| The first part of this thesis investigates properties of three recently proposed weighted density functional theories and proposes an extension of these theories. These weighted density approximation theories are extended by using the Percus condition which, we show, completely determines the above theories.; The second part deals with the application of the three kinds of extended weighted density approximation theories. For the extended weighted density approximation(EWDA) and extended modified weighted density approximation II(EMWDAII) theories, the low density expansion is used to calculate the second order pair distribution function and the fourth virial coefficient for the hard sphere system and for the Gaussian model. We also show that the extended modified density approximation I(EMWDAI) implies the hypernetted chain equation for homogeneous states. Our results show that the EWDA theory gives very good numerical values, better than the EMWDAI and EMWDAII and the standard integral equations. An undesirable property of these theories is that they fail at low temperatures for systems whose intermolecular potential has an attractive part.; The third part deals with the numerical solution of the EWDA theory in the one dimensional hard sphere system. These results show that the EWDA theory gives good numerical values up to the intermediate density region, within estimated numerical errors. We summarize the numerical problems and possible future applications. |
