Utilities lev1 (old) and lev2 (new)

Either utility is used to prepare data files for lev00 for the calculation of the partial charge density as well as DOS/LDOS using CASTEP wavefunctions. To compile lev1, you should run the shell-script lev1.comp from the current directory using the same param.inc file. lev2 should be compiled in directories LEV2_f77 (f77 version, compile every time you get a new param.inc file) or LEV_f90 (f90 version, to be compiled only once).

First of all, run CASTEP in the band-structure mode to write the wavefunctions. Note that the $\mathbf{k}$-points mesh as given by tetr must to be used for the DOS/LDOS calculation. Then you can run lev1. It is an interactive menu-driven program and five options are available: DOS, DOp, SRF and MAP. At the end of the run a file psi2.[option]is produced that is needed for the subsequent run of the plotter lev00. Note that the utility lev1 needs the file fort.14 which contains the information necessary to perform the Fast Fourier Transform (FFT) from the reciprocal to the real space.

All states available (their number is NBANDS) can participate. However, it is possible to do a more sophisticated job by creating islands of bands, each island being a continuous manifold of states which can overlap, and then run the calculation for every island. This way it is possible to do a specific job on particular states. If all states are to be included, just specify one island with all states from 1 to NBANDS.

The five options available are listed below:

1. DOS $\rightarrow$ $s$-projected DOS as in Eqs. (3.5) and (3.7) (with $l=0$) is calculated using conserving algorithm for the space integration. The projection is made either on a single Slater type AO,
   

   $$R(r)=N(\xi)r^{n-1}e^{-\xi r}$$ (6.2)

   
   
   or on a linear combination of Gaussians
   

   $$R(r)=\sum_{i=1}^{N_{G}}C_{i}N(\alpha_{i})e^{-\alpha_{i}r^{2}}$$ (6.3)

   
   
   Here $N$ is the normalisation of a single orbital which depends on the exponentials, $\xi$ or $\alpha_{i}$. Noninteractive option. All the information needed should be provided in the file fort.14.DOS (see below). Up to Ntask0 spheres (set in dos_task.inc) can be defined for a single run of lev1.
2. PRO $\rightarrow$ local DOS, Eqs. (3.5) and (3.6), and $s,p,d$-projected DOS, Eqs. (3.5) and (3.7), are calculated using nonconserving algorithm for the space integration. The projection is made on a single AO; its radial part is made either of a single Slater type AO, or of a linear combination of Gaussians. Noninteractive option. All the information needed should be provided in the file fort.14.PRO (see below). Up to Ntask0 spheres can be defined for one run of lev1.
3. DOp $\rightarrow$ this is DOS projected on a layer, see Eqs. (3.5) and (3.8). Interactive option: you will be asked about each layer, its position and thickness. Up to Ntask0 layers can be specified for one run of lev1. Islands of bands $n$ should be provided in the file fort.14a (see below).
4. MAP $\rightarrow$ partial electronic density as in Eq. (3.1) or (3.2). Islands of bands $n$ should be provided in the file fort.14a (see below).
5. SRF $\rightarrow$ partial electronic density which is 2D integrated over the plane parallel to the slab, i.e.
   

   $$\rho_{n}(i_{3})=\frac{1}{N_{1}N_{2}}\sum_{i_{1}=1}^{N_{1}}\sum_{i_{2}=1}^{N_{2}}\rho_{n}(i_{1},i_{2},i_{3})).$$ (6.4)

   
   
   where $N_{1}$ and $N_{2}$ are the number of grid points along vectors $\mathbf{a}_{1}$ and $\mathbf{a}_{2}$ of the cell and $i_{3}$ runs from 1 to $N_{3}$ ($N_{1}$, $N_{2}$, $N_{3}$ correspond to NGX, NGY, NGZ in param.inc). You will be asked to provide islands of bands (as in the file fort.14.SRF) and an output file psi2.SRF will be produced. Islands of bands $n$ should be provided in the file fort.14a (see below).

Formats of the input files mentioned in this section are provided below:

• fort.14a: islands of states are provided, i.e.
  • number of islands of states (1 integer)
  • the first and the last states for the 1st island (2 integers)
  • the first and the last states for the 2nd island (2 integers)
  • etc.
• fort.14.DOS:
  • islands of states as above;
  • number of spheres (1 integer);
  • then for each sphere:
    • on 1 line: Cartesian coordinates of the sphere (in Å), sphere radius (in Å), 1 or 0 (for Slater or Gaussian AO, respectively)
    • if Slater, Eq. (6.2), then on the next line: $n$ and $\xi$ (in Å$^{-1}$)
    • if Gaussian, Eq. (6.3), then on the next line: and on the following line all the coefficients and exponentials (in Å) are provided as .
• fort.14.PRO:
  • islands of states as above;
  • number of spheres (1 integer);
  • then for each sphere:
    • on 1 line: Cartesian coordinates of the sphere (in Å), sphere radius (in Å), 1 or 0 (for Slater or Gaussian AO, respectively), one integer corresponding to the fine grid of the nonconserving method, and three flags (0 for 'no' and 1 for 'yes') for whether to do $s$, $p$ and $d$ projected DOS.
    • then separately for every angular momenta with nonzero flag: specify the radial part of the orbital (see fort.14.DOS)
• fort.14.DOp:
  • islands of states as in other cases;
  • number of layers (1 integer);
  • then for each layer you provide the following information (one line per layer):
    • Cartesian position of the layer on the $z$-axis (in Å);
    • layer thickness (in Å);
    • 0 for conserving and 1 for non-conserving;
    • numbers of grid points along each of the x,y,z directions necessary for the non-conserving method (3 integers); note that in the case of the conserving method this data will be ignored.