Actual Symmetry of Symmetric Molecular Adducts in the Gas Phase, Solution and in the Solid State

: This review discusses molecular adducts, whose composition allows a symmetric structure. Such adducts are popular model systems, as they are useful for analyzing the effect of structure on the property selected for study since they allow one to reduce the number of parameters. The main objectives of this discussion are to evaluate the inﬂuence of the surroundings on the symmetry of these adducts, steric hindrances within the adducts, competition between different noncovalent interactions responsible for stabilizing the adducts, and experimental methods that can be used to study the symmetry at different time scales. This review considers the following central binding units: hydrogen (proton), halogen (anion), metal (cation), water (hydrogen peroxide).


Introduction
If something is perfectly symmetric, it can be boring, but it cannot be wrong. If something is asymmetric, it has potential to be questioned. Note, for example, the symmetry of time in physics [1,2]. Symmetry also plays an important role in chemistry. Whether it is stereochemistry [3], soft matter self-assembly [4,5], solids [6,7], or diffusion [8], the dependence of the physical and chemical properties of a molecular system on its symmetry is often a key issue. Symmetric molecular adducts are popular model systems; they are used to analyze the effect of structure on the property chosen for research since they allow one to reduce the number of parameters [9][10][11][12]. On the other hand, symmetry in chemistry is a matter of the size and time scale in question [13]. The same molecular system can be symmetric for one experimental method and asymmetric for another. It is important to understand what processes are hidden behind this discrepancy in each specific case.
The problem of the size scale already begins at the level of the model adducts composition. What structure has the simplest model adduct with which it is possible to investigate the property under consideration? The Zundel cation (H 5 O 2 + ) and the Eigen cation (H 9 O 4 + ) seem to be the most illustrative example [14,15]. Which of these two structures is the best for simulating a hydrated proton? It seems that neither experiment nor theory can answer this question regardless of the property being discussed [16][17][18][19][20]. The same is valid for the hydration of the hydroxide ion [21][22][23][24]. Of course, bulk water is one of the most complex solvents in this content. The time scale problem has to do with tautomerism. For some methods, its rate is slow. In this case, experimental parameters can be observed for each of the structures presented. For other methods, this rate is fast and only average experimental parameters can be observed.
This short review discusses molecular adducts whose composition allows a symmetric structure. These adducts should be stable in organic solvents at least on the millisecond time scale. It should be possible to model the effect of the surroundings on their structure by considering the environment as a polarizable continuum. It is not limited only to the polarizable continuum model (PCM) and solvation model based on density (SMD) approximations [25][26][27][28][29]. It is important that the solute-solvent interactions do not have to Reference [51] reviews the symmetry of the H-bond of the maleate anion with different cations in the crystalline phase. Using the position of the mobile proton available from low-temperature neutron-diffraction studies on nine different hydrogen maleate salts [52][53][54][55][56][57], the authors established a correlation that allows determination of this position from X-ray diffraction (XRD) data [51,58]. There are three groups of crystals in which the deviation of the proton position from the H-bond center is below 0.06 Å, about 0.2 Å, and about 0.3 Å [51]. The symmetry of these H-bonds changes under pressure [59].
Similar results have been obtained for hydrogen phthalate, Figure 1b. Its intramolecular H-bond is symmetric in the gas phase [60]. In solution it becomes asymmetric due to solute-solvent and anion-cation interactions [60][61][62][63]. Note that the strength of this H-bond suffers from significant steric stress [64]. The energy of this bond in crystalline phthalic acid is only 9.5 kJ/mol [65] while it can be more than 100 kJ/mol for strong intermolecular H-bonds [66]. In the crystalline phase, the position of the mobile proton within the intramolecular H-bond of lithium hydrogen phthalate depends on the environment and can be both very close to the center and very asymmetric [67]. However, there does not appear to be a crystalline hydrogen phthalate with a perfectly symmetric intramolecular H-bond [68]. The symmetry of the maleate anion in solution was studied using a primary H/D isotope effect on the NMR chemical shift, p ∆(H/D) ≡ δ(ADB) − δ(AHB). The motion of the binding hydron within a H-bond should always be treated as quantum [35]. Consequently, when the mobile proton is substituted for deuteron, the geometry of the H-bond changes. For a symmetric H-bond this substitution results in a contraction of the heavy nuclei distance, that is, the strengthening of the H-bond; for an asymmetric H-bond it causes a lengthening of this distance, that is, the weakening of the H-bond [36]. These geometric changes lead to chemical shift changes. It is expected that p ∆(H/D) > 0 for symmetric H-bonds and negative for asymmetric ones (note, that other authors may define the isotope effects as δ(AHB) − δ(ADB)) [37]. For the maleate anion p ∆(H/D) = 0.08 ppm at 150 K [38] in an aprotic, highly polar CDF 3 /CDF 2 Cl mixture [39] and 0.03 ppm at 218 K in CD 2 Cl 2 [40]. These results suggested that under these conditions this H-bond The distance between the nitrogen atoms of 1,8-naphthyridine (2,2 -bipyridine) is too large to form a strong intramolecular H-bond, Figure 1d. In the gas phase [91], on silica surfaces [92], and in many crystals it occurs in the trans-configuration [93,94]. Coordination to a metal [95,96] or protonation [97] are required to stabilize the cis-configuration shown in Figure 1d. This cis-configuration of 1,8-naphthyridine-H + has been used to study in detail the counterion effect on intramolecular H-bonds and proton transfer using 1 H and 15 N NMR at 150-115 K in CDF 3 /CDClF 2 [98]. Figure 2 shows the main results of this study. Dichloroacetic acid forms a strong intermolecular H-bond with one of the nitrogen atoms of 1,8-naphthyridine. At low temperature in the aprotic solvent this complex is stable on the millisecond time scale. The configuration of the base is unknown, but it is probably fluctuating between the transand cis-configurations. The position of the mobile proton depends on the current polarity of the solvent. The lower the temperature, the higher the polarity, the closer the proton is to the nitrogen atom [39]. At 115 K the geometry of this H-bond is (N-H + )···O -. However, the local polarity fluctuates and causes the proton to move in the intermediate temperature range at around 120 K with a large amplitude within the H-bond. The moment the proton is at the oxygen atom, it can change the nitrogen atom with which it will be bound. Consequently, at 120 K there is an intramolecular proton exchange in the absence of the intramolecular H-bond, Figure 2a. The tetrafluoroborate anion is a weak base and it does not break the intramolecular H-bond in 1,8-naphthyridine-H + . However, there is still a specific interaction in this anion-cation pair that makes the intramolecular proton transfer slow on the millisecond time scale, Figure 2b. Only a very bulky anion, tetrakis[3,5-bis-(trifluoromethyl)phenyl] borate, does not exhibit a preferential interaction with one of the pyridine rings. A very fast degenerate intramolecular proton transfer was detected in this case, Figure 2c. The geometry of this intramolecular H-bond was estimated to be: N-H = 1.1 Å and H···N = 1.7 Å [98]. environment [75][76][77]. In general, it appears that the intramolecular H-bond in all known protonated proton sponges is asymmetric both in solution and in the solid state [78,79]. Due to the strength of the intramolecular H-bond and a slow intermolecular proton exchange in solution, proton sponges are very popular model systems for benchmark studies of spectral manifestations of H-bonding [80][81][82][83][84][85][86]. Alternatively, the H-bond symmetry can be purposefully lowered to investigate competing interactions [87][88][89][90].
The distance between the nitrogen atoms of 1,8-naphthyridine (2,2′-bipyridine) is too large to form a strong intramolecular H-bond, Figure 1d. In the gas phase [91], on silica surfaces [92], and in many crystals it occurs in the trans-configuration [93,94]. Coordination to a metal [95,96] or protonation [97] are required to stabilize the cisconfiguration shown in Figure 1d. This cis-configuration of 1,8-naphthyridine-H + has been used to study in detail the counterion effect on intramolecular H-bonds and proton transfer using 1 H and 15 N NMR at 150-115 K in CDF3/CDClF2 [98]. Figure 2 shows the main results of this study. Dichloroacetic acid forms a strong intermolecular H-bond with one of the nitrogen atoms of 1,8-naphthyridine. At low temperature in the aprotic solvent this complex is stable on the millisecond time scale. The configuration of the base is unknown, but it is probably fluctuating between the trans-and cis-configurations. The position of the mobile proton depends on the current polarity of the solvent. The lower the temperature, the higher the polarity, the closer the proton is to the nitrogen atom [39]. At 115 K the geometry of this H-bond is (N-H + )···O -. However, the local polarity fluctuates and causes the proton to move in the intermediate temperature range at around 120 K with a large amplitude within the H-bond. The moment the proton is at the oxygen atom, it can change the nitrogen atom with which it will be bound. Consequently, at 120 K there is an intramolecular proton exchange in the absence of the intramolecular H-bond, Figure 2a

Proton-Bound Homodimers
The question "What factors determine whether a proton-bound homodimer has a symmetric or an asymmetric hydrogen bond?" was answered for homodimers of the [XHX] + type in [99,100]. It was shown that the symmetry of such homodimers depends on the electronegativity of the atom X. "A more electronegative X atom tends to produce a more positively charged shared proton, which in turn facilitates the closer approach of the two X atoms and the formation of a symmetric hydrogen bond" [99]. In the gas phase, the symmetric [X···H···X] + homodimers are expected for X = F and, with some exceptions, O and sp-hybridized N. For X = sp 2 -and sp 3 -hybridized N such homodimers will be asymmetric, although proton transfer within such H-bonds can be fast. Protonbound homodimers involving second-row atoms were studied as well [101]. Note that the calculation result can critically depend on the level of approximation [102]. High level calculations can show very good agreement with experimentally observed values [103][104][105].
