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In the present paper, we consider the following singularly perturbed problem:\begin{equation*}  \left\{  \begin{array}{ll}  -\varepsilon^2\triangle u+V(x)u=\varepsilon^{-\alpha}(I_{\alpha}*F(u))f(u), &x\in \R^N;  u\in H^1(\R^N),  \end{array}  \right. \end{equation*} where $\varepsilon>0$ is a parameter, $N\ge 3$,$\alpha\in (0, N)$, $F(t)=\int_{0}^{t}f(s)\mathrm{d}s$ and $I_{\alpha}:\R^N\rightarrow \R$ is the Riesz potential. By introducing some new tricks, weprove that the above problem admits a semiclassical ground state solution($\varepsilon\in (0,\varepsilon_0)$) and a ground state solution($\varepsilon=1$) under the general "Berestycki-Lions assumptions" on thenonlinearity $f$ which are almost necessary, as well as some weak assumptionson the potential $V$. When $\varepsilon=1$, our results generalize and improvethe ones in [V. Moroz, J. Van Schaftingen, T. Am. Math. Soc. 367 (2015)6557-6579] and [H. Berestycki, P.L. Lions, Arch. Rational Mech. Anal. 82 (1983)313-345] and some other related literature. In particular, our approach isuseful for many similar problems.

Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions