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Molecular Modelling Lecture Notes
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CHM695Feb. 25
Basis Set Superposition Error (BSSE)
• Eg. if binding energy of water has to be computed
Eb
= Edimer
� 2Emonomer
6-31G**more than 6-31G** due to overlap of basis
functions
Counterpoise method: needs the same basis as
water dimer
S. F. Boys and F. Bernardi (1970)
Gaussian Input for counterpoise correction
# HF/6-31G(d) Counterpoise=2
Counterpoise on water dimer
0,1 0,1 0,1O(Fragment=1) 0.00 0.00 0.00O(Fragment=2) 0.00 0.00 2.98H(Fragment=1) 0.49 0.76 -0.29H(Fragment=1) 0.49 -0.76 -0.29H(Fragment=2) -0.91 0.00 3.24H(Fragment=2) -0.01 0.00 2.03
number of fragments
frag. 1 frag. 2
total system frag. 1
frag. 2
Output will print the BSSE corrected energy
• Another way to reduce the BSSE is to use large basis set
• Technique called “Chemical Hamiltonian Approach” will modify the basis set such that overlap of basis set will not occur.
Making XYZ file
• using molden
Hybridization
• MOs from HF calculations are having mixing of AOs
• Mixing of AOs of an atom to form a MO is called “hybridization”
MO treatment of polyatomic molecules
• We can use DFT or HF methods to solve for MOs
• Let us take the example of H—Be—H (i.e. BeH2)
Minimal basis set:
Be1s, Be2s, Be2px, Be2py , Be2pz H1sA H1sB
• For the linear BeH2 structure: center of symmetry
• ⇒ g or u labels for MOs
• Looking at orbital energy of Be and H ⇒1�g = Be1s (nonbonding)
H H 1�g
+⇒
Be
Z-axis
• 2s and 2p valence AOs of Be and 1s valence AOs of HA and HB (their orbital energies are the same)
• MOs should maintain the symmetry of the molecule: either g or u symmetry for MOs
• So, HA,1s+HB,1s and HA,1s-HB,1s contributions should come in the remaining MOs
• Symmetry of the basis set
�g �u⇡u
Be1s, Be2s, Be2px, Be2py, Be2pz, H1sA+H1sB, H1sA-H1sB
�g
H H
H H
H H
⇡u �u�g
H HBe
H HBeH1sA-H1sB
H1sA+H1sB
Be2pz,
Be2px
Be
Be1s
• basis set with identical symmetry can only combine
With and
H HBe
(bonding orbital)
H HBe
With
doubly degenerate MOs
antibonding MOs
Be1s
Be2s
Be2p
HA1s HB1s
LUMO
HOMO
Home Work: (a) Do HF/STO-3G and compare your results (b) Do the same for H2O (see Atkins, Phys. Chem.)
Localized MOs
H HBe
H HBe
Bonding MOs are delocalised!
Can we understand the bonding in terms
of individual bonds?
• MOs from HF calculations are called “canonical orbitals” (these are delocalised orbitals)
Slater Determinant of BeH2:
such operations will not change the wfn. & energy
Linear combinations of spin orbitals can be taken, such that localised MOs can be formed
H HBe H HBe
H HBeH HBe
b1 b2
Localized MOs
bonding (b)
inner shell (i)
lone pair (l)
creates charge buildup between atoms
has the same energy as the original
depending on nodes along bond axisbonds are named
Calculations will show that and s-p hybrids
• s-p hybridization on Be:
H HBe
H HBe
Homework 1: Work out the bonding in CH4 based on similar
analysis using HF/STO-3G basis. a) identify non-bonding MOs b) identify canonical MOs c) obtain, canonincal to localized MOs d) Based on that, show that C is sp3 hybridised.
Homework 2: Do the same for acetylene
If you do a similar calculation in ethene, localisation yields
Banana bonds
C C C C
CH2=CH2
instead of 1 pi and 1 sigma bonds
Similarly, there are molecules, where 3-centre 2-e bonds
are formed! e.g. B2H6
Natural Bonding Orbitals (NBO)
• A self consistent procedure to obtain localised orbitals (called natural orbitals) from the wavefunction (either HF or KS-DFT)
http://www.cup.uni-muenchen.de/ch/compchem/pop/nbo2.htmlWorkout example using Gaussian:
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