Traditionally, density-functional theory (DFT) has been a theory of the ground state of a multi-electronic system. Although excited states were of concern since the beginning of DFT history, realistic calculational schemes have evolved only recently. The reason is that the techniques of ground-state DFT are not suitable enough for an adequate description of excited states. However, there are recent approaches to excited-state DFT that have turned out to be very promising in this notoriously difficult area The object is to find accurate approximations to excited-state energies and densities. In this dissertation several main approaches of modern excited-state DFT are reviewed, certain interrelation between them are revealed, and several new results announced Two universal functionals F1r and F1r are defined. By the use of constraint-search, the following property is proven: E0v<min F1r +&smallint;d 3vrr r r =E1v ≤E1v≤ E1v=min F1r +&smallint;d3rv rrr , 1 r where E0(v) and E1(v) are the round-state energy and the first excited-state energy, respectively, for a given external potential v(r). The minima in the above are achieved at the densities r1r and r1r , respectively Two universal tack-on functionals F'r and F'r are found. Once the minimizations are done in Eq. (1), they correct the minimizing values E1( v) and E1( v) to the exact first excited-state energy E 1(v), i.e. E1v=E 1v+F 'r1 2 and E1v=E 1v+F 'r1 , 3 respectively New properties of the Levy-Nagy's bifunctional F1r,rv 0 are announced. For example, a new derivation of dF1rv 1,rd r&vbm0;r=ru 0=0 4 is given. Moreover, d3rd 3r'd2F1 ru1,r dr rdrr '&vbm0; r=ru0f rfr' ≤0 5 for any function f(r). These properties could be used to model F1r,r0 A new scaling relation of the correlation part of F1r,r0 is presented: Ec,ara ,r0,a=a 2Ec,1r,r0 , 6 It could be used as a key formula for a Goerling-Levy type perturbation theory in which the first excited-state density r1r (instead of r0r as in the original Goerling-Levy perturbation theory) is kept fixed along the adiabatic-connection path. This perturbation theory could very well be adapted for excited-state DFT Two theorems are proven concerning a new universal unifunctional! Theorem 1 states that there is a universal functional U1r , such that E1v=mi nU1 r+ d3rv rrr =U1r 1&d5;+ d3 rvrr&d5; 1r 7 r for any external potential v(r). However, the minimizing density r&d5;1 r is not necessarily the true first excited-state density r1r . Theorem 2 states that there is a universal map M:r&d5;1 r →r1r . (Similarly: M':r1 r →r1r and M'':r 1r →r1r .) A sketch of the local-scaling method (LSM) approximation to the Levy-Nagy bifunctional is presented and a technical (for LSM purposes but with general validity) 'sewing theorem' is proven. It is used for variations with certain types of constraints The exact equivalence between first-order Goerling-Levy perturbation theory and the time-dependent optimized potential model (OPM) for excitation energies of two-electron systems is proven at the end / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_26768 |
| Date | January 2000 |
| Contributors | Zahariev, Federico E (Author), Levy, Mel (Thesis advisor) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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