The binding energies of such homodimers depend on the electronic properties of X. For example, there is a quadratic correlation between the binding energy and the proton affinity of X within a given set of X-R, where R is a substituent. The energy reaches its maximum at a certain value of the proton affinity [100]. This relationship is the result of a compromise between the penalty for partially deprotonating [XH] + and the benefit of partially protonating X.
In condensed matter, various noncovalent interactions compete with each other. Very specific conditions are required to observe centrosymmetric [X···H···X] + complexes. For example, it can be noble-gas (Ng) matrices, X = Ng [106,107]. The only complex for which the presence of a centrosymmetric structure was experimentally proved in various solvents and solids is [F···H···F] - [108][109][110][111]. The bond dissociation energy of [FHF]is about 190 kJ/mol [112]. This energy is twice that of the next candidate, [ClHCl] -, 100 kJ/mol [113]. It is not yet clear whether [ClHCl] -, can be centrosymmetric in condensed matter [114,115]. The presence of a competing H-bond can completely break the symmetry of [FHF]as it happens in pyridine-H + ···F -···H-F [116]. Figure 3 shows 1 H, 2 H, and 19 F NMR spectra of a solution containing the [FHF]and [FDF]anions and the tetrabutylammonium cation in CDF 3 /CDF 2 Cl at 130 K [38]. For this complex p ∆(H/D) ≡ δ(FDF) − δ(FHF) = 0.32 ppm and 2 ∆ 19 F(D) ≡ δ(FDF) − δ(FHF) = −0.37 ppm. These values were quantitatively reproduced in MP2 calculations, which confirms the centrosymmetric structure of these anions [47]. The geometry of [FHF]in solution depends on specific interactions with solvent molecules. Molecular dynamics simulations show that in CH 2 Cl 2 the main interaction is F···H-CHCl 2 H-bonding, while in CCl 4 it is a weaker F···Cl-CCl 3 halogen-halogen bonding [117]. Symmetric solvation should lead to a contraction of [FHF] - [118]. Asymmetric solvation will perturb the symmetry of [FHF] -. Surprisingly, the effect can be stronger due to the halogen-halogen interactions in CCl 4 than due to the H-bonding in CH 2 Cl 2 [117]. These geometric changes cannot be measured using either 1 H or 19 F NMR, because these chemical shifts are independent of the F . . . F distance at 2.3 Å [118].  [FHF] ⁻ can be centrosymmetric in solids when the environment of the fluorine atoms is symmetric [108]. The supposed examples can be found elsewhere [108,110]. Structural, energetic, and spectral properties of [FHF] ⁻ were considered in a very large number of publications. Here are just a few of the newest [119][120][121][122][123].
Nitrogen-containing heterocycles are probably the most experimentally studied proton-bound homodimers of the [X···H···X] + type. More specifically, these are symmetrically substituted pyridine derivatives. There are several reasons for this. The basicity of such derivatives can be varied over a wide range in small steps. Orthosubstituents can be used to protect the mobile proton from competing interactions, that extends the lifetime of such homodimers. It is easy to switch from homo-to heterodimers to study asymmetric H-bonds. The last, but not least, reason is that H-bonded complexes of pyridines are ideally suited for their NMR study, since one is not limited to 1 H NMR. [FHF]can be centrosymmetric in solids when the environment of the fluorine atoms is symmetric [108]. The supposed examples can be found elsewhere [108,110]. Structural, energetic, and spectral properties of [FHF]were considered in a very large number of publications. Here are just a few of the newest [119][120][121][122][123].
Nitrogen-containing heterocycles are probably the most experimentally studied protonbound homodimers of the [X···H···X] + type. More specifically, these are symmetrically substituted pyridine derivatives. There are several reasons for this. The basicity of such Symmetry 2021, 13, 756 6 of 23 derivatives can be varied over a wide range in small steps. Ortho-substituents can be used to protect the mobile proton from competing interactions, that extends the lifetime of such homodimers. It is easy to switch from homo-to heterodimers to study asymmetric H-bonds. The last, but not least, reason is that H-bonded complexes of pyridines are ideally suited for their NMR study, since one is not limited to 1 H NMR. The isotropic 15 N NMR chemical shift, δ iso ( 15 N), of such pyridine derivatives characteristically depends on the N . . . H distance [124][125][126]. For all of them, if δ iso ( 15 N) ≡ 0 in the absence of Hbonding, δ iso ( 15 N) ≈ 125 ppm for the protonated base [127]. Due to this, for H-bonds of medium strength, the δ iso ( 15 N) values can be converted to N . . . H distances with high accuracy, Figure 4 [128]. This correlation has been successfully applied to measure H-bond geometries in solution [129,130], interfaces [131,132], enzyme environments [133,134], and solids [135,136].
[FHF] ⁻ can be centrosymmetric in solids when the environment of the fluorine atoms is symmetric [108]. The supposed examples can be found elsewhere [108,110]. Structural, energetic, and spectral properties of [FHF] ⁻ were considered in a very large number of publications. Here are just a few of the newest [119][120][121][122][123].
