Theoretical insights into structure, bonding, reactivity and importance of ion-pair interactions in Kirby's tetrafluoroboric acid salts of twisted amides

Abstract

The geometries of the amides 1-azatricyclo [3.3.1.1^3,7] decan-2-one, tetrafluoroboric acid salt (1), 3-methyl-1-azatricyclo [3.3.1.1^3,7] decan-2-one, tetrafluoroboric acid salt (2), and 3,5,7-trimethyl-1-azatricyclo [3.3.1.1^3,7] decan-2-one, tetrafluoroboric acid salt (3) have been calculated at the DFT-D3 (BJ) level using density functionals PBE, PBE0, TPSS and TPSSH. The optimized structure of (1) at the DFT/PBE0-D3(BJ) level of theory in methanol is in excellent agreement with the experimental structure. The geometries of the hydrolyzed products (4–7) have been optimized with PBE and PBE0 functionals. In the studied compounds (1–3), the [BF₄]⁻ anion interacts with cationic fragments [1]⁺, [2]⁺ and [3]⁺ through the N–H⋯F hydrogen bond. The ion-pair interactions affect the C–N–H bond angles which are relatively smaller (110.3° in 1, 109.9° in 2, 110.0° in 3) than those for cationic fragments (104.8° in 1⁺, 104.8° in 2⁺, 105.1° in 3⁺). The charge analysis formulates the salts (1–3) as [cation]^q+[BF₄]^q− with q = ∼0.81. The high stability of ion-pairs is due to significant flow of charge from the BF₄⁻ anion to the cation. There is significant hydrogen bonding (H⋯F) interaction in 1–3. Salt 1 has the lowest ion pair dissociation energy of ΔE = 5.46 kcal mol⁻¹ in methanol and 4.91 kcal mol⁻¹ in acetonitrile. The hydrolysis reaction of 1 is most exothermic (ΔE = −11.84 kcal mol⁻¹) and thus it is more favourable. The hydrolysis of amides 2 and 3 with a bridgehead methyl is relatively less favourable. Hydrolysis reactions of amides 1 and 3 at the DFT/PBE-D3(BJ) level in acetonitrile have been investigated. The calculated enthalpies of the hydrolysis product formation are 4, 41.61 kcal mol⁻¹ and 7, 32.43 kcal mol⁻¹.

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Introduction

The amide bond plays an essential role in chemistry and biology.^1,2 Due to the strong resonance stabilization between π-orbitals of the O–C–N linkage³ the vast majority of amides are planar. When the planar geometry is disrupted and resonance stabilization between π-orbitals of the O–C–N linkage no longer occurs, the stability and chemistry of the amide functionality changes dramatically.^4–18 These include enhanced reactivity toward amide bond hydrolysis and toward a nucleophilic attack on the carbonyl group, different regiochemistry of amide protonation and alkylation reactions, and different spectroscopic and physical properties. Twisted amides have been invoked in a variety of enzymatic transformations, including peptide hydrolysis,^19–22 protein splicing,^23–26 cis–trans isomerization of peptidyl–proline bonds. Inhibition of the cis–trans isomerization of peptidyl–proline bonds is of considerable interest in the treatment of drug-resistant cancer cells²⁷ and neurodegenerative diseases.²⁸ The chemistry of bridged amides had been the subject of a number of reviews,^29–32 including a comprehensive review by Szostak and Aubé.³²

In 1998, Kirby et al. reported the first structurally characterized perpendicularly twisted 1-aza-2-adamantanone (A) (Scheme 1).^33,34 Recently, Kirby's group reported X-ray structure of another example of most twisted amide (B).³⁵ Synthesis, characterization, reactivity and bonding of essentially perpendicular twisted amide were investigated by Kirby's group.^33–39 In 2006, Tani and Stoltz reported first representative example of structurally characterized N-protonated twisted amide, 1-N-quinuclidonium tetrafluoroborate.⁴⁰ The X-ray structure of this protonated amide indicated a fully twisted amide bond (twist angle τ = 90.9°). Stoltz and co-workers reported a gas-phase synthesis, reactivity and bonding of the protonated 2-quiniclidonium salt.⁴¹

Scheme 1

Kirby and coworkers also reported the synthesis, spectroscopic characterization and hydrolysis of tetrafluoroborate salts of most twisted protonated amides 1-azatriclo[3.3.1.1^3,7]deca-2-one (1), 3-methyl-1-azatriclo[3.3.1.1^3,7]deca-2-one (2) and 3,5,7-trimethyl-1-azatriclo[3.3.1.1^3,7]deca-2-one (3) (Scheme 2) together with single crystal X-ray diffraction structures for tetrafluoroborate salt protonated amides 1-azatriclo[3.3.1.1^3,7]deca-2-one (1). It has been observed that the salts (Scheme 3) react with water at very different rates. Salt (1) is hydrolyzed cleanly to the corresponding amino acid (4). Hydrolysis of (2) yield an equilibrium mixture of three compounds in solution: the starting material, the amino acid (5) and the protonated tricyclic hemiaminal (6), while compound (3) is converted to the tricyclic protonated hemiaminal (7).³⁵

Scheme 2

Scheme 3

Several theoretical studies addressing the hydrolysis of nonplanar lactams have been published.^{5–9,13,35,41} Greenberg and coworkers predicted that related bridged lactams display higher electron density at nitrogen as compared to planar amides.¹² Computational studies on the stability of (A) revealed that methyl substituent destabilize the amino acid form and contribute to the overall stability of Kirby's amide.³⁵ Experimental and calculated geometrical parameters of Kirby's most twisted amides (A–B in Scheme 1) as well as of tetrafluoroborate salt of protonated amide (1, Scheme 2) are presented in Table 1.

Table 1 Selected geometrical parameters of Kirby's most twisted amides (A–C) and tetrafluoroborate salt of protonated amide (1)

	A		B		C		1
	X-ray^a	M06-2X^b	X-ray^b	M06-2X^b	M06-2X^b	B3LYP^c	X-Ray
a Ref. 34.b Ref. 35.c Ref. 13c.
Twist angle (°)	90.5	89.5	90.0	90.8	90.55	90.0	90.0
Bond distance (Å)
C–N	1.475	1.449	1.448	1.449	1.450	1.457	1.508
C=O	1.196	1.204	1.201	1.204	1.203	1.210	1.186

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The effects of dispersion and hydrogen-bonding interactions have been evaded in the theoretical studies. The effects of counter ions have been evaded in most of the studies. To the best of our knowledge, the interactions between non-covalently nonbonded ion-pairs and effects of anion on the cation and the dispersion corrected density functional studies of twisted amides and related compounds have not been reported so far. An ionic bond must have some covalent character in addition to ionic character. A clear understanding of the cation–anion interactions in salts of most twisted amides has yet to be delineated. The dispersion and hydrogen-bonding interactions are requisite to understanding many important phenomena in chemistry, biology, and materials science. Accurate structural predictions of various properties of dispersive bound systems have been extensively studied.^42–53

In the present study, we report for the first time (i) the accurate optimized geometries of tetrafluoroborate salts of protonated most twisted Kirby's amides (1–3 in Scheme 2), (ii) the interactions between cation–anion pairs in order to estimate the character of N–H⋯F(BF₄) hydrogen bond between ion-pairs, (iii) the effects of nonbonded interactions between ion-pairs on the structure of cationic fragments, (iv) the optimized geometries of (4–7) the products of hydrolysis of salts (1–3), (v) energies of hydrolysis of salts (1–3) and (vi) the mechanism for hydrolysis of salts 1 and 3. Dispersion corrected density functional theory is used in conjunction with conductor-like screening model (COSMO) to take into account of solvent effects. The findings of the present study are interesting, and can be useful to the chemistry community working in the area of twisted amides.

Computational methods

All the calculations were performed using the ORCA-3.0.3 program package.⁵⁴ The standard all electron def2-TZVPP basis sets were used for all atoms.⁵⁵ Grimme's dispersion corrected DFT-D3 method⁵³ with Becke–Johnson damping⁵⁶ was used to account for the dispersion interactions. Gas-phase structures of salts 1–3 were optimized with (i) generalized gradient approximation (GGA), PBE⁵⁷ (ii) meta-GGA, TPSS⁵⁸ (iii) meta-hybrid, TPSSH⁵⁸ and (iv) hybrid functional, PBE0.⁵⁹ Geometries of 1–3 were also optimized in solution (methanol) using the conductor-like screening model (COSMO) implemented in ORCA program with hybrid functional, PBE0. Geometry of the hydrolysis products 4–7 were optimized with density functionals PBE and PBE0. The bonding energies between the ion-pairs of salts (1–3) were calculated in gas-phase as well as in solvents (methanol and acetonitrile). Calculations of vibrational frequencies were carried out in acetonitrile.

The electronic energies and enthalpies for the hydrolysis of the salts of protonated twisted amides 1–3 were calculated at DFT-D3(BJ)/PBE0 level of theory in acetonitrile solvent. The calculated frequencies were used to verify the nature of the stationary points encountered along the potential energy surface. Thus reactants and products showed real frequencies for the normal mode of vibrations, whereas transition states showed one imaginary frequency.

Results and discussion

Geometries

Important optimized geometrical parameters of the amides 1-azatricyclo[3.3.1.1^3,7]decan-2-one, tetrafluoroboric acid salt (1), 3-methyl-1-azatricyclo[3.3.1.1^3,7]decan-2-one, tetrafluoroboric acid salt (2), 3,5,7-trimethyl-1-azatricyclo[3.3.1.1^3,7]decan-2-one, tetrafluoroboric acid salt (3) calculated at DFT-D3(BJ) level using density functional PBE, PBE0, TPSS and TPSSH are presented in Table 2. The optimized structures of 1–3 at DFT/PBE0-D3(BJ) level of theory in methanol and the experimental data of 1–3 are shown in Fig. 1. The optimized Cartesian coordinates are given in the ESI.†

Table 2 Important geometrical parameters of the tetrafluoroboric acid salts of twisted amides (1–3) optimized at DFT/D3(BJ)/def2-TZVPP level with density functionals PBE, TPSS, TPSSH and PBE0 in gas-phase^a

	Bond distances (Å)					Bond angles (°)
	C5–O	C5–N	C4–C5	N–H8	H8–F2	O–C5–C4	O–C5–N	C5–N–H8
a Numbering of atoms is given in Fig. 1.b Geometrical parameters for (1)^+, (2)^+ and (3)^+ cations are given in parenthesis.
(1)
PBE	1.197	1.516	1.505	1.086	1.486	129.2	119.9	110.5
TPSS	1.196	1.517	1.504	1.073	1.520	129.4	119.8	110.4
TPSSH	1.192	1.505	1.510	1.064	1.546	129.3	119.5	110.1
PBE0	1.185, (1.180)	1.492, (1.532)	1.488, 1.487	1.066, (1.021)	1.505	128.9	119.9, (116.5)	110.3, (104.8)^b
(2)
PBE	1.198	1.515	1.514	1.085	1.489	128.9	119.3	110.1
TPSS	1.196	1.517	1.512	1.073	1.522	129.0	119.3	110.1
TPSSH	1.192	1.505	1.512	1.063	1.548	128.9	119.0	109.7
PBE0	1.185, (1.180)	1.492, (1.535)	1.507, 1.494	1.065, (1.021)	1.507	128.5	119.4, (116.4)	109.9, (104.8)^b
(3)
PBE	1.198	1.514	1.513	1.084	1.492	129.0	119.4	110.2
TPSS	1.197	1.513	1.510	1.070	1.542	129.2	119.1	109.9
TPSSH	1.192	1.503	1.508	1.064	1.546	129.1	119.1	109.8
PBE0	1.185, (1.179)	1.491, (1.535)	1.505, 1.493	1.065, (1.021)	1.509	128.7	119.4, (116.9)	110.0, (105.1)^b

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Fig. 1 Optimized structures of (1–3) at DFT/PBE0-D3(BJ) level of theory in methanol and the experimental data of 1.

Structurally characterized 1-azatricyclo[3.3.1.1^3,7]decan-2-one, tetrafluoroboric acid salt (1) has been reported by Kirby et al.³⁵ The structure of 3-methyl-1-azatricyclo[3.3.1.1^3,7]decan-2-one, tetrafluoroboric acid salt (2), 3,5,7-trimethyl-1-azatricyclo[3.3.1.1^3,7]decan-2-one, tetrafluoroboric acid salt (3) have not been reported yet. Thus we report for the first time the optimized geometries of ion pair amides (1–3). The optimized geometries with metaGGA TPSS and metahybrid TPSSH functionals yield longer bond distances. The optimized structure of (1) at DFT/PBE0-D3(BJ) level of theory in methanol is in excellent agreement with the experimental structure (see Fig. 1). Similar accuracy is expected for the other studied compounds. The PBE0-D3(BJ) geometries shall be considered for discussion and for the calculations of electronic properties and energy analysis. There is no significant effect of substituted methyl substituent on C=O and C–N bond distances, while C–C bond distance varies as: 1.488 Å in (1), 1.507 Å in (2) and 1.505 Å in (3). The experimental and calculated values of C–N bond distances for twisted amide salts 1–3 (Table 2 and Fig. 1) are longer than those for free base twisted amides (A–C) (Table 1). On the other hand the values of C=O bond distances for 1–3 are shorter than those for free base twisted amides (A–C). The X-ray values for Kirby's neutral twisted amide 3,5,7-trimethyl-1-aza tricycle[3.3.1.11,5] decan-2-one (A) are a C–N bond distance of 1.475 Å and a C–O one of 1.196 Å.³⁴ Morgan and co-workers reported the optimized the geometry of 1-aza-2-adamantone (C) at B3LYP/6-31+G(d) level of theory and their values for the amide unit are 1.46 Å for the C–N bond distance and 1.21 Å for the C–O bond distance.^13c Lopez and co-workers computed bond distances 1.488 Å for the C–N and 1.216 Å for the C–O for 1-aza-bicyclo[2.2.2]octan-2-one at B3LYP/6-31+G(d) level of theory.⁷

We also describe here the theoretical insights into ion-pairs interactions in amide salts. In the studied compounds (1–3), the [BF₄]⁻ anion interacts with cationic fragments [1]⁺, [2]⁺ and [3]⁺ through the N–H⋯F hydrogen bond. The H⋯F bond distances, which are smaller than the sum of van der Waal radii of hydrogen and fluorine (H⋯F = 2.66 Å)⁶⁰ are shown in Fig. 1. In order to investigate the effects of anion [BF₄]⁻ on the cationic fragments, the calculations for cationic fragments [1]⁺, [2]⁺ and [3]⁺ have also been carried out. The important geometrical parameters of [1]⁺, [2]⁺ and [3]⁺ are presented in Table 2 and Fig. 2. Small lengthening of (O)C–N and shortening of C=O bond distances are observed in cationic fragments (1⁺, 2⁺ and 3⁺) as compared to contact ion pair salts (1–3). The ion-pairs interactions affect the C–N–H bond angles (Table 1) which are relatively smaller (110.3° in 1, 109.9° in 2, 110.0° in 3) than those for cationic complexes (104.8° in 1⁺, 104.8° in 2⁺, 105.1° in 3⁺).

Fig. 2 Optimized structures of cationic fragments (1⁺, 2⁺ and 3⁺) at DFT/PBE0-D3(BJ) level of theory.

Electronic properties of salts of twisted amides (1–3)

It is mandatory for the numerical analysis of the ion-pairs interactions in the salts of twisted amides (1–3) to present and to discuss molecular orbitals for interactions between cations (1)⁺, (2)⁺ and (3)⁺ and (BF₄)⁻ anion. Fig. 3 displays the visualization of important molecular orbitals of C=O, C–N, N–H and H⋯F interactions. Orbitals HOMO-23, HOMO-30 and HOMO-31 depict significant non-covalent H⋯F interactions in (1–3). The LUMO orbital is π* orbital of the C=O group (see also Fig. S1 in ESI†). The observation reveals that during the hydrolysis reaction, H₂O interacts with CO group. The molecular orbitals concerning the –C(=O)–N part of 1 are displayed as HOMO-30 in Fig. 3. The π electron delocalizes over the –C(=O) group in HOMO-30. The orbital of N has an sp³ hybridized character so that we cannot find any delocalization of the π electron over the –C(=O)–N. The lobe of the orbital of N expanding downward will readily join with a proton. The localized C=O π orbital in 1 (2 and 3, see Fig. S2 and S3†), because its delocalization becomes geometrically impossible. The pictorial representation of the molecular orbital shall now be complemented with the numerical analysis of the electronic structure and bonding analysis of the salts of twisted amides (1–3).

Fig. 3 Important molecular orbitals of tetrafluoroborate salts of twisted protonated amides 1-azatriclo[3.3.1.1^3,7]deca-2-one (1) visualizing C=O, C–N, N–H and H⋯F interactions.

We first discuss the analysis of the ion-pairs bonding with the results of Mullikan charges and Mayer bond orders (Table 3). The charge analysis of the ion pair is interesting. Changes in the electronic density due to the formation of the ion pair from the precursors were analyzed by conducting a charge analysis on the precursors (1)⁺, (2)⁺ and (3)⁺ and (BF₄)⁻ anion and the ion pair (1–3). The total charge on the cations and (BF₄)⁻ anion were calculated for the ion pairs. The charge analysis underlines a distinct flow of electron density from the cation (1)⁺, (2)⁺ and (3)⁺ to the borate anion in the ion pairs. The total charge of the CO group decreased from average value −0.13 in the cations to average value −0.19 in the ion pair compounds. The charge on the boron atom decreased and fluorine atoms increased from precursors to those in the ion pair. It is clear that the cationic fragments (1)⁺, (2)⁺ and (3)⁺ are quite effective in withdrawing electron density from the BF₄⁻ anion and this explains why the stability of the subsequent ion pair formed is high. Our charge analysis is consistent with a formulation of the salts of twisted amide (1–3) as [cation]^q+[BF₄]^q− with q = ∼0.81.

Table 3 Mulliken charges and Mayer bond orders in the tetrafluoroboric acid salts of twisted amides (1–3) and cations and anion calculated at DFT/PBE0-D3(BJ)/def2-TZVPP level

	(1)	(2)	(3)	(1)^+	(2)^+	(3)^+	BF4^−
Mulliken charges
CO	−0.17	−0.20	−0.20	−0.11	−0.13	−0.14
N	0.15	0.17	0.20	0.17	0.19	0.21
H(NH)	0.25	0.25	0.25	0.21	0.21	0.21
F(HF)	−0.33	−0.33	−0.33				−0.42
(BF4)^q−	−0.80	−0.81	−0.81
Mayer bond order
C–O	2.26	2.26	2.27	2.24	2.25	2.26
C–N	0.87	0.86	0.86	0.83	0.86	0.86
N–H	0.80	0.80	0.80	0.92	0.92	0.92
H⋯F	0.23	0.23	0.22
B–F(BFH)	0.82	0.82	0.83				0.96
B–F	0.92–1.11	0.92–1.11	0.92–1.11

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The values of Mayer bond orders⁶¹ for the weak dispersion interactions (H⋯F hydrogen bond) between ion-pairs are 0.23 in (1), 0.23 in (2) and 0.22 in (3). It can be inferred from these results that there are effective H⋯F bonding in (1–3), which is supported by Fig. 3 and also Fig. S2 and S3 (ESI†). Moreover, the N–H bond orders (0.80) in ion-pairs (1–3) are significant smaller than the N–H bond orders (0.92) in cations (1⁺, 2⁺ and 3⁺). The B–F bond orders decreased in ion-pairs (1–3) than in free BF₄⁻ anion.

Energy analysis

Ion pair dissociation energy. The ion pair dissociation energies (ΔE) of salts (1–3) have been calculated according to the processes:

(1) → (1)⁺ + (BF₄)⁻

(2) → (2)⁺ + (BF₄)⁻

(3) → (3)⁺ + (BF₄)⁻

To account the solvation effect, the energy change associated with the dissociation of (1–3) is calculated for methanol (ε = 32.6) and acetonitrile (ε = 37.5) on optimized gas phase structures using the conductor-like screening model (COSMO) available within the ORCA program. In the gas phase, the electrostatic interactions are fairly strong as indicated by the large ion pair dissociation energies: 96.92 kcal mol⁻¹ in (1), 93.40 kcal mol⁻¹ in (2) and 92.38 kcal mol⁻¹ in (3) (Table 4). The gas-phase calculations usually overestimate the energy of reactions involving the separation of neutral complexes into its ionic components. When solvation energies were taken into account, a dramatic decrease in the dissociation energy was observed. As expected, dissociation into the separated ions becomes more favorable in methanol and acetonitrile as the solvent polarity is increased. The dissociation into ionic fragments is highly dependent on the solvent polarity (Table 3). The ion pair formed from the (1)⁺ and (BF₄)⁻ has the lowest ion pair dissociation energy of ΔE, 5.46 kcal mol⁻¹ in methanol and 4.91 kcal mol⁻¹ in acetonitrile.

Table 4 Influence of solvent on the ion pair dissociation energy (ΔE) of the tetrafluoroboric acid salts of twisted amides (1–3) calculated at DFT/PBE0-D3(BJ)/def2-TZVPP level^a,b

Ion pair	Gas	Methanol	Acetonitrile
a Corresponding to the processes: (1) → (1)^+ + (BF4)^−; (2) → (2)^+ + (BF4)^− and (3) → (3)^+ + (BF4)^−.b In units of kcal mol^−1.
(1)	96.92	5.46	4.91
(2)	93.40	5.53	4.98
(3)	92.38	5.76	5.22

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Hydrolysis of salts of twisted amides (1–3)

Hydrolysis of (1) yield an amino acid (4), while hydrolysis of (2) give an equilibrium mixture of the amino acid (5) and tricycle protonated hemiaminal (6). Salt (3) is hydrolyzed to produce tricycle protonated hemiaminal (7). The geometries of the hydrolyzed products (4–7) have been optimized with PBE and PBE0 functionals. The optimized geometries at DFT/PBE0-D3(BJ) level are presented in Fig. 4. The energy of amide hydrolysis at DFT/PBE0-D3(BJ) in acetonitrile are:

(1) + H₂O → (4) ΔE = −11.84 kcal mol⁻¹

(2) + H₂O → (5) ΔE = −9.63 kcal mol⁻¹

(2) + H₂O → (6) ΔE = −9.53 kcal mol⁻¹

(3) + H₂O → (7) ΔE = −10.22 kcal mol⁻¹

Fig. 4 Optimized geometries of products of hydrolysis (4–7) at DFT/PBE0-D3(BJ) level.

The hydrolysis reaction of (1) is more exothermic and thus it is more favorable. The calculated results are consistent with the experimental finding that the nonmethyl-substituted 1-azatricyclo[3.3.1.1^3,7]decan-2-one, tetrafluoroboric acid salt (1) is the most reactive amide.³⁵ The energy of amide hydrolysis is sensitive to the presence of a methyl substituent on the bridgehead carbon. The hydrolysis of amide salts (2) and (3) with bridgehead methyl are relatively less favorable. The formation of (5) and (6) is nearly same with the hydrolysis of (2) and the formation of (5) is more favorable. These observations also support the Kirby's experimental results.³⁵ Morgan and coworkers^13c investigated the hydrolysis of base free amides (A–C) in gas phase. The results revealed that nonmethyl-substituted derivative (C) is the most reactive amide. The methyl alpha to the carboxyl group should exert the biggest stabilizing effect. Monomethyl-substituted twisted amide (B) reacts with water slightly faster than trimethyl-substituted twisted amide (A). The faster reactivity of water with amide salt (1) is consistent with the result of Morgan's calculation. On the other hand, the rates of hydrolysis reactions of monomethyl- substituted and trimethyl-substituted amide salts contradict the Morgan's observations. The results of present study conclude that trimethyl-substituted twisted amide salt (3) reacts with water faster than monomethyl-substituted twisted amide salt (2). The contradiction may be due to solvent effect in present study.

The reaction profile for the hydrolysis reaction [(1) + H₂O → (4)] is shown in Fig. 5. The change in enthalpy has been calculated at DFT/PBE-D3(BJ) level in acetonitrile. The reference energy is taken as the sum of the enthalpy values of ion pair (1) and a water molecule. In the product amino acid ion pair (4), the H⋯F and O⋯H distances are close enough to felicitate hydrogen bonded non covalent interactions. The transition state, labelled as structure (8) (Fig. 7), lies 32.25 kcal mol⁻¹ above the ion pair (1) and water molecule. The product ion pair (4) lies 41.61 kcal mol⁻¹ below the transition state or 9.36 kcal mol⁻¹ below the ion pair (1) and water molecule. The transition state corresponds to the nucleophilic attack of water molecule on the amidic carbon and a transfer of a proton from water molecule to the nitrogen with cleavage of the amide bond. All of these geometrical changes happen in a concerted but asynchronous way. At the transition state the N–H(H₂O) distance is 1.635 Å. The attacking O(H₂O) is still at 2.249 Å from carbonyl carbon. In the product structure (4), the proton transfer is completed, and correspondingly, the N–H(H₂O) distance is 1.023 Å. The optimized structure of 4 (Fig. 4) shows a carboxylic group with a C–OH bond distance of 1.341 Å and C=O bond distance 1.199 Å.

Fig. 5 Reaction energy profile for hydrolysis of (1) obtained at DFT/PBE-D3(BJ)/def2-TZVPP level.

The reaction profile of the hydrolysis reaction [(3) + H₂O → (7)] is presented in Fig. 6. The reference energy is taken as sum of the enthalpy values of ion pair (1) and a water molecule. The transition state, labelled as structure (9) (Fig. 7), lies 28.30 kcal mol⁻¹ above the ion pair (1) and water molecule. The product after hydrolysis is a contact ion pair as depicted by structure (7). It lies 32.43 kcal mol⁻¹ below the transition state or 4.13 kcal mol⁻¹ below the ion pair (3) and water molecule. The transition state (9) corresponds to the attack of oxygen of water molecule on the amidic carbon and hydrogen of water on the carbonyl oxygen. The C–O(H₂O) distance of the transition state is 1.677 Å. The bridged hydrogen is almost equally shared by both carbonyl and water oxygens (the H–O(CO) and H–O(H₂O)) are 1.332 and 1.195 Å, respectively). The bridged hydrogen is almost equally shared by both carbonyl and water oxygens (the H–O(CO) and H–O(H₂O) are 1.332 and 1.195 Å, respectively. In the hydrolysis product (7), the carbonyl carbon is now making two single C–OH bonds with similar distances, namely, 1.377 and 1.368 Å for C–OH and C–OH(H₂O), respectively. Now the carbonyl carbon presents a tetrahedral shape. There is a slight elongation of the C–N bond to 1.530 Å as compared to C–N bond distances in reactant (3) (1.514 Å) and in a transition state (9) (1.518 Å).

Fig. 6 Reaction energy profile for hydrolysis of (3) obtained at DFT/PBE-D3(BJ)/def2-TZVPP level.

Fig. 7 Optimized geometries of transition state (8) and (9).

Conclusions

From the above-presented theoretical studies of the structure, bonding and reactivity of twisted amide salts (1–3) and hydrolysis products (4–7), one can draw the following conclusions:

(i) Here, for the first time (except the amide salt 1), we reported the geometry and electronic structure of, as well as reactivity with water of twisted amide salts 1–3. The optimized structure of (1) at DFT/PBE0-D3(BJ) level of theory in methanol is in excellent agreement with available experimental values.³⁵

(ii) In the twisted amide salts (1–3), the [BF₄]⁻ anion interacts with cationic fragments [1]⁺, [2]⁺ and [3]⁺ through the N–H⋯F hydrogen bond.

(iii) The ion-pairs interactions affect the C–N–H bond angles which are relatively smaller in salts than those for cationic fragments (1⁺, 2⁺ and 3⁺).

(iv) The cationic fragments (1)⁺, (2)⁺ and (3)⁺ are quite effective in withdrawing electron density from the BF₄⁻ anion.

(v) There is significant hydrogen bond H⋯F interaction in (1–3). The ion pair formed from the (1)⁺ and (BF₄)⁻ has the lowest ion pair dissociation energy of ΔE, 5.46 kcal mol⁻¹ in methanol and 4.91 kcal mol⁻¹ in acetonitrile.

(vi) The hydrolysis reaction of (1) is more exothermic and thus it is more favorable. The hydrolysis of amide salts (2) and (3) with bridgehead methyl are relatively less favorable.

(vii) The results of present study reveal that trimethyl-substituted twisted amide salt (3) reacts with water faster than monomethyl-substituted twisted amide salt (2).

(viii) The product ion pair (4) lies 41.61 kcal mol⁻¹ below the transition state or 9.36 kcal mol⁻¹ below the ion pair (1) and water molecule, while the product ion pair (7) lies 32.43 kcal mol⁻¹ below the transition state or 4.13 kcal mol⁻¹ below the ion pair (3) and water molecule.

Acknowledgements

Author gratefully thanks Prof. Frank Neese and ORCA developing group for providing ORCA-3.0.3 program.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra22792e

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