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Integration Keywords

These keywords control the numerical integration grid used when the AOM is computed internally (i.e., when filedat is a fuzzy-partition keyword: mindefrho, netrho, becke, promrho).

They may also be given directly on the same line as the fuzzy keyword in Record 2. See Input Format — Record 2.


LEBEDEV nang

Number of angular grid points in the Lebedev quadrature used for the angular part of the fuzzy AOM integration. Default is 434.

Available Lebedev grid sizes are the standard Lebedev orders (e.g., 110, 194, 302, 434, 590, 770, …). Higher values increase accuracy at the cost of compute time.


NRAD nrad

Number of radial grid points in the Becke-type integration. Default is 100.

Higher values improve accuracy for atoms with steep density variations near the nucleus (heavy elements). Values of 200–400 are common for production calculations.


IRMESH irmesh

Selects the radial mapping function that transforms the \([0, \infty)\) range to the finite integration interval. Default is 1.

irmesh Mapping
1 Becke mapping (default)
2 Gauss-Chebyshev

KPOWER pow

The iterative K parameter in Becke's fuzzy-cell partitioning scheme, controlling how sharply the weight function \(w_A\) transitions between atoms. Default is 3 (the standard value from Becke's original paper).

Higher values make the partition more step-like (sharper atom boundaries); lower values make it smoother.

Only relevant when filedat = becke.


RHOPOW rhopow

Exponent applied to each promolecular atomic density \(\rho_A\) when computing the weight:

\[w_A = \frac{\rho_A^{\text{rhopow}}}{\sum_B \rho_B^{\text{rhopow}}}\]

Default is 1.0 (standard Hirshfeld / promolecular weights). Only relevant when filedat = promrho.


Inline integration parameters

For mindefrho, netrho, and becke, the integration parameters may be given directly on the filedat line in Record 2:

mindefrho  NANG  NRAD  IRMESH
netrho     NANG  NRAD  IRMESH
becke      NANG  NRAD  IRMESH  POW

These are equivalent to using the LEBEDEV, NRAD, IRMESH, and KPOWER keywords later in the input.