general chemical stability (like it is used in organic chemistry) of molecular (especially organic) materials for technical applications. A recent example is the search for new organic electrolyte solvents for Lithium-air battery devices, where current design principles strongly rely on pKa values (see for instance http://pubs.rsc.org/en/Content/ArticleLanding/2015/CP/C5CP02937F#!divAbstract ).

Round 2

Reviewer: 1

Recommendation: This paper is not recommended because it does not provide new physical insights.

Since the ms was not modified according my comments I cannot recommend it for publication.

Reviewer: 3

Recommendation: This paper is publishable subject to minor revisions noted.  Further review is not needed.

This paper evaluates a number of semi-empirical quantum mechanical (SQM) methods for their suitability in calculating the pKa’s of amine groups in drug-like molecules, with the hope that these methods can be used for high-throughput screening.  This paper is suitable for publication in the special issue, subject to minor revision.

(a) The paper shows that pKa’s calculated by some SQM methods is sufficiently accurate for high-throughput screening.

(b) Indicate the accuracy of related QM calculations (e.g. Eckert and Klamt) and the relative cost of QM vs SQM calculations (order of magnitude will do)

(c) How much better is the SQM approach than the empirical methods cited by the author? (add a comparison in the tables)

(d) The need for 26 reference compounds for 53 amine groups in 48 molecules is disturbingly high (so much so that the null hypothesis has errors only a factor of 2 larger than the best results). What are the errors in the SQM calculated pKa’s if a much smaller number of reference compounds are used? (e.g. 6 or less)  If the errors are acceptable, this could make it possible to automate the procedure so that it could be used to screen larger sets of molecules extracted from typical industrial databases (10,000 – 10,000,000 compounds).

### Reviews of Protein structure refinement using a quantum mechanics-based chemical shielding predictor

I have been remiss in posting reviews of my papers. I received this review on November 11, 2016 of a manuscript I submitted to Chemical Science on September 29, 2016.  The paper was accepted November 17 and has appeared online.

REVIEWER REPORT(S):
Referee: 1

Recommendation: Accept

Review of 'Protein Structure Refinement Using a Quantum Mechanics-Based
Chemical Shielding Predictor'

The authors present a method to refine protein structures with respect to
chemical shifts evaluated by their QM-based ProCS15 method. First applications
to a set of different protein structures showed that small structural changes
lead to a significant reduction of the RMSD.

Empirical methods to predict NMR shifts have shown to be able to deliver
results that correlate well with experimental at almost no computational cost,
in particular in comparison with quantum chemical methods. However, these
methods are also insensitive with respect to structural changes of the
molecular structure. In this work, the authors analyse their empirical ProCS15
method, which is parametrized based on quantum chemical reference calculations,
with respect to structural changes in the molecular geometry. First examples
show that their method has a similar high sensitivity with respect to structure
changes as quantum chemical methods. The results indicate that ProCS15 can
hold a 'predictive power' beyond previous empirical methods, i.e., in
applications to more exotic molecular geometries and conformations.

The manuscript is well written and of appropriate length, and certainly of
great interest for the readers of Chemical Science. The presented applications
have been thoroughly analyzed and results are well outlined for the reader.
Since I've have only a few comments/suggestions, no further revision prior to
publication is necessary. However, I would strongly suggest to consider my
suggestion on the ordering of sections (see below).

+ My main point is actually regarding to the order of sections in the
manuscript.  Since the different methods used are constantly refered to in
the result-section, I would recommend to first outline the
theory/computational methodology and then present the results of the
illustrative calculations on the test systems.

+ In the summary, the authors mention that their method might be used to
improve the accuracy of QM or QM/MM calculations of NMR chemical shifts.
It is certainly difficult to judge the quality of the ProCS15-optimized
structures objectively, i.e., without refering to secondary properties like
NMR shifts. However, it would be interesting to see the impact of the
structural changes in quantum chemical calculations.
This point might be beyond the scope of this work, but is certainly worthwile
to be considered by the authors as a future project.

+ Just a comment on the DFT-based reference calculations used to parametrize
the ProCS15 method: It might be worthwile considering the use of the KT2
functional by Keal and Tozer [JCP 119, 3015 (2003)] and the basis sets
pcS-x/pcSseg-x by Frank Jensen [JCTC 4, 719 (2008):JCTC 10, 1074 (2014)].
Both functional and basis sets are optimized for NMR chemical shift
calculations. A benchmark of those method was done by Flaig et al. [JCTC 10,
572 (2014)].