# Vibronic Density of States using the AH-FC method¶

The `FCFDOS`

class allows one to easily calculate the density of states for an energy or charge transfer at the AH-FC level of theory by combining the results from two vibronic spectra calculations.

For an example, see Vibronic Density of States with ADF.

```
# from .scmjob import SCMJob, SCMResults
import math
import numpy
from scm.plams.tools.kftools import KFFile
__all__ = ["FCFDOS"]
class FCFDOS:
"""
A class for calculating the convolution of two FCF spectra
"""
# Conversion factor to cm-1 == ( me^2 * c * alpha^2 ) / ( 100 * 2pi * amu * hbar )
G2F = 120.399494933
# J2Ha = 1.0 / (scipy.constants.m_e * scipy.constants.speed_of_light**2 * 0.0072973525693**2)
J2Ha = 2.293712278400752e17
def __init__(self, absrkf, emirkf, absele=0.0, emiele=0.0):
"""
absrkf : KFFile from an FCF absorption calculation for the acceptor, as name, path, or KFFile object
emirkf : KFFile from an FCF emission calculation for the donor, as name, path, or KFFile object
absele : Acceptor absorption electronic energy cm-1
emiele : Donor emission electronic energy in cm-1
"""
if isinstance(absrkf, str):
self.absrkf = KFFile(absrkf)
else:
self.absrkf = absrkf
if isinstance(emirkf, str):
self.emirkf = KFFile(emirkf)
else:
self.emirkf = emirkf
self.absele = absele
self.emiele = emiele
self.spc = None
def _getstick(self, source):
spclen = source.read("Fcf", "nspectrum")
rawspc = source.read("Fcf", "spectrum")
stick = numpy.reshape(numpy.array(rawspc), (2, spclen)).transpose()
# Reorder spectrum if decreasing
if stick[0, 0] > stick[-1, 0]:
for ix in range(numpy.size(stick, 0) // 2):
XX = numpy.copy(stick[ix, :])
stick[ix, :] = stick[-ix - 1, :]
stick[-ix - 1, :] = XX
# Get frequencies in cm-1
frq1 = numpy.array(source.read("Fcf", "gamma1")) * self.G2F
frq2 = numpy.array(source.read("Fcf", "gamma2")) * self.G2F
# Calculate energy in Joules
# factor = scipy.constants.pi * scipy.constants.hbar * scipy.constants.speed_of_light * 100.0
factor = 9.932229285744643e-24
viben1 = sum(frq1) * factor
viben2 = sum(frq2) * factor
# Convert to Hartree
viben1 = viben1 * self.J2Ha
viben2 = viben2 * self.J2Ha
# Add ZPE and electronic energy
stick[:, 0] = stick[:, 0] + viben2 - viben1 + self.absele + self.emiele
return stick
def _spcinit(self):
# Get absorption and emission spectra
absspc = self._getstick(self.absrkf)
emispc = self._getstick(self.emirkf)
# Find spectrum bounds
absmin = numpy.amin(absspc[:, 0])
absmax = numpy.amax(absspc[:, 0])
emimin = numpy.amin(emispc[:, 0])
emimax = numpy.amax(emispc[:, 0])
spcmin = min(absmin, emimin)
spcmax = max(absmax, emimax)
# Find spectrum length and grain
absdlt = abs(absspc[0, 0] - absspc[1, 0])
emidlt = abs(absspc[0, 0] - absspc[1, 0])
spcgrn = min(absdlt, emidlt)
spclen = math.floor((spcmax - spcmin) / spcgrn) + 1
# Initialize spectrum
self.spc = self.newspc(spcmin, spcmax, spclen)
return None
def dos(self, lineshape="GAU", HWHM=100.0):
"""
Calculate density of states by computing the overlap of the two FCF spectra
The two spectra are broadened using the chosen lineshape and Half-Width at Half-Maximum in cm-1
"""
# Initialize spectrum
self._spcinit()
# Get stick spectra
absstick = self._getstick(self.absrkf)
emistick = self._getstick(self.emirkf)
# Convolute with gaussians
absspc = numpy.copy(self.spc)
emispc = numpy.copy(self.spc)
absspc = self.convolute(absspc, absstick, lineshape, HWHM)
emispc = self.convolute(emispc, emistick, lineshape, HWHM)
# Integrate
# Calculate DOS
self.spc[:, 1] = absspc[:, 1] * emispc[:, 1]
dos = self.trapezoid(self.spc)
return dos
def newspc(self, spcmin, spcmax, spclen=1000):
# Dimensions of the spectrum
delta = (spcmax - spcmin) / (spclen - 1)
spc = numpy.zeros((spclen, 2), dtype=float)
for ix in range(spclen):
spc[ix, 0] = spcmin + delta * ix
return spc
def convolute(self, spc, stick, lineshape=None, HWHM=None):
"""
Convolute stick spectrum with the chosen width and lineshape
lineshape : Can be Gaussian or Lorentzian
HWHM : expressed in cm-1
"""
if HWHM is None:
raise ValueError("HWHM not defined")
if lineshape is None:
raise ValueError("Lineshape not defined")
# Data for the convolution
delta = spc[1, 0] - spc[0, 0]
if lineshape[0:3].upper() == "GAU":
# Gaussian lineshape
idline = 1
# This includes the Gaussian prefactor and the factor to account for the reduced lineshape width
# factor = 1. / scipy.special.erf(2*math.sqrt(math.log(2)))
factor = 1.0188815852036244
factA = math.sqrt(numpy.log(2.0) / math.pi) * factor / HWHM
factB = -numpy.log(2.0) / HWHM**2
# We only convolute between -2HWHM and +2HWHM which accounts for 98.1% of the area
ishft = math.floor(2 * HWHM / delta)
elif lineshape[0:3].upper() == "LOR":
# Lorentzian lineshape
idline = 2
# This includes the Lorentzian prefactor and the factor to account for the reduced lineshape width
factA = (math.pi / math.atan(12) / 2) * HWHM / math.pi
factB = 0.0
# We only convolute between -12HWHM and +12HWHM which accounts for 94.7% of the area
ishft = math.floor(12 * HWHM / delta)
else:
raise ValueError("invalid lineshape")
# Loop over peaks in the stick spectrum
spclen = numpy.size(spc, 0)
for ix in range(numpy.size(stick[:, 0])):
# Find peak position in the convoluted spectrum
peakpos = 1 + math.floor((stick[ix, 0] - spc[0, 0]) / delta)
# Convolution interval, limited to save computational time
i1 = max(peakpos - ishft, 1)
i2 = min(peakpos + ishft, spclen)
factor = factA * stick[ix, 1]
if idline == 1: # Gaussian
for i in range(i1, i2):
spc[i, 1] = spc[i, 1] + factor * math.exp(factB * (spc[i, 0] - stick[ix, 0]) ** 2)
elif idline == 2: # Lorentzian
for i in range(i1, i2):
spc[i, 1] = spc[i, 1] + factor / (HWHM + (spc[i, 0] - stick[ix, 0]) ** 2)
return spc
def trapezoid(self, spc):
"""
Integrate spectrum using the trapezoid rule
"""
value = (spc[0, 1] + spc[-1, 1]) / 2
value = value + sum(spc[1:-1, 1])
# The abscissas must be equally spaced for this to work
value = value * (spc[1, 0] - spc[0, 0])
return value
def __str__(self):
string = f"Absorption from {self.absrkf.path}\nEmission from {self.emirkf.path}\nAcceptor absorption electronic energy = {self.absele} cm-1\nDonor emission electronic energy = {self.emiele} cm-1"
return string
```