Increasing the applicability of density functional theory

We devise a Non variational DFT, meaning it is non variational in the sense that the density is obtained from wave-function theory rather than by minimizing the DFT functional. The Becke exchange and the LYP correlation energy evaluated using the Hartree-Fock (HF) density augmented the HF kinetic energy and classical coulomb interaction is used to obtain the DFT energy. We also developed an analytical gradient scheme for such an approach and showed that our non-variational approach provides much better transition states and activation energies than variational DFT.;In order to assess the quality of the potential, we used Bartlett's theorem as our criteria and compared the negative of the KS eigenvalues obtained using the 52 different explicit density dependent exchange-correlation potential in the KS operator with the principle vertical ionization energies. None of the explicit density dependent potential provide a good approximation of the vertical ionization energies in terms of the negative of the KS eigenvalue spectra. Even, the HOMO energies are far from the desired accuracy. However, when the KS operator has the orbital dependent exchange-correlation potential such as OEP2-sc, we obtain a good approximation of the vertical ionization energies of the valence orbitals in terms of the negative of the KS eigenvalue spectra.;We also question, the recent prominently used approach in DFT community to design a exchange and correlation functional ( e.g. M05, M06, B3LYP, B2-PLYP, DF2-D etc.) by combining the stand alone well known functional such as SLATER exchange ,BECKE exchange, Hartree-Fock exchange PBE exchange, LYP correlation, MP2 correlation etc with the parameters obtained by doing mindless data mining. We call this an a, b ,c approach of the DFT and show first by constructing a potential corresponding to one of the most widely successful functional B2-PLYP or the double hybrid and asking the question if it provides a consistent potential, an absolute average deviation of 2 eV for ionization energies proves that the potential obtained does not have same degree of exactness as the functional has, second by constructing our own potential instead of a functional that will provide vertical ionization energies in terms of the negative of the KS eigenvalues spectra within a desired accuracy of 1 eV, that these approaches are nothing but an elegant ways of suppressing the inherit deficiencies of the explicit density dependent exchange-correlation functional or the potential.;The exact exchange-correlation functional can be obtained using the adiabatic connection and the fluctuation dissipation framework via an integration over the coupling constant and the dynamic density-density response function. The various approximations of the dynamic density-density response function can be obtained using the non-interacting density-density response and the exchange-correlation kernel. The unperturbed density-density response function after doing the coupling constant integration gives the exact exchange energy (non-local exchange energy) in terms of reference orbitals. And the simplest approximation of the coupling constant can be obtained by ignoring the kernel, which is often called the random-phase approximation. Using the plasmon model or the equivalence between the RPA and the ring-CCD, frequency integration and coupling strength integration can be avoided. Using our OEP procedure (by insisting that the density correction the KS determinant should vanish) we obtain ring-CCD correlation potential which is equivalent to the RPA correlation potential. Shell oscillations demonstrated by the exact potential, can be reproduced by the RPA potential as well as the MBPT-2 potential. The RPA correlation potential has a correct long range behavior. We also improved the RPA potential by exploiting the relationship between RPA and coupled cluster theory, considering various ways to include singles excitation effects, and additional double excitation diagrams. Potentials obtained showed similar spatial behavior as the RPA potential except they are correct in the near nucleus region as well. The potential are computationally demanding but in the right direction towards a consistent DFT as not only potential show correct spatial behavior and HOMO energies are within desired accuracy but also the total energies. (Abstract shortened by UMI.).