high-quality DFT orbitals for electronically simple materials such as c-BN. DMC for solids has been demonstrated to give significantly more accurate cohesive energies[8], equatio ns of state and Raman frequencies[9], and phase transitions[10] than DFT. We have used both the CASINO QMC software suite[11] and QMCPACK[12]. QMC simulations of solids are currently performed within the pseudopotential (PP) approximation, in which the core electrons are eliminated and their effect replaced by a nonlo- cal potential operator[8]. Since PPs are presently constructed with a lower-accuracy theory, such as Hartree-Fock (HF) or DFT, this replacement represents an uncontrolled approxima- tion. To eliminate this error, we develop a method for all- electron (AE) QMC simulations of solids in QMCPACK using trial wave functions derived from full-potential linearized aug- mented plane wave (FP-LAPW) calculations using the EX- CITING code[13]. Space is divided into spherical muffin tin regions around the nuclei, and an interstitial region. Or- bitals are represented inside the muffin tins as a product of r a- dial functions and spherical harmonics, and outside as plane- waves. To ensure that a wavefunction satisfies the variation al principle, it must be both continuous and smooth. We utilize a super -LAPW formalism that enforces continuity and smooth- ness at the muffin tin boundary. For efficiency, we represent the orbitals as 3D B-splines in the interstices and the product of radial splines and spherical harmonics in the muffin tins. Since AE QMC simulations are computationally expen- sive, we perform these simulations in 8-atom cubic supercells. Simulation cells this small would typically have significan t finite-size errors. We eliminate these errors by combining d ata from AE simulations with that from PP simulations performed in both 8-atom and 64-atom supercells. Thus, we are able to simultaneously eliminate systematic errors from pseudpoten- tials and from finite-size effects. The corrected static-la ttice energy is given at each volume as where the term in brackets removes the psuedopotential bias. Δ MPC 64 and Δ kinetic 64 are, respectively, potential[14] and kinetic[15] corrections for finite-size errors. We perform this procedure with three different PP sets commonly used in QMC: HF PPs from Trail and Needs (TN)[16, 17]; HF PPs from Burkatzki, Filippi, and Dolg (BFD)[18]; and DFT- GGA[19] PPs generated with OPIUM (WC)[20]. Perform- ing the same procedure with 128-atom PP simulations and 16-atom AE simulations yields statistically indistinguishable results, demonstrating that finite-size errors are converg ed at this size. Additional methodological details and the finite -size data can be found in EPAPS document No. #. E = E PP 64 + [ E AE 8 − E PP 8 ] + Δ MPC 64 + Δ kinetic 64 , (1) To compute the phonon free energy, we use density functional perturbation theory (DFPT) in the QUANTUM ESPRESSO package[21] with the Wu-Cohen functional and the OPIUM PPs. The phonon density of states, from which we derive thermodynamic data, is usually very well-described with DFT. where P 300 K is the room-temperature contribution, fit to the Vinet form. The phonon contribution is written in an aug- Figure 1 shows the EOS of c-BN at 300 K, with experi- mental data from Datchi et al. [24] and Goncharov et al. [7], as well as the present work from simulations with three different PPs. The residuals in (c) are derived from DMC simulation with PPs alone, while those in (b) combine all-electron and PP data. There is significant discrepancy between the theo- retical curves in (c), suggesting that PP simulation alone does not provide sufficient accuracy. Once the PP data is combined with AE data, as in (b), all the theoretical curves come into good agreement. Our theoretical EOS agrees reasonably with that in Refs. [24] and [7] within the experimentally measured pressure range, but the experimental extrapolation shows sig- nificant deviation at high pressure. We may write the thermal equation of state in the form P ( V,T ) = P 300 $_{K}$( V ) + P$_{th}$ ( V,T ) − P$_{th}$ ( V,T = 300) , (2) We compute the free energy for our c-BN system at twelve unit-cell volumes, spanning volume compression ratios from 0.84 to 2.0, corresponding to pressures of about -50 GPa to 900 GPa. While it is not fully certain that the cubic phase of BN is stable to 900 GPa, no other structure has been observed, and theoretical studies have not identified any transitionsbe- low 1 TPa[22]. We use the Vinet form[23] for the isother- mal EOS, which we find represents our free-energy data very well, yielding the bulk modulus, B 0 , its pressure derivative, B ′ $_{0}$, and the equilibirum volume, V 0 (Table I(a)). The statisti- cal error bars for each data point are directly determined from our QMC data. We compute statistical confidence ranges, tak- ing into account parameter cross-correlations with a simple Monte Carlo procedure. (a) Parameters for 300K EOS Source PP/AE atoms V 0 ( ˚ A $^{3}$) B 0 (GPa) B ′ 0 (nondim.) Trail-Needs PP + AE 64/8 11.792(18) 381(6) 3.87(6) OPIUM GGA PP + AE 64/8 11.769(17) 385(6) 3.86(6) BFD HF PP + AE 64/8 11.781(20) 382(7) 3.87(7) BFD HF PP + AE 128/16 11.812(8) 378(3) 3.87(3) Datchi et al. [24] 11.8124 395(2) 3.62(5) Goncharov et al. 11.817(32) 387(4) 3.06(15) (b) Parameters for thermal pressure θ 0 n ( K ˚ A − 3 $^{n}$) α n ( K − 1 ˚ A − 3 $^{n}$) β n ( K ˚ A − 3 $^{n}$) n = 0 4.836656 × 10 3 2.598608 × 10 − 3 -4.869563 × 10 3 n = 1 -6.929704 × 10 1 -1.200504 × 10 − 4 1.763443 × 10 2 n = 2 4.634278 × 10 − 1 2.789128 × 10 − 6 -2.186053 × 10 0 n = 3 -1.273468 × 10 − 3 -2.008994 × 10 − 8 9.303181 × 10 − 3 (c) Parameters for Raman calibration c 0 ( cm − $^{1}$) c 1 ( cm − $^{1}$) c 2 ( K ) b R 0 ( GPa ) R 1 ( GPa ) R 2 ( GPa ) 1055.9 -144.24 1497.8 3.0155 349.87 1849.4 112.33 TABLE I: Parameters for the c-BN EOS and Raman calibration. 2