Effects of Degrees of Freedom on Calculating Diffusion Properties in Nanoporous Materials

Abstract

If one carries out a molecular simulation of N particles using periodic boundary conditions, linear momentum is conserved, and hence, the number of degrees of freedom is set to 3N – 3. In most programs, this number of degrees of freedom is the default setting. However, if one carries out a molecular simulation in an external field, one needs to ensure that degrees of freedom are changed from this default setting to 3N, as in an external field the velocity of the center of mass can change. Using the correct degrees of freedom is important in calculating the temperature and in some algorithms to simulate at constant temperature. For sufficiently large systems, the difference between 3N and 3N – 3 is negligible. However, there are systems in which the comparison with experimental data requires molecular dynamics simulations of a small number of particles. In this work, we illustrate the effect of an incorrect setting of degrees of freedom in molecular dynamic simulations studying the diffusion properties of guest molecules in nanoporous materials. We show that previously published results have reported a surprising diffusion dependence on the loading, which could be traced back to an incorrect setting of the degrees of freedom. As the correct settings are convoluted and counterintuitive in some of the most commonly used molecular dynamics programs, we carried out a systematic study on the consequences of the various commonly used (incorrect) settings. Our conclusion is that for systems smaller than 50 particles the results are most likely unreliable as these are either performed at an incorrect temperature or the temperature is incorrectly used in some of the results. Furthermore, a novel and efficient method to calculate diffusion coefficients of guest molecules into nanoporous materials at zero-loading conditions is introduced.

Further cautionary tales on thermostatting in Molecular Dynamics: energy equipartitioning and non-equilibrium processes in gas-phase simulations

“…When carrying out small-scale NVT simulations, special attention should also be paid to the default settings (thermostat implementation and effective number of dof) in the specific MD code. Very recently Xu et al 14 demonstrated the importance of correct dof setting by calculating diffusion in nanoporous materials; incorrect settings are particularly disruptive when only a subset of atoms is coupled to a thermostat, or isolated non-continuous systems are simulated. In addition to the fact that the Langevin thermostat realizes correct kinetic energy distributions irrespective of the dof settings, 14 we have demonstrated that in gas-phase simulations it leads to perfect thermalization and equipartition with a minimal computational effort, making it an ideal choice for system initialization, where dynamics are secondary.…”

“…Some standard thermostats are, however, problematic as they do not produce a proper canonical ensemble and/or are prone to introduce spurious unphysical dynamics to the simulated system. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] Perhaps the most famous of such thermostatting problems is the so-called "flying ice cube" effect, 1,2,15 which arises from unphysical transfer of kinetic energy from fast to slow modes of motion, causing the system's vibrational modes to freeze, while simultaneously resulting in enormous translational and rotational energies. These kinds of violations of the equipartition theorem, which states that the thermal energy should be equally distributed over the system's degrees of freedom (dof), ultimately affect the structural, dynamic, and thermodynamic properties of the simulated system.…”

“…2,12,15 Since most atomistic simulations rely on the use of available, well-tested simulation packages, understanding the implementation details of different thermostats in these codes is crucial, especially for systems with a small number of dof. 14 Despite a large body of studies and cautionary publications, pitfalls of thermostatting are still recurring issues in many fields of computational physics, chemistry, and molecular biology. 12,14,15 In condensed matter systems, continuous energy exchange between molecules usually ensures equipartition of intramolecular dof.…”

“…14 Despite a large body of studies and cautionary publications, pitfalls of thermostatting are still recurring issues in many fields of computational physics, chemistry, and molecular biology. 12,14,15 In condensed matter systems, continuous energy exchange between molecules usually ensures equipartition of intramolecular dof. However, in the gas phase, this form of thermal equilibration or energy relaxation is not efficient due to infrequent collisions at low densities.…”

Inverse design of metal–organic frameworks for C2H4/C2H6 separation

“…For all MD simulations, we used the LAMMPS package with the Nose-Hoover thermostat for controlling the temperature. The detailed settings follow the protocol suggested in the literature for infinite dilution 47 .…”