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

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 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!)

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 Some Elementary Checks  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! -- will reveal input errors and program bugs.

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 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

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 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

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 SCF Tolerance  Parameter elec_energy_tol is convergence criterion for exit from electronic minimizer. N.B. Ensure max_SCF_cycles not reached.  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.

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1  Total energy is variational functional of density, but forces are not. But

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 Plane-wave cutoff  Cutoff determines highest representable spatial fourier component of density.  n(r) varies most rapidly near nucleus.  Gmax depends only on types of atoms, not number.  Required cutoff is largest of any PSP in system. Dd

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 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  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!

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 Error Cancellation  Reaction energy.  Energy diffs 500->4000eV  MgO: 0.021eV  H2O: 0.566eV  Mg(OH)2: 0.562eV  Reaction: 0.030eV

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 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:  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.

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 Finite basis-set corrections

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 Consistency of Energy and Stress

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 Brillouin-Zone Sampling  Like cutoff, number of k-points used to sample BZ is a convergence parameter.  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.

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 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!

Nuts and Bolts 2001 Lecture 10: Testing, testing. 1 Application to various tasks  Cohesive energies  Phase Stability  Chemical Reaction  Geometry optimization  Unit cell optimization  MD