A Robust and Accurate Tight-Binding Quantum Chemical Method for Structures, Vibrational Frequencies, and Noncovalent Interactions of Large Molecular Systems Parametrized for All spd-Block Elements (Z = 1−86)

Stefan Grimme, Christoph Bannwarth, and Philip Shushkov (2017)
Highlighted by Jan Jensen

Copyright American Chemical Society (2017)

Inspired by the success of the sTDA-xTB method for predicting electronic spectra, Grimme and co-workers present the tight binding DFT method GFN-xTB for predicting Geometries, vibrational Frequencies and Noncovalent interactions ("x" stands for extensions in the AO basis set and the form of the Hamiltonian).  

The method is implemented in a new program called xtb which includes shared memory parallelization, angeometry optimizer, MD, conformational searches, reaction path optimisation modules, and a GB solvation model supplemented with analytical nuclear gradients.  The software is free to academics and can be obtained by writing to the authors.

Importantly, the method is parameterized for all spd elements, so finally there is an alternative to PM6 for heavier elements. A Fermi smearing technique helps convergence for molecules with small HOMO-LUMO gaps and GFN-xTB gives structures organometallic compounds that are in good agreement with DFT.

As implied by the name, GFN-xTB is not parameterized against reaction energies but the methods gives reasonable results for properties like heats of formation.  However, as the authors write

A key premise of the present method is its special purpose character. In our view, low-cost semiempirical QM methods cannot describe simultaneously very different chemical proper- ties, such as structures and chemical reaction energies, and the GFN-xTB method (as the name conveys) focuses on structural properties. The efficiently computed structures and vibrational frequencies or the conformers obtained from global search procedures can (and should) be used subsequently for more accurate DFT or WFT refinements. We hope that the method can serve as a general tool in quantum chemistry and in particular recommend GFN-xTB optimized structures (and thermostatistical corrections) in a multilevel scheme together with PBEh-3c single-point energies. Large-scale molecular dynamics, screening of huge molecular spaces (libraries), parametrization of force-fields, or providing input for novel machine learning techniques are obvious other fields of application.

I thank Anders Christensen for bringing this paper to my attention


This work is licensed under a Creative Commons Attribution 4.0 International License.

A few review articles

Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

A few nice review/opinion pieces have been piling up in my folder of papers of interest for this Blog. So, this post provides a short summary of a number of review articles that computationally-oriented chemists may find of interest.

Holy Grails in computational chemistry

Houk and Liu present a short list of “Holy Grails” in computationally chemistry.¹ They begin by pointing out a few technical innovations that must occur for the Grails to be found: development of a universal density functional; an accurate, generic force field; improved sampling for MD; and dealing with the combinatorial explosion with regards to conformations and configurations. Their list of Grails includes predicting crystal structures and structure of amorphous materials, catalyst design, reaction design, and device design. These Grails overlap with the challenges I laid out in my similarly-themed article in 2014.²

Post-transition state bifurcations and dynamics

Hare and Tantillo review the current understanding of post-transition state bifurcations (PTSB).³ This type of potential energy surface has been the subject of much of Chapter 8 of my book and many of my blog posts. What is becoming clear is the possibility of a transition state followed by a valley-ridge inflection leads to reaction dynamics where trajectories cross a single transition state but lead to two different products. This new review updates the state-of-the-art from Houk’s review⁴ of 2008 (see this post). Mentioned are a number of studies that I have included in this Blog, along with reactions involving metals, and biochemical systems (many of these examples come from the Tantillo lab). They close with the hope that their review might “inspire future studies aimed at controlling selectivity for reactions with PTSBs” (italics theirs). I might offer that controlling selectivity in these types of dynamical systems is another chemical Grail!

The Hase group has a long review of direct dynamics simulations.⁵ They describe a number of important dynamics studies that provide important new insight to reaction mechanism, such as bimolecular S_N2 reactions (including the roundabout mechanism) and unimolecular dissociation. They write a long section on post-transition state bifurcations, and other dynamic effects that cannot be interpreted using transition state theory or RRKM. This section is a nice complement to the Tantillo review.

