Global Search for Stable C4H5NO Compounds—Guinness Molecules and Stability Islands

Global reaction route mapping (GRRM) analysis for compounds with the formula C4H5NO allowed for the detection of the corresponding “Guinness molecules” 000 and 001, as well as around 150 other stable minima of the same composition. The results suggest that compounds of similar functionality form a kind of “Stability Island” with their free energies of formation falling within s relatively limited range.


Introduction
The term "Guinness molecules" was introduced in 2014 by Suhm to describe the most stable molecule for a certain chemical formula [1]. It was argued that the results of a systematic search for such molecules (which inevitably must involve the ranking by energy of all other molecules with the same composition) could be useful for the astronomical search for interstellar molecules, prediction of X-ray structures, etc. However, eight years later, we are aware of only one report exploiting the idea of a "Guinness molecule" devoted to the study of low molecular weight carbohydrates [2]. Interestingly, it was found in this study that the most stable structures of molecules of the formula CnH 2 nOn, up until n = 5, are small molecules aggregates rather than conventional molecules.
As we are interested in the concept of "Guinness molecules" and in the chemistry of relatively small molecules characterized by a high reactivity, we have chosen the sum formula of C 4 H 5 NO for a systematic search for corresponding stable molecules and the Guinness molecule.
A useful tool for such kind of computations is the GRRM (global reaction routes mapping) software developed by Ohno et al. [3][4][5]. GRRM is a computer program for automated exploration of chemical reaction pathways. It can be used for reaction route mapping for the potential surface of a certain chemical formula. Starting from an equilibrium structure, an automated search of dissociation and isomerization reactions can be performed [6][7][8][9][10].

Computational Details
We used the GRRM-12 version of the software for a global search of configurational minima of the formula C 4 H 5 NO. The Gaussian 09 software package [11] was used for optimizations using the BLYP3/6-31G(d) level of theory. A HPC workstation equipped with 64 processors and 256 Gb of memory carried out the task for 163 days, and complete conversion was not reached. Hence, we cannot report all possible equilibrium structures on the potential surface. Nevertheless, we can confidently claim the detection of two "Guinness molecules" with a negligible difference in their Gibbs free energies (see Table 1, compounds 000 and 001, and Figure 1) and over 140 other compounds of C 4 H 5 NO in 14 different classes (see Tables S1-S14). the potential surface. Nevertheless, we can confidently claim the detection of two "Guinness molecules" with a negligible difference in their Gibbs free energies (see Table 1, compounds 000 and 001, and Figure 1) and over 140 other compounds of C4H5NO in 14 different classes (see Tables S1-S14).
In total, 489 minima were located during the GRRM-12 implementation. This number included numerous conformers. In most cases, only the most stable conformer was further reoptimized for inclusion in the tables. Only a very limited number of conformers were reoptimized and included in Table S1.
All conformational minima were reoptimized using the ωB97XD functional [12] with the 6-31G(d,p) basis set. Mostly only singlet multiplicity was considered. In the cases of isonitriles and carbenes, the stability of the wavefunction was checked prior to optimization and when necessary, the stable=opt option was used, leading to singlet multiplicities in all cases. ZPVE energies were unscaled. Note that the relative values of EZPVE, H and G were very close for each structure (Tables S1-S14).
Despite the lack of conversion of the GRRM computation, the data was good enough to build a free energy map for C4H5NO molecules. All computed structures are listed in Tables S1-S14, whereas Table 1 shows the most and the least stable isomers for each group of compounds.   In total, 489 minima were located during the GRRM-12 implementation. This number included numerous conformers. In most cases, only the most stable conformer was further reoptimized for inclusion in the tables. Only a very limited number of conformers were reoptimized and included in Table S1.
All conformational minima were reoptimized using the ωB97XD functional [12] with the 6-31G(d,p) basis set. Mostly only singlet multiplicity was considered. In the cases of isonitriles and carbenes, the stability of the wavefunction was checked prior to optimization and when necessary, the stable=opt option was used, leading to singlet multiplicities in all cases. ZPVE energies were unscaled. Note that the relative values of E ZPVE , H and G were very close for each structure (Tables S1-S14).
Despite the lack of conversion of the GRRM computation, the data was good enough to build a free energy map for C 4 H 5 NO molecules. All computed structures are listed in Tables S1-S14, whereas Table 1 shows the most and the least stable isomers for each group of compounds.

