A Stochastic Algorithm for the Isobaric-Isothermal Ensemble with Ewald Summations for all Long Range Forces

. Author manuscript; available in PMC: 2016 Dec 8.

Published in final edited form as: J Chem Theory Comput. 2015 Nov 25;11(12):5624–5637. doi: 10.1021/acs.jctc.5b00648

e^{L_{1} ν \frac{Δ t}{2}}

P_{V} \leftarrow P_{V} exp (\frac{P_{ξ}}{M_{ξ}} \frac{ν Δ t}{2})

Π^{*} \leftarrow \frac{1}{3 V} \sum_{μ} M_{μ} {\dot{\vec{R}}}_{μ}^{2} + \frac{1}{6 V} \sum_{μ} \sum_{μ^{'}} \sum_{i \in μ} \sum_{j \in μ^{'}} ({\vec{R}}_{μ} - {\vec{R}}_{μ^{'}}) \cdot ({\vec{f}}_{μ i} - {\vec{f}}_{μ^{'} j})

e^{L_{2} ν \frac{Δ t}{2}}

P_{V} \leftarrow P_{V} + (Π^{*} - Π_{ext}) \frac{ν Δ t}{2}

e^{δ L_{1} ν \frac{Δ t}{2}}

P_{V} \leftarrow e^{- γ \frac{ν Δ t}{2}} P_{V} + \frac{σ M_{V}^{1 / 2}}{\sqrt{2 γ}} \sqrt{1 - e^{- γ ν Δ t}} R (t)

e^{L_{3} ν \frac{Δ t}{2}}

V \leftarrow V + \frac{P_{V}}{M_{V}} \frac{ν Δ t}{2}