Validation

After minimization, each candidate conformer must pass a series of geometric validation checks. If any check fails, the conformer is rejected and the pipeline retries with a new random embedding.

Validation Pipeline

Check 1: Energy Per Atom

After bounds force field minimization, the energy per atom must be below a threshold:

$$\frac{E_{\text{total}}}{N}<0.05$$

High energy indicates the optimizer couldn't satisfy the distance constraints — typically from a bad initial embedding where atoms are placed too close together or too far apart.

Check 2: Tetrahedral Centers

For each carbon or nitrogen atom that:

• Has degree 4 (4 neighbors)
• Is in 2 or more SSSR rings
• Is NOT in any 3-membered ring

The volume of the tetrahedron formed by its 4 neighbors must be substantial:

Volume Computation

For center atom $C$ with neighbors $A,B,D,E$:

1. Compute normalized direction vectors from each neighbor to the center:

$${\hat{v}}_{AC}=\frac{{\mathbf{x}}_C-{\mathbf{x}}_A}{|{\mathbf{x}}_C-{\mathbf{x}}_A|}$$

2. Compute 4 triple products (one for each triple of neighbors):

$$V_1={\hat{v}}_{AC}\cdot ({\hat{v}}_{BC}\times {\hat{v}}_{DC})$$

3. All 4 triple products must exceed the threshold:

$$|V_k|>\{\begin{array}{ll}0.50& \text{normal atoms}\\ 0.25& \text{atoms in small rings}\end{array}$$

4. Additionally, the center must be inside the tetrahedron — all 4 face normals must point outward relative to the center (tolerance: 0.30).

Check 3: Chiral Volume Signs

For atoms with @ or @@ stereo specification:

$$\text{sign}(V_{\text{actual}})=\text{sign}(V_{\text{expected}})$$

where:

• @ (counterclockwise) → volume should be positive
• @@ (clockwise) → volume should be negative

The volume is $V={\overrightarrow{v}}_1\cdot ({\overrightarrow{v}}_2\times {\overrightarrow{v}}_3)$ with vectors computed from the chiral center to its neighbors, in the order specified by the SMILES.

A 20% tolerance is applied — the absolute volume must be at least 20% of the target:

$$|V|>0.2\cdot |V_{\text{target}}|$$

Check 4: Planarity

For SP2 centers (C=C, C=O, aromatic C, amide N), the out-of-plane energy is computed using UFF inversions:

$$E_{\text{oop}}=K\sum _{\text{impropers}}(1-\sin Y)$$

where $Y$ is the Wilson out-of-plane angle.

Rejection criterion:

$$E_{\text{oop}}>N_{\text{improper}}\times 0.7$$

This accepts conformers where most SP2 centers are planar, rejecting only those with severely distorted geometry.

Additionally, SP-hybridized atoms (triple bonds, allenes, linear) are checked for linearity:

$${\theta }_{\text{actual}}>175°$$

Check 5: Double-Bond Geometry

For each double bond, the substituents on each side must not be linear with the bond axis:

$$\cos \theta +1>{10}^{-3}$$

where $\theta$ is the angle between a substituent and the double bond vector. A value near 180° (cos θ ≈ −1) would mean the substituent is collinear with the double bond — a physically impossible configuration.

Summary of Thresholds

Check	Threshold	What It Catches
Energy/atom	< 0.05	Bad embedding, stuck optimization
Tetrahedral volume	> 0.50 (0.25 small ring)	Collapsed ring junctions
Chiral sign	±20% tolerance	Wrong stereochemistry
Planarity	< 0.7 × $N_{\text{improper}}$	Puckered SP2 centers
Double bond	$\cos \theta +1>{10}^{-3}$	Linear substituents

Retry Budget

The pipeline allows up to $10N$ total retry iterations, where $N$ is the number of atoms. For a typical drug-like molecule with 30 atoms, this gives 300 attempts — which is almost always sufficient.

In practice, most molecules succeed within 1–5 attempts. Molecules with many chiral centers or strained ring systems may need 10–50 attempts.