# Example: Basis Set Superposition Error (BSSE): Cr(CO)5 +CO¶

Download BSSE_CrCO6.run

#! /bin/sh

# A study of the Basis Set Superposition Error (BSSE) in the formation of
# Cr(CO)_6. from CO and Cr(CO)_5.

# For the BSSE calculation special chemical elements must be created to describe
# the 'ghost' atoms, which have zero nuclear charge and mass. They do have basis
# functions (and fit functions), however, and they are used to calculate the
# lowering of the energy of the system to which the ghost atoms are added, due
# to the enlargement of the basis by the ghost basis. The ghost atom has the
# same basis and fit set as the normal element but no nuclear charge and no
# frozen core. The BASIS key recognizes elements denoted with Gh.atom in the
# ATOMS key as being ghost atoms. If the basis file specifies a frozen core ADF
# will treat it as if no frozen core is present.

# The following calculations are carried out:

# 1. CO from C and O. This yields the bond energy of CO with respect to
#    the (restricted) basic atoms.
# 2. CO from the fragments CO (as calculated in 1) and the ghost atom Cr
#    and 5 Carbon and 5 Oxygen ghost atoms. The ghost atomic fragments
#    provide basis and fit functions but do not contribute charge or
#    potential to the molecule. The bond energy of this calculation is
#    the energy lowering of CO due to the additional basis functions.
#    This is the BSSE for CO.
# 3. Cr(CO)5 from Cr and 5 CO's. This yields the ('normal') bond energy
#    with respect to the given fragments.
# 4. Cr(CO)5 from Cr(CO)5 as fragment (as calculated in 3) but with the
#    CO basis functions added on the position of the 6th CO ('ghost' CO).
#    The bond energy is the BSSE for Cr(CO)5 .
# 5. Cr(CO)6 with Cr(CO)5 and CO as fragments. The bond energy is the one
#    without BSSE. This bond energy can now be corrected by the sum of
#    superposition contributions of calculations 2 and 4.

# This series of calculations is carried out with basis set DZ.

# Finally, the whole thing might be redone with basis set TZP, to show that the
# BSSE decreases with larger basis.

# The calculations for the type DZ basis are contained in the sample script
# (with input- and output files). Those for type TZP bases can be set up easily
# and may be done as an exercise.

# For the first series of calculations, with basis type DZ, the input files are
# discussed below and the relevant parts are echoed from the output files where
# the energy decomposition and the total bond energy are printed.

# For the other series, using type TZP basis sets, only a summary of the results
# is given.

# =====================
# Computational details
# =====================

# The calculations in this example all use:

# Small core DZ basis set Frozen core level for the Chromium atom: 2p, for
# Carbon and Oxygen: 1s Numerical integration precision 4.0 (in Create runs
# 10.0, the default) Default settings for model parameters such as density
# functional (key XC) and for the remaining computational settings For the BSSE
# calculations we first do the 'normal' calculations of CO and Cr(CO)5 ,
# yielding the fragment files t21.CO and t21.CrCO5. The input files for these
# calculations are not shown here.

# ===========
# BSSE for CO
# ===========

# For the CO BSSE calculation the standard CO must have been computed first. In
# the BSSE run a Cr(CO)5 ghost fragment basis set is then added to the 'normal'
# CO input. Important is the use of the BASIS key. In this case the BASIS key is
# used for the generation of the ghost atoms, it should have the same definition
# for the atoms as will be used later for the Cr(CO)5 fragment. The FRAGMENTS
# key is used for the fragment CO. The energy change (the printed 'bond energy'
# in the output) is the BSSE.

$ADFBIN/adf <<eor title CO (normal run) atoms C 0 0 1.86 O 0 0 3.03 end Basis Type DZ Core Small end symmetry C(lin) eor mv TAPE21 CO.t21 rm logfile # The input file for the CO-BSSE run is:$ADFBIN/adf <<eor
title  BSSE for CO due to Cr(CO)5 ghost
noprint sfo,frag,functions

atoms
Gh.Cr    0       0       0
Gh.C    -1.86    0       0
Gh.C     1.86    0       0
Gh.C     0       1.86    0
Gh.C     0      -1.86    0
Gh.C     0       0      -1.86
Gh.O     3.03    0       0
Gh.O    -3.03    0       0
Gh.O     0       3.03    0
Gh.O     0      -3.03    0
Gh.O     0       0      -3.03
C     0       0       1.86       f=CO
O     0       0       3.03       f=CO
end

Basis
Type DZ
Core Small
end

fragments
CO     CO.t21
end

symmetry  C(4V)

eor

mv TAPE21 CO_with_fake_CrC5O5.t21
rm logfile

# In the output we find in the Bond Energy section: The BSSE for CO is computed
# as 2.43 kcal/mol

# ================
# BSSE for Cr(CO)5
# ================

# In similar fashion the BSSE is computed for Cr(CO)_5 . In the BSSE run a ghost
# atoms C and O at the positions they will have in the Cr(CO)_6 molecule are
# added to the normal Cr(CO)_5 input:

