  We present a multi-scale density functional theory (DFT) informed molecular
dynamics and tight-binding (TB) approach to capture the interdependent atomic
and electronic structures of twisted bilayer graphene. We calibrate the flat
band magic angle to be at $\theta_{\rm M} = 1.08^{\circ}$ by rescaling the
interlayer tunneling for different atomic structure relaxation models as a way
to resolve the indeterminacy of existing atomic and electronic structure models
whose predicted magic angles vary widely between $0.9^\circ \sim 1.3^\circ$.
The interatomic force fields are built using input from various stacking and
interlayer distance dependent DFT total energies including the exact exchange
and random phase approximation (EXX+RPA). We use a Fermi velocity of
$\upsilon_{\rm F} \simeq 10^{6}$~m/s for graphene that is enhanced by about
$\sim 15\%$ over the local density approximation (LDA) values. Based on this
atomic and electronic structure model we obtain high-resolution spectral
functions comparable with experimental angle-resolved photoemission spectra
(ARPES). Our analysis of the interdependence between the atomic and electronic
structures indicates that the intralayer elastic parameters compatible with the
DFT-LDA, which are stiffer by $\sim$30\% than widely used reactive empirical
bond order force fields, can combine with EXX+RPA interlayer potentials to
yield the magic angle at $\sim 1.08^{\circ}$ without further rescaling of the
interlayer tunneling.
