Functional groups in chemistry: molecular dynamics experiments

When it comes to identify the building blocks of middle sized organic molecules, chemists mainly think in terms of functional groups. Is that picture truly representative of the dynamics of molecules? We try to answer this question with an experimental mindset: we run simulations that artificially “decouple” pairs of atoms and see how the system as a whole reacts to that. In practice, if an atom A perceive a strong force from an atom B, we soften up the perceived force and examine how much this artificial decoupling influences the whole system. With that in mind, we propose a perturbed Hamiltonian function, namely Hdec(q,p,α) = H(q,p) + D(q,α), where the second is a decoupling function, which is a potential energy contribution that depends on the “pair-softening parameters” α. In the limiting case of no decoupling it is easy to establish that, for a tiny decoupling, the system looses energy proportionally to the off-diagonal entries of the hessian matrix. Non-equilibrium contributions are recovered with a classical MD sampling. We can draw molecular graphs that quantitatively show that the “functional groups picture”, at a quasi-classical level, is often a good description of the molecule’s dynamics, yet unexpected subgroups often appears. However, when the decoupling is finite, we cannot make reliable estimates. Therefore we rigorously derived a family of simple integration algorithms to simulate the dynamics of the pair-decoupling Hamiltonian for any value of α, to confirm and extend our investigation. The integration algorithms are proven to be symplectic for harmonic/bilinear potentials.