Dmitrij Rappoport—Beta Living Through Theoretical Chemistry

Predicting chemical reactions is hard. Without experimental data or prior experience, the enterprising theoretical chemist is forced to examine the potential energy surface (PES) of the reaction, tracing the energy valleys from the reactants to potential products in a high-dimensional space, searching for favorable transition states—the mountain passes on the energy landscape—relevant to chemical transformations. The brute-force solution of searching the entire PES is a computationally prohibitive task, which is why many sophisticated techniques of PES exploration have been developed.¹

Alternatively, we can pick any first-semester textbook of organic chemistry to learn how to predict reactions without worrying about any of the complexities of the PES. The first-semester textbook will teach us heuristics—simple rules for finding plausible chemical reactions, however, without guaranteed success. Heuristics are a time-tested approach for solving computationally hard tasks, for example, the A^* search algorithm in robotics.²

What are good chemical heuristics? For polar reactions, breaking bonds into ionic fragments and making bonds from ions are a sensible starting point. The heuristics-aided quantum chemistry (HAQC)³ method uses bond-breaking and bond-making heuristics to construct models of polar organic reactions, complete with the corresponding energy profiles. With the help of additional kinetic heuristics, we are able to distinguish feasible reaction pathways from infeasible ones. The arc heuristic criterion³ accounts for changes in energy along the reaction pathway while penalizing long reaction sequences.

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1. (a) Schlegel, H. B. Geometry optimization. WIREs Comput. Mol. Sci. 2011, 1, 790. (b) Henkelman, G.; Jóhannesson, G.; Jónsson, H. Methods for finding saddle points and minimum energy paths. In Theoretical methods in condensed phase chemistry; Schwartz, S. D., Ed.; Kluwer: Dordrecht, 2002; Vol. 5, pp. 269–302.
2. Pearl, J. Heuristics: Intelligent search strategies for computer problem solving. Addison-Wesley: Reading, MA, 1984.
3. Rappoport, D.; Galvin, C. J.; Zubarev, D. Yu.; Aspuru-Guzik, A. Complex chemical reaction networks from heuristics-aided quantum chemistry. J. Chem. Theory Comput., 2014, 10, 897–907.

Once considered as little more than an academic curiosity, complex reaction networks are now found everywhere—in metabolism, in origins of life, and in many more reaction flasks than previously realized.¹ These reaction networks are composed of many parallel and competing reaction pathways, branching and merging in a complex pattern with tens or even hundreds of chemical species involved.

Perhaps the longest-known complex reaction network, the formose reaction, was obtained by Alexander Butlerov in 1861 by treating an aqueous formaldehyde solution with base. The result is a complex mixture of sugars, sugar alcohols, and other products, with > 50 individual substances identified thus far.² What's more, the formose reaction starts out slow and then suddenly accelerates, a property known as autocatalysis. Because the formose reaction produces sugars—compounds central to cell metabolism—in an autocatalytic manner, it is often thought of as a key component in the origins of life on Earth.

The above model of the formose reaction network constructed by reacting glycolaldehyde (HOCH₂CH=O) with two molecules of formaldehyde (CH₂=O) by means of the heuristics-aided quantum chemistry (HAQC)³ approach has 149 nodes and 445 edges and includes all triose and tetrose sugars, among many other compounds. Moreover, the aldotetrose molecule is shown to undergo retroaldol cleavage into two glycolaldehyde molecules, thus closing the autocatalytic loop and demonstrating the standout feature of the formose reaction.

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1. Jeong, H.; Tombor, B.; Oltvai, Z. N.; Barabási, A.-L. The large-scale organization of metabolic networks. Nature, 2000, 407, 651–654.
2. (a) Boutlerow, A. Formation synthétique d'une substance sucrée. C. R. Acad. Sci. Paris, 1861, 53, 145–147. (b) Breslow, R. On the mechanism of the formose reaction. Tetrahedron Lett., 1959, 1, 22–26.
3. Rappoport, D.; Galvin, C. J.; Zubarev, D. Yu.; Aspuru-Guzik, A. Complex chemical reaction networks from heuristics-aided quantum chemistry. J. Chem. Theory Comput., 2014, 10, 897–907.

The promise of molecular electronics lies in the precise control, with which chemists can create molecular structures. New experimental results in molecular electronics challenge our understanding of conductance phenomena in materials. Molecules that do not carry electric current by the traditional drift mechanism, such as oligopeptides, can act as tunneling conductors.¹

A simple model for understanding the tunneling conductance through molecules is the superexchange model.² It assumes that the molecule has available a series of localized orbitals interacting with each other. Molecules with stronger interactions between neighboring groups are expected to be better tunneling conductors than molecules with weaker interactions.

For linear molecules, the superexchange model predicts a characteristic splitting pattern in the orbital energies. Using the computed values of the in-plane and out-of-plane peptide bond orbitals from density functional theory (DFT) calculations, we are able to derive the key parameters V and ε₀ of the superexchange model for oligopeptides CysGly_n (n=1, …, 5).³

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1. Jortner, J.; Nitzan, A.; Ratner, M. A. Foundations of molecular electronics—Charge transport in molecular conduction junctions. In Introducing molecular electronics; Cuniberti, G., Richter, K., Fagas, G., Eds.; Springer: Berlin, 2006; pp. 13–54.
2. Kosloff, R.; Ratner, M. A. Superexchange-assisted through-bridge electron transfer: Electronic and dynamical aspects. Isr. J. Chem., 1990, 30, 45–48.
3. Baghbanzadeh, M.; Bowers, C. M.; Rappoport, D.; Żaba, T.; Gonidec, M.; Al-Sayah, M. H.; Cyganik, P.; Whitesides, G. M. Charge tunneling along short oligoglycine chains. Angew. Chem. Int. Ed., 2015, 54, 14743–14747.

The crucial first step toward a deeper understanding of chemical structure is the definition of a suitable non-empirical distance function expressing similarities between chemical and spatial structures of molecules. In conformational studies of small molecules and proteins, root-mean-square deviation (RMSD) has been the tool of choice for quantifying structural similarity. Unfortunately, RMSD cannot be applied to molecules of different composition.

Our starting point is the 3D molecular structure. The atomic coordinates are first converted to a translationally and rotationally invariant representation. A discrete spherical grid is constructed with the center of mass as the origin. The nuclear charge q along with the discretized spherical polar coordinates r, θ, and ϕ form a four-dimensional discrete metric space. In order to preserve locality, the positions of the four-dimensional space (q, r, θ, and ϕ) are encoding usign a space-filling curve, e.g., Morton's Z-curve.¹

Thanks to the discretization and traversal along a space-filling curve], the atomic and spatial properties are encoded as a fixed-length binary string, while the distances in the Cartesian space are approximated by string distances (Levenshtein distance is an example) or set distances (Hausdorff distance). Unlike RMSD and similar properties, string and set distances are well-defined for objects of different cardinality, i.e., molecules of different size or composition².

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1. (a) Sagan, H. Space-filling curves. Springer: New York, NY 1994. (b) Morton, G. M. A computer-oriented geodetic data base; and a new technique in file sequencing; Technical Report for IBM Ltd.: Ottawa, Canada, 1966.
2. Jasrasaria, D.; Pyzer-Knapp, E. O.; Rappoport, D.; Aspuru-Guzik, A. Space-filling curves as a novel crystal structure representation for machine learning models. 2016, arXiv:1608.05747.