Density functionals electronic excitation energy

We conclude this chapter with an overview of how modem density functional theory deals with electronic excitation energies. From the very beginning, electronically excited states... 

The paramagnetic term is expressed as a function of excitation energy, bond order, and electron density according to the sum-over-state(SOS) method in the simple form as follows. 

S. Comi, R. Cammi, B. Mennucci, J. Tomasi, Electronic excitation energies of molecules in solution within continuum solvation models Investigating the discrepancy between state-specific and linear-response methods, Formation and relaxation of excited states in solution A new time dependent polarizable continuum model based on time dependent density functional theory. J. Chem. Phys. 123, 134512 (2005)... 

The total number density of electrons excited, ni can be obtained by integrating over the energy range E = Ec to the top of the CB and, in a similar way, the total density of holes, p, is obtained by integrating eqn. (3) from the top of the VB to Ev. Clearly, these integrals cannot be performed unless the functional forms of Nv and Nc are available in practice, this is rarely so, but it is often found that the top of the valence band and the bottom of the conduction band have simple parabolic shapes of the form... 

Jacquemin D, Perpete EA, Ciofini 1, Adamo, C, Valero R, Zhao Y, Truhlar DG (2010) On the performances of the M06 family of density functionals for electronic excitation energies. J Chem Theory Comput 6 2071-2085... 

Time-dependent density functional theory (TDDET)i" within the linear response formalismi -" ] is nowadays the most widely used approach to the calculation of electronic excitation energies of molecules and solids. Applied within the adiabatic approximation and with the usual local or semilocal density functionals, TDDFT... 

Gao T, Sun S-L, Shi L-L et al (2009) An accurate density functional theory calculation for electronic excitation energies the least-squares support vector machine. J Chem Phys 130 184104. doi 10.1063/1.3126773... 

DA. (2003) Ionization potential, electron affinity, electronegativity, hardness, and electron excitation energy molecular properties from density functional theory orbital energies. J. Phys. Chem. A,... 

Based on the Runge-Gross theorem, it is shown that the three-dimensional density of a many body quantum system is sulScient to describe the TD response of the system to an external perturbation, such as electromagnetic field and vibrational motion, R t). This is known as time dependent density functional theory (TDDFT). In the linear response approximation, TDDFT is frequently used to evaluate electronic excitation energies. Here, we use full TDDFT where the density is explicitly propagated in time. Application of the TD (Dirac) vibrational principle to KS energy generates density evolution ... 

Semiconductor materials are rather unique and exceptional substances (see Semiconductors). The entire semiconductor crystal is one giant covalent molecule. In benzene molecules, the electron wave functions that describe probabiUty density ate spread over the six ting-carbon atoms in a large dye molecule, an electron might be delocalized over a series of rings, but in semiconductors, the electron wave-functions are delocalized, in principle, over an entire macroscopic crystal. Because of the size of these wave functions, no single atom can have much effect on the electron energies, ie, the electronic excitations in semiconductors are delocalized. 

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