OT

References: VandeVondele2003, Weber2008

Sets the various options for the orbital transformation (OT) method. Default settings already provide an efficient, yet robust method. Most systems benefit from using the FULL_ALL preconditioner combined with a small value (0.001) of ENERGY_GAP. Well-behaved systems might benefit from using a DIIS minimizer.

Advantages: It’s fast, because no expensive diagonalisation is performed. If preconditioned correctly, method guaranteed to find minimum.

Disadvantages: Sensitive to preconditioning. A good preconditioner can be expensive. No smearing, or advanced SCF mixing possible: POOR convergence for metallic systems. [Edit on GitHub]

Keywords

• SECTION_PARAMETERS

• ALGORITHM

• BROYDEN_ADAPTIVE_SIGMA

• BROYDEN_BETA

• BROYDEN_ENABLE_FLIP

• BROYDEN_ETA

• BROYDEN_FORGET_HISTORY

• BROYDEN_GAMMA

• BROYDEN_OMEGA

• BROYDEN_SIGMA

• BROYDEN_SIGMA_DECREASE

• BROYDEN_SIGMA_MIN

• CHOLESKY

• ENERGIES

• ENERGY_GAP

• EPS_IRAC

• EPS_IRAC_FILTER_MATRIX

• EPS_IRAC_QUICK_EXIT

• EPS_IRAC_SWITCH

• EPS_TAYLOR

• GOLD_TARGET

• IRAC_DEGREE

• LINESEARCH

• MAX_IRAC

• MAX_TAYLOR

• MINIMIZER

• NONDIAG_ENERGY

• NONDIAG_ENERGY_STRENGTH

• N_HISTORY_VEC

• OCCUPATION_PRECONDITIONER

• ON_THE_FLY_LOC

• ORTHO_IRAC

• PRECONDITIONER

• PRECOND_SOLVER

• ROTATION

• SAFE_DIIS

• STEPSIZE

Keyword descriptions

SECTION_PARAMETERS: logical = F

Lone keyword: T

Usage: &OT T

controls the activation of the ot method [Edit on GitHub]

ALGORITHM: enum = STRICT

Usage: ALGORITHM STRICT

Valid values:

• STRICT Strict orthogonality: Taylor or diagonalization based algorithm.

• IRAC Orbital Transformation based Iterative Refinement of the Approximative Congruence transformation (OT/IR).

References: VandeVondele2003, VandeVondele2005, Weber2008

Algorithm to be used for OT [Edit on GitHub]

BROYDEN_ADAPTIVE_SIGMA: logical = T

Lone keyword: T

Usage: BROYDEN_ADAPTIVE_SIGMA ON

Enable adaptive curvature estimation [Edit on GitHub]

BROYDEN_BETA: real = 9.00000000E-001

Usage: BROYDEN_BETA 0.9

Underrelaxation for the broyden mixer [Edit on GitHub]

BROYDEN_ENABLE_FLIP: logical = T

Lone keyword: T

Usage: BROYDEN_ENABLE_FLIP ON

Ensure positive definite update [Edit on GitHub]

BROYDEN_ETA: real = 7.00000000E-001

Usage: BROYDEN_ETA 0.7

Dampening of estimated energy curvature. [Edit on GitHub]

BROYDEN_FORGET_HISTORY: logical = F

Lone keyword: T

Usage: BROYDEN_FORGET_HISTORY OFF

Forget history on bad approximation [Edit on GitHub]

BROYDEN_GAMMA: real = 5.00000000E-001

Usage: BROYDEN_GAMMA 0.5

Backtracking parameter [Edit on GitHub]

BROYDEN_OMEGA: real = 1.10000000E+000

Usage: BROYDEN_OMEGA 1.1

Growth limit of curvature. [Edit on GitHub]

BROYDEN_SIGMA: real = 2.50000000E-001

Usage: BROYDEN_SIGMA 0.25

Curvature of energy functional. [Edit on GitHub]

BROYDEN_SIGMA_DECREASE: real = 7.00000000E-001

Usage: BROYDEN_SIGMA_DECREASE 0.7

Reduction of curvature on bad approximation. [Edit on GitHub]

BROYDEN_SIGMA_MIN: real = 5.00000000E-002

Usage: BROYDEN_SIGMA_MIN 0.05

Minimum adaptive curvature. [Edit on GitHub]

