Adiabatic and Diabatic Potential Surfaces Calculator

Calculator Inputs

Reaction Coordinate q

Surface 1 Curvature A1

Surface 1 Center q1

Surface 1 Offset E1

Surface 2 Curvature A2

Surface 2 Center q2

Surface 2 Offset E2

Peak Coupling C

Coupling Decay Beta

Coupling Center qc

Calculate Surfaces Reset

Formula Used

The calculator uses a two-state diabatic Hamiltonian with a coordinate-dependent coupling term.

Diabatic Surface 1: V11(q) = A1(q - q1)² + E1

Diabatic Surface 2: V22(q) = A2(q - q2)² + E2

Coupling: V12(q) = C × exp[-Beta(q - qc)²]

Adiabatic Surfaces: E±(q) = (V11 + V22)/2 ± √{[(V11 - V22)/2]² + V12²}

Adiabatic Gap: Gap = E+(q) - E-(q)

Mixing Angle: Theta = 0.5 × atan2[2V12, V11 - V22]

State Weights on Lower Surface: cos²(Theta) and sin²(Theta)

How to Use This Calculator

1. Enter the reaction coordinate q where you want the energies.
2. Set curvature, center, and offset values for both diabatic surfaces.
3. Enter the peak coupling strength C.
4. Enter Beta to control how fast the coupling decays.
5. Enter qc to place the coupling maximum along the coordinate.
6. Click the calculate button.
7. Review the diabatic energies, adiabatic energies, gap, and mixing angle.
8. Use the CSV button for spreadsheet work and the PDF button for reports.

Example Data Table

Sample parameters used here: A1 = 1.2, q1 = -1.0, E1 = 0.1, A2 = 1.0, q2 = 1.0, E2 = 0.5, C = 0.30, Beta = 0.70, qc = 0.0.

Adiabatic and Diabatic Potential Surfaces in Physics

Adiabatic and diabatic potential surfaces describe energy changes during nuclear motion. They are basic tools in molecular physics, photochemistry, and quantum dynamics. These surfaces help researchers understand electronic structure changes during reactions, scattering events, and excited state processes.

Diabatic surfaces keep electronic character fixed as the coordinate changes. Adiabatic surfaces come from diagonalizing the coupled Hamiltonian. When diabatic states interact, the adiabatic surfaces avoid direct crossing. This repulsion creates the avoided crossing pattern seen in many physical systems.

This calculator models a two-state system with tunable parameters. You can control both diabatic wells, their offsets, and the coupling profile. The tool then computes the lower and upper adiabatic surfaces, the coupling term, the energy gap, and the mixing angle.

The energy gap is a key diagnostic. A small gap often means strong nonadiabatic effects are possible. The mixing angle also matters. It shows how much the lower adiabatic state borrows character from each diabatic state. Near strong interaction regions, the state composition can change quickly.

The model is useful for learning and rapid estimation. Students can see how a crossing shifts when offsets change. Analysts can inspect how coupling width changes the avoided crossing region. Larger coupling usually increases the minimum adiabatic gap. Different curvatures reshape wells and barriers.

These ideas appear in charge transfer, radiationless decay, vibronic coupling, and surface hopping studies. They also connect to Landau-Zener style transition analysis. While this page uses a one-dimensional reduced model, it still captures important physical intuition.

Use the example table to validate trends before testing your own values. Then calculate results for any chosen coordinate point. Export the output to CSV for further analysis. Download the PDF version for class notes, lab summaries, or technical documentation. This compact workflow makes repeated surface analysis faster and clearer.

Frequently Asked Questions

1. What is the difference between adiabatic and diabatic surfaces?

Diabatic surfaces keep electronic identity fixed as coordinates change. Adiabatic surfaces are the coupled eigenvalue surfaces. When interaction exists, adiabatic curves repel and create an avoided crossing.

2. Why does the calculator show an energy gap?

The energy gap measures the separation between the upper and lower adiabatic surfaces. It helps identify strong interaction regions and estimate where nonadiabatic transitions may become important.

3. What does the mixing angle mean?

The mixing angle shows how much the diabatic states blend into the adiabatic states. A larger angle means stronger state hybridization near the interaction region.

4. Why is the coupling term Gaussian here?

A Gaussian coupling is simple and practical. It creates a localized interaction region around a chosen coordinate and is often used for compact teaching models and fast parameter studies.

5. Can this tool represent avoided crossings?

Yes. If the diabatic surfaces approach each other and the coupling is nonzero, the adiabatic surfaces will separate instead of crossing directly. That is the avoided crossing behavior.

6. Is this calculator suitable for real molecular systems?

It is best for reduced models, teaching, and quick exploration. Real systems can need many coordinates, more states, and ab initio data, but this model still gives strong physical insight.

7. What happens if the coupling is set to zero?

If coupling becomes zero, the adiabatic and diabatic descriptions coincide at that coordinate. The surfaces can cross directly because no interaction remains to split them apart.

8. When should I export CSV or PDF results?

Export CSV when you want spreadsheet analysis, plotting, or record keeping. Export PDF when you need a clean report for classwork, documentation, or sharing results with others.