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1）局域态密度、分态密度和投影态密度的物理含义

2）局域态密度、分态密度和投影态密度各软件的处理方法

局域态密度按原子分，分态密度和投影态密度按轨道角动量分（s、p、d?）Partial and local density of states

Partial density of states (PDOS) and local density of states (LDOS) represent useful semi-qualitative tools for analyzing electronic structure.

  LDOS shows which atoms in the system contribute electronic states to various parts of the energy spectrum.

PDOS further qualifies these results by resolving the contributions according to the angular momentum of the states. It is often useful to know whether the main peaks in the DOS are of s, p, or d character.

LDOS and PDOS analyses give a qualitative handle on the nature of electron hybridization in the system, on the origin of the main features in XPS and optical spectra, etc.

 

PDOS calculations are based on Mulliken population analysis, which allows the contribution from each energy band to a given atomic orbital to be calculated. 【计算基于布局分析？】Summation of these contributions over all bands produces a weighted DOS. DMol³ and CASTEP allow you to select the type of weighting required. It is possible, for example, to generate LDOS by adding together all the contributions due to orbitals on a given atom.

 

Note: PDOS analysis formalism is not valid for high energy states in the conduction band: PDOS representation will usually decay to zero at about 20 eV above the Fermi level. This is related to the fact that expansion of essentially free electron states in terms of a limited number of atomic-like basis functions is impossible to carry out with any degree of accuracy. Only the valence band and lower part of the conduction band are meaningful in the PDOS plot.

The calculation itself can be carried out using either Gaussian smearing or linear interpolation, similar to the total DOS calculation. In this case, the latter method includes the interpolation of the weights as well as the electronic energies.

 

 

 

 

DOSCAR file

The file DOSCAR contains the DOS and integrated DOS. The units are ``number of states/unit cell''. For dynamic simulations and relaxations, an averaged DOS and an averaged integrated DOS is written to the file. For a description of how the averaging is done see  6.21, 6.37). The first few lines of the DOSCAR file are made up by a header which is followed by NDOS lines holding three data energy DOS integrated DOS

The density of states  (DOS) , is actually determined as the difference of the integrated DOS between two pins, i.e.

 

where is the distance between two pins (energy difference between two grid point in the DOSCAR file), and is the integrated DOS

 

This method conserves the total number of electrons exactly.  For spin-polarized calculations each line holds five data

energy DOS(up) DOS(dwn) integrated DOS(up) integrated DOS(dwn)

If RWIGS or LORBIT (Wigner Seitz radii, see section 6.336.34)  is set in the INCAR file, a lm- and site-projected DOS is calculated and also written to the file DOSCAR. One set of data is written for each ion, each set of data holds NDOS lines with the following data

energy s-DOS p-DOS d-DOS

or

energy s-DOS(up) s-DOS(down) p-DOS(up) p-DOS(dwn) d-DOS(up) d-DOS(dwn)

for the non spin-polarized and spin polarized case respectively. As before the written densities are understood as the difference of the integrated DOS between two pins.

For non-collinear calculations, the total DOS has the following format: energy DOS(total) integrated-DOS(total)

Information on the individual spin components is available only for the site projected density of states, which has the format:

energy s-DOS(total) s-DOS(mx) s-DOS(my) s-DOS(mz) p-DOS(total) p-DOS(mx) ...

In this case, the  (site projected) total density of states (total) and  the  (site projected) energy resolved magnetization density in the   (mx), (my) and (mz)  direction are available.

In all cases, the units of the  l- and site projected DOS are states/atom/energy.

The site projected DOS is not evaluated in the parallel version for the following cases:

In vasp.4.6 the site projected DOS can be evaluated for LORBIT=10-12, even if NPAR is not equal 1 (contrary to previous releases).

Mind:  For relaxations, the DOSCAR is usually useless. If you want to get an accurate DOS for the final configuration, first copy CONTCAR to POSCAR and continue with  one  static (ISTART=1; NSW=0) calculation.

 

 

PROCAR file

For static calculations, the file PROCAR contains the spd- and site projected wave function character of each band. The wave function character is calculated by projecting the wavefunctions onto spherical harmonics that are non zero within spheres of a radius RWIGS around each ion. RWIGS must be specified in the INCAR file in order to obtain the file (see section 6.33).

Mind: that the spd- and site projected character of each band  is not evaluated in the parallel version if NPAR1.

 

 

 

RWIGSRWIGS= [real array]  

Default
RWIGS	=	values read from POTCAR

The Wigner Seitz radius is optional. It must be supplied for each species in the POSCAR file i.e.   RWIGS = 1.0 1.5

for a system with 2 species (types of atoms). If the RWIGS values is supplied and LORBIT10, the spd- and site projected wavefunction character of each band is evaluted, and the local partial DOS is calculated. If  LORBIT10, RWIGS is ignored  (see sections 5.16 and 5.15).  RWIGSmust  be set in calculations with constraining the  local magnetic moments (see section 6.69 For mono-atomic system RWIGS can be defined unambiguously. The sum of the volume of the spheres around each atom should be the same as the total volume of the cell (assuming that you do not have a  vacuum region within your cell).  This is in the spirit of atomic sphere calculations. VASP writes a line

Volume of Typ 1: 98.5 %

to the OUTCAR file. You should use a RWIGS value which yields a  volume of  approximately .

For binary systems there is no unambiguous way to define RWIGS and several choices are possible.  In all cases, the sum of   the volume of the spheres should be close to the total volume of the cell (i.e the sum of the values given by VASP should be around ).

• One possible choice is to set  RWIGS such that the overlap between the spheres is minimized.

• However in most cases, it is simpler to choose the radius of each sphere such that they are close to the covalent radius  as tabulated  in most periodic tables. This  simple criterion can be used in most cases, and it relies at least on some ``physical intuition''.

Please keep in mind that results are qualitative -- i.e. there is no unambiguous way to determine the location of an electron. With the current implementation, it is for instance  hardly possible to determine charge transfer. What  can be derived from the partial DOS is the typical character of a peak in a DOS. Quantitative results can be obtained only by carefull comparison with  a reference system  (e.g. bulk versus surface).

 

 

 

 

 

 

 

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