Atom Bond Connectivity Calculator

bond strain energy index

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About Atom Bond Connectivity Calculator

An atom-bond connectivity calculator computing ABC(G) = Σ √((d(i)+d(j)-2)/(d(i)·d(j))). Estrada et al. (1998). Models strain energy of chemical bonds. Excellent for predicting heat of formation. ABC-conjecture for trees. Client-side.

Atom Bond Connectivity Calculator Features

  • ABC(G)
  • √((d+d-2)/dd)
  • Strain
  • Heat form.
  • Common graphs
ABC index: Σ √((dᵢ+dⱼ-2)/(dᵢdⱼ)). Estrada et al. (1998). Quantifies bond strain energy from degree disparity. ABC predicts heat of formation better than Randić for many molecular classes. The ABC-conjecture for trees remains open.

How to Use

Select graph:

  • ABC: ABC index
  • Per edge: Strain term
  • vs R: Compare

Bond Strain

The factor (dᵢ+dⱼ-2)/(dᵢdⱼ) measures 'strain' at an edge. When both endpoints have high degree, strain is low (stable). When one is low-degree, strain increases. √ ensures positivity and smoothness.

ABC Conjecture

For trees, which tree minimizes ABC? The 'ABC-minimal trees' conjecture: for large n, the minimum ABC tree has specific balanced structure. Partially solved. Active research area.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2For each edge: compute ABC term.
  3. 3Sum all terms.
  4. 4Compare with Randić.
  5. 5Predict heat of formation.

Atom Bond Connectivity Calculator — Frequently Asked Questions

What does ABC measure physically?+

Bond strain: how much energy is stored in the bond due to degree imbalance. A leaf-to-hub bond has high strain (asymmetric). Hub-to-hub has low strain (symmetric). Total ABC = total network strain.

How does ABC compare to Randić?+

ABC incorporates bond-specific information (dᵢ+dⱼ-2). Randić uses only degree product. For heat of formation predictions, ABC often outperforms Randić. But Randić is better for some other properties.

What is the ABC-minimal tree problem?+

Which tree on n vertices minimizes the ABC index? For small n: path. For large n: specific 'balanced-ish' trees. The exact structure is complex and partially characterized. Major open problem.

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