12.7.4 ALMO Force Decomposition Analysis

Building on the success of the adiabatic EDA (Section 12.7.3), a similar extension can be introduced which decomposes the forces at any geometry. Instead of following the forces to generate a geometry and evaluate the energy in that geometry as in the adiabatic EDA, the force decomposition analysis decomposes and analyzes the forces on their own at a given geometry. One important feature emerges from this approach which is the ability to decompose the frozen force, uncovering the frozen component relevant to a geometric change. This decomposition is not meaningful in the the adiabatic EDA since following purely attractive forces, for example, would collapse the molecules into each other.

Work by Aldossary et al. implements the analytical derivative of the classical electrostatics energy ³⁶ Aldossary A. et al.
J. Phys. Chem. A
(2023), 127, pp. 1760. Link , allowing the frozen force to be broken down into classical electrostatics and van der Waals (Pauli and Dispersion) forces:

Additionally, the frozen forces are now defined to subtract the geometric distortion forces (forces arising from geometric distortion energy). The frozen force term is now:

where the second term on the right hand side the geometric distortion forces. Similar to the geometric distortion energy, the geometric distortion forces are subtracted from those of the isolated geometry which evaluate to zero for a geometric minimum. In other words, the geometetric distortion forces are nothing but the isolated fragments’ forces in the complex geometry. The geometric distortion forces are printed separately for analysis.

By decomposing the intermolecular forces into geometric distortion, electrostatics, van der Waals, polarization, and charge transfer, we have now generated 5 times more forces than a regular force job. The $5(3N)$ forces can be difficult to analyze manually, and we use internal coordinates to make chemical sense of these forces. The Wilson’s B matrix is generated using the new opt3 library and we apply the usual transformation. The user can then hone in to the bond, angle, or dihedral of interest to analyze the which force components are relevant to the stretch or compression. Despite the usefulness of the redundant internal coordinates, they are not unique, and the order of the atoms in the input file can affect the results.