Solve molecular orbital energies for bonded atomic interactions. View coefficients, splitting, occupancy, and bond order. Export clean results as CSV or PDF after calculation.
| Pair | AO Energy A | AO Energy B | β | S | Electrons | Bonding MO | Antibonding MO | Gap | Bond Order |
|---|---|---|---|---|---|---|---|---|---|
| AB Diatomic | -13.6 eV | -11.2 eV | -2.4 eV | 0.20 | 2 | -13.644243 eV | -11.189090 eV | 2.455153 eV | 1.0000 |
This calculator uses a two state linear combination of atomic orbitals model. The Hamiltonian and overlap matrices are reduced to a 2 × 2 secular equation.
Secular determinant: |H - ES| = 0
With H11 = εA, H22 = εB, H12 = β, and overlap S12 = S, the energy equation becomes:
(1 - S²)E² + (2βS - εA - εB)E + (εAεB - β²) = 0
The lower root is treated as the bonding molecular orbital energy. The higher root is treated as the antibonding molecular orbital energy.
The coefficient ratio is estimated from (εA - E)cA + (β - ES)cB = 0. For quick interpretation, coefficients are normalized so cA² + cB² = 1.
Energy gap: ΔE = Eantibonding - Ebonding
Bond order: (bonding electrons - antibonding electrons) / 2
Total electronic energy: nbEb + naEa
A molecular orbital energy calculator helps estimate orbital mixing in simple diatomic systems. It combines two atomic orbital energies with coupling and overlap terms. The result shows bonding and antibonding levels. It also reports coefficients, energy splitting, total electronic energy, and bond order.
Molecular orbital theory explains how electrons spread across a molecule. Electrons do not stay on isolated atoms. They occupy delocalized orbitals formed from atomic combinations. Lower bonding orbitals stabilize the system. Higher antibonding orbitals reduce stability when occupied. The energy gap between them affects bonding strength, spectra, and reactivity.
This page uses a two orbital LCAO model. One input represents orbital energy on atom A. Another represents orbital energy on atom B. The resonance term describes interaction strength. The overlap term corrects for non orthogonal basis functions. Solving the secular equation gives two eigenvalues. These become the bonding and antibonding molecular orbital energies.
The calculator returns more than two numbers. It estimates bonding occupation, antibonding occupation, total pair energy, and bond order. It also gives coefficient ratios and approximate atomic contributions. These values help compare homonuclear and heteronuclear cases. They also support quick classroom checks, homework review, and early stage model building.
Use this calculator when you want a compact molecular orbital estimate. It works well for introductory physics, chemistry, and materials problems. It is especially useful for visualizing how overlap and coupling change energy splitting. It is not a replacement for full quantum calculations. Still, it provides fast insight with transparent formulas and practical exports.
A more negative bonding value usually means stronger stabilization. A larger energy gap often indicates stronger interaction between the starting orbitals. Unequal coefficients suggest polarized bonding, where one atom contributes more strongly than the other. Bond order summarizes occupation effects in a familiar way. Positive bond order supports net bonding. Zero bond order suggests no net stabilization from that orbital pair. These simple trends make the calculator useful for teaching, comparison, and quick parameter exploration during early molecular model studies.
It estimates bonding and antibonding energies for a two orbital diatomic model. It also returns splitting, coefficients, occupancy, total electronic energy, and bond order.
Yes. Choose the input unit before calculation. The tool converts values internally, then shows equivalent energies in eV, Hartree, and kJ/mol.
Overlap S measures how strongly the two basis orbitals spatially overlap. Larger magnitude changes the secular equation and can shift both orbital energies and mixing behavior.
In this two state model, the lower eigenvalue corresponds to the stabilized combination. That lower level is conventionally identified as the bonding molecular orbital.
Unequal coefficients usually mean the two atomic orbitals have different starting energies or coupling conditions. That creates polarized molecular orbitals with uneven atomic character.
Enter a value from 0 to 4 for this orbital pair. Up to two electrons fill the bonding level first. Additional electrons enter the antibonding level.
No. It is a transparent teaching and screening model. It is useful for trends, comparisons, and quick checks, not high accuracy electronic structure prediction.
Avoid it for strongly multiorbital, many electron, or highly correlated systems. Use a more complete computational method when detailed spectroscopy or precise energies matter.
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.