\batchmode


\documentclass[10pt,fleqn]{book}
\RequirePackage{ifthen}


\hbadness=100000
\vbadness=100000
\usepackage{html,fullpage,latexsym}
\usepackage[dvips]{graphicx}
\usepackage{psfig}

\setlength{\parskip}{6pt}
%
\providecommand{\nwchemversion}{4.6}%
\providecommand{\nwchemyear}{2004}%
\providecommand{\nwchemmonth}{May}
%
\providecommand{\angstroms}{Angstr{\o}ms}


\usepackage[dvips]{color}


\pagecolor[gray]{.7}

\usepackage[latin1]{inputenc}



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$CH_4$%
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$R-CH_2$%
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$\lambda$%
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{k_{ET}}=
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$P$%
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$A^{ -}$%
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{\newpage\clearpage
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$B$%
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$He_{}$%
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$He^{ +}$%
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$nm$%
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$0.005 au$%
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$0.001 au$%
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$0.1 e$%
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$0.001 e$%
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$atom2$%
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$forc1$%
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{\newpage\clearpage
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$dist1$%
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\lthtmlinlinemathA{tex2html_wrap_inline7505}%
$dist2$%
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$forc2$%
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$dist3$%
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$^{-1}$%
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$^{-2}$%
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$fguide$%
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$\Delta t$%
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$<=$%
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$+$%
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I-1-1 & a1     & \$ to identify the start of a segment \\%%$ for emacs
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I-2-3 & i5     & number of angles in the segment\\
I-2-4 & i5     & number of proper dihedrals in the segment\\
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\begin{table}\begin{center}
\begin{tabular*}{150mm}{p{15mm}p{12mm}l}
\hline\hline
Deck & Format & Description \\\hline
\mbox{\bf For each atom one deck II} \\
II-1-1  & i5     & atom sequence number \\
II-1-2  & a6     & atom name \\
II-1-3  & a5     & atom type, generic set 1 \\
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II-1-5  & a1     & dynamics type\\
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II-1-8  & i5     & charge group\\
II-1-9  & i5     & polarization group\\
II-1-10 & i5     & link number\\
II-1-11 & i5     & environment type\\
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        &        & 3: tetrahedral, using improper torsion\\
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II-2-3  & f12.6  & atomic partial charge in e, set 2\\
II-2-4  & f12.6  & atomic polarizability/$4\pi\epsilon_o$\  in nm$^3$, set 2\\
II-2-5  & f12.6  & atomic partial charge in e, set 3\\
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\begin{table}\begin{center}
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III-2-3 & f12.6  & bond length in nm, set 2\\
III-2-4 & e12.5  & bond force constant in kJ nm$^2$\  mol$^{-1}$, set 2 \\
III-2-5 & f12.6  & bond length in nm, set 3\\
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\begin{table}\begin{center}
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Deck & Format & Description \\\hline
\mbox{\bf For each angle a deck IV} \\
IV-1-1 & i5     & angle sequence number \\
IV-1-2 & i5     & angle atom i \\
IV-1-3 & i5     & angle atom j \\
IV-1-4 & i5     & angle atom k \\
IV-1-5 & i5     & angle type \\
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IV-2-3 & f10.6  & angle in radians, set 2\\
IV-2-4 & e12.5  & angle force constant in kJ mol$^{-1}$, set 2 \\
IV-2-5 & f10.6  & angle in radians, set 3\\
