AVR: overclocking ADC
The maximal frequency of the ADC is specified as 1MHz. 

The actual problem is not exactly the ADC itself, but the sample and hold device, that in the first 2 clocks of the ADC have to get a sample of the input voltage. 

When these 2 clocks are two short, the storage capacitor of the S/H is not able to follow the input signal with sufficient accuracy.

BTW, that is why there is minimal frequency as well. In this case, the huge conversion time allows the storage capacitor to discharge during the conversion.

On 1MHz clock, you will get 13us conversion time or approximately 77ksps. 
On 200kHz clock - 15ksps.