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We report a detailed theoretical study of the electronic structure, spectralproperties, and lattice parameters of bulk FeSe under pressure using a fullycharge self-consistent implementation of the density functional theory plusdynamical mean-field theory method (DFT+DMFT). In particular, we perform astructural optimization and compute the evolution of the lattice parameters(volume, $c/a$ ratio, and the internal $z$ position of Se) and the electronicstructure of the tetragonal (space group $P4/nmm$) paramagnetic FeSe. Ourresults for the lattice parameters are in good quantitative agreement withexperiment. The $c/a$ ratio is slightly overestimated by about $3$~\%,presumably due to the absence of the van der Waals interactions between theFeSe layers in our calculations. The lattice parameters determined within DFTare off the experimental values by a remarkable $\sim$$6$-$15$~\%, implying acrucial importance of electron correlations. Upon compression to $10$~GPa, the$c/a$ ratio and the lattice volume show a decrease by $2$ and $10$~\%,respectively, while the Se $z$ coordinate weakly increases by $\sim$$2$~\%.Most importantly, our results reveal a topological change of the Fermi surface(Lifshitz transition) which is accompanied by a two- to three-dimensionalcrossover. Our results indicate a small reduction of the quasiparticle massrenormalization $m^*/m$ by about $5$~\% for the $e$ and less than $1$~\% forthe $t_2$ states, as compared to ambient pressure. The behavior of themomentum-resolved magnetic susceptibility $\chi({\bf q})$ shows no topologicalchanges of magnetic correlations under pressure, but demonstrates a reductionof the degree of the in-plane $(\pi,\pi)$ stripe-type nesting. Our results forthe electronic structure and lattice parameters of FeSe are in good qualitativeagreement with recent experiments on its isoelectronic counterpartFeSe$_{1-x}$S$_x$.

Correlation strength, Lifshitz transition and the emergence of a two- to three-dimensional crossover in FeSe under pressure