CHOLESKY: enum = REDUCE

Usage: CHOLESKY REDUCE

Valid values:

• OFF The cholesky algorithm is not used

• REDUCE Reduce is called

• RESTORE Reduce is replaced by two restore

• INVERSE Restore uses operator multiply by inverse of the triangular matrix

• INVERSE_DBCSR Like inverse, but matrix stored as dbcsr, sparce matrix algebra used when possible

If FULL_ALL the cholesky decomposition of the S matrix is used. Options on the algorithm to be used. [Edit on GitHub]

ENERGIES: logical = F

Lone keyword: T

Usage: ENERGIES

Optimize orbital energies for use in Fermi-Dirac smearing (requires ROTATION and FD smearing to be active). [Edit on GitHub]

ENERGY_GAP: real = -1.00000000E+000

Usage: ENERGY_GAP 0.001

Should be an estimate for the energy gap [a.u.] (HOMO-LUMO) and is used in preconditioning, especially effective with the FULL_ALL preconditioner, in which case it should be an underestimate of the gap (can be a small number, e.g. 0.002). FULL_SINGLE_INVERSE takes it as lower bound (values below 0.05 can cause stability issues). In general, higher values will tame the preconditioner in case of poor initial guesses. A negative value will leave the choice to CP2K depending on type of preconditioner. [Edit on GitHub]

EPS_IRAC: real = 1.00000000E-010

Usage: EPS_IRAC 1.0E-5

Targeted accuracy during the refinement iteration. [Edit on GitHub]

EPS_IRAC_FILTER_MATRIX: real = 0.00000000E+000

Usage: EPS_IRAC_FILTER_MATRIX 1.0E-5

Sets the threshold for filtering the matrices. [Edit on GitHub]

EPS_IRAC_QUICK_EXIT: real = 1.00000000E-005

Usage: EPS_IRAC_QUICK_EXIT 1.0E-2

Only one extra refinement iteration is done when the norm is below this value. [Edit on GitHub]

EPS_IRAC_SWITCH: real = 1.00000000E-002

Usage: EPS_IRAC_SWITCH 1.0E-3

The algorithm switches to the polynomial refinement when the norm is below this value. [Edit on GitHub]

EPS_TAYLOR: real = 1.00000000E-016

Aliases: EPSTAYLOR

Usage: EPS_TAYLOR 1.0E-15

Target accuracy of the taylor expansion for the matrix functions, should normally be kept as is. [Edit on GitHub]

GOLD_TARGET: real = 1.00000000E-002

Usage: GOLD_TARGET 0.1

Target relative uncertainty in the location of the minimum for LINESEARCH GOLD [Edit on GitHub]

IRAC_DEGREE: integer = 4

Usage: IRAC_DEGREE 4

The refinement polynomial degree (2, 3 or 4). [Edit on GitHub]

LINESEARCH: enum = 2PNT

Aliases: LINE_SEARCH

Usage: LINESEARCH GOLD

Valid values:

• NONE take fixed length steps

• 2PNT extrapolate based on 2 points

• 3PNT … or on 3 points

• GOLD perform 1D golden section search of the minimum (very expensive)

1D line search algorithm to be used with the OT minimizer, in increasing order of robustness and cost. MINIMIZER CG combined with LINESEARCH GOLD should always find an electronic minimum. Whereas the 2PNT minimizer is almost always OK, 3PNT might be needed for systems in which successive OT CG steps do not decrease the total energy. [Edit on GitHub]

MAX_IRAC: integer = 50

Usage: MAX_IRAC 5

Maximum allowed refinement iteration. [Edit on GitHub]

MAX_TAYLOR: integer = 4

Usage: MAX_TAYLOR 5

Maximum order of the Taylor expansion before diagonalisation is preferred, for large parallel runs a slightly higher order could sometimes result in a small speedup. [Edit on GitHub]

MINIMIZER: enum = CG

Usage: MINIMIZER DIIS

Valid values:

• SD Steepest descent: not recommended

• CG Conjugate Gradients: most reliable, use for difficult systems. The total energy should decrease at every OT CG step if the line search is appropriate.

