Simple effective interaction for dimensional crossover

We show that the effective electron-electron interaction veff[n](r,r′)=erf|r-r′|b(n)/|r-r′|, with n being the electronic density and b(n) fixed from the compressibility sum rule, is remarkably accurate in both three and two dimensions, competing with the actual state-of-the-art exchange-correlation static kernels. Using this result, we propose a simple isotropic approximation for the quasi-two-dimensional regime, which gives a realistic wave vector analysis of the correlation energy, in the context of the linear response time-dependent density functional theory.