CD and CPL for spin-forbidden electronic transitions¶

Relatively cheap settings¶

As the settings that are used in the paper will lead to a long calculation, first a gas phase PBE calculation will be performed with a DZ frozen core basis set, using spin-orbit coupled TD-DFT with TDA to calculate rotatory strengths. This is a relatively cheap calculation and thus does not take so long.

Use the Main panel

XC functional → GGA → PBE

Relativity → Spin-Orbit

Use the panel bar Properties → Excitations (UV/Vis), CD

Type of excitation → Spin-Orbit (SCF)

Check the ‘TDA’ checkbox

Enter 3 for the ‘Number of excitations`

Check the calculate ‘Rotatory strengths (CD)’ checkbox

We are now ready to run the calculation.

Save your input as P-3c_pbe_dz using File → Save As….

Run the calculation with File → Run.

Wait for the calculation to finish.

Open → Output

In AMSoutput, search for “Rotatory Strengths”

In AMSoutput, search for “lifetime”

The calculated results are quite sensitive to small numerical changes, since we are looking at a small effect.

The averaged dissymmetry factor for the emission can be computed using rotatory and dipole strengths that are Boltzmann-averaged over the triplet components:

In this case the energy of the triplet components are very close (1.75762, 1.75808, and 1.75866 eV), thus we will use

Also the averaged radiative lifetime can be computed using lifetimes that are Boltzmann-averaged over the triplet components:

In this case we will use again that the energy of the triplet components are very close, thus we will use

Note that here no refractive index of a solvent is included, as this is a gas phase calculation.

#!/usr/bin/env amspython
import numpy as np
from scm.plams import Units


def get_values():
    E_eV = np.array([1.7576, 1.7581, 1.7587])
    D = np.array([4.6005, 26.599, 196.61])
    R = np.array([-0.34615e-1, -0.35678e-1, 0.10183])
    tau = np.array([0.2433e-2, 0.4205e-3, 0.5683e-4])
    refractive_index = 1
    return E_eV, R, D, tau, refractive_index


def main():
    E_eV, R, D, tau, refractive_index = get_values()

    use_boltzmann_weights = False

    if use_boltzmann_weights:
        weights = calc_boltzmann_weights(E_eV, T=298)
    else:
        weights = np.ones(np.shape(E_eV))

    g = 4 * np.dot(R, weights) / np.dot(D, weights)
    print(f"g_lum_av: {g:.3e}")

    tau_av = 1.0 / refractive_index**2 * np.sum(weights) / np.dot(1.0 / tau, weights)
    print(f"tau_av: {tau_av:.3e} s")


def calc_boltzmann_weights(E_eV, T=298):
    k_B = Units.constants["k_B"] * Units.convert(1, "J", "eV")  # eV/K
    boltzmann_weights = np.exp(-(E_eV - np.min(E_eV)) / (k_B * T))
    return boltzmann_weights


if __name__ == "__main__":
    main()

Settings as in the paper¶

Next we will try to use the same settings as are used in Ref. 1: spin-orbit coupled TD-DFT with TDA to calculate rotatory strengths, the hybrid PBE0 XC functional, full XC kernel, a TZ2P basis all electron basis set on Pt, DZ all electron on H, and DZP all electron on all other elements, dichloromethane as COSMO solvent, and numerical quality good. This is a much more demanding calculation than with the previous settings.

Use the Main panel

XC functional → Hybrid → PBE0

Relativity → Spin-Orbit

Basis set → DZP

Frozen Core → None

Numerical Quality → Good

Use the panel bar Properties → Excitations (UV/Vis), CD

Type of excitation → Spin-Orbit (SCF)

Check the ‘TDA’ checkbox

Enter 3 for the ‘Number of excitations’

Check the calculate ‘Rotatory strengths (CD)’ checkbox

We are now ready to run the calculation. As this may take several hours on a cluster, and maybe even longer on a desktop, one could also skip the calculation, and directly look at the results below.

The averaged dissymmetry factor for the emission can be computed using rotatory and dipole strengths that are Boltzmann-averaged over the triplet components. In this case the energy of the triplet components are very close (1.79177, 1.79194, and 1.79222 eV), thus we will use

Also the averaged radiative lifetime is calculated without using Boltzmann factors as

where \(n=1.42\) is the refractive index of the dichloromethane solvent used in the measurements. For comparison, experimental data reported in Ref. 1 for P-3 c are 1.93 eV for the transition energy, a phosphorescence lifetime of 21 \(\mu s\), and a \(g_{lum}\) of 3 10^-3, see also the discussion of the results in the paper.

1(1,2,3,4)

H.D. Ludowieg, M. Srebro-Hooper, J. Crassous, J. Autschbach, Optical Activity of Spin-Forbidden Electronic Transitions in Metal Complexes from Time-Dependent Density Functional Theory with Spin-Orbit Coupling, ChemistryOpen 2022, 11, e202200020