Sterimol

The Sterimol parameters L, B₁ and B₅ as described by Verloop [1][2] are implemented. Note that Sterimol parameters should be calculated with H as the dummy atom, to be consistent with values in the literature (see Background)

Module

The Sterimol class calculates and stores Sterimol parameters.

Example

>>> from morfeus import Sterimol, read_xyz
>>> elements, coordinates = read_xyz("tBu.xyz")
>>> sterimol = Sterimol(elements, coordinates, 1, 2)
>>> sterimol.L_value
4.209831193078874
>>> sterimol.B_1_value
2.8650676183152837
>>> sterimol.B_5_value
3.26903261263369
>>> sterimol.print_report()
L         B_1       B_5
4.21      2.87      3.27

Radii can be changed with the argument radii_type=<str> and custom radii can be supplied as a list with radii=<list>.

The bond length between atoms 1 and 2 and the uncorrected L values (without the historical addition of 0.40 Å) can also be obtained.

Uncorrected L values

>>> sterimol.L_value_uncorrected
3.8098311930788737
>>> sterimol.bond_length
1.1
>>> sterimol.print_report(verbose=True)
L         B_1       B_5       L_uncorr  d(a1-a2)
4.21      2.87      3.27      3.81      1.10

More information can be found with help(Sterimol) or in the API: Sterimol.

Buried Sterimol

The Sterimol vectors can be “buried”:

Delete

>>> elements, coordinates = read_xyz("P_p-Tol_3.xyz")
>>> sterimol = Sterimol(elements, coordinates, 1, 2)
>>> sterimol.print_report()
L         B_1       B_5
7.44      4.94      7.44
>>> sterimol.bury(method="delete")
>>> sterimol.print_report()
L         B_1       B_5
6.92      4.27      6.04

Truncate

>>> elements, coordinates = read_xyz("P_p-Tol_3.xyz")
>>> sterimol = Sterimol(elements, coordinates, 1, 2)
>>> sterimol.print_report()
L         B_1       B_5
7.44      4.94      7.44
>>> sterimol.bury(method="truncate")
>>> sterimol.print_report()
L         B_1       B_5
5.90      4.27      5.01

Slice

>>> elements, coordinates = read_xyz("P_p-Tol_3.xyz")
>>> sterimol = Sterimol(elements, coordinates, 1, 2)
>>> sterimol.print_report()
L         B_1       B_5
7.44      4.94      7.44
>>> sterimol.bury(method="slice")
>>> sterimol.print_report()
L         B_1       B_5
5.82      3.77      5.24

There are three different methods for doing this:

delete

Atoms outside the sphere + 0.5 vdW radius are deleted and the Sterimol vectors are calculated. This is the default.

truncate

Sterimol vectors are calculated as usual, but truncated in length by the sphere.

slice

A point vdW surface is constructed from the atoms and all points outside the sphere are removed. Then the Sterimol vectors are computed based on the remaining points.

A standard sphere radius of 5.5 Å is used that can be changed with sphere_radius=<float>. For the delete method, the scaling factor for the atom cutoff can be changed with radii_scale=<float>. For more information, see the API: Sterimol.bury

Command line script

The command line script gives access to the basic functionality from the terminal.

Example

$ morfeus sterimol tBu.xyz - 1 2 - print_report
L         B_1       B_5
4.21      2.86      3.27

Background

The Sterimol parameters were developed by Verloop to describe the steric size of substituents. The atom attached to the substituent in the calculation (by definition H) is called atom 1 and the first atom in the substituent is called atom 2. L can be described as the depth of the substituent. It is defined as the length of the vector going from atom 1, through atom 2 and ending on the tangent of the vdW surface. For historical reasons, L is corrected by adding 0.40 Å to this length. This was due to a shift from using C(sp²) to H as dummy atom.

B₁ and B₅ can be described as the minimum and maximum rotational size of the substituent. They are defined as the shortest and longest vectors from atom 2 to a tangent plane of the vdW surface which are perpendicular to the L vector, respectively.

ᴍᴏʀғᴇᴜs has been benchmarked against Paton’s Sterimol package. Using exactly the same radii (Paton’s modified Bondi), almost identical results are obtained. (Note that ᴍᴏʀғᴇᴜs normally uses 1.20 Å as the Bondi vdW radius for H).ᴍᴏʀғᴇᴜs calculates the B₁ and B₅ parameters by a different approach from the original code. First, atomic spheres are created with a certain density of points. B₁ and B₅ are then obtained by projection of atoms onto vectors spanning the whole 360 degrees in the plane perpendicular to L. B₅ is obtained from the largest projection, while B₁ is obtained from the smallest maximum projection for the set of vectors.

Buried Sterimol was developed by Tobias Gensch while working in the group of Matthew Sigman at the University of Utah [3]. It is intended to limit the Sterimol vectors to a volume of interest in the philosophy of the buried volume. The original implementation uses the delete algorithm. ᴍᴏʀғᴇᴜs uses the CRC handbook radii by default instead of the modified Bondi radii in the original article, so results with the defualt settings might be slighly different.

References

[1]

A. Verloop, W. Hoogenstraaten, and J. Tipker. Development and application of new steric substituent parameters in drug design. In Everhardus Jacobus Ariëns, editor, Drug Design, pages 165–207. Elsevier, 1976. doi:10.1016/B978-0-12-060307-7.50010-9.

[2]

A Verloop. The Sterimol approach: further development of the method and new applications. In P. Doyle and T. Fujita, editors, Pesticide chemistry: Human welfare and environment: Synthesis and structure-activity relationships, pages 339–344. Pergamon, 1983. doi:https://doi.org/10.1016/B978-0-08-029222-9.50051-2.

[3]

Tobias Gensch, Gabriel dos Passos Gomes, Pascal Friederich, Ellyn Peters, Théophile Gaudin, Robert Pollice, Kjell Jorner, AkshatKumar Nigam, Michael Lindner-D’Addario, Matthew S. Sigman, and Alán Aspuru-Guzik. A comprehensive discovery platform for organophosphorus ligands for catalysis. Journal of the American Chemical Society, 144(3):1205–1217, January 2022. doi:10.1021/jacs.1c09718.