Molecules James-Coolidge function

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. 

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. 

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. 

The simplest molecular system exhibiting effects of electron correlation is the hydrogen molecule. For this molecule the explicitly correlated wave function has been applied in the early days of quantum mechanics (James and Coolidge, 1933), It was later generalised by Kolos and Wolniewicz (Kcrfos and Wolniewicz, 1965) and successfully used to solve variety of problems in the ground and excited states of the hydrogen molecule. This wave function, called there the Kolos-Wolniewicz function (Kolos and Wolniewicz, 1965) is assumed in the form of an expansion ... 

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... 

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. 

A natural idea was to extend the concept of Hylleraas to molecules. It was done in 1933 by James and Coolidge [8], and the generalized function was of the form... 

Now consider the use of ri2 in H2 trial functions. The first really accurate calculation of the hydrogen-molecule ground state was done by James and Coolidge in 1933. They used the trial function... 

In 1933, James and Coolidge expressed their explicitly correlated wave function for the H2 molecule in elliptic coordinates,... 

In 1933, James and Coolidge offered the first purely variational treatment of the hydrogen molecule not developed directly from atomic orbital functions (LCAO). The mathematical complexity of this treatment made it both theoretically demanding and practically time-consuming to apply. But James and Coolidge argue forcefully that despite its computational complexity the procedure has important theoretical virtues absent in its predecessors ... 

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