Oppenheimer, father of the atomic bomb, pioneer of the quantum world

The movie Oppenheimer, released in July 2023, has renewed interest in the life of the enigmatic scientist J. Robert Oppenheimer. Oppenheimer will always be known as the father of the atomic bomb, while his early contributions to quantum mechanics formed the cornerstone of modern quantum chemistry.

--His findings continue to influence scientists' thinking about molecular structure to this day.

Early in the film, prominent scientific figures of the day, including Nobel laureates Werner Heisenberg and Ernest Lawrence, praise the young Oppenheimer for his pioneering work on molecules. As a physical chemist, Oppenheimer's work on the quantum mechanics of molecules also played an important role.

Robert Oppenheimer (right) talking with mathematician Oswald Veblen at the Institute for Advanced Study in Princeton in 1947.

The concept of "molecular quantum mechanics" was introduced in 1927 in a paper by Max Born and Oppenheimer.

Imagine that you want to use quantum mechanics to calculate the optimal molecular structure, bonding patterns and physical properties of a molecule. First, you need to define the positions and motions of all nuclei and electrons, and calculate the important charge attraction and repulsion forces between these particles in a molecule.

Calculating the properties of molecules becomes even more complicated at the quantum level because particles have wave-like properties and scientists can't pinpoint their positions. Instead, particles like electrons must be described by a wave function: a wave function describes the probability of an electron appearing in a certain region of space. Determining this wave function and the corresponding energy of the molecule is known as solving the molecular Schrödinger equation.

Unfortunately, even the simplest molecule, H₂⁺, cannot accurately solve this equation because it consists of three particles: two hydrogen nuclei (or protons) and one electron.

Oppenheimer's method provided a way to obtain an approximate solution. He observed that the nucleus is much heavier than the electron, and that a single proton has nearly 2000 times the mass of an electron. This meant that the nucleus moved much slower than the electron, so scientists could treat the nucleus as a stationary object and solve Schrödinger's equation for the electron only.

Illustration of conceptual results triggered by Born and Oppenheimer in their seminal work. (a) The total energy of a molecule can be decomposed into the sum of the electron energy (black), vibrational energy (blue), and rotational energy (red). (b) The eigenvalue of the electron Hamiltonian (electron energy) is a function of the nuclear coordinates and gives rise to the concept of the potential energy surface. The Born-Oppenheimer approximation allows only one of the potential energy surfaces to be considered under certain conditions.

This approach reduces the computational complexity and allows scientists to determine the wave function of a molecule with relative ease.

This approximation may seem like a minor tweak, but the Born-Oppenheimer approximation does much more than simplify quantum mechanical calculations of molecules: it actually shapes the way chemists view molecules and chemical reactions.

When scientists visualize molecules, we usually think of them as a fixed set of nuclei that share electrons between them. In chemistry classes, students often construct "ball-and-stick" models, which include rigid nuclei (balls) that share electrons through bonding frameworks (sticks).

--These models are a direct result of the Born-Oppenheimer approximation.

The ball-and-stick model shows the nucleus represented by a sphere (or ball) and the shared electron bonds represented by sticks; this diagram shows the structure of the benzene molecule.

The Born-Oppenheimer approximation has also influenced scientists' thinking about chemical reactions. During a chemical reaction, atomic nuclei do not stand still; they rearrange and move. Electron interactions direct the movement of nuclei by creating energy surfaces on which the nuclei can move throughout the reaction. In this way electrons propel molecules forward in chemical reactions. Oppenheimer demonstrated that the way electrons behave is the essence of the science of chemistry.

Molecules change structure during chemical reactions.

In the century since the publication of the Born-Oppenheimer approximation, the ability of scientists to calculate the chemical structure and reactivity of molecules has improved dramatically.

This field, known as computational quantum chemistry (CQC), has grown exponentially with the availability of faster and more powerful high-end computing resources. Currently, chemists use computational quantum chemistry for a variety of applications, from discovering new drugs to designing better photovoltaic products before attempting to manufacture them in the lab. Central to this field of research is the Born-Oppenheimer approximation.

While the Born-Oppenheimer approximation has many uses, it is not perfect. For example, the approximation often fails in light-driven chemical reactions and in chemical reactions that enable animals to see light. Chemists are working on workarounds for these situations. Nonetheless, the applications of quantum chemistry enabled by the Born-Oppenheimer approximation will continue to expand and improve.

In the future, a new era of quantum computers could make computational quantum chemistry even more powerful by allowing faster calculations on larger and larger molecular systems.

Reference Links:

[1] https://royalsocietypublishing.org/doi/10.1098/rsta.2020.0375

[2] https://theconversation.com/before-he-developed-the-atomic-bomb-j-robert-oppenheimers-early-work-revolutionized-the-field-of- quantum-chemistry-and-his-theory-is-still-used-today-210428

[3] https://www.theochem.ru.nl/files/dbase/born-oppenheimer-translated-s-m-blinder.pdf