% 
%  Psi Programmer's Manual
%
%  files in psi
%
%  Brian Kellogg, 02/02/96 (groundhog day!) 

Psi uses several text files to store certain types of information.  Storing
information in text files makes it much easier for users to inspect 
and manipulate that
information, provided that the user understands the format of that file.
In the following file format descriptions, I will use the notation 
${ x_i, y_i,}$ and ${z_i}$ to denote the x, y and z coordinates of nucleus i,
respectively,
${\eta_{ i}}$ will denote the ${i^{\rm th}}$ internal coordinate, and
E will denote the sum of the electronic energy and nuclear repulsion energy. 

\begin{verbatim}
	geom.dat
\end{verbatim}

A vectorized format which is appropriate for the routines in libipv1 or
iomr is employed in \geomdat\ 
Generally, the first line of \geomdat\ is 
\begin{verbatim}
%%
\end{verbatim}
Though this does not affect the parsing routines in libipv1, or 
any of the common programs which read \geomdat\ 
(i.e. \module{rgeom} or \module{ugeom}), some  \PSItwo\ modules (\module{bmat}, etc.)
expected this line and
would muddle up \geomdat\ if it is not present.  \geomdat\ will 
frequently have several entries, with the topmost being the most recent
addition by bmat.

format: {\em n} = number of atoms.
\begin{eqnarray}
\begin{array}{lcccr} 
{\tt geometry = (}\\
{\tt (} &x_1 \hspace{0.8in} &y_1 \hspace{0.8in} &z_1 \hspace{0.8in} &{\tt )} \\
{\tt (} &x_2 \hspace{0.8in} &y_2 \hspace{0.8in} &z_2 \hspace{0.8in} &{\tt )} \\
 &\vdots\hspace{0.8in}&\vdots\hspace{0.8in}&\vdots\hspace{0.8in}&\\
{\tt (} &x_n \hspace{0.8in} &y_n \hspace{0.8in} &z_n \hspace{0.8in} &{\tt )} \\
\ \ {\tt )}
\end{array}
\end{eqnarray}
Other geometries of the same format may follow.  

\begin{verbatim}
	fconst.dat
\end{verbatim}

This file contains the force constant matrix produced by \module{optking} or
\module{intder95}.  Because the force constant matrix is symmetric, only the lower diagonal is stored
here.  The force constant matrix may be represented in either cartesian or
internal coordinates, depending upon what flags were used when \module{intder95} was
run to produce \fconstdat .  \module{optking} is the program which uses
\file{fconst.dat} most frequently, and it assumes that the force constant
matrix will be in terms of the internal coordinates as defined in
\inputdat\ or \intcodat.  For this reason, it is best to have
\module{intder95} produce a \fconstdat\ in internal coordinates.  The order of
internal coordinates is determined by the order set up in \inputdat\ or
\intcodat .  The totally symmetric coordinates always come first,
followed by all asymmetric coordinates.  

In the following format, ${f_{\eta_i}}$ is the force constant for internal
coordinate ${\eta_i}$ and ${f_{\eta_i,\eta_j}}$ is the force constant for
the mixed displacement of internal coordinates i and j.

format: {n = total number of internal coordinates in \intcodat\ 
or \inputdat .
\begin{eqnarray}
\begin{array}{lllll}
f_{\eta_1} \\
f_{\eta_2,\eta_1} & f_{\eta_2} \\
f_{\eta_3,\eta_1} & f_{\eta_3,\eta_2} & f_{\eta_3} \\
\vdots & \vdots & \vdots \\
f_{\eta_{n},{\eta}_1} & f_{\eta_{n},\eta_2} & f_{\eta_{n},\eta_3} & \cdots 
& f_{\eta_{n}} \\
\end{array}
\end{eqnarray}
If the force constant matrix is stored in cartesian coordinates, however,
the format, using a similar notation, with {\em n} now equal to the total
number of atoms, is as follows:
\begin{eqnarray}
\begin{array}{llllll}
f_{x_1} \\
f_{y_1,x_1} & f_{y_1} \\
f_{z_1,x_1} & f_{z_1,y_1} &f_{z_1} \\
f_{x_2,x_1} & f_{x_2,y_1} & f_{x_2,z_1} &f_{x_2} \\
\vdots & \vdots & \vdots & \vdots \\
f_{z_n,x_1} & f_{z_n,y_1} & f_{z_n,z_1} & f_{z_n,x_2} & \cdots & f_{z_n} \\
\end{array}
\end{eqnarray}
\begin{verbatim}
	file11.dat
\end{verbatim}

