2.1.1. The Open-Closed Method (OCM)
The simplest and the most frequently used method of estimating the energy of intramolecular interactions, including intramolecular hydrogen bonds, is the so-called open-closed method (OCM) [
5,
19]. Apart from the molecule that contains a given interaction (i.e., the closed or chelate form), OCM requires the use of one more reference form (the so-called open), in which this interaction is absent [
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45]. It is then assumed that
which means that the total energy of another conformer, i.e., the open form, can be used instead of the impossible to obtain total energy of the fictitious closed system. Substituting expression (3) to (2) leads to a simple expression for the intramolecular hydrogen bond energy in OCM:
It should be emphasized that this article adopts the convention according to which a negative value of the obtained interaction energy means local stabilization that results from H⋯Y, while on the contrary, a positive value means local destabilization. Thus, of course, as being stabilizing interactions, hydrogen bonds should be characterized by negative values.
Equation (
3) requires that the open form does not differ much from the (fictitious) closed form. Therefore, the open form is most often obtained by rotating the donor or acceptor group by 180
, as shown in
Figure 1.
It is understood that, in general, these reference open forms give different values of
[
33]. In principle, one can also try to use a different open form. However, I will come back to this issue further. Although the expression (3) suggests that the open form should be fully optimized, i.e., it should correspond to a local minimum on the potential energy hypesurface, another possibility is to use an open form having the geometry (more precisely, geometrical parameters) of the closed form [
5,
19,
33,
38,
39,
42,
44,
45]
Of course, this leads to a different energy value
since
. In fact, Schuster advocated this option, suggesting that the reference open form should have "the least changes in molecular geometry besides a cleavage of the H-bond” and proclaiming that it "need not be a local minimum of the energy surface” [
5]. Moreover, in his opinion, the full optimization of the open form geometry is even inadvisable, because this approach mixes the energy of isomerization (resulting from the change of the conformer) into the determined energy value [
5]. In fact, both of these approaches introduce different definitions of the intramolecular interaction energy (cf. Equations (4) and (6)). This situation is somewhat similar to the one that occurs when determining the interaction energy from Equation (
1). Namely, the use of the monomers A and B with their geometries taken from the AB dimer defines the interaction energy, while their full optimization leads to the binding energy. The latter quantity also takes into account the correction for geometry change that takes place during the transition from the isolated form to the bound form in the dimer. Because of the fact that, in OCM, the fictitious closed form is replaced by the open form obtained by some conformational change, Schuster stressed that any splitting of the energetical difference between both forms is artificial [
5]. However, it seems that this opinion may be slightly weakened by some corrective approaches [
39,
44]. It is valuable to present both variants of the partition of the total energy of the closed form in one scheme, as shown in
Figure 2, where more concise notations are used for the respective energies.
It is worth noting that
, which, in principle, should lead to the relationship
. It seems that at present the variant based on full geometry optimization of the open form (leading to
and then
) is much more popular [
37] than the variant based on single point calculations (leading to
and then
). In this variant, the isomerization energy mentioned by Schuster [
5] is ‘absorbed’ into the interaction energy. In other words, this variant assumes that the changes in geometrical parameters that take place during the open form → closed form transition are related to the continuous process of creating the interaction (e.g., an intramolecular hydrogen bond) in the closed form [
42,
45].
Although OCM seems to be the most frequently [
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45] used theoretical method of estimating the energy of an intramolecular interaction, it is not free from further problems. The rotation of the proton-donor or the proton-acceptor group quite often leads to a new, significant interaction (either repulsive or attractive) in an open form [
24,
27,
28,
29,
31,
33,
39,
40,
41,
42,
43,
44,
45,
46]. Unfortunately, this possibility is quite often ignored. Moreover, sometimes, one or even both of the open forms cannot be used due to symmetry of these groups. Some simpe examples representing both cases are shown in
Figure 3. Of course, similar examples can be easily invented endlessly.
