Function, James-Coolidge

Molecular wave functions of the accuracy of the James-Coolidge function do not, of course, exist except for the H2 molecule. Consequently avail-... 

Up to now such a large spread of W00 values compels a number of authors (see, e.g., Chengrui et al., 1981) to suppose that an adequate calculation of the / decay in molecules larger than HT is not possible at all, since the wave functions used for large molecules are less accurate than the James-Coolidge functions. 

However, as was shown by Michels (1966), the calculations of Toh (1940) contain a numerical error, so the result of Schwartz, W00 = 0.93, which was based on these calculations, should not be taken into account. The rest of the results show that improvement of the James-Coolidge functions does not change the value of W00 so drastically the calculations with binomial and polynomial James-Coolidge functions give very close reults—0.572 and 0.58, respectively. 

The simplified form of this function with A = A and B B = 0 is the James-Coolidge function, thanks to which the later authors enjoyed the most accurate result for the hydrogen molecule in 27 years. 

Hylleraas function (p. 506) harmonic helium atom (p. 507) James-Coolidge function (p. 508) Kolos-Wolniewicz function (p. 508) geminal (p. 513)... 

First, there were the molecules or atomic systems of one to six electrons, for which one could effectively calculate energies as accurately as they can be measured. Second, the all too realistic prospects for faster computers allowed one to extend the range of molecules for which it would become possible to have effectively exact solutions to those with 6 to 20 electrons. Nevertheless, accurate results for these cases were achieved at the expense of visualizability even in the five-term James Coolidge function— which Coulson believed to be "the best compromise between accuracy and simplicity"— there was nothing easily visualized about the wave function, and it required a further numerical integration on an electronic computer to derive from the full 13-term wave function the electronic charge density of the electron. 

Explicitly correlated wave functions described above have been specifically designed for two-electron molecular systems. As it was demonstrated in the previous section these functions give the energies which appear to be superior to the variational energies reported. Therefore several attempts have been made to extend this approach to many-electron molecules. The James-Coolidge (JC) type of function has been extended to three- and four-electron diatomic molecules by Clary and... 

A calculation of the contact contributions to nuclear spin coupling in the H-D molecule has been carried out (114) using the James-Coolidge wave function (55). This calculation gave... 

For H2 and D2 the procedure is much the same but there is more experimental information with which we can compare. Explicitly electron-correlated functions of the James-Coolidge type were chosen as basis functions. They were defined in terms of elliptical coordinates as ... 

It is well known, of course, that the n and cr orbitals that are used in these calculations are built from atomic orbitals which are rough approximations to the accurate wave functions. Thus the electronic density calculated from the James and Coolidge function for the hydrogen molecule is very different from that obtained from the usual functions built from atomic orbitals.63 It is thus at least possible that a very accurate wave function for an aromatic hydrocarbon would give an electronic density which could resemble Fig. 4a. If this should prove not to be the case, then scheme 4b could be used where the delocalized bond of naphthalene now contains 32 electrons. 

The trial functions /ip, may involve the ru-coordinate like the James-Coolidge Junction - for Hg. In using such functions the (VrVp) is first split off according to Eqs. (104) to (106). 

Goodisman (89) used the Hartree-Fock method to calculate the variation of the force on the nuclei in H2 withR, where the variation wave function is of the James-Coolidge t5q>e in confocal elliptic co-ordinates. The normal Hartree-Fock method (without configuration interaction)... 

The family of variational methods with explicitly correlated functions includes the Hylleraas method, the Hyller-aas Cl method, the James-Coolidge and the KcAos-Wolniewicz approaches, as well as a method with exponentially correlated Gaussians. The method of explicitly correlated functions is very successful for two-, three-, and four-electron systems. For larger systems, due to the excessive number of complicated integrals, variational calculations are not yet feasible. 

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