Excitation correlation potential

The quality of the TD-DFT results is determined by the quality of the KS molecular orbitals and the orbital energies for the occupied and virtual states. These in turn depend on the exchange-correlation potential. In particular, excitations to Rydberg and valence states are sensitive to the behavior of the exchange-correlation potential in the asymptotic region. If the exchange-correla-... 

To perform excited-state calculations, one has to approximate the exchange-correlation potential. Local self-interaction-free approximate exchange-correlation potentials have been proposed for this purpose [73]. We can try to construct these functionals as orbital-dependent functionals. There are different exchange-correlation functionals for the different excited states, and we suppose that the difference between the excited-state functionals can be adequately modeled through the occupation numbers (i.e., the electron configuration). Both the OPM and the KLI methods have been generalized for degenerate excited states [37,40]. 

Table 9.1 presents excitation energies for a few atoms and ions. Calculations were performed with the generalized KLI approximation [69,74], For comparison, experimental data and the results obtained with the local-spin-density (LSD) exchange-correlation potential [75] are shown. The KLI method contains only the exchange. 

The potential curves derived from such calculations can often be empirically improved by comparison with so-called experimental curves derived from observed spectroscopic data, using Rydberg-Klein-Rees (RKR) or other inversion procedures. It is often found, particularly for the atmospheric systems, that the remaining correlation errors in a configuration interaction (Cl) calculation are similar for many excited electronic states of the same symmetry or principal molecular-orbital description. Thus it is often possible to calibrate an entire family of calculated excited-state potential curves to near-spectroscopic accuracy. Such a procedure has been applied to the systems described here. 

The effective Time Dependent Kohn-Sham (TDKS) potential vks p (r>0 is decomposed into several pieces. The external source field vext(r,0 characterizes the excitation mechanism, namely the electromagentic pulse as delivered by a by passing ion or a laser pulse. The term vlon(r,/) accounts for the effect of ions on electrons (the time dependence reflects here the fact that ions are allowed to move). Finally, appear the Coulomb (direct part) potential of the total electron density p, and the exchange correlation potential vxc[p](r,/). The latter xc potential is expressed as a functional of the electronic density, which is at the heart of the DFT description. In practice, the functional form of the potential has to be approximated. The simplest choice consists in the Time Dependent Local Density Approximation (TDLDA). This latter approximation approximation to express vxc[p(r, /)]... 

As was mentioned above, in KS-TDDFT the effects of electron exchange and Coulomb correlation are incorporated in the exchange-correlation potential vxaJ and kernel fxl- While the potential determines the KS orbitals (j)ia and the zero-order TDDFRT estimate (35) for excitation energies, the kernel determines the change of vxca with Eqs. 21, 22, 24. Though both vxca and are well defined in the theory, their exact explicit form as functionals of the density is not known. Rather accurate vxca potentials can be constructed numerically from the ab initio densities p for atoms [35-38] and molecules [39-42]. However, this requires tedious correlated ab initio calculations, usually with some type of configuration interaction (Cl) method. Therefore, approximations to vxcn and are to be used in TDDFT. 

We did not look at other properties, but it is worthwhile to mention the work performed by Casida et al. with the time dependent DFT formalism for the determination of polarizabilities and excitation energies within the linear response approach, both properties being very sensitive to the large r behavior of the exchange-correlation potential [78]. They made use of the VLB functional and obtained a strong improvement of the polarizabilities over the LDA, although they observed also an overcorrection of LDA vs experiment [82]. 

The ab initio spin-coupled valence bond (SCVB) approach continues to provide accurate ground and excited state potential energy surfaces for use in a variety of subsequent applications, with particular emphasis on intermolecular forces and reactive systems. The compactness of the various wavefunctions allows direct and clear interpretation of the correlated electronic structure of molecular systems. Recent developments, in the form of SCVB and MR-SCVB, involve the optimization of virtual orbitals via an approximate energy expression. These improved virtuals lead to still higher accuracy for the final variational wavefunctions, but with even more compact wavefunctions. 

In case of a new design, the designer must obtain the anticipated force input, i.e., excitation environment, for the structural system and correlate the frequency content of this information with the results of a natural frequency analysis of the structure. If natural frequencies occur in the frequency band of excitation, the potential of dynamic problems exists and should be addressed. 

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