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\begin{tabular*}{150mm}{p{15mm}p{12mm}l}
\hline\hline
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\mbox{\bf For each proper dihedral a deck V} \\
V-1-1 & i5     & proper dihedral sequence number \\
V-1-2 & i5     & proper dihedral atom i \\
V-1-3 & i5     & proper dihedral atom j \\
V-1-4 & i5     & proper dihedral atom k \\
V-1-5 & i5     & proper dihedral atom l \\
V-1-6 & i5     & proper dihedral type \\
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V-1-7 & i5     & proper dihedral parameter origin\\
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V-2-1 & i3     & multiplicity, set 1\\
V-2-2 & f10.6  & proper dihedral in radians, set 1\\
V-2-3 & e12.5  & proper dihedral force constant in kJ mol$^{-1}$, set 1 \\
V-2-4 & i3     & multiplicity, set 2\\
V-2-5 & f10.6  & proper dihedral in radians, set 2\\
V-2-6 & e12.5  & proper dihedral force constant in kJ mol$^{-1}$, set 2 \\
V-2-7 & i3     & multiplicity, set 3\\
V-2-8 & f10.6  & proper dihedral in radians, set 3\\
V-2-9 & e12.5  & proper dihedral force constant in kJ mol$^{-1}$, set 3 \\
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\begin{table}\begin{center}
\begin{tabular*}{150mm}{p{15mm}p{12mm}l}
\hline\hline
Deck & Format & Description \\\hline
\mbox{\bf For each improper dihedral a deck VI} \\
VI-1-1 & i5     & improper dihedral sequence number \\
VI-1-2 & i5     & improper dihedral atom i \\
VI-1-3 & i5     & improper dihedral atom j \\
VI-1-4 & i5     & improper dihedral atom k \\
VI-1-5 & i5     & improper dihedral atom l \\
VI-1-6 & i5     & improper dihedral type \\
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VI-1-7 & i5     & improper dihedral parameter origin\\
       &        & 0: from database, next card ignored \\
       &        & 1: from next card\\
VI-2-1 & 3x,f10.6  & improper dihedral in radians, set 1\\
VI-2-2 & e12.5  & improper dihedral force constant in kJ mol$^{-1}$, set 1 \\
VI-2-3 & 3x,f10.6  & improper dihedral in radians, set 2\\
VI-2-4 & e12.5  & improper dihedral force constant in kJ mol$^{-1}$, set 2 \\
VI-2-5 & 3x,f10.6  & improper dihedral in radians, set 3\\
VI-2-6 & e12.5  & improper dihedral force constant in kJ mol$^{-1}$, set 3 \\
\hline\hline
\end{tabular*}
\end{center}
\end{table}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{table9685}%
\begin{table}\begin{center}
\begin{tabular*}{150mm}{p{15mm}p{12mm}l}
\hline\hline
Card & Format & Description \\\hline
I-1-1  & a1     & \$ to identify the start of a sequence \\%%$ for emacs
I-1-2  & a10    & name of the sequence\\
\hline
\mbox{\bf Any number of cards 1 and 2 in deck II to specify the system} \\
\hline
II-1-1 & i5     & segment number\\
II-1-2 & a10    & segment name, last character will be determined from chain\\
\hline
II-2-1 & a      & \verb+break+ to identify a break in the molecule chain\\
\hline
II-2-1 & a      & \verb+molecule+ to identify the end of a solute molecule\\
\hline
II-2-1 & a      & \verb+fraction+ to identify the end of a solute fraction\\
\hline
II-2-1 & a5     & \verb+link + to specify a link\\
II-2-2 & i5     & segment number of first link atom\\
II-2-3 & a4     & name of first link atom \\
II-2-4 & i5     & segment number of second link atom\\
II-2-5 & a4     & name of second link atom \\
\hline
II-2-1 & a      & \verb+solvent+ to identify solvent definition on next card\\
\hline
II-2-1 & a      & \verb+stop+ to identify the end of the sequence\\
\hline
II-2-1 & a6     & \verb+repeat+ to repeat next $ncard$\  cards $ncount$times\\
II-2-2 & i5     & number of cards to repeat ($ncards$)\\
II-2-3 & i5     & number of times to repeat cards ($ncount$)\\
\mbox{\bf Any number of cards in deck II to specify the system} \\
\hline\hline
\end{tabular*}
\end{center}
\end{table}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{table9701}%
\begin{table}\begin{center}
\begin{tabular*}{150mm}{p{15mm}p{12mm}l}
\hline\hline
Card & Format & Description \\\hline
I-1-1  & a6     & keyword \verb+header+ \\
\hline
I-2-1  & i10    & number of atoms per solvent molecule \\
I-2-2  & i10    & number of solute atoms \\
I-2-3  & i10    & number of solute bonds \\
I-2-4  & i10    & number of solvent bonds \\
\hline
\mbox{\bf For each atoms per solvent molecule one card I-3} \\
\hline
I-3-1  & a5     & solvent name \\
I-3-2  & a5     & atom name \\
I-3-3  & 6x,i10 & solvent atom counter \\
\hline
\mbox{\bf For each solute atom one card I-4} \\
