#! /bin/sh

# This is a small but important example to illustrate what goes into an accurate
# calculation of the 'true' bond energy of a molecule. The (ADF-specific)
# problem is that in a straightforward molecular calculation, the bond energy is
# computed as the energy difference between at the one hand the molecule, and at
# the other hand the isolated spherically symmetric spin-restricted atoms. The
# italic-typed features imply that the reference (comparison) state is usually
# not the physical ground state of the reference system (isolated atoms) and
# hence the computed energy difference has no direct relation to experimental
# data. To account for the true atomic ground states, one has to add correction
# terms. Study this sample carefully to make sure that you fully understand the
# steps to take and consult the User's Guide for details. See also the this
# document for a discussion of multiplet states.

# See also the example, SD_Cr(NH3)6.

# The H2 case consists of a sequence of simple calculations to demonstrate the
# Unrestricted Fragments option. The energy difference between an unrestricted
# fragment as it is used in adf and a self-consistent unrestricted fragment is
# also computed. This turns out to be quite small, confirming that the adf
# approach, although not formally exact, is adequate for practical purposes.

$ADFBIN/adf -n1 <<eor
create H    file=$ADFRESOURCES/DZP/H
eor

mv TAPE21 t21H

$ADFBIN/adf <<eor
title H unrestr., not self-consistent (as used in unr.frag. calcs)

EPRINT
SFO eig ovl
END

scf
iterations 0  ! prohibit relaxation
end

unrestricted

charge 0 1   !  if not specified up and down electrons
!               will both get 0.5 electron: in fact restricted

fragments
H  t21H
end

atoms
H 0 0 0
end

eor

rm TAPE21 logfile

# By setting the scf iterations to zero (a value of one (1) would give the same
# result) we prevent cycling to self-consistency. The energy of the 'final' one-
# electron orbitals is consequently computed in the start-up potential, i.e. the
# field of the restricted (basic) atom, where spin-alpha and spin-beta are equally
# occupied, in this case by 0.5 electron each. The not-self-consistent,
# unrestricted H atom is precisely the 'unrestricted' fragment as it can be used
# in an adf calculation with unrestricted fragments. The fragment file must be
# the TAPE21 result file from a restricted run, but at start-up you can specify
# that the Fragment Orbitals are, for purposes of reference and comparison,
# occupied in an unrestricted way in the final molecule.

# A calculation that uses restricted fragments right away computes the bonding
# energy relative to the restricted fragments. The difference between using
# restricted and unrestricted fragments is the 'bonding' energy computed in the
# run above.


$ADFBIN/adf <<eor
title  H  unr. self-consistent from unr.0

EPRINT
SFO eig ovl
END

unrestricted
charge 0  1

fragoccupations
H
s  1 // 0
subend
end

Atoms
H  0 0 0
end

fragments
H         t21H
end

eor

rm TAPE21 logfile


# Here we start with the unrestricted fragment and relax to self-consistency.
# The 'bonding energy', i.e. the relaxation energy, is very small, demonstrating
# that using non-self-consistent unrestricted fragments involves only a small
# error (which, moreover, can be computed as shown here).

# The key UnRestricted sets the spin-unrestricted mode. The key Charge is used
# to specify a net total charge of zero and a net total spin polarization by an
# excess of 1.0 spin-alpha electrons over spin-beta.

$ADFBIN/adf <<eor
title   H2 restricted, from restricted fragments

EPRINT
SFO eig ovl
END

ATOMS
H   0  0   0.375
H   0  0  -0.375
end

fragments
H   t21H
end

eor

rm TAPE21 logfile

# This is the simplest approach, using restricted fragments. The bonding energy
# must be corrected because the reference (restricted H atoms, with 0.5
# electrons in spin-alpha and 0.5 in spin-beta) is far from the true H-atom
# ground state: see the previous runs on the single H atom.

$ADFBIN/adf <<eor
title   H2 from unrestricted fragments

EPRINT
SFO eig ovl
END

ATOMS
H.1   0   0   0.375            
H.2   0   0  -0.375
end

fragments !  two different fragment types are necessary
!            because the two atoms get different FragOccupations
!            (see below), while the key FragOc.. addresses 
!            only fragmentTYPES
H.1  t21H
H.2  t21H
end

charge  0

IrrepOccupations
  sigma   2  !  specify the state (not always
             !  necessary)
end

fragoccupations
  H.1
    s  1 // 0
  subend
  H.2
    s  0 // 1
  subend
end

modifystartpotential
H.1  1 // 0    !  this helps SCF start-up
H.2  0 // 1    !  but is here not necessary
end

eor

rm TAPE21 logfile

# This should be a fair approximation (in the lda model) to the bonding energy
# of H2 with respect to the unrestricted H atoms. The difference between the
# bonding energies of this and the previous run should be very close to the
# energy of the not-self-consistent unrestricted H-atom with respect to the
# restricted basic atom (calculation #2).

# == Excited state ==

$ADFBIN/adf <<eor
title   H2  excited 

EPRINT
SFO eig ovl
END

ATOMS
H    0 .0     0.375            
H    0 .0    -0.375
end

fragments
H    t21H
end

fragoccupations
H
s  1 // 0
subend
end

unrestricted

charge 0  2

IrrepOccupations
sigma.g   1 // 0
sigma.u   1 // 0
end

eor

# Finally the calculation of an excited state, with respect to unrestricted
# fragments. The excitation energy is obtained by comparing the energy with the
# energy of the ground state calculation. This difference compares reasonably,
# but not accurately, to the difference in one-electron ground state energies of
# the involved orbitals (Koopman's theorem).

# Note that excitation energies can also be calculated with Time-Dependent DFT,
# using the RESPONSE module of ADF. See related sample runs.