Helium molecule correlation energy

The data points are fitted in a least-square sense to a fourth degree polynomial, and the properties thereby obtained are presented in Table 3. Since the atom possesses spherical symmetry there is only a single independent component of the a-tensor as well as the y-tensor. The curvature of the energy, or the polarizability, at the SCF level differs by less than 5% compared to the FCI result, and the MP2 value captures slightly more than half of the correlation effect. Electron correlation plays a more important role in the determination of the fourth-order property y. Again the MP2 method captures slightly more than half of the total contribution, which amounts to 21% at the FCI level of theory. The trends we have seen here in the example of the helium atom are more or less representative for closed-shell molecules in general. 

There is, of course, much that remains to be understood with regard to the physical interpretation. For example, the correlation-kinetic-energy field Z, (r) and potential W, (r) need to be investigated further. However, since accurate wavefunctions and the Kohn-Sham theory orbitals derived from the resulting density now exist for light atoms [40] and molecules [54], it is possible to determine, as for the Helium atom, the structure of the fields P(r), < P(r), and Zt (r), and the potentials WjP(r), W (r), W (r), and W (r) derived from them, respectively. A study of these results should lead to insights into the correlation and correlation-kinetic-energy components, and to the numerical determination of the asymptotic power-law structure of these fields and potentials. The analytical determination of the asymptotic structure of either [Z, (r), W, (r)] or [if (r), WP(r)] would then lead to the structure of the other. 

Unfortunately there is as yet no known way to obtain the repulsion energy from properties of the separate molecules. An attempt has been made to characterise the repulsive surface of a molecule by performing IMPT calculations between the molecule and a suitable test particle, such as a helium atom. Because the helium atom has only one molecular orbital and is spherically symmetrical, such calculations can be done much more easily than calculations involving two ordinary molecules. From the data for the repulsion between molecule A and the test particle, and between B and the test particle, it may be possible to construct a repulsive potential between A and B. Some limited progress has been made with this idea. An alternative approach has been based on the suggestion that the repulsion energy is closely correlated with the overlap between the molecular wavefunctions, but this seems likely to be more useful as a guide to the form of analytic models than as a direct route to accurate potential functions. 

Recently, impressive calculations using Hylleraas wave functions have been done for the H2 molecule by the Hylleraas method [44,63], the Iterative Complement Iteration (ICI) [36], and Explicitly Correlated Gaussian (ECG) [12] methods. Few molecules have yet been calculated using Hylleraas-type wave functions HeH+ and some other species [72] using the Hylleraas method, the helium dimer He2 interaction energy [46] and the ground state of the BH molecule [7], both using the ECG method. 

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