What I Do...
As a theoretical chemist I'm often asked, with varying degrees of subtlety, "What exactly do you do?" I try to provide a simple, one- or two-sentence explanation having something to do with "chemistry on computers". Unfortunately, my answer usually neither does justice to my field nor sheds any substantive light on the matter for the person asking (who often happens to be family, friends, or even my wife). So here I make a feeble attempt to explain what happens in the windowless bowels of chemistry buildings...
What I Don't Do
Let me clear up one thing first. Contrary to what my experimental colleagues might quip, the term "theoretical chemist" does not mean that I am "theoretically a chemist". It means that I study and develop the theories that underly chemistry. We'll dive into what that means in a moment.
With this requisite clarification out of the way, let's begin with a common distinction among branches of chemistry:
The Big Picture
Instead, I fall under the category of a physical chemist. One of my forefathers in the field is often attributed with saying, "Physical chemistry is the study of that which is interesting." I wholeheartedly agree, although my judgment may be clouded for obvious reasons. Physical chemists study the physical properties of chemicals, i.e., atoms and molecules. I'll refresh the memories of those of you who may have dozed off during high school chemistry by reminding you that a molecule is a collection of atoms that are chemically "bonded" together. Water (H2O), for example, is a molecule made of hydrogen (H) and oxygen (O) atoms:
Come to think of it, water is a great reference point here. Non-chemists might think of water as a clear, blue liquid. Physical chemists picture water as being composed of water molecules, each of which has two hydrogens and an oxygen bonded at roughly 104.5 degrees, as shown in the picture above. More generally, physical chemists usually take a "bottom-up" approach to describing chemical properties. What happens at the molecular scale is not only interesting; it directly affects the properties of things on the macroscopic (i.e., things-you-see) scale. Thus, a physical chemist might ask—and hopefully answer—the following questions about water:
For example, the answer to the first question can (mostly) be explained by the study of a single water molecule. It is "blue" because a water molecule absorbs red light. The red part of the spectrum makes it wiggle in a specific way, and the energy of the light is converted to a wiggle. The blue part does not make it wiggle and, therefore, passes right through the water. See, for example, this link. Physical chemists know this reasoning from two sources: Experimentally, this property can be determined by shining light at a sample of water and measuring what comes out. Theoretically, we know that water wiggles at these wavelengths from quantum mechanics (the stuff I do).
The second question can also be explained at the molecular level. For reasons that are a bit complicated, water molecules like to stick together. The things I do can explain why...see below. At really cold temperatures, water sticks together quite well and forms ice. At higher temperatures, the thermal energy (which makes things spin, wiggle, and move through space) partially negates the sticking of the water molecules, so they only weakly stick together on average...giving us liquid water. At even higher temperatures, the happy sticking is insufficient to balance the thermal energy, and we get steam. A physical chemist would seek to figure out what makes the molecules stick together and quantify this interaction. (For the answers to the other questions, you'll have to ask me over a meal.)
Okay, if you've made it this far I applaud you. Have a Scotch and come back.
Physical chemists may be further subdivided into experimentalists and theorists, as well as the occasional person who does both. These distinctions are pretty self-explanatory... physical chemists either work in a lab with chemicals or at a computer with fake chemicals. I fall in the latter category, although I often work closely with experimentalists in order to keep me grounded in (our version of) reality.
Theorists describe the chemical world with physics and math. Ultimately, chemistry comes down to the motion of molecules, atoms, and the particles that make up atoms. The equations that describe them are quantum mechanics, developed in the 1920s-1930s. And, in fact, all of these equations are known! So, you may ask, what in the world do we do all day??? The most famous answer to this question comes from Paul Dirac, one of the founders of quantum mechanics:
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.This point is pretty incredible. We have at our disposal the equations that govern the properties and motion of every single atom and molecule in the universe. They describe what the molecules are, how they act, and how they will act for all time. They describe the water molecules mentioned above, DNA, cancer, construction materials, brain cells, etc, etc, etc. But Dirac's point is that there's a catch... While we have the equations, they are impossible to solve for even the simplest of molecules, let alone big molecules (like DNA) or large collections of molecules (like liquids). We, therefore, use computers to solve these equations for us, to varying degrees of approximation. Just to clarify, these "unsolvable" equations aren't unsolved because we're lazy. These aren't your garden-variety homework problems, for which we simply haven't tried the right technique. They are problems that have no "normal" solution, and so we turn to computers to help us.
Electronic Structure TheoryDuring graduate school, I fell under a subheading of theoretical chemistry called "electronic structure theory". We all know that molecules are made of positively charged nuclei and negatively charged electrons. But let's stop right there... We have a bunch of stuff that attracts (opposite charges) and a bunch of stuff that repels (like charges). How do we predict what the resulting molecule is? A very intricate dance of the electrons makes these particles stick together into molecules and take the shapes they do. Electronic structure theory calculates these structures from basic physics (i.e., without experimental input). Our field asks the following questions:
Now to practical matters... Those hard equations mentioned above are hard because all of the electrons interact. If they were just little balls bouncing around independently, we'd have no problem. But when one electron moves, all of the others adjust. In short, we develop computer algorithms for solving this electron half of the problem.