\hline
I-4-1  & a5     & segment name \\
I-4-2  & a5     & atom name \\
I-4-3  & i6     & segment number \\
I-4-4  & i10    & solute atom counter \\
\hline
\mbox{\bf For each solvent bond one card I-5} \\
\hline
I-5-1  & i8     & atom index i for bond between i and j \\
I-5-2  & i8     & atom index j for bond between i and j \\
\hline
\mbox{\bf For each solute bond one card I-6} \\
\hline
I-6-1  & i8     & atom index i for bond between i and j \\
I-6-2  & i8     & atom index j for bond between i and j \\
\hline
\mbox{\bf For each frame one deck II} \\
\hline
II-1-1  & a5     & keyword \verb+frame+ \\
II-2-1 & f12.6  & time of frame in ps \\
II-2-2 & f12.6  & temperature of frame in K \\
II-2-3 & e12.5  & pressure of frame in Pa \\
\hline
II-3-1 & f12.6  & box dimension x \\
II-3-2 & 12x,f12.6  & box dimension y \\
II-3-3 & 24x,f12.6  & box dimension z \\
\hline
II-4-1 & l1     & logical lxw for solvent coordinates \\
II-4-2 & l1     & logical lvw for solvent velocities \\
II-4-3 & l1     & logical lxs for solute coordinates \\
II-4-4 & l1     & logical lvs for solute velocities \\
II-4-5 & i10    & number of solvent molecules \\
II-4-6 & i10    & number of solvent atoms \\
II-4-7 & i10    & number of solute atoms \\
\hline
\mbox{\bf For each solvent molecule one card II-5 for each atom} \\
\hline
II-5-1 & 3f8.3  & solvent atom coordinates, if lxw or lvw \\
II-5-4 & 3f8.3  & solvent atom velocities, if lvw \\
\hline
\mbox{\bf For each solute atom one card II-6 for each atom} \\
\hline
II-6-1 & 3f8.3  & solute atom coordinates, if lxs or lvs \\
II-6-4 & 3f8.3  & solute atom velocities, if lvs \\
\hline\hline
\end{tabular*}
\end{center}
\end{table}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{table9732}%
\begin{table}\begin{center}
\begin{tabular*}{150mm}{p{15mm}p{12mm}l}
\hline\hline
Card & Format & Description \\\hline
\mbox{\bf For each step in $\lambda$\  one deck I} \\
I-1-1  & i7     & number $nderiv$\  of data summed in derivative decomposition array $deriv$\  \\
I-1-2  & i7     & length $ndata$\  of total derivative array $drf$\  \\
I-1-3  & f12.6  & current value of $\lambda$\  \\
I-1-4  & f12.6  & step size of $\lambda$\  \\
\hline
I-2-1  & 4e12.12 & derivative decomposition array $deriv(1:24)$\  \\
\hline
I-3-1  & 4e12.12 & total derivative array $dfr(1:nda)$\  \\
\hline
I-4-1  & i10    & size of ensemble at current $\lambda$\  \\
I-4-2  & e20.12 & average temperature at current $\lambda$\  \\
I-4-3  & e20.12 & average exponent reverse perturbation energy at current $\lambda$\  \\
I-4-4  & e20.12 & average exponent forward perturbation energy at current $\lambda$\  \\
\hline\hline
\end{tabular*}
\end{center}
\end{table}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{table9745}%
\begin{table}\begin{center}
\begin{tabular*}{150mm}{p{15mm}p{12mm}l}
\hline\hline
Card & Format & Description \\\hline
\mbox{\bf For each analyzed time step one card I-1} \\
I-1-1  & f12.6  & time in ps \\
I-1-2  & f12.6  & total rms deviation of the selected atoms before superimposition \\
I-1-3  & f12.6  & total rms deviation of the selected atoms after superimposition \\
\hline
II-1-1 & a8     & keyword \verb+analysis+ \\
\hline
\mbox{\bf For each solute atom one card II-2} \\
\hline
II-2-1  & a5     & segment name \\
II-2-2  & a5     & atom name \\
II-2-3  & i6     & segment number \\
II-2-4  & i10    & atom number \\
II-2-5  & i5     & selected if 1 \\
II-2-6  & f12.6  & average atom rms deviation after superimposition \\
\hline
III-1-1 & a8     & keyword \verb+analysis+ \\
\hline
\mbox{\bf For each solute segment one card III-2} \\
III-2-1 & a5     & segment name \\
III-2-2 & i6     & segment number \\
III-2-3 & f12.6  & average segment rms deviation after superimposition \\
\hline\hline
\end{tabular*}
\end{center}
\end{table}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{table9764}%
\begin{table}\begin{center}
\begin{tabular*}{150mm}{p{15mm}p{12mm}l}
\hline\hline
Card & Format & Description \\\hline
I-1-1  & i7     & number $nprop$\  of recorded properties \\
I-1-2  & 1x,2a10 & date and time \\
\hline
\mbox{\bf For each of the $nprop$\  properties one card I-2} \\
\hline
I-2-1  & a50    & description of recorded property \\
\hline
\mbox{\bf For each recorded step one deck II} \\
\hline
II-1-1 & 4(1pe12.5) & value of property \\
\hline\hline
\end{tabular*}
\end{center}
\end{table}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}

