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We prove that, for totally irregular measures $\mu$ on $\mathbb{R}^{d}$ with$d\geq3$, the $(d-1)$-dimensional Riesz transform $$ T_{A,\mu}^{V}f(x) =\int_{\mathbb{R}^d} \nabla_{1}\mathcal{E}_{A}^{V}(x,y) f(y) \, d \mu(y) $$adapted to the Schr\"{o}dinger operator $L_{A}^{V} = -\mathrm{div} A \nabla +V$ with fundamental solution $\mathcal{E}_{A}^{V}$ is not bounded on$L^{2}(\mu)$. This generalises recent results obtained by Conde-Alonso,Mourgoglou and Tolsa for free-space elliptic operators with H\"older continuouscoefficients $A$ since it allows for the presence of potentials $V$ in thereverse H\"{o}lder class $RH_{d}$. We achieve this by obtaining new exponentialdecay estimates for the kernel $\nabla_{1} \mathcal{E}_{A}^{V}$ as well asH\"older regularity estimates at local scales determined by the potential'scritical radius function.

Unboundedness of potential dependent Riesz transforms for totally irregular measures