Structural relaxation¶

This section describes how to find the zero-Kelvin equilibrium structure, given a starting structure with non-zero forces and/or stresses. CONQUEST can employ a variety of algorithms algorithm to minimise energy with respect to atomic positions, including: L-BFGS; conjugate gradients; and damped molecular dynamics (both MDMin and FIRE approaches). The minimisation of energy or enthalpy with respect to cell vectors is restricted to conjugate gradients at present, though L-BFGS will be implemented.

Setting AtomMove.WriteXSF T for all flavours of optimisation will dump the trajectory to the file trajectory.xsf, which can be visualised using VMD. Setting AtomMove.AppendCoords T will append the structure at each step to UpdatedAtoms.dat in the format of a CONQUEST structure input.

For the L-BFGS and conjugate gradients relaxations, the progress of the calculation can be monitored by searching for the word GeomOpt; grepping will print the following:

$ grep GeomOpt Conquest_out
GeomOpt - Iter:    0 MaxF:   0.00329282 H:  -0.14168571E+03 dH:   0.00000000
GeomOpt - Iter:    1 MaxF:   0.00331536 H:  -0.14168995E+03 dH:   0.00424155
GeomOpt - Iter:    2 MaxF:   0.00350781 H:  -0.14168997E+03 dH:   0.00001651
GeomOpt - Iter:    3 MaxF:   0.00504075 H:  -0.14169161E+03 dH:   0.00164389
GeomOpt - Iter:    4 MaxF:   0.00725611 H:  -0.14169172E+03 dH:   0.00010500
GeomOpt - Iter:    5 MaxF:   0.01134145 H:  -0.14169329E+03 dH:   0.00157361
GeomOpt - Iter:    6 MaxF:   0.01417229 H:  -0.14169385E+03 dH:   0.00056077
GeomOpt - Iter:    7 MaxF:   0.01434628 H:  -0.14169575E+03 dH:   0.00190304
GeomOpt - Iter:    8 MaxF:   0.01711197 H:  -0.14170001E+03 dH:   0.00425400
GeomOpt - Iter:    9 MaxF:   0.02040556 H:  -0.14170382E+03 dH:   0.00381110
GeomOpt - Iter:   10 MaxF:   0.01095167 H:  -0.14170752E+03 dH:   0.00370442

In this example, MaxF is the maximum single force component, H is the enthalpy and dH is the change in enthalpy.

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Ionic relaxation¶

To optimise the ionic positions with respect to the DFT total energy, the following flags are essential:

AtomMove.TypeOfRun lbfgs
AtomMove.MaxForceTol 5e-4
AtomMove.ReuseDM T

The parameter AtomMove.TypeOfRun can take the value lbfgs or cg for iterative optimisation. Both algorithms are robust and relatively efficient in most instances; L-BFGS is preferred. The parameter AtomMove.MaxForceTol specifies the force convergence criterion in Ha/bohr, i.e. the calculation will terminate when the largest force component on any atom is below this value. The parameter AtomMove.ReuseDM specifies that the density matrix (the K-matrix for diagonalisation or L-matrix for O(N) calculations) from the previous step will be used as an initial guess for the SCF cycle after propagating the atoms; this should generally decrease the number of SCF cycles per ionic step.

If the self-consistency tolerance is too low, the optimisation may fail to converge with respect to the force tolerance; this may necessitate a tighter minE.SCTolerance for diagonalisation (also possibly minE.LTolerance for O(N) calculations). A grid which is too coarse can also cause problems with structural relaxation to high tolerances.

For problematic cases where the conjugate gradients algorithm fails to find a downhill search direction, it may be worth trying quenched molecular dyanamics, which propagates the equations of motion following a simple NVE approach, but resets the velocities to zero when the dot product of force and velocity is zero.

AtomMove.TypeOfRun md
AtomMove.QuenchedMD T
AtomMove.MaxForceTol 5e-4
AtomMove.ReuseDM T

The FIRE algorithm [SR1] is a variant of quenched MD that has been shown to outperform conjugate gradients in some circumstances.

AtomMove.TypeOfRun md
AtomMove.FIRE T
AtomMove.MaxForceTol 5e-4
AtomMove.ReuseDM T

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Cell optimisation¶

The unit cell can be optimised with respect to enthalpy with fixed fractional coordinates (AtomMove.OptCellMethod 1) using the following input:

AtomMove.TypeOfRun cg
AtomMove.OptCell T
AtomMove.OptCellMethod 1
AtomMove.TargetPressure 1.0
AtomMove.ReuseL T
AtomMove.EnthalpyTolerance 1E-6
AtomMove.StressTolerance 0.01

Here, we specify the target pressure in GPa and two new tolerances, the enthalpy tolerance in Ha and the stress tolerance in GPa.

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Combined optimisation¶

For simple crystals, the fractional ionic coordinates vary trivially with changes in the lattice vectors; however for more complicated systems such as molecular crystals and amorphous materials, it is necessary simultaneously relax the ionic positions and lattice vectors. This can be done by setting AtomMove.OptCellMethod 3

AtomMove.TypeOfRun cg
AtomMove.OptCell T
AtomMove.OptCellMethod 3
AtomMove.TargetPressure 1.0
AtomMove.ReuseL T
AtomMove.MaxForceTol 5e-4
AtomMove.EnthalpyTolerance 1E-6
AtomMove.StressTolerance 0.01

Note that the enthalpy will generally converge much more rapidly than the force and stress, and that it may be necessary to tighten minE.SCTolerance (diagonalisation) or minE.LTolerance (order(N)) to reach the force tolerance, if it is even possible.

Due to the nature of the complex partitioning system, large and sudden changes in volume may cause the calculation to crash, particlularly in the case of combined optimisation. In such cases, it may help to try AtomMove.OptCellMethod 2, which uses a simple but robust double-loop minimisation: a full ionic conjugate gradients relaxation for the inner loop and a single cell steepest descent relaxation for the outer loop. This is considerably less efficient, but may help in particularly problematic cases.

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SR1: E. Bitzek, P. Koskinen, F. Gähler, M. Moseler, and P. Gumbsch. Structural Relaxation Made Simple. Phys. Rev. Lett., 97:2897, 2006. doi:10.1103/PhysRevLett.97.170201.

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