\newcounter{algcounter}[chapter]%


\newedenvironment{algorithm}[1]{ \refstepcounter{algcounter}
                \begin{center}
                  {\bf Algorithm} \thechapter.\arabic{algcounter}: #1
                \end{center}
               \begin{center}\begin{enumerate} \begin{em}}
               {\end{em}\end{enumerate}\end{center}}%

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10596}%
$<$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10616}%
$\mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10664}%
$\frac{MIN(\left| \vec{a_i} \right|)}{\pi}, i=1,2,3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10666}%
$||$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10692}%
$\gamma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10786}%
$\equiv$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10788}%
$P_{electron}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10796}%
$T_{electron}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10804}%
$P_{ion}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10812}%
$T_{ion}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10820}%
$\tau_{electron}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10828}%
$\tau_{ionic}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10898}%
$1s^2 2s^2 2p^6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10900}%
$2s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10902}%
$2p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10904}%
$r_{cut}(l)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10908}%
$\rho_{semicore}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10910}%
$\rho_{core}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20290}%
$\displaystyle \rho_{semicore}(r) = \left\{ \begin{array}{ll}
\rho_{core} & \mbox{if $r \geq r_{semicore}$} \\
c_0 + c_3 r^3 + c_4 r^4 + c_5 r^5 + c_6 r^6 &  \mbox{if $r < r_{semicore}$}
\end{array}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10964}%
$(-2||-1||1||2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10972}%
$-2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20477}%
$\displaystyle KE(\{\psi_{i,\sigma}(\vec{r})\})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20478}%
$\textstyle =$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20479}%
$\displaystyle \sum_{i,\sigma}^{occ}
\int d\vec{r}\ \mu \left|
\dot{\psi}_{i,\sigma}(\vec{r}) \right|^2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20481}%
$\displaystyle L$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20483}%
$\displaystyle \sum_{i,\sigma}^{occ} \int d\vec{r}\ \mu \left|
\dot{\psi}_{i,\sigma}(\vec{r}) \right|^2
+ \frac 12 \sum_I M_I \left| \dot{\vec{R}}_I \right|^2
- E\left[ \left\{ \psi_{i,\sigma}(\vec{r})\right\},\left\{\vec{R}_I \right\} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20484}%
$\displaystyle +\sum_{ij,\sigma} \Lambda_{ij,\sigma} \left( \int d\vec{r}\ 
\psi_{i,\sigma}^{*}(\vec{r}) \psi_{j,\sigma}(\vec{r}) - \delta_{ij,\sigma}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11238}%
$\psi_{i,\sigma}(\vec{r})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11240}%
$\vec{R}_I$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20488}%
$\displaystyle \mu \ddot{\psi}_{i,\sigma}(\vec{r},t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20490}%
$\displaystyle -\frac{\delta E}{\delta \psi_{i,\sigma }^{*}
\left( \vec{r},t \right) } + \sum\limits_j \Lambda_{ij,\sigma}
\psi_{j,\sigma} \left( \vec{r},t \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20492}%
$\displaystyle M_I \ddot{\vec{R}}_I$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20494}%
$\displaystyle -\frac{\partial E}{\partial \vec{R}_I}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11244}%
$M_I$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11248}%
$\Lambda_{ij,\sigma}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20502}%
$\displaystyle \psi_{i,\sigma}^{t+ \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20503}%
$\textstyle \leftarrow$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20504}%
$\displaystyle 2 \psi_{i,\sigma}^{t} - \psi_{i,\sigma}^{t-\Delta t}
+ \frac{(\Delta t)^2}{\mu}
\left[
\frac{\delta E}{\delta \psi_{i,\sigma}^{*}}
+ \sum_{j} \psi_{j,\sigma} \Lambda_{ji,\sigma}
\right]_{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20506}%
$\displaystyle \vec{R}_I^{t+\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20508}%
$\displaystyle 2 \vec{R}_I^{t} - \vec{R}_I^{t-\Delta t}
+ \frac{(\Delta t)^2}{M_I}
\frac{\partial E}{\partial \vec{R}_I}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11252}%
$\frac{\delta E}{\delta \psi_{i,\sigma}^{*}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20513}%
$\displaystyle \frac{\delta E}{\delta \psi_{i,\sigma}^{*}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20515}%
$\displaystyle -\frac{1}{2} \nabla^2
\psi_{i,\sigma}(\vec{r})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20516}%
$\textstyle +$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20517}%
$\displaystyle \int d\vec{r^{\prime}}
W_{ext}(\vec{r},\vec{r^{\prime}})
