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1. What is being asked?

A student has performed a constrained CASSCF(12,10)/VTZP scan of the O‑C‑C‑O dihedral in the open‑ring (biradical) form of 1,2‑dioxetane.

Four singlet states (S₀–S₃) were state‑averaged and the energies were plotted versus the dihedral angle (0–180°).

The unexpected observation is that the lowest‑energy singlet surface (S₀) shows a minimum near 120° rather than a transition‑state maximum (the way a simple ethane‐like torsional scan would look).

The question is:

Why does the CASSCF scan give a minimum at ~120° for the singlet biradical, and what does this tell us about the electronic structure of the open‑ring 1,2‑dioxetane?

We need to explain the shape of the four PESs, relate them to the singlet vs. triplet biradical coupling, and show why the “usual” torsional barrier (≈120°) does not appear here.

2. Step‑by‑step analysis

2.1 Geometry and electronic structure of the open‑ring species

  1. Ring opening of 1,2‑dioxetane cleaves the O–O bond, giving a four‑atom biradical

    [ \mathrm{O_1–C_1–C_2–O_2} ]

    with two singly‑occupied molecular orbitals (SOMOs) located mainly on the two oxygen atoms.

  2. In the closed‑ring (four‑membered) system the relevant valence orbitals are

    • σ(C–C) and σ*(C–C)
    • σ(O–C) and σ*(O–C) (both O atoms)
    • two non‑bonding O lone‑pair orbitals that lie perpendicular to the ring plane.

  3. The active space (12 electrons in 10 orbitals) therefore contains

    • σ and σ* for C–C and O–C bonds
    • the two O‑lone‑pair orbitals (π‑type, perpendicular to the ring)

    This is exactly the set that can describe bond breaking (σ → σ*) and the biradical coupling of the two O‑based SOMOs.

2.2 What does rotating the O–C–C–O dihedral do?

The dihedral angle (ϕ = OCC′O′) controls the relative orientation of the two O‑lone‑pair orbitals (the SOMOs) with respect to each other and to the central C–C σ bond.

ϕ (°) Relative orientation of the two SOMOs Expected electronic interaction
0 / 180 (eclipsed) Both lobes point toward each other (parallel) Strong through‑bond overlap with σ(C–C) → destabilisation (steric + Pauli repulsion)
90 (perpendicular) SOMOs are orthogonal → no overlap Triplet biradical favoured (no singlet pairing)
≈120 (gauche) SOMOs are tilted so that their lobes overlap constructively through the C–C σ framework Singlet pairing is maximised → stabilisation

Thus, unlike ethane where the barrier arises mainly from steric repulsion of the C–H bonds, here the electronic interaction between the two radical centres dominates.

2.3 Singlet vs. triplet coupling in a biradical

A biradical can exist in two spin‑coupled states:

Spin state Required orbital symmetry Energy trend with ϕ
Singlet (paired) The two SOMOs must be in‑phase (constructive overlap) to form a bonding interaction. Energy lowest when the overlap is maximal → around 120°.
Triplet (parallel spins) The two SOMOs must be orthogonal (no overlap) to avoid the exchange penalty. Energy lowest near 90° where overlap vanishes; rises when the lobes start to overlap (≈0°/180°).

Because the state‑average CASSCF includes the first four singlet roots, the S₀ surface corresponds to the lowest‑energy singlet biradical. Consequently, it follows the singlet‑favoured trend described above, giving a minimum near 120°.

2.4 Why the usual “120° transition state” is absent

In a simple alkane (e.g., ethane) the torsional profile is governed by repulsion between eclipsing C–H bonds. The maximum occurs when the H‑C bonds are eclipsed (0°) and the minimum when they are staggered (≈60°, 180°).

In the open‑ring dioxetane biradical:

  • The C–C bond is already weakened (σ → σ* occupation) and the dominant interaction is the through‑bond coupling of the two O‑based SOMOs.
  • The steric component of the barrier is very small (the substituents are only H atoms).
  • Therefore the electronic term (singlet pairing) outweighs the steric term, shifting the stationary point from a maximum (as in ethane) to a minimum.

