Quantum Chemistry Laboratory # Exercise 6

### Topics

• Analysis of Gaussian output
• Atomization energy of water

### Analysis of Gaussian Output

In this exercise Gaussian output shall be analyzed. Complete Gaussian output files for the following species are available:
In the output for water please locate (in that order)
• charge of the molecule
• spin multiplicity
• H-O distance
• H-O-H angle
• name of the basis set
• total Becke3LYP energy E(RB+HF-LYP)
• energies and irreducible representations of the occupied molecular orbitals (MO)
• dipole moment
• CPU time

### Atomization Energy of Water

Find the Becke3LYP total energies of the two atoms in the corresponding output files. Calculate the energy De necessary for dissociating water into atoms according to the formula

De = 2 E(H) + E(O) - E(H2O)

Give De also in kJ/mol. For unit conversion see the help section. The experimental value is : 971.6 kJ/mol. Compare to the calculated value !

### Remark

The formula above can only be used for a quantum chemical method that is size consistent, i.e. when the total energy of a supermolecule A······B with infinite separation between A and B obeys the following relationship:

E(A······B) = E(A) + E(B)

Not every quantum chemical method exhibits the property that the accuracy of the resulting total energy is independent of the numbers of electrons of a molecular system. For example, the Configuration Interaction method with Single and Double substitutions (CISD) lacks size consistency. To calculate the binding energy of a molecue AB using CISD, the energy of the supermolecule A······B is also required, not just the total energies of the two sub-systems A and B.

Here, we leave aside the discussion under which circumstances density functional methods and related methods as the Becke3LYP hybrid method are size consistent. We calculated the binding energy in the straightforward fashion, as indicated above.

### Send in

To have your solution checked, send in the following results for the water molecule as calculated with the Becke3LYP method and basis set 6-31G(d):
• energies and irreducible representations of the occupied MOs
• dipole moment
• binding energy De in kJ/mol

### Reference

  Calculated from data in: M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D. J. Frurip, R. A. McDonald, and A. N. Syverud, "JANAF Thermochemical Tables, Third Edition", J. Phys. Chem. Ref. Data, 14 (1985) Supplement No. 1, p. 1274.

Copyright © 2003 N. Rösch, Technische Universität München