Calculating Interlayer Distance Using Quantum ESPRESSO

Analyze 2D Van der Waals heterostructures and multilayer systems with precision.

What is Calculating Interlayer Distance Using Quantum ESPRESSO?

Calculating interlayer distance using quantum espresso is a fundamental task for computational materials scientists working on 2D materials like graphene, transition metal dichalcogenides (TMDCs), and MXenes. In the context of Density Functional Theory (DFT), the interlayer distance refers to the physical gap separating two atomic sheets within a crystalline structure.

Who should use it? Researchers designing van der Waals (vdW) heterostructures or studying the exfoliation of bulk materials into monolayers. A common misconception is that the lattice parameter c is equivalent to the interlayer distance. In reality, c includes both the thickness of the atomic layer itself and the vacuum gap between them.

Calculating Interlayer Distance Using Quantum ESPRESSO Formula

The mathematical derivation for finding the gap between layers depends on how you define your unit cell in the pw.x input file. For a standard periodic system:

The formula is expressed as:

d = (C_total / N) – h

Variable	Meaning	Unit	Typical Range
C_total	Lattice parameter c	Angstrom (Å)	10 – 30 Å
N	Number of Layers	Integer	1 – 4
h	Atomic layer thickness	Angstrom (Å)	0 – 7 Å
d	Interlayer distance	Angstrom (Å)	2 – 5 Å

Mathematical Derivation

1. Obtain the optimized lattice vector in the z-direction from the vc-relax output.
2. Calculate the intrinsic thickness (h) by finding the difference between the maximum and minimum z-coordinates of atoms within a single layer.
3. Subtract this thickness from the vertical periodicity to find the void space.

Practical Examples (Real-World Use Cases)

Example 1: Bilayer Graphene Optimization

Suppose you are calculating interlayer distance using quantum espresso for a bilayer graphene system. Your CELL_PARAMETERS show c = 20.0 Å. Graphene has zero intrinsic thickness (atoms lie in one plane, so h = 0). Since there are 2 layers in the cell, the spacing between centers is 20/2 = 10.0 Å. If you find the physical distance between atoms of layer 1 and layer 2, that’s your d. Using the tool, you find a stable gap of 3.35 Å after adding vdW corrections.

Example 2: MoS2 Monolayer in Vacuum

For a monolayer of MoS2, c is often set to 15.0 Å to avoid periodic image interaction. The thickness h (S-to-S distance) is ~3.12 Å. The effective calculating interlayer distance using quantum espresso result here is the vacuum gap: 15.0 – 3.12 = 11.88 Å.

How to Use This Calculating Interlayer Distance Using Quantum ESPRESSO Calculator

• Step 1: Enter the c lattice parameter from your QE output file (found under “CELL_PARAMETERS” or “alat”).
• Step 2: Input the number of layers defined in your ATOMIC_POSITIONS.
• Step 3: Input the thickness of the layer. For flat graphene, this is 0. For MoS2, it’s the vertical distance between the two Sulfur planes.
• Step 4: Review the “Interlayer Distance” result to ensure your vacuum gap is sufficient (typically > 10 Å for isolated sheets).

Key Factors That Affect Calculating Interlayer Distance Using Quantum ESPRESSO Results

• Van der Waals (vdW) Corrections: Standard DFT (LDA/PBE) fails to capture long-range dispersion. Using vdw_corr = 'grimme-d3' or input_dft = 'vdw-df' is critical for accurate d values.
• K-point Sampling: While z-direction dispersion is low in 2D, a dense grid in the xy-plane affects the electronic density which subtly influences the optimal c.
• Pseudopotentials: Choice of PAW vs. NC pseudopotentials can change bond lengths and consequently the interlayer gap.
• Kinetic Energy Cutoff: Low cutoffs lead to “Pulay Stress,” causing the lattice to artificially contract or expand.
• Vacuum Size: In 2D systems, the vacuum must be large enough to prevent dipole interactions between periodic images.
• Relaxation Convergence: Ensure forc_conv_thr and etot_conv_thr are sufficiently small (e.g., 10^-4 or 10^-5) before measuring distance.

Frequently Asked Questions (FAQ)

1. Is interlayer distance the same as the lattice constant c?

No. In 2D materials, c is the total height of the unit cell, whereas the interlayer distance is the empty space between the surfaces of the layers.

2. Why does my d-spacing change with different functionals?

Functional choice (PBE vs. vdW-DF2) affects how the code models the weak attractive forces between sheets, which directly dictates the equilibrium distance.

3. How much vacuum should I use?

Generally, 12-15 Å of vacuum is sufficient to eliminate periodic interaction in calculating interlayer distance using quantum espresso.

4. Can this tool handle heterostructures?

Yes, by averaging the thickness of the two different layers and using the total cell height.

5. What is the experimental interlayer distance of graphene?

The experimental value for graphite (which translates to bilayer graphene) is approximately 3.35 Å.

6. How do I get the coordinates from QE?

Check the “ATOMIC_POSITIONS” section in the final pw.x output after a vc-relax calculation.

7. Does temperature affect these calculations?

Standard Quantum ESPRESSO calculations are at 0K. Thermal expansion requires ab-initio molecular dynamics (AIMD).

8. What units should I use?

Quantum ESPRESSO uses Bohr by default or Angstrom if specified. Our calculator uses Angstroms (Å).