  The interplanar bond strength in graphite has been identified to be very low
owing to the contribution of the van der Waals interaction. However, in this
study, we use microscopic picosecond ultrasound to demonstrate that the elastic
constant, $C_{33}$, along the $c$ axis of defect-free monocrystalline graphite
exceeds 45 GPa, which is higher than reported values by 20\%. Existing theories
fail to reproduce this strongly correlated interplanar system, and our results,
thus, indicate the necessity for improvement. Since the LDA+U+RPA method,
including both random phase approximation correlation and short-range
correlation in $p$ Wannier orbitals, shows better agreement with the
observation than LDA or even than ACFDT-RPA, the experimental results indicate
non-negligible electron correlation effects with respect to both the
short-range and long-range interactions.