The number of atoms ({\em n}), total energy 
as predicted by the final wavefunction, 
cartesian geometry, cartesian gradients, atomic charges ({\em Z$_i$})
and a label are all contained in \FILE{11}.  The exact nature of the label
depends upon the type of wavefunction for which the gradient was calculated.
The first part of the label is determined by the label keyword in input.dat.
If an SCF gradient is run, then the calculation type ({\em calctype}), and 
derivative type ({\em dertype}) will also appear.  
If a correlated  gradient has been run, {\em calctype}
[CI, CCSD, or CCSD(T)] and derivative type (FIRST) appear.
\FILE{11} will
frequently have several entries, with the last entry being the latest
addition by \module{cints --deriv1}.  

format:
\begin{eqnarray}
\begin{array}{l}
label\hspace{0.5in} calctype \hspace{0.5in} dertype \hspace{0.7in} \\
n  \hspace{0.5in}   E \\
\begin{array}{cccc}
\hspace{0.3in}Z_1 \hspace{0.3in}& \hspace{0.4in}x_1\hspace{0.4in} &
\hspace{0.4in} y_1 \hspace{0.4in} & \hspace{0.4in} z_1 \hspace{0.4in} \\
Z_2 & x_2 & y_2 & z_2 \\
\vdots & \vdots & \vdots & \vdots \\
Z_n & x_n & y_n & z_n \\
\vspace{0.02in} 
& \frac{\delta E}{\delta x_1} & \frac{\delta E}{\delta y_1} 
& \frac{\delta E}{\delta z_1} \\
& \frac{\delta E}{\delta x_2} & \frac{\delta E}{\delta y_2} 
& \frac{\delta E}{\delta z_2} \\
& \vdots & \vdots & \vdots \\
& \frac{\delta E}{\delta x_n} & \frac{\delta E}{\delta y_n} 
& \frac{\delta E}{\delta z_n} \\
\end{array}
\end{array}
\end{eqnarray}


\begin{verbatim}
	file12.dat
\end{verbatim}

Internal coordinate values and gradients, the number of atoms ({\em n}), and
the total energy ({\em E}) may be found in \FILE{12}. \FILE{12} is produced
by \module{intder95}, which can convert cartesian
gradients into internal gradients.  
Generally,
\FILE{12} will have several entries, with each entry corresponding to an
entry in the \FILE{11} of interest.  

format:
\begin{equation}
\begin{array}{l}
   n\hspace{1.5in} E \\
\begin{array}{cc}
\vspace{0.02in}
\hspace{0.5in} \eta_1 \hspace{0.5in}
& \hspace{1.2in} \frac{\delta E}{\delta \eta_1}  \hspace{1.2in}\\
\hspace{0.5in} \eta_2 \hspace{0.5in}
& \hspace{1.2in} \frac{\delta E}{\delta \eta_2} \hspace{1.2in} \\
\vdots & \vdots \\
\hspace{0.5in} \eta_n \hspace{0.5in}
& \hspace{1.2in} \frac{\delta E}{\delta \eta_n} 
\hspace{1.2in}\\
\end{array}
\end{array}
\end{equation}

\begin{verbatim}
	file12a.dat
\end{verbatim}
In order to calculate second derivatives from gradients taken at geometries
finitely displaced from a particular geometry, \module{intdif} requires a
\FILE{12a}.  This file contains essentially the same information as
\FILE{12}, but each entry also has information concerning which
internal coordinate ({\em numintco}) was displaced in the gradient
calculation and by how much ({\em disp}) it was displaced.  

format: 
\begin{equation}
\begin{array}{l}
numintco\hspace{0.5in}disp\hspace{1.5in}E \\
\begin{array}{cc}
\vspace{0.02in}
\hspace{0.5in} \eta_1 \hspace{0.5in}
& \hspace{0.8in} \frac{\delta E}{\delta \eta_1}  \hspace{0.8in}\\
\hspace{0.5in} \eta_2 \hspace{0.5in}
& \hspace{0.8in} \frac{\delta E}{\delta \eta_2} \hspace{0.8in} \\
\vdots & \vdots \\
\hspace{0.5in} \eta_n \hspace{0.5in}
& \hspace{0.8in} \frac{\delta E}{\delta \eta_n} \hspace{0.8in}\\
\end{array}
\end{array}
\end{equation}

\begin{verbatim}
	file15.dat
\end{verbatim}

The cartesian Hessian matrix is found in \FILE{15}.  The first line of 
this file gives the number of atoms ({\em n})
and, in case you are curious, six times the number of atoms 
({\em sixtimesn}).