\psi_{i,\sigma}(\vec{r^{\prime}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20519}%
$\displaystyle \int d\vec{r^{\prime}}
\frac{n(\vec{r^{\prime}})}{|\vec{r}-\vec{r^{\prime}}|}
\psi_{i,\sigma}(\vec{r})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20521}%
$\displaystyle \mu_{xc}^{\sigma}(\vec{r})
\psi_{i,\sigma}(\vec{r})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20522}%
$\textstyle \equiv$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20523}%
$\displaystyle \hat{H} \psi_{i,\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11260}%
$\psi_{i,\sigma}^{t+\Delta t}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11262}%
$x_e$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11264}%
$x_R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20530}%
$\displaystyle ION\_THERMOSTAT(x_R)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20532}%
$\displaystyle \frac{1}{2} Q_R \dot{x_R} + E_{R0}x_R$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20533}%
$\displaystyle ELECTRON\_THERMOSTAT(x_e)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20535}%
$\displaystyle \frac{1}{2} Q_e \dot{x_e} + E_{e0}x_e$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20537}%
$\displaystyle E_{R0} = \frac{1}{2} f k_B T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11268}%
$k_B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20541}%
$\displaystyle E_{e0} = 4 k_B T \frac{\mu}{M} \sum_i <\psi_i|-\frac{1}{2} \nabla^2 |\psi_i>$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11272}%
$M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11274}%
$\sum_i <\psi_i|-\frac{1}{2} \nabla^2 |\psi_i>$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11276}%
$Q_e$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$Q_R$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20548}%
$\displaystyle P_{ion}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20550}%
$\displaystyle 2\pi \sqrt{\frac{Q_R}{4E_{R0}}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20551}%
$\displaystyle P_{electron}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20553}%
$\displaystyle 2\pi \sqrt{\frac{Q_e}{4E_{e0}}}$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay20557}%
$\displaystyle T_e(t) = T_e^0 \exp^{-\frac{t}{\tau_e}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay20558}%
$\displaystyle T_{ionic}(t) = T_{ionic}^0 \exp^{-\frac{t}{\tau_{ionic}}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11284}%
$T_e^0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11286}%
$T_{ionic}^0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11288}%
$\tau_e$%
\lthtmlinlinemathZ
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$\Gamma$%
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\stepcounter{section}
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\lthtmlinlinemathA{tex2html_wrap_inline11306}%
$\alpha=\beta=\gamma=90^o$%
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\stepcounter{section}
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\stepcounter{subsection}
\stepcounter{subsection}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11741}%
$2H_2 + C_2H_4 \rightarrow 2CH_4$%
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$He_2$%
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{\newpage\clearpage
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$H + H_2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11969}%
$OH + H_2$%
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\stepcounter{subsection}
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$s < 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11977}%
$s > 0$%
\lthtmlinlinemathZ
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\appendix
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\stepcounter{subsection}
\stepcounter{section}
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\stepcounter{section}
\stepcounter{section}
\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12882}%
$\sigma_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12886}%
$C_2$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12888}%
$\sigma_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12892}%
$D_{\infty h}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12898}%
$\sigma$%
\lthtmlinlinemathZ
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\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
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$C_3$%
\lthtmlinlinemathZ
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\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12918}%
$C_5$%
\lthtmlinlinemathZ
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\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12946}%
$\sigma_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12956}%
$C_6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12958}%
$C_2'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12960}%
$C_2''$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline12992}%
$C_4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13020}%
$S_5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}

\end{document}