Nitrogen-containing heterocycles are probably the most experimentally studied proton-bound homodimers of the [X···H···X] + type. More specifically, these are symmetrically substituted pyridine derivatives. There are several reasons for this. The basicity of such derivatives can be varied over a wide range in small steps. Orthosubstituents can be used to protect the mobile proton from competing interactions, that extends the lifetime of such homodimers. It is easy to switch from homo-to heterodimers to study asymmetric H-bonds. The last, but not least, reason is that H-bonded complexes of pyridines are ideally suited for their NMR study, since one is not limited to 1 H NMR. The isotropic 15 N NMR chemical shift, δiso( 15 N), of such pyridine derivatives characteristically depends on the N…H distance [124][125][126]. For all of them, if δiso( 15 N) ≡ 0 in the absence of H-bonding, δiso( 15 N) ≈ 125 ppm for the protonated base [127]. Due to this, for H-bonds of medium strength, the δiso( 15 N) values can be converted to N…H distances with high accuracy, Figure 4 [128]. This correlation has been successfully applied to measure H-bond geometries in solution [129,130], interfaces [131,132], enzyme environments [133,134], and solids [135,136]. In the gas phase, the proton-bound homodimer of pyridine has an asymmetric [N···H-N] + H-bond [99]. The N…N distance is about 2.69 Å [137] and the bond dissociation energy is 105 [138] or 109 kJ/mol [139]. In solution, the N…N distance shortens to 2.62 Å [140] and the bond dissociation energy in CD2Cl2 is about 15 kJ/mol [139]. The geometry In the gas phase, the proton-bound homodimer of pyridine has an asymmetric [N···H-N] + H-bond [99]. The N . . . N distance is about 2.69 Å [137] and the bond dissociation energy is 105 [138] or 109 kJ/mol [139]. In solution, the N . . . N distance shortens to 2.62 Å [140] and the bond dissociation energy in CD 2 Cl 2 is about 15 kJ/mol [139]. The geometry of this H-bond is temperature dependent. Cooling leads to an increase in the polarity of the solvent, which causes an increase in the H-N distance and a reduction of the N···H and N...N distances. Figure 5 shows NMR spectra of the proton-bound homodimer of pyridine in solution down to 120 K [141]. For this complex, p ∆(H/D) = −0.95 ppm, which unambiguously indicates the asymmetry of the H-bond, while the multiplicity of the 1 H and 15 N NMR spectra indicates a fast, reversible proton transfer within this H-bond. The observed contraction of the N . . . N distance in solution is not confirmed by calculations using the polarizable continuum model (PCM [25,26]) and solvation model based on density (SMD [28]) approaches. On the contrary, these calculations predict that this distance must be about 2.75-2.77 Å [34,142]. This discrepancy was explained using the Adduct under Field (AuF) approach [143][144][145]. The driving force of this reversible proton transfer is a fluctuating solvation environment. The potential energy curve of this mobile proton changes from a symmetric double-well to an asymmetric single-well one. This proton tautomerism is fast on the NMR time scale that is its rate is faster than 10 3 s −1 . This proton transfer occurs through transition states in which the N . . . N distances are shorter than in the initial [N···H-N] + and the final [N-H···N] + structures. As a result, the mean N . . . N distance measured in NMR experiments is shorter than that of the most energetically favorable structures obtained in static calculations [146]. This proton tautomerism is slow on the electronic absorption and IR time scales [147,148]. The frequencies of the symmetric and antisymmetric CN vibrations are affected by H-bonding strong enough to discriminate between the spectral pattern of the H-bonded and protonated pyridines [148]. Consequently, the rate of this proton tautomerism is slower than 10 11 s −1 .
