关注：

1)  wigner-seitz radius (au A)的物理含义；Wigner–Seitz radius与体积有关，那么会随压力变化而变化吗？

2） 晶体的填充效率计算

请问，晶体的填充效率sphere packing efficiency 如何计算？

    空间利用率=晶胞中球的体积/晶胞体积；即球的半径怎么取？

如文献中提到：

Our calculations show that the sphere packing efficiency at 14 Mbar increases continuously in the order of 25.5%→29.4%→32.1%→33.93%→35.44% for ice X, Pbcm, Pbca, I-42d, and P21 structure, respectively.

Huayung  解答：

  晶体中最近邻原子间距的一半作为原子球半径，来考察填充效率。

附：RWIGS半径会随赝势不同而变化，如：

POTCAR_O:   RWIGS  =    1.550; RWIGS  =     .820    wigner-seitz radius (au A)

POTCAR_O_h:   RWIGS  =    1.400; RWIGS  =     .741    wigner-seitz radius (au A)

POTCAR_O_s:   RWIGS  =    1.700; RWIGS  =     .900    wigner-seitz radius (au A)

POTCAR_O_sv:   RWIGS  =    1.000; RWIGS  =    0.529    wigner-seitz radius (au A

POTCAR_H:   RWIGS  =     .700; RWIGS  =     .370    wigner-seitz radius (au A)

POTCAR_H_h:   RWIGS  =     .700; RWIGS  =     .370    wigner-seitz radius (au A)

附-Wigner–Seitz radius

   The Wigner–Seitz radius , named after Eugene Wigner and Frederick Seitz, is the radius of a sphere whose volume is equal to the mean volume per atom in a solid.^[1] This parameter is used frequently in condensed matter physics to describe the density of a system.

In a 3-D system with particles in a volume , the Wigner–Seitz radius is defined by^[1]

Solving for we obtain

where is the particle density of the valence electrons.

For a non-interacting system, the average separation between two particles will be . The radius can also be calculated as

where is molar mass, is mass density, and is the Avogadro number.

This parameter is normally reported in atomic units, i.e., in units of the Bohr radius.

Values of for single valence metals^[2] are listed below:

Element
Li	3.25
Na	3.93
K	4.86
Rb	5.20
Cs	5.62

更多参看：http://en.wikipedia.org/wiki/Wigner–Seitz_cell 

http://en.wikipedia.org/wiki/Sphere_packing

附-H的赝势文件头部分

PAW_PBE H 15Jun2001

1.00000000000000000

parameters from PSCTR are:

  VRHFIN =H: ultrasoft test

  LEXCH  = PE

  EATOM  =    12.4884 eV,     .9179 Ry

  TITEL  = PAW_PBE H 15Jun2001

  LULTRA =        F    use ultrasoft PP ?

  IUNSCR =        0    unscreen: 0-lin 1-nonlin 2-no

  RPACOR =     .000    partial core radius

  POMASS =    1.000; ZVAL   =    1.000    mass and valenz

  RCORE  =    1.100    outmost cutoff radius

  RWIGS  =     .700; RWIGS  =     .370    wigner-seitz radius (au A)

  ENMAX  =  250.000; ENMIN  =  200.000 eV

  RCLOC  =     .701    cutoff for local pot

  LCOR   =        T    correct aug charges

  LPAW   =        T    paw PP

  EAUG   =  400.000

  RMAX   =    2.174    core radius for proj-oper

  RAUG   =    1.200    factor for augmentation sphere

  RDEP   =    1.112    radius for radial grids

  QCUT   =   -5.749; QGAM   =   11.498    optimization parameters

  Description

    l     E      TYP  RCUT    TYP  RCUT

    0   .000     23  1.100

    0   .500     23  1.100

    1  -.300     23  1.100

  Error from kinetic energy argument (eV)

  NDATA  =      100

  STEP   =   20.000   1.050

 5.77      5.50      5.37      5.11      4.99      4.75      4.52      4.40

 4.19      3.98      3.88      3.68      3.49      3.31      3.14      2.98

 2.83      2.68      2.54      2.35      2.22      2.11      1.94      1.84

 1.74      1.61      1.48      1.40      1.29      1.19      1.09      1.01

 .925      .851      .782      .719      .642      .590      .526      .482

 .430      .382      .339      .301      .267      .236      .209      .178

 .157      .133      .113      .988E-01  .832E-01  .697E-01  .562E-01  .467E-01

 .386E-01  .305E-01  .239E-01  .186E-01  .143E-01  .109E-01  .820E-02  .580E-02

 .425E-02  .291E-02  .195E-02  .130E-02  .808E-03  .544E-03  .368E-03  .278E-03

 .239E-03  .227E-03  .225E-03  .224E-03  .218E-03  .204E-03  .181E-03  .156E-03

 .127E-03  .983E-04  .735E-04  .520E-04  .369E-04  .274E-04  .225E-04  .204E-04

 .201E-04  .200E-04  .193E-04  .178E-04  .151E-04  .121E-04  .914E-05  .676E-05

 .512E-05  .437E-05  .412E-05  .410E-05

END of PSCTR-controll parameters