Guinness Molecules and 5-Membered Heterocycles of C 4 H 5 NO
We have found that there are two Guinness molecules in the multitude of potential C 4 H 5 NO compounds, viz., γ-lactams 000 and 001 ( Figure 1, Table 1). Interestingly, their isomers, with the NH unit positioned near the C=C bond (005), are about 10 kcal/mol less stable due to the lack of conjugation of the nitrogen lone pair with the C=C-C=O unit (the nitrogen atom is pyramidal in 005 and flat in 000 and 001). To check the accuracy of this observation, we recomputed the structures 000, 001 and 005 using coupled-cluster calculations [13] with both single and double substitutions [14], see Figure 1 for the results.
As can be seen from Figure 1, the results of the higher level computations are in accord with the initial observations. The free energy difference between the structures 000 and 001 remains within 0.1 kcal/mol, whereas 005 is more than 10 kcal/mol destabilized compared to the other two. Moreover, the distortions in planarity of the molecule of 005 computed by CCSD are even stronger ( Figure 1). Since the coupled-cluster calculations are known to provide an accurate estimation of non-bonding interactions [15], we concluded that: (a) conjugation of the nitrogen lone pair with the adjacent C=C bond is relatively weak and (b) to partially compensate for this effect, the planarity of the molecule 005 is avoided to achieve a closer contact between the NH proton and one of the protons of the nearby CH 2 group.
Of interest is the unusual stability of the enol 006, especially compared to its rotamer 012 ( Figure 2). Both molecules are flat. We can conclude that stabilizing effect of the combination of O-H···H-C and C-O···H-N non-bonding interactions in 006 is roughly 4 kcal/mol more effective than that of the combination of O-H···H-N and C-O···H-C interactions in 012.  In total, the relative Gibbs free energies of about 30 five-membered heterocycles wit the formula C4H5NO (including some rotamers) fall within the region of 30 kcal/mol. W named this region the "Stability Island" (see Figure 3). In total, the relative Gibbs free energies of about 30 five-membered heterocycles with the formula C 4 H 5 NO (including some rotamers) fall within the region of 30 kcal/mol. We named this region the "Stability Island" (see Figure 3). Molecules 2023, 28, x FOR PEER REVIEW 6 of 13  Oxazoles are important heterocycles found in numerous natural compounds and they are biologically active themselves [16]. Several quantum-chemical studies of compounds containing an oxazole ring have been published [17][18][19], but we are unaware of any computations of oxazoles with the formula C 4 H 5 NO.
Due to the lack of aromaticity, the oxazole 032 is approximately 25 kcal/mol less stable than three other oxazoles: 027, 029 and 030 (Scheme 1). Following the above terminology, we classified 032 as belonging to the "Instability Archipelago" (Figure 3). Furthermore, we have applied this classification to compounds from other structural group.
lecules 2023, 28, x FOR PEER REVIEW 7 o Oxazoles are important heterocycles found in numerous natural compounds they are biologically active themselves [16]. Several quantum-chemical studies of c pounds containing an oxazole ring have been published [17][18][19], but we are unawar any computations of oxazoles with the formula C4H5NO.
Due to the lack of aromaticity, the oxazole 032 is approximately 25 kcal/mol less ble than three other oxazoles: 027, 029 and 030 (Scheme 1). Following the above termi ogy, we classified 032 as belonging to the "Instability Archipelago" (Figure 3). Furth more, we have applied this classification to compounds from other structural group.

6-Membered Heterocycles of C4H5NO
Only eight 6-membered heterocycles were found (Table S1). They are significa less stable than the 5-membered heterocycles. Thus, the most stable 6-membered het cycle 100 is characterized by almost the same value of Gibbs free energy as the 26 th m stable 5-membered heterocycle, 025 (Scheme 2). As in the previous case, the least sta compounds, 105-107, containing N-O bonds were placed in the Instability Archipelag

4-Membered Heterocycles of C4H5NO2.
A compact Stability Island is observed, constituting six compounds, where sev evident positional isomers and rotamers were neglected (Scheme 3 see also

Saturated 3-Membered Heterocycles of C4H5NO
A relatively populated Stability Island was observed between the astonishingly Scheme 1. Relatively stable oxazoles containing an N-O bond and their relative Gibbs free energies (kcal/mol).

