Simplification of the molecular dynamics that preserves thermodynamics

A systematic algorithm to reduce the potential energy surface is presented, which is based on successive inversions of virial data, so that the molecular dynamics is capable of preserving the thermodynamics of the system. The algorithm is tested by reducing the potential energy surface of diatomic molecules that interact through a non-spherically symmetric potential, into an effective potential which is spherically symmetric, showing that all rotational degrees of freedom of the molecules can be disregarded from the thermodynamic point of view, as long as the virial expansion is a good description of the system. Furthermore, our analysis allows us to understand how we can make use of the non-uniqueness of the solution of an inverse problem to generate simplified models.

Figure 1

Comparison between the two-body spherical symmetric potential $N_2$ produced by the NN, and four times the Lennard-Jones potential to which converges the full diatomic potential when $a=0$. Lennard-Jones diatomic parameters are $a=2^{1/6}\sigma$. We note that these two potentials do not agree as expected. Three neurons in the hidden layer were used.

Figure 2

Comparison between the second virial of the spherical symmetric potential obtained from a Lennard-Jones diatomic potential and the second virial of such potential.

Figure 3

Three-body spherical symmetric potential $N_3$, evaluated at $r=r_{1,2}=r_{1,3}=r_{1,3}$, obtained from a Lennard-Jones diatomic potential. Three neurons in the hidden layer were used.

Figure 4

Comparison between the third virial of the spherical symmetric potential obtained from a Lennard-Jones diatomic potential and the third virial of such potential.

Figure 5

Comparison between the microscopic potential energy of a fluid of diatomic molecules (dots), the microscopic potential energy of a fluid of monoatomic molecules interacting by our two-body spherically symmetric potential (continuous line), and the internal energy predicted by the virial expansion truncated up to quadratic order in $\rho$ (dashed line), for different temperatures as a function of the number density.