Benchmarking quantum chemical methods

Mata and Suhm look at our process of benchmarking computational methods.⁶ They point out the growing use of high-level quantum computations as the reference for benchmarking new methods, often with no mention of any comparison to experiment. In defense of theoreticians, they do note the paucity of useful experimental data that may exist for making suitable comparisons. They detail a long list of better practices that both experimentalists and theoreticians can take to bolster both efforts, leading to stronger computational tools that are more robust at helping to understand and discriminate difficult experimental findings.

References

1) Houk, K. N.; Liu, F., "Holy Grails for Computational Organic Chemistry and Biochemistry." Acc. Chem. Res. 2017, 50 (3), 539-543, DOI: 10.1021/acs.accounts.6b00532.

2) Bachrach, S. M., "Challenges in computational organic chemistry." WIRES: Comput. Mol. Sci. 2014, 4, 482-487, DOI: 10.1002/wcms.1185.

3) Hare, S. R.; Tantillo, D. J., "Post-transition state bifurcations gain momentum – current state of the field." Pure Appl. Chem. 2017, 89, 679-698, DOI: 0.1515/pac-2017-0104.

4) Ess, D. H.; Wheeler, S. E.; Iafe, R. G.; Xu, L.; Çelebi-Ölçüm, N.; Houk, K. N., "Bifurcations on Potential Energy Surfaces of Organic Reactions." Angew. Chem. Int. Ed. 2008, 47, 7592-7601, DOI: 10.1002/anie.200800918

5) Pratihar, S.; Ma, X.; Homayoon, Z.; Barnes, G. L.; Hase, W. L., "Direct Chemical Dynamics Simulations." J. Am. Chem. Soc. 2017, 139, 3570-3590, DOI: 10.1021/jacs.6b12017.

6) Mata, R. A.; Suhm, M. A., "Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction?" Angew. Chem. Int. Ed. 2017, ASAP, DOI: 10.1002/anie.201611308.

'
This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Intrinsic map dynamics exploration for uncharted effective free-energy landscapes

Eliodoro Chiavazzo, Roberto Covino, Ronald R. Coifman, C. William Geard, Anastasia S. Georgiou, Gerhard Hummer, and Ioannis G. Kevrekidis. PNAS June 20, 2017
Contributed by Jesper Madsen

The desire to use enhancing sampling to save computational expense in simulations has been there from the beginning. Broadly speaking, there are two main approaches of enhancing molecular dynamics (MD) simulations in order to determine the free-energy surface (FES) of a computationally expensive Hamiltonian: 1) Trajectory-based enhanced sampling (e.g. temperature replica-exchange) and 2) collective variable (CV)-based methods (e.g. umbrella sampling). It is worth noting that the “zoo” of actual techniques to date is rather large. Either type of method, trajectory-based or CV-based, comes with its own set of advantages and disadvantages and mixing-and-matching is popular. 

Here I highlight a newcomer that is spun off from the rapidly growing field of Machine Learning – a field that most of us is keeping a keen eye on these days. 

The algorithm is called intrinsic map dynamics (iMapD) and it is conceptually simple (See Fig. 1 from the paper). 

1. Run a MD trajectory

2. Figure out, in some abstract sense, what region of configuration space you have sampled.

3. Determine the (non-linear) boundary of the sampled region in the abstract space

4. Initialize new MD trajectories in these boundary areas and explore the uncharted territories of the FES.

It is with the concretization of each step above that machine learning has contributed its ideas and tools. Specifically, the map of the configuration space is data mined and a d-dimensional manifold learning technique called diffusion maps (DMAPs) is applied to find the appropriate manifold and its dimensionality. The (d-1)-dimensional boundary manifold of the explored region is determined by a “wrapping” algorithm (here they use alpha shapes). Outward extrapolation is done by performing local principal component (LPC) analysis in ambient space. New simulations are seeded from these extended initial configurations and the algorithm loops back to the beginning. 

