QnAs with Martin Head-Gordon

Introductory chemistry courses characterize chemical bonds as one of several types, such as ionic and covalent bonds. Bonds differ in their strength and mechanism of joining atoms together. However, bonds form through multiple mechanisms, each contributing to the bond’s strength and character. Martin Head-Gordon is a theoretical chemist at the University of California, Berkeley and Lawrence Berkeley National Laboratory, and a recently elected member of the National Academy of Sciences. He develops electronic structure theory to permit improved calculations of molecules, including the strength of chemical bonds. To better understand how and why bonds form, he also works on energy decomposition analysis (EDA), which gives the value of physically different contributions to chemical bonds. Head-Gordon’s Inaugural Article (1) presents an advance in EDA for understanding chemical bonds by properly including spin-coupling effects. Head-Gordon recently spoke to PNAS about his findings.

PNAS: How did you become interested in theoretical chemistry?

Head-Gordon: I picked chemistry as my major and then discovered that I was neither greatly talented at nor greatly interested in laboratory work. But that was the era when you could build your own computer. I got hooked on that. I fell into theoretical chemistry as the intersection between my major and my hobby.

PNAS: When picturing the chemical bonds between atoms, many people might think of the ball-and-stick diagrams in introductory chemistry. Is there a more accurate way to picture chemical bonds?

Head-Gordon: Chemists often think of chemical bonds a little the same as how botanists classify plants. You can classify bonds as single bonds and double bonds, and then we know them by their bond strength. A carbon–carbon single bond is roughly 100 kilocalories per mole. That’s the energy you have to put in to break the chemical bond, or conversely the energy that you get out if you make that chemical bond. Chemists have an understanding of bond types by bond strengths as the next evolution beyond ball-and-stick Lewis structure cartoons.

PNAS: What is an EDA and what information does it give us?

Head-Gordon: The field of EDA is probably at least 40-years-old. But historically they were really designed for nonbonded interactions: for example, the way in which a hydrogen bond forms between a Lewis acid and a Lewis base. The new ground that ours breaks is that it’s designed from the very beginning for the very strongest chemical interactions: the chemical bond. As a caution, we can justify the energetic terms that are involved in the EDA and connect them to well-understood intermolecular interactions when the fragments that interact are far apart. However, in the chemically interesting regime where the partners are closer together and strongly interacting, it’s not possible to make unique definitions of these chemical interactions. That’s the challenge of an EDA, to try to make some definitions that are reasonable and can be checked in various ways, and at the same time not lose sight of the fact that those definitions are not unique in the same way that the total interaction energy is unique.

We understand that there are several archetypes of chemical bonds. One would be the ionic bond, which in idealized form couples a positive ion and a negative ion. Thus, it’s a result of the charge transfer between the atoms. At the other extreme is the idealized notion of electron sharing in a covalent bond, and there’s a whole continuum of bonds of intermediate character. An energy decomposition analysis tries to understand the chemical bond energy as a sequence of additive contributions. For instance, a contribution from charge transfer, a contribution from maybe spin-coupling together two electrons on different atoms to make an electron pair, a contribution from polarizing the electron pair and other electrons on the two fragments that combined to make the bond, maybe up to four or five of these contributions. Our paper (1) tries to make mathematically reasonable definitions of these terms by a series of variational constraints and actually compute them for a range of bonds stretching from the familiar to the somewhat exotic. My coauthor and postdoctoral researcher, Daniel Levine, did the heavy lifting of turning our proposed definitions into a functioning computer program that can be applied to molecules.

PNAS: Theoretical chemists and synthetic chemists understand chemical bonds differently. What is the difference between how they understand these bonds and how does your work bridge that gap?

Head-Gordon: The concepts that a synthetic chemist thinks about are qualitative in nature. It allows them to make intuitive back-of-the-envelope predictions about reactivity. The theoretical chemist mixes together nuclei and electrons in a computer beaker to then finally solve for the energy and properties of the molecule. That kind of quantum mechanical simulation, the numerical experiment—if you will—is a long way from the synthetic chemists’ view of what properties are important in determining a bond. So getting to that final quantum mechanical answer in stages by an energy decomposition analysis tries to bridge those two worlds.

PNAS: Why did you choose the case study molecules that you presented in the Inaugural Article (1)?

Head-Gordon: The objective was to first connect with bonds that all chemists think they understand and show that our quantum mechanical EDA works reasonably for such systems and recovers existing conventional wisdom. Then we went to look at some exotic metal–metal bonds, suggested by Daniel [Levine], who has a far stronger background in inorganic chemistry than I do. Perhaps an average chemist would not be so sure what their character is, relative to the bonds they’re familiar with.

PNAS: What can we do now with these tools you developed that we could not do before?

Head-Gordon: The hope is that we can play a role in understanding trends in chemical bonds as a function of substituents. If you decorate a carbon–carbon bond with different substituents, that influences the bond strength in a secondary way, and we can perhaps understand that through these kinds of tools. The more ambitious goal is that these tools can become part of a practicing chemist’s toolkit when they want to predict the reactivity of a new species.

Existing EDA schemes don’t properly describe the way in which electron spins couple together to make a chemical bond. The quantum mechanical word is “entangled.” Treating that coupling correctly is the distinctive new feature in our EDA, with direct consequences in the results.