format:
\begin{equation}
\begin{array}{l}
n\hspace{0.4in}sixtimesn \\
\begin{array}{ccc}
\vspace{0.02in}
\hspace{0.3in}\frac{\delta^2 E}{\delta^2 x_1} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta x_1\delta y_1} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta x_1\delta z_1} \hspace{0.3in}\\
\hspace{0.3in}\frac{\delta^2 E}{\delta x_1\delta x_2} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta x_1\delta y_2} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta x_1\delta z_2} \hspace{0.3in}\\
\vdots & \vdots & \vdots \\
\vspace{0.02in}
\hspace{0.3in}\frac{\delta^2 E}{\delta z_1\delta x_n} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta z_1\delta y_n} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta z_1\delta z_n} \hspace{0.3in}\\
\hspace{0.3in}\frac{\delta^2 E}{\delta x_2\delta x_1} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta x_2\delta y_1} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta x_2\delta z_1} \hspace{0.3in}\\
\vdots & \vdots & \vdots \\
\hspace{0.3in}\frac{\delta^2 E}{\delta z_n\delta x_n} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta z_n\delta y_n} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta^2 z_n} \hspace{0.3in}\\

\end{array}
\end{array}
\end{equation}

\begin{verbatim}
	file16.dat
\end{verbatim}
The second derivatives of the total energy with respect to the internal
coordinates are found in \FILE{16}.  
As in \FILE{15}, the number of
atoms ({\em n}) and six times that number ({\em sixtimesn}) are given.

format:
\begin{equation}
\begin{array}{l}
n\hspace{0.4in}sixtimesn \\
\begin{array}{ccc}
\vspace{0.02in}
\hspace{0.3in}\frac{\delta^2 E}{\delta^2 \eta_1} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta \eta_1\delta \eta_2} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta \eta_1\delta \eta_3} \hspace{0.3in}\\
\vdots & \vdots & \vdots \\
\hspace{0.3in}\frac{\delta^2 E}{\delta \eta_1\delta \eta_{n-2}} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta \eta_1\delta \eta_{n-1}} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta \eta_1\delta \eta_n} \hspace{0.3in}\\
\vdots & \vdots & \vdots \\
\vspace{0.02in}
\hspace{0.3in}\frac{\delta^2 E}{\delta \eta_n\delta \eta_{n-2}} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta \eta_n\delta \eta_{n-1}} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta^2 E}{\delta^2 \eta_n} \hspace{0.3in}\\

\end{array}
\end{array}
\end{equation}
\begin{verbatim}
	file17.dat
\end{verbatim}
First derivatives of the cartesian dipole moments (${\mu_x,\mu_y,\mu_z}$)
with respect to the
cartesian nuclear coordinates may be found in \FILE{17}.  The first
line and subsequent format are similar to that of \FILE{15}.

format:
\begin{equation}
\begin{array}{l}
n\hspace{0.4in}threetimesn \\
\begin{array}{ccc}
\vspace{0.02in}
\hspace{0.3in}\frac{\delta \mu_x}{\delta x_1} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_x}{\delta y_1} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_x}{\delta z_1} \hspace{0.3in}\\
\hspace{0.3in}\frac{\delta \mu_x}{\delta x_2} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_x}{\delta y_2} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_x}{\delta z_2} \hspace{0.3in}\\
\vdots & \vdots & \vdots \\
\vspace{0.02in}
\hspace{0.3in}\frac{\delta \mu_x}{\delta x_n} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_x}{\delta y_n} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_x}{\delta z_n} \hspace{0.3in}\\
\hspace{0.3in}\frac{\delta \mu_y}{\delta x_1} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_y}{\delta y_1} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_y}{\delta z_1} \hspace{0.3in}\\
\vdots & \vdots & \vdots \\
\hspace{0.3in}\frac{\delta \mu_z}{\delta x_n} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_z}{\delta y_n} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_z}{\delta z_n} \hspace{0.3in}\\
\end{array}
\end{array}
\end{equation}

\begin{verbatim}
	file18.dat
\end{verbatim}
First derivatives of the cartesian dipole moments (${\mu_x,\mu_y,\mu_z}$)
with respect to the
internal nuclear coordinates may be found in \FILE{18}. 

format:
\begin{equation}
\begin{array}{l}
n\hspace{0.4in}threetimesn \\
\begin{array}{ccc}
\vspace{0.02in}
\hspace{0.3in}\frac{\delta \mu_x}{\delta \eta_1} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_x}{\delta \eta_2} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_x}{\delta \eta_3} \hspace{0.3in}\\
\hspace{0.3in}\frac{\delta \mu_x}{\delta \eta_4} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_x}{\delta \eta_5} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_x}{\delta \eta_6} \hspace{0.3in}\\
\vdots & \vdots & \vdots \\
\hspace{0.3in}\frac{\delta \mu_z}{\delta \eta_{n-2}} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_z}{\delta \eta_{n-1}} \hspace{0.3in}&
\hspace{0.3in}\frac{\delta \mu_z}{\delta \eta_{n}} \hspace{0.3in}\\
\end{array}
\end{array}
\end{equation}