The computational cost of quantum Monte Carlo (QMC) calculations of realistic periodic systems depends strongly on the method of storing and evaluating the many-particle wave function. Previous work [A. J. Williamson et al., Phys. Rev. Lett. 87, 2464
06 (2001); D. Alf`e and M. J. Gillan, Phys. Rev. B 70, 161101 (2004)] has demonstrated the reduction of the O(N^3) cost of evaluating the Slater determinant with planewaves to O(N^2) using localized basis functions. We compare four polynomial approximations as basis functions -- interpolating Lagrange polynomials, interpolating piecewise-polynomial-form (pp-) splines, and basis-form (B-) splines (interpolating and smoothing). All these basis functions provide a similar speedup relative to the planewave basis. The pp-splines have eight times the memory requirement of the other methods. To test the accuracy of the basis functions, we apply them to the ground state structures of Si, Al, and MgO. The polynomial approximations differ in accuracy most strongly for MgO and smoothing B-splines most closely reproduce the planewave value for of the variational Monte Carlo energy. Using separate approximations for the Laplacian of the orbitals increases the accuracy sufficiently to justify the increased memory requirement, making smoothing B-splines, with separate approximation for the Laplacian, the preferred choice for approximating planewave-represented orbitals in QMC calculations.
The melting curve of Ni up to 100 GPa has been calculated using first principles methods based on density functional theory (DFT). We used two complementary approaches: i) coexistence simulations with a reference system and then free energy correctio
ns between DFT and the reference system, and ii) direct DFT coexistence using simulation cells including 1000 atoms. The calculated zero pressure melting temperature is slightly underestimated at $1637 pm 10$ K (experimental value is 1728 K), and at high pressure is significantly higher than recent measurements in diamond anvil cell experiments [Phys. Rev. B {bf 87}, 054108 (2013)]. The zero pressure DFT melting slope is calculated to be $30 pm 2$ K, in good agreement with the experimental value of 28 K.
