Ring Strain and Other Factors Governing the Basicity of Nitrogen Heterocycles – An Interpretation by Triadic Analysis †

M06–2X/6–311++G(2df,2pd)//M06–2X/6–31+G(d) computations were employed to investigate the intrinsic gas phase basicity of strained nitrogen heterocycles involving aziridine, azetidine, pyrrolidine and piperidine, together with their N-methyl and N-phenyl derivatives, NR(CH2)n (n = 2–5; R = H, Me and Ph). Basicity constants were compared with the corresponding acyclic counterparts, NR(CH3)2 (R = H, Me and Ph), and were, based on triadic analysis, resolved into contributions mirroring features of both initial base and the final protonated form as well as their interplay, thus offering quantitative insight into the obtained results. In general, the N-methyl derivatives provided strongest bases investigated here, and, within each group of molecules, the basicity increased on going from threeto six-membered rings, consistent with a decrease in ring strain, with four-membered systems already surpassing or coming close to the basicity of the acyclic gauge molecule. Calculated basicities were found in a very good agreement with available experimental data, except for N–methylazetidine, where a remarkable discrepancy was revealed, suggesting that this system should be experimentally reassessed and its gas-phase basicity parameters revised. Triadic analysis showed different behaviour of individual contributions governing basicities, both among and within distinct families of molecules. It also convincingly demonstrated that, if a proper and a quantitatively accurate interpretation of observed basicity trends is desired, one should not rely only on concepts such as localized reactive hybrid orbitals (RHO) or thus derived nitrogen electron-donating ability (T. Ohwada et al., J. Org. Chem. 69 (2004) 7486), which take into account only properties of the initial base in question, but rather consider protonation reaction in its entirety. (doi: 10.5562/cca2121)


INTRODUCTION
−10 Features like bonding, property, reactivity, and synthetic accessibility have been the constant subject of research activities in this area.−14 In cyclopropane, the concept of ring strain is supported by the high electron density in the interior of the three-member ring, 15−17 the relatively short C-C and C-H bond distances, 15,16 and the upfield shifts of its proton 18 and 13 C NMR signals. 19In most cases, ring strain energy cannot be determined experimentally; it is relative rather than absolute quantity that must be defined and assessed by comparison with arbitrary reference species considered by convention to be "strain free".Nevertheless, since the former is often invoked to explain the enhanced reactivity of transformations involving small ring compounds, 20−22 numerous computational methods and attempts to quantify these energetic values have appeared in the literature, remaining a hotly debated topic.The latter include isodesmic, 23 homodesmotic, 24 hyperhomodesmotic 25,26 and group equivalent schemes. 27s part of our continuing studies concerned with the identification of electronic and geometric effects responsible for the high basicity of organic compounds, 28−33 we report here the effect that ring strain Croat.Chem.Acta 85 (2012) 495.exhibits on the nitrogen basicity of small heterocycles.We selected the nitrogen atom, since it represents the basic site of a large variety of strongest superbases known today. 28,34,35Proper insight into the mentioned intrinsic effect is important, since strain relief on protonation can have major impact on the basicity of strained compounds.For example, this was clearly demonstrated by Abboud, Koppel and co-workers, 36 who employed modified G2(MP2) approach to calculate the gas-phase basicity (GB) of cubane, C 8 H 8 , to be as large as GB = 258.8kcal mol -1 , and attributed pronounced basicity to the formation of the rearrangement product, namely tetracyclo[4.2.0.0 2,4 .0 3,8]oct-7-ylium cation, created after strain relief and the opening of the rigid framework of cubane upon protonation.However, their calculated GB value differed by about 60 kcal mol -1 from that measured experimentally, 37 suggesting that the latter value, determined by FT-ICR mass spectrometry, does not correspond to the reversible protonation of cubane and that the proposed cation is not the final protonation product.This discrepancy was later clarified by Fokin, Schreiner and coworkers 38 who suggested 1,8-dihydropentalene as the final cubane protonation product along the most favourable protonation/isomerization/deprotonation downhill path at the CCSD(T)/cc-pVDZ//MP2/cc-pVDZ level, in that way tying in with experimental thermodynamics.As an even more typical example, one should mention the original paradigmatic superbasic proton sponge, namely Alder's 1,8-bis(dimethylamino)naphthalene, DMAN.Its gas-phase proton affinity was calculated at the B3LYP/6-31+G(d,p)//HF/6-31G(d,p) level by Howard 39 to be PA = 246.3kcal mol -1 being in perfect agreement with the experimental value of PA = 246.2kcal mol -1 measured by Kebarle and co-workers. 40At the same level of theory, Howard demonstrated that DMAN is by as much as 22.4 kcal mol -1 a stronger base than monosubstituted 1-(dimethylamino)naphthalene, 39 which is remarkable.Employing series of isodesmic reactions and model systems, Howard separated the mentioned difference in PA values into contributions from the strain-induced repulsion (SR) of both nitrogen lone pairs in the destabilized neutral molecule, DMAN, and that of the stabilizing effect due to the formation of strong intramolecular N + -H ··· N hydrogen bond (HB) in the protonated form, DMANH + .He obtained values of SR = 6.4 kcal mol -1 and HB = -16.0kcal mol -1 , 39 in that way demonstrating that strain energy largely determines the basicity of DMAN and related compounds, and that it cannot be neglected but rather employed as a useful electronic effect to promote the basicity when designing novel superbases.Furthermore, in a recent article, Alder proposed 41 that the key to the design of even stronger bases than either DMAN or related systems having amino groups replaced by more basic functionalities, 34 is to further enhance ring strain in the initial bases by "limiting conformational freedom, especially by preventing nitrogen inversion, through the introduction of additional ring fusions." A consistent and thorough analysis of the gasphase basicity of simple cyclic amines, NH(CH 2 ) n (n = 2-5), and their corresponding N-methyl and Nphenyl derivatives, was recently performed by Ohwada and co-workers 42 using CBS-Q, G3 and B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) computational methods.They observed that basicity within a family of compounds increases with the increase in the ring size n, but that aziridines, NR(CH 2 ) n (n = 2, R = H, Me, Ph), are notably less basic than other systems with n = 3-5.The authors attempted to interpret calculated basicity constants by plotting the corresponding proton affinity values against the HOMO energies obtained at the HF/6-31G(d)//B3LYP/6-31G(d) level, but obtained a significant scatter of points with no correlation.They tried to improve the correlation by employing the reactive hybrid orbital (RHO) concept 43 and thus calculated electrondonating abilities of the nitrogen atom.The latter resulted in a better overall picture indicating a trend that an increase in RHO orbital energies leads to higher basicity.Still, for any predictive or interpretative purposes the correlation offered by Ohwada and co-workers was of very limited use.One should emphasize, that their analysis was based on considering only the properties of initial bases, namely neutral cyclic amines, thus it was very much incomplete.Specifically, no features of the protonated conjugate acids contributed to their correlation in any way, which, in principle, leads to wrong conclusions.It is quite obvious that molecular basicity is determined by features of both neutral base and its protonated form, where in some cases the properties of the latter could even prevail and should be explicitly considered.Therefore, since basicity of cyclic amines is a fundamental property in organic chemistry and for all the reasons stated above, we found it necessary to reexamine the intrinsic gas-phase basicity of simple nitrogen heterocycles investigated by Ohwada and coworkers, 42 and provide an insight into the calculated values employing our triadic analysis.The latter considers protonation reaction in its entirety and offers quantitative estimation of properties of both molecular forms during protonation reaction (for a review on triadic formalism see Ref. 44).In finishing this section, it is worth to note that since acid-base behaviour can be a sensitive experimental probe of various structural features including ring strain, some other properties of the strained organic molecules, such as carbon acidities 45−47 have been studied as well.

COMPUTATIONAL METHODOLOGY
According to Brønsted, basicity is the measure of the capability of a molecule to accept a proton in a chemical reaction.In the gas phase, it is expressed by Equation (1), where GB is the gas phase basicity (a free-energy term) and PA is the proton affinity (an enthalpy term) for the reaction: Here B and BH + denote the base in question and its protonated form, the conjugate acid, respectively.ΔG° gives intrinsic basicity of a compound not contaminated by the presence of the solvent molecules or counterions.The corresponding proton affinity is related to the electronic structure of the base and its conjugate acid, and has two contributions: where ΔE° represents the change in the total molecular energy in reaction (1), which includes the electronic and the zero-point vibrational energies, ZPVEs, as well as the finite temperature (298.15K) correction, while Δ(pV) denotes the pressure-volume work term.Both GB and PA values are computed here and compared to available experimental values, but our analysis will focus only on the proton affinities, because they offer a good description of basicities, being simpler for the interpretation at the same time.
In order to get an insight into the origin of the basicity of studied molecules, we performed triadic separation 44 of proton affinities, Equation (3), which enables the estimation of the influence of the properties of the initial (neutral base) and the final state effects (protonated molecule), as well as their interplay on Brønsted basicities for molecules in the gas phase.
−57 Initial state effects of neutral bases are reflected in Koopmans' ionisation energies, 58 IE(B) n Koop , calculated in the frozen electron density and clamped atomic nuclei approximation (i.e., ionisation from the nth molecular orbital, counting the HOMO as the 1 st ).

The IE(B) n
Koop values reflect the price to be paid for taking an electron from the neutral molecule in the bond association process with the incoming proton, assuming that the ionisation is a sudden process.Since Koopmans' ionisation energies depend exclusively on the electron distribution of the investigated neutral base, they reflect genuine properties of the initial state and are most affected by ring strain.The geometric and electronic reorganisation effects following electron ejection are given by the relaxation energy E(ei) n rex , defined by Equation ( 4): where IE(B) 1 ad is the first adiabatic ionisation energy of the base.This is the intermediate phase of the protonation process.Finally, the electron affinity of the proton is experimentally determined to be exactly 313.6 kcal mol -1 , 59 whereas the bond association energy describing homolytic bond formation between created radicals is given by the (BAE) •+ term, and will be used in connection with the properties of the final state (protonated molecule).The latter is calculated as an enthalpy of the reaction in which hydrogen atom, H • , and the radical cation of the investigated base, B •+ , combine to form protonated conjugate acid, BH + .Since we are mostly interested in trends of changes obtained by relative values against the reference molecule, it is useful to define the triad of contributions to proton affinities as: where B and B REF denote molecule in question and the reference base, respectively, whereas square brackets imply summation of the three terms within, defined as: Although the above procedure is a simple extension of the well known thermodynamic cycle, where the sum of IE(B) n Koop and E(ei) n rex is replaced by a single term IE(B) 1 ad , inclusion of the Koopmans' ionisation energies offers large interpretative advantages.The IE(B) n Koop corresponds to the n-th ionisation energy, which is related to the specific highest MO most affected by the protonation, which is conveniently termed PRIMO (PRIncipal Molecular Orbital). 60 that get attacked by the proton in the protonation reaction.As such, it does not always have to be the HOMO; it could be one of the lower-lying molecular orbitals, which is a very important feature of the triadic analysis.
As a good compromise between the accuracy and the computational feasibility of the model, all molecular geometries were optimized by the very efficient M06-2X/6-31+G(d) method.ZPVEs and thermal corrections were extracted from the corresponding frequency calculations without the application of scaling factors.The final single-point energies were attained with a highly flexible 6-311++G(2df,2pd) basis set using M06-2X functional, which has been shown in the literature to provide very accurate thermodynamic and kinetic parameters for organic systems, being particularly successful in treating nonbonding interactions. 61,62This gives rise to the M06-2X/6-311++G(2df,2pd) //M06-2X/6-31+G(d) model employed here.Koopmans' ionisation energies (IE) n Koop were computed by the HF/6-311++G(2df,2pd)//M06-2X/6-31+G(d) level of theory.Radical cations were treated with unrestricted approach.All calculations were performed using the Gaussian 09 63 suite of programs.

RESULTS AND DISCUSSION
Molecules studied in this work are presented in Figure 1.They include aziridine 2, azetidine 3, pyrrolidine 4, and piperidine 5, together with their N-methyl (7-10) and N-phenyl (12-15) derivatives.We also included the    3), are given in Table 1, together with the gas-phase basicities (GBs).As a final notice, we would like to emphasize that protonation-induced changes in both the geometry and the electron distribution in these cyclic systems have already been discussed in the literature 42,64 and are not subject matter of the present study.Before we start analyzing the results presented in Table 1, let us take a look at some general features emerging from these numbers.The overall agreement between M06-2X calculated and experimental data 59 is very good.This holds in particular for calculated PA and GB values, which are for all molecules, but two, found within 3 kcal mol -1 from experimental data.Exceptions are provided by molecules 14 and 8, where deviations assume 3.2 and 15.8 kcal mol -1 for PAs, respectively, and 3.9 and 15.8 kcal mol -1 for GBs, in the same order.Particularly worrisome is the latter molecule 8, where the discrepancy seems unusually high.For N-methylazetidine 8, Ohwada and co-workers 42 calculated PAs of 227.3 and 227.9 kcal mol -1 using highlevel CBS-Q and G3 composite methodologies, thus being in close agreement with our values.Together with the overall success of M06-2X approach in reproducing experimental gas-phase basicity constants presented here, these numbers suggest that both experimental values, PA EXP (8) = 210.9kcal mol -1 , and GB EXP (8) = 203.6 kcal mol -1 , quoted by the NIST database, 59 are probably too low, and should be re-examined and measured again.Having that in mind, if we exclude 8 from the correlation, the average absolute deviation between calculated and experimental PAs and GBs drops down to only 2.3 and 2.1 kcal mol -1 , respectively, which lends credence to the results presented here.
The data in Table 1 reveal several notable trends.Molecules investigated here are all moderately strong bases spanning a range of PA values from 214.6 (2) to 229.9 kcal mol -1 (10).In all systems, the reactive PRIMOs are always HOMO orbitals (Figure 2), mean- ing that the lone pair electrons on the nitrogen atom, that gets protonated, lie in the orbital that is most exposed to the incoming proton.Relative to the parent acyclic strainless compounds, HOMO orbital energies in aziridines are increased by around 13 kcal mol -1 , which are then reduced back in azetidines, pyrrolidines and piperidines to values close to those found in the corresponding acyclic systems.The reason for that is the fact that upon decrease of the C-N-C bond angle, the nominally sp 3 -hybridized nitrogen atom rehybridizes to increase the p-character of two orbitals directed toward carbon, which correspondingly increases the scharacter of the other two hybrids, namely the orbital involved in the N-H bond and the nitrogen lone pair. 65ince s electrons are closer to the nucleus, this increases the stability of the latter two orbitals.Knowing that C-N-C bond angle compression is largest in three-membered rings 2, 7 and 12, it follows that their PRIMOs are stabilized the most, leading to the conclusion that the price to be paid for their single-electron ionization within Koopmans' approximation is the largest.As a result, this hybridization effect of the nitrogen atom leads to a continuous increase of the basic strength on going from three-to six-membered cyclic amines.This relationship between orbital energies and PA values is evidenced in molecules investigated here (Table 1), but qualitatively at best.A notable exception to latter relation is provided with 15, in which the energy of the HOMO is unexpectedly high, although 15 maintains pronounced basicity within the same group of molecules 11-15.This offers particular evidence that the consideration of the properties of initial bases only could lead to wrong conclusions about their basicities, or other properties related to the reactivity, and that the whole protonation reaction should be considered if a quantitatively correct prediction of the trend of PA values is desired.Since, within triadic picture, Koopmans' ionization energies mirror properties of the initial state, therefore being a consequence of the magnitude of the ring strain in neutral bases, we could draw a conclusion that there is no simple relation between ring strain and the basicity, being in agreement with Ohwada and co-workers who also reached the conclusion that "angle strain in cyclic amines is not the major source of the difference in the strength of basicity". 42e will start our analysis with the smallest parent acyclic system dimethylamine 1.Its calculated proton affinity is PA(1) = 219.8kcal mol -1 , making compound 1 reasonably basic molecule with PA value similar to, for example, the imino compound 9H-purine (PA EXP = 219.9kcal mol -1 ). 59Relative to 1, the basicity of cyclic molecule 2 is lower, whereas values for 3-5 are all higher, increasing in the same order as well.Triadic formula (5)  to the HOMO orbital.Thus, in this case, single-electron ionization is less costly and the difference in Koopmans' ionization energies works towards the increasing basicity of 5, which together with second largest relaxation energy of all compounds investigated here, makes this molecule the strongest base within this family of molecules (1-5).At the end, it is useful to emphasize that triadic analysis clearly reveals not only that the correct trend in basicity of systems 2-5 cannot be explained by considering only the features of initial bases, but also that, in all four cases, both properties of different states and their diverse relative significance are factors governing their basicities.We note in passing that, despite the fact that throughout this work, cyclic amines NR(CH 2 ) n , with n = 3-5 and R = H, Me and Ph, exhibit an increase in the basicity with the ring size n, and that, within family of molecules, the corresponding amplifications in PA values cover ranges between 3.2 and as much as 7.4 kcal mol -1 , in water solution a distinct levelling behaviour was found in aqueous pK a values, 64 such that systems 3-5, 8-10 and 13-15 possess pK a values in a very narrow range between 11.22-11.29,10.08-10.46 and 3.57-5.22pK a units, respectively.This provides convincing evidence to why it is important to investigate and understand intrinsic solvent-free acidbase properties of target molecules.Nevertheless, it remains a challenge for future studies to examine the influence of ring strain on solution-phase basicity constants, such as aqueous pK a values, in the investigated cyclic amines.For such narrowly spaced data, the difficulty lies in the selection of the appropriate computational methodology to (re)produce accurate pK a values, since, for example, brute force calculations employing implicit continuum solvation could yield estimates easily diverging by over 4-5 pK a units. 66−70 These are, however, associated with high computational costs and are beyond the scope of the present manuscript.N-methyl derivatives 6-10 are by around 3-6 kcal mol -1 stronger bases than the matching systems 1-5.This is not surprising, since the methyl group is an efficient electron-donating substituent, and it helps in accommodating the positive charge produced upon protonation.In our triadic picture, the latter effect is evident in the increased relaxation energy, since the positive charge is generated during electron ionization already in the intermediate radical cation stage.For the case of parent molecule 6, this becomes apparent as PA(6) -PA(1) = [8.2;2.8; -6.2] = 4.8 kcal mol -1 .Still, the predominant reason to the increased basicity of 6 is the increased Koopmans' term, which is a consequence of the C-H bond electron pair/nitrogen lone electron pair repulsion.In other words, the nitrogen lone pair in trimethylamine 6 is placed in the HOMO orbital, which lies higher in energy (i.e., it is destabilised) than the matching orbital in dimethylamine 1 (Table 1).The (IE) n Koop term for 6 is therefore lower, implying a less costly ejection of an electron in the triadic scheme.The initial favourable effect is somewhat reduced by a considerably lower homolytic bond formation energy, but the overall effect is an increase in the basicity of 6.The same trend of values can be obtained by considering other cyclic amines 7-10 within this family of compounds.Now, the question arises: What is the effect of the ring strain on basicity within N-methyl derivatives 6-10?It turns out, that most of the conclusions drawn in the previous section for systems 1-5 hold here as well.Taking 6 as the reference acyclic molecule, the triadic analysis gives: One can easily notice that, compared to secondary amines 1-5, the trend in the above values is maintained for the tertiary amines.During protonation, the predominant influence of various states governing basicity is the same as in the previous set of molecules, emphasizing once again advantages that the triadic analysis offers in the interpretation of PA values by considering the protonation reaction in its entirety.We could mention that relative triadic contributions as well as changes in proton affinities on going from three-to sixmembered rings are slightly smaller here than in 1-5.In other words, the spread of the PAs of compounds 6-10 is smaller than that in the series 1-5.
At the end we will focus on the N-phenyl derivatives.The phenyl group, -C 6 H 5 , is a substituent that is much different from the methyl residue, as it displays its influence predominantly through the polarisation and the π-resonance effects of its electron-rich aromatic fragment.Still, one observes that the basicity of the N-phenyl derivatives is very similar to that of the corresponding N-methyl counterparts, being only slightly smaller as a rule (Table 1  What is even more interesting for the present purpose is the difference in basicity between compounds 11-15 and parent molecules 1-5 to estimate the effect of the N-phenyl substitution.It turns out that the Nphenyl derivatives are characterized by (a) further less stable HOMO orbitals, thus even less costly ionization energies than those found for systems 6-10, (b) lower relaxation energies upon electron ionization, and (c) lower homolytic bond association energies.The first effect promotes, while the other two reduce the basicity of molecules 11-15.Consequently, 11 is, though not as much as 6, but still slightly more basic than 1, PA(11) -PA(1) = [54.3;-29.7; -22.4] = 2.2 kcal mol -1 .These numbers suggest that by making N-phenyl substitution, one facilitates electron ionization from the nitrogen lone pair, which strongly promotes its reactivity towards protonation, the same effect already noticed with the Nmethyl derivatives, but much more pronounced here.However, this large favourable effect is almost completely neglected by the fact that the phenyl group also strongly stabilizes the intermediate radical state through the resonance effect with the newly formed N-centred radical, which disfavours the subsequent N + -H bond formation present in the protonated form.All of the three triadic contributions show regular behaviour but are varying in magnitudes.This leads to the deviating trend in the resulting PA values, in a way that molecules 11, 12 and 15 are stronger bases than the corresponding parent molecules 1, 2 and 5, respectively, whereas 13 and 14 are weaker bases than 3 and 4, in the same order.
It remains to answer the question how the cyclization affects the basicity within the N-phenyl derivatives?Analogously, one can select 11 as a gauge molecule and write the triadic analysis as: Interestingly, the first three molecules here, 12-14, are weaker bases than acyclic reference 11, which is a behaviour that is changed to what was already observed in other compounds studied here.Moreover, the trend in triadic contributions is different in all three systems.In 12, the lower basicity is primarily determined by the initial state effect, while it is a consequence of interplays between initial and final state effects in 13, and that of intermediate and final state contributions in 14.
Molecule 15 is clearly a case on its own.At first sight one notices an increase in the orbital energy relative to 14, because of a strong resonance interaction of the nitrogen lone pair electrons and the phenyl π-orbitals (Figure 2).Relative to 11, this interaction stabilizes the initial system by 8.3 kcal mol -1 and works towards the reduction of the basicity of 15.However, upon electron ionization, the newly formed nitrogen radical centre is in 15 significantly stabilized by the presence of the phenyl substituent, which is not so pronounced in 11.This process overcomes the unfavourable influence of the Koopmans' term and together with a small contribution originating from the bond association energy makes 15 by 6.2 kcal mol -1 a stronger base than its acyclic counterpart 11.

CONCLUSION
Triadic decomposition of the gas-phase proton affinities (PAs) of twelve small strained nitrogen heterocycles, including aziridine, azetidine, pyrrolidine and piperidine, and their N-methyl and N-phenyl derivatives, was calculated employing the M06-2X/6-311++G(2df,2pd) //M06-2X/6-31+G(d) level of theory.We obtained excellent agreement between computationally obtained adiabatic ionisation energies, proton affinities and the gas-phase basicities (GBs), and the available experimental data, with the only exception being Nmethylazetidine, for which a remarkable discrepancy in the calculated PA and GB values assumes 15.8 kcal mol -1 in both cases, suggesting that these two quantities should be experimentally revised and measured again.
The results were compared with the corresponding acyclic molecules and revealed that there is no simple relationship between the resulting basicity, on one hand, and the magnitude of ring strain or any other feature depending only on the properties of initial bases, on the other.Our analysis led us to safely conclude that angular ring strain in the initial state is not the major source of the basicity trends in the investigated cyclic amines.Quite interestingly, it turned out that, if one considers a subset of closely related molecules, for example only the N-unsubstituted systems, in each case different triadic contributions, originating either from the properties of the initial base, final protonated form or their interplay, are predominantly responsible in determining their basicity.This emphasizes the usefulness of the triadic approach in rationalizing molecular reactivity and suggests that, for a complete picture of the protonation process and the accurate interpretation of the subtle differences in PA values one needs to consider all three terms appearing in the triadic scheme separately.
of Croatia through grant no.098-0982933-2932.In addition, we would like to thank the Zagreb University Computing Centre (SRCE) for generously granting computational resources on the ISABELLA cluster (isabella.srce.hr).

Figure 1 .
Figure 1.Schematic representation of investigated cyclic and reference acyclic amines.
corresponding acyclic amines NR(Me) 2 in the analysis with R = H, Me and Ph (systems 1, 6 and 11, respectively), which by definition have no Baeyer strain and which will serve as reference gauge molecules in the interpretation of PA values.Calculated proton affinities (PAs), dissected according to triadic analysis, proposed in Equation (
It is usually the highest molecular orbital corresponding to lone pair electrons Croat.Chem.Acta 85 (2012) 495.

Table 1 .
Calculated proton affinities (PAs) , their resolution into triadic components, and gas-phase basicities (GBs) of selected (a)All values are in kcal mol -1 .bIndex n represents the PRIMO orbital which is ionized in the protonation process, corresponding here always to HOMO (n = 1).cExperimental data (EXP) for IE, PA and GB values are taken from the NIST database (Ref.59).Croat.Chem.Acta 85 (2012) 495.
yields:It follows that 2 is by 5.2 kcal mol -1 a weaker base than parent compound 1, because, on one hand, the HOMO of 2 is by 15.5 kcal mol -1 more stabilized than in 1 leading to lower basicity.In contrast, the bond association energy in 2 is increased by 17.3 kcal mol -1 .These two trends, cancelling each other out, are intuitively clear.When the lone pair is more tightly bound and the price for ionization is larger, like in 2, then the energy gain upon formation of a new N-H bond is more beneficial.This conclusion is correct, however, qualitatively but not quantitatively as it will become obvious later.The mentioned increase of (BAE) •+ in 2 is not enough to make it more basic than 1, since the relaxation energy in 2 is lower as well.Taken all together, lowering of the relaxation energy, an intermediate state effect, is an effectively decisive term leading to the lower basicity of 2 relative to 1. Similarly, in larger cyclic amines, differences in the bonding C-N-C angles and the hybridization effect of the initial state become even less important, whereas the relaxation effect prevails due to the larger number of neighbouring carbon atoms leading to enhanced basicity in cyclic amines.It is easy to see that the basicity of investigated amines cannot be satisfactorily rationalized by considering the initial state only.Along that line, if we would consider only features of the neutral base in 3, it would predict that 3 is a weaker base than 1 by at least 2.4 kcal mol -1 .This is not the case, as 3 is by 2.8 kcal mol -1 a stronger base than 1, as a result of a joint effect of the intermediate and final state effects.Again different trend of values is further observed for 4.Although 4 maintains some Lastly, piperidine 5 has almost no ring strain, the corresponding C-N-C angle assumes 111.8° at the M06-2X/6-31+G(d) level, which induces no rehybridization of the nitrogen atom and no particular stabilizing effect Croat.Chem.Acta 85 (2012) 495.
, reveals that this is a cumulative result of an interplay between the favourable initial state effect, and destabilizing intermediate and final state effects, both large in magnitudes but opposite in signs.Data in Table1expose that the same trend of values is ob- Croat.Chem.Acta 85 (2012) 495.