IP/EA Estimator

Properties

Notes

Ionization Potential (IP) and Electron Affinity (EA) in solid-state

recommended

Workflow

We make the estimation of the solid-state IP/EA of the embedded molecules using:

\[ \begin{align}\begin{aligned}IP = IP_{GW}^{vac} - P^+_{DFT}\\EA = EA_{GW}^{vac} + P^-_{DFT}\end{aligned}\end{align} \]

where:

  • \(IP_{GW}^{vac}\) and \(EA_{GW}^{vac}\) are the negative of GW HOMO and LUMO.

  • \(P^{+}_{DFT}\) and \(P^-_{DFT}\) is the DFT-level polarization energies.

Below, more details are given on how every of these quantities is computed in practice.

Polarization Energies

Polarization energies are derived from gas-phase (vacuum) \(IP^{vac}_{DFT}\)/\(EA^{vac}_{DFT}\) and COSMO calculations. The latter serve as the estimation for the solid-state IP and EA, referred to as \(IP_{COSMO}\) and \(EA_{COSMO}\). The difference between both are polarization energies at a DFT level:

\[P^{+}_{DFT} = IP_{DFT}^{vac} - IP_{DFT}^{COSMO}\]
\[P^{-}_{DFT} = EA_{DFT}^{COSMO} - EA_{DFT}^{vac}\]

The mentioned \(IP_{DFT}^{vac/COSMO}/EA_{DFT}^{vac/COSMO}\) are computed as the difference between the cation/anion energy and the neutral molecule energy in vacuum or implicit solvent (COSMO model), respectively:

\[\text{IP} = E_{\text{cation}} - E_{\text{neutral}}\]
\[\text{EA} = E_{\text{neutral}} - E_{\text{anion}}\]

In these last formulas we omitted indices (\(^{vac/COSMO}\) and \(_{DFT}\)) for brevity.

Vacuum IP and EA from GW Calculations

\(IP_{GW}^{vac}\) and \(EA_{GW}^{vac}\) are computed from many-body perturbation theory using the \(G_0W_0\) approximation on top of PBE0 (i.e., \(G_0W_0\) @ \(\text{PBE0}\)). \(G_0W_0\) slow basis set convergence is a well-known. We thus first perform calculations using two correlation-consistent basis sets:

  • aug-cc-pVDZ (DZ)

  • aug-cc-pVTZ (TZ),

and then extrapolate it to the complete basis set (CBS) limit using the cardinal number \(N\), assuming a convergence behavior of:

\[E(\infty) = E(N) - \frac{A}{N^3},\]

where:

  • \(E(N)\) is the computed IP or EA using the basis set of cardinal number \(N\),

  • \(E(\infty)\) is the extrapolated energy at the CBS limit,

  • \(A\) is a constant that is determined along with \(E(\infty)\) because \(E(N)\) is known for two different \(N\), in our case 2(DZ) and 3(DZ).

IP/EA Estimator Workflow Overview

Nanomatch Software

Scientific Role

Illustration

Parametrizer
Ground State
Geometry optimization
 ../../_images/parametrizer.png

Parametrizer
IP in vacuum (DFT)
 ../../_images/Parametrizer3.png

Parametrizer
EA in vacuum (DFT)
 ../../_images/Parametrizer3.png

Parametrizer
IP in medium (COSMO)
 ../../_images/Parametrizer3.png

Parametrizer
EA in medium (COSMO)
 ../../_images/Parametrizer3.png

Parametrizer
HOMO and LUMO (GW)
 ../../_images/Parametrizer3.png

IP/EA Analysis
Compute IP and EA as:
\(\mathrm{IP} = -\mathrm{HOMO}_\mathrm{GW} - P^+_\mathrm{DFT}\)
\(\mathrm{EA} = -\mathrm{LUMO}_\mathrm{GW} + P^-_\mathrm{DFT}\)
 ../../_images/StokesShiftAnalysis.png

Implemented Scientific Methods

Step

Method

Ground-State Geometry Optimization

DFT, B3LYP/def2-SVP

DFT Single Point Calculations (vacuum / COSMO)

DFT, BP86/def2-SVPD

GW Calculations in complete basis set limit

G₀W₀@PBE0/(aug-cc-pVDZ, aug-cc-pVTZ)

Software:

Output

Displayed Results

The data below will be displayed as the workflow ends (backend name: result.yml):

QLQHAHDIYGVQJO-UHFFFAOYSA-N:
  EA:
    results:
      EA in eV: 2.5607947915471554
      LUMO_vacuum in eV: -1.6542377032731708
      P_minus in eV: 0.9065570882739848
    value: 2.5607947915471554
  IP:
    results:
      HOMO_vacuum in eV: -6.784890425832648
      IP in eV: 5.928143563226561
      P_plus in eV: 0.8567468626060872
    value: 5.928143563226561

Here, not only computed estimated solid-state EA/IP estimators are saved (EA/IP), but also the quantities used to calculate them:

  • EA/IP are the solid-state values of the IP and EA.

  • P_plus and P_minus are cation and anion polarization energies, respectively.

  • HOMO_vacuum and LUMO_vacuum are computed in vacuum with GW method.

Files

In addition to parsed output, the following file are available upon the workflow completion:

No.

File

Description

1

Molecule_opt.mol2

Ground State geometry in MOL2 format

Benchmark

Benchmark set:

../../_images/4.png

Molecule Names:

  1. NPD

  2. BFDPB

  3. BPAPF

  4. TCTA

Verification

We compare the polarization energies \(P+\) computed with this calculator to the values computed using explicit solvent model, QuantumPatch [1] as shown below:

../../_images/benchmark.png

The deviation between the reference (QuantumPatch) and the given method does not exceed 50 meV.

References