Defining Spheres and Rays

The first step in ray tracing steric hindrance is to define the molecule as a set of spheres with given radii, and to define the rays as a number of vectors emanating (evenly) from a given location.

To define the spheres with which the rays interact, atom_access first shifts the cartesian coordinates of the molecule such that the atom interest is centred at the origin. Then, each atom is assigned a spherical radius from a list of known van der Waals atomic radii.[1] Finally, we discard all atoms which have no intersection with a spherical region of radius \(r_\text{cutoff}\) centered on the central atom from the subsequent ray tracing process.

An angular Zaremba-Conroy-Wolfsberg (ZCW) grid with variable density index \(\rho\),[2][3][4] is used to define a set of rays emanating from the origin (atom of interest) which evenly sample the surface of a sphere. The number of rays is controlled by the density index, as given in Table 1.

Table 1: Number of rays for each ZCW density index value.

ZCW density index \(\rho\)

Number of rays

0

21

1

34

2

55

3

89

4

144

5

233

6

377

7

610

8

987

9

1597

10

2584

11

4181

12

6765

13

10946

14

17711

15

28657