fluctuating solvation environment. The potential energy curve of this mobile proton changes from a symmetric double-well to an asymmetric single-well one. This proton tautomerism is fast on the NMR time scale that is its rate is faster than 10 3 s ⁻1 . This proton transfer occurs through transition states in which the N…N distances are shorter than in the initial [N···H-N] + and the final [N-H···N] + structures. As a result, the mean N…N distance measured in NMR experiments is shorter than that of the most energetically favorable structures obtained in static calculations [146]. This proton tautomerism is slow on the electronic absorption and IR time scales [147,148]. The frequencies of the symmetric and antisymmetric CN vibrations are affected by H-bonding strong enough to discriminate between the spectral pattern of the H-bonded and protonated pyridines [148]. Consequently, the rate of this proton tautomerism is slower than 10 11 s ⁻1 . How short can be the N…N distance in the proton-bound homodimers of pyridines? The binding energy of such homodimers will reach a maximum at a certain value of the proton affinity of the involved pyridine derivative [100]. Figure 6 shows experimental N…N distances in the proton-bound dimers of ortho-unsubstituted and ortho-methyl substituted pyridines in CDF3/CDF2 at 120K as a function of calculated gas-phase proton affinities [137,140]. The N…N distance clearly correlates with the gas-phase proton affinity. The shortest distance of 2.613 Å was observed for pyridine [140]. Steric interaction between the ortho-methyl groups becomes operative at the N…N distance of ∼2.7 Å and How short can be the N . . . N distance in the proton-bound homodimers of pyridines? The binding energy of such homodimers will reach a maximum at a certain value of the proton affinity of the involved pyridine derivative [100]. Figure 6 shows experimental N . . . N distances in the proton-bound dimers of ortho-unsubstituted and ortho-methyl substituted pyridines in CDF 3 /CDF 2 at 120K as a function of calculated gas-phase proton affinities [137,140]. The N . . . N distance clearly correlates with the gas-phase proton affinity. The shortest distance of 2.613 Å was observed for pyridine [140]. Steric interaction between the ortho-methyl groups becomes operative at the N . . . N distance of ∼2.7 Å and limits the closest approach to 2.665 Å. However, this interaction is not a pure repulsion. London dispersion contributes to the binding energy of ortho-substituted homodimers [139,155]. As a result, the homodimers of ortho-substituted pyridines can be more stable than that of ortho-unsubstituted ones at low temperatures as long as the entropic costs are not too high. The thermodynamic parameters of a large number of the proton-bound homodimers of pyridines are available in the Supporting Information to [139].
In solution, effective proton affinities depend on solvation [156]. For example, consider derivatives of pyridine and acridine with the same gas phase proton affinity. In solution, the effective proton affinity of this acridine will be smaller than that of the pyridine derivative and the N···N distance in the proton-bound homodimer of acridine will be shorter [140]. This effect was attributed to the local ordering of the solvent molecules, which increases with the size of the solute and causes an increase in the local reaction field. The deviation from the general trend observed for halogen-substituted pyridines, 5 in Figure 6, is also probably caused by the peculiarities of the mean local surroundings. The influence of halogen-halogen interactions on molecular systems can be quite large [157,158].
Within the framework of this review, it is impossible to summarize even the main properties of carboxylic acid dimers and carboxylate-carboxylic acid dimers. These systems and their importance in practice require a special review. Cyclic dimers of carboxylic acid exhibit a rapid degenerate double proton transfer in the gas-phase [159][160][161][162], solu-  [163,164], and solids [165]. The binding energies of such cyclic dimers in the gas phase are about 50-70 kJ/mol [166]. In the presence of other proton acceptors, these cycles are easily opened [66,[167][168][169]
not too high. The thermodynamic parameters of a large number of the proton-bound homodimers of pyridines are available in the Supporting Information to [139].
In solution, effective proton affinities depend on solvation [156]. For example, consider derivatives of pyridine and acridine with the same gas phase proton affinity. In solution, the effective proton affinity of this acridine will be smaller than that of the pyridine derivative and the N···N distance in the proton-bound homodimer of acridine will be shorter [140]. This effect was attributed to the local ordering of the solvent molecules, which increases with the size of the solute and causes an increase in the local reaction field. The deviation from the general trend observed for halogen-substituted pyridines, 5 in Figure 6, is also probably caused by the peculiarities of the mean local surroundings. The influence of halogen-halogen interactions on molecular systems can be quite large [157,158]. Within the framework of this review, it is impossible to summarize even the main properties of carboxylic acid dimers and carboxylate-carboxylic acid dimers. These systems and their importance in practice require a special review. Cyclic dimers of carboxylic acid exhibit a rapid degenerate double proton transfer in the gas-phase [159][160][161][162], solution [163,164], and solids [165]. The binding energies of such cyclic dimers in the gas phase are about 50-70 kJ/mol [166]. In the presence of other proton acceptors, these cycles are easily opened [66,[167][168][169]. A rapid degenerate [O-H···O] -⇌ [O···H-O] -proton transfer also occurs in carboxylate-carboxylic acid dimers [170].
The most studied type of halogen bound homodimers are (FH)nF ⁻ complexes. These anionic clusters are ideal objects for theoretical, structural, and spectroscopic studies of H- Figure 6. Experimental N . . . N distances in the proton-bound dimers of pyridines as a function of calculated gas-phase proton affinities (PA) [137,140]. The dotted lines are for eye guidance only.