In the case of (a) relating to the intramolecular hydrogen bond O-H⋯O in malondialdehyde, the rotation of the proton-donor group -OH leads to a new rather significant interaction O⋯O, while the rotation of the proton-acceptor group -CHO leads to also rather significant new interaction H⋯H. In the case of (b) (3-aminoacrolein), due to the symmetry of the amino group, its rotation leads to practically the same system, while the rotation of the aldehyde group leads to a new significant H⋯H interaction, similar to the case of (a). The closed form of 1-amino-2-nitroethylene does not have any such simple open forms due to the symmetry of both groups, i.e., -NH2 and -NO2.
Another, but important, question is whether these new interactions can be completely ignored [
24,
27,
28,
29,
33,
39,
40,
41,
42,
43,
44,
45,
46]. For example, in the case of malondialdehyde, geometry optimizations (B3LYP/aug-cc-pVTZ) of the open form shown on the left-hand side of
Figure 3 gives 2.89 Å for the O⋯O distance and 2.02 Å for H⋯H in the open form shown in the right-hand side of this figure. In the case of the open form of 3-aminoacrolein, the distance H⋯H is 2.18 Å. Therefore, it would seem that these distances are too large for the interaction energy to be uncertain. However, on the other hand, the comparison of the CCC angle values in both forms (119.6
vs. 126.8
and 125.2
in malondialdehyde and 122.0
vs. 125.1
in 3-aminoacrolein) shows that the closed form → open form transition leads to an opening of the molecular skeleton, which may suggest significant repulsive actions of both these interactions. It seems that the O⋯O contact, in particular, cannot be completely ignored here. It is worth mentioning that both forms, i.e., closed and open, may differ in some structural aspects, e.g., the amino group in 3-aminoacrolein (b) is flat in the closed form, whereas slightly pyramidal in the optimized open form. In this case, one would have to decide whether the pyramidalization energy of the amino group should be shelled out or included in the hydrogen bond energy value [
47].
In such and similar cases, it may be tempting to find other reasonable open forms, obtained after the rotation of one of the groups around the CC double bond. On the one hand, such new interactions will be avoided, but on the other hand, the configuration of the carbon skeleton of the molecule will be changed. For example, Buemi et al. [
33] rebuked the use of the most extended enol and enethiol tautomers of thiomalondialdehyde [
48,
49] as reference structures [
24,
50], because, in their opinion, the
trans configuration of double bonds seems to be too different that the
cis arrangement in the closed form (
Figure 4).
It is also worth adding that the most extended conformers are very often the global minima of a given molecule. On the other hand, open systems with a changed configuration of backbone atoms can be more reasonable in many cases. In fact, the selection of the most reasonable reference system is an individual matter for the closed form of the molecule under consideration. Therefore, this issue should be carefully analyzed before starting the appropriate calculations while using OCM.
The fundamental issue for OCM is that the presence of a new significant interaction in the reference open form leads to either an overestimation or underestimation of the determined value of the interaction energy in the closed form [
42,
45]. Both of the situations are shown in
Figure 5.
The presence of a new significantly repulsive interaction in the reference open form leads to a less negative total energy of this form (
), and thus to an overestimation of the determined value of the interaction energy (
). Conversely, the presence of a significant attractive (stabilizing) interaction, e.g., a new hydrogen bond, results in underestimating the determined energy value (
). Moreover, because the most extended forms are often the most stable (as already mentioned),
, their frivolous use can underestimate the value of the interaction energy so much that this value can even change the sign (
) [
42]. As open forms with presence of new locally repulsive interactions X⋯Y (e.g., O⋯O, O⋯S, S⋯S, etc.) and, in particular, H⋯H are often treated favorably, the resulting energies may often be overestimated. This, in turn, may lead to overinterpretations of the considerable strength of some intramolecular hydrogen bonds [
39].
Given the fact that the full geometry optimization of the open form can lead to a new significant interaction (repulsive or attractive) or to a significant change in structure as compared to the closed form, a solution may be to perform a partial (i.e., constrained) geometry optimization [
42]. In many cases, it is enough to ‘freeze’ one or two dihedral angles that define the spatial orientation of the proton-donor or proton-acceptor group, the optimization of which would lead to the previously mentioned undesirable effects. However, sometimes, it is also necessary to freeze other geometric parameters [
42]. The approach that is based on partial geometry optimization of the open form is, in fact, another variant of OCM, leading to the interaction energy value between these described by Formulas (4) and (6).
