Abstract
Many physical properties of interest about solids and molecules can be considered as the reaction of the system to an external perturbation, and can be expressed in terms of response functions, in time or frequency and in real or reciprocal space. Response functions in TDDFT can be calculated by a variety of methods.
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Notes
- 1.
This is the causal KS response function. The time-ordered KS response function would have \(-\hbox{i}\eta\) in the second term.
- 2.
Note this differs from (4.89a) in the last term: Equation 4.89a defined the nth-order response by the terms in the density expansion proportional to n factors of \(\delta v_{\rm ext}(\user2{r},t)=v_{\rm ext}(\user2{r},t)-v_{\rm ext}(\user2{r},0)\). Here, on the other hand, we define the nth-order response as being proportional to the nth-power of the field strength.
- 3.
Note that \(\user2{K}\) has units of electric field times time.
- 4.
Note that the integration begins from \(t=0^-\) instead of \(-\infty\), which basically corresponds to adding a Heaviside function \(\theta(t-0^-)\) inside the Fourier transform.
- 5.
Note that this expansion is not a Taylor expansion.
- 6.
Remember that we are working within the adiabatic approximation here, and therefore, the TD-KS Hamiltonian has no memory.
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© 2012 Springer-Verlag Berlin Heidelberg
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Strubbe, D.A., Lehtovaara, L., Rubio, A., Marques, M.A.L., Louie, S.G. (2012). Response Functions in TDDFT: Concepts and Implementation. In: Marques, M., Maitra, N., Nogueira, F., Gross, E., Rubio, A. (eds) Fundamentals of Time-Dependent Density Functional Theory. Lecture Notes in Physics, vol 837. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23518-4_7
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DOI: https://doi.org/10.1007/978-3-642-23518-4_7
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