4 and can be used to cross-calibrate scales based on other ma- terials. Since the accuracy of our methods should not depend on compression, our calibration can be used up to 900 GPa. This work was supported under the National Science Foun- dation Grant EAR-0530282. This research used resources of the National Center for Computational Sciences and the Cen- ter for Nanophase Materials Sciences, which are sponsored by the U.S. Department of Energy. This work was partially supported by the National Center for Supercomputing Appli- cations under MCA07S016 and utilized the Abe and Lincoln clusters. We thank Alexander Goncharov, F. Mauri and M. Lazzeri for helpful suggestions and discussions. (a) Fit to present theory for Raman shift. (b) Comparison of Raman experiment and theory. FIG. 2: TO Raman frequency of c-BN as a function of temperature and pressure. (a) gives compares our theoretical Raman frequency with the fitted form in Eqs. 9 and 10. (b) compares our calibrat ion at 300K with the experimental results from [25] and [26]. The black dots with error bars are the QMC frequencies, while the blue solid line gives the fit. The lower inset gives an expanded view at lo w pressure, in which the shaded region gives the statistical confidence region. The upper inset gives the variation with temperature. the pressure calibration of 50 GPa at 900 GPa. The devia- tions with respect to [26] are 70 cm − 1 and 120 GPa. The experimental parameters capture the correct qualitative high- pressure behavior up to 900 GPa, despite the fact that data was available only to 20 and 64 GPa, respectively. This suggests the form for the fit was well-chosen. We have presented a fully ab initio pressure calibration based on quantum Monte Carlo simulations, and have intro- duced a method for all-electron simulations of solids to elimi- nate bias from pseudopotentials. This method should be appli- cable to at least first-row solids, allowing increased accur acy in the study of other materials and providing a new benchmark for other methods. The only remaining systematic error in the static contribution to the EOS is from the fixed-node approxi - mation used in DMC. For simple materials such as c-BN this error should be quite small, and tends to cancel between dif- ferent volumes. Thus we believe the EOS is robust enough to be used directly in experiment as a primary pressure calibrant, [1] Yingwei Fei et al. , PNAS 104 , 9182 (2007). [2] H.K. Mao, J. Xu, and P.M. Bell, J. Geophys. Res. 91 , 4573 (1986). [3] Chang-Sheng Zha, Ho-kwang Mao, and Russell J. Hemley, PNAS 97 , 13494 (2000). [4] J. R. Asaya et al. , Int. J. of Impact Engineering 23 , 27 (1999). [5] J. Remo and M. Furnish, Int. J. of Impact Engineering 35 , 1516 (2008). [6] W. B. Holzapfel, High Pressure Research 25 , 87 (2005). [7] Alexander F. Goncharov et al , Phys. Rev. B 75 , 224114 (2007). [8] W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, Rev. Mod. Phys. 73 , 33 (2001). [9] Ryo Maezono, A. Ma, M.D. Towler, and R.J. Needs, Phys. Rev. Lett. 98 , 025701 (2007). [10] J. Kolorenˇc and L. Mitas, Phys. Rev. Lett. 101 , 185502 (2008). [11] R. J. Needs, M. D. Towler, N. D. Drummond, and P. L. Rios, J. Phys.: Condensed Matter 22 , 023201 (2010). [12] Jeongnim Kim, K. Esler, J. McMinis, B. Clark, J. Gergely, S. Chiesa, K. Delaney, J. Vincent, and D. Ceperley. [13] J. K. Dewhurst et al. , The EXCITING FP-LAPW code , http://exciting.sourceforge.net. [14] A. J. Williamson et al. , Phys. Rev. B 55 , R4851 (1997). [15] S. Chiesa, D.M. Ceperley, R.M. Martin, and M. Holzmann, Phys. Rev. Letts. 97 , 076404 (2006). [16] J.R. Trail and R.J. Needs, J. Chem. Phys. 122 , 174109 (2005). [17] J.R. Trail and R.J. Needs, J. Chem. Phys. 122 , 014112 (2005). [18] M. Burkatzki, C. Filippi, and M. Dolg, J. Chem. Phys. 126 , 234105 (2007). [19] Zhigang Wu and R.E. Cohen, Phys. Rev. B 73 , 235116 (2006). [20] Opium pseudopotential generation project , http://opium.sourceforge.net. [21] S. Baroni et al. , J.Phys.:Condens.Matter 21 , 395502 (2009). [23] P Vinet et al. , J. Phys.: Condensed Matter 1 , 1941 (1989). [22] J. Furthm¨uller, J. Hafner, and G. Kresse, Phys. Rev. B 50 , 15606 (1994). [24] F. Datchi, A. Dewaele, Y. Le Godec, and P. Loubeyre, Phys. Rev. B 75 , 214104 (2007). [25] F. Datchi and B. Canny, Phys. Rev. B 69 , 144106 (2004). [26] Alexander F. Goncharov, Jonathan C. Crowhurst, J. K. De- whurst, and S. Sharma, Phys. Rev. B 72 , 100104(R) (2005). [27] I. V. Alexandrov et al. , High pressure study of diamond, graphite and related materials (Terrepub AGU, Washington- Tokyo, 1992), pp. 409–416. ∗ Electronic address: esler@uiuc.edu