Principal Moment of Intertia (PMI)-Derived Properties

This node calculates Principal Moment of Intertia (PMI)-Derived Properties

The properties are:

• PMI 1 - First (smallest) Principal Moment of Inertia (also referred to as: I₁)
• PMI 2 - Second Principal Moment of Inertia (also referred to as: I₂)
• PMI 3 - Third (largest) Principal Moment of Inertia (also referred to as: I₃)
• npr1 - First Normalised PMI (i.e. I₁ / I₃) (See: Sauer and Schwartz, J. Chem. Inf. Comput. Sci., 2003, 43, 987-1003)
• npr2 - Second Normalised PMI (i.e. I₂ / I₃) (See: Sauer and Schwartz, J. Chem. Inf. Comput. Sci., 2003, 43, 987-1003)
• Sigma npr - npr1 + npr2 (also referred to as: Flatsum, npr1+npr2, Σnpr) (See: )
• Sphericity - npr1 + npr2 - 1 (also referred to as: S) (See: Wirth et al., J. Comput. Aided Mol. Des., 2013, 27, 511-524)
• Rodlikeness - npr2 - npr1 (also referred to as: R, Rod-likeness) (See: Wirth et al., J. Comput. Aided Mol. Des., 2013, 27, 511-524)
• Disklikeness - 2 - 2 × npr2 (also referred to as: D, Disc-likeness) (See: Wirth et al., J. Comput. Aided Mol. Des., 2013, 27, 511-524)
• Asphericity - 0.5 × [(I₁ - I₂)² + (I₁ - I₃)² + (I₂ - I₃)²]/[I₁² + I₂² + I₃²]; 0 corresponds to a spherical top and 1 to a linear molecule. ~0.25 corresponds to prolate (cigar-shaped) molecules, and disc-shaped ~1 (also referred to as: ΩA) (See: Arteca, Reviews in Computational Chemistry, Vol 9 VCH, NY, 1991, 191-253)
• Inertial Shape Factor - I₂ / (I₁ × I₃); Undefined for planar molecules (also referred to as: S_I) (See: Lister et al., Internal Rotation and Inversion, Academic Press, London, 1978)
• Molecule Eccentricity - √(I₁² - I₃²) / I₂; 0 corresponds to a spherical top, and 1 to a linear molecule (also referred to as: ε) (See: Arteca, Reviews in Computational Chemistry, Vol 9 VCH, NY, 1991, 191-253)
• Gyradius - Radius of Gyration (also referred to as: RG, Radius of Gyration, Gyradius) (See: )
• Gyradius 2D - Radius of Gyration (2D) = √(I₁ × I₂) / MWt (also referred to as: RG, Radius of Gyration, Gyradius) (See: Volkenstein 'Configurational Statistics of Polymeric chains' Wiley, NY, 1963)
• Gyradius 3D - Radius of Gyration (3D) = ∛(I₁ × I₂ × I₃) / MWt (also referred to as: RG, Radius of Gyration, Gyradius) (See: Tanford 'Physical Chemistry of Macromolecules', Wiley, NY, 1961)
• PRG 0 - 1st Principle Radius of Gyration (R0 = √(I₁ / MWt)) (also referred to as: R0) (See: Jian et al., 'A dimension map for molecular aggregates', J. Mol. Graphics. Model., 2015, 58, 10-15)
• PRG 1 - 2nd Principle Radius of Gyration (R1 = √(I₂ / MWt)) (also referred to as: R1) (See: Jian et al., 'A dimension map for molecular aggregates', J. Mol. Graphics. Model., 2015, 58, 10-15)
• PRG 2 - 3rd Principle Radius of Gyration (R2 = √(I₃ / MWt)) (also referred to as: R2) (See: Jian et al., 'A dimension map for molecular aggregates', J. Mol. Graphics. Model., 2015, 58, 10-15)
• Gyradius Ratio 1 - 1st Gyradius Ratio (r1 = PRG1 / PRG0) (also referred to as: r1) (See: Jian et al., 'A dimension map for molecular aggregates', J. Mol. Graphics. Model., 2015, 58, 10-15)
• Gyradius Ratio 2 - 2nd Gyradius Ratio (r2 = PRG2 / PRG0) (also referred to as: r2) (See: Jian et al., 'A dimension map for molecular aggregates', J. Mol. Graphics. Model., 2015, 58, 10-15)

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Input ports

1. Type: Table
   Input table
   Input table

Output ports

1. Type: Table
   Principal Moment of Intertia (PMI)-Derived Properties
   Input table with calculated properties appended