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# Computation of HOMO/LUMO-level, EA, IP, Redox Potential, Electrical Conductivity

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### Introduction of HOMO/LUMO-level

The orbit with the highest energy level of the occupied electron is called the highest occupied molecular orbit, and is represented by HOMO. The orbit with the lowest energy level of the unoccupied electrons is called the lowest unoccupied molecular orbit and is denoted by LUMO. HOMO and LUMO are collectively referred to as the front-line orbit, and the electrons on the front-line orbit are called the front-line electrons.

### Introduction of Ionization Potential (IP)

IP usually refers to the first ionization potential, which is the energy change (also called ionization energy) when a neutral atom or molecule in a gaseous state loses an electron and becomes a +1 valence ion. There are two types of ionization potential: Vertical ionization potential (VIP) and adiabatic ionization potential (AIP). IP can be defined as:

IP = E[N-1]-E[N]

Where E[N-1] is the electron energy in the ground state of a +1 valence ion, E[N]) is the electron energy in the ground state of a neutral atom or molecule, and N is the total number of electrons in the system. When the ionization potential value is positive, it indicates that the neutral molecule loses an electron and needs to absorb energy. Figure 1. Frontier molecular orbitals of ImTPh. (Masoome,S.; et al. 2014)

### Introduction of Electron Affinity (EA)

EA refers to the first affinity, which is the energy change when a neutral atom or molecule in a gaseous state gets an electron and becomes a -1 valence ion. There are also two kinds of affinity: Vertical electron affinity (VEA) and adiabatic electron affinity (AEA). EA is defined as:

EA = E[N]-E[N+1]

Where E[N+1] is the electron energy in the ground state of -1 valent ion, E[N] is the electron energy in the ground state of a neutral atom or molecule, and N is the total number of electrons in the system. When the affinity value is positive, it indicates that the neutral molecule will release energy when it gains an electron.

### Redox Potentials

The redox potential reflects the macroscopic redox performance of all substances in the aqueous solution. The higher the redox potential, the stronger the oxidation. The lower the redox potential, the stronger the reduction. A positive potential means that the solution shows a certain degree of oxidation, and a negative potential means that the solution shows a certain degree of reducibility. Calculating the redox potential of chemicals plays an essential role in understanding and predicting the electrochemistry of the chemical reaction.

### Electrical Conductivity

Electrical conductivity is the most important basic property of electronic materials such as conductors and semiconductors. Our calculations of electrical conductivity only start from the structure of the material and do not rely on empirical parameters.

### HOMO/LUMO-level Calculation

We apply self-consistent field calculation using Hartree Fock approximation to perform HOMO/LUMO-level calculation:

1. First, diagonalize the Hamiltonian under the average field approximation to obtain a series of energy levels and corresponding molecular orbitals.

2. Then, fill the electrons of the system from the lowest energy level (the Hartree Fock ground state) upwards.

3. Finally, the highest occupied molecular orbital and the lowest non-occupied molecular orbital can be obtained.

### IP and EA Calculation

At Alfa Chemistry, we have developed a mature process for the calculation of VIP, AIP, VEA and AEA.

• Steps to calculate the VIP and VEA:

1) First, optimize the structure of the neutral molecule.
2) Based on the neutral molecular structure, the same basis used in density functional theory (DFT) method is used to calculate the single-point energy of +1 valent ions (for calculating VIP) or -1 valent ions (for calculating VEA).
3) The energy is subtracted according to the formula of IP or EA.

• Steps to calculate AIP and AEA:

1) First, optimize the structure of the neutral molecule.
2) Optimize the structure of the neutral molecule and the corresponding +1-valent ion (for calculating AIP) or -1 valent ion (for calculating AEA).
3) Perform frequency analysis.

• The energy is subtracted according to the formula of AIP or AEA. Figure 2. The variation of ionization potential (IP) and electron affinity (EA) with respect to thickness is shown for surface unit cells with and without pseudohydrogens (-wPH). (Gupta, S. S.; et al. 2019)

### Redox Potentials Calculation

At Alfa Chemistry, a DFT-based molecular dynamics protocol for the calculation of redox potentials of metal complexes is developed. The redox potentials are calculated in terms of Gibbs free energy change of the redox reaction at the theory level of CAM-B3LYP/6-31+G(d,p)/SMD. In addition, the calculated Gibbs free energy change of solvation is corrected by a unified correction factor as the second-layer Gibbs free energy change of solvation and other interactions for each redox reaction.

### Electrical Calculation

• Neural network analysis

We have developed a neural network computation to estimate several kinds of physicochemical properties of molten slag. Alfa Chemistry supports the neural network calculation for estimating the electrical conductivity of molten slag composed of SiO2, CaO, MgO, MnO, Al2O3, FeO, Fe2O3, and Na2O.

• Ab initio molecular dynamics (AIMD) and DFT

Our teams have combined DFT and AIMD to effectively predict the transmission and diffusion of metal ions in the material, thereby predicting the electrical conductivity.

### Our Capabilities

• We can also plot the electron density distribution of molecular orbitals in real space.
• Our experts can use various basis and methods such as apfd/6-311+G(d,p), m062x and wb97xd in the DFT calculation.

Our computation of HOMO/LUMO-level, EA, IP, redox potential, electrical conductivity services remarkably reduce the cost, promote further experiments, and enhance the understanding of chemical process for customers worldwide. Our personalized and all-around services will satisfy your innovative study demands. If you are interested in our services, please don't hesitate to contact us. We are glad to cooperate with you and witness your success!

References

• Masoome,S.; et al. Dft Study on 4(5)-Imidazole-Carbaldehyde-N(5)-Phenylthiosemicarbazone (Imtph): Nmr Shielding Tensors, Thermodynamic Parameters, Nbo Analysis, Molecular Electrostatic Potential (Mep), Homo and Lumo Studies. Oriental Journal of Chemistry. 2014, 30(1): 345-350.
• Gupta, S. S.; et al. Strained epitaxial interfaces of metal (Pd, Pt, Au) overlayers on nonpolar CdS (1010 ) surfaces from first-principles. Journal of Physics: Condensed Matter. 2019, 31(50). Company
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