JDFTx: Partial Vibrational Frequencies For Adsorbates

Calculating vibrational frequencies for a molecule adsorbed on a surface, while keeping the substrate atoms fixed, is a common task in computational materials science. This article addresses how to achieve this in JDFTx, similar to the Selective Dynamics functionality in VASP (IBRION=5).

The Challenge: Freezing Substrate Atoms During Vibrational Calculations

The goal is to calculate the vibrational modes of an adsorbate (e.g., CO) on a surface, such as a metal or semiconductor. To simplify the calculation and focus on the adsorbate's vibrations, one wants to keep the substrate atoms fixed in place. The user initially attempted to use the move_flag in the input file to achieve this, but encountered issues.

Initial Attempt and the Problem

The user's initial approach involved setting the move_flag to 0 for all substrate atoms within the JDFTx input file. This was intended to prevent these atoms from moving during the vibrational calculation. Here’s an example of the attempted input:

# --- My Attempt ---

# Substrate atoms
ion Si 0.0 0.0 0.0  0  # Attempting to fix
ion Si 0.5 0.5 0.0  0  # Attempting to fix
... (many more substrate atoms) ...

# Adsorbate atoms
ion C  0.1 0.1 0.5  1  # Allowed to move
ion O  0.1 0.1 0.6  1  # Allowed to move

# Then in my vibrations.in, I call:
vibrations \
    dr 0.01 \
    centralDiff yes

However, upon running the vibrations calculation, JDFTx appeared to ignore the move_flag = 0 setting. The log file indicated that the calculation was attempting to displace all atoms, including those that were intended to be fixed. This discrepancy raises the question of whether the vibrations command is designed to recognize and respect the move_flag set by the ion command.

Understanding the move_flag and Vibrational Calculations

It seems the direct use of move_flag as intended in the initial attempt doesn't directly translate to fixing atoms during vibrational calculations in JDFTx. The move_flag is more relevant for structural relaxation or molecular dynamics simulations, where it dictates which atoms are allowed to move during the optimization process. In vibrational calculations, a different approach is needed to constrain the movement of specific atoms.

Is move_flag Supported in Vibrations?

Based on the user's experience, the vibrations command in JDFTx does not inherently recognize or obey the move_flag set by the ion command. This means that simply setting move_flag = 0 for substrate atoms will not prevent them from being displaced during the vibrational calculation.

The Correct Method: Constraining Atoms in JDFTx Vibrational Calculations

So, what is the correct approach to calculate vibrations for only a subset of atoms (i.e., the adsorbate) in JDFTx? There are a couple of strategies you might employ, depending on the level of control you need and the capabilities of JDFTx.

1. Using Constraints or Masks (If Available)

Some DFT codes provide direct ways to apply constraints or masks during vibrational calculations. These constraints explicitly remove the degrees of freedom associated with the fixed atoms. Examine the JDFTx documentation for options like constraints, fix_atoms, or similar keywords within the vibrations command or the broader input structure. If JDFTx supports such a feature, it would be the most straightforward method.

For example, you might find a syntax like this (this is illustrative and may not be the actual JDFTx syntax):

vibrations \
    dr 0.01 \
    centralDiff yes \
    fix_atoms Si  # Fix all atoms with element Si

Or, alternatively, a more general constraint mechanism:

vibrations \
    dr 0.01 \
    centralDiff yes \
    constraints "atom_index < N_adsorbate" # N_adsorbate = number of adsorbate atoms

2. Modifying the Dynamical Matrix (Advanced)

If JDFTx doesn't offer direct constraint options, a more advanced approach involves manually modifying the dynamical matrix after it's calculated. The dynamical matrix contains the second derivatives of the energy with respect to atomic displacements. By setting the rows and columns corresponding to the fixed atoms to zero, you effectively remove their contribution to the vibrational modes.

Here’s a conceptual outline:

1. Perform a vibrational calculation without constraints: Calculate the full dynamical matrix for all atoms.
2. Extract the dynamical matrix: Access the calculated dynamical matrix from the JDFTx output files or using post-processing tools.
3. Modify the matrix: Set the rows and columns corresponding to the fixed substrate atoms to zero. This enforces that these atoms experience no forces and do not contribute to the vibrational modes.
4. Diagonalize the modified matrix: Diagonalize the modified dynamical matrix to obtain the vibrational frequencies and modes for the adsorbate only.

This approach requires more scripting and post-processing, as it is not a built-in feature of JDFTx. It also demands a good understanding of the underlying theory of vibrational calculations and the structure of the dynamical matrix.

3. Supercell Approach with Large Substrate

An alternative, though computationally more expensive, method involves using a very large supercell for the substrate. By making the substrate sufficiently large, the impact of its vibrations on the adsorbate's vibrational modes becomes negligible. In this case, you can perform a standard vibrational calculation on the entire system (adsorbate + large substrate) without explicitly fixing any atoms. The modes primarily localized on the adsorbate will then approximate the desired partial vibrational frequencies.

This approach relies on the assumption that the coupling between the adsorbate and the substrate vibrations is weak, which is often valid for well-defined adsorption systems.

Important Considerations

• Accuracy: The accuracy of the calculated vibrational frequencies depends on the quality of the DFT calculation, the size of the supercell (if used), and the convergence of the force calculations.
• Computational Cost: Vibrational calculations can be computationally demanding, especially for large systems. Constraining the number of vibrating atoms can significantly reduce the computational cost.
• Symmetry: Exploiting the symmetry of the system can also help to reduce the computational cost and simplify the analysis of the vibrational modes.

Conclusion

Calculating partial vibrational frequencies for adsorbates in JDFTx requires a different approach than simply using the move_flag. You must explore the possibility of using constraints or masks within JDFTx (if available). Alternatively, manually modifying the dynamical matrix or using a large supercell might be viable options. Always refer to the JDFTx documentation for the most accurate and up-to-date information on available features and best practices. By using above techniques you can improve your partial vibrational frequencies calculations for adsorbates using JDFTx.

For more information on vibrational spectroscopy and computational methods, check out resources like this page on vibrational modes from LibreTexts. It may contain useful context and complementary information.