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Dipole polarizability

$\displaystyle \alpha_{\epsilon\tau}(-\omega; \omega) = - \langle\langle \hat{\mu}_{\epsilon};\hat{\mu}_{\tau} \rangle\rangle _{\omega}$ (3.3)

For the static dipole polarizability $ \alpha$(0;0)

$\displaystyle \alpha(0;0) = -\left.\frac{\partial^{2}{\cal E}\left({\bf E}\right)}{\partial {\bf E}^2}\right\vert _{{\bf E} = {\bf0}}$ (3.4)

Polarizability $ \alpha_{\mu\nu}(-\omega;~\omega)$ $ \propto$ $ \langle\langle $ $ \hat{r}_{\mu}$; $ \hat{r}_{\nu}$ $ \rangle\rangle $$ _{\omega}$

Symmetry

tensor, second order, symmetric

Calculation type
linear response, $ \langle\langle $r;r $ \rangle\rangle $ 2.Linear!$ <<$r;r$ >>$

@XDIPLEN XDIPLEN 7.478371663959D+00

Units
1 au of $ \alpha \equiv e^2 a_0^2 E_h^{-1} $ $ \equiv e^2 a_0^4 m_e \hbar^{-2} $ $ \cong 1.648777251 \times 10^{-41}$ C$ ^2$ m$ ^2$ J $ ^{-1}
\cong 1.481847 \times 10^{-25}\ 4 \pi \epsilon_0 $ cm$ ^3$ (esu)

Comments Frequency dependence may be described using Cauchy moments (sec. 3.9). Similarly, Cauchy moments can be used to obtain long range dispersion interaction coefficients C$ _n$, there is no need to compute the polarizability at imaginary frequencies.



Subsections

Michal Jaszunski 2002-11-10