Ground-state theory

One obvious drawback of the LDA-based band theory is that the self-interaction term in the Coulomb interaction is not completely canceled out by the approximate self-exchange term, particularly in the case of a tightly bound electron system. Next, the discrepancy is believed to be due to the DFT which is a ground-state theory, because we have to treat quasi-particle states in the calculation of CPs. To correct these drawbacks the so-called self-interaction correction (SIC) [6] and GW-approximation (GWA) [7] are introduced in the calculations of CPs and the full-potential linearized APW (FLAPW) method [8] is employed to find out the effects. No established formula is known to take into account the SIC. 

DFT is a ground state theory. In order to calculate MCD spectra it is obviously necessary to know something about excited states. TDDFT allows DFT calculations to provide the necessary information about excited states. 

DFT today is mainly a ground-state theory, although ways of applying it to excited states are being developed. 

Several years ago Caspar [11] proposed a parameter-free exchange potential in the ground-state theory. This method is applied to determine the... 

Density Functional Theory is a ground state theory in principle this is due to the fact that the variational principle is an essential element of DFT. Despite this, determination of excited state energies and properties is still possible in the framework of DFT. There are two main approaches to this problem. 

A deeper argument is that local density functional derivatives appear to be implied by functional analysis [2,21,22]. The KS density function has an orbital structure, p = Y.i niPi = X fa- For a density functional Fs, strictly defined only for normalized ground states, functional analysis implies the existence of functional derivatives of the form SFj/ Sp, = e, — v(r), where the constants e, are undetermined. On extending the strict ground-state theory to an OFT in which OEL equations can be derived, these constants are determined and are just the eigenvalues of the one-electron effective Hamiltonian. Since they differ for each different orbital energy level, the implied functional derivative depends on a direction in the function-space of densities. Such a Gateaux derivative [1,2] is equivalent in the DFT context to a linear operator that acts on orbital functions [23]. 

However, as shown above, comparison with the orbital Schrodinger equations implies a sum rule ,e, = N/x. This sum rule requires all e = p, in violation of the exclusion principle for more than two electrons [7]. Thus it is incorrect to assume that the undetermined constants in ground-state theory can be set to the same value for different orbital energy levels. In contrast, Kohn and Sham [4] were correct in substituting t for 8T/bp in the KS-equations. There is no equivalent exact Thomas-Fermi theory. 

Fifth, the theory has been developed as a ground-state theory. Accordingly, it allows, in principle, for the calculation of any ground-state property for the system of interest. However, it can easily be generalized so that it allows for the... 

The Hohenberg-Kohn-Sham theory is basically a ground-state theory. Versions of KS DFT applicable to excited states have been developed [see Parr and Yang, Section 9.2 K. Burke and E. K. U. Gross in D. Joubert (ed.). Density Functionals, Springer, 1998], but the theory has not reached the point where it allows accurate, practical calculations to be readily done on individual molecular excited states. (One can use DFT to calculate the lowest state of each symmetry for example, one can calculate the lowest singlet state and the lowest triplet state.)... 

And all the excited states wave functions as well This is an intriguing conclusion, supported by experts see W. Koch and M.C. Holthausen, A Chemist s Guide to Density Functional Theory, 2d ed., Wiley, Weinheim, 2001. On p. 59, it says the DFT is usually termed a ground state theory. The reason for this is not that the ground state density does not contain the information on the excited states—it actually does. -bui because no practical way to e.xtract this information is known so far. ... 

The DFT is usually considered as a ground-state theory. One should, however, remember that the exact ground-state electron density po contains information about all the excited states (remember the discussion on p. 235). Well, the problem is that we do not know yet how to extract this information from po- Some of the excited states ate the lowest-energy states belonging to a... 

As a first guess, it may serve the orbital energy differences from the ground-state theory. 

Grob-type fragmentation, 154—155 Ground-state spectroscopies, 213—220 Ground-state theory, 207—210 GSH. See Glutathione (GSH)... 

For the ground-state theory, the Thomas-Fermi functional can be made more accurate by adding the gradient correction to it. For ground states, the gradient correction up to the second order is given as [3-5]... 

The virial theorem was also derived for ensanbles of excited states (Nagy 2002a). In the ground-state theory, several forms of the virial theoran were derived. The local and differential forms proved to be especially useful. In this chapter, the local virial theorem is derived for ensembles of excited states. In Section 7.2, the ensemble theory of excited states is summarized. The ensemble local virial theoran is derived in Section 7.3. Extension of the differential virial theorem of Holas and March (1995) to ensembles is presented in Section 7.4. Finally, Section 7.5 is devoted to discussion. 

The Hohenberg-Kohn-Sham theory is basically a ground-state theory. LR-TDDFT can only be applied to certain kinds of excited states. (One can use DFT to calculate the lowest state of each symmetry for example, one can calculate the lowest singlet state and the lowest triplet state.)... 

---