2.5 Interpretation of the four plotted singlet surfaces

State Description Behaviour with ϕ
S₀ Ground‑state singlet biradical (dominant configuration: σ(C–C)² σ*(C–C)⁰ + paired O‑lone‑pairs) Minimum ≈ 120°, shallow rise toward 0°/180°.
S₁ First excited singlet, often σ → σ* excitation (one electron promoted to the C–C σ*). The extra electron reduces the benefit of singlet pairing, so the surface is flatter and the minimum is less pronounced. Broad minimum near 120°, but higher overall energy.
S₂ Second excited singlet, typically a π → π* excitation on the O atoms or a configuration where the two O SOMOs are both singly occupied (triplet‑like but forced into singlet symmetry). Shows a maximum near 120° because the configuration prefers orthogonal SOMOs (triplet‑like).
S₃ Higher‑lying configuration, often a combination of σ* occupation and O‑π* excitation. Monotonic increase; little torsional dependence.

The cross‑overs seen in Figure 2 (where S₁ and S₂ approach each other) are the classic avoided crossings typical for a biradical when the dihedral is changed; they further confirm that the electronic character is changing from paired to unpaired as the overlap varies.

2.6 Supporting evidence from the C–C bond length (Figure 3)

The C–C distance shortens slightly at the 120° minimum (≈1.55 Å) and lengthens toward 0°/180° (≈1.62 Å).

When the SOMOs overlap constructively (≈120°) the bond order of C–C is increased (partial restoration of the σ bond), so the bond contracts.
When the SOMOs are eclipsed the extra electron density in the antibonding σ* orbital weakens the C–C bond, giving a longer distance. This geometric trend is exactly what one expects for a singlet biradical that re‑forms a weak σ bond at the favourable dihedral.

3. Final answer

The minimum at ~120° on the ground‑state singlet PES is not an artifact; it is a genuine consequence of the electronic coupling between the two oxygen‑centered SOMOs in the open‑ring 1,2‑dioxetane biradical.

  • In the singlet biradical the two SOMOs must overlap in‑phase to gain a bonding interaction through the central C–C σ framework. The dihedral angle of ~120° provides the optimal tilt for this constructive overlap, thus stabilising the molecule and giving a minimum.

  • The triplet‑like configuration (which would appear in a pure triplet state or in higher singlet roots that are essentially “triplet‑forced”) prefers the SOMOs to be orthogonal (≈90°), producing a maximum in the singlet surface at the same angle.

Consequently, the torsional profile of the biradical is dominated by spin‑coupling effects, not by the steric “eclipsed vs. staggered” barrier familiar from ethane. The CASSCF active space correctly captures the σ/σ* and O‑lone‑pair mixing, so the computed PES reflects the true electronic preference for a gauche (≈120°) conformation in the singlet ground state.

4. Common mistakes when analysing this kind of problem

Mistake Why it’s wrong How to avoid it
Assuming the torsional barrier must be the same as in ethane Ethane’s barrier is steric; the biradical’s barrier is electronic (spin‑coupling). Examine the nature of the frontier orbitals and the spin state before comparing to simple alkane scans.
Ignoring the spin‑state dependence of the PES Singlet and triplet biradicals have opposite preferences for orbital overlap. Plot both singlet and triplet (or the relevant excited singlet states) to see opposite trends.
Treating the CASSCF state‑average energies as “exact” single‑state surfaces Averaging over several roots can smooth out sharp features and shift minima. Verify by a state‑specific CASSCF calculation on the S₀ root; the minimum at ~120° persists.
Neglecting geometry relaxation of the “fixed” dihedral If other dihedrals or bond lengths are frozen, artificial strain can appear. Keep only the targeted dihedral constrained; allow all other coordinates (including the other HCCO dihedral) to relax, as done in the scan.
Overlooking the C–C bond length trend The bond length provides a direct clue about σ‑bond restoration vs. weakening. Always check key bond lengths along the scan; a shortening at the minimum supports the electronic‑coupling explanation.

By keeping these points in mind, one can correctly interpret torsional PESs for biradical systems such as the open‑ring 1,2‑dioxetane.

Original question: Rotation around CC bond in 1,2-dioxetane: transition states and local minimum structures on Chemistry Stack Exchange, licensed CC BY-SA.