Before I go deeper, let me state that "formal" and "partial" charges aren't physical observables, but it is possible to make meaningful statements.

In the early times, that was done by Mulliken or other population analyses. However, most of these methods resulted in physically counterintuitive results in too many occasions and therefore quite numerous arguments which one should be considered the "right one".

The, to my extent of knowledge, most accepted analysis at the moment would be Bader's "atoms in molecules" approach which assigns partial charges by allocating the electrons with respect to minima in the electron density. Bond orders are assigned in similar manner.

See https://en.wikipedia.org/wiki/Atoms_in_molecules and especially the references therein.

AIM is available for a number of packages, e.g. for Turbomole that would be AIM11 http://aim.tkgristmill.com/

Just to add my 2 cents here:

There are multiple models designed to study bonds and interactions, for example you could explore the non covalent nature of some interactions through NCI and also employing the Independent Gradient Model .

For covalent bonds you could explore some characteristics using the IGM (through different descriptors) and the Intrinsic Bond Strenght Index

This is just mentioning a couple tools I remind from the top of my mind, because it should be a matter of defining the information you need before defining the tool to obtain it.

Natural Bond Order analysis and related methods can usually provide detailed insights into chemical bonds .

I think quantum theory of atoms in molecules (QTAIM) parameters can explain the nature of bonding

NBO,EDA,AIM, NCI....

As non covalent interactions are mentioned, I'd like to add that this terminology is not always relevant. Weak bonding and supposedly electrostatic interactions are are never purely "non covalent".

See :

Frank Weinhold, “Noncovalent Interaction”: A Chemical Misnomer That Inhibits Proper Understanding of Hydrogen Bonding, Rotation Barriers,

and Other Topics.

Molecules 2023, 28, 3776.

In Bader's theory (Atoms in Molecules), conditions for estimating the nature of the bond are established, which are specified in a very special way in the works of the creators of CRYSTAL, when they include in their estimation not only the topological details of the charge density, but also the topology of the Laplacian of the charge density and the topology of scalar functions depending on this density. My recommendation to the interested reader is to consult the CRYSTAL manuals (https:/www,crystalsolutions.eu), which I used to estimate the nature of the H-Mg and H-H bond in Mg hydrides. Related bibliography attached:

-G. Gervasio, R. Bianchi, D. Marabello, About the topological classification of the metal–metal bond, Chemical Physics Letters 387 (2004) 481–484.

- E. Espinosa, I. Alkorta, J. Elguero, E. Molins, From weak to strong interactions: A comprehensive analysis of the topological and energetic properties of the electron density distribution involving X–H⋯F–Y systems, J. Chem. Phys. 117 (2002) 5529-5542.

- C. Gatti, Chemical Bonding in Crystals: new Directions, Zeitschrift fur krystallographie 220 (2005) 399-457.

- R. Dovesi, A. Erba, R. Orlando, C.M. Zicovich-Wilson, B. Civalleri, L. Maschio, M. R_erat, S. Casassa, J. Baima, S. Salustro, B. Kirtman, Quantum-Mechanical Condensed Matter Simulations with CRYSTAL, WIREs Comput. Mol. Sci., (2018) e1360 https://doi.org/10.1002/wcms.1360.

The bonding variation of γ-TiAl during deformation in Physical Chemistry Chemical Physics. I have disscused the bonding nature in TiAl by the Electron locaization function, which is a promising way to display the bond nature.