Molecular modelling

Molecular modelling is the use of theoretical and computational techniques to simulate or replicate how molecules behave. These techniques are applied in computational chemistry, drug design, computational biology, and materials science, and they cover systems from tiny chemical compounds to large biological molecules and material assemblies. While very simple calculations can be done by hand, computers are necessary for modelling any system of a reasonable size. What all molecular modelling methods share is an atomistic-level description of the system. This description can range from treating whole atoms as the smallest unit (molecular mechanics) to explicitly modelling subatomic particles like protons, neutrons, quarks, electrons, and photons (quantum chemistry).

In molecular mechanics, a branch of molecular modelling, classical Newtonian mechanics provides the physical basis for the models. Atoms—meaning the nucleus and electrons together—are typically represented as point charges with a specific mass. Neighbouring atoms interact through spring-like forces that stand in for chemical bonds, as well as through Van der Waals forces, which are often described using the Lennard-Jones potential. Electrostatic interactions are calculated using Coulomb's law. Atoms are given coordinates in either Cartesian space or internal coordinates, and in dynamic simulations they can also be assigned velocities. These atomic velocities relate to the system’s temperature, a macroscopic property. The combined mathematical description is called a potential function, which relates to the system’s internal energy (U), a thermodynamic quantity equal to the sum of potential and kinetic energy. Methods that minimise this potential energy are known as energy minimisation methods (such as steepest descent and conjugate gradient), while methods that simulate how the system changes over time are called molecular dynamics.

The potential function calculates molecular potential energy by adding together terms for bond length deviations, bond angle deviations, torsion angle deviations, and non-bonded interactions (which include electrostatic and Van der Waals forces). The set of parameters used—equilibrium bond lengths, bond angles, partial charges, force constants, and Van der Waals parameters—is collectively called a force field. Different molecular mechanics implementations use different mathematical forms and different parameters for this function. Today’s common force fields are built from chemical theory, experimental reference data, and high-level quantum calculations. Energy minimisation finds positions where the gradient of energy is zero for all atoms—in other words, a local energy minimum. These lower-energy states are more stable and are often studied because of their role in chemical and biological processes. In contrast, a molecular dynamics simulation calculates how a system behaves over time by solving Newton’s laws of motion, mainly the second law (F = ma). Using various integration algorithms, these laws produce atomic trajectories through space and time. The force on an atom is the negative gradient of the potential energy function. While energy minimisation provides a static picture for comparing similar systems, molecular dynamics reveals dynamic processes and inherently includes temperature effects.

Molecules can be modelled either in a vacuum or in the presence of a solvent like water. Simulations without solvent are called gas-phase simulations, while those that include solvent molecules are explicit solvent simulations. Another approach uses an empirical mathematical expression to estimate the solvent’s effect, known as implicit solvation simulations.

Most force fields depend on distance, making Cartesian coordinates the most convenient representation. However, because bonds between specific atoms are relatively rigid—and this rigidity essentially defines what a molecule is—an internal coordinate system is more logical. In some fields, this internal coordinate representation (bond length, bond angle, and torsion angle) is called a Z-matrix or torsion angle representation. A drawback is that continuous motions in Cartesian space often require discontinuous angular branches in internal coordinates, making it relatively cumbersome.