Morse Potential Calculator

Model interatomic energy curves with adjustable bond parameters. See force trends near equilibrium and dissociation. Use export tools, examples, and steps for reliable analysis.

Enter Morse Potential Values

Reset

Example Data Table

De (eV) a (1/Å) re (Å) r (Å) Reference V(r) (eV) F(r) (eV/Å)
4.75 1.85 1.27 1.15 Shifted -4.4565 5.4546
4.75 1.85 1.27 1.27 Shifted -4.7500 0.0000
4.75 1.85 1.27 1.40 Shifted -4.5329 -2.9538

These rows show compression, equilibrium, and extension around the same molecular bond.

Formula Used

Morse potential models molecular bond energy with an anharmonic curve.

Shifted form: V(r) = De(1 - e-a(r-re))2 - De

Unshifted form: V(r) = De(1 - e-a(r-re))2

Force: F(r) = -2Dea e-a(r-re)(1 - e-a(r-re))

Equilibrium stiffness: ke = 2Dea2

Harmonic estimate near equilibrium: Vharm(r) = 0.5ke(r-re)2 with the selected reference offset.

Here, De is bond dissociation energy, a controls curve width, re is equilibrium distance, and r is the evaluated separation.

How to Use This Calculator

  1. Enter the bond dissociation energy De.
  2. Enter the range parameter a for the bond.
  3. Enter the equilibrium distance re.
  4. Enter the actual bond distance r you want to test.
  5. Select energy, distance, and inverse distance units.
  6. Choose shifted or unshifted potential reference.
  7. Set the number of decimal places.
  8. Press Calculate to see results above the form.
  9. Use the CSV or PDF button to download the current result.

About the Morse Potential Calculator

Why this model matters

The Morse potential calculator helps you estimate bond energy at any internuclear separation. It is useful in physics, physical chemistry, spectroscopy, and molecular modeling. Unlike a simple harmonic model, the Morse function captures bond stretching more realistically. It allows the curve to flatten as the atoms move apart. That makes it better for studying dissociation behavior.

What the calculator returns

This calculator computes the Morse potential energy, force, displacement, dimensionless coordinate, and a harmonic estimate near equilibrium. It also reports the effective stiffness at the minimum of the well. These values help you inspect attractive and repulsive regions in a bond energy curve. Positive force indicates short-range repulsion. Negative force shows attraction during bond extension.

Inputs used in the model

The key inputs are the bond dissociation energy De, range parameter a, equilibrium bond length re, and evaluation distance r. You can work in eV, joules, kJ/mol, or kcal/mol. Distance units include angstroms, nanometers, picometers, and meters. That flexibility is helpful when you move between laboratory data, textbooks, and simulation results.

When to use shifted or unshifted forms

The shifted form places zero energy at dissociation. This is common in molecular physics. The unshifted form places the well minimum at zero. Both versions describe the same curve shape. The difference is only the energy reference level. Choose the format that matches your notes, research source, or classroom convention.

Best practices for interpretation

Check that your energy and distance units stay consistent. The range parameter must match the selected inverse distance unit. Near r = re, the curve behaves almost harmonically. Far from equilibrium, anharmonic behavior becomes important. That is where the Morse model adds value. Use the example table, formulas, and export tools to document each calculation clearly.

FAQs

1. What does the Morse potential describe?

It describes the potential energy of a diatomic bond as atoms move closer or farther apart. It captures repulsion, equilibrium, and dissociation more realistically than a purely harmonic spring model.

2. Why is the Morse model better than a harmonic oscillator?

A harmonic oscillator stays symmetric and never dissociates. The Morse model becomes flatter at large separation, so it better represents real molecular bonds and vibrational anharmonicity.

3. What is De in this calculator?

De is the bond dissociation energy. It controls the depth of the potential well and sets the energy scale for the molecular interaction.

4. What does the range parameter a control?

The parameter a controls how quickly the curve rises and falls around equilibrium. Larger values create a narrower well. Smaller values produce a broader interaction region.

5. Why can the force be positive or negative?

The sign shows direction. Positive values indicate repulsion at short distances. Negative values indicate attraction when the bond is stretched beyond equilibrium.

6. Should I choose shifted or unshifted potential?

Choose shifted when you want zero energy at dissociation. Choose unshifted when your source defines the minimum energy as zero. The physical shape stays the same.

7. Can I use different unit systems?

Yes. The calculator supports multiple energy, distance, and inverse distance units. Just keep the selected range parameter unit consistent with the chosen distance scale.

8. What is the harmonic estimate useful for?

It gives a local approximation near equilibrium. This is useful when you want a quick comparison between anharmonic Morse behavior and the simpler quadratic spring model.

Related Calculators

center of mass calculatorbond energy calculatorbond angle calculatorchemical shift calculatorbond length calculatorelectron transfer calculatorforce constant calculatorelectrostatic energy calculatorplanck relation calculatorabsorbance concentration calculator

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.