rate =/ rate coefficient... this might wind up on my headstone...

Author: hmayes

paper/basic_training.tex

@@ -202,14 +202,14 @@ \subsection{Thermodynamics}
 \subsubsection{Key concepts}
 A variety of thermodynamic concepts are particularly important for molecular simulations:
 \begin{itemize}
-\item Temperature, pressure, stress
-\item Internal energy, enthalpy
+\item Temperature and pressure % removed stress; seems out of place
+\item Internal energy and enthalpy
 \item Gibbs and Helmholtz free energy
 \item Entropy
 \end{itemize}
 
 One of the main objectives of molecular simulations is to estimate/predict thermodynamic behavior of real systems as observed in the laboratory.
-Typically this means we are interested in macroscopic systems, consisting of $10^{23}$ particles or more (i.e. at least several moles of particles). 
+Typically this means we are interested in macroscopic systems, consisting of $10^{23}$ particles or more (i.e. at least a mole of particles). 
 But properties of interest include not only macroscopic, bulk thermodynamic properties, such as density or heat capacity,
 but also microscopic properties like specific free energy differences associated with, say, changes in the conformation of a molecule.
 For this reason, it is important to understand key concepts in thermodynamics, such as temperature, pressure, entropy, internal energy, various forms of free energy, and the relationships between them.
@@ -273,17 +273,18 @@ \subsubsection{Key concepts}
 \begin{figure}[h]
 \centering
 \includegraphics[width=\linewidth]{simplelandscapes.pdf}
-\caption{Energy landscapes.  (a) A highly simplified landscape used to illustrate rate concepts and (b) a schematic of a complex landscape with numerous minima and ambiguous state boundaries.}
+\caption{Energy landscapes.  (a) A highly simplified landscape used to illustrate rate concepts and (b) a schematic of a more complex landscape with numerous minima and ambiguous state boundaries.}
 \label{landscapes}
 \end{figure}
 
 The key dynamical concept to understand is embodied in the twin characteristics of timescales and rates.  
 The two are literally reciprocals of one another.  
 In Fig.\ \ref{landscapes}(a), assume you have started an MD simulation in basin A.  
-The trajectory is likely to remain in that basin for a period of time -- the ``dwell'' timescale -- which increases exponentially with the barrier height according to the (reciprocal) Arrhenius factor as $\exp[(U^\ddagger - U_A)/k_B T]$; barriers many times the thermal energy $k_BT$ imply long dwells.  
-The rate $k_{AB}$, which is the transition probability per unit time, exhibits reciprocal behavior -- i.e., $k_{AB} \sim \exp[-(U^\ddagger - U_A)/k_B T]$ according to the traditional Arrhenius factor.  
-Note that all transitions occur in a random, \emph{stochastic} fashion and are not predictable except in terms of average behavior.  
-More detailed discussions of rate constants can be found in numerous textbooks (e.g.,~\cite{DillBook, Zuckerman:2010:}).
+The trajectory is likely to remain in that basin for a period of time -- the ``dwell'' timescale -- which increases exponentially with the barrier height, $(U^\ddagger - U_A)$. 
+Barriers many times the thermal energy $k_BT$ imply long dwell timescales, approximated as the reciprocal of $\exp[(U^\ddagger - U_A)/(k_B T)]$. 
+The rate coefficient $k_{AB}$, which relates to the transition probability per unit time per amount of reactant(s).
+All transitions occur in a random, \emph{stochastic} fashion and are predictable only in terms of average behavior.  
+More detailed discussions of rates and rate coefficients can be found in numerous textbooks (e.g.,~\cite{DillBook, Zuckerman:2010:}).
 
 Once you have understood that MD behavior reflects system timescales, you must set this behavior in the context of an \emph{extremely} complex energy landscape consisting of almost innumerable minima and barriers, as schematized in Fig.\ \ref{landscapes}(b).  
 Each small basin represents something like a different rotameric state of a protein side chain or perhaps a tiny part of the Ramachandran spaces (backbone phi-psi angles) for one or a few residues.  
@@ -305,7 +306,7 @@ \subsubsection{Key concepts}
 There is a closely related connection for on- and off-rates with the binding equilibrium constant.   
 For a \emph{continuous} coordinate (e.g., the distance between two residues in a protein), the probability-determining free energy is called the ``potential of mean force'' (PMF); the Boltzmann factor of a PMF gives the relative probability of a given coordinate.  
 Any kind of free energy implicitly includes \emph{entropic} effects; in terms of an energy landscape (Fig.\ \ref{landscapes}), the entropy quantifies the \emph{width} of a basin.  
-These points are discussed in textbooks, as are the differences between free energies for different thermodynamic ensembles -- e.g.., $F$, the Helmholtz free energy, when $T$ is constant, and $G$ , the Gibbs free energy, when both $T$ and pressure are constant -- which are not essential to our introduction~\cite{DillBook, Zuckerman:2010:}.
+These points are discussed in textbooks, as are the differences between free energies for different thermodynamic ensembles -- e.g.., $F$, the Helmholtz free energy, when $T$ is constant, and $G$, the Gibbs free energy, when both $T$ and pressure are constant -- which are not essential to our introduction~\cite{DillBook, Zuckerman:2010:}.
 
 A final essential topic is the difference between equilibrium and non-equilibrium systems.  
 We noted above that an MD trajectory is not likely to represent the equilibrium ensemble because the trajectory is probably too short.  
@@ -320,7 +321,7 @@ \subsubsection{Books}
 Books which we recommend as particularly helpful in this area include:
 \begin{itemize}
 \item Reif's ``Fundamentals of Statistical and Thermal Physics''~\cite{Reif:2009:}
-\item McQuarrie ``Statistical Mechanics''~\cite{McQuarrie:2000:}
+\item McQuarrie's ``Statistical Mechanics''~\cite{McQuarrie:2000:}
 \item Dill and Bromberg's ``Molecular Driving Forces''~\cite{DillBook}
 \item Hill's ``Statistical Mechanics: Principles and Selected Applications''~\cite{Hill:1987:}
 \item Shell's ``Thermodynamics and Statistical Mechanics''~\cite{ShellBook}