Deciphering Stability of Five-Membered Heterocyclic Radicals

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Deciphering Stability of Five-Membered Heterocyclic Radicals: Balancing Act Between Delocalization and Ring Strain Chitranjan Sah, Ajit Kumar Yadav, and Sugumar Venkataramani J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03145 • Publication Date (Web): 23 May 2018 Downloaded from http://pubs.acs.org on May 23, 2018

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The Journal of Physical Chemistry

Deciphering Stability of Five-membered Heterocyclic Radicals: Balancing Act Between Delocalization and Ring Strain Chitranjan Sah‡, Ajit Kumar Yadav‡ and Sugumar Venkataramani* Department of Chemical Sciences, Indian Institute of Science Education and Research Mohali Sector 81, SAS Nagar, Knowledge city, Mohali, Punjab–140306, India E-mail: [email protected]

Abstract Computational studies on five membered heterocycles with single heteroatom and their isomeric dehydro-borole 1a-c, cyclopentadiene 2a-c, pyrrole 3a-c, furan 4b-c, phosphole 5a-c and thiophene 6b-c radicals have been carried out. Geometrical aspects through ground state electronic structures and stability aspects using bond dissociation energies (BDE) and radical stabilization energies (RSE) have been envisaged in this regard. Spin densities, electrostatic potentials (ESP) and natural bond orbital (NBO) analysis unveiled the extent of spin delocalization. The estimated nucleus-independent chemical shifts (NICS) values revealed the difference in aromaticity characteristics of radicals. Particularly the heteroatom centered radicals

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exhibit odd electron -delocalized systems with a quasi-antiaromatic character. Various factors such as, the relative position of the radical center with respect to heteroatoms, resonance, ring strain and orbital interactions influence the stability that follows the order: heteroatom centered > -centered > -centered radicals. Among the influences of various factors, we confirmed the existence of a competition between delocalization and the ring strain, and the interplay of both decides the overall stability order.

1. INTRODUCTION Free radicals signifies an important class of classical reactive intermediates that recently evolved as building blocks for molecular materials.1-3 Due to their characteristic high reactivity, they have been proposed as intermediates in synthesis,4-8 atmospheric chemistry,9-11 combustion chemistry,12-15 and biological implications.16-18 The transient character and/or the stability of the radicals often influenced by spin delocalization, conjugation, and orbital interactions.19-24 Hence, they can structurally be modified and tuned to obtain stable radicals in constructing organic molecular based magnets.25-29 In this regard, various approaches such as enhancing delocalization through resonance, hindering the reactivity through steric bulkiness and creating radicals at the heteroatoms have been profoundly explored.30-33 Alternatively, introduction of heteroatoms in the rings containing radical center and enhancing resonance stabilization through heteroaromatic systems have also been attempted.34-36 Recently, the radicals and heterocyclic radicals acquire fascination of theoreticians and experimentalists immensely for their various roles in free radical reactions37-40, reactive oxygen species (ROS)41, biofuels42-44, material chemistry45-47 and tuning of the reactivity48-50 etc.


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Traditionally ESR spectroscopy has been employed as a prominent technique to study many radicals.51 Through this technique, Shlotani and coworkers have investigated heterocyclic radical cations of furan, thiophene, pyrrole and related derivatives that exhibited -centered radicals.52 In a similar way, Aramaki et al. have synthesized a stable B-heterocyclic -radical and characterized it.53 Using threshold photoelectron spectroscopy, pyrrolyl radical has been characterized through the pyrolysis of 3-methoxypyridine.54 Adopting the same technique, Lineberger and coworkers have determined the electron affinity of pyrrolyl radical to be 2.145 ± 0.010 eV.55 Computational bond dissociation energies (BDE) for various heterocyclics such as pyrrole, furan and thiophene have been estimated at DFT level and the radical stability has been discussed based on those results.56 The pyrolysis pathways of many heterocycles such as pyrrole, thiophene and furan have been computationally investigated with relevance to the combustion processes of asphaltenes and in understanding the kinetics with the radical intermediacy.57-59 Five- and six-membered three-center-five-electrons (3c-5e) boryl radicals have been computationally investigated to tune the reactivity pattern through flipping of radical electron from - to -center.60 Studies on neutral and charged heterocyclic radicals, particularly with the emphasis on their synthetic utility has been observed in recent times. However, many fundamental questions such as the role of heteroatoms in the stability and mode of interactions such as 2c-3e (2 centered – 3 electron) in radicals are still under exploration.61-63 One of the research goals in our laboratory is to understand the effects of heteroatoms and their influences in the stability of heterocyclic radicals. Earlier literature reports, and also our recent investigations clarified that the nitrogen lone pair provides a stabilizing effect if it is coplanar to the radical electron.64-68 Particularly for the pyridyl and diazinyl radicals, the radical center is stabilized by the interactions with the nitrogen lone pair either through space (TS) or


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through intervening bonds (TB). Such interactions got lowered in the five-membered ring systems such as dehydro- oxazole, thiazole and imidazole radicals.69 Despite the presence of lone pairs on O/S/N-H (in oxazole/thiazole/imidazole), the stability order is controlled by the position of the other nitrogen atom carrying a lone pair in the -orbital relative to the radical center. Besides that, the N-centered imidazole radical was found to be the most stable isomer and a centered radical with strong delocalization of spin. However, in the case of five membered heterocyclic radicals with one heteroatom, the interactions between the radical electron and the lone pair will be lowered due to the involvement of the latter in the aromaticity. At this juncture, the decisive factors for the stability order of the isomeric five-membered heterocyclic radicals will be more than the corresponding six membered analogues. In this regard, we have raised the following questions: (a) What is/are the major factor(s) for stabilizing and/or destabilizing the radical? Since five membered ring systems will have more strain70-75, to what extent it can control the stability? (b) How different the roles of oxygen and sulfur (divalent) from the other heteroatoms such as boron, nitrogen and phosphorus (trivalent) in stabilizing the heterocyclic radicals? (c) If a radical center is present in the heteroatoms (boron, nitrogen and phosphorus), whether it will prefer - or -centered radical? (d) How the heteroatoms influence the symmetry, geometry and other molecular properties of the heterocyclic radicals? To understand these questions, we investigated the simplest five membered dehydro-borole 1a-c, pyrrole 3a-c, furan 4b-c, phosphole 5a-c and thiophene 6b-c radicals (Scheme 1). For comparison, we have utilized the dehydroradicals of cyclopentadiene 2a-c as well. Furthermore, various properties of these isomeric radicals have been compared with their respective parent that include geometrical parameters, stability order, thermodynamic stability, spin densities, and electrostatic potential mapping. NBO analysis has been performed to


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quantify and also to understand the mode of the interactions. Furthermore, NICS, ring strain and resonance energy calculations have also been performed to explain the relative stability order of the isomeric radicals. The outcomes of these studies are discussed in detail.

Scheme 1. Five Membered Hetero- and Carbocyclics, Borole 1, Cyclopentadiene 2, Pyrrole 3, Furan 4, Phosphole 5, Thiophene 6 and Their Corresponding Dehydro Radical Isomers.

2. COMPUTATIONAL DETAILS For majority of the computations, Gaussian 09 software package has been utilized.76 All of the structures have been optimized at different levels including B3LYP,77 BLYP,78-80 and M06-2X81 levels with an unrestricted formalism for all of the doublet states. Single-point energy calculations have also been carried out at (U)CCSD(T)82,83 level using pre-optimized geometries at (U)B3LYP/cc-pVTZ84 level of theory. Apart from that, composite CBS-QB385 level calculations have been performed to obtain more accurate thermochemistry data. Different basis sets such as (6-311++G(d,p),86,87 and Dunning basis sets cc-pVDZ,88 cc-pVTZ, cc-pVQZ,89 augcc-pVDZ, aug-cc-pVTZ, and aug-cc-pVQZ90 have been used for optimization at the (U)B3LYP level. Vibrational frequencies in the harmonic approximation calculations have been performed to confirm the minima and also to obtain thermochemistry data including zero-point energy corrections.91 The second-order perturbation energy values have been computed from natural bonding orbital (NBO) calculations92,93 using the G09/NBO package and optimized geometries at


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the (U)B3LYP/cc-pVTZ and (U)M06-2X/cc-pVTZ levels of theory. Multireference calculations to understand the molecular orbitals have been carried out at CASSCF94,95/cc-pVTZ level of theory using the MOLPRO software package.96,97 To construct the active space, five π-orbitals of the aromatic ring, radical-centered orbital, and the orbitals corresponding to the lone pair(s) of the heteroatom were chosen, wherever necessary. The molecular orbitals were visualized using the Molden package.98 NICS calculations were performed at (U)B3LYP/cc-pVTZ and (U)M062X/cc-pVTZ levels of theory.99-102 Probe atom (Bq) has been used to designate the position for NICS evaluation. Probe atom (Bq) has been fixed at different positions along the perpendicular axis to the molecular plane. The reaction enthalpies corresponding to BDE and RSE have been estimated using (U)B3LYP/cc-pVTZ, (U)M06-2X/cc-pVTZ and CBS-QB3 levels of theory whereas, the strain103-108 and resonance energies109-118 have been computed at (U)B3LYP/ccpVTZ and (U)M06-2X/cc-pVTZ levels of theory.

3. RESULTS AND DISCUSSION 3.1. Geometry Computational studies of dehydro- borole (1a-c), cyclopentadiene (2a-c), pyrrole (3a-c), furan (4b-c), phosphole (5a-c) and thiophene (6b-c) have been carried out at different levels of theory (Figure 1). Key features like change in bond length, bond angle and planarity in radical isomers have been compared with their respective parent analogues. Parent compounds as well as majority of their radical analogues have been optimized to C2v or Cs point group symmetries. The exceptions are 5b and 5c, which attained C1 symmetry. All of the radical species are found to be spin doublets at their ground states. Structures 1a and 5 were found to be saddle points at C2v geometries and so optimized at Cs point group. Likewise, in our previous studies, we found out


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that the bond lengths adjacent to the radical centers got shortened, whereas the inter-nuclear distances alternate to the radical position got elongated relative to the parent.64-66

Figure 1. Optimized structures of borole 1, cyclopentadiene 2, pyrrole 3, furan 4, phosphole 5, thiophene 6 and their corresponding radical isomers 1a-c, 2a-c, 3a-c, 4b-c, 5a-c and 6b-c. Selected geometrical parameters (bond distances in Å and bond angles in degrees) corresponding to the computed geometries at (U)B3LYP/cc-pVTZ (black) and (U)M06-2X/cc-pVTZ (red) levels of theory are indicated.


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Similarly, bond angles at radical centers increased except in 3a (N-centered radical), for which it got decreased, whereas in the case of 5a, the bond angle was found to be nearly the same. Interestingly, the angle at heteroatom connecting two-carbon atoms ∠CXC (X=heteroatom) strongly depends on the position of the radical center. Among the various radicals, the Bcentered and N-centered radicals exhibited the maximum angle change at the radical center, viz +15.2o and −5.1o, respectively with respect to the parent (Table S2 in Supporting Information). In the case of C-centered radical, it is less positive, whereas the P-centered radical showed almost no change. These changes are mainly a consequence of the heteroatom/carbon atom to adopt a geometry in such a way to satisfy Bent’rule. The expanded version of the rule states that the electronegativity and covalent radii is crucial for an atom to gain and impart s- or p-character to the bonds it form with the substituents.119,120 For B- and N-centered radicals, the angle of deviation leads to the attainment of more s- and p-characters, respectively. Also, -radicals exhibit a decrease in those bond angles, whereas they increase in the case of -radicals as compared to ∠CXC of their respective parents. Presumably the change in the ring strain can be the reason for it. The geometrical parameters at both (U)B3LYP/cc-pVTZ and (U)M06-2X/ccpVTZ levels of theory predict the similar trend. 3.1. Stability aspects 3.1.1 Relative Stability order In order to understand the influence of heteroatoms on the stability aspects of various heterocyclic radicals, we compared the relative stability among the individual heterocyclic radical isomers. These data have been obtained by comparing the absolute energies within the individual sets of isomeric radical species. For dehydro- borole (1a-c), cyclopentadiene (2a-c), pyrrole (3a-c), furan (4b-c), phosphole (5a-c) and thiophene (6b-c), the relative energies have


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been estimated at different levels of theory and are listed in Table 1. Based on these data, insights into the influence of the heteroatom on the radicals and also the interaction between the lone pair and the radical electron can be envisaged. Particularly, nitrogen and phosophorus with one lone pair and oxygen and sulphur with two lone pairs can interact with radical centers in different ways. On contrast, the presence of an empty -orbital in the case of borolyl radicals, and the sp3 center in the case of cyclopentadienyl radical isomers provide entirely different situation, where no such interactions are possible. Interestingly, the radicals 1a, 2a, 3a and 5a are found to have their radical centers located at the heteroatoms, possesses −character.121 All of the other radicals are carbon-centered and -radicals, which differ in their relative position with respect to heteroatom. In all of the cases, heteroatom centered radicals are found to be more stable than their respective carbon centered isomers. The reason for their enhanced stability can be attributed to the ease of delocalization in −centered radicals. Surprisingly, in all of the cases, a significant preference in stability for the -centered radicals over -centered radicals has been observed that range between near degenerate (in furan) to substantial difference in other cases. This is in contrast to the stability of six membered heterocyclic radicals such as pyridyl and diazinyl radicals, where the -centered radicals are found to more stable. Among the radical pairs (2b, 2c) and (3b, 3c) pairs, different levels of theory predict the energy difference ranging between 0.3 to 0.9 kcal/mol favoring the -centered radicals. The preference for -centered radical is still maintained in the cases of (1b, 1c), (5b, 5c), and (6b, 6c) pairs with an energy difference ranging between 2.0 to 3.7 kcal/mol. On the other hand, either 4b or 4c attained minima depending on the level of the theory. At B3LYP level, the -centered was found to be more stable, whereas with the dispersion corrected M06-2X or CBS-QB3 level, the -centered radical was found to be stabilized. Also, single point energy


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calculations at (U)CCSD(T) level predict a degeneracy between - and -centered radicals.122 All the results are, however, consistent with the effect of basis sets at (U)B3LYP level and the complete data on the relative stability order is given (Table S3 in the Supporting Information).

Table 1. Relative Stability of Isomeric Dehydro- Borole 1a-c, Cyclopentadiene 2a-c, Pyrrole 3ac, Furan 4b-c, Phosphole 5a-c and Thiophene 6b-c Radicals at Different Levels of Theory

Relative Energy (kcal/mol) Level of theory

1a

1b

1c

2a

2b

2c

3a

3b

3c

A

0.0

11.1

7.4

0.0

35.5

34.6

0.0

24.7

24.3

B

0.0

12.4

9.1

0.0

33.2

32.5

0.0

21.9

21.5

C

0.0

8.2

6.1

0.0

32.8

32.5

0.0

25.0

24.5

D

0.0

8.3

5.2

0.0

33.6

33.0

0.0

24.4

24.1

4b

4c

5a

5b

5c

6b

6c

A

0.1

0.0

0.0

40.8

37.4

2.9

0.0

B

0.0

0.4

0.0

40.9

38.0

2.5

0.0

C

0.0

0.0

0.0

43.5

41.2

2.0

0.0

D

0.0

0.2

0.0

40.7

37.6

2.4

0.0

A= (U)B3LYP/cc-pVTZ; B= (U)M06-2X/cc-pVTZ; C= (U)CCSD(T)/cc-pVTZ//(U)B3LYP/ccpVTZ; D = CBS-QB3


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3.1.2 Bond Dissociation Energy (BDE) In order to examine the thermodynamic stability order, bond dissociation energies (BDE) for each radical species have been estimated. In this regard, the enthalpy changes accompanying the reactions, where C-H or X-H bond dissociation of the parent heterocycle leading to the heterocyclic radical and hydrogen atom as products have been considered. The estimated BDEs at (U)B3LYP/cc-pVTZ, (U)M06-2X/cc-pVTZ and CBS-QB3 levels of theory are listed (Table S4 in the supporting information). In general, lower the BDE value, the reaction is more favorable that accounts for higher thermodynamic stability of the radical. On the basis of BDE values, 5a was found to be the most stable radical followed by 2a, 3a and 1a. On the other hand, 4b was the least stable among all of the computed radicals. Indeed, the thermodynamic stability order predicted by the estimation of BDE’s for individual heterocyclic/carbocylic radicals follow the same trend as compared to the order predicted based on their relative energies.123 However, factors such as bond strengths and steric bulkiness can influence the BDEs leading to incorrect qualitative behavior particularly when DFT methods have been adopted. Hence, we computed the same using composite CBSQB3 level of theory as well.124 The results revealed that CBS-QB3 values are consistent with the DFT methods, however, with a slight underestimation of energy in relative terms. The radical stabilization energies (RSE) have also been computed and the results are consistent with the BDEs (Table S5 in the supporting information). 4. Factors influencing stability order of radical isomers 4.1. Spin density, Electrostatic potential and Multireference character The difference in the electron density of one spin ( spin) relative to the opposite spin ( spin) is known as the spin density, which is a measure of the radical character. The understanding of


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the spin density will provide additional insights into the stability aspects such as delocalization of the electron spin. Larger the spin density values, localization of the spin at the radical center will be more, and the resulting species will be expected to have a higher reactivity. On the other hand, those with more delocalization of the spin thrive to enhanced stability of the resulting radicals. In this regard, we have calculated spin densities of all the radicals at (U)B3LYP/cc-pVTZ and (U)M06-2x/cc-pVTZ levels of theory. The spin density values are listed in figure 2. Through these values, we found out that all of the carbon-centered radicals except 2a have large positive spin densities indicating a high radical character. Based on the orientation of the spin lobe, all of the carbon-centered radicals except 2a can be ascertained as −radicals. On the other hand, Ncentered 3a, B-centered 1a, C-centered 2a and P-centered 5a follow a different trend. Among them, the radicals 3a and 2a possess a negative spin density values at nitrogen and carbon atoms, respectively, whereas the other carbon atoms of the ring show positive values. The negative spin density values at the carbon and nitrogen atoms are due to the polarization effect, as a consequence of interaction of singly occupied molecular orbital (SOMO) with the fully filled inner orbitals. Both 2a and 3a have nearly the same spin density values since both are isoelectronic species. Interestingly, both of them possesses no significant spin density values at the radical centers, which are indeed completely delocalized. On contrast, elements that are less electronegative than carbon such as B, and P gets a non-zero coefficient in their SOMO i.e Bcentered 1a and P-centered 5a radicals, and accumulating partial spins at − and −orbitals of the radical centers.125 As a result, the extent of spin delocalization is less in those radicals compared to the N-centered (3a) and C-centered (2a) radicals. The stability order among these radicals follows the trend: 5a > 2a > 3a > 1a. The higher stability of P-centered radical 5a indicates the possible involvement of d-orbital for the spin delocalization. Many boryl radicals,


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in particular with electron withdrawing groups and -conjugation have been reported to attain stability on the basis of flipping of radical electron from −orbital to an −orbital.60 However, in the case of 1a, due to partial delocalization, the radical was found to be the least stable. Again, the involvement of −orbitals and delocalization of spin are attributed to the stability of Ccentered 2a and N-centered 3a radicals. Except in the cases of pyrrolyl (3b, 3c) and furanyl (4b, 4c) radicals, spin density values are also supportive of the higher stability of -centered over centered radicals. As indicated before, -centered and -centered isomeric pyrrolyl and furanyl radicals are close in energy at different levels of theory with an energy difference equal or less than 0.5 kcal/mol. In line with these observations, the multireference CASSCF calculations have also been performed to understand the nature of the radical orbitals. The resulting singly occupied molecular orbitals (SOMO) from those calculations have confirmed that all of the carboncentered radicals except 2a are −radicals, whereas, the C-centered 2a and N-centered 3a radicals are −radicals. On contrast, B-centered 1a, and P-centered 5a radicals possess orbital coefficients at the ring as well as at the heteroatoms. All of the SOMO’s are indicated in figure 2 and the complete active space orbitals are provided (Figure S1 in the supporting information). Apart from these, we have inspected at the electrostatic potential surfaces of all the radicals at (U)B3LYP/cc-pVTZ level of theory (Figure S2 in the supporting information). The results suggest that except in the case of the three-pyrrolyl radical isomers, all other radicals gain only a minimal negative potential at their respective radical centers. However, all of the radical centers of the pyrrolyl radicals are observed with a maximum negative charge. In the case of 3a, the observed maximum negative charge at the nitrogen (radical) center can be attributed to the presence of lone pair at the −orbital of the N-center, which can be rationalized based on the spin


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density and the SOMO. However, the 3b and 3c radical isomers also gained more negative charges at the radical centers that can be due to the involvement of the lone pair of electrons of nitrogen in the aromaticity. As a result, the nitrogen atom is no longer a negative center that implies the accumulation of more negative charge at the radical center. Apparently, the N-H part of the molecule gains a positive potential in a relative scale, which is nearly of the same order of magnitude as the negative charge at the radical center.

Figure 2. Spin density values (at (U)B3LYP/cc-pVTZ (black) and (U)M06-2X/cc-pVTZ (red) levels of theory) and SOMO (at CASSCF/cc-pVTZ) of isomeric borole 1a-c, cyclopentadiene


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2a-c, pyrrole 3a-c, furan 4b-c, phosphole 5a-c and thiophene 6b-c radicals. (The electronic state of the radicals and the orbital number corresponding to the SOMO are indicated) 4.2. NBO analysis On the basis of optimized geometries, stability order, spin density and electrostatic potential mapping, qualitative aspects with respect to the interactions between heteroatoms and the radical center have been rationalized thus far. NBO analysis has been carried out to estimate the interactions between the radical centers and the heteroatoms, to quantify hyperconjugation and also to understand those interactions stabilizing -centered radicals over -centered radicals. Since the heteroatom centered or −centered radicals are found to have a delocalized radical electron, the NBO analysis has been focused on the C-centered or −radicals. In the case of borolyl radicals 1b, and 1c, we observed no direct interaction between the radical electron and the boron atom, possibly due to an empty −orbital at boron center. Indeed, all of the major interactions at the radical centers are mainly through intervening bonds. The same trend is followed in the case of 2b and 2c, as there is no availability of lone pair. However, in the pyrrolyl and phospholyl radicals, the presence of one lone pair at the heteroatom, opens up a possibility for through space interactions. Still only in the case of 5b, a very weak through space interaction (0.75 kcal/mol) has been observed, whereas in 3b, 3c and 5c, no TS interactions have been observed. This can be rationalized on the basis of geometrical changes in 5b and 5c due to the possible d-orbital involvement that forces the hydrogen connected to the phosphorus to deviate from the planarity. As a result, the phosphorus lone pair can possibly have a slight overlap with the radical orbital. Due to the increased distance, no such interactions are possible in the case of 5c. Similarly, the involvement of additional lone pairs of oxygen and sulfur leads to furanyl and thiophenyl radicals exhibiting through space (TS) interactions. Indeed, 4b showed


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significant TS interaction, whereas a weak TS interaction was observed for 6b. Similarly, a weak TS interaction has also been observed for 4c that was completely absent in the case of 6c. Due to the greater internuclear distances in C-P and C-S bonds, the orbital overlap weakens between the lone pair and the radical leading to weak interactions.126,127 As expected, in all of the cases, TB interactions are found to be the important stabilizing interactions between the radical center and the lone pairs or heteroatoms. The most significant interactions involving either the radical center or the heteroatoms in this regard are tabulated (Table S6 in the supporting information). Based on the analysis for all of the radicals, the TS interactions are either weak or non-existent. Despite the presence of stronger TB interactions, no general trend has been observed for various radicals. Hence, the orbital interactions alone cannot provide the evidences favoring -centered over centered radicals. For the stability of all these radicals, we have also considered the possibility of hyperconjugation. Since all of the radicals possess C-H or X-H (X=B, N, P) bonds in either side of the radical center, the interaction between the radical electron and the C/X-H * bond was considered in this regard. Although all of the radical isomers showed the presence of hyperconjugation, the interaction energies were observed in the range of 0.3 and 1.1 kcal/mol. We have also considered the situations where the radical electron is having an -spin (Donor) or a -spin (Acceptor). In both the cases such interactions were found to be in the same range. The low values of hyperconjugation interactions in these radicals can be attributed to the geometrical constraints and hybridization. In the case of phosphole and thiophene based radicals, such interactions have still appeared to be small, although the bond distances between the radical center and the adjacent C-H bonds are relatively small. This situation clearly demonstrates that the hyperconjugation is not a major stabilizing factor for these radical isomers.


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4.3. Resonance energy and aromaticity character Due to the presence of conjugated −bonds, all of the radical isomers are stabilized by resonance, which can be enhanced with the participation of the heteroatom. In order to understand the involvement of the heteroatom, the resonance energies and the aromaticity have also been estimated for all of the parent compounds and their respective radical isomers. For resonance energy estimation, a hypothetical reaction has been considered, where a saturated heterocycle/heterocyclic radical analogue and cyclohexadiene are the reactants.106-110 This led to the formation of an unsaturated parent heterocycle/heterocyclic radical (our desired radical) and cyclohexene as the products. The enthalpy change (H) accompanying such reactions is calculated as a measure of as the resonance energy. More negative or less positive H value indicates the presence of greater resonance stabilization. In all of the cases, -centered radicals are found to have higher resonance energy values than their corresponding -centered radical isomers. Thus, resonance energy calculations support the higher stability of -centered radicals. Based on the resonance stabilization energy alone, the B-centered radical 1a is found to be more stable than its parent, despite the attainment of non-planarity. On the other hand, cyclopentadiene and phosphole are non-planar due to the presence of sp3 center and the deviation from planarity of P-H bond, respectively. However, their analogous radicals (2a and 5a) are found to be planar and gain extra stability due to the enhanced delocalization or resonance. Conversely, the resonance stabilization lowers in the N-centered pyrrolyl radical due to the loss of aromaticity as compared to the parent pyrrole. In this regard, the aromaticity character in the parent heterocycles and their respective radical isomers has also been estimated through nucleus-independent chemical shifts (NICS). Based on the NICS method, aromatic, antiaromatic and non-aromatic characters of the various


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heterocycles and their radical isomers have been evaluated using the computed magnetic shielding. The resulting NICS indices are useful in the classification of the ring currents as diatropic (negative, aromatic) and paratropic (positive, antiaromatic). Both resonance energy and NICS for all of the heterocyclic/carbocyclic radicals have been estimated at (U)B3LYP/cc-pVTZ and (U)M06-2X/cc-pVTZ levels of theory and are given in Table 2 and Figure 3. At both levels of theory, the values NICS (0), NICS (0.5), NICS (1.0), NICS (1.5) and NICS (2.0) are obtained by varying the position of probe atom along the perpendicular axis to the molecular plane and are tabulated (Table S7 in the supporting information).

Figure 3. NICS (1.0) indices for borole 1, cyclopentadiene 2, pyrrole 3, furan 4, phosphole 5, thiophene 6 and their corresponding radical isomers 1a-c, 2a-c, 3a-c, 4b-c, 5a-c, 6b-c performed at (U)B3LYP/cc-pVTZ level of theory. (Blue – Positive NICS values; Red – Negative NICS values) NICS (1.0) value for each parent molecule and their respective radical isomers are shown in Figure 3. These values are in line with our initial claim on the preferential stabilization of the centered radicals over the -centered radical. Based on the resonance energy and NICS


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calculations thus far, the radicals 2a, 3a and 5a can be interesting candidates with respect to aromaticity character. Independent to the aromaticity character of their respective parents (aromatic for N, and P containing heterocycle, non-aromatic for CH2 and antiaromatic for B), the resulting X-centered radicals (X = B, C-H, N and P) exhibit a common way in flipping of unpaired electron from the - to -orbital. Thus, all of them led to −centered, cyclic, 4n+1 −delocalized and planar radicals. Apparently, all of the heteroatom-centered/C-centered radicals containing (4n+1) −electrons, the NICS (1.0) values clearly showed the evidences for a weak antiaromatic character. Thus, heteroatom centered/C-centered radicals containing odd number of delocalized −electrons can be classified as “quasi-antiaromatic” systems. Table 2. Resonance Energies of Borole 1, Cyclopentadiene 2, Pyrrole 3, Furan 4, Phosphole 5, Thiophene 6 and their Corresponding Radical Isomers at (U)B3LYP/cc-pVTZ (Bold) and (U)M06-2X/cc- pVTZ (Italics) Levels of Theory

Reactants

Products

Resonance energy (H) (kcal/mol) 11.7/10.1 7.9/6.0 37.2/34.2 26.2/22.8 −2.3/−4.1 −15.4/−17.1


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19.7/16.0 18.8/15.3

−27.2/−30.0 −20.9/−24.4 3.8/−1.9 −3.5/−8.3 −17.9/−20.5 10.9/5.5 6.2/1.6 −3.4/−4.4 −7.4/−8.7 17.4/14.0 10.5/8.1 −16.8/−18.8 11.1/6.4 2.0/−1.7


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4.4. Ring strain Since all of the parent compounds and their isomeric radicals are five-membered ring systems, one of the important destabilizing factors is the ring strain. It will be very intriguing to understand the influence of the radical center in the ring strain. Also, for understanding the relative stability of various radical isomers, estimation of the strain energy is inevitable. In this regard, group equivalence reactions have been considered to quantify the ring strain for the parent heterocycle and their respective radical isomers (Scheme 2). The group equivalence