Molecular Shape, Catalytic Pockets and 3D Fields

Steric Descriptors and Three-Dimensional Fields

Quantify molecular size as directional widths, occupied volume around a reactive center, and spatial fields, then relate those representations to reaction selectivity.

Role: Sterimol L, B1, and B5
Typical input: 3D conformers and aligned fields
Typical output: %Vbur, steric maps, feature matrices

1. Representing steric effects

Steric effects are directional. Sterimol retains dimensions along a specified axis, %Vbur measures total occupancy around a center, quadrant volumes retain coarse asymmetry, and steric maps or voxel fields preserve spatial distributions.

Representation	Retained information	Lost information
Sterimol	Length and extreme widths about an axis	Detailed angular shape
%Vbur	Total occupancy in a sphere	Direction of crowding
Quadrant %Vbur	Coarse asymmetry	Fine shape within each quadrant
Steric map or field	Spatial distribution	Simple low-dimensional interpretation

2. Sterimol L, B1, and B5

L: length along the primary attachment axis.
B1: minimum width perpendicular to that axis.
B5: maximum width perpendicular to that axis.

Some software uses Bmin/Bmax. Coordinates, atom order, reference-axis direction, van der Waals radii, and hydrogen treatment are part of the descriptor definition.

3. Conformer dependence

For flexible substituents, one minimum does not represent the descriptor distribution. Compute values across a conformer ensemble and report distributions or Boltzmann-weighted summaries.

w_{i} = \frac{\exp [- Δ G_{i} / (R T)]}{\sum_{j}^{N} \exp [- Δ G_{j} / (R T)]}

Population estimates inherit energy errors

Boltzmann weighting depends exponentially on relative free energies. Report the method, temperature, duplicate treatment, and uncertainty; also inspect unweighted distributions when energy differences are uncertain.

4. Percent buried volume

%Vbur is the fraction of a sphere centered on a metal or putative reactive site that is occupied by ligand van der Waals volume.

% V_{bur} = 100 \times \frac{V_{occupied}}{4 π R^{3} / 3}

Sphere center, radius, metal-ligand distance, excluded atoms, hydrogens, radii scaling, and grid spacing must be fixed for comparisons.

%Vbur is not a universal molecular constant. The center, radius, orientation, excluded atoms, hydrogen treatment, van der Waals radii, scaling factor, and grid spacing are part of its definition.

5. Steric maps and quadrants

Place the reactive center at the origin, align the coordination or reaction axis with z, fix x/y orientation using chemically corresponding references, remove excluded atoms, and generate all maps with the same radius, mesh, radii, and color scale.

Orientation is data

Rotation or reflection inconsistencies invalidate quadrant and pixelwise comparisons.

Place the reactive center at the origin, align the reaction or coordination axis with z, and define x/y using chemically corresponding atoms. A rotation or reflection changes quadrant and pixelwise descriptors.

6. DBSTEP and SambVca

DBSTEP calculates Sterimol, %Vbur, Sterimol2Vec, and Vol2Vec from 3D structures. SambVca provides buried volumes and topographic steric maps.

Shell

python -m dbstep conformer.xyz --sterimol --atom1 2 --atom2 5
python -m dbstep conformer.xyz --volume --atom1 2 --radius 3.5

Check option names against the installed version and store all reference-atom definitions.

DBSTEP atom indices are normally one-based. Save reference atoms and command-line options. For SambVca, preserve the center, orientation, exclusions, sphere radius, mesh, and radii scale.

7. Extension to three-dimensional electronic fields

Sterimol and %Vbur mainly describe van der Waals shape. Electrostatic potential, density deformation, frontier-orbital fields, and NCI/IGMH/IRI fields can add electronic and interaction information on a common aligned grid.

See the cube chapter for grids and the Multiwfn chapter for real-space functions. Since voxel count greatly exceeds sample count, use masks, regional integration, PCA, or regularization.

Field	Possible information	Key caution
Electron density	Molecular boundary and density deformation	Grid and isovalue dependence
Electrostatic potential	Spatial electrostatic tendency	Fix surface and units
Frontier orbital	Phase and local amplitude	Match orbitals and phases
NCI/IGMH/IRI	Interaction regions	Not an energy decomposition

8. Connecting descriptors to selectivity

Enantioselectivity can be transformed to a free-energy difference under a fixed sign and temperature convention.

ΔΔ G^{‡} = - R T \ln (\frac{1 + ee}{1 - ee})

Define a common reactive coordinate system.
Generate conformer ensembles consistently.
Calculate shape and field features with fixed definitions.
Evaluate scaling, correlation, and conformer uncertainty.
Use grouped validation for new substrate or catalyst series.
Compare statistical interpretations with transition states and experiments.

Correlation does not establish mechanism

A statistically important region is a mechanistic hypothesis. Combine it with transition structures, energy decomposition, perturbation experiments, or other independent evidence.

9. References

Last reviewed: August 4, 2026. Check the linked official documentation for syntax specific to the installed software version.