c20 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come
336 QUANTUM MOLECULAR MODELINGthe difference in calculated enthalpies in Fig 20.7 because it is the enthalpyinputfor
the reaction forming the molecule from its constituent elements.
The total drop in enthalpy for all the steps on the left-hand side of Fig. 20.7 is
–115.471973Eh. When we substitute our recently found STO-3G numbers to find(^) fH^298 , we get−115.471973 –(-113.5386327)=−1.93334 hartrees with a sign
change to+1.93334Eh. The result is a disaster, more than 5000 kJ mol−^1 for a (^) fH^298
that we expect will be no more than 100 kJ mol−^1 or so on the basis of experimental
thermochemistry done on molecules of comparable size. What went wrong?
The procedure as described involves a serious mismatch. The atomic numbers on
the left-hand side of Fig. 20.7 are state-of-the-art experimental and computational
results, while the molecular number on the right-hand side is an STO-2G approxima-
tion. A large approximate number subtracted from a large accurate number gives a
very poor result. We could go back and substitute STO-3G energies for the atoms, but
a more rewarding approach is to go forward and try to improve the molecular enthalpy.
The experimental value of (^) fH^298 (methanol) is about –200 kJ mol−^1 , that is,
∼0.0767 Eh. In order to obtain 1% accuracy in the calculated result, we must
achieve a cumulative accuracy of± 0. 000767 Ehin our calculations. This demanding
standard is the reason why computed energies and enthalpies are usually expressed
to a precision of five or six digits beyond the decimal point. In other words, we
are working in the realm of microhartrees. We must look further into the daunting
problem of finding ways to achieve 0.000767% or 767parts per millionaccuracy in
ourab initiocalculations.
When the STO-2G basis set is expanded to STO-6G, we get aTOTAL ENERGY
= -114.6409388873. At a higher level of 6-31G (MP2), the output file yields
aTOTAL ENERGY =-115.1928829735.Using the opt keyword, the out-
put file readsTOTAL ENERGY =-115.2040086436 OPTIMIZED.These
results lead to (^) fH^298 0.831034Eh=2182 kJ mol−^1 and (^) fH^298 =0.27909Eh=
733 kJ mol−^1 and (^) fH^298 =0.267965Eh=704 kJ mol−^1. Evidently we are moving
in the right direction but we still have a long way to go.
20.14 FURTHER BASIS SET IMPROVEMENTS
The literature documents a long history of improved basis sets. Details of what may
be the culminating effort in this series, the basis setG3MP2Large, are given in the
original publications (Curtiss et al., 1999). The basis set itself is available on the web
(http://chemistry.anl.gov/compmat/g3theory.htm) for use with thegenkeyword if
desired.20.15 POST-HARTREE–FOCK CALCULATIONS
No matter how good the basis set is made by extension toward an infinite set,
one encounters theHartree–Fock limiton the accuracy of molecular energy, because
the influence of one electron upon the others has not been fully accounted for in the