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We develop an all-electron quantum Monte Carlo (QMC) method for solids thatdoes not rely on pseudopotentials, and use it to construct a primary ultra-highpressure calibration based the equation of state of cubic boron nitride(c-BN).We compute the static contribution to the free energy with QMC, and obtain thephonon contribution from density functional theory, yielding a high-accuracycalibration up to 900 GPa usable directly in experiment. Furthermore, wecompute the anharmonic Raman frequency shift with QMC as a function of pressureand temperature, allowing optical pressure calibration in table-topexperiments. In contrast to present experimental approaches, small systematicerrors in the theoretical EOS do not increase with pressure, and noextrapolation is needed. This all-electron methodology is generally applicableto first-row solids, and can be used to provide a new reference for ab initiocalculations of solids and to benchmark pseudopotential accuracy.

Fundamental high pressure calibration from all-electron quantum Monte Carlo calculations