Isomers of the Allyl Carbocation C₃H₅⁺ in Solid Salts: Infrared Spectra and Structures

Abstract

Three isomers of the allyl cation C₃H₅⁺ were obtained in salts with the carborane anion CHB₁₁Cl₁₁^–. Two of them, angular CH₃–CH=CH⁺ (I) and linear CH₃–C⁺=CH₂ (II), were characterized by X-ray crystallography, and the third one, (CH₂CHCH₂)⁺ (III), is formed in an amorphous salt. The stretch vibration of the charged double bond C=C⁺ of I and II is decreased by 162 cm^–1 (I) or 76 cm^–1 (II) as compared to that of neutral propene. This result contradicts the prediction of DFT and MP2 calculations with the 6-311G++(d,p) basis set that the appearance of the positive charge on the C=C bond should increase its stretch vibration by 200 cm^–1 (I) or 210 cm^–1 (II). According to infrared spectra, the CC bonds in isomer III have one-and-a-half bond status. Isomers I and II in the crystal lattice are stabilized due to uniform ionic interactions with neighboring anions with partial transfer of a positive charge to them. Additional stabilization of II is provided by a weak hyperconjugation effect. Isomer III is stabilized in the amorphous phase due to ion paring with a counterion and a strong intramolecular hyperconjugation effect.

1. Introduction

Considerable progress has been achieved in the research on saturated and aromatic carbocations.¹⁻³ The same cannot be said about unsaturated alkene cations. Despite extensive theoretical and experimental research in the past five decades,⁴⁻¹² our knowledge about the simplest alkene carbocations not stabilized by heteroatoms and aromatic groups remains limited. It derives mainly from theoretical research and a moderate number of experimental studies. For instance, the simplest vinyl cation C₂H₃⁺ and isomers of cations C₃H₃⁺ and C₃H₅⁺ have been studied experimentally in vacuum by mass-selected IR spectroscopy.¹³⁻¹⁵ In a solid phase, not stabilized alkene carbocations are isolated without a counterion in a cryogenic Ar matrix¹⁶ or superacidic SbF₅ matrix.¹⁷ It looks like these cations cannot be stable under ambient conditions. Nonetheless, the isobutylene⁺ carbocation obtained as a carborane salt and characterized by IR spectroscopy and X-ray crystallography appears to be stable up to 100 °C. It has specific IR spectroscopic properties.¹⁸

From studies on solvolysis reactions, it has been concluded that vinyl- or allyl-type carbocations are highly reactive and therefore difficult to study.^5,7,10 On the other hand, Mayr and co-workers have shown that their expected reactivity is exaggerated.¹⁹ Recently, the high reactivity of the benzyl carbocation was explained: when acting as a strong protonating agent, it converts into a carbene molecule, whose high reactivity can be perceived as the reactivity of the carbocation.²⁰ Thus, the latest research revealed unexpected properties of unsaturated alkene carbocations.

In this work, we studied isomers of the allyl carbocation C₃H₅⁺ in amorphous and crystalline phases at room temperature by IR spectroscopy and X-ray crystallography. As a counterion, the undecachlorocarborane anion CHB₁₁Cl₁₁^– was chosen. Its extreme stability and low basicity promote the formation of stable salts with highly reactive cations.²¹

2. Results

Injection of gaseous 1,2-dichloropropane (hereinafter abbreviated as DCP) into an IR cell-reactor with a thin layer of H(CHB₁₁Cl₁₁^–) (hereafter abbreviated as H{Cl₁₁}) covering the Si windows leads to a surface reaction with a release of HCl. It was found that the molar ratio of the formed HCl to the reacted acid is close to 2 (see the Experimental Section), that is, the overall reaction proceeds according to eq 1

1

It is a two-step reaction: First, the unstable cation C₃H₆Cl⁺ is formed, which rapidly decomposes to C₃H₅⁺ + HCl, similar to the reaction of dichlorobutane with H{Cl₁₁}, forming the butene cation, C₄H₇⁺.¹⁸ In the course of reaction 1, absorption intensity of the free acid decreased, and when it approached zero, the reaction was stopped by removing the gas phase in vacuum. The spectra of the products formed by the reaction were isolated from the recorded spectrum by successive subtraction of the spectra of DCP vapors, gaseous HCl, and unreacted acid. They showed (Figure 1) that the carbocation C₃H₅⁺ with the most characteristic frequencies at 2806, 1301, 1267, and 1210 cm^–1 forms first. Then, the formation of the second carbocation begins with a broad intense absorption pattern in the range of 1200–1600 cm^–1. It will be shown below that this is the product of the interaction of C₃H₅⁺ with DCP.