• DIIS Direct inversion in the iterative subspace: less reliable than CG, but sometimes about 50% faster

• BROYDEN Broyden mixing approximating the inverse Hessian

Minimizer to be used with the OT method [Edit on GitHub]

NONDIAG_ENERGY: logical = F

Lone keyword: T

Usage: NONDIAG_ENERGY

Add a non-diagonal energy penalty (FD smearing) [Edit on GitHub]

NONDIAG_ENERGY_STRENGTH: real = 1.00000000E+000

Usage: NONDIAG_ENERGY_STRENGTH

The prefactor for the non-diagonal energy penalty (FD smearing) [Edit on GitHub]

N_HISTORY_VEC: integer = 7

Aliases: NDIIS ,N_DIIS ,N_BROYDEN

Usage: N_DIIS 4

Number of history vectors to be used with DIIS or BROYDEN [Edit on GitHub]

OCCUPATION_PRECONDITIONER: logical = F

Lone keyword: T

Usage: OCCUPATION_PRECONDITIONER

Preconditioner with the occupation numbers (FD smearing) [Edit on GitHub]

ON_THE_FLY_LOC: logical = F

Usage: ON_THE_FLY_LOC T

On the fly localization of the molecular orbitals. Can only be used with OT/IRAC. [Edit on GitHub]

ORTHO_IRAC: enum = CHOL

Usage: ORTHO_IRAC POLY

Valid values:

• CHOL Cholesky.

• POLY Polynomial.

• LWDN Loewdin.

The orthogonality method. [Edit on GitHub]

PRECONDITIONER: enum = FULL_KINETIC

Usage: PRECONDITIONER FULL_ALL

Valid values:

• FULL_ALL Most effective state selective preconditioner based on diagonalization, requires the ENERGY_GAP parameter to be an underestimate of the HOMO-LUMO gap. This preconditioner is recommended for almost all systems, except very large systems where make_preconditioner would dominate the total computational cost.

• FULL_SINGLE_INVERSE Based on H-eS cholesky inversion, similar to FULL_SINGLE in preconditioning efficiency but cheaper to construct, might be somewhat less robust. Recommended for large systems.

• FULL_SINGLE Based on H-eS diagonalisation, not as good as FULL_ALL, but somewhat cheaper to apply.

• FULL_KINETIC Cholesky inversion of S and T, fast construction, robust, and relatively good, use for very large systems.

• FULL_S_INVERSE Cholesky inversion of S, not as good as FULL_KINETIC, yet equally expensive.

• NONE skip preconditioning

References: VandeVondele2003, Weber2008, Schiffmann2015

Type of preconditioner to be used with all minimization schemes. They differ in effectiveness, cost of construction, cost of application. Properly preconditioned minimization can be orders of magnitude faster than doing nothing. [Edit on GitHub]

PRECOND_SOLVER: enum = DEFAULT

Usage: PRECOND_SOLVER DIRECT

Valid values:

• DEFAULT the default

• DIRECT Cholesky decomposition followed by triangular solve (works for FULL_KINETIC/SINGLE_INVERSE/S_INVERSE)

• INVERSE_CHOLESKY Cholesky decomposition followed by explicit inversion (works for FULL_KINETIC/SINGLE_INVERSE/S_INVERSE)

• INVERSE_UPDATE Performs a Hotelling update of the inverse if a previous preconditioner is present. Mainly useful for GPU accelerated systems (works for FULL_KINETIC/SINGLE_INVERSE/S_INVERSE)

How the preconditioner is applied to the residual. [Edit on GitHub]

ROTATION: logical = F

Lone keyword: T

Usage: ROTATION

Introduce additional variables so that rotations of the occupied subspace are allowed as well, only needed for cases where the energy is not invariant under a rotation of the occupied subspace such as non-singlet restricted calculations or fractional occupations. [Edit on GitHub]

SAFE_DIIS: logical = T

Aliases: SAFER_DIIS

Usage: SAFE_DIIS ON

Reject DIIS steps if they point away from the minimum, do SD in that case. [Edit on GitHub]

STEPSIZE: real = -1.00000000E+000

Usage: STEPSIZE 0.4

Initial stepsize used for the line search, sometimes this parameter can be reduced to stabilize DIIS or to improve the CG behavior in the first few steps. The optimal value depends on the quality of the preconditioner. A negative values leaves the choice to CP2K depending on the preconditioner. [Edit on GitHub]