**3. DFT approach to the molecular binding in organic liquids**

In this section, we have presented the traditional methods of DFT calculations together with our approach. In most works, the application of DFT to the problem of formation mechanism and arrangement of organic liquids is reduced to the noncovalent interactions' model of dimers with hydrogen bond. Although this approach is available for the gas phase binding only, such interactions arise quite rarely in the gaseous systems. Nevertheless, this concept is conventionally extrapolated to the condensed phase structure. However, the geometry and molecular interactions in this system sufficiently differ from the gaseous one. Therefore, we have suggested the DFT approach based on our IR spectral observations that indicates the certain changes of the molecular structure in the organic liquids in comparison to a single molecular state (see Section 3.4).

## **3.1 Geometry optimization (GO) procedure in DFT calculations of molecular system**

The basic idea of system geometry optimization (GO) is that in *ab initio* calculations the SCF energy optimization procedure often leads not to a global minimum but to the local extremum. Therefore, besides of the SCF procedure, the additional mathematical method named GO is practically used.

For large molecules, which to a certain extent can simulate a supramolecular system, a method of delocalized internal coordinates within the framework of the DFT has been proposed. It was shown that the combination of the trust radius and line search method gives good accuracy in the geometry calculation of a single molecule. A performance analysis of the new geometry optimizer using different start Hessian matrices, basis sets and grid accuracies is given in [38]. This scheme has been successfully used for the study of enzyme reactions, treating the active site by a high-level method, particularly DFT, and the protein environment by molecular mechanics.

The minimum of energy is reached when the geometry characteristics of molecule is close to the experimental values. A few variants of the GO procedure for the DFT calculation can be found in the other papers, in which the findings are in a good agreement with experimental data [39, 40].

Considering these results, one can ask, firstly, why the calculation referring to single molecule can reproduce the geometry of condensed phase so well while the thermodynamic, kinetic, and spectral properties of molecular bulk differ from the individual species; secondly, the used regularity of energy change from geometric parameters, for example, from bond length, is strictly suitable only for diatomic molecules. For the polyatomic ones, this procedure can be attributed only with a sufficient approximation, because the bonds and angles in a molecule cannot vary independently. This situation is well known for the small vibrations of point masses near the interatomic equilibrium [24–26]. The solution of vibrational problem in, so called, internal natural coordinates (bonds and angles between neighboring bonds), requires involving the coefficients of the interactions between them. Besides, in organic liquids, the potential energy surface consists of the infinite closely located energy extremums of the single molecules. Therefore, in the real system the minimum of energy is broadly smoothed. Since the electron density in these systems is strongly delocalized, the geometric optimization procedure loses its real physical meaning. The arguments above show that the GO is an additional mathematical fit in the standard iterations shape, and it can be applied for the real systems only with the reasonable restriction. For this reason, the DFT calculations with the GO for the simplest organic molecules forming the stable liquid bulk (for example,

tetrachloromethane, dichloroethane and non-substituted hydrocarbons etc.), does not lead to the energy minima even for two-molecule interaction (see Section 3.4). Thus, the DFT calculation without the GO procedure seems to be applicable in this field as well.