Imagine a room full of 100 people; some like each other, some despise each other. Where does everybody end up? This already is a hard enough problem for people (remember that ol' wedding seating chart?)...now imagine that all 100 of them were running as fast as they could. Where do they all go? I dunno. To make things worse, electrons have additional properties that make the problem even harder, and we quickly run into a problem that not only is unsolvable "by hand" but is practically impossible for even computers to solve exactly. I was careful in that last sentence to say "practically" impossible. We almost always have what we call "numerical" methods for solving our equations. They don't solve things in the way you might normally think about solving equations, but they do break the problem up into many (!) bite-sized chunks that computers are good at handling. (Computers are very good at doing very simple things very many times. We exploit this fact.) Though it's a far cry from our algorithms, the old "guess and check" method you undoubtedly experimented with in grade school is a simple example. If you don't know how to solve a problem, guess a random number. If it's wrong, change your number, and keep doing so until you get very close to the right answer. This would be a tedious process for a human, but a machine that can do trillions of operations per second is pretty good at it.
The problem is that these methods do not scale linearly with the size of the system we are studying. In other words, if we double the number of particles (i.e., two molecules instead of one), the cost of the computer calculation does not stay the same nor even increase by only a factor of two. In fact, most of the methods we use scale with some power of the size of the system. Consider, for example, the simplest approximation that we use...it scales roughly with the fourth power of the sytem size. Let's say that a calculation of the electrons of the water molecule above takes one second on the computer...about the amount of time it might take this webpage to load. If we now consider a blob of 1000 water molecules—still nowhere near the size of something seen with the naked eye—the calculation would require 10004 seconds. How long is this? It's 1012 seconds, or 3x108 hours, or 1.2x107days, or...ready?...31,710 years. So, in order to somewhat accurately obtain a description of the electrons in water, it would require over thirty thousand years of computer time. Not exactly a promising prospect.
A great analogy to this non-linear scaling is compound interest. If you get a 7% annual interest rate in your favorite investment account, we would say that your money grows as [amount of $]1.07. In other words, compound interest makes your money grow non-linearly...the more you have, the more you make. While such scaling is wonderful for investments, it's terrible for computations. The fourth-order scaling mentioned above is equal to a 400% interest rate...except that it's on a loan, not an investment. Imagine how quickly you'd be under water if your mortage rate was 400%!
Therefore, we must develop "tricks" to make these calculations more manageable. These tricks form the cornerstore of electronic structure theory and also give us a simple framework for viewing the utterly hopeless complexity of molecules (try drawing a 15-dimensional picture the next time you're bored at the office). I'll spare you the details of how these algorithms work. The important lesson is that we constantly develop faster and more accurate techniques for describing the behavior of electrons. Along the way, we also (in theory...heh heh) develop tools for describing properties relevant to chemists.
Most of electronic structure theory (above) deals with the properties of the electrons inside of a molecule. But molecules also move, wiggle, and dance, which involves the motion of the nuclei. This other half of the problem—and how it couples to the electronic half—is the focus of my current work. This branch of theoretical chemistry is called "dynamics". In short, we describe how molecules move.
In order to describe the relevance of dynamics, let's consider an illustrative example that we all know: the greenhouse effect. Regardless of your stance on global warming, the greenhouse effect is real...if it wasn't, we'd all be popsicles. The gradeschool version of this effect that we've all learned is that sunlight shines on the earth, and the atmosphere traps the heat. Have you ever considered how this works? Sunlight itself is not heat. Heat is the motion of molecules, but there are hardly any molecules in space. Light itself travels through space and then somehow turns into heat here on earth.
From the physical chemistry side of things, here's what happens... Light from the sun is absorbed by many things around us—dirt, plants, buildings, even skin. This absorption process excites the electrons in molecules. But then what? On a very short time scale, this electronic motion is funneled into the wiggling of molecules (vibrations and rotations). These motions are what we call heat. The wiggling of one thing (let's say dirt) then turns into the wiggling of another molecule, such as air. This process is called heat transfer. Now the kicker... Gas molecules, such as carbon dioxide, do not absorb the original light from the sun. Their electrons are not arranged in the correct way to be plucked by light (if they did, air wouldn't be clear). The atoms in carbon dioxide do, however, really like to vibrate. Thus, they let sunlight go straight through, but what comes back from the ground—the wiggling—is readily absorbed by these molecules. So all of the light can come in, but little of the heat can go out. This is the greenhouse effect.
Underlying the previous discussion is an assessment of what happens when molecules interact with light and with each other. Who likes light? Who turns light into wiggling? Who readily transfers vibrations? How quickly do all of these processes happen? These types of questions are the subject of chemical dynamics.
So that's what I do in a (big) nutshell. Like I said at the beginning, we simulate chemical systems on a computer. But we also dig into the meat of what causes chemistry to happen and, ideally, provide predictive tools that can be used throughout chemistry, physics, biology, medicine, etc. In order to make these things possible, we have to be computer and math nerds because the equations that govern chemistry are wholly unsolvable. The algorithmic part is really more of an engineering task, but our ultimate goal is always to lend insight to chemical problems. We've had quite a bit of success in the last few decades, and experimentalists now almost always involve theory in their research. The "scaling" discussion above, however, provides job security for the foreseeable future.
I'll leave you with one of my favorite sayings. I, of course, recognize the irony of including this quote, given that most of what is written above probably doesn't make sense.