6-Membered Heterocycles of C 4 H 5 NO
Only eight 6-membered heterocycles were found (Table S1). They are significantly less stable than the 5-membered heterocycles. Thus, the most stable 6-membered heterocycle 100 is characterized by almost the same value of Gibbs free energy as the 26th most stable 5membered heterocycle, 025 (Scheme 2). As in the previous case, the least stable compounds, 105-107, containing N-O bonds were placed in the Instability Archipelago. Oxazoles are important heterocycles found in numerous natural compounds and they are biologically active themselves [16]. Several quantum-chemical studies of compounds containing an oxazole ring have been published [17][18][19], but we are unaware of any computations of oxazoles with the formula C4H5NO.
Due to the lack of aromaticity, the oxazole 032 is approximately 25 kcal/mol less stable than three other oxazoles: 027, 029 and 030 (Scheme 1). Following the above terminology, we classified 032 as belonging to the "Instability Archipelago" (Figure 3). Furthermore, we have applied this classification to compounds from other structural group.

6-Membered Heterocycles of C4H5NO
Only eight 6-membered heterocycles were found (Table S1). They are significantly less stable than the 5-membered heterocycles. Thus, the most stable 6-membered heterocycle 100 is characterized by almost the same value of Gibbs free energy as the 26 th most stable 5-membered heterocycle, 025 (Scheme 2). As in the previous case, the least stable compounds, 105-107, containing N-O bonds were placed in the Instability Archipelago.

4-Membered Heterocycles of C4H5NO2.
A compact Stability Island is observed, constituting six compounds, where several evident positional isomers and rotamers were neglected (Scheme 3 see also Table S3). The compound 206 is located about 40 kcal/mol away in the Instability Archipelago ( Figure 3).

Saturated 3-Membered Heterocycles of C4H5NO
A relatively populated Stability Island was observed between the astonishingly stable isocyanate 300 and extremely unstable oxime 310 (NB-N-O bond, Scheme 4).

4-Membered Heterocycles of C 4 H 5 NO 2
A compact Stability Island is observed, constituting six compounds, where several evident positional isomers and rotamers were neglected (Scheme 3 see also Table S3). The compound 206 is located about 40 kcal/mol away in the Instability Archipelago (Figure 3).
Oxazoles are important heterocycles found in numerous natural compounds and they are biologically active themselves [16]. Several quantum-chemical studies of compounds containing an oxazole ring have been published [17][18][19], but we are unaware of any computations of oxazoles with the formula C4H5NO.
Due to the lack of aromaticity, the oxazole 032 is approximately 25 kcal/mol less stable than three other oxazoles: 027, 029 and 030 (Scheme 1). Following the above terminology, we classified 032 as belonging to the "Instability Archipelago" (Figure 3). Furthermore, we have applied this classification to compounds from other structural group.

6-Membered Heterocycles of C4H5NO
Only eight 6-membered heterocycles were found (Table S1). They are significantly less stable than the 5-membered heterocycles. Thus, the most stable 6-membered heterocycle 100 is characterized by almost the same value of Gibbs free energy as the 26 th most stable 5-membered heterocycle, 025 (Scheme 2). As in the previous case, the least stable compounds, 105-107, containing N-O bonds were placed in the Instability Archipelago.

4-Membered Heterocycles of C4H5NO2.
A compact Stability Island is observed, constituting six compounds, where several evident positional isomers and rotamers were neglected (Scheme 3 see also Table S3). The compound 206 is located about 40 kcal/mol away in the Instability Archipelago ( Figure 3).

Saturated 3-Membered Heterocycles of C4H5NO
A relatively populated Stability Island was observed between the astonishingly stable isocyanate 300 and extremely unstable oxime 310 (NB-N-O bond, Scheme 4).

Saturated 3-Membered Heterocycles of C 4 H 5 NO
A relatively populated Stability Island was observed between the astonishingly stable isocyanate 300 and extremely unstable oxime 310 (NB-N-O bond, Scheme 4).

Unsaturated 3-Membered Heterocycles of C4H5NO
This Stability Island is not less populated than the 5-membered heterocycles Stability Island, and the potential for building further structures seems to be higher. Of note are the anti-records for the relative instability (compounds 419 and 420, Figure 4) and for the difference between the most and least stable compounds in the series (85 kcal/mol).

Bicyclic Compounds of C4H5NO
These compounds have a somewhat expected limited population, thinly spread from 60 to 110 kcal/mol with significant potential for increasing towards the high energy side (Scheme 5).

