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.
# 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