Using Computational Chemistry to Understand & Discover Chemical Reactions K. N. Houk & Peng Liu Abstract: Chemistry, the “science of matter,” is the investigation of the fabulously complex interchanges Downloaded from http://direct.mit.edu/daed/article-pdf/143/4/49/1830827/daed_a_00305.pdf by guest on 28 September 2021 of atoms and bonds that happen constantly throughout our universe and within all living things. Com- putational chemistry is the computer modeling of chemistry using mathematical equations that come from physics. The ½eld was made possible by advances in computer algorithms and computer power and continues to flourish in step with developments in those areas. Computational chemistry can be thought of as both a time-lapse video that slows down processes by a quadrillion-fold and an ultramicroscope that provides a billion-fold magni½cation. Computational chemists can quantitatively simulate simple chemistry, such as the chemical reactions between molecules in interstellar space. The chemistry inside a living organism is dramatically more complicated and cannot be simulated exactly, but even here com- putational chemistry enables understanding and leads to discovery of previously unrecognized phenomena. This essay describes how computational chemistry has evolved into a potent force for progress in chem- istry in the twenty-½rst century. In chemistry class, we learn that chemists study mat - ter and its properties; they wear lab coats and safety glasses and mix chemicals together and ob serve the amazing things that happen. But there is no need to go into a chemical laboratory to ½nd chemistry. In fact, chemistry is literally everywhere: it is the thou - sands of chemical processes that result in the emer- K. N. HOUK, a Fellow of the Amer - gence of a growing plant from a seed, the transfor- ican Academy since 2002, is the Saul mation of flower nectar into the flight of a humming - Winstein Chair in Organic Chemis - bird, or the conversion in chemical factories of oil try in the Department of Chemistry from decayed ancient life into polymers that are made and Biochemistry at the University into stylish fabrics or spacesuits. How do these things of California, Los Angeles. happen? Chemists learn how chem i cal reactions oc - PENG LIU is an Assistant Professor cur and how to control them for hu man purposes. In of Chemistry at the University of the twenty-½rst century, com puta tional chemistry Pittsburgh. plays a major role in chemical discovery. (*See endnotes for complete con- Before the twentieth century, knowledge about the tributor biographies.) properties and transformations of matter was gained © 2014 by the American Academy of Arts & Sciences doi:10.1162/DAED_a_00305 49 Using through experimen ta tion. Early chem ical to obtain ever more accurate solutions to Compu - theories and rules, such as Mendeleev’s pe - small problems. tational Chemistry riodic table, were em pirically derived from to Under - observations of chemical phenomena. xperiments yield facts, such as which stand & E Discover Some theories were wrong (for example, products are formed when various chem- Chemical the phlogiston theory, which posited the icals come into contact or how much elec - Reactions existence of an element called phlogiston tricity is generated when sunlight shines on in order to explain com bus tion), while oth - a chunk of silicon or sandwich of organic ers were very crude mod els. The discovery polymers. However, experiments do not of quantum me chan ics in the 1920s revolu - tell us why such results occur. For example, tionized science. Heisenberg, Schrödinger, why are certain products formed and not Dirac, and other physicists developed a others, or why is only a few percent of the Downloaded from http://direct.mit.edu/daed/article-pdf/143/4/49/1830827/daed_a_00305.pdf by guest on 28 September 2021 theo ry based on pure mathematics that energy in sunlight converted to electricity? explains how chem istry arises from the in - Both theory and computation are needed teractions of nu clei and electrons.1 Paul Di - to answer these questions: theory to pro- rac, one of the Nobel Laureates for quan- vide the general framework and simple tum me chan ics, noted in 1929: mod els for a qualitative conceptual under - pinning of experimental phenomena, and The underlying physical laws necessary for computation to flesh out an accurate mi - the mathematical theory of a large part of cro scopic account of them. Today’s chem - physics and the whole of chemistry are thus ists attempt to employ computations to completely known, and the dif½culty is only explain phenomena and guide new exper - that the exact application of these laws leads iments, but quantitative modeling of to equations much too complicated to be chem ical reactions is very challenging due soluble. It therefore becomes desirable that to problems of scale. The chemical phe- approximate practical methods of applying nomena