MERSY descriptors

MerSy (MERA Symmetry) descriptors are calculated usung 3D repres= entation of molecules in the framework of MERA algorithm and include the qu= antitative estimations of molecular symmetry with respect to symmetry axes = from C2 to C6 and to inversion-rotational axis from S1 to S6 in the space o= f principal rotational invariants about each orthogonal component. Addition= ally the molecular chirality is quantitatively evaluated in agreement with = the negative criterion of chirality (the absence of inversion-rotational ax= es in the molecular point group).

Authors:

V.Potemkin
M.Grishina [1]

All MerSy descriptors vary in the range from 0 to 1 and possess a meanin= g of the presence of the symmetry element.

SYMC2X is the C2 point group of symmetry about the first (X) rotatio= nal invariant.
SYMC2Y is the C2 point group of symmetry about the second (Y) rotationa= l invariant.
SYMC2Z is the C2 point group of symmetry about the third (Z) rotational= invariant.
SYMC2 is the aggregate estimate of the C2 point group presence.

SYMC3X is the C3 point group of symmetry about the first (X) rotational= invariant.
SYMC3Y is the C3 point group of symmetry about the second (Y) rotationa= l invariant.
SYMC3Z is the C3 point group of symmetry about the third (Z) rotational= invariant.
SYMC3 is the aggregate estimate of the C3 point group presence.

SYMC4X is the C4 point group of symmetry about the first (X) rotational= invariant.
SYMC4Y is the C4 point group of symmetry about the second (Y) rotationa= l invariant.
SYMC4Z is the C4 point group of symmetry about the third (Z) rotational= invariant.
SYMC4 is the aggregate estimate of the C4 point group presence.

SYMC5X is the C5 point group of symmetry about the first (X) rotational= invariant.
SYMC5Y is the C5 point group of symmetry about the second (Y) rotationa= l invariant.
SYMC5Z is the C5 point group of symmetry about the third (Z) rotational= invariant.
SYMC5 is the aggregate estimate of the C5 point group presence.

SYMC6X is the C6 point group of symmetry about the first (X) rotational= invariant.
SYMC6Y is the C6 point group of symmetry about the second (Y) rotationa= l invariant.
SYMC6Z is the C6 point group of symmetry about the third (Z) rotational= invariant.
SYMC6 is the aggregate estimate of the C6 point group presence.
SYMS1X is the S1 point group of symmetry about the first (X) rotational= invariant (plane of symmetry YOZ).
SYMS1Y is the S1 point group of symmetry about the second (Y) rotationa= l invariant (plane of symmetry XOZ).
SYMS1Z is the S1 point group of symmetry about the third (Z) rotational= invariant (plane of symmetry XOY).
SYMS1 is the aggregate estimate of the S1 point group (plane of symmetr= y) presence.

SYMS2 is the aggregate estimate of the S2 point group presence. S2 poin= t group is the center of symmetry which is independent from axes.

SYMS3X is the S3 point group of symmetry about the first (X) rotational= invariant.
SYMS3Y is the S3 point group of symmetry about the second (Y) rotationa= l invariant.
SYMS3Z is the S3 point group of symmetry about the third (Z) rotational= invariant.
SYMS3 is the aggregate estimate of the S3 point group presence.

SYMS4X is the S4 point group of symmetry about the first (X) rotational= invariant.
SYMS4Y is the S4 point group of symmetry about the second (Y) rotationa= l invariant.
SYMS4Z is the S4 point group of symmetry about the third (Z) rotational= invariant.
SYMS4 is the aggregate estimate of the S4 point group presence.

SYMS5X is the S5 point group of symmetry about the first (X) rotational= invariant.
SYMS5Y is the S5 point group of symmetry about the second (Y) rotationa= l invariant.
SYMS5Z is the S5 point group of symmetry about the third (Z) rotational= invariant.
SYMS5 is the aggregate estimate of the S5 point group presence.

SYMS6X is the S6 point group of symmetry about the first (X) rotational= invariant.
SYMS6Y is the S6 point group of symmetry about the second (Y) rotationa= l invariant.
SYMS6Z is the S6 point group of symmetry about the third (Z) rotational= invariant.
SYMS6 is the aggregate estimate of the S6 point group presence.

CHIR is the chirality of a molecule estimating as a probability of= absence of inversion-rotational axes in the molecular point group (the neg= ative criterion of chirality).