# Diels-Alder cycloaddition

## Status

specified-next: not executable as a chemically faithful v2 rule yet because geometry/stereochemistry guards are missing.

## Scope

- substrate: Conjugated diene plus alkene dienophile.
- product: Cyclohexene skeleton with two new sigma bonds and one shifted pi bond.
- note: Specified as a concerted guarded composite of primitive endpoint moves. Current HEG v2 lacks stereochemical/geometric guards, so this is a mechanism-design target.

## HEG v2 State Sketches

These panels are rendered from ownership-structured HEG v2 objects. For `specified-next` examples they are state sketches, not yet products of executable v2 rules.

### Diels-Alder substrate HEG sketch

![Diels-Alder substrate HEG sketch](heg_states/diels_alder_start.png)

Butadiene plus ethene with explicit pi-pair resources.

### Diels-Alder composite snapshot 1

![Diels-Alder composite snapshot 1](heg_states/diels_alder_step1_first_sigma.png)

Composite-rule snapshot: first terminal sigma pair is present. This is not meant as an isolated chemical intermediate.

### Diels-Alder composite snapshot 2

![Diels-Alder composite snapshot 2](heg_states/diels_alder_step2_second_sigma.png)

Composite-rule snapshot: both terminal sigma pairs are present before the final pi-shift snapshot.

### Diels-Alder route product

![Diels-Alder route product](heg_states/diels_alder_product.png)

Cyclohexene skeleton: two new sigma pairs and one retained pi pair.

## DPO-like Step Panels

Each primitive snapshot is shown as `L/K/R`. Red marks the ownership edge removed from `L`, orange marks the halfedge whose owner changes, and green marks the ownership edge created in `R`. `K` keeps the common atoms, halfedges, pair objects, and unchanged ownership records. For `specified-next` examples this is an explanatory span derived from route snapshots, not yet a checked executable rule application.

### Diels-Alder composite route step 1

Diels-Alder substrate HEG sketch -> Diels-Alder composite snapshot 1

Changed ownership: `h11: a5 -> a6; h12: a6 -> a1`

| L | K | R |
|---|---|---|
| ![L](heg_steps/diels_alder_main_step1_left.png) | ![K](heg_steps/diels_alder_main_step1_interface.png) | ![R](heg_steps/diels_alder_main_step1_right.png) |

### Diels-Alder composite route step 2

Diels-Alder composite snapshot 1 -> Diels-Alder composite snapshot 2

Changed ownership: `h7: a3 -> a4; h8: a4 -> a5`

| L | K | R |
|---|---|---|
| ![L](heg_steps/diels_alder_main_step2_left.png) | ![K](heg_steps/diels_alder_main_step2_interface.png) | ![R](heg_steps/diels_alder_main_step2_right.png) |

### Diels-Alder composite route step 3

Diels-Alder composite snapshot 2 -> Diels-Alder route product

Changed ownership: `h3: a1 -> a2; h4: a2 -> a3; h7: a4 -> a3; h8: a5 -> a4; h9: a3 -> a4; h10: a4 -> a5; h11: a6 -> a5; h12: a1 -> a6; h13: a5 -> a6; h14: a6 -> a1`

| L | K | R |
|---|---|---|
| ![L](heg_steps/diels_alder_main_step3_left.png) | ![K](heg_steps/diels_alder_main_step3_interface.png) | ![R](heg_steps/diels_alder_main_step3_right.png) |

## Reaction Sketch

![Diels-Alder cycloaddition reaction sketch](reaction_scheme.png)

## Mechanism Flow

![Diels-Alder cycloaddition mechanism flow](mechanism_flow.png)

## Primitive HEG Patterns Used

| pattern | invariant |
|---|---|
| concerted pair cycle | Each elementary ownership move is local, but chemical admissibility belongs to the guarded composite. |

## Mechanism Steps

### first terminal diene-dienophile sigma bond forms

- group: concerted cycloaddition
- primitive: concerted pair cycle
- resource move: `pi(diene terminus) + pi(dienophile) -> sigma(C1,C6)`
- roles: new bond: C1-C6
- guard note: requires s-cis diene and dienophile pi resource
- executable note: -

### second terminal diene-dienophile sigma bond forms

- group: concerted cycloaddition
- primitive: concerted pair cycle
- resource move: `pi(diene terminus) + pi(dienophile) -> sigma(C4,C5)`
- roles: new bond: C4-C5
- guard note: requires no pre-existing terminal-dienophile bonds
- executable note: -

### internal diene pi bond shifts to cyclohexene pi bond

- group: concerted cycloaddition
- primitive: concerted pair cycle
- resource move: `pi(C2,C3) -> pi(cyclohexene)`
- roles: shifted pi: internal ring pair
- guard note: requires cyclic ordering and admissible valence after composite
- executable note: -

## Guard Checklist

- diene must be in s-cis topology.
- dienophile must provide pi resource.
- new sigma bonds must be absent before application.
- regio- and stereochemical constraints are not yet represented by current labels.

## Alternative Route Probes

- endo/exo and regioisomeric paths are genuine alternatives, but need geometry/stereochemistry metadata.
- Without those guards a graph-only expansion would overgenerate.

## Expansion

No expansion yet; use this report as a constraint checklist before implementation.

## Interpretation

The chemical rule is treated as a guarded composite of primitive HEG moves. The primitive move tells us what is composable at the electron-resource level; the guards say when that move has the intended chemical meaning.