NRLMOL MeshΒΆ

In the NRLMOL, mesh is generated by specifying the accuracy of various intergals. The mesh is refined until the specified accuracy of the integrals is accomplished. In this sense, the mesh is variational. There are two types of meshes used in the calculation. One is the radial mesh used for calculations within the atomic spheres and the other is the interstitial mesh (mesh between atomic spheres). The defaults for these are 1.E-06. The mesh parameters are stored in the MESHDAT file. The default will look like It is possible to change the default mesh by the user. The parameters used in creating the mesh are listed in the MESHDAT file. The default MESHDAT file contains the following parameters :

   F                                                                     line 1
  0.10000E-06   1.2000                                                     line 2
   6                                                                       line 3
  0.20000      0.40000      0.60000       1.0000       1.6000              line 4
   4                                                                       line 5
   2.1000       10.100       18.100                                        line 6
   2   1   3   5   5   7   9  11  19  21                                   line 7
   4   1   3   5   5   7   9  11  19  21                                   line 8
   4   1   3   6   5   7   9  11  19  21                                   line 9
   6   1   3   6   7   7   9  11  19  21                                   line 10
  0.20000E-06   1.2000                                                     line 11
   2.0000       8                                                          line 12
   2.0000                                                                  line 13

As noted above are two types of meshes used in the calculation. One is the radial mesh use for calculations within atomic spheres and the other is the interstitial mesh.

Line 1:

Line 2: The numbers in this line pertains to the radial mesh. The radial mesh is constructed to give integrations involving various Gaussians from short to long range. The small number is the error allowed in integration by the mesh. The second number 1.2 separates the exponentials of the Gaussians which are tested i.e. the n+1st exponential is 1.2 times nth exponent. Decreasing the error tolerance will result in increase in number of mesh points and better integrals.

Line 3: The atomic sphere is divided into different concentric regions with different numbers of mesh points. The number of such radial zones is written in line 3.

Line 4: The outer radii of the radial zones.

Line 5: The mesh has to be different for different atoms. Hence the periodic table (upto Z=56) is divided in 4 types of meshes.

Line 6: This line shows the 4 types of meshes for atoms : first one for Z<2.1, second one for Z<10.1 and third on for Z<18.1 and the last one for Z>18.

Line 7,8,9,10: The four lines contain the parameters for each type of atomic mesh. The numbers are

NPATS, NPIST, NTHET, NPHI, LMAX FOR EACH RADIAL ZONE

NPATS :

NPIST, NTHET, NPHI : Before creating the mesh, the space is divided into boxes such that each atom is contained in one box. Then a sphere around the atom is assumed and the radial mesh is created. The space at the box corners between the atomic sphere and the rectangular box is divided in a different mesh. The parameters NPIST, NTHET and NPHI correspond to the mesh at the box corners.

LMAX : LMAX for the each radial zone. This mesh will integrate a function of the type r lmax exp(-. r2) within the given error limit in this region. Increasing LMAX results in a more refined mesh.

Line 11 : This line contains the same parameters as line 2 but for the interstitial mesh. Decreasing the error limit results in more accurate integrals in the interstitial region.

Line 12: Cutfac, mx1d

CUTFAC: If a box transforms into itself due to symmetry, it will be split if it is larger than cutfac times the distance to the closest atom.

MX1D: max. number of points in a one-dimensional interstitial partition

Line 13: Splrat

SPLRAT: largest allowed ratio for: the size of an atomic box divided by the distance of another atom to the box boundary

NRLMOL allows setting of these paramaters by user to excersize control over the quality of calculation. Above values are default. Perhaps the simplest thing you can do to improve mesh is to improve the quality of interstial mesh by changing the line 11. Warning When taking energy differeces and comparing the energies it advisable to ensure that same quality of mesh was used in all pertaining calculations.