This variant was first proposed [
42] to estimate the energy of Si-H⋯Al intramolecular charge-inverted hydrogen bonds [
51,
52] in ten model systems. The energy values of Si-H⋯Al in these systems were determined while using seven variants of OCM. In addition to either the full optimization (OPT) or complete freeze (SP) of the open form geometry, five variants of the constrained optimizations of the open form geometry were also used: (P1) only bonds optimized, (P2) only bonds and plane angles optimized, (P3) all geometric parameters optimized but dihedral angles governing the positions of the Si atom and the -AlH
2 group in relation to the carbon skeleton of the reference form, (P4) all geometric parameters optimized but dihedral angles governing the positions of the Si atom and both hydrogen atoms from the -AlH
2 group, and (P5) all geometric parameters optimized, but dihedral angles governing the positions of both hydrogen atoms from -AlH
2. Of course, the values of the non-optimized geometric parameters in the variants SP and P1–P5 were taken from the closed form. Therefore, it can be seen that the P1–P2 variants in a controlled manner increase the number of optimized parameters (degrees of freedom), which increases the flexibility of the approach. Because the obtained results [
42] very well reflect the mentioned problems related to the use of OCM, these results are shown for three molecules (
Figure 6) in
Table 1.
First of all, it can be seen that the determined values of the interaction energy vary widely, depending on the variant of the open-closed method used in the calculations. In the case of molecule
1, it is from −7 to −1 kcal/mol and, in the case of
3, from −10.6 to about −0.8 kcal/mol. The values decrease (i.e., become less negative) with an increased degree of flexibility regarding the geometric parameters optimized in a given variant. It can be seen that especially even a partial optimization of dihedral angles has a large influence on the determined interaction energy values. Moreover, the rotation of the -SiH
3 group in general gives significantly different values from that when the −AlH
2 group is rotated. This is especially visible for the least flexible variant SP, while on going from P1 to P5 these differences become smaller and smaller. It is instructive to analyze the results from the last column of
Table 1, i.e., regarding the variant with full geometry optimization of the proposed open form. While in case of
1 one reasonable value was found (−1.08 kcal/mol), in the case of
6 two significantly different values were obtained (−4.97 and −0.75 kcal/mol). The latter results from the fact that two open reference forms (see
and
in
Figure 6) with quite different characteristics were obtained. Despite the fact that both forms have identical carbon frame configuration (
cis), the
form has two new H
H
interactions. On the other hand, the
form has two pairs of probably less important H
H
interactions. Case
2, on the other hand, is an important example illustratating the significant impact of the presence of a completely new type of interaction in an open form on the quality of the estimation of the interaction energy is a closed form. Namely, in both open forms (
and
), the -AlH
group (Al has an empty
p orbital) takes a coplanar position to the CH=CH fragment with a formal C=C double bond. This arrangement allows for the
Al coupling (highlighted in
Figure 6 by drawing a C=Al double bond), which significantly lowers total energies of these forms. Consequently, the estimates of the interaction energy of Si-H⋯Al in
are highly unreliable.
The variant of OCM with partial geometry optimization of the open form was then used [
45] to estimate energies of Si-H⋯B contacts in some 1-silacyclopent-2-enes and 1- silacyclohex-2-enes and helped to successfully support the earlier Wrackmeyer’s suggestion based on NMR spectroscopic data [
53] that this contact is considerably stronger in the latter system than in the former one. Additionally, the energies of Ge-H⋯Al and Ge-H⋯H-N interactions in some alkenylhydrogermanes were estimated [
46] in a similar way (see
Figure 7).
The variant of OCM with partial geometry optimization of the open form should rather be treated as a certain, but probably not the only, possible solution when the full geometry optimization of this form gives (for the reasons discussed earlier) highly unreliable estimates of the interaction energy [
42,
45].
