10: Testing Testing. Basic procedure to validate calculations

Transcription

1 The Nuts and Bolts of First-Principles Simulation 10: Testing Testing. Basic procedure to validate calculations Durham, 6th-13th December 2001 CASTEP Developers Group with support from the ESF ψ k Network

2 Not a Black Box: the need to test. Are your input files correct? Many different convergence parameters and tolerances. Always a tradeoff between degree of convergence and accuracy. Full convergence is usually prohibitively expensive. Electronic minimizers not foolproof. Some cases hard to converge, eg metal surfaces. Schettino's Law. (All programs contain bugs!)

3 Some Elementary Checks -- will reveal input errors and program bugs. Has the run iterated to the ground state? Did it converge or run out of iterations? If problems, try a different minimizer. Is the cohesive energy sensible? Should be close to experimental values from tables. Total Energy should be extensive quantity. Do calculation of bulk energy in large cell and compare with unit. Is surface energy reasonable? Are forces close to zero for bulk solid? N.B. perturb atoms away from special points as it may be maximum!

4 Outline Not a black box: the need for testing Some elementary tests What number do you want? Convergence parameters SCF Tolerance Plane-wave cutoff. Brillouin-Zone sampling

5 Convergence and Accuracy How accurately do you need to know the energy to test your hypothesis? Sensitivity of different tasks. SCF Tolerance Plane-wave cutoff, Gmax, Ecut and grid. Finite basis-set correction. Density of BZ k- point sampling Error cancellation

6 SCF Tolerance Parameter elec_energy_tol is convergence criterion for exit from electronic minimizer. max_scf_cycles not reached. N.B. Ensure How accurate does it need to be? Case 1. Cohesive energy: same as accuracy of result. Case 2. Geometry optimization: smaller tolerance required to converge forces. Cost of higher tolerance is small; a few additional SCF iterations since convergence is exponential.

7 Total energy is variational functional of density, but forces are not. E tot H º n 2 But F H º n

8 Plane-wave cutoff Cutoff determines highest representable spatial fourier component of density. n(r) varies most rapidly near nucleus. E cut = Gmax depends only on types of atoms, not number. Required cutoff is largest of any PSP in system. 2 2 / 2 m G max

9 Cutoff and Error Cancellation Detailed form of orbitals near nucleus has small effect on bonding. Therefore energy differences converge much faster with cutoff than absolute energy Compute time varies as N pw H G max H E c In practice, calculations are almost never fully converged with cutoff energy. Strategy: test cutoff convergence on small, bulk system, preferably with symmetry. Then very high cutoffs can be used at reasonable cost. Warning: don't rely on uniform convergence behaviour. There are plateaus!

10 Error Cancellation Reaction energy. Energy diffs 500->4000eV MgO s ƒ H 2 O g Ô Mg OH 2 MgO: H2O: 0.021eV 0.566eV Mg(OH)2: 0.562eV Reaction: 0.030eV

11 Grid parameters Params grid_scale and fine_gmax set size of FFT grid. FFT grid should be large enough to accommodate all G-vectors of density, n(r), within cutoff: G 2G max GRID_SCALE parameter sets this ratio, 1.75 by default. Guaranteed to avoid "aliasing" errors with value 2, but can get away with lower depending on XC functional. Values as low as 1.5 have been used with LDA, but beware if using GGAs. Finer grid may me necessary to represent augmentation charges with USPs for some elements. Set by FINE_GMAX parameter.

12 Finite basis-set corrections

13 Consistency of Energy and Stress

14 Brillouin-Zone Sampling Like cutoff, number of k-points used to sample BZ is a convergence parameter. lim N kp ΠE=E tot Unlike cutoff, inadequate sampling can give either higher or lower energy. Also unlike cutoff, sampling required is a function of simulation cell used. (Because it is specified in fractional k-space co-ordinates). Therefore you can not rely on error cancellation between calculations using different cells. Insulators typically require few k-points for large systems.

15 Metals In case of metals, kp-points must be sufficient to model band occupancy as well as dispersion, ie represent the fermi surface. In case of simple metals a smallish grid will do. Pathalogical case such as hcp Zn may require 5000 or more k- points to represent fermi surface features. An 8X8x8 k- point grid gives wrong value for c/a!

16 Application to various tasks Cohesive energies Phase Stability Chemical Reaction Geometry optimization Unit cell optimization MD