The most studied type of halogen bound homodimers are (FH) n Fcomplexes. These anionic clusters are ideal objects for theoretical, structural, and spectroscopic studies of H-bonding, since on the one hand they are small, and on the other hand, their geometry changes noticeably due to small external interactions or H/D isotopic substitution. There are experimental evidences that complexes (FH) n F -, where n = 2-5, can present in solution and solid state [109,[175][176][177][178][179][180]. These and similar complexes have been used in theoretical studies of H-bonding binding energies [181], H-bonding with fluorine [182], vibrations of H-bonds [183,184], and NMR spin-spin coupling across H-bonds [185][186][187][188][189][190][191][192]. Of particular importance is the cooperativity (anticooperativity) of the H-bonds in these and similar complexes [193][194][195][196]. The cooperativity of H-bonds plays a very important role in biochemical reactions [197,198], molecular self-assembly [199,200], and the structure of water solvation clusters [201,202]. Only this topic will be discussed here. Figure 7 shows 1 H, 2 H and 19 F NMR spectra of solutions containing FH···F -···HF, FH···F -···DF and FD···F -···DF anions in CDF 3 /CDF 2 Cl at 130 K [203]. The protons of FH···F -···HF are located at the outer fluorine atoms. The corresponding spin-spin scalar coupling 1 J HF = 354 Hz. The protons also couple to the central fluorine atom across the H-bonds, h J H···F = −24 Hz. Therefore, these protons give rise to a doublet of doublet signal, Figure 7a. The outer and central fluorine atoms couple to each other, 2h J F . . . F = 147 Hz, and give rise to a doublet of doublet signal, Figure 7f, and a triplet of triplet signal, Figure 7d. The rate constant for proton and H-bond exchange is less than 10 3 s −1 . This complex is not linear, the FFF angle is about 130 • [191]. There is an anti-cooperative coupling of these two H-bonds. As a result, the FH···F -···DF anion is asymmetric. The 1 H NMR chemical shift of the FH···Fproton is larger than the 2 H NMR chemical shift of the F -···DF deuteron. The former is also larger, and the latter is less than the 1 H NMR chemical shift of the protons in FH···F -···HF (see the arrows in Figure 7b,c). Consequently, the FH···F -H-bond is shorter and the F -···DF one longer than the bonds in FH···F -···HF. This conclusion is confirmed by changes of the coupling constants and 19 Figure 7a. The outer and central fluorine atoms couple to each other, 2h JF…F = 147 Hz, and give rise to a doublet of doublet signal, Figure 7f, and a triplet of triplet signal, Figure 7d. The rate constant for proton and H-bond exchange is less than 10 3 s ⁻1 . This complex is not linear, the FFF angle is about 130° [191]. There is an anti-cooperative coupling of these two H-bonds. As a result, the FH···F ⁻ ···DF anion is asymmetric. The 1 H NMR chemical shift of the FH···F ⁻ proton is larger than the 2 H NMR chemical shift of the F ⁻ ···DF deuteron. The former is also larger, and the latter is less than the 1 H NMR chemical shift of the protons in FH···F ⁻ ···HF (see the arrows in Figure 7b,c). Consequently, the FH···F ⁻ H-bond is shorter and the F ⁻ ···DF one longer than the bonds in FH···F ⁻ ···HF. This conclusion is confirmed by changes of the coupling constants and 19   A detailed analysis of the experimentally obtained NMR parameters made it possible to measure the geometry of these H-bonds, Figure 8. Surprisingly, the resulting effect of the double deuteration corresponds approximately to the algebraic sum of the direct and the vicinal isotope effects [203]. These sum rules are valid for NMR parameters as well as for the F…F distances. For example, the midpoints of the sums of the F ⁻ …F distances in the F-H···F ⁻ ···D-F anion, RHD = (F ⁻ …F(H) + F ⁻ …F(D))/2, and in the F-H···F ⁻ ···H-F and F-D···F ⁻ ···D-F anions, RHHDD = (F ⁻ …F(H) + F ⁻ …F(D))/2, are shown by arrows in Figure 8. It is A detailed analysis of the experimentally obtained NMR parameters made it possible to measure the geometry of these H-bonds, Figure 8. Surprisingly, the resulting effect of the double deuteration corresponds approximately to the algebraic sum of the direct and the vicinal isotope effects [203]. These sum rules are valid for NMR parameters as well as for the F . . .  Figure 8. It is obvious that R HD and R HHDD are almost equal. The same rules are valid for the (FH) 3 Fanion. There is hardly any other molecular system for which such a detailed analysis of such small effects would be possible. obvious that RHD and RHHDD are almost equal. The same rules are valid for the (FH)3F ⁻ anion. There is hardly any other molecular system for which such a detailed analysis of such small effects would be possible.

Metal (Cation) as the Binding Unit
Symmetric transition metal organometallics are not necessarily the most effective catalysts. However, the elucidation of their structure in solution can be greatly facilitated if they are or can be symmetric. Although 1 H and 13 C NMR are not always sufficient to

Metal (Cation) as the Binding Unit
Symmetric transition metal organometallics are not necessarily the most effective catalysts. However, the elucidation of their structure in solution can be greatly facilitated if they are or can be symmetric. Although 1 H and 13 C NMR are not always sufficient to determine the structure of organometallic species, 31 P NMR can be very useful when phosphorous is coordinated to the metal center. Only 1,3,5-triaza7-phosphaadamantane (PTA, Figure 9) complexes will be considered here. The rationale for this choice is explained as follows. The 31 P isotope is the only stable isotope of phosphorus. It has a spin quantum number of 1/2 and a wide chemical shift range of about 400 ppm. This nucleus is a very convenient NMR probe for studying molecular complexes [99,[204][205][206], organometallics [207][208][209][210], and mobility at interfaces [211][212][213]. For example, 31 P NMR has been used to study the effect of temperature and hydration on the mobility of small to bulky molecules loaded onto mesoporous silica [214]. However, 31 P NMR shielding can depend on the conformation of the molecule [215], the crystalline electric field [216], while various noncovalent interactions can cause similar changes [217]. These disadvantages are completely absent in the case of PTA. PTA is a rigid and relatively chemically inert molecule. In acidic solution, PTA would be protonated at one of its nitrogen atoms. This protonation results in a 6 ppm change in δ iso ( 31 P) [218]. In contrast, when PTA is coordinated to transition metals, its chemical shift varies in a wide range [219]. Moreover, the value of its δ iso ( 31 P) in transition metal organometallics depends on the trans-ligand [220,221]. Therefore, 31 P NMR of PTA can be used to study whether the symmetry of its complexes is the same in the solid and solution phases.     . δ iso ( 31 P) of PTA in these complexes were calculated under the wB97XD/Def2QZVP approximation [222][223][224] and compared to the experimental δ iso ( 31 P) in solution [9], Table 1. For Ni(0)(PTA) 4 , Pd(0)(PTA) 4 and Cu + (I)(PTA) 4 , the calculated values are very close to the experimental ones. A small spread in the calculated values reflects the fact that the optimized structures used in these calculations were slightly asymmetric. This flaw is not important because of the flexibility of such complexes in solution. On the contrary, the reported experimental δ iso ( 31 P) for Pt(0)(PTA) 4 cannot correspond to this symmetric structure. The symmetry of the Cl 2 M(II)(PTA) 2 complexes in solution depends on the metal. For Ni, the configuration in the crystalline state was not reported. For Pd, the configuration in the crystalline state is cis-Cl 2 Pd(PTA) 2 [225]. Both the cis-Cl 2 Pt(PTA) 2 and the trans-Cl 2 Pt(PTA) 2 configurations are possible in the crystalline state [226,227]. According to the calculations [9], the reported experimental δ iso ( 31 P) in solution correspond to the cis-Cl 2 Ni(PTA) 2 , cis-Cl 2 Pd(PTA) 2 , and trans-Cl 2 Pt(PTA) 2 configurations, Table 1.

Water (Hydrogen Peroxide) as the Binding Unit
Water molecules like each other. Being adsorbed on a silica surface, water tends to self-aggregate even at concentrations below the monolayer, when many other molecules are still uniformly distributed on the surface [233][234][235]. In aprotic organic solvents at low concentrations, water molecules can be in a monomeric state. In this state, the 1 H NMR chemical shift of water is less than 2 ppm [236]. At higher concentrations, water molecules form clusters. In this state, their 1 H NMR chemical shift is about 4.8 ppm. The concentration at which water changes the state depend on the solvent and temperature [236]. The stronger H-bonding with the solvent and the higher the temperature, the higher the concentration at which water prefers homoclusters. At room temperature, it occurs when the water concentration is above 10-50 mM [236]. In dimethyl sulfoxide, water presents in the monomeric state at much higher concentrations. In this solvent, the 1 H NMR chemical shift of water is 3.3 ppm. Therefore, it is obvious that water is strongly H-bonded to solvent molecules. These are most likely symmetric complexes in which two solvent molecules share one water molecule. This type of complex has been observed experimentally in organic solutions at low temperatures in the presence of an excess of pyridine [237] and in frozen pyridine-water mixtures in porous materials [201]. Figure 10 shows the structure of 2:1 pyridine:water and collidine:water complexes, where collidine stands for 2,4,6trimethylpyridine. In these complexes, the experimentally measured N···H distances are 1.82 Å for pyridine and 1.92 Å for collidine [237]. The basicity of collidine is higher than that of pyridine. Consequently, the greater distance is the result of steric interactions of the ortho-methyl groups in the 2:1 collidine:water complex. Indeed, in 1:n base:water complexes, where n >> 1, the experimentally measured N···H distances are 1.69 Å for pyridine and 1.64 Å for collidine. The strong shortening of the distances in both cases is the result of the anticooperative interaction of H-bonds in the 2:1 base:water complex and the cooperative interaction of H-bonds in water clusters.