Acyclic Nitriles
This group consists of numerous compounds inhabiting a compact Stability Island

Unsaturated 3-Membered Heterocycles of C 4 H 5 NO
This Stability Island is not less populated than the 5-membered heterocycles Stability Island, and the potential for building further structures seems to be higher. Of note are the anti-records for the relative instability (compounds 419 and 420, Figure 4) and for the difference between the most and least stable compounds in the series (85 kcal/mol).

Unsaturated 3-Membered Heterocycles of C4H5NO
This Stability Island is not less populated than the 5-membered heterocycles Stability Island, and the potential for building further structures seems to be higher. Of note are the anti-records for the relative instability (compounds 419 and 420, Figure 4) and for the difference between the most and least stable compounds in the series (85 kcal/mol).

Bicyclic Compounds of C4H5NO
These compounds have a somewhat expected limited population, thinly spread from 60 to 110 kcal/mol with significant potential for increasing towards the high energy side (Scheme 5).

Acyclic Nitriles
This group consists of numerous compounds inhabiting a compact Stability Island with an energy interval of 10-40 kcal/mol. Of interest is a very small gap between the most

Bicyclic Compounds of C 4 H 5 NO
These compounds have a somewhat expected limited population, thinly spread from 60 to 110 kcal/mol with significant potential for increasing towards the high energy side (Scheme 5).

Unsaturated 3-Membered Heterocycles of C4H5NO
This Stability Island is not less populated than the 5-membered heterocycles Sta Island, and the potential for building further structures seems to be higher. Of not the anti-records for the relative instability (compounds 419 and 420, Figure 4) and fo difference between the most and least stable compounds in the series (85 kcal/mol).

Bicyclic Compounds of C4H5NO
These compounds have a somewhat expected limited population, thinly spread 60 to 110 kcal/mol with significant potential for increasing towards the high energy (Scheme 5).

Acyclic Nitriles
This group consists of numerous compounds inhabiting a compact Stability Is with an energy interval of 10-40 kcal/mol. Of interest is a very small gap between the Scheme 5. Members of the bicyclic Stability Island and their relative Gibbs free energies (kcal/mol).

Acyclic Nitriles
This group consists of numerous compounds inhabiting a compact Stability Island with an energy interval of 10-40 kcal/mol. Of interest is a very small gap between the most and the least stable compounds (Scheme 6), especially in view of compound 616 being well-known as a high energy material, which has also been confirmed computationally [20].
Molecules 2023, 28, x FOR PEER REVIEW 9 of 13 and the least stable compounds (Scheme 6), especially in view of compound 616 being well-known as a high energy material, which has also been confirmed computationally [20].

Trienes
Only five compounds that can be formally considered as hetero-trienes were found in this study (Scheme 7). Comparing their relative stabilities, one can conclude that the N=CH2 moiety brings a considerable amount of instability into the molecule.

Acetylenes
The least stable compound among the three containing a triple bond is an acetylenic ester 704 (Scheme 8). This is in accordance with the well-known high reactivity of acetylenic esters that makes them useful synthons for organic synthesis [21].

Trienes
Only five compounds that can be formally considered as hetero-trienes were found in this study (Scheme 7). Comparing their relative stabilities, one can conclude that the N=CH 2 moiety brings a considerable amount of instability into the molecule.
Molecules 2023, 28, x FOR PEER REVIEW 9 of 13 and the least stable compounds (Scheme 6), especially in view of compound 616 being well-known as a high energy material, which has also been confirmed computationally [20].

Trienes
Only five compounds that can be formally considered as hetero-trienes were found in this study (Scheme 7). Comparing their relative stabilities, one can conclude that the N=CH2 moiety brings a considerable amount of instability into the molecule.

Acetylenes
The least stable compound among the three containing a triple bond is an acetylenic ester 704 (Scheme 8). This is in accordance with the well-known high reactivity of acetylenic esters that makes them useful synthons for organic synthesis [21].

Acetylenes
The least stable compound among the three containing a triple bond is an acetylenic ester 704 (Scheme 8). This is in accordance with the well-known high reactivity of acetylenic esters that makes them useful synthons for organic synthesis [21].
Molecules 2023, 28, x FOR PEER REVIEW 9 of 13 and the least stable compounds (Scheme 6), especially in view of compound 616 being well-known as a high energy material, which has also been confirmed computationally [20].