The results that are presented here are enough to show that OCM in which only one reference system is utilized must be used with great caution so as not to write with reserve. It should be so especially when its—nevertheless the most popular—variant with the full geometry optimization of the reference open form is used. Not as rare as it may seem at first, the occurrence of new interactions (whatever attractive or repulsive) or significant structural changes (e.g., changing the skeleton of a molecule) can lead to highly unreliable estimates of the energy value of the intramolecular interaction of interest in a closed form. Indeed, Rozas et al. [
32] went so far as to say that the energy value obtained from OCM should scarcely be taken as the value of the energy of the interaction in a closed form. Simply, it should rather be treated as the energetical difference between the respective forms of a molecule. On the other hand, this criticism seems a bit exaggerated. If the open form is very similar to the closed form both in terms of structure and the interactions occurring in these forms, then it seems that OCM is a worthy method of choice. The substantial similarity that is referred to herein can be provided by the presence of some rigid part of the molecule to which both the donor and acceptor groups are attached. This is the case, for example, with a benzene ring, leading to the variant of OCM, described as the
ortho-
para method [
38,
54,
55], which is described in more detail in the next subsection.
2.1.2. Ortho-Para Method (opM)
The
ortho–
para method (opM) was most likely used for the first time by Estácio et al. [
38] for estimating the energy of intramolecular hydrogen bonds in four 1,2-disubstituted benzene derivatives: 1,2-dihydroxybenzene (catechol), 1,2-benzenedithiol, benzene-1,2-diamine, and 2-methoxyphenol (guaiacol). To describe opM, it is enough to refer to the O-H⋯O hydrogen bond in 1,2-dihydroxybenzene, i.e., catechol (
Figure 8).
The use of the open form that was simply obtained by rotating the hydroxyl group around the C-O bond resulted in hydrogen bond energy estimates of −3.7 or −4.0 kcal/mol at the MPW1PW91/aug-cc-pVDZ and CBS-QMPW1 levels of theory, respectively. These values were considered to be unreliable and significantly overestimated as a result of the presence of new repulsive interactions between oxygen atoms as well as the O-H dipole–dipole interactions [
38]. As a consequence, it was concluded that the energetic difference between the open and closed forms cannot be regarded as the energy of the O-H⋯O hydrogen bond in the latter form. However, in this and similar cases, the
para form is a very reliable reference form. The comparison of total energy of this form with the total energy of the closed form of the
ortho configuration gives opM, which can be seen as a variant of OCM. Based on this approach, the respective hydrogen bond energies were −2.1 and −2.3 kcal/mol [
38].
It is worth emphasizing here that the high reliability of the estimate obtained by means of opM results from the high stiffness of the main part of the molecule, i.e., the benzene ring and, hence, the significant transferability of the related geometric parameter values. In other words, the stiffness of the molecular framework and its high preservation when going to the
para-substituted reference system allowed for avoiding the typical problems that are faced by the standard version of OCM which were mentioned earlier. On the other hand, it should be noted that this method assumes that the substituent electronic effects in the
ortho and
para forms are similar. However, this is in line with the general knowledge on substituent effects [
56,
57,
58,
59]. Nevertheless, another question, which is completely not addressed by Estácio et al., is which form of the
para conformer (see (a) and (b) in
Figure 8) to use. While this rather purely theoretical issue seems to be insignificant for catechol due to the negligible difference in total energies between the two forms (e.g., 0.1 kcal/mol at the B3LYP/aug-cc-pVTZ level of theory), the difference may become slightly larger for other substituents or molecular frameworks.
It should be mentioned that Estácio et al. described the O-H⋯O hydrogen bond in the closed form of catechol by means of a simple model that is based on the description of interacting dipoles of the O-H bonds. This model resulted in the following formula
where
is the Lennard–Jones interaction energy for the relevant pair of oxygen atoms and
is the dipole-dipole interaction energy for the closed form [
38]. The energy value that was determined using this formula was −2.0 kcal/mol (MPW1PW91/aug-cc-pVDZ) and it was very closed to the one determined while using opM (−2.1 kcal/mol). Estácio et al. considered this result to be significant, because it shows that opM correctly describes both interactions, i.e., the O⋯O repulsion and the interaction between the dipoles of both O-H bonds in the closed form of catechol.
