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Polarizability

The linear electric-dipole polarizabilty is determined from the linear response function

ααβ(ω)=−⟨⟨μ^α;μ^β⟩⟩ω\alpha_{\alpha\beta}(\omega) = - \langle\langle \hat{\mu}_\alpha; \hat{\mu}_\beta \rangle \rangle_\omega
(1)

where μ^α\hat{\mu}_\alpha is the electric-dipole operator along Cartesian coordinate α\alpha and ω\omega is the optical angular frequency.

At optical frequencies well separated from transition frequencies in the system, the polarizability is real, whereas in near-resonance or resonance regions of the spectrum, it becomes complex. For further theoretical details, see Norman et al. (2018).

Nonresonant region

Python script

import veloxchem as vlx

molecule = vlx.Molecule.read_name("methane")
basis = vlx.MolecularBasis.read(molecule, "def2-svpd")

scf_drv = vlx.ScfRestrictedDriver()
scf_drv.xcfun = "b3lyp"
scf_results = scf_drv.compute(molecule, basis)

lr_drv = vlx.LinearResponseDriver()

lr_drv.property = "polarizability"
lr_drv.frequencies = [0.0656]  # static field is default

lr_results = lr_drv.compute(molecule, basis, scf_results)

Text file

@jobs
task: response
@end

@method settings
basis: aug-cc-pvdz
@end

@response
property: polarizability
frequencies: 0-0.25 (0.05)
@end

@molecule
charge: 0
multiplicity: 1
xyz:  
...
@end

The frequencies of the perturbing electric field is specified as a list in the Python script input file and as a frequency region with a frequency point separation in parenthesis in the text file input.

Resonant region

import numpy as np
import veloxchem as vlx

molecule = vlx.Molecule.read_molecule_string("""
C        0.67759997    0.00000000    0.00000000
C       -0.67759997    0.00000000    0.00000000
H        1.21655197    0.92414474    0.00000000
H        1.21655197   -0.92414474    0.00000000
H       -1.21655197   -0.92414474    0.00000000
H       -1.21655197    0.92414474    0.00000000
""")
basis = vlx.MolecularBasis.read(molecule, "def2-svpd")

scf_drv = vlx.ScfRestrictedDriver()

scf_drv.xcfun = "b3lyp"
scf_results = scf_drv.compute(molecule, basis)

crs = vlx.ComplexResponse()

# to be implemented (together with a plot function)
#crs.property = "polarizability"

crs.a_operator = "electric dipole"
crs.b_operator = "electric dipole"

crs.a_components = ["x"]
crs.b_components = ["x"]

crs.frequencies = np.arange(0.0, 0.4, 0.0025)

crs_results = crs.compute(molecule, basis, scf_results)
<Figure size 640x480 with 1 Axes>

Laser pulse propagation

VeloxChem allows for calculation of the linear response to a Gaussian-envelope pulse.

The time-domain shape parameters for this pulse may be specified by the user, optionally storing a collection of pertinent results in an HDF5-formatted file or a plain text ASCII file whose name may be specified by the user.

An example of an input file that when run will carry out such a calculation is given below. Note in particular that the default of carrier envelope phase may need adjustment to match your desired setup.

@jobs
task: pulses
@end

@method settings
basis: aug-cc-pvdz
@end

@molecule
charge: 0
multiplicity: 1
xyz:
...
@end

@pulses
envelope: gaussian
field_max : 1.0e-5
number_pulses: 1
centers: 300 
field_cutoff_ratio: 1e-5
frequency_range : 0.2-0.4(0.001)
carrier_frequencies: 0.325
pulse_widths: 50 
pol_dir: xyz
h5 : pulsed
ascii : pulsed
@end

If HDF5-formatted data was produced during this calculation, that data may used for plot generation using the script located at utils/pulsed_response_plot.py from the VeloxChem root folder.

Also note that other standard python modules such as matplotlib must be installed on the system from which this script is run. The script will take the HDF5-formatted data produced during the VeloxChem calculation and generate a plot of the real and imaginary frequency-domain electric dipole polarizability, a representation of the perturbing field in the frequency domain, the resulting (real-valued) first-order dipole moment correction in the time domain and a representation of the perturbing field in the time domain.

For more information and further description of how to run this script, please consult the documentation written inside it.

References
  1. Norman, P., Ruud, K., & Saue, T. (2018). Principles and practices of molecular properties. John Wiley & Sons, Ltd.
Properties
UV/vis absorption/emission
Properties
Optical activity and dichroism