Trienes
Only five compounds that can be formally considered as hetero-trienes were found in this study (Scheme 7). Comparing their relative stabilities, one can conclude that the N=CH2 moiety brings a considerable amount of instability into the molecule.

Acetylenes
The least stable compound among the three containing a triple bond is an acetylenic ester 704 (Scheme 8). This is in accordance with the well-known high reactivity of acetylenic esters that makes them useful synthons for organic synthesis [21].

Isonitriles
The unusual electronic structure of isonitriles underlies their rich chemistry and numerous applications [22]. Most structures found in this study are hydroxy-substituted compounds, with the exception of the most stable ketone 1000 (Scheme 10). This explains Scheme 9. Members of the allene Stability Island and their relative Gibbs free energies (kcal/mol).

Isonitriles
The unusual electronic structure of isonitriles underlies their rich chemistry and numerous applications [22]. Most structures found in this study are hydroxy-substituted compounds, with the exception of the most stable ketone 1000 (Scheme 10). This explains the very close relative free energies of the compounds 1001-1009.

Isonitriles
The unusual electronic structure of isonitriles underlies their rich chemistry an merous applications [22]. Most structures found in this study are hydroxy-substi compounds, with the exception of the most stable ketone 1000 (Scheme 10). This exp the very close relative free energies of the compounds 1001-1009.

Bipolar Compounds
Two located bipolar compouynds are shown in Figure 5. They have very similar stabilitis, approximately 60 kcval/mol away from structurally similar Guiness molecules 000 and 001.

Molecular Associates
Contrary to the study of carbohydrates [2], molecular associates of the formula C4H5NO are not very numerous. Only two examples, 1300 and 1301, were found in this study (Scheme 12). This is probably due to the structural limitations stipulated by the chemical formula.

Conclusions
The main conclusion of our study is that we have gained valuable information, although this information has comes at a cost. Although the progress in computer performance and software development is fast, so far, only the accurate analysis of systems with a maximum of five heavy atoms (six in the case of HC6 + ) has been reported [11]. There must be a cheaper way to locate Guinness molecules, as at the moment, a complete energy mapping without gaps is hardly conceivable even for such relatively small molecules. Nevertheless, it seems that obtaining even approximate estimations on the energy gaps for certain molecule groups, such as those collected in Table 1, could be useful. Indeed, any interested chemist can easily construct a C4H5NO molecule not listed in this report. Optimization and frequency calculations for such a molecule take less than 5 minutes on a regular desktop computer (ωB97XD/6-31G(d,p)). Then, the data provided in our paper

Molecular Associates
Contrary to the study of carbohydrates [2], molecular associates of the formula C 4 H 5 NO are not very numerous. Only two examples, 1300 and 1301, were found in this study (Scheme 12). This is probably due to the structural limitations stipulated by the chemical formula.

Molecular Associates
Contrary to the study of carbohydrates [2], molecular associates of the formula C4H5NO are not very numerous. Only two examples, 1300 and 1301, were found in this study (Scheme 12). This is probably due to the structural limitations stipulated by the chemical formula. Scheme 12. Molecular associates located in this study and their relative Gibbs free energies (kcal/mol). Scheme 12. Molecular associates located in this study and their relative Gibbs free energies (kcal/mol).

Conclusions
The main conclusion of our study is that we have gained valuable information, although this information has comes at a cost. Although the progress in computer performance and software development is fast, so far, only the accurate analysis of systems with a maximum of five heavy atoms (six in the case of HC 6 + ) has been reported [11]. There must be a cheaper way to locate Guinness molecules, as at the moment, a complete energy mapping without gaps is hardly conceivable even for such relatively small molecules. Nevertheless, it seems that obtaining even approximate estimations on the energy gaps for certain molecule groups, such as those collected in Table 1, could be useful. Indeed, any interested chemist can easily construct a C 4 H 5 NO molecule not listed in this report. Optimization and frequency calculations for such a molecule take less than 5 minutes on a regular desktop computer (ωB97XD/6-31G(d,p)). Then, the data provided in our paper could help to estimate the relative energetics of this molecule compared to other similar compounds, and probably will give a rough idea of its reactivity.
We are considering further activities in these directions.

Supplementary Materials:
The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules28020728/s1, Tables S1-S14 containing thermodynamic parameters and Cartesian coordinates for all located molecules of C 4 H 5 NO.