Pressure dependence of a photon energy emitted from a material and an advanced density functional theory Kimichika Fukushima Theoretical Division, South Konandai Science Research, Japan E-mail: km.fukushima@mx2.ttcn.ne.jp In calculations for energy of a photon absorbed by a material, a linear response method 1 is used with the aid of density functional theory (DFT). To solve the time-dependent Schrödinger equation, a usual treatment including the linear response approach imposes the orthogonality on the relation among the ground and excited states. This orthogonality also leads to the completeness, which is seen in Fourier series. However, for many-electron systems beyond one-electron system, DFT is an exact theory, which is supported by the author’s theorem 2 for both the excited and ground states at the same level; in this DFT, the ground and excited states are not always orthogonal to each other. In addition, to the author’s knowledge, it is not fully reported (i) how the linear response formalism in a DFT based on the Runge-Gross theory 3 is represented in the Heisenberg picture; and (ii) how the formalism is unitary-transformed to that in the Schrödinger picture. Therefore, the above linear response approach seems to be one of applications and approximations. Furthermore, in a claim 4 , which is against the existence of an excited-state DFT, the electronic density is not precise due to a linear response approximation of this density for a non-linear response to a nuclear potential. In the claim, eigen energy of each state for a textbook problem is not given (a unique eigen energy and electronic density distribution do not provide duplicate potentials); therefore, this claim is avoided. In this study, the author reports an application of the DFT, which is based on the above author’s excited-state theorem, to the pressure dependence of an emitted energy in a material. The analysis method employed is the discrete variational (DV) method. The exchange-correlation term employed is the Vosko-Wilk-Nusair form derived from Monte Carlo calculations. The emission energy is evaluated using the Slater’s transition state theory for a model cluster with multi atoms. A force applied on a material can be related to the corresponding internuclear distance. The theoretical energy photon emitted from a relaxed state of a material increases with the decrease in the internuclear distance. This tendency is seen in luminescence experiments. In summary, the pressure dependence of the photon emission energy was evaluated, using the above advanced DFT for both the excited and ground states at the same level. References
1. M. E. Casida, J. Mol. Struct.:THEOCHEM, 2009, 914 , 3-18. 2. K. Fukushima, J. Phys. Chem. Solids, 2022, 161 , 110406. 3. E. Runge and E. K. U. Gross, Phys. Rev. Lett., 1984, 52 , 997-1000. 4. R. Gaudoin and K. Burke, Phys. Rev. Lett., 2004, 93 , 173001.
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