[QE-users] ZERO-POINT ENERGY IN QUANTUM ESPRESSO

Kazume NISHIDATE nisidate at iwate-u.ac.jp
Tue Aug 12 15:14:46 CEST 2025 

And I asked it to Gemini, Google’s AI.
Here is her response 😲

=========================

Yes, it's possible to include the zero-point energy (ZPE) correction for both a 2D surface and a 2D surface with adsorbed atoms using Quantum ESPRESSO. This correction is crucial for accurately calculating energies, such as adsorption energies, as it accounts for the vibrational energy of the atoms even at absolute zero temperature (0 K).

To calculate the ZPE correction, you must perform phonon calculations for your systems. Quantum ESPRESSO's phonon code, ph.x, is the primary tool for this. The ZPE is half the sum of all vibrational frequencies, represented by the following formula:
ZPE=21​i∑​ℏωi​
Where:
    • ℏ is the reduced Planck constant.
    • ωi​ are the vibrational frequencies (eigenfrequencies) of the system's normal modes.

1. Zero-Point Energy Correction for a 2D Surface
    To calculate the ZPE for a 2D surface, you'll follow these general steps:
    • Optimize the geometry of your 2D surface slab to find the lowest-energy configuration.
    • Run a self-consistent field (SCF) calculation on the optimized structure. This calculation is a prerequisite for the phonon calculation.

    • Perform a phonon calculation using ph.x. This involves calculating the vibrational modes across a q-point grid in the Brillouin zone. The output will be the phonon frequencies.
    • Process the phonon output to get the total ZPE. This often involves using a post-processing tool like matdyn.x to diagonalize the dynamical matrices and sum up the positive frequencies. The ZPE is then calculated from this sum.

For a 2D surface, it's important to use a supercell that is large enough to minimize the interactions between periodic images and to ensure a sufficient vacuum layer in the z-direction.

2. ZPE Correction for an Adsorbed System

For a system with an adsorbed molecule on a 2D surface, the process is similar but with an important distinction: you need to calculate the ZPE correction for three separate systems to determine the corrected adsorption energy.

The ZPE-corrected adsorption energy (ΔEadsZPE​) is calculated as follows:

ΔEadsZPE​=(Eslab+adsorbateDFT​+ZPEslab+adsorbate​)−(EslabDFT​+ZPEslab​)−(EadsorbateDFT​+ZPEadsorbate​)

Where:
    • EDFT is the ground-state electronic energy from a standard DFT calculation (e.g., using pw.x).

    • ZPE is the zero-point energy of each system.
To get the ZPEs, you'll perform a phonon calculation for each of the three components:

    • Adsorbed System (Slab + Adsorbate):
        • Optimize the geometry of the combined system.
        • Run an SCF calculation.
        • Run a phonon calculation using ph.x. To save computational time, you can often freeze the atoms of the bulk surface layers and only allow the adsorbate atoms and the top surface layer atoms to move. This is a common approximation.
        • Calculate the ZPE from the phonon frequencies.
    • Isolated Surface (Slab):
        • Optimize the geometry of the clean surface slab.
        • Run an SCF calculation.
        • Run a phonon calculation. Again, you can freeze the bottom layers to reduce the computational cost.
        • Calculate the ZPE.
    • Isolated Adsorbate (Molecule):
        • Optimize the geometry of the isolated molecule in a large vacuum cell.
        • Run an SCF calculation.
        • Run a phonon calculation. For a molecule, all atoms are allowed to move.
        • Calculate the ZPE from the frequencies.

After obtaining the ZPE values for all three systems, you can substitute them into the equation to get the final ZPE-corrected adsorption energy.



> 2025/08/12 17:28、Chiara Cignarella via users <users at lists.quantum-espresso.org>のメール:
> 
> Dear Ashley,
> 
> You can use the frequencies obtained by phonon calculations to compute the zero-point energy using the formula (you can find that in textbooks on the quantum harmonic oscillator part - for example Ashcroft pag. 451- ), i.e. doing the sum  \sum_i 1/2 * \omega_i * hbar (divided by appropriate normalization factor for your sum)
> 
> Note that the computed phonons do not contain themselves the ZPM contributions!
> 
> 
> Hope this is useful.
> 
> 
> Best regards,
> 
> Chiara Cignarella
> -------------------------------------
> Post-doc researcher
> University of Bremen
> 
>> On 12 Aug 2025, at 09:51, Barsha Pal <barsha.pal at aus.ac.in> wrote:
>> 
>> Hello, 
>> I have a small doubt regarding whether or not zero-point energy calculation is possible in Quantum Espresso, I want to perform that for a 2D material and adsorption cases. The property that I aim, includes the zero-point energy correction for the 2D surface and the 2D surface with adsorbed atoms. AI tells me that it is possible to do by phonon calculation. If indeed this is possible, can you guide me towards a short example? 
>> 
>> Thank you.
>> Ashley Cooper
>> Phd
>> _______________________________________________________________________________
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西館数芽
Kazume NISHIDATE Ph.D

Department of Systems Innovation Engineering,
Graduate School of Science and Engineering, Iwate University
4-3-5 Ueda, Morioka, Iwate, 020-8551 JAPAN
Phone:+81-19-621-6391
kazume.nishidate at gmail.com, nisidate at iwate-u.ac.jp
https://sites.google.com/site/nisidatelab/

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