Dihedral–torsion model potentials that include angle-damping factors†

This groundbreaking study derives and tests several new dihedral torsion model potentials for constructing classical forcefields for atomistic simulations of materials. (1) The new angle-damped dihedral torsion (ADDT) model potential is preferred when neither contained equilibrium bond angle is linear (i.e., (θ^eq_ABC and θ^eq_BCD) ≠ 180°), at least one of the contained equilibrium bond angles is ≥ 130° (i.e., (θ^eq_ABC or θ^eq_BCD) ≥ 130°), and the dihedral torsion potential contains some odd-function contributions (i.e., U[ϕ] ≠ U[−ϕ]). (2) The new angle-damped cosine only (ADCO) model potential is preferred when neither contained equilibrium bond angle is linear (i.e., (θ^eq_ABC and θ^eq_BCD) ≠180°), at least one of the contained equilibrium bond angles is ≥ 130° (i.e., (θ^eq_ABC or θ^eq_BCD) ≥ 130°), and the dihedral torsion potential contains no odd-function contributions (i.e., U[ϕ] = U[−ϕ]). (3) The new constant amplitude dihedral torsion (CADT) model potential is preferred when neither contained equilibrium bond angle is linear (i.e., (θ^eq_ABC and θ^eq_BCD) ≠ 180°), both contained equilibrium bond angles are <130° (i.e., (θ^eq_ABC and θ^eq_BCD) < 130°), and the dihedral torsion potential contains some odd-function contributions (i.e., U[ϕ] ≠ U[−ϕ]). (4) The constant amplitude cosine only (CACO) model potential is preferred when neither contained equilibrium bond angle is linear (i.e., (θ^eq_ABC and θ^eq_BCD) ≠180°), both contained equilibrium bond angles are <130° (i.e., (θ^eq_ABC and θ^eq_BCD) <130°), and the dihedral torsion potential contains no odd-function contributions (i.e., U[ϕ] = U[−ϕ]). (5) The new angle-damped linear dihedral (ADLD) model potential is preferred when at least one contained equilibrium bond angle is linear (i.e., (θ^eq_ABC or θ^eq_BCD) = 180°). Most importantly, this article derives combined angle-dihedral coordinate branch equivalency conditions and angle-damping factors that ensure the angle-damped torsion model potentials (e.g., ADDT, ADCO, and ADLD) are mathematically consistent and continuously differentiable even as at least one contained bond angle approaches linearity (i.e., as (θ_ABC or θ_BCD) → 180°). This article introduces the torsion offset potential (TOP). I show the TOP gives rise in some materials to the unusual physical phenomenon of slip torsion. For various molecules, extensive quantitative comparisons to high-level quantum chemistry calculations (e.g., CCSD) and experimental vibrational frequencies showed these new dihedral torsion model potentials perform superbly.