$ADFBIN/adf <<eor title Cr(CO)5 (normal run) noprint sfo,frag,functions SCF mixing 0.1 END atoms Cr 0 0 0 C 1.86 0 0 f=CO/1 C -1.86 0 0 f=CO/2 C 0 1.86 0 f=CO/3 C 0 -1.86 0 f=CO/4 C 0 0 -1.86 f=CO/5 O 3.03 0 0 f=CO/1 O -3.03 0 0 f=CO/2 O 0 3.03 0 f=CO/3 O 0 -3.03 0 f=CO/4 O 0 0 -3.03 f=CO/5 end Basis Type DZ Core Small end fragments CO CO.t21 end symmetry C(4v) eor mv TAPE21 CrCO5.t21 rm logfile$ADFBIN/adf <<eor
title BSSE for Cr(CO)5 due to CO ghost
noprint sfo,frag,functions

atoms
Cr    0       0       0        f=CrCO5
C     1.86    0       0        f=CrCO5
C    -1.86    0       0        f=CrCO5
C     0       1.86    0        f=CrCO5
C     0      -1.86    0        f=CrCO5
C     0       0      -1.86     f=CrCO5
O     3.03    0       0        f=CrCO5
O    -3.03    0       0        f=CrCO5
O     0       3.03    0        f=CrCO5
O     0      -3.03    0        f=CrCO5
O     0       0      -3.03     f=CrCO5
Gh.C   0       0       1.86
Gh.O   0       0       3.03
end

Basis
Type DZ
Core Small
end

fragments
CrCO5   CrCO5.t21
end

symmetry C(4v)

eor

rm TAPE21 logfile

# The Bond Energy result yields 1.93 kcal/mole for the BSSE.

# ============================================
# Bond Energy calculation with BSSE correction
# ============================================

# The bonding of CO to Cr(CO)5 is computed in the normal way: from fragments CO
# and Cr(CO)5 . The obtained value for the bond energy can then simply corrected
# for the two BSSE terms, 4.36 kcal/mole together.

# ===========================
# Relevance of Core Functions
# ===========================

# The two BSSE runs can also be repeated, but now with the core
# orthogonalization functions omitted from the ghost bases. To to this one can
# not use the BASIS key, but one needs to explicitly 'create' the ghost atoms.
# This will not be done here, but only the results will be discussed. One may
# argue about whether these functions should be included in the ghost basis
# sets, but since they are very contracted around the ghost nuclei they are not
# expected to contribute significantly anyway and may then just as well be
# omitted. This has been explicitly verified by test examples. /p The Core
# Functions (the functions in the valence basis set that serve only for core-
# orthogonalization, for instance the 1S 5.40 in the Carbon basis set (see the
# $ADFHOME/atomicdata/DZ/C.1s basis set file) are removed from the Create data # files used for the creation of the ghost atoms. This yields as BSSE values for # CO and Cr(CO)5 respectively 2.33 and 1.87 kcal/mole (compare 2.43 and 1.93 # kcal/mole for the case with Core Functions included). The net total effect of # including/removing the Core Functions is therefore # (2.43-2.33)+(1.93-1.87)=0.16 kcal/mole. This is an order of magnitude smaller # than the BSSE effect itself. # ================================== # BSSE and the size of the basis set # ================================== # BSSE effects should diminish with larger bases and disappear in the limit of a # perfect basis. This can be studied by comparing the BSSE for basis DZ, see # above, with the BSSE for basis TZP. The procedure is completely similar to the # one above and yields: For the BSSE terms: 0.7 kcal/mole for CO (compare: 2.4 # kcal/mole for basis DZ), and 0.6 kcal/mole for Cr(CO)5 (1.9 for basis DZ) The # total BSSE drops from 4.4 kcal/mole in basis DZ to 1.3 in basis TZP. # ========= # Reference # ========= # A systematic study with adf of the BSSE in metal-carbonyl complexes can be # found in Rosa, A., et al., Basis Set Effects in Density Functional # Calculations on the Metal-Ligand and Metal-Metal Bonds of Cr(CO)5-CO and # (CO)5. Journal of Physical Chemistry, 1996, 100: p. 5690-5696.$ADFBIN/adf <<eor
title Bond energy without BSSE for Cr(CO)6 made of Cr(CO)5 and CO
noprint sfo,frag,functions

atoms
Cr    0       0       0        f=CrCO5
C     1.86    0       0        f=CrCO5
C    -1.86    0       0        f=CrCO5
C     0       1.86    0        f=CrCO5
C     0      -1.86    0        f=CrCO5
C     0       0      -1.86     f=CrCO5
O     3.03    0       0        f=CrCO5
O    -3.03    0       0        f=CrCO5
O     0       3.03    0        f=CrCO5
O     0      -3.03    0        f=CrCO5
O     0       0      -3.03     f=CrCO5
C     0       0       1.86     f=CO
O     0       0       3.03     f=CO
end

Basis
Type DZ
Core Small
end

fragments
CrCO5   CrCO5.t21
CO      CO.t21
end

eor

rm TAPE21 logfile