关注：

1） 零点振动能的本质；

  Perosonal view:

  ZPE是物质的固有属性，不随计算方法而改变，即选取不同的参数如赝势种类、截断能大小等，只要精度足够，不影响计算得到的零点能数值。

2） 零点能的表达式；

3） 从PWscf获取零点能的步骤

感谢LHY分享此脚本：

#!/usr/bin/python

# this program is for calculating zero point energy (ZPE), combination with PWSCF.

# note: integrating DOS of phonon.

# date: April 23,2011

# Hanyu <ouuing@gmail.com>

import sys

import math

def getZPE(phdos,natom):

temperature = 300

f = open(phdos)

dos = []

E_zpe = 0.0

sum_dos = 0.0

free_energy = 0.0

sinh_tmp = 0.0

for line in f:

  dos.append(map(float,line.split()))

f.close

for index in range(len(dos)):

  sum_dos +=dos[index][1]

for index in range(len(dos)-1):

  if dos[index][0] >= 0:

    domega=dos[index+1][0]-dos[index][0]

#     E_zpe+=domega*dos[index][1]*dos[index][0]*0.5

    E_zpe+=dos[index][1]*dos[index][0]*0.5

    if temperature == 0:

      continue

    sinh_tmp = 2.0*math.sinh(float(dos[index][0])/2.0/(temperature/50.0*33.356631209780147))

    if sinh_tmp <= 0:

      continue

    log_tmp = math.log(sinh_tmp)

#     free_energy += temperature/50.0/0.02998*domega*dos[index][1]*log_tmp

    free_energy += temperature/50.0/0.02998*dos[index][1]*log_tmp

#     print free_energy/8065.5/int(natom)

print E_zpe/8065.5/int(natom), 'eV', 'Zero point energy'

print free_energy/8065.5/int(natom), 'eV', 'Free energy', 'at', temperature, 'K'

print sum_dos,'modes of phonon'

if len(sys.argv) < 2:

   print 'No PHDOS.',

   print "executing: "

   print "./pw_zero.py phonon.dos 12"

   print "           file       atoms"

   sys.exit()

if len(sys.argv) == 2:

 natom=1

 phdos=sys.argv[1]

if len(sys.argv) == 3:

 natom=sys.argv[2]

 phdos=sys.argv[1]

getZPE(phdos,natom)