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

```
#! /bin/sh
# A study of the Basis Set Superposition Error (BSSE) in the formation of
# Cr(CO)_6. from CO and Cr(CO)_5.
# This example uses scalar relativistic ZORA calculations.
# 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.
AMS_JOBNAME=CO $AMSBIN/ams <<eor
Task SinglePoint
System
atoms
C 0 0 1.86
O 0 0 3.03
end
end
Engine ADF
title CO (normal run)
basis
Type DZ
Core Small
End
symmetry C(lin)
EndEngine
eor
# The input file for the CO-BSSE run is:
AMS_JOBNAME=CO_with_fake_CrC5O5 $AMSBIN/ams <<eor
Task SinglePoint
System
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 adf.f=CO
O 0 0 3.03 adf.f=CO
end
end
Engine ADF
title BSSE for CO due to Cr(CO)5 ghost
noprint sfo,frag,functions
basis
Type DZ
Core Small
end
fragments
CO CO.results/adf.rkf
end
symmetry C(4V)
EndEngine
eor
# In the output we find in the Bond Energy section: The BSSE for CO is computed
# as 2.40 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:
AMS_JOBNAME=CrCO5 $AMSBIN/ams <<eor
Task SinglePoint
System
atoms
Cr 0 0 0
C 1.86 0 0 adf.f=CO|1
C -1.86 0 0 adf.f=CO|2
C 0 1.86 0 adf.f=CO|3
C 0 -1.86 0 adf.f=CO|4
C 0 0 -1.86 adf.f=CO|5
O 3.03 0 0 adf.f=CO|1
O -3.03 0 0 adf.f=CO|2
O 0 3.03 0 adf.f=CO|3
O 0 -3.03 0 adf.f=CO|4
O 0 0 -3.03 adf.f=CO|5
end
end
Engine ADF
title Cr(CO)5 (normal run)
noprint sfo,frag,functions
SCF
mixing 0.1
END
basis
Type DZ
Core Small
end
fragments
CO CO.results/adf.rkf
end
symmetry C(4v)
EndEngine
eor
AMS_JOBNAME=final $AMSBIN/ams <<eor
Task SinglePoint
System
atoms
Cr 0 0 0 adf.f=CrCO5
C 1.86 0 0 adf.f=CrCO5
C -1.86 0 0 adf.f=CrCO5
C 0 1.86 0 adf.f=CrCO5
C 0 -1.86 0 adf.f=CrCO5
C 0 0 -1.86 adf.f=CrCO5
O 3.03 0 0 adf.f=CrCO5
O -3.03 0 0 adf.f=CrCO5
O 0 3.03 0 adf.f=CrCO5
O 0 -3.03 0 adf.f=CrCO5
O 0 0 -3.03 adf.f=CrCO5
Gh.C 0 0 1.86
Gh.O 0 0 3.03
end
end
Engine ADF
title BSSE for Cr(CO)5 due to CO ghost
noprint sfo,frag,functions
basis
Type DZ
Core Small
end
fragments
CrCO5 CrCO5.results/adf.rkf
end
symmetry C(4v)
EndEngine
eor
# The Bond Energy result yields 1.97 kcal/mol 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, (2.40+1.97=) 4.37 kcal/mol 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. 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
# $AMSHOME/atomicdata/ADF/ZORA/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 2.32 and 1.97 kcal/mol (compare 2.40 and 1.97
# kcal/mol for the case with Core Functions included). The net total effect of
# including/removing the Core Functions is therefore
# (2.40-2.32)+(1.97-1.97)=0.08 kcal/mol. 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/mol for CO (compare: 2.4
# kcal/mol for basis DZ), and 0.5 kcal/mol for Cr(CO)5 (1.9 for basis DZ) The
# total BSSE drops from 4.4 kcal/mol in basis DZ to 1.2 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.
$AMSBIN/ams <<eor
Task SinglePoint
System
atoms
Cr 0 0 0 adf.f=CrCO5
C 1.86 0 0 adf.f=CrCO5
C -1.86 0 0 adf.f=CrCO5
C 0 1.86 0 adf.f=CrCO5
C 0 -1.86 0 adf.f=CrCO5
C 0 0 -1.86 adf.f=CrCO5
O 3.03 0 0 adf.f=CrCO5
O -3.03 0 0 adf.f=CrCO5
O 0 3.03 0 adf.f=CrCO5
O 0 -3.03 0 adf.f=CrCO5
O 0 0 -3.03 adf.f=CrCO5
C 0 0 1.86 adf.f=CO
O 0 0 3.03 adf.f=CO
end
end
Engine ADF
symmetry C(4V)
title Bond energy without BSSE for Cr(CO)6 made of Cr(CO)5 and CO
noprint sfo,frag,functions
basis
Type DZ
Core Small
end
fragments
CrCO5 CrCO5.results/adf.rkf
CO CO.results/adf.rkf
end
EndEngine
eor
```