Size and Shape Descriptors

Size and shape descriptors quantify how a molecule occupies space, how compact it is, and how strongly it deviates from simple spherical or planar geometries.

Overview

These descriptors are useful when a property depends on:

  • steric accessibility

  • exposed surface extent

  • compactness versus extension

  • molecular anisotropy

  • planarity

Descriptor Families

Basic Composition

Atom Number

  • Number of atoms in the molecule

  • Unitless

Molecule Weight

  • Total molecular mass

  • Units: Da

Occupied Orbitals

  • Number of occupied molecular orbitals

  • Unitless

Surface and Dimension Descriptors

Isosurface Area

  • Surface area of the 0.01 a.u. electron-density isosurface

  • Units: Ų

Sphericity

  • Measures how close the molecular surface is to a sphere

  • Unitless

Farthest Distance

  • Maximum separation between two atoms

  • Units: Å

Molecular Size Short / Medium / Long

  • Bounding-box dimensions after alignment to the principal axes

  • Units: Å

Long/Sum Size Ratio

  • Normalized elongation descriptor

  • Unitless

Length/Diameter

  • Aspect-ratio-like descriptor for anisotropy

  • Unitless

Molecular Radius

  • Effective outer radial size from the center of mass

  • Units: Å

Planarity Descriptors

Molecular Planarity Parameter (MPP)

  • Root-mean-square deviation from the best-fit plane

  • Units: Å

Span of Deviation from Plane (SDP)

  • Full signed spread of atomic deviations around the fitted plane

  • Units: Å

Shape Descriptors

Principal Moments of Inertia (I1, I2, I3)

  • Rotation-invariant measures of mass distribution

  • Units: amu·Å²

Shape_Asphericity

  • Deviation from spherical symmetry based on mass distribution

  • Unitless

  • Typical range: 0 to 0.5

Shape_Gyradius

  • Radius of gyration

  • Units: Å

  • Larger values generally indicate more extended structures

Shape_Relative_Gyradius

  • Radius of gyration normalized against an equivalent sphere

  • Unitless

  • Useful for comparing molecules of different sizes

Shape_Waist_Variance

  • Cross-sectional variation along the principal molecular axis

  • Units: Ų

  • High values often indicate dumbbell-like or constricted shapes

Shape_Geometric_Asphericity

  • Geometric version of asphericity based on bounding-box dimensions

  • Unitless

  • Useful when you want shape information independent of atomic masses

How to Interpret Them Quickly

  • larger Isosurface Area often means more exposed surface for interaction

  • larger Molecular Radius usually means a bulkier molecular envelope

  • lower Sphericity generally means less compact geometry

  • larger Shape_Asphericity or Shape_Geometric_Asphericity means stronger anisotropy

  • larger Shape_Waist_Variance suggests stronger shape variation along the long axis

  • smaller MPP and SDP usually mean a more planar structure

Why They Matter

These descriptors are often useful for interpreting:

  • solubility and exposed surface effects

  • steric control in catalysis

  • scaffold compactness versus extension

  • shape complementarity in recognition problems

In practice, Surfacia often combines them with electronic and surface descriptors so that shape effects are interpreted together with ESP, ALIE, and LEAE.