Dear friend Manoj Wijesingha

The Computational Hydrogen Electrode model is a computational approach used in electrochemical studies to simulate reactions occurring at the electrode-electrolyte interface. It serves as a reference electrode in computational simulations, allowing the calculation of reaction energies and potential values relative to the hydrogen electrode.

In the CHE model, the hydrogen electrode is typically considered as a standard and defined to have a potential of 0 V. By using the CHE model, researchers can calculate and compare the thermodynamics and reaction energies of various electrochemical processes.

To obtain a free energy diagram using the CHE model, you would need to perform calculations using density functional theory (DFT) methods or other suitable computational approaches. These calculations involve considering the initial and final states of the reaction, calculating the energy differences, and determining the reaction barriers. The resulting energy profile can then be used to analyze the reaction mechanism and determine the thermodynamic feasibility of the process.

Hi Dr. Shandilya,

Thank you so much for your response and really appreciate it. Furthermore, to calculate Gibbs free energies of each intermediates for the free energy diagram, we can use this equation, G = E + ZPE - TS + U.

E is DFT energy of the calculation, and we can get ZPE from the frequency calculations. So my question is how we can get TS values and U values from the calculations in VASP ( for example; CO2 + 2(H+(plus) + e) ---> CO + H2O)?

Thank you.

Dear friend Manoj Wijesingha

To obtain the values of TS (entropy) and U (internal energy) for a reaction like CO2 + 2H+ + 2e- → CO + H2O using calculations in VASP, you would typically follow these steps:

1. Perform electronic structure calculations: Use VASP to perform electronic structure calculations (e.g., using density functional theory, DFT) to obtain the electronic energy (E) of each species involved in the reaction.

2. Calculate zero-point energy (ZPE): Perform frequency calculations on each species using VASP to obtain the vibrational frequencies. From these frequencies, you can calculate the zero-point energy (ZPE) contribution, which is typically computed as the sum of the energies of the individual harmonic oscillators. The ZPE is then added to the electronic energy (E) obtained in step 1.

3. Compute the entropic contribution (TS): To calculate the entropy (TS) contribution, you would need to consider the vibrational and configurational degrees of freedom. This involves accounting for the number of accessible states or configurations for each species at the given temperature. Obtaining accurate TS values often requires more advanced computational methods, such as including anharmonic effects or performing ab initio molecular dynamics simulations. The TS term is usually computed using statistical mechanics principles.

4. Determine the internal energy (U): The internal energy (U) term represents the total energy of the system, including contributions from electronic energy, vibrational energy (ZPE), and thermal energy (TS). You can obtain U by summing the electronic energy (E) and the ZPE (from step 2), and then subtracting the TS term.

It's important to note that calculating accurate values for TS and U can be challenging and often requires more advanced computational techniques beyond the standard DFT calculations. The specific method and level of theory used for the calculations may vary depending on the system and desired accuracy.

References:

Hi Dr. Shandilya,

Your explanation is great and understandable. Thank you for your detailed answers. According to my question, after vibrational frequency calculation, how we can grab the T*S value of OUTCAR (for example, entropy T*S EENTRO = -0.00332145, is this right)? For the frequency calculation, ISMEAR should be one or zero for non-metal system, for example graphene (on VASP it should be greater one for metal) and SIGMA=0.05?

Thanks.

Dear friend Manoj Wijesingha

In VASP, after performing the vibrational frequency calculation, you can obtain the T*S value (entropy contribution) from the OUTCAR file. However, it is important to note that VASP does not directly output the T*S value. Instead, you can calculate it using the vibrational frequencies and the standard entropy equation.

To calculate the entropy (T*S) contribution, you need to sum over all vibrational modes using the following equation:

T*S = R * ∑[ν * ln(ν/T)]

where:

- T is the temperature in Kelvin

- S is the entropy

- R is the gas constant (8.314 J/(mol·K))

- ν is the vibrational frequency in cm^-1

You will need to extract the vibrational frequencies from the OUTCAR file and perform the necessary calculations using the above equation to obtain the T*S value.

Regarding the ISMEAR and SIGMA parameters in VASP, these are related to the electronic structure calculations and may not directly affect the calculation of the entropy contribution. The ISMEAR parameter determines the smearing method for the electronic occupancies, while the SIGMA parameter sets the width of the smearing in eV. These parameters primarily influence the electronic convergence and should be chosen based on the specific system and desired level of accuracy for electronic properties.

For more detailed information and guidance on using VASP for vibrational frequency calculations, entropy calculations, and setting appropriate parameters, it is recommended to consult the VASP manual, which provides comprehensive documentation and examples on the usage of the software.

Hi Dr. Shandilya,

This is a very informative response, and really appreciate for your detailed answer. So, if we have imaginary frequencies (very low less than 20 cm-1), we should ignore these imaginary values to sum of all other frequencies (non-imaginary) for getting the vibrational frequency. Could you please provide a reference if you have for the equation, T*S = R * ∑[ν * ln(ν/T)].

Thank you.

Dear friend Manoj Wijesingha

The equation is derived from statistical mechanics and is commonly used to calculate the vibrational entropy of a system. It takes into account the vibrational frequencies of the different modes of motion in the system and calculates their contributions to the overall entropy.

Pathria, R. K., & Beale, P. D. (2011). Statistical Mechanics (3rd ed.).

McQuarrie, D. A., & Simon, J. D. (2005). Physical Chemistry: A Molecular Approach.

Kittel, C., & Kroemer, H. (1980). Thermal Physics (2nd ed.).

Hi Dr. Shandilya,

Thank you so much for your supporting details, and really appreciate it.

Hi Dr. Shandilya,

To calculate entropy and Gibbs free energy, can we use vaspkit after frequency calculation by VASP? Is this same method, you mentioned ? I have attached some examples they mentioned on vaspkit.

Thank you.