
	
                   --------- NEO-NCI NOTES ---------
	
  This document only pertains to examples and explanations of the NEO-NCI
  method. For information on input keywords for a NEO-NCI calculation read the
  NEOINP.DOC  For equations and further information on the NEO-NCI theory see
  the reference: J.H. Skone et. al. JCP 123, 134108 (2005).
  In addition to correctly obtaining delocalized NEO wavefunctions for
  transition state geometries, NEO-NCI can be used to calculate proton tunneling
  splittings and proton-coupled electron transfer (PCET) vibronic couplings. For 
  an illustration of its use for calculating PCET vibronic couplings see the 
  reference: M.K. Ludlow, J.H. Skone, and S. Hammes-Schiffer, J. Phys. Chem. B, 
  (in press).  

  The test directory HeHHe contains several NEO-NCI test jobs of the
  [HeHHe]+ molecule with each input file showcasing different options available
  to the method.  

  ----------------------------------
  LOCALIZATION OF MOLECULAR ORBITALS
  ----------------------------------

  In order to carry out a NEO-NCI calculation a set of localized molecular
  orbitals (both right and left) must first be generated. This is done by
  setting up two separate NEO-GAMESS energy calculations with the addition of
  the keyword "LOCORB" in the $NEO dollar group specifying the localization
  of the orbitals (1= left, 2= right). When LOCORB=1 the electronic molecular
  orbitals and the proton molecular orbitals localized on the left will be 
  written to the DAT file under the dollar groups $LOCEL1 and $LOCPR1,
  respectively. When LOCORB=2 the electronic molecular orbitals and the 
  proton molecular orbitals localized on the right are written to the DAT
  file under the dollar groups $LOCEL2 and $LOCPR2, respectively. To 
  later use these localized orbitals in a NEO-NCI calculation you must copy 
  them from the DAT files (both left and right) into your NEONCI input file.

  At the transition state the NEO nuclear wavefunction is represented by 
  two basis function centers, which are equally spaced from the donor and 
  acceptor. Each basis function center contains both electronic and nuclear
  basis functions. If the proton molecular orbitals are localized, nuclear 
  density should predominantly reside on one of the two centers and not be 
  equally shared between the two centers (delocalized over both centers). The
  convention is to label the state with proton density localized on basis 
  function center one as "left" and the state with proton density localized on
  basis function center two as "right". Localizing the nuclear density on one of
  the two centers can be done by using a set of electronic orbitals for the 
  GUESS that were previously generated  from a regular electronic structure
  energy calculation (non-NEO) with one of the basis function centers perturbed
  so that they are not equally spaced from the donor and acceptor groups.  

  An illustration of the localization of the electronic molecular orbitals by
  perturbing the basis function centers in a regular electronic structure 
  calculation is shown below.  The basis function centers (x) are equally spaced
  from the donor group (D) and acceptor group (A) in the NEO-NCI calculation.
   
   D     x   x     A     This corresponds to symmetric placement

                         ***GENERATE LOCALIZED ELECTRONIC DENSITY***
   D   x     x     A     asymmetric placement of bfc (x) pertrubed left for regular electronic 
                         structure calculation (non-NEO) of left localized elec orbitals. 
   D     x     x   A     asymmetric placement of bfc (x) pertrubed right for regular electronic
                         structure calculation (non-NEO) of right localized elec orbitals. 

                         ***GENERATE NEO ORBITALS WITH THE LOCALIED ELEC DENSITY***
   D     x   x     A     symmetric placement of basis function centers (x) for NEO-NCI,
                         left localized NEO-HF, and right localized NEO-HF calculations.

   Another way to obtain localized states is to use a single basis function
   center for the localized NEO energy calculations, but then use both basis
   function centers in the NEO-NCI calculation. For this input in the NEO-NCI
   calculation you must specify in the $NCIINP group that the number centers
   used to generate the localized orbitals was 1 by setting NUMCNT=1. 
   Additionally the QM nucleus for this calculation must be the last atom in the
   $DATA group. 

   Illustration of localization by use of single centers: 

                         ***left locailzed NEO-HF***
   D     x         A     single center with density localized on center 1

                         ***right localized NEO-HF***
   D         x     A     single center with density localized on center 2 

   D     x   x     A     NEO-NCI calculation


  -----------------------------------------------
  USING LOCALIZED STATES THAT ARE DEGENERATE IN A 
  2x2 NEO-NCI (INFO FOR NCISYM KEYWORD)
  -----------------------------------------------
  
  If the classical nuclear geometry is symmetric and the localized states used 
  as input for the NEO-NCI calculation are degenerate and from a NEO-HF or
  NEO-DFT calculation then the evaluation of the diagonal matrix elements 
  can be skipped for a 2x2 NEO-NCI calculation. This is possible since
  a NEO-HF or NEO-DFT calculation always preceedes the NEO-NCI calculation
  thus allowing the energy from either calculation to be later retrieved in the
  in the NEO-NCI calculation and the diagonal matrix elements set to this value.
  Note this option is only valid for a 2x2 NEO-NCI calculation and requires
  that the orbitals used in the $VEC group of the NEO-NCI input file correspond
  to either one of the localized orbitals $LOCELE1 or LOCELE2.  
  By taking advantage of skipping the calculation of the diagonal elements a
  computational savings of 3X can be acheived. This can be done by setting the 
  keyword NCISYM=.T. in the $NCIINP group. 


      
