Molecular Mechanics

Quantum Mechanics and the Origins of Computational Chemistry

Quantum mechanics is the foundation of modern chemistry and, by extension, all of computational chemistry. It was developed in the 1920s to address several outstanding challenges, including explaining atomic spectra and the wave–particle duality of electrons. A central simplification enabling practical calculations is the Born–Oppenheimer approximation, which separates nuclear and electronic degrees of freedom by exploiting their vastly different timescales. While this makes molecular quantum calculations tractable in principle, the computational cost still grows steeply with system size. Even with modern methods, fully quantum mechanical simulations of systems with ~100 atoms are typically limited to timescales on the order of picoseconds.

Emergence of Force Fields (1950s–1960s)

To access larger systems and longer timescales, simplified potential energy functions were introduced to approximate quantum mechanical effects. This takes the central idea of the Born-Oppenheimer approximation even further, by effectively integrating out the electronic degrees of freedom, without treating any electrons explicitly. For example, chemically-bonded atoms in hte low-ebergy limit can be approximated via a harmonic potential:
\(V(x) = \frac{k}{2}(x-x_0)^2\)

Nonbonded interactions can be modeled using the Lennard Jones potential (“atoms are sticky, but cannot overlap with each othter”):
\(V(r) = \epsilon\left[\left(\frac{R_{min}}{r}\right)^{12} - 2\left(\frac{R_{min}}{r}\right)^6\right]\)

Models two key quantum effects:

• Dispersion (London forces): attractive, arising from mutually-induced polarization, decaying approximately as (-1/r^6).
• Pauli repulsion: steep short‐range repulsion due to wavefunction overlap, approximated by the (1/r^{12}) term.

The first molecular dynamics (MD) simulation of a Lennard–Jones fluid (liquid argon) was published in 1964 by A. Rahman. The calculation simulated 864 particles and required ~45 s per integration step on the CDC 3600 supercomputer. Specialized force fields were developed for large molecular systems, such as proteins.

Select Milestones

• Particle Mesh Ewald (PME, early 1990s)
  Eliminated crude electrostatic cutoffs by enabling efficient, long‐range Coulomb calculations in periodic systems.

• Free energy methods (1980s–present)
  Foundations laid by McCammon, Jorgensen, and others; modern alchemical methods (FEP/TI/BAR/MBAR) now central to binding affinity prediction.

• Protein force fields (1990s-2010s) Amber and CHARMM all-atom additive protein force fields become widely tested and shown to be highly balanced

• 2013 Nobel Prize in Chemistry
  Karplus, Levitt, and Warshel for multiscale modeling: QM, QM/MM, MM.

• GPU acceleration (2007–present)
  Consumer and scientific GPUs transformed MD throughput by orders of magnitude.

• Ongoing and future prospects Polarizable force fields, machine-learning potentials, and direct prediction of complete ensembles.