Fig.1: Pictorial illustration of the iMapD exploration procedure with (Left) 1D and (Right) 2D effective FESs. In Left Inset, a good collective coordinate is already available—the collective coordinates in Left and Right are not a priori known. "Copyright (2017) National Academy of Sciences

Since iMapD is a trajectory-based approach, absolutely no prior knowledge about the mechanistics of the process we study is required, which is appealing. One can think of the method as a clever hybrid MD/Monte Carlo algorithm and time will show how it stacks up against other alternative approaches in terms of practical usefulness. 

WInote that the algorithm is pedagogically presented in the paper and if you fancy Indiana Jones, well then there’s a little treat for you in the main text. Enjoy.

The Structure of the Elusive Simplest Dipeptide Gly-Gly

Cabezas, C.; Varela, M.; Alonso, J. L., Angew. Chem. Int. Ed. 2017, 56, 6420-6425
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Continuing their application of laser ablation molecular beam Fourier transform microwave (LA-MB-FTMW) spectroscopy and computational chemistry to biochemical molecules (see these previous posts), the Alonso group reports on the structure of the glycine-glycine dipeptide 1.¹ The microwave spectrum shows three different conformers. MP2/6-311++G(d,p) computations, the same method they have previously utilized for predicting geometries, revealed a number of different conformations. By matching the spectroscopic parameters obtained from the spectrum with those of the computed structures, they proposed the three conformations 1a, 1b, and 1c, shown in Figure 1.

1a

1b

1c

Figure 1. ωb97xd/6-31G(d) optimized structures of the three conformers of 1.
Note that the authors did not report their structures in their supporting materials(!) so I have optimized them.

The structures of conformers 1a and 1b are nearly planar. MP2 predicts a non-planar rotomer of 1a, which brings the carboxyl group out of plane, to be the lowest conformation in terms of electronic energy. With the M06-2x functional, this non-planar rotomer is about isoenergetic with 1a. With all computational levels 1a is the lowest in free energy. The barrier for rotation between the non-planar rotomer and 1a is very small, and this explains why it is not observed in the supersonic expansion.

References

1) Cabezas, C.; Varela, M.; Alonso, J. L., "The Structure of the Elusive Simplest Dipeptide Gly-Gly." Angew. Chem. Int. Ed. 2017, 56, 6420-6425, DOI: 10.1002/anie.201702425.

InChIs

1: InChI=1S/C4H8N2O3/c5-1-3(7)6-2-4(8)9/h1-2,5H2,(H,6,7)(H,8,9)
InChIKey=YMAWOPBAYDPSLA-UHFFFAOYSA-N

'
This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Development of a 13C NMR Chemical Shift Prediction Procedure Using B3LYP/cc-pVDZ and Empirically Derived Systematic Error Correction Terms: A Computational Small Molecule Structure Elucidation Method

Xin, D.; Sader, C. A.; Chaudhary, O.; Jones, P.-J.; Wagner, K.; Tautermann, C. S.; Yang, Z.; Busacca, C. A.; Saraceno, R. A.; Fandrick, K. R.; Gonnella, N. C.; Horspool, K.; Hansen, G.; Senanayake, C. H., J. Org. Chem. 2017, ASAP
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Here’s another take on automating a procedure for using computer ¹³C chemical shifts to assess chemical structure.¹ (Have a look at these previous posts for some alternative methods and applications.) The approach here is to benchmark a few computational methods against a conformationally flexible drug-like molecule, in this case 1. A variety of conformations were optimized using the different computational methods, and ¹³C chemical shifts evaluated from a Boltzmann-weighted distribution. While the best agreement with the experimental chemical shifts (based on the root-mean-squared deviation) is with ωB97XD/cc-pVDZ, the authors opt for B3LYP/cc-pVDZ for its computational efficiency with only slightly poorer performance. (It should be note that WC04/cc-pVDZ, a functional designed for computing ¹³chemical shifts,² is almost as good as ωB97XD/cc-pVDZ. Also, not mentioned in the article is the dramatically poorer performance of the pcS-2 basis set, despite the fact that it was parametrized³ for NMR computation!)

