| 90 |
|
site ({\bf a}) that has a charge $(C_{\bf a})$, dipole |
| 91 |
|
$(\mathbf{D}_{\bf a})$, and quadrupole $(\mathbf{Q}_{\bf a})$} |
| 92 |
|
\begin{ruledtabular} |
| 93 |
< |
\begin{tabular}{llcc} |
| 93 |
> |
\begin{tabular}{lccc} |
| 94 |
|
Multipole order & Summed Quantity & Self-neutralization & Reciprocal \\ \hline |
| 95 |
|
Charge & $C_{\bf a}^2$ & $-f(r_c)$ & $-\frac{2 \alpha}{\sqrt{\pi}}$ \\ |
| 96 |
< |
Dipole & $|D_{\bf a}|^2$ & $\frac{1}{3} \left( h(r_c) + \frac{2 |
| 96 |
> |
Dipole & $|\mathbf{D}_{\bf a}|^2$ & $\frac{1}{3} \left( h(r_c) + \frac{2 |
| 97 |
|
g(r_c)}{r_c} |
| 98 |
|
\right)$ & $-\frac{4 \alpha^3}{3 \sqrt{\pi}}$\\ |
| 99 |
< |
Quadrupole & $2 \text{Tr}[Q_{\bf a}^2] + \left(\text{Tr}[Q_{\bf a}]\right)^2$ & |
| 99 |
> |
Quadrupole & $2 \text{Tr}(\mathbf{Q}_{\bf a}^2) + \text{Tr}(\mathbf{Q}_{\bf a})^2$ & |
| 100 |
|
$- \frac{1}{15} \left( t(r_c)+ \frac{4 s(r_c)}{r_c} \right)$ & $-\frac{8 |
| 101 |
|
\alpha^5}{5 \sqrt{\pi}}$ \\ |
| 102 |
< |
Charge-Quadrupole & $-2 C_{\bf a} \text{Tr}[Q_{\bf a}]$ & $\frac{1}{3} \left( |
| 102 |
> |
Charge-Quadrupole & $-2 C_{\bf a} \text{Tr}(\mathbf{Q}_{\bf a})$ & $\frac{1}{3} \left( |
| 103 |
|
h(r_c) + \frac{2 g(r_c)}{r_c} \right)$& $-\frac{4 |
| 104 |
|
\alpha^3}{3 \sqrt{\pi}}$ \\ |
| 105 |
|
\end{tabular} |
