  In this paper, we consider the longtime dynamics of the solutions to focusing
energy-critical Schr\"odinger equation with a defocusing energy-subcritical
perturbation term under a ground state energy threshold in four spatial
dimension. This extends the results in Miao et al. (Commun Math Phys
318(3):767-808, 2013, The dynamics of the NLS with the combined terms in five
and higher dimensions. Some topics in harmonic analysis and applications,
advanced lectures in mathematics, ALM34, Higher Education Press, Beijing, pp
265-298, 2015) to four dimension without radial assumption and the proof of
scattering is based on the interaction Morawetz estimates developed in Dodson
(Global well-posedness and scattering for the focusing, energy-critical
nonlinear Schr\"oinger problem in dimension $d=4$ for initial data below a
ground state threshold, arXiv:1409.1950), the main ingredients of which
requires us to overcome the logarithmic failure in the double Duhamel argument
in four dimensions.
