Concise Physical Chemistry

c20 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

MOLECULAR ORBITALS 329

#gen

H2mol gen

01

h

h1r

r=0.7

1

S2

1.00 0.40

0.25 0.60

****

2

S2

1.00 0.40

0.25 0.60

****

FILE 20.5 (Input) A molecular orbital input file for H 2 .Thefileisinz-matrix GAUSSIAN

format.

parameters refers to H atom 1, and the second set of parameters refers to H atom 2.

The only difference is in the atom identifiers: 1 in line 11 and 2 in line 16.

The energy output is designated arestrictedHartree Fock energyE(RHF),

E(RHF) =-1.07637168255 Eh

because it is the energy of the 1σorbital calculated on the assumption that both

spin paired electrons will be in it. If the spins were unpaired and the electrons

were in different orbitals, as in an excited state, theunrestricted Hartree Fockenergy

E(UHF)would be used. Unrestricted HF calculations are somewhat more demanding

on computer resources because calculations are done on each set of electrons forα

andβspin rather than on the pair. In this simple case, the difference is negligible.

The experimental dissociation energy of H 2 is 0.174Eh. The STO-2G calculated

energy is only about 44% of the experimental value in this crude approximation. The

input file for the same task usingz-matrix input and stored parameters is shown in

File 20.6.

Now the energy outputE(RHF) =-1.0934083Ehis 53% of the experimen-

tal value of 0.174Eh. Neither the arbitrary parameters in File 20.5 nor the STO-2G

stored basis set gives a very convincing calculation of the total bond energy of H 2

(44 and 54%, respectively). However, when compared to the energy of two H atoms

calculatedusing the same basis set, the result –1.0764 – 2(–0.4572)=–0.162Ehis

93% of the experimental bond energy. This is due to cancellation of error between two