Section LOW_SCALING

• Cubic scaling RI-RPA, GW and Laplace-SOS-MP2 method using the imaginary time formalism. EPS_GRID in WFC_GPW section controls accuracy / req. memory for 3-center integrals. SORT_BASIS EXP should be specified in DFT section.

• Section path: CP2K_INPUT / ATOM / METHOD / XC / WF_CORRELATION / LOW_SCALING

• This section cannot be repeated.

• Subsections

  • CPHF

• Keywords

  • SECTION_PARAMETERS
  • DO_EXTRAPOLATE_KPOINTS
  • DO_KPOINTS
  • EPS_EIGVAL_S
  • EPS_EIGVAL_S_GAMMA
  • EPS_FILTER
  • EPS_FILTER_FACTOR
  • EPS_STORAGE_SCALING
  • EXPONENT_TAILORED_WEIGHTS
  • KEEP_QUADRATURE
  • KPOINTS
  • KPOINT_WEIGHTS_W
  • K_MESH_G_FACTOR
  • MAKE_CHI_POS_DEFINITE
  • MAKE_OVERLAP_MAT_AO_POS_DEFINITE
  • MEMORY_CUT
  • MEMORY_INFO
  • MIN_BLOCK_SIZE
  • MIN_BLOCK_SIZE_MO
  • REGULARIZATION_RI
  • REL_CUTOFF_TRUNC_COULOMB_RI_X
  • TRUNC_COULOMB_RI_X

• Keyword descriptions

  SECTION_PARAMETERS
  	&LOW_SCALING {Logical}
  	Activates cubic-scaling RPA, GW and Laplace-SOS-MP2 calculations.
  	This keyword cannot be repeated and it expects precisely one logical.
  	The lone keyword behaves as a switch to .TRUE.
  	Default value: .FALSE.

  DO_EXTRAPOLATE_KPOINTS
  	DO_EXTRAPOLATE_KPOINTS {Logical}
  	If true, use a larger k-mesh to extrapolate the k-point integration of W. For example, in 2D, when using KPOINTS 4 4 1, an additional 6x6x1 mesh will be used to extrapolate the k-point integration of W with N_k^-0.5, where Nk is the number of k-points.
  	This keyword cannot be repeated and it expects precisely one logical.
  	The lone keyword behaves as a switch to .TRUE.
  	Default value: .TRUE.

  DO_KPOINTS
  	DO_KPOINTS {Logical}
  	Besides in DFT, this keyword has to be switched on if one wants to do kpoints in. cubic RPA.
  	This keyword cannot be repeated and it expects precisely one logical.
  	The lone keyword behaves as a switch to .TRUE.
  	Default value: .FALSE.

  EPS_EIGVAL_S
  	EPS_EIGVAL_S {Real}
  	Parameter to reduce the expansion coefficients in RI for periodic GW. Removes all eigenvectors and eigenvalues of S_PQ(k) that are smaller than EPS_EIGVAL_S.
  	This keyword cannot be repeated and it expects precisely one real.
  	Default value: 0.00000000E+000

  EPS_EIGVAL_S_GAMMA
  	EPS_EIGVAL_S_GAMMA {Real}
  	Parameter to reduce the expansion coefficients in RI for periodic GW. Removes all eigenvectors and eigenvalues of M_PQ(k=0) that are smaller than EPS_EIGVAL_S.
  	This keyword cannot be repeated and it expects precisely one real.
  	Default value: 0.00000000E+000

  EPS_FILTER
  	EPS_FILTER {Real}
  	Determines a threshold for the DBCSR based multiply.Normally, this EPS_FILTER determines accuracy and timing of low-scaling RPA and GW calculations.
  	This keyword cannot be repeated and it expects precisely one real.
  	Default value: 1.00000000E-009

  EPS_FILTER_FACTOR
  	EPS_FILTER_FACTOR {Real}
  	Multiply EPS_FILTER with this factor to determine filter epsilon for DBCSR based multiply P(it)=(Mocc(it))^T*Mvirt(it) Default should be kept.
  	This keyword cannot be repeated and it expects precisely one real.
  	Default value: 1.00000000E+001

  EPS_STORAGE_SCALING
  	EPS_STORAGE_SCALING {Real}
  	Scaling factor to scale EPS_FILTER. Storage threshold for compression will be EPS_FILTER*EPS_STORAGE_SCALING.
  	This keyword cannot be repeated and it expects precisely one real.
  	Default value: 1.00000000E-003
  	Alias names for this keyword: EPS_STORAGE

  EXPONENT_TAILORED_WEIGHTS
  	EXPONENT_TAILORED_WEIGHTS {Real}
  	Gives the exponent of exactly integrated function in case 'KPOINT_WEIGHTS_W TAILORED' is chosen.
  	This keyword cannot be repeated and it expects precisely one real.
  	Default value: -2.00000000E+000

  KEEP_QUADRATURE
  	KEEP_QUADRATURE {Logical}
  	Keep the Laplace quadrature defined at the first energy evaluations throughout the run. Allows to have consistent force evaluations.
  	This keyword cannot be repeated and it expects precisely one logical.
  	The lone keyword behaves as a switch to .TRUE.
  	Default value: .TRUE.
  	Alias names for this keyword: KEEP_WEIGHTS, KEEP_QUAD, KEEP_WEIGHT

  KPOINTS
  	KPOINTS {Integer} {Integer} {Integer}
  	Keyword activates periodic, low-scaling GW calculations (&LOW_SCALING section also needed). For periodic calculations, kpoints are used for the density response, the Coulomb interaction and the screened Coulomb interaction. For 2d periodic systems, e.g. xz periodicity, please also specify KPOINTS, e.g. N_x 1 N_z.
  	This keyword cannot be repeated and it expects precisely 3 integers.
  	Default values: 0 0 0

  KPOINT_WEIGHTS_W
  	KPOINT_WEIGHTS_W {Keyword}
  	For kpoints in low-scaling GW, a Monkhorst-Pack mesh is used. The screened Coulomb interaction W(k) needs special care near the Gamma point (e.g. in 3d, W(k) diverges at the Gamma point with W(k) ~ k^alpha). KPOINT_WEIGHTS_W decides how the weights of the Monkhorst-Pack mesh are chosen to compute W(R) = int_BZ W(k) exp(ikR) dk (BZ=Brllouin zone).
  	This keyword cannot be repeated and it expects precisely one keyword.
  	Default value: UNIFORM
  	List of valid keywords: AUTO As 'TAILORED', but alpha is chosen automatically according to dimensionality (3D: alpha = -2 for 3D, 2D: alpha = -1 for exchange self-energy, uniform weights for correlation self-energy). TAILORED Choose k-point integration weights such that the function f(k)=k^alpha is exactly integrated. alpha is specified using EXPONENT_TAILORED_WEIGHTS. UNIFORM Choose the same weight for every k-point (original Monkhorst-Pack method).

  K_MESH_G_FACTOR
  	K_MESH_G_FACTOR {Integer}
  	The k-mesh for the Green's function can be chosen to be larger than the k-mesh for W (without much higher computational cost). The factor given here multiplies the mesh for W to obtainthe k-mesh for G. Example: factor 4, k-mesh for W: 4x4x1 -> k-mesh for G: 16x16x1 (z-dir. is non-periodic).
  	This keyword cannot be repeated and it expects precisely one integer.
  	Default value: 1

  MAKE_CHI_POS_DEFINITE
  	MAKE_CHI_POS_DEFINITE {Logical}
  	If true, makes eigenvalue decomposition of chi(iw,k) and removes negative eigenvalues. May increase computational cost significantly. Only recommended to try in case Cholesky decomposition of epsilon(iw,k) fails.
  	This keyword cannot be repeated and it expects precisely one logical.
  	The lone keyword behaves as a switch to .TRUE.
  	Default value: .TRUE.

  MAKE_OVERLAP_MAT_AO_POS_DEFINITE
  	MAKE_OVERLAP_MAT_AO_POS_DEFINITE {Logical}
  	If true, makes eigenvalue decomposition of S_mu,nu(k) and removes negative eigenvalues. Slightly increases computational cost. Only recommended to try in case Cholesky decomposition of S_mu,nu(k) fails (error message: Cholesky decompose failed: matrix is not positive definite or ill-conditioned; when calling create_kp_and_calc_kp_orbitals).
  	This keyword cannot be repeated and it expects precisely one logical.
  	The lone keyword behaves as a switch to .TRUE.
  	Default value: .FALSE.

  MEMORY_CUT
  	MEMORY_CUT {Integer}
  	Reduces memory for sparse tensor contractions by this factor. A high value leads to some loss of performance. This memory reduction factor applies to storage of the tensors 'M occ' / 'M virt' but does not reduce storage of '3c ints'.
  	This keyword cannot be repeated and it expects precisely one integer.
  	Default value: 5

  MEMORY_INFO
  	MEMORY_INFO {Logical}
  	Decide whether to print memory info on the sparse matrices.
  	This keyword cannot be repeated and it expects precisely one logical.
  	The lone keyword behaves as a switch to .TRUE.
  	Default value: .FALSE.

  MIN_BLOCK_SIZE
  	MIN_BLOCK_SIZE {Integer}
  	Minimum tensor block size. Adjusting this value may have minor effect on performance but default should be good enough.
  	This keyword cannot be repeated and it expects precisely one integer.
  	Default value: 5

  MIN_BLOCK_SIZE_MO
  	MIN_BLOCK_SIZE_MO {Integer}
  	Tensor block size for MOs. Only relevant for GW calculations. The memory consumption of GW scales as O(MIN_BLOCK_SIZE_MO). It is recommended to set this parameter to a smaller number if GW runs out of memory. Otherwise the default should not be changed.
  	This keyword cannot be repeated and it expects precisely one integer.
  	Default value: 64

  REGULARIZATION_RI
  	REGULARIZATION_RI {Real}
  	Parameter to reduce the expansion coefficients in RI for periodic GW. Larger parameter means smaller expansion coefficients that leads to a more stable calculation at the price of a slightly worse RI approximation. In case the parameter 0.0 is chosen, ordinary RI is used.
  	This keyword cannot be repeated and it expects precisely one real.
  	Default value: 0.00000000E+000

  REL_CUTOFF_TRUNC_COULOMB_RI_X
  	REL_CUTOFF_TRUNC_COULOMB_RI_X {Real}
  	Only active in case TRUNC_COULOMB_RI_X = True. Normally, relative cutoff = 0.5 is good choice; still needs to be evaluated for RI schemes.
  	This keyword cannot be repeated and it expects precisely one real.
  	Default value: 5.00000000E-001

  TRUNC_COULOMB_RI_X
  	TRUNC_COULOMB_RI_X {Logical}
  	If true, use the truncated Coulomb operator for the exchange-self-energy in periodic GW.
  	This keyword cannot be repeated and it expects precisely one logical.
  	The lone keyword behaves as a switch to .TRUE.
  	Default value: .TRUE.