2.4. Dimeric Solutes
The issue to be considered in this section is similar to those that have been discussed above. Solutes with two polar sites for the monomer may form one or even two hydrogen bond(s) within a dimer, which is/are intramolecular from the perspective of this species. Then the created intramolecular H-bond(s) compete(s) with the intermolecular H-bonds between the monomeric solutes in the dissociated form and the solvent molecules. Specifically, monomers with HX–C=O (X = N, O) and N–C–OH substructures would belong to this category. Formation of an intramolecular H-bond in a four-member ring with two polar functionals would lead to a strained structure. Although covalently bound four-member rings exist, a moderately strong H-bond could not maintain this relationship. B97D/aug-cc-pvtz geometry optimization [79] found geometry parameters for the gas-phase acetic acid carboxylic group very close to experimental values [28]. Accordingly, the H…O= distance is 230 pm and the O–H…O= angle is 75.5°. This bond angle is quite far from the favorable O–H…O angle of about 170° generally found to be favorable intermolecular H-bond. Thus the OCOH moiety should not be considered to be a ring, and the better way to stabilize the HX–C=O or N–C–OH substructure is the formation of a dimer.
The gas-phase structure of formic acid was determined from the microwave spectrum by Lerner et al. [108]. The main geometric parameters were obtained by their fit to the rotational constants. However, formic acid assumes mostly a dimeric structure (FAD) in the gas phase. In a theoretical study, Turi [109] identified seven stable dimeric structures on the potential energy hypersurface. The doubly-hydrogen-bonded isomer of C2h symmetry was found to be the most stable arrangement. Experiments confirmed this theoretical prediction. A comprehensive discussion of the formic acid dimer related issues, the paradigm of symmetric hydrogen bonding, and a collection of former experimental papers were provided by Zielke and Suhm [110]. Rotationally resolved spectra were recorded under supersonic jet conditions for the FAD by Matylitsky et al. [111]. With the assumption of unperturbed monomers, a center-of-mass distance of R = 299.0 ± 0.1 pm for the monomers within the dimer was calculated from the spectroscopic results. A recent update of the experimental results on FAD augmented with theoretical calculations up to the MP2/aug-cc-pvtz level was provided by Balabin [112].
Geometric parameters for monomeric and dimeric acetic and propionic acids in the gas phase were experimentally determined by Derissen [28,113]. Structures of the short-chain carboxylic acids to be discussed below are shown in Figure 5.
Figure 5  Structures of the syn (11) and anti (12) acetic acid, the s-cis propenic acid (13) and the s-trans pyruvic acid (14). The carboxylic group is syn for the latter two.   Simple aliphatic carboxylic acids assume predominantly doubly H-bonded, symmetrical dimeric forms (52%–87%) in the gas phase. The intermolecular H-bonds for acetic acid–acetic acid methyl ester complexes were studied by Emmeluth and Suhm [114] by FT-IR (Fourier transform infrared) spectroscopy for the mixed clusters in supersonic jet expansions. The methyl ester has two hydrogen-bond acceptor sites without having a strong donor site. The structural issues for the closest analogues of the acetic acid dimer and the acid-ester complexes were discussed on the basis of the recorded spectra and theoretical calculations at the MP2/6-311++G** and B3LYP/6-31G+G* levels. An interesting question is then: Will the dimeric forms be maintained in aqueous solution, or will the stabilizing “intramolecular” hydrogen bonds become disrupted so that the monomers can form intermolecular H-bonds with the water molecules.
Another important problem is the protonation state of the elements in the complexes of short-chain acids and bases. Such hydrogen-bonded complexes are stably formed from a neutral acid and a neutral amine in the gas phase, although acid—Guanidine complexes in the form of a hydrogen-bonded ion-pair are also stable in the gas phase [115]. In aqueous solution, the acid-amine ion-pair complexes are more stable, whereas the hydrogen-bonded complexes of the neutral elements are more stable in a low-polarity environment [116]. Such studies are important for the exploration of the ligand-receptor interactions in the binding cavity of the muscarinic acetylcholine receptor. At physiological pH of 7.4, a ligand with an amine function must be mainly protonated in the aqueous environment characteristic for the extracellular side of a transmembrane protein. When the ligand penetrates into the protein, most of the surrounding water molecules must be left behind. In the binding cavity of the receptor, at about 1100 pm from the surface, the ligand interacts with an aspartic acid side chain. According to a general consensus, the side chain is originally deprotonated. Thus a theoretical study of the protonation states for the partners under the modeling condition is justified [116].
The studies for dimer/complex formations in solution start with the geometry optimization of the associated species in the selected solvent. Using the continuum solvent approach, the poor handling of the solute-solvent H-bonds is less dramatic for the dimers of aliphatic acids. The main H-bond forming sites are involved in bonds to the partner, thus a less polar molecular surface of the dimer is seen by the solvent within the cavity. An acetic acid—Alkyl amine (mainly trimethyl amine) complex exhibits even larger non-polar molecular surface. The polar sites interact with each other in the depth of the complex, irrespective of whether the H-bond formed between the constituents is neutral or ionic.
The possible dimerization/complex formation in solution can be followed by calculating the potential of mean force (pmf) curve. This curve reflects the change of the solution free energy as a function of the solutes’ separation, taking the free energy of the solution with largely separated solutes as the reference state. If the pmf is calculated by the FEP procedure, the “R” separation of two reference atoms of the solutes should change only slightly by, e.g., 20 pm, and the free energy at separations R ± 10 pm could be calculated as a perturbation. Local minima of a pmf indicate stably associated forms, local maxima indicate barrier tops for association. The pmf may have more than one minimum site, also could decrease monotonically from the large-solute-separation reference state until reaching the minimum. The latter shape of the pmf indicates solute association without activation free energy. At small solute separations generally below 350 pm, the curves steeply ascend due to the quickly increasing van der Waals repulsions.
For large, more than 500–600 pm separation of the reference atoms, acceptance of the monomeric geometry and the related net atomic charges is reasonable. When the formation of the intermolecular H-bond(s) may start between the solutes, the geometry and the charge parameters should be gradually transformed into the values that were obtained for the optimized dimer. The related charges were fitted to the corresponding in-solution MEP [79,117].