Hybrid path integral Monte Carlo simulation of rigid diatomic molecules: effect of quantized rotations on the selectivity of hydrogen isotopes in carbon nanotubes

We present a multiple time step algorithm for hybrid path integral Monte Carlo simulations involving rigid linear rotors. We show how to calculate the quantum torques needed in the simulation from the rotational density matrix, for which we develop an approximate expression suitable in the case of heteronuclear molecules. We use this method to study the effect of rotational quantization on the quantum sieving properties of carbon nanotubes, with particular emphasis to the para-T2/para-H2 selectivity at 20 K. We show how to treat classically only some of the degrees of freedom of the hydrogen molecule and we find that in the limit of zero pressure the quantized nature of the rotational degrees of freedom greatly influence the selectivity, especially in the case of the (3,6) nanotube, which is the narrowest tube that we have studied. We also use path integral Monte Carlo simulations to calculate adsorption isotherms of different hydrogen isotopes in the interior of carbon nanotubes and the corresponding selectivity at finite pressures. It is found that the selectivity increases with respect to the zero pressure value and tends to a constant value at saturation. We use a simplified effective harmonic oscillator model to discuss the origin of this behavior.