2.1.4. Geometry-Corrected Method (GCM)
All of the methods for estimating the energy of intramolecular interactions (e.g., hydrogen bonds) discussed so far do not take into account changes in the values of geometric parameters upon considering an open reference form of a molecule. However, the presence of a conjugated system of double bonds, which is characteristic for 3-aminoacrolein and, thus, the existence of its four conformers (
Figure 9) allowed for proposing a method to estimate the energy of the N-H⋯O intramolecular hydrogen bond in the ZZ conformer with simultaneous partial consideration of geometric factors [
39]. This method initially functioned under the name “Scheme A” [
39,
40,
41,
43], but later its meaningless name was changed to the Geometry-Corrected Method (GCM) [
44].
Very helpful in understaning the idea of GCM and how to derive it are the diagrams presented in
Figure 10, which show the energy relationships between the respective forms of 3-aminoacrolein.
As in Equation (
2), in the first step, it is assumed that the hydrogen bond in the ZZ form of 3-aminoacrolein can be simply ’turned off’ without any changes in the electron density distribution of the system, therefore also without any changes in the geometrical parameters of this form. By introducing an approximation of the energy additivity, we obtain:
where
is simply the total energy of the fictitious form of ZZ with the hydrogen bond just ‘turned off’. The rotation of the aldehyde group around the C=C double bond, i.e., the transition ZZ→EZ leads not only to breaking the hydrogen bond, but also to some changes in the geometrical parameters. If the energy associated with these changes in geometric parameters is
, then
and quite similarly for the ZZ→EE transition
Dividing the sum of Equations (13) and (14) by two, one obtains an expression that can be interpreted as the averaged energy that is related to the configuration change Z→E:
Combining this equation with (12) gives the expression for the hydrogen bond energy in the conformer ZZ
but in which there is (so far) the unknown quantity
. In fact, the hydrogen bond energy,
, and the averaged contribution to the configuration change Z→E,
, are formally non-separable quantities. However, the existence of conformers allowed for determining the unknown contribution
from yet another source. Let us introduce the fictitious equivalents of the conformers EZ and EE (EZ
and EE
, respectively), having the same values of all (of course, except the dihedral angle(s) changing the conformation) geometrical parameters as the conformer ZZ (see
Figure 10). The energy that is associated with the transition ZZ
EZ can then be assumed in the form
where
is the energy resulting from the change of the Z→E configuration while maintaining the constant values of all geometrical parameters, while
is the relaxation energy of the fictitious EZ
form to its fully relaxed equivalent obtained after the full geometry optimization. The energy associated with the transition ZZ
EE can be presented quite similarly
Changing the conformation from ZZ
to either EZ
or EE
(i.e., maintaining the same values of bond lengths and angles) should not have a significant influence on the energy change. With the neglect of changing the interactions between ’unbound’ atoms, it can therefore be assumed that
. This approximation gives, after adding Equations (17) and (18) to each other, another expression for
which, inserted into Equation (
16), gives the final formula for the value of the hydrogen bond energy in ZZ-3-aminoacrolein [
39]
Thus, it can be seen that, to determine , only the total energy of the fully optimized ZZ conformer and the total energies of the fictitious EZ and EE conformers with the values of geometric parameters (except for the dihedral angle O=C–C=O) from the ZZ conformer are needed. It is worth repeating at this point that GCM, i.e., formula (20), to some extent takes into account the changes in geometric parameters when moving from the ZZ form to the reference forms.
At this point, it is instructive to compare GCM with the OCM variant, in which the open reference form is the ZE conformer, i.e.,
(cf. with Equation (
4)). As already discussed, the assumption of OCM is that the reference open system does not differ significantly from the closed form, whereas, in the case of ZZ-3-aminoacrolein, the rotation of the aldehyde group around the C–C bond leading to the ZE conformer introduces a new rather significant interaction of the H⋯H type (see
Figure 9). This interaction is practically not present in the closed form ZZ. Any estimate that refers to the ZE conformer as the reference form should take this change into account. Suppose (similar to the hydrogen bond in the ZZ conformer) that this H⋯H interaction in the fictitious ZE
form can be ‘turned off’, which gives ZE
(note the prime sign in the superscript). The energy associated with the rotation of the aldehyde group (
) at the transition ZZ
ZE
can be assumed to be negligible due to both the conservation of the same geometric parameters as in the conformer ZZ and also due to the neglect of additional H⋯H repulsion at this stage (additionally, the negligible influence of changes in the interactions of unbound atoms other than H⋯H is also assumed). This repulsion leads to an energy increase of
and to the form ZE
, which still maintains the geometry of ZZ. Only full relaxation of the ZE
geometry leads to the optimized ZE conformer. The energy that is associated with this relaxation has been designated as
(see
Figure 11).
