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: