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Using time-dependent density functional theory (tdDFT) with exchange kernelswe calculate and test imaginary frequency-dependent dipole polarizabilities forall atoms and many ns in rows 1-6 of the periodic table. These are thenintegrated over frequency to produce $C_6$ coefficients. Results are presentedunder different models: straight tdDFT calculations using two differentkernels, "benchmark" tdDFT calculations corrected by more accurate quantumchemical and experimental data, and "benchmark" tdDFT with frozen orbitalanions. Parametrisations are presented for 411+ atoms and ions, allowingresults to be easily used by other researchers. A curious relationship,$C_{6,XY}\propto [\alpha_X(0)\alpha_Y(0)]^{0.73}$ is found between $C_6$coefficients and static polarizabilities $\alpha(0)$. The relationship$C_{6,XY}=2C_{6,X}C_{6,Y}/[\alpha_X/\alpha_YC_{6,Y}+\alpha_Y/\alpha_XC_{6,X}]$is tested and found to work well ($<5$\% errors) in about 80\% of cases, butcan break down badly ($>30$\% errors) in a small fraction of cases.

$C_6$ coefficients and dipole polarizabilities for all atoms and many ions in rows 1-6 of the periodic table