Metadynamics is a powerful method for forcing a system to overcome energy barriers by depositing Gaussian bias potentials, preventing it from remaining trapped in local minima on the free energy landscape.
However, to perform efficient and accurate calculations, it is crucial to appropriately set parameters such as the height and width of the Gaussian functions and the bias factor. This article explains the rules of thumb and guidelines for parameter settings when executing Well-Tempered Metadynamics using PLUMED.
PLUMED Configuration Example
Metadynamics can be executed using the PLUMED METAD command. Below is an example of a command script to run Metadynamics in PLUMED.
# Unit settings (Length: Å, Energy: eV)
UNITS LENGTH=A ENERGY=eV
# CV definition (Interatomic distance) *Atom IDs start from 1
dist: DISTANCE ATOMS=1,2
# Wall potential (Distance upper limit 3.5Å)
uwall: UPPER_WALLS ARG=dist AT=3.5 KAPPA=15.0 EXP=2 EPS=1 OFFSET=0
# Metadynamics settings (300K, BIASFACTOR 80.0)
METAD ARG=dist SIGMA=0.2 HEIGHT=0.05 PACE=200 BIASFACTOR=80.0 TEMP=300.0 LABEL=metad FILE=output/HILLS
Point 1: Gaussian Height (HEIGHT)
This sets the initial height of the Gaussian potentials being deposited.
Recommended Value:
Generally, it is safe to start considering values around the scale of thermal fluctuations.
For example, at T=300K, kT ~ 0.6 kcal/mol ~ 0.025 eV, so values near this range are often used.
Adjustment Guidelines:
Since an excessively high Gaussian height can cause system instability due to abrupt changes in the bias potential, it is recommended to start with a small value near thermal fluctuations. However, if state transitions or reactions are slow to proceed, consider using a higher value to accelerate the accumulation of bias.
Point 2: Gaussian Width (SIGMA)
This sets the width of the Gaussian potentials being deposited.
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Recommended Value:
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Empirically, it is best to set this to approximately 5% to 10% of the fluctuation range that the Reaction Coordinate (Collective Variables: CV) can take.
(Example 1) When performing Metadynamics on an interatomic distance in the range of 1–5 Å, set the Gaussian width to 0.2 Å (5% of the range).
(Example 2) When using a CV with a range of 0–1, such as coordination number, set the Gaussian width to 0.05 (equivalent to 5% of the range).
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Caution:
If the Gaussian width is too large, fine features of the energy landscape may be flattened out, preventing the acquisition of an accurate Free Energy Surface (FES).
If the Gaussian width is too small, a massive number of calculation steps will be required to fill the energy landscape, reducing exploration efficiency.
Point 3: Bias Factor (BIASFACTOR)
Specifying a BIASFACTOR executes Well-Tempered Metadynamics. This method improves convergence by gradually decaying the height of the deposited Gaussians during the simulation. The BIASFACTOR (γ) controls how quickly the Gaussian height decays as bias accumulates.
Larger γ The decay of the Gaussian height is slower, making it easier to overcome high free energy barriers. However, as γ→∞, it becomes equivalent to standard Metadynamics; consequently, when γ is large, the energy surface tends to oscillate, making FES convergence criteria difficult to determine.
Smaller γ: The decay of the Gaussian height is faster, but simpler simulations may require longer runtimes to overcome free energy barriers.
Guideline for Setting BIASFACTOR
There is a relationship between the maximum free energy barrier you wish to overcome (ΔF_{max}), the temperature (T), and the bias factor (γ):
γ = (1 + ΔT/T) ≈ ΔF_{max} / (kT)
Therefore, you can estimate an appropriate γ value from the height of the barrier you intend to cross.
For example, if the maximum barrier is ΔF_{max} = 20 kcal/mol and the temperature is T= 300K (KT = 0.6 kcal/mol):
If you wish to take a safer approach, it is recommended to start with a value smaller than this estimate (e.g., γ = 10 ~ 15).
Point 4: Wall Potentials (UPPER_WALLS / LOWER_WALLS)
To execute Metadynamics efficiently, it is often effective to set wall potentials that limit the search range of the reaction coordinates.
Metadynamics is a method that raises the energy of "already explored locations" by stacking Gaussian functions, pushing the system into unknown regions. However, if there are no restrictions on the CV's range of motion—for example, in bond dissociation calculations—if the interatomic/molecular distance becomes too large, the number of possible configurations (entropy) increases drastically. This creates a problem where the system cannot return to the bonded state during the simulation.
To prevent this, setting UPPER_WALLS and LOWER_WALLS to confine the system within a range suitable for free energy exploration is highly effective.