Therefore, the energy that is associated with the transition from the ZZ
conformer to the ZE conformer can be expressed as:
Given the assumption (12) and by the similarity to the previously defined changes in energies
(13) and
(14), one gets
Inserting this expression together with Equation (
21) into Equation (
12) gives a relationship between the estimation of the hydrogen bond energy in ZZ-3-aminoacrolein that is obtained by GCM and that obtained by OCM with the ZE conformer as the reference open form
Equation (
23) shows that, when compared to OCM, the estimation that is based on GCM takes into account two terms with opposite signs. The repulsive term
is positive, whereas the relaxation term
is negative. The mutual weights of these two terms cause that the value of the intramolecular hydrogen bond energy determined by GCM is either below or above the value obtained by OCM. Strong hydrogen bonds should cause significant changes within the X-H⋯Y bridge and, thus, both a small distance H⋯Y in the conformer ZZ and a small distance H⋯H in the fictitious form ZE
(or ZE
) obtained after rotation of the proton-acceptor group while maintaining the geometrical parameters from the conformer ZZ (except for the dihedral angle O=C–C=C). As a consequence, in molecules with a strong intramolecular hydrogen bond, the role of H⋯H repulsion at the ZE
ZE
should be significant. On the other hand, the significance of the relaxation term
should be dominant in the case of relatively small distances H⋯H in the ZE
form (H⋯Y in ZZ) and, which seems more important, in the case of bulky proton-acceptors.
At this point, it is worth comparing the hydrogen bond energy values that were obtained with GCM with those obtained with the traditional variant of OCM. The first comparison of this type was made for the ZZ-3-aminopropenal (ZZ-3-aminoacrolein) [
47] discussed here and for the related ZZ-3-aminopropential [
39], where sulfur atom replaces the oxygen atom. The energy values of hydrogen bonds
and
are shown in
Table 2. Additionally, this table also shows the relative energies (in relation to ZZ) of the respective conformers, the H⋯H distances in ZE
and ZE forms, and the values of
, which will be used in the current discussion. All of these values are limited to the best method used (MP2/6-311++G**), so as not to increase the amount of numerical data [
39].
In the case of 3-aminoacrolein, the following order of relative energies of conformers was obtained:
. It suggests a significant relaxation of the most extended EE conformer and a significant role of the H⋯H repulsion in the ZE conformer. In the case of 3-aminopropential (Y = S), the relative energy of the EZ conformer, on the other hand, is significantly lifted up, so that it equals that of the ZE conformer. In turn, this result suggests a greater role of S⋯H valence repulsion in 3-aminopropential than O⋯H in the EZ conformer (a complementary explanation may also be the greater role of the attractive component in the O⋯H interaction than S⋯H, which lowers the relative energy of EZ-3-aminoacrolein in relation to EZ-3-aminopropential). It is also manifested by the values of the angle CCY, which is 128.3
and only 125.4
for Y = S and O, respectively. As for the estimated values of the hydrogen bond energy, interestingly, OCM suggests a somewhat stronger N-H⋯O hydrogen bond in ZZ-3-aminoacrolein (−6.50 kcal/mol) than N-H⋯S in ZZ-3-aminopropential (−6.02 kcal/mol), whereas, in the case of GCM, the opposite is obtained, i.e., this method suggests that the latter bond is stronger (−6.96 kcal/mol) than the former one (−5.28 kcal/mol).
