Correlation and Response in Spherical Many-Electron Systems

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Dobson, John

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Gray, Evan

Knight, Alan

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Ab initio prediction of the electronic properties of solids is traditionally performed using groundstate Density Functional Theory. These methods are unreliable however, for a class of important problems involving weak attractive forces. These problems include (i) the energetics of hydrogen storage and metal interactions in graphene, (ii) cohesion properties of some polymer systems and (iii) possibly, the weak hydrophobic forces in biomolecules. For these cases a more powerful method than groundstate DFT are timedependent DFT (tdDFT) methods related to the Random-Phase Approximation (RPA). All of these methods proceed by looking at the dynamic density-density response function, whose long-ranged properties naturally lead to the weak forces referred to above. In this thesis we have tested these ideas by investigating electronic response and correlation on the predicted properties of spherical atoms. We have developed and tested a variety of approximations to the timedependent response function through approximations of the tdDFT class and a new method involving greater self-consistency in the screening equation, the inhomogenous STLS approach. Through the development of new methods and computer code, we have solved the response equation allowing us to test our approximations on atoms. Calculation of certain dynamic and static properties of a variety of atoms within our approximations generally agree well with known results. In this thesis we have calculated excitation energies of Helium, dipole polarisabilities and C6 van der Waals (vdW) coefficients of a variety of atoms, and groundstate correlation energies Ec of some atoms. The excitation spectra of Helium generated in our new PGG+c approximation are in good agreement with experiment. The dipole polarisabilities are generally in good agreement with known results, with the exception of Magnesium, Beryllium and Sodium. The C6 coefficients are a little poorer with the exception of Helium where they are nearly exact. Correlation energies are generally reasonable in the PGG+c approximation although they are considerably less accurate than the other properties we have calculated for all atoms other than He. The ISTLS correlation energy of Helium is within 5% suggesting that this method may perform well for larger atoms where our present numerical techniques require improvement. These generally positive results suggest that the approximations we have developed may be applied to more complicated systems such as those described above with good results.

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Thesis (PhD Doctorate)

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Doctor of Philosophy (PhD)


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spherical many-electron systems


spherical atoms

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