$CEEIS group  (optional, for extrapolation to FCI limit)
 
     The method termed Correlation Energy Extrapolation by
Intrinsic Scaling (CEEIS) allows one to extrapolate
sequences of CI energies, computed with the ORMAS program,
to what is effectively the full CI limit for a given basis
set.  Typically, the energy for SD and SDT excitation
levels using all orbitals (m=M, meaning occupied + all
virtuals) is combined, using certain scaling relations,
with explicit computations using m orbitals for quadruple,
quintuple... excitations (x), using a smaller m for each
higher excitation, to obtain the extrapolated FCI limit,
within an estimated error bar.  When this is done for
several basis sets, it is possible to extrapolate the
individual full CI energies to the limit of the complete
basis set.
 
     A series of papers combines complete basis set CEEIS
energies with scalar relativistic, spin-orbit, and long
range electrostatic corrections to produce a very accurate
rotational-vibrational spectrum of F2, see
L.Bytautas, T.Nagata, M.S.Gordon, K.Ruedenberg
        J.Chem.Phys. 127, 164317/1-20 (2007)
L.Bytautas, N.Matsunaga, T.Nagata, M.S.Gordon, K.Ruedenberg
        J.Chem.Phys. 127, 204301/1-12 (2007)
L.Bytautas, N.Matsunaga, T.Nagata, M.S.Gordon, K.Ruedenberg
        J.Chem.Phys. 127, 204313/1-19 (2007)
L.Bytautas, K.Ruedenberg
        J.Chem.Phys. 130, 204101/1-14 (2009)
 
     The input description below is quite terse.  A full
description of how to use CEEIS with ORMAS is provided in a
separate file (a Word document) named
     ~/gamess/tools/ci-tools/ceeis/CEEIS.doc
containing a much more detailed description of how to do
this kind of calculation.  This document explains how to
use an Excel spreadsheet to allow visual checking of the
energy data that are being extrapolated.  Several input
examples are given in the same directory.
 
 
ENREF  = reference energy, usually either a zero-excited
         ORMAS reference wavefunction, or some SCF level
         energy (if the reference is one determinant).
 
ISTPEX = highest excitation level considered by the CEEIS,
         the default is 8 (octuple excitations).
 
M1M2EX = an array to specify the various ORMAS computations
         to be performed, at each excitation level x.
         0's start the specification of m values for each
         level x=3,4,...ISTPEX.  Some examples follow,
  M1M2EX(1)= 0,0,0,
             0,7,10,-14,20
             0,7,10,-14   ISTEPX=5
The final two zero's on the first (SDT) line mean do the
SDT computations with the entire virtual space, and also
for all m values used at the higher excitations.  The SDTQ
energies are found for m=7,10,11,12,13,14,20, that is, the
minus sign implies all values in the range 10-14.  The
SDTQ5 computations do not include m=20.  If there is not
enough memory to do the entire SDT calculation, this can be
extrapolated (losing accuracy in the entire CEEIS process),
by input such as
  M1M2EX(1)= 0,7,10,-14,20,27,
             0,7,10,-14,20
             0,7,10,-14   ISTEPX=5
Changing the 0,0 part of the triples line to what is shown
extrapolates from m=27.  Note that it is an error not to
include the same m values that higher excitations will use.
There is no input for doubles, as in all cases the program
will generate the SD energy for the entire virtual space,
and additional SD energies for the m values chosen for use
by the higher excitation levels.
  M1M2EX(1)= all 0's will carry out a fully automated CEEIS
using MMIN to MMIN+4, testing convergence, possibly adding
MMIN+5 to MMIN+9 and so forth.
 
IDELTM = range increment for the m1,m2 ranges given as
         {m1,-m2} in M1M2EX.  Default=1.
 
ISCHME = extrapolation choice (the default is 1) for energy
         increments (DEMAT = differences of EMAT values):
       = 1 means extrapolate excitation level "x" by
              DEMAT(m,x) = a*DEMAT(m,x-2) + b
       = 2 means extrapolate quadruples as above, but
           x=5+6 or x=7+8,... are extrapolated together:
              DEMAT(m,x) = A*DEMAT(m,2) + B*DEMAT(m,3) + C
           In this case energies for odd excitation levels
           are not needed, and their computation can be
           avoided by making the odd levels in M1M2EX be
           the same input for 5+6, 7+8, ...
 
MMIN   = "m" value of the lowest virtual orbital to be
         considered in the extrapolation.  The default is
         NCORE + 1 + MAX(no. valence e-, no. valence orbs),
         which is in fact the lowest "m" that should ever
         be used.
 
XTRTOL = an array of thresholds for each extrapolated
         energy E(x), if the automated CEEIS is being used.
         default = 2D-4 Hartree for all levels x.
 
NSEXT  = an array containing NSPACE entries.  Each entry
         corresponds to an ORMAS orbital group defined by
         MSTART in $ORMAS, and can be either 0 or 1.
         An entry of 1 means include excitations from this
         space during the CEEIS.  0 means do not include
         any such excitations, meaning electrons in this
         subspace are NOT being correlated, apart from the
         correlation built into the original ORMAS.  The
         final entry in the list is the virtual space, and
         must be given as 1.  The default is all 1's.
 
RESTRT = a flag to say that the CEEIS calculation is being
         restarted, in which case energies provided in the
         $CEDATA input are read, and only the missing
         energies will be calculated.  Default = .FALSE.
 
IEXPND = expands the excitation level in restarts, e.g. if
         the previous data was computed for ISTPEX=6, and
         you now wish to use ISTPEX=8, enter IEXPND=2 to
         add two more columns to the matrix EMAT(m,x) being
         read in $CEDATA.
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