Figure 1.

IR spectra of carbocations produced by the interaction of DCP with H{Cl₁₁} until complete consumption of the free acid (red spectrum). The spectra of gaseous HCl and DCP and those of the free acid are compensated.

Repetition of this experiment with a thinner layer of the sublimated acid leads to faster completion of the reaction (the H{Cl₁₁} acid is polymeric,²² which slows down its interaction with bases) with the formation of the first cation less contaminated by the second (Figure 2).

Figure 2.

IR spectra of carbocations formed during the interaction of DCP with a thinner H{Cl₁₁} layer than in the experiment shown in Figure 1. Spectra of the free acid, DCP vapors, and HCl are compensated. The red spectrum corresponds to complete consumption of the acid.

The purest salt of the C₃H₅⁺ cation is obtained through the interaction of DCP with monomeric molecules of the CH₂Cl⁺{Cl₁₁^–} salt via eq 2.

2

By this reaction, using dichlorobutane, the C₄H₇⁺ cation has been obtained.¹⁸ The completion of reaction 2 was monitored by measuring the absorption intensity of the formed gaseous CH₂Cl₂ and HCl. The CH₂Cl⁺{Cl₁₁^–} salt was prepared as described previously²³ according to eq 3

3

After the completion of reaction 2, the absorption intensity of the released HCl reaches that of HCl formed during the preparation of the CH₂Cl⁺{Cl₁₁^–} salt when the molar ratio of HCl/H{Cl₁₁} is 1.0 (eq 3). This finding confirms the mechanism of the reaction presented in eq 2. The IR spectrum of the resultant product belongs to the high-quality C₃H₅⁺{Cl₁₁^–} salt (Figure 3). If DCP vapors continue to be in contact with C₃H₅⁺{Cl₁₁^–} for more than 1 min, the spectrum of side products emerges. In this work, only salts of the carbocation C₃H₅⁺ were studied; the products of its interaction with DCP will be a subject of a separate study.

Figure 3.

IR spectra of salt C₃H₅⁺{Cl₁₁^–}, formed by the interaction of DCP with CH₂Cl⁺{Cl₁₁^–}.

The easiest way to obtain a large amount of the salt of the carbocation C₃H₅⁺ is the direct interaction of liquid DCP with the H{Cl₁₁} acid. When a small drop of DCP is added to the acid powder, the attenuated total reflectance (ATR) IR spectrum shows the formation of a salt of the C₃H₅⁺ cation contaminated with the byproducts of its interaction with DCP. The intensity of the byproducts’ spectrum depends on the quantity of added DCP. By repeating this experiment several times with different amounts of DCP injected, we were able to obtain a sample with a high-quality spectrum of C₃H₅⁺ (Figure 4). It matches the spectra of the salts of C₃H₅⁺ obtained in the IR cell reactor after an interaction of DCP vapors with the sublimed acid or the CH₂Cl⁺{Cl₁₁^–} salt.

Figure 4.

ATR IR spectrum (with ATR correction) of the amorphous C₃H₅⁺{Cl₁₁^–} salt. Some frequencies of the C₃H₅⁺ cation are indicated; the other intense bands belong to the anion.

To determine the structure of the carbocation, X-ray structural analysis was used. The pure C₃H₅⁺ {Cl₁₁^–} salt obtained by completing the reaction of DCP with CH₂Cl⁺{Cl₁₁^–} in a gas cell was dissolved in dichloromethane (DCM) and kept over hexane vapor. After a while, the crystals grew. X-ray structural analysis revealed that this is a C₃H₅⁺{Cl₁₁^–} salt with discrete cations and anions. Despite the rather large R-factor due to low-quality crystals (they are twins), the shape of the cation is clear-cut, making it possible to determine its main structural features (Figure 5): it is an angular molecule with a central sp² carbon atom and one shortened CC bond close to a double one. Hereafter, we will refer to it as isomer I.

Figure 5.

Structure of isomer I in the C₃H₅⁺{Cl₁₁^–} salt as determined by X-ray crystallography. The CC distances are given in Å, and the CCC angle are given in degrees.

Crystals of the salt of another isomer of C₃H₅⁺ were obtained as well. The salt C₃H₅⁺{Cl₁₁^–} obtained by the direct interaction of the acid with a small amount of DCP (its IR spectrum is given in Figure 4) was dissolved in ortho-dichlorobenzene and left over CCl₄ vapors for crystal growth. After a while, a viscous dark-brown phase separated out. It was dissolved in DCM and left over hexane vapor. Crystals grew after 1–3 days. Their X-ray structure revealed that this is a C₃H₅⁺{Cl₁₁^–} salt with discrete cations and anions. Cations are linear, with the CCC angle of 180°, which means that the central C atom features sp hybridization, that is, we are dealing with the isomer CH₃–C⁺=CH₂, which we designated as II. In the crystal lattice, the cations of this isomer are positioned in two orientations at an angle of 90° toward each other, which leads to different interactions with neighboring cations (Figure 6) and, as a consequence, to different distances between terminal carbon atoms, 1.513 and 1.432 Å. Thus, isomer II can be subdivided into two nonequivalent states: IIa and IIb. The longer isomer (1.513 Å) will be designated below as IIa, and the shorter one (1.432 Å) will be designated as IIb. The finding that crystallographic CC distances in both states, IIa and IIb, are aligned means that their visible structures are the result of the superposition of two oppositely oriented species, as shown in Scheme 1. Isomer IIa is in one crystallographic layer, and isomer IIb is in the other. IIa and IIb are arranged relative to each other at an angle of 90°, and their crystallographic overlap looks like a cross (Scheme 1, Figure 6), in which the weight of the occupancy of position C1,4 is 1.0, whereas the weights of the occupancy of other positions, C3–C6, are 0.5.

Figure 6.

Structure of the C₃H₅⁺{Cl₁₁^–} salt containing isomer II in two orientations (at an angle of 90° toward each other), which are superimposed on each other (see Scheme 1). The shortest C···Cl distances (in Å) between the cation and anion are indicated.

Scheme 1. Schematic Representation of Isomer II in Different Orientations in the Crystal Lattice.

3. Discussion

IR spectra of three isomers of the C₃H₅⁺ cation in its salts with the {Cl₁₁^–} anion were registered, but crystal structures of only two of them (I and II) could be determined (Figures 5 and 6, Scheme 1).

The IR spectrum of angular isomer I contains intense bands of C=C and C–C stretching. Their frequencies actually match those of the (CH₃)₂C=CH⁺ cation (Figure 7), in which the charge is localized on the CH=CH⁺ group.¹⁸ If one CH₃ group in the isobutylene⁺ cation is replaced by an H atom to form I, then, the charge on CH=CH⁺ can increase because the H atom is more electronegative than the CH₃ group. Nevertheless, this does not happen (the C=C stretching actually does not change), probably due to the participation of the CH₃ group of I in weak hyperconjugation with the p_z orbital of the central C atom (its CH stretches decrease to 2890 cm^–1), while the isobutylene⁺ cation does not undergo hyperconjugative stabilization (Figure 7). In other words, a decrease in cation size from isobutylene⁺ to propylene⁺ leads to a decrease in the population of the 2p_z orbital of the central sp² C atom and to involvement of the CH₃ group in hyperconjugation that promotes the dispersion of the charge onto the H atoms of the CH₃ group without increasing positive-charge density on the CH=CH⁺ moiety.

Figure 7.

ATR IR spectra of crystalline salts with isomer I (red) or its analogue, butylene⁺ cation (CH₃)₂CH=CH⁺ (blue),¹⁸ as analyzed by X-ray diffraction. The intense bands marked with asterisks belong to anion CHB₁₁Cl₁₁^–, and the weak bands at 1576 and 1537 cm^–1 marked with black club suit belong to byproducts (for details see Figure S1 in the Supporting Information).

Cation I is located rather loosely in the cage of the crystal lattice formed by bulky anions and is engaged in a purely ionic interaction with them because the shortest C···Cl distances between the cation and the surrounding anions are 3.934 Å (Figure S2 in the Supporting Information), which exceeds the sum of van der Waals radii r_C and r_Cl (3.53 Å).²⁴ This observation indicates a uniform distribution of the positive charge over the cation.

Linear isomer II has two nonequivalent states, IIa and IIb, which, being differently oriented in the crystal lattice, interact differently with counterions. The shortest C···Cl distances between C atoms of the cation and Cl atoms of the anions in IIa are smaller (3.189 and 3.444 Å), while in IIb, they exceed (3.642 Å; Figure S3 in the Supporting Information) the sum of van der Waals radii r_C and r_Cl (3.53 Å). Therefore, isomer IIa strongly interacts with the surrounding anions through H-bonding, which lengthens its averaged CC bonds (1.513 Å) as compared with isomer IIb (1.432 Å). Therefore, isomers IIa and IIb should certainly differ in frequencies of C=C stretches, showing two νC=C bands in the IR spectra. Moreover, because each cation, IIa and IIb, has two opposite orientations (Scheme 1) in which they can be nonequivalent, the number of νC=C bands can reach three–four. In fact, the IR spectra show three bands of the C=C stretch at 1588, 1576, and 1564 cm^–1 (Figure 8). Accordingly, in the frequency range of C–H stretch vibrations, three broad bands are observed—at 2897, 2854, and 2823 cm^–1—which are characteristics of CH₃ groups participating in hyperconjugation of different strengths. Therefore, we can say that at least three of the four differently oriented isomers II are nonequivalent, that is, each shows distinct charge dispersion over the cation.

Figure 8.

ATR IR spectrum of isomer II in crystalline salt C₃H₅⁺{Cl₁₁^–}.

The IR spectrum of the cation in the amorphous C₃H₅⁺{Cl₁₁^–} salt, arising when DCP interacts with the powdered acid, differs greatly from the spectra of isomers I and II (Figure 4) and belongs to another isomer, denoted as III. Its salt is a precursor for obtaining crystals containing isomers I and II but does not yield crystals of isomer III itself and therefore could not be characterized by X-ray crystallography. The main features of the IR spectrum of III (Figures 3 and 4) are low frequencies of CC and CH stretches, which almost match those of i-propyl⁺ and t-butyl⁺, CH₃–C⁺X–CH₃ (where X = H or CH₃) or the charged moiety −CH₂–C⁺H–CH₂– in cyclo-pentyl⁺ carbocations (Table 1). Their CH₃ or CH₂ groups take part in the hyperconjugation with the p_z orbital of the central sp² C atom, thereby decreasing the CH stretches and bringing the CC stretch vibrations closer to the values typical for one-and-a-half bond status. Such a good match of C–H and C–C stretches of III to those of saturated carbocations suggests that isomer III is a symmetric allyl cation (CH₂CHCH₂)⁺. If it has the structure IIIa (Scheme 2), then, the charge should be more concentrated on the terminal CH₂ groups, thus reducing the probability of their involvement in hyperconjugation. If two CH₂ groups form a weak CC bond, converting the isomer to cyclic IIIb′ (Scheme 2), then, the “+” charge will be more concentrated on the central C atom, and its p_z orbital may be empty enough to accept σ-electrons of CH₂ groups. Moreover, the orientation of their CH bonds will be optimal for the hyperconjugation with the 2p_z orbital. The similarity of frequencies of C–H stretches of III to those of saturated carbocations means that we are dealing with isomer III stabilized by stronger hyperconjugation than I and II are. The (H₂)C···C(H₂) bond in IIIb′ should be weak because after the salt of IIIb is dissolved in DCM followed by crystallization, this bond breaks, giving rise to open-chain isomers I and II.

Table 1. Comparison of the Most Characteristic CH and CC Stretch Frequencies of Isomer III with Those of the Saturated Carbocations in the Salts with {Cl₁₁^–} Ions.

cation	C–H stretcha	CC stretches		refs
isomer III	2806	1303	1264	Present work
i-C3H7+	2780	1256 broad		(3)
t-C4H9+	2791	1289	1262	(25)
cyclo-pentyl+	2780	1260 broad		(3)

^aThe most intense highly characteristic band of CH stretch vibration of the CH₃ or CH₂ group involved in hyperconjugation.

Scheme 2. Schematic Representation of Possible Structures of Isomer III.

It is demonstrated below that upon optimization of structures IIIa and IIIb′ (at the MP2 level), isomer IIIb′ is transformed into IIIa, that is, it is unstable in vacuum. In the solid amorphous phase, IIIb can be stabilized by ion pairing, as seen in the salt of isobutylene, C₄H₇⁺{Cl₁₁^–}:¹⁸ the disordered anionic environment of the cation in the amorphous phase promotes a closer interaction of one of the anions with the most charged CH⁺ group via H-bonding (Scheme 1). This situation increases intramolecular stabilization of the cation through the hyperconjugation effect.

Ionic pairing may also be responsible for the increased thermal stability of isomer IIIb. If a thin layer of the salt of III is quickly heated on the Si window of an evacuated IR cell to 100 °C, kept at this temperature for 5 min, and then quickly cooled down to room temperature, then, no changes are observed in the IR spectrum of the sample. Upon repeated heating of the sample under the same conditions to 120 °C, the intensity of the initial spectrum of isomer III decreases to 92%, and therefore, 8% of the isomer transitions to another species. Next, after the sample is heated to 150 °C, 34.4% of the intensity of the III spectrum is retained, and spectrum intensity of the new products increases significantly.

Isomer I formally derives from neutral propene upon elimination of H^– from its =CH₂ group (Scheme 3). This event decreases electron density on the double C=C bond, and C=C stretch frequency should decrease. Indeed, the observed decrease in νC=C is (1652 – 1490) = 162 cm^–1.

Scheme 3. Illustration of the Formation of I from Propene.

Rearrangement of the −CH=CH⁺ group into the −C⁺=CH₂ group, when I transitions to II, promotes a “+” charge shift to the central C atom, thereby somewhat enhancing the participation of the CH₃ group in hyperconjugation (its CH stretch decreases, Table 2). Better scattering of the positive charge onto the atoms of the CH₃–C moiety weakens its effect on the C=C bond, thus reducing the low-frequency shift of the C=C stretch relative to neutral propene to ∼76 cm^–1 (recall that for I, this decrease is 162 cm^–1, Table 2).

Table 2. Most Characteristic Frequencies of CH and CC Stretches of Isomers I–III and of the i-Butylene⁺ Cation^a.

^aThe difference between calculated (scaled by a factor of 0.9674) or experimental CC stretches and those of neutral propene or isobutene is given in parentheses.

^bThe most intense C–H stretch vibration of the CH₃ or CH₂ groups; underlined frequencies belong to those groups that are involved in hyperconjugation.

^cA difference from the calculated C=C stretch for neutral propene (1643 cm^–1) or butene (1655 cm^–1).

^dA low-frequency shift relative to the experimental C=C stretch of neutral propene (1652 cm^–1) or butene (1660 cm^–1).

Isomer III does not contain a double CC bond; therefore, the difference between its asymmetric CCC vibration and the C=C stretch of neutral butane is the greatest (∼350 cm^–1). Consequently, the frequencies of CC stretches are the best indicators for the identification of isomers I–III of the C₃H₅⁺ cation (Table 2).

Our results are not consistent with the predictions of quantum chemical calculations for bare cations in vacuum. Geometry optimizations of isomers I–III (Scheme 4) and harmonic frequency calculations at the MP2 level of theory with the 6-311G++(d,p) basis set (Table S3 in the Supporting Information) yielded the following results.

Scheme 4. Optimized Structures at the MP2 Level of Theory with the 6-311G++(d,p) Basis Set.

Isomer IIIa is the most energetically favorable in vacuum. In comparison to it, the energies of II and I are higher by 12.5 and 25.1 kcal/mol, respectively. When isomer IIIb was optimized, the energy minimum was not reached because it is transformed into IIIa. In linear isomer II, the sum of two CC bond lengths (2.658 Å) is significantly less than experimentally determined values of 2.864 and 3.026 Å, thereby definitely indicating a strong influence of the environment. The optimized geometry of I differs most strongly from the experimental one. In fact, it represents an acetylene molecule, to which bridging CH₃⁺ is attached, forming two long CC bonds of 1.695 and 1.873 Å, which are unheard of for hydrocarbon molecules. Optimization of isomers I, II, IIa, and IIIb at the B3LYP/6-311++G(d,p) level of theory predicts the stability of only two isomers, II and IIIa, while isomer I is converted to II, and IIIb is converted to IIIa. Thus, in the solid phase, the interaction of the cation with the anionic environment plays an extremely important role in the stabilization of cations by changing their energy state and electron density distribution. Therefore, it is not surprising that the calculated frequencies of such isomers also differ from the experimental ones. The greatest differences are seen in the frequencies of C=C stretches. For isomers I and II, they exceed those calculated for neutral propene by as much as 200 and 210 cm^–1, respectively, while experimental νC=C values are decreased by 162 cm^–1 (I) and ∼76 cm^–1 (II). This is a drastic mismatch, reaching 362 and 286 cm^–1. Indeed, the formation of the C₃H₅⁺ cation upon elimination of H^– from the propene molecule lowers electron density on the bonding MO of the C=C bond, and its vibration frequency can only decrease, which is observed experimentally. By contrast, according to calculations, the C=C stretch frequency in this case should greatly increase with the shortening of the C=C bond, which means its strengthening. This is possible if the electron density decreases in the populated antibonding orbital. On the other hand, the C=C bond of propene does not contain such a populated orbital. Consequently, the results of calculations are unclear and cannot be used for a comparison with experimental data for cations I–III. A similar discrepancy between the experimental and calculated spectra has been reported for the isobutylene⁺ cation.¹⁸

Direct examination of the allyl cation formation in a cryogenic superacid matrix (130 K) by IR spectroscopy has been performed by von R Schleyer et al.¹⁷ The observed intense IR band at 1577–1581 cm^–1, which is closest to the calculated (CISD/6-31g**) asymmetric CCC vibration of isomer IIIa, was assigned to isomer IIIa, while it matches that of isomer II of the present work. On warming to 170 K, the allyl cation is converted to an undefined product with a band at 1547 cm^–1, perhaps a polymer. The assumption about the polymerization of the allyl cation at temperatures above 180 K cannot be correct because we found that all the identified isomers of C₃H₅⁺ do not polymerize even at room temperature. The transition of the band near 1578 cm^–1 to another one at 1547 cm^–1 upon heating to 170 K and above can be caused by a change in the interaction of isomer II with the immediate environment. Given that the observed spectra contain many more peaks than are computed for the allyl cation, these authors¹⁷ proposed that oligomerization or other side reactions must have occurred even at the low temperatures. By contrast, we found that oligomerization can occur only in the presence of an excess of the precursor that interacts with the formed allyl cation. One of the highly intense “extra” bands of the allyl cation observed at 170 K and shown in a figure in ref (17) has a frequency slightly lower than 1500 cm^–1, which is similar to the C=C stretch of isomer I. These authors did not show the frequency of this band because they did not classify it as an allyl cation, probably owing to its unexpectedly low frequency, which does not match any of the calculated CC stretch frequencies. Unfortunately, the CH stretches are not specified and discussed in that work. Thus, we can say that in a cryogenic superacidic matrix, the IR spectra of the allyl cation contain the bands of C=C stretches similar in frequency to those of isomers II and possibly I found in the present study.

There is an experimental study on the allyl cation, C₃H₅⁺, tagged with either an N₂ or Ar molecule in vacuum by IR photodissociation spectroscopy.¹⁵ Although we concluded that an IR spectroscopic comparison of allyl cations between solid and gas phases is inappropriate due to the strong influence of the environment, such a comparison is useful to make. The C=C stretches of two isomers C₃H₅⁺ were detected at 1581_N2/1585_Ar and 1877_N2/1880_Ar cm^–1. The former is very close to the νC=C calculated for IIIa (1583 cm^–1 after scaling by a factor of 0.955); this result allowed the authors to assign it to isomer IIIa, while it is close to the νC=C of isomer II, which we identified by X-ray crystallography. The latter spectrum with a frequency of the C=C stretch at 1877_N2/1880_Ar cm^–1 is close to that calculated for isomer II, thereby allowing assignment to isomer II. Unfortunately, a spectrum with νC=C = 1877_N2/1880_Ar cm^–1 is different from any of the three possible isomers of C₃H₅⁺ identified in the present work.

Bally et al. have generated the C₃H₅⁺cation by ionization of the C₃H₅^• radical in an Ar matrix.¹⁶ Its IR spectrum is in good agreement with that of gaseous C₃H₅⁺·Ar(N₂),¹⁵ and they also assigned it to isomer IIIa because of its good correlation with the calculated spectrum (for the frequency region below 1600 cm^–1). Nevertheless, its most characteristic strong band of the CC stretch at 1577 cm^–1 matches one of the νC=C bands of the isomer II studied in the present work by X-ray crystallography.

It is possible that such a discrepancy between the results of the study of allyl cations in the gas phase according to the interpretation of IR spectra using quantum chemical calculations and solid-phase studies based on X-ray data is indeed due to the different distributions of electron density in cations I–III when they are isolated in vacuum versus cations I–III surrounded with anions in a solid phase. Nevertheless, the authors¹⁵ left without an explanation the following important questions: Why does the experimental frequency of the C=C stretch at 1877/1880 cm^–1, assigned to isomer II, exceeds that of neutral propene by 228 cm^–1? (Which means that the emergence of the positive charge on the C=C bond causes a significant increase in the electron density on it, bringing it closer to a triple bond.) Why is the frequency at 1585 cm^–1 (ref (15)) or at 1577 cm^–1 (ref (16))—assigned to the asymmetric CCC stretch of IIIa—close to stretch vibration of the C=C double bond of neutral propene?

4. Conclusions

The formation of all three possible isomers of the C₃H₅⁺ cation in its solid carborane salts was demonstrated. The energetically most favorable symmetric allyl cation III forms in an amorphous phase and is stabilized by ion paring and strong hyperconjugation. The available experimental data indirectly point to its possible cyclization giving rise to a weak (H₂)C···C(H₂) bond. In the crystal lattice, isomer III is converted into identified isomers I and II with the disappearance of ion paring.

Linear isomer II is located in a loose cage of the crystal lattice and is oriented differently toward the anions. Due to the nonequivalent interactions with them, it manifests three distinct C=C stretches. This finding indicates that the distribution of electron density along its CC bonds is very sensitive to the influence of the environment. Identical frequencies of the C=C stretch of isomer II have been registered for the allyl cation in a cryogenic superacidic matrix (where it was attributed to the isomer III).¹⁷

The existence of angular isomer I (the least thermodynamically stable in vacuum) in crystalline salts was proved by X-ray structural analysis. It is an analogue of isobutylene carbocation (CH₃)₂C=CH⁺, which should also be the least stable in vacuum among all possible isomers of the butene cation, but has been proven to exist in carborane salts by X-ray crystallography.¹⁸ IR spectra of isomer I and carbocation (CH₃)₂C=CH⁺ are very similar too. IR spectra of isolated C₃H₅⁺ cations in a cryogenic SbF₅ matrix¹⁷ apparently contain the characteristic C=C stretch vibrations of isomer I. Isomers I and II are stabilized in the crystal lattice by uniform ionic interactions with neighboring anions. Cation II shoes additional intramolecular stabilization by weak hyperconjugation. The influence of the environment should cause a noticeable difference between the IR spectra of the C₃H₇⁺ isomers in the solid phase and those in the gas phase. These differences were found and require further study.

The discovered discrepancies between the experimental data and the predictions of quantum chemical calculations can be illustrated by means of the following example. The observed significantly lower frequencies of the C=C stretch of isomers I and II relative to neutral propene correspond to those expected when H^– is subtracted from the C₃H₆ molecule affording an electron-deficient C₃H₇⁺ cation. However, quantum chemical calculations predict that in this case, electron density on the C=C bond of the cation should increase. This contradiction is yet to be resolved.

5. Experimental Section

All sample handling was carried out in an inert atmosphere (H₂O, O₂ < 1 ppm) in a glovebox. The carborane acid, H{Cl₁₁}, was prepared as described previously.²⁶ It was purified by sublimation at 150–160 °C under a pressure of 10^–5 Torr on cold Si windows in a specially designed IR cell reactor, whose detailed description is given in ref (18). The formed thin translucent layer yielded an intense IR spectrum. The C₃H₇⁺{Cl₁₁^–} salt was obtained by injection of gaseous DCP under anaerobic conditions into the IR cell reactor containing the acid. To determine the molar ratio of released HCl to reacted H{Cl₁₁}, absorption intensity of the formed gaseous HCl was measured at a frequency of 2821 cm^–1 (I₂₈₂₁), and using the calibration plot of I₂₈₂₁ versus HCl content (in millimoles) for a given IR cell, it is converted to millimoles. The amount of the reacted acid was determined by treating the final reaction product with a 0.1 M NaOH solution, followed by back titration with a standard 0.1 M HCl solution. The observed molar ratio of HCl/reacted acid is close to 2, which corresponds to the overall reaction described by eq 1. The second way to obtain C₃H₇⁺{Cl₁₁^–} by means of the CH₂Cl⁺{Cl₁₁^–} salt is described in the main text.

DCP from Toronto Research Chemicals Inc. was used without further purification.

X-ray diffraction data were obtained on a Bruker Kappa Apex II CCD diffractometer using φ and ω scans of narrow (0.5°) frames with Mo Kα radiation (λ = 0.71073 Å) and a graphite monochromator. The structures were solved by direct methods by means of the SHELX-97 software suite²⁷ and were refined by the full-matrix least-square method against all F(2) in anisotropic approximation in SHELXL-2014/7.²⁸ Absorption corrections were applied by the empirical multiscan method in SADABS software.²⁹ Hydrogen atoms’ positions were calculated with the riding model. Crystallographic data and details of the X-ray diffraction experiment are listed in Table S1 in the Supporting Information. CCDC 2063010 and 2063011 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/cgi-bin/catreq.cgi or from the Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: (+44) 1223 336 033; email: deposit@ccdc.cam.ac.uk.

The high R-factor for the salt of the CH₃–CH=CH⁺ cation is explained by the bad quality of the crystals obtained. They are twins, and we failed to obtain crystals of the best quality. The structure was refined as 0.85:0.15 2-component twins. The structure of the salt of isomer CH₃–C⁺=CH₂ is formed by crystallographically independent 1/2 part of the molecules of the anion and cation. The cation is located at the center of symmetry and is disordered at two positions.

The crystal structures were analyzed for short contacts between nonbonded atoms using PLATON³⁰ and MERCURY programs.³¹

DFT calculations were performed at the B3LYP/6-311G++(d,p) level plus the D3 dispersion correction energy term³² with an ultrafine integration grid within the framework of the Gaussian’09 package. MP2 calculations were performed with the same 6-311G++(d,p) basis set with an ultrafine integration grid within the framework of the Gaussian 09 package.³³ To compare calculated and experimental vibrational frequencies, the calculated harmonic frequencies were scaled by a factor of 0.9674, as recommended by Kesharwani et al.³⁴

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.1c01316.

• Details of X-ray data, additional IR spectra, and calculated frequencies for propene and C₃H₇⁺ isomers (PDF)

The authors declare no competing financial interest.