I find your question somewhat ambiguous. If you ask about ab-initio methods available to describe properly your system, of course there are. If you go for biological systems, DFT would be more useful due to the size. Concerning DFT, others have already given to you detailed answers. You can even think of using linear scaling techniques applied to CC or MP2 (L-CCSD, L-MP2) could be still affordable, depending on the size of your system.

If you ask for techniques to analyise which type of bonds you have in the molecule, the presence of hydrogen bonds, weak bonds, electrostatic interactions, there's a bunch of techniques: Bader's Atoms-in-Molecules (AIM), ELF, Natural Bonding Orbitals (NBO), Non-Covalent Interaction plots (NCI-plots), energy decomposition analysis (EDA) either by Morokuma (for HF wavefunctions) or Ziegle (DFT, in ADF), Natural Orbitals of Chemical Valence with Extended Transition State method (NOCV-ETS, an very interesting extension of EDA with get rids of symmetry constraints). The techniques you use depend on what you want to find and the programs you have available.

to my knowledge, ab-initio calculations with a reasonnable precision are limited to quite simple systems with few atoms. The technique I use : MQDT, is mostly used for excited rydberg states of light molecules.

Probably the most sophisticated methodology (mathematically most rigorous) is the Bader population analysis.

I presume your biological system is BIG to treat as a whole ab-initio. Depending on your computer capabilities you can calculate ab-initio (and that includes DFT methods) systems with up to a few hundreds of atoms. As the accuracy increases this number reduces. Scaling of these methods is a big limiting factor and they usually scale with N^3-N^4 where N is the number of electrons or the number of basis elements. However, there are options if you just focus on a small region of a big biological system: The region of interest can be treated ab-initio and the rest with molecular mechanics. This is called QM-MM (combination of quantum mechanics with molecular mechanics). Many programs perform such calculations. For instance Gaussian has an implementation that is called ONIOM that allows you to split your molecule in areas of different accuracy.

Several studies have shown remarkable results for DFT if an empirical dispersion correction is used. Most popular is the fit of Stefan Grimme. Also the M06 functional might be a good choice. However, the latter tend to show convergence problems of the iteration cycle. Overall, these functionals tend to produce better results than MP2 without a counter poise correction compared to CCSD(T). If you want to investigate large systems, I suggest to use an GGA functional for which several fast and efficient methods are available to decrease the computational time. If you prefer to run MP2 calculations instead of DFT, the fragment molecular orbital ansatz as available in Gamess US might be an option. If you prefer CCSD(T) DLPNO-CCSD(T) might be an option which is implemented in ORCA and was already used for the Crambin protein. However, I have not used the last approach so far. The setup of an fragment molecular orbital calculation can be a little bit tedious.

The bond nature in biological systems includes different kinds going from the tight bonding to loose one. For this reason, the question does appear to be not so much specific. In the biological systems the dispersion forces, the long range interactions and similar play a crucial role such as the covalent bond indicates a particular behaviour in that particular case...Now at DFT level the functionals including dispersion correction along with other as M06 works well. Therefore any kind of ab-initio calculations (post-HF, DFT) is able to describe all the previous cases ( irrespective of the size of system to investigate) but it depends on what I want investigate (what kind of bond I want describe and so on).

For big systems is possible to use Fragment Molecular Orbital method (FMO) (http://staff.aist.go.jp/d.g.fedorov/fmo/main.html). The main use of FMO is to compute very large molecular systems by dividing them into fragments and performing ab initio or density functional quantum-mechanical calculations of fragments and their dimers, whereby the Coulomb field from the whole system is included. It is implemented in GAMESS (). Then it is possible to use the Quantum Theory of Atoms in Molecules (QTAIM) to study the bonds (http://aim.tkgristmill.com/index.html).

Just to add to the discussion, you can use Maximally Localized Wannier Functions to describe the atoms in detail, probably it does not have the background of the Bader partition but I am sure, the interpretation by using WFs is quite conveying. Wannier90 is code developed to interface with several DFT codes.

Yes, one method with the lowest computational cost is the DFT.

However the quality of the basis enters the issue of time, eg 4 zeta quality basis tend to be slower than double-zeta bases.

