Keywords for Periodic Electrostatic Embedded Cluster Method

The Periodic Electrostatic Embedded Cluster Method (PEECM) functionality provides electronic embedding of a finite, quantum mechanical cluster in a periodic, infinite array of point charges. It is implemented within HF and DFT energy and gradient TURBOMOLE modules: DSCF, GRAD, RIDFT, RDGRAD, and ESCF. Unlike embedding within a finite set of point charges the PEEC method always yields the correct electrostatic (Madelung) potential independent of the electrostatic moments of the point charges field. It is also significantly faster than the traditional finite point charges embedding.

The basic PEECM settings are defined in the $embed block. It can be redirected to an external file using $embed file=SPMlt;file_name>;.

Following keywords are used for the PEECM calculation setup:

periodic

Specifies the number of periodic directions. Allowed values for number are 3 for a bulk three-dimensional system, 2 for a two-dimenional surface slab, and 1 for a one-dimensional system. Default value is 3.

cell

Unit cell parameters in a form of six real values $\vert$ mathend000#a$\vert$ mathend000#, $\vert$ mathend000#b$\vert$ mathend000#, $\vert$ mathend000#c$\vert$ mathend000#, $\alpha$ mathend000#, $\beta$ mathend000#, $\gamma$ mathend000#, where $\vert$ mathend000#a$\vert$ mathend000#, $\vert$ mathend000#b$\vert$ mathend000#, $\vert$ mathend000#c$\vert$ mathend000# are lengths of the appropriate cell vectors, $\alpha$ mathend000# is the angle between vectors b and c, $\beta$ mathend000# is the angle between vectors a and c, and $\gamma$ mathend000# is the angle between vectors a and b. Default are atomic units and degrees. You can specify unit cell parameters in Å and degrees using cell ang.

content
  label x y z
end

Content of the unit cell, where label is the label of the point charge Content of the unit cell, where label is the label of the point charge type and x y z are corresponding Cartesian or fractional crystal coordinates. Defaults are Cartesian coordinates and atomic units. You can specify Cartesian coordinates in Å using content ang and fractional coordinates using content frac. Note that Cartesian coordinates assume that the cell vector a is aligned along the $x$ mathend000# axis, and the vector b on the $xy$ mathend000# plane.

cluster
  label x y z
end

Atomic coordinates of the piece of the crystal to be replaced by the QM cluster and surrounding isolation shell (ECPs amd explicit point charges), where label is the point charge label and x y z are corresponding Cartesian or fractional crystal coordinates. Defaults are Cartesian coordinates and atomic units. You can specify Cartesian coordinates in Å using cluster ang and fractional coordinates using cluster frac.

charges
  label charge
end

Values of point charges, where label is the point charge label and charge specifies charge in atomic units.

Additionally, the following keywords control the accuracy of PEECM calculation:

lmaxmom

Maximum order of the multipole expansions in periodic fast multipole method (PFMM). Default value is 25.

potval

Electrostatic potential at the lattice points resulting from periodic point charges field will be output if this keyword is present. Default is not to output.

wsicl

Well-separateness criterion for PFMM. Default is 3.0.

epsilon

Minimum accuracy for lattice sums in PFMM. Default is 1.0d-8.