that we observe are the outcomes quantum mechanics should be developed, of rearrangements of the atomic structures which can lead to an explanation of the main of a huge number of very small molecules. features of complex atomic systems without A water droplet contains around one sex- too much computation.2 tillion (1021) molecules, each with a slight ly Exactly as Dirac envisioned, a hierarchy different shape, velocity, and energy at any of mathematical models, with different given moment. The atoms in each wa ter lev els of approximation, has been devel- molecule are moving rapidly inside the oped over the last century.3 But Dirac could droplet: the atoms change to a new ar - not foresee the discovery and development rangement 1014 times per second. To com - of powerful computers with which we can pletely reproduce the properties of that solve some of these highly complex prob- droplet and predict how it will change up - lems of applied mathematics. While we still on heating or mixing with other chemicals cannot obtain exact solutions to the quan - would require simulating all sextillion of tum mechanical equations for chemical the droplet’s fast-moving molecules, were systems with very large numbers of atoms, we to compute everything from exact we can calculate answers as close as de - quan tum mechanical equations (or “½rst sired to the exact mathematical solution, principles”). Modern computers can calcu - given enough computer time. When more late how one molecule changes over time, powerful computers become available, but to calculate all sextillion or even a sig - com putational chemists will set out to ni½cant fraction of them is not practical, solve bigger and bigger problems and try nor will it be anytime in the foreseeable 50 Dædalus, the Journal ofthe American Academy of Arts & Sciences future. However, approximate equations– this, calculations on such large mol e cules K. N. Houk model systems calibrated with empirical must involve shortcuts that make the cal- & Peng Liu data to capture the average properties of a culations faster but less accu rate. water molecule and its interactions with oth er molecules–can be computed to al- Computational modeling is the simula- low us to understand what occurs in the tion of chemical structures, properties, and drop of water and to estimate its proper- reactions with a computer. Simulation is ties: density, surface tension, viscosity, and sometimes described as the third form of even chemical reactivity. science. The ½rst form, experimental sci- Aside from the daunting numbers of cal - ence, starts with empirical observations culations that must be performed to mim - and models created from inductive logic. ic reality, there is also the issue of the size of The second form is theoretical science, for - Downloaded from http://direct.mit.edu/daed/article-pdf/143/4/49/1830827/daed_a_00305.pdf by guest on 28 September 2021 some important molecules: smaller mol - mulated in equations that describe the e cules are, of course, much simpler to mod - phe nomena of the natural world. Simula- el. As the number of electrons in a molecule tion is a third form where mathematical increases, the time needed to perform cal- equations are coded into computer pro- culations on it goes up rapidly. A hydrogen grams to predict what happens in various H molecule ( 2) con sists of two of the light - hypothetical chemical situations. est atoms bond ed to gether and only two The fundamental theories used in these electrons; natural gas con sists pri marily of computer programs are based on classi- CH meth ane ( 4), which has on ly ½ve light cal and quantum mechanics. Galileo, Kep - at oms and ten electrons. Everything about ler, Newton, and other scienti½c revolu- individual hy dro gen and meth ane mole- tionaries of the late seventeenth century cules can be com puted near ly ex actly in a developed what we now call classical me - short time. How ever, many mol ecules of chanics, which describes the physics of crucial importance for life, and those that relatively large objects moving on a hu man make up com mon materials, are much timescale. Newton’s equations of motion larg er. Consider a nucleic acid mol ecule, (as these classical mechanics equa tions are such as a strand of dna, or a protein that often called) are used for molecular dy - controls so many of the pro cesses of life, namics simulations to derive the motion of or a polymer molecule in a poly styrene cup: atoms in molecules or larger ob jects over each molecule contains thousands of at - time. Classical mechanics can also be used oms and can ex ist in many different three- to study structures of molecules by ½tting dimensional ar rangements that in ter con - equations to empirical data–what chem - vert very quickly. To simulate the be hav - ists call “molecular mechanics.” However, ior of chemicals with so many atoms takes classical mechanics cannot predict chemi- many computer re sources.