Is negative activation energy possible?
No, it's not possible to have a negative activation energy in a simple reaction such as an isomerisation because there is no possible way to draw to potential energy curves to give a negative activation energy. The best you can do is to be activationless, and is commonly observed in electron transfer reactions (see for example J. Am. Chem. Soc. 2002, 124 (19), 5518–5527).

Experimentally, however, negative activation energies can be observed when the reaction comprises several steps some of which are not identified at the time of doing the experiment. For example if each reaction follows an Arrhenius type rate constant, the first may be $k_a = A_a\exp(-E_a/RT)$ and the second $k_b=A_b\exp(-E_b/RT)$, but because there are, say, equilibria involved in the mechanism, what may be observed without realising it is that the rate is a ratio of the two individual rates:

$$\begin{align}
k_\mathrm{obs} &amp;\propto \frac{k_a}{k_b} \\
&amp;\propto \frac{\exp(-E_a/RT)}{\exp(-E_b/RT)} \\
&amp;= \exp\left(\frac{-(E_a-E_b)}{RT}\right) \\
&amp;= \exp\left(-\frac{E_\mathrm{obs}}{RT}\right)
\end{align}$$

so it is possible for $E_\mathrm{obs} = E_a - E_b$ to be positive or negative.