Hydrogen molecule improvements

Kolos W and Wolniewicz L 1968 Improved theoretical ground-state energy of the hydrogen molecule J. Chem. Phys. 49 404-10... 

The presence of intermolecular forces also accounts for the variation in the compression factor. Thus, for gases under conditions of pressure and temperature such that Z > 1, the repulsions are more important than the attractions. Their molar volumes are greater than expected for an ideal gas because repulsions tend to drive the molecules apart. For example, a hydrogen molecule has so few electrons that the its molecules are only very weakly attracted to one another. For gases under conditions of pressure and temperature such that Z < 1, the attractions are more important than the repulsions, and the molar volume is smaller than for an ideal gas because attractions tend to draw molecules together. To improve our model of a gas, we need to add to it that the molecules of a real gas exert attractive and repulsive forces on one another. 

Summaries of G3X(MP3) and G3X(MP2) mean absolute deviations from experiment for the G3/99 test set of 376 energies are given in Table 3.4. The overall mean absolute deviations for G3X(MP3) and G3X(MP2) theories are 1.13 and 1.19 kcal/mol, respectively. These are improvements over G3(MP3) and G3(MP2), which have mean absolute deviations of 127 and 131 kcal/mol, respectively, for the same set of energies. For enthalpies of formation, the mean absolute deviations decrease from 1.29 to 1.07 kcal/mol [G3X(MP3)] and from 1.22 to 1.05 kcal/mol [G3X(MP2)]. Much of the improvement in enthalpies is due to non-hydrogen molecules, although other types of species also improve slightly or stay the same. The G3X(MP3) and G3X(MP2) methods save considerable computational time and have a reasonable accuracy. The ratio of the computational costs for G3X, G3X(MP3), and G3X(MP2) theories is approximately 52 1 for a molecule such as benzene. 

This review has attempted to illustrate the relevance and the widespread utility of the CM model. Indeed, the author believes it is difficult to specify any area of structural or mechanistic chemistry where the CM approach is not applicable. The reason is not hard to find the CM model has its roots in the Schrodinger equation and as such its relevance to chemistry cannot be easily overstated. Even the fundamental chemical concept of a covalent bond derives from the CM approach. The covalent bond (e.g. in H2) owes its energy to the configuration mix HfiH <— H H. A wave-function for the hydrogen molecule based on just one spin-paired form does not lead to a stable bond. Both spin forms are necessary. Addition of ionic configurations improves the bond further and in the case of heteroatomic bonds generates polar covalent bonds. 

Polarity and hydrogen-bonding stiffen the polymer molecule, improving mechanical properties and especially resistance to hot water. This improvement is useful in household products, autos, and appliances. 

---