They apply the procedure to a number of test cases. For example, the HIV-1 reverse transcriptase inhibitor nevirapine hydrolyzes to a compound whose structure has been difficult to identify. The four proposed structures 2a-d were subjected to the computational method, and the ¹³C chemical shift RMSD for 2d is only 2.3ppm, significantly smaller than for the other 3 structures. Compound 2d was then synthesized and its NMR matches that of the nevirapine hydrolysis product.

References

1) Xin, D.; Sader, C. A.; Chaudhary, O.; Jones, P.-J.; Wagner, K.; Tautermann, C. S.; Yang, Z.; Busacca, C. A.; Saraceno, R. A.; Fandrick, K. R.; Gonnella, N. C.; Horspool, K.; Hansen, G.; Senanayake, C. H., "Development of a 13C NMR Chemical Shift Prediction Procedure Using B3LYP/cc-pVDZ and Empirically Derived Systematic Error Correction Terms: A Computational Small Molecule Structure Elucidation Method." J. Org. Chem. 2017, ASAP, DOI: 10.1021/acs.joc.7b00321.

2) Wiitala, K. W.; Hoye, T. R.; Cramer, C. J., “Hybrid Density Functional Methods Empirically Optimized for the Computation of ¹³C and ¹H Chemical Shifts in Chloroform Solution,” J. Chem. Theory Comput. 2006, 2, 1085-1092, DOI: 10.1021/ct6001016.

3) Jensen, F., “Basis Set Convergence of Nuclear Magnetic Shielding Constants Calculated by Density Functional Methods,” J. Chem. Theory Comput., 2008, 4, 719-727, DOI: 10.1021/ct800013z.

InChIs

1: InChI=1S/C24H26F4N2O4S/c1-4-35(33,34)18-7-8-20-15(10-18)9-17(30-20)13-23(32,24(26,27)28)22(2,3)12-14-5-6-16(25)11-19(14)21(29)31/h5-11,30,32H,4,12-13H2,1-3H3,(H2,29,31)/t23-/m0/s1
InChIKey=ILKZCEOVIFOUBJ-QHCPKHFHSA-N

2d: InChI=1S/C15H16N4O2/c1-9-6-8-17-14(18-10-4-5-10)12(9)19-13-11(15(20)21)3-2-7-16-13/h2-3,6-8,10H,4-5H2,1H3,(H,16,19)(H,17,18)(H,20,21)
InChIKey=ZLFOGBWAZNUXAD-UHFFFAOYSA-N

'
This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Does Proton Conduction in the Voltage-Gated H+ Channel hHv1 Involve Grotthuss-Like Hopping via Acidic Residues?

Siri C. van Keulen, Eleonora Gianti, Vincenzo Carnevale, Michael L. Klein, Ursula Rothlisberger, and Lucie Delemotte (2017)
Contributed by Dries Van Rompaey

Voltage gated proton channels are membrane channels that are are regulated by both the pH gradient and the voltage. In most cases these channels only open when the electrochemical proton gradient is outwards, functioning as a passive acid extrusion mechanism. They have an exquisite selectivity for protons, prompting Delemotte and coworkers to investigate the mechanism of proton transport and the origin of this selectivity.

The mechanism for proton transport was explored using an integrative approach, combining classical simulations with QM/MM. Three separate cation binding sites can be observed in the channel, each consisting of a pair of negatively charged residues. QM/MM simulations were used to examine binding and unbinding of the proton, while conformational rearrangements were sampled using classical simulation. In contrast to the classic Grotthus mechanism, where the proton is transported through a water wire by subsequent bond formation and bond breaking, simulations indicated that the proton may traverse the channel by jumping between the acidic residues, assisted by a water molecule. As shown by classical MD, structural rearrangements occur upon proton binding, orienting the residues for the next proton jump, allowing for the proton to move through the channel. This integrative modelling study provides an interesting and novel mechanism for the transfer of a proton across a membrane. It will be interesting to see where future work on this channel leads.