Table 2 also presents the values of the distances H⋯H in the ZE
and ZE forms of both molecules, as well as the changes of these distances at the ZE
ZE transition, i.e., upon relaxation of this conformer. The much higher
value for the ZE-3-aminoacrolein (−0.301 Å) than for ZE-3-aminopropential (−0.159 Å) suggests a much stronger H⋯H repulsion in the former of these systems, which is most likely due to the much shorter initial distance (1.840 Å vs. 1.968 Å). This suggestion is actually confirmed by the obtained results. Namely, as can be seen from the last column of
Table 2, 3-aminoacrolein and 3-aminopropential are characterized by the same value (−1.87 kcal/mol) of
, i.e., the relaxation term ZE
ZE. Therefore, the greater change in the H⋯H distance at the transition ZE
ZE for the former of these molecules must result primarily from the greater repulsion
, which, as a consequence, should significantly exceed the relaxation component
. In turn, this should lead to a significantly lower
when compared to
. As can be seen from
Table 2, such a relationship for ZZ-3-aminoacrolein does indeed take place since
and
amount to −5.28 and −6.50 kcal/mol, respectively. This result shows that the hydrogen bond energies obtained within GCM are consistent with the observable geometric changes.
In addition to the case of 3-aminoacrolein [
47] and 3-aminopropential [
39] discussed here, GCM was later used to estimate the energy of intramolecular C-H⋯O/S interactions in few systems featuring a similar
quasi-ring structure (
Figure 12) [
40,
41].
Importantly, contrary to popular belief, these calculations showed that the C-H⋯O/S contacts in these systems are actually destabilizing. Therefore, no hydrogen bond in the usual sense is formed between the proton-donating C-H bond and proton-acceptor O or S atoms. This result was interpreted [
40,
41] in terms of the steric compression, which leads to the dominance of the valence repulsion contribution in the C-H⋯O contact and it was further supported by observing both the increase in contact destabilization and the corresponding geometric changes during the flattening of some systems. Further detailed studies on an even larger group of systems (
vide infra) showed, however, that intramolecular C-H⋯O interactions may be destabilizing in some systems, while stabilizing in others [
44]. The fact that the large number of X⋯O (X = F, Cl, Br, I), O⋯O and F⋯F interactions, which some consider stabilizing due to the presence of a bond path tracing these contacts are, in fact, destabilizing in many molecules was also shown [
43] by means of the energy values obtained,
inter alia, by GCM and OCM. An example is shown in
Figure 13.
Theoretical studies [
39,
40,
41,
43,
44] show that GCM can be considered to be a reliable method of estimating the energy of both intramolecular hydrogen bonds as well as intramolecular non-bonding interactions. As this method takes into account changes in geometric parameters that occur when passing to reference systems, it is a more reliable approach than the standard OCM, which does not take into account these changes at all. Of course, the applicability of GCM, like most other methods, is limited. For example, the presence of bulky substituents can significantly reduce the reliability of this method. Moreover, of course, the analyzed molecule must have appropriate conformers, which is not always the case. However, OCM also has to deal with similar requirements. Nevertheless, OCM is less tricky.
It is obvious that obtaining the individual conformers needed while using conformational methods requires a great deal of care and attention. Unfortunately, this is not always the case. In their study of the N-H⋯O and N-H⋯S intramolecular hydrogen bonds in
-aminoacrolein,
-thioaminoacrolein, and their halogenated derivatives, Nowroozi and Masumian claimed that GCM performs worse than RBM and RRM, in particular [
63]. However, it is enough to look at their Scheme 3 to realize that they used wrong conformers labeled as EZ and EE. Briefly, both of these conformers should have H and R
at reversed positions! (Starting with the ZZ conformer, rotation of the -NHR
group around the C=C double bond obviously leaves the H atom rotated with this group on the “inside” of the molecule, i.e., at the R
site and close to R
.) Because EZ and EE conformers (either real or fictitious) are used in RRM and GCM, it is obvious that the results that are presented by Nowroozi and Masumian [
63] are completely wrong (as evidenced, e.g., by low
values). Moreover, these authors ignored the fact that some of the conformers they used experience new significant interactions, such as O⋯Br, which, of course, significantly affect the total energy of a given conformer.