Similar symmetric complexes can often be found in crystals. For example, Figure 11a  shows [240]. Presumably, this mobility reflects a specific property of the P=O group. This group can simultaneously form two equally strong H-bonds [241]. For example, Figure 11b shows the structure of tricyclohexylphosphine oxide monohydrate [213]. These two water molecules are already immobile [217]. This H-bond network is asymmetric, with two O . . . O distances of 2.844 and two of 2.897 Å [213]. Surprisingly, water can be replaced with hydrogen peroxide. Figure 11c shows the structure of hydrogen peroxide tricyclohexylphosphine oxide [242]. This H-bond network is asymmetric as well, with two O . . . O distances of 2.743 and two of 2.771 Å. In hydrogen peroxide triphenylphosphine oxide these distances are 2.677 and 2.718 Å [243]. The decreasing distances indicate that the total energy of hydrogen peroxide H-bond networks is higher than in the case of water. This may be the reason that there are several other complexes of hydrogen peroxide with phosphine oxides of the same structure. For example, in tBu 3 -phosphine oxide hydrogen peroxide the O . . . O distances are 2.728 and 2.737 Å [243]. In hydrogen peroxide tris(4methylphenyl)(oxo)-phosphine they are 2.765 and 2.774 Å [244]. chemical shift of water is less than 2 ppm [236]. At higher concentrations, water molecules form clusters. In this state, their 1 H NMR chemical shift is about 4.8 ppm. The concentration at which water changes the state depend on the solvent and temperature [236]. The stronger H-bonding with the solvent and the higher the temperature, the higher the concentration at which water prefers homoclusters. At room temperature, it occurs when the water concentration is above 10-50 mM [236]. In dimethyl sulfoxide, water presents in the monomeric state at much higher concentrations. In this solvent, the 1 H NMR chemical shift of water is 3.3 ppm. Therefore, it is obvious that water is strongly Hbonded to solvent molecules. These are most likely symmetric complexes in which two solvent molecules share one water molecule. This type of complex has been observed experimentally in organic solutions at low temperatures in the presence of an excess of pyridine [237] and in frozen pyridine-water mixtures in porous materials [201]. Figure 10 shows the structure of 2:1 pyridine:water and collidine:water complexes, where collidine stands for 2,4,6-trimethylpyridine. In these complexes, the experimentally measured N···H distances are 1.82 Å for pyridine and 1.92 Å for collidine [237]. The basicity of collidine is higher than that of pyridine. Consequently, the greater distance is the result of steric interactions of the ortho-methyl groups in the 2:1 collidine:water complex. Indeed, in 1:n base:water complexes, where n >> 1, the experimentally measured N···H distances are 1.69 Å for pyridine and 1.64 Å for collidine. The strong shortening of the distances in both cases is the result of the anticooperative interaction of H-bonds in the 2:1 base:water complex and the cooperative interaction of H-bonds in water clusters. Similar symmetric complexes can often be found in crystals. For example, Figure 11a shows the structure of triphenylphosphine oxide hemihydrate. In this symmetric complex the O…O distance is 2.91 Å [238]. There is another modification of triphenylphosphine oxide hemihydrate with two different P=O··H-O-H····O=P H-bonds with the O…O distances of 2.84 and 2.87 Å [239]. 31 P NMR study of the crystalline triphenylphosphine oxide hemihydrate demonstrated that this water is mobile at least within the borders of one structural unit [240]. Presumably, this mobility reflects a specific property of the P=O group. This group can simultaneously form two equally strong H-bonds [241]. For example, Figure 11b shows the structure of tricyclohexylphosphine oxide monohydrate [213]. These two water molecules are already immobile [217]. This H-bond network is asymmetric, with two O…O distances of 2.844 and two of 2.897 Å [213]. Surprisingly, water can be replaced with hydrogen peroxide. Figure 11c shows the structure of hydrogen peroxide tricyclohexylphosphine oxide [242]. This H-bond network is asymmetric as well, with two O…O distances of 2.743 and two of 2.771 Å. In hydrogen peroxide triphenylphosphine oxide these distances are 2.677 and 2.718 Å [243]. The decreasing distances indicate that the total energy of hydrogen peroxide H-bond networks is higher than in the case of water. This may be the reason that there are several other complexes of hydrogen peroxide with phosphine oxides of the same structure. For  The NH2 group of anilines is another example of the binding units that can initiate the formation of symmetric H-bonded molecular adducts [245][246][247].

Conclusions
The possibility of being something does not guarantee the ability to actually become that. Molecular adducts, whose composition allows a symmetric structure, can actually be symmetric, symmetric on a certain time scale, or asymmetric. Analysis of this symmetry in a given system can be used to assess its properties and interactions with the environment. Only a few types of such molecular systems are considered in this review. These examples reflect the most important aspects of symmetric molecular adducts: (i) Steric hindrance and structural rigidity are not the only reasons why complexes can be asymmetric in the gas phase. The NH 2 group of anilines is another example of the binding units that can initiate the formation of symmetric H-bonded molecular adducts [245][246][247].

Conclusions
The possibility of being something does not guarantee the ability to actually become that. Molecular adducts, whose composition allows a symmetric structure, can actually be symmetric, symmetric on a certain time scale, or asymmetric. Analysis of this symmetry in a given system can be used to assess its properties and interactions with the environment. The reader may find it useful to refer to other recent publications on the interactions of tetrahedral pnicogen and tetrel centres with Lewis bases [248], the coordination of triel centers [249], tetraphosphido complexes [250], dinuclear metal hydride complexes [251], crystalline peroxosolvates [252], the self-association of phosphonic acids [253], intramolecular H-bond dynamics [254], and a consistent description of noncovalent interactions [255].