  We study one-dimensional Schr\"{o}dinger operators $\mathrm{S}(q)$ on the
space $L^{2}(\mathbb{R})$ with potentials $q$ being complex-valued generalized
functions from the negative space $H_{unif}^{-1}(\mathbb{R})$. Particularly the
class $H_{unif}^{-1}(\mathbb{R})$ contains periodic and almost periodic
$H_{loc}^{-1}(\mathbb{R})$-functions. We establish an equivalence of the
various definitions of the operators $\mathrm{S}(q)$, investigate their
approximation by operators with smooth potentials from the space
$L_{unif}^{1}(\mathbb{R})$ and prove that the spectrum of each operator
$\mathrm{S}(q)$ lies within a certain parabola.