Tradutor

With regard to different codes exist which can be used, such as NWChem, dalton, see for example:

http://en.wikipedia.org/wiki/List_of_quantum_chemistry_and_solid_state_physics_software

other methods may be considered, such as mechanics or molecular dynamics. Both methods use parameters easier to be calculated, such as electrostatic forces between the atomic nuclei, however the accuracy is very low.

If you are focusing about a small molecule's orientation within a biological system, then mostly you are looking for H-bonding, Ionic, and VdW (such as hydrophobic, cation-pi, pi-pi stacking) interactions. The accuracy, as many said, is in the eye of the behold and what question you would like to address. For example, docking methodologies are done on a faster time-scales through appropriate force fields that reproduce with reasonable accuracy. Even the experimental crystal structure of a biological system limits within 1Ang, thus position of hydrogen atoms can not be identified. Thus, accuracy even if an ab-initio calculation can reproduce, has its experimental limitation to verify !!!

I find your question somewhat ambiguous. If you ask about ab-initio methods available to describe properly your system, of course there are. If you go for biological systems, DFT would be more useful due to the size. Concerning DFT, others have already given to you detailed answers. You can even think of using linear scaling techniques applied to CC or MP2 (L-CCSD, L-MP2) could be still affordable, depending on the size of your system.

If you ask for techniques to analyise which type of bonds you have in the molecule, the presence of hydrogen bonds, weak bonds, electrostatic interactions, there's a bunch of techniques: Bader's Atoms-in-Molecules (AIM), ELF, Natural Bonding Orbitals (NBO), Non-Covalent Interaction plots (NCI-plots), energy decomposition analysis (EDA) either by Morokuma (for HF wavefunctions) or Ziegle (DFT, in ADF), Natural Orbitals of Chemical Valence with Extended Transition State method (NOCV-ETS, an very interesting extension of EDA with get rids of symmetry constraints). The techniques you use depend on what you want to find and the programs you have available.

Although you have already many nice ideas, I just want to add one more. Have a look to a potent (and free) code called NCIPlot that can be easily used to interpret chemical contact in large systems, among other applications.

http://www.lct.jussieu.fr/pagesperso/contrera/nci-oprograms.html

Hope that helps,

Jose

You can certainly estimate the bonding via ab initio calculations in principle, but the size of system you can study depends on the method you want to use and the computational power available to you.

If you consider density functional theory (DFT), then the computational time for a conventional implementation scales cubically with the size of your system. If you have, say, 2000 atoms of C, N, H, O then on 500 cores it'll take a plane-wave program like CASTEP around an hour to compute the electronic ground state and atomic forces. The cubic scaling means if you double the atoms to 4000, you'd expect it to take 2^3 times longer = 8 hours. Whether this is practical for your system depends on how many atoms you have, and how big a computer you can use (and for how long). For large systems you could look at linear-scaling DFT programs such as ONETEP, which have been used to look at systems with 1000s to 10 000s of atoms.

Of course this is just to get the electronic ground state for a fixed set of atoms, if you want to use the forces to optimise the atomic configuration, then you might easily need a hundred or more ground-state calculations to reduce the forces to an acceptable level -- especially for all the hydrogen atoms, which show up poorly in most crystallography techniques so there is often large uncertainty in their position.

If you're looking at the forces, then you'd also have to consider the lack of van der Waals bonding in most DFT functionals, so you'd probably have to look at the semi-empirical dispersion corrections (e.g that of Tkatchenko-Scheffler). In my experience these work pretty well for first-row elements. You also need to think about the water permeating the system, and whether to treat it all explicitly, implicitly or a mixture of both.

So to sum up: it's possible to look at bonding in large systems with ab initio techniques such as DFT, but it itsn't trivial.

There are many aspects to bonding. The bond energy and bond order are two entirely different, but complementary, chemical descriptors. The binding energy (or dissociation energy) is of course very important. You may also want to compute bond order that quantify the number of electrons exchanged between two atoms in a material. Please see the following paper for a description of how to compute the bond orders: http://dx.doi.org/10.1039/c7ra07400j