Edit barostats section

Author: davidlmobley

paper/basic_training.tex

@@ -762,7 +762,7 @@ \subsubsection{Summary}
 Do note that depending on the system of interest, it might not be necessary to worry about some of this information when initializing the system for a production run.
 For example, if the thermal history of the system is not necessary during equilibration, a faster algorithm like Andersen or Berendsen could possibly be employed, with a switch to Nos\'{e}-Hoover for the production run.
 Knowing the system you are simulating and the benefits and weaknesses to each thermostat is crucial to successfully and efficiently collect meaningful, physical data.
-In general, deterministic thermostats should never be employed for production use; Langevin, Andersen, and Nos\'{e}-Hoover chains can serve as reasonable general-purpose thermostats, and other choices should be employed only with considerable caution.
+In general, deterministic thermostats should never be employed for production use; Langevin, Andersen, Bussi, and Nos\'{e}-Hoover chains can serve as reasonable general-purpose thermostats, and other choices should be employed only with considerable caution.
 
 \begin{figure}[h]
 \centering
@@ -773,50 +773,40 @@ \subsubsection{Summary}
 \end{figure}
 
 \subsection{Barostats}\label{sec:barostats}
-\begin{itemize}
-\item Motivation
-\item Background
-\item Brief description of how it works
-\item Popular barostats
-\item Summary
-\end{itemize}
+
+Here, we discuss why barostats are used, give their background, discuss roughly how they work, describe some popular options, and summarize with some recommendations.
 
 \subsubsection{Motivation}
-When browsing the literature for many physical properties of various materials, you will observe that a multitude of the thermodynamic
-properties of interest are measured under some contstant temperature and pressure.
-Whether it is standard temperature and pressure (STP), or a more extreme value, many experimental studies are performed under these conditions.
-Termed the isothermal-isobaric ensemble, this might be one of the most popular ensembles for simulationists in general.
+Typically, thermodynamic properties of interest are measured under open air conditions in a laboratory, which (for short timescales) means at they are measured at essentially constant temperature and pressure.
+Such conditions correspond to what is called the isothermal-isobaric ensemble, probably one of the most popular ensembles for MD simulationsl.
 As is the case with thermostats, if the pressure must be maintained in a simulation, a barostat algorithm will be needed to sample this ensemble.
-This section will review the background of the barostats, a general overview of how they work, and introduce some popular barostats.
 
 \subsubsection{Background and How They Work}
-Recall that in the majority of experimental set-ups, the container the experiment is being conducted in is either open to the atmosphere, which is subjected to a constant pressure of one atmosphere; or under some enclosure, which will control the volume, thus controlling the pressure.
-If an experimenter would prefer to run their simulation at a different pressure, some device, like a piston, inert gas, etc\@., would be needed to control the pressure and volume of the system~\cite{tuckermanBook, ShellNotes}.
+In many experiments, the container is either open to the atmosphere, meaning that it is subject to a roughly constant pressure of approximately one atmosphere. % is subjected to a constant pressure of one atmosphere; or under some enclosure, which will control the volume, thus controlling the pressure.
+%DLM: Removed this; if it was sealed, it is constant volume, not constant pressure, yes?
+To obtain a different pressure, some device, like a piston, inert gas, etc\@., would be needed to control the pressure and volume of the system~\cite{tuckermanBook, ShellNotes}.
 
-For the purpose of molecular modeling, consider a system with a fictitious piston of some fictitious mass.
-We are describing the system with a fictitious piston due to the way in which the piston acts on the system.
-Since the piston is acting on the system from all directions, a uniform compression or expansion will be applied to these example systems.
-This is difficult/impossible to do with the traditional view of a piston, which compresses or expands the system in one general direction.
+For the purpose of molecular modeling, consider a hypothetical system that is being compressed and/or expanded by a fictitious piston that has some mass which acts in all directions uniformly.
+Since the piston is acting on the system from all directions, it can be considered as applying a uniform compression or expansion.
 The mass of the piston can be tuned to change the compression of the system, which will change how often the particles in the system will interact with the system enclosure.
 These impacts from the particles on the ``enclosure'' will impart a stress on the system box which can be related to the stress the surroundings are imparting on the system.
-With this relationship, we can use the virial theorem to calculate the pressure that the system is experiencing~\cite{ShellNotes}.
-However, this is much more challenging when considering pairwise interactions and periodic boundary conditions~\cite{allenTildesleyLiquids, tuckermanBook, ShellNotes}.
-A different approach to the virial theorem is necessary at that point.
-The math is a bit more complex and is out of the scope of this article.
-We encourage the readers to read the articles referenced here for more information.
-
-Finally, this treatment described above only covers holding the pressure constant (the NP of NPT).
-When a barostat is applied without an additional thermostating algorithm, only the amount of particles (N), the pressure (P), and the enthalpy (H) of the system is held constant.
+With this relationship, we can use the virial theorem (an expectation value relating to positions and forces) to calculate the pressure of a system~\cite{ShellNotes, LeachBook}.
+However, this is much more challenging when considering pairwise interactions and periodic boundary conditions~\cite{allenTildesleyLiquids, tuckermanBook, ShellNotes}, and a different approach is often utilized.
+Our main point here, however, is that pressure can be related to instantaneous properties of the system allowing us to calculate an instantaneous pressure in a similar manner to how we calculate an instantaneous temperature for thermostats.
+
+Thus, barostat algorithms apply to keep the instantaneous pressure of a system at or near the target pressure.
+
+Barostat algorithms control pressure alone, not temperature, so if the target ensemble is isothermal-isobaric, they must also be applied with a thermostat.
+If a barostat is applied without a thermostat, only the number of particles (N), the pressure (P), and the enthalpy (H) of the system is held constant.
 This is known as the isoenthalpic-isobaric ensemble (NPH).
-To sample from the isothermal-isobaric ensemble (NPT), a thermostating algorithm like the ones dicussed earlier must also be applied.
+To sample from the isothermal-isobaric ensemble (NPT), a thermostating algorithm like the ones discussed earlier must also be applied.
 
-Like thermostats, many barostats have been developed during the lifetime of molecular dynamics.
-However, they usually can be classified into three main categories: volume rescaling, weakly coupled, and extended ensemble barostats~\cite{ShellNotes, tuckermanBook}. 
+Many barostats are available, but can usually can be classified into three main categories: volume rescaling, weakly coupled, and extended ensemble barostats~\cite{ShellNotes, tuckermanBook}. 
 The next section will describe the main differences between these barostats, and give some recommendations for proper use.
 
 
 \subsubsection{Popular and Notable Barostats}
-Within this section, a few notable barostats will be introduced to the reader, describing a high-level summary of each, with some of the issues associated with them as well.
+Here, we introduce a few notable barostats and give a high-level summary of each, noting some key issues.
 This is not an exhaustive list of barostats and barostat algorithms, just a sampling of popular and historic ones used in MD\@.
 
 \subparagraph{Volume Rescaling}
@@ -825,8 +815,8 @@ \subsubsection{Popular and Notable Barostats}
 
 Volume rescaling barostats are the simplest example of pressure control in molecular simulations.
 Every time this barostat is executed, the volume of the system is modified to produce the exact pressure desired.
-This does \textbf{not} sample the proper ensemble, this cannot be used for production sampling~\cite{ShellNotes}.
-This also does not smoothly approach the target pressure either, which might cause very unphysical issues with the system during time integration and force calculation.
+This does \textbf{not} sample the proper ensemble and thus cannot be used for production sampling~\cite{ShellNotes}.
+This also does not smoothly approach the target pressure either, which might cause very unphysical issues with the system during integration.
 
 \end{enumerate}
 
@@ -861,25 +851,26 @@ \subsubsection{Popular and Notable Barostats}
 
 \item \textbf{Martyna-Tuckerman-Tobias-Klein (MTTK) Barostat}
 
-Generally the same that holds true for the Parrinello-Rahman barostat and the Andersen barostat are still true for the MTTK barostat.
-Parrinello-Rahman's equations of motion were discovered to only hold true in the limit of large systems, the MTTK barostat introduced their own equations of motion to correctly sample the ensemble for these systems as well~\cite{martyna1994constant, martyna1996explicit}.
-MTTK~\cite{martyna1994constant, martyna1996explicit} is usually seen as an improvement over Parrinello-Rahman~\cite{Parrinello1981} in the regime of small systems.
+The MTTK barostat has substantial similarity to the Parrinello-Rahman and Andersen barostats.
+When Parrinello-Rahman's equations of motion were discovered to only hold true in the limit of large systems, the MTTK barostat introduced alternate equations of motion to correctly sample the ensemble for smaller systems as well~\cite{martyna1994constant, martyna1996explicit}.
+Thus, MTTK~\cite{martyna1994constant, martyna1996explicit} is usually seen as an improvement over Parrinello-Rahman~\cite{Parrinello1981} for such systems.
 
 \end{enumerate}
 
 \subsubsection{Summary}
 
 In summary, there are three types of barostats usually implemented in molecular dynamics codes which can greatly affect the data you are collecting from the system. 
-Volume rescaling is not recommended for any equlibrium data sampling.
+Volume rescaling is not recommended for collection of production data.
 This barostat does not sample from any correct ensemble, nor does it utilize any ``realistic'' approach to achieve the target pressure.
-Weak coupling barostats are a bit of an improvement compared to volume rescaling methods.
-However, these methods cannot be used to bring the system to a final equilibrium.
-They can be used for approaching the target pressure in a more realistic fashion compared to the volume rescaling barostat.
-Which allows the system to reach the target pressure more slowly, possibly avoiding overlaps or other issues during the beginning stages of a simulation.
-Finally, the barostats that can be used for the production runs of most systems are the extended ensemble barostats.
+Weak coupling barostats provide some improvement compared to volume rescaling methods.
+However, these methods cannot be used to bring the system to equilibrium effectively.
+They can be used for approaching the target pressure in a more realistic fashion compared to the volume rescaling barostat, which itself is primarily useful only as a very stable thermostat for very early simulation stages if other algorithms have trouble beginning from particularly strained starting structures. 
+(Alternatively, such issues can be avoided by running NVT equilibration before using a barostat, Figure~\ref{eqworkflow}.)
+Finally, extended ensemble barostats are suitable for the production runs of most systems.
 It is usually not recommended to use these for the equilibration process, as these barostats do not behave as well when not near the target pressure.
 These can be affected by the starting configuration and pressure values much more than the Berendsen or volume rescaling barostats.
-MTTK and Parinello-Rahman allow for more flexibility in terms of the shape modulation of the simualtion box, but it usually distills to using the extended-ensemble barostat that has been implemented in your simuation engine of choice.
+MTTK and Parinello-Rahman allow for more flexibility in terms of the shape modulation of the simulation box.
+Ultimately, however, one's choice often is limited by which extended-ensemble barostat has been implemented in your simulation engine of choice.
 It is recommended to begin with a volume rescaling or weakly coupled barostat to quickly bring the system to the target pressure, then switch to an extended ensemble barostat for final equilibration and production.
 
 \subsection{Integrators}