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Localization Keywords

These keywords request an isopycnic (Cioslowski) localization of molecular orbitals. All localization methods maximize a localization criterion constructed from the AOM and produce a set of MOs that are normalized but not necessarily orthogonal.

Localization strategies

FULLOC [ALLCENTER]

Localize the natural orbitals from the input WFN using isopycnic localization. The localization function is built from the fragments defined by NGROUP.

If ALLCENTER is given, the localization function is built using every atomic center as an individual fragment (instead of the user-defined groups).

CANLOC [ALLCENTER]

Localize the canonical orbitals from the input WFN. Otherwise identical to FULLOC.

CHEMLOC

Chemical localization variant. Uses the same isopycnic algorithm but with different weighting — the criterion is more directly linked to chemical bond regions.

AOMLOC

A second chemical localization variant, closer to the AOM-based formulation.

DAFHLOC

Localization via progressive diagonalization of the Domain-Averaged Fermi Hole (DAFH) in 1-, 2-, 3-, … center domains up to MXCENT centers. Produces MOs that are localized on a growing number of atomic centers, yielding 1c-2e (lone pairs), 2c-2e (bonds), and higher-center contributions.

OPENLOC

Localization by diagonalizing the Open Quantum System (OQS) 1-RDM, i.e., \(S_A^{1/2} \cdot \text{1-RDM} \cdot S_A^{1/2}\), for each fragment \(A\). Produces Fragment Natural Orbitals (FNOs) localized on each domain.

Block keywords

DODAFH … END

Provides full manual control over the DAFH localization sequence. Within the DODAFH … END block, each line specifies one localization step:

ncen  cutoff  atom1  [atom2 …]  [DEPLET]
Field Meaning
ncen Number of centers to localize on
cutoff Acceptance threshold (close to but below 1.0)
atom1 … Indices of the ncen atoms
DEPLET After this step, deplete (remove found MO from) the full DAFH

Example — C₂H₆, manual DAFH sequence: 

dodafh
  1 0.95 1
  1 0.95 2   deplet
  2 0.95 1 2 deplet
  2 0.95 1 5
  2 0.95 1 6
  2 0.95 1 7 deplet
  2 0.95 2 3
  2 0.95 2 4
  2 0.95 2 8 deplet
end

OTHEROPEN … END

Equivalent to DODAFH … END but uses OQS 1-RDM diagonalization instead of DAFH. Same syntax.

Localization control parameters

DAFHSELECT n n1 n2 … nn

Restrict the DAFH progressive localization to specific atom tuples. For n-center steps, only the tuples (n1, n2, …, nn) are explored instead of all combinations.

Multiple DAFHSELECT lines with the same n accumulate — all listed tuples are explored. If no DAFHSELECT line is given for a value of n, all n-tuples are explored.

Currently only works for single-determinant wavefunctions in DAFHLOC mode.

CRITICS real

When CANLOC or CHEMLOC is active, an MO is considered to have partial localization on a fragment if its self-overlap \(S^A_{ii} > \text{real}\) in that fragment. Default is 0.02.

COVX real

Bond detection scaling factor. Atoms A and B are considered bonded if their distance is less than \((R_A + R_B) \times \text{COVX}\) where \(R_A\) and \(R_B\) are stored covalent radii. Default is 1.2.

DAMPS real

Damping factor for CHEMLOC. In each localization cycle, all CRITOV values are multiplied by DAMPS to progressively relax the localization criterion. Must be less than 1.0. Default is 0.95.

MXCENT n [skip1 skip2 …]

Maximum number of centers in the progressive DAFH localization (1c, 2c, …, up to nc). Default is 6.

Optional integers after n specify center counts to skip. For example:

MXCENT 6 3 4

analyzes 1-, 2-, 5-, and 6-center localizations, skipping 3 and 4.

CRITOV [n critval]

Overlap threshold for accepting an MO as localized on an n-center domain. Default for all CRITOV(1..MXCENT) is 0.95.

  • CRITOV alone — no change.
  • CRITOV n critval — set CRITOV(n) = critval.
  • CRITOV critval (real number, no integer first) — set all CRITOV(1..MXCENT) = critval.

Shorthand forms: CRITOV1 critval sets CRITOV(1), CRITOV2 critval sets CRITOV(2).

MAXBOND maxbond

In the progressive DAFH partitioning for atom pairs, the maximum number of bonds separating atom1 from atom2 that is actually explored. Default is 1 (only directly bonded pairs). Maximum is 4.

SKIPH

When true, hydrogen atoms are skipped in the single-atom DAFH analysis. Default is false.

EPSNEG [epsneg]

Largest allowed (in absolute value) negative eigenvalue in OPENLOC/OTHEROPEN diagonalizations of matrices that should be positive definite. Default is -1e-6.

EPSEIGEN [epseigen]

Eigenvalues smaller than epseigen in the OQS 1-RDM diagonalization are considered to correspond to MOs localized outside the fragment and are discarded.

SMALLEIGEN [smalleigen]

Minimum eigenvalue floor when computing \(S_A^{-1/2}\). Eigenvalues of \(S_A\) below this value are replaced by smalleigen to avoid division by zero.