Langevin integration for isothermal-isobaric condition with a large time step

We propose an accurate method for evaluating temperature and pressure in Langevin integration, based on the approach by Leimkuhler and Matthews (J. Chem. Phys. 138, 174102). This method improves the quality of configuration space than other Langevin dynamics methods. However, it encounters issues in pressure evaluation due to inaccuracies in momentum space. In particular, the conventional approach for calculating kinetic temperature using the full-time step momentum introduces errors proportional to the square of the time step (Δt2), leading to unreliable results when employing a large time step under isothermal-isobaric conditions. By calculating kinetic energy using the half-time step momentum in pressure evaluation, we can reduce the numerical errors. We performed molecular dynamics (MD) simulations using our refined pressure evaluation and improved accuracy and stability in the isothermal-isobaric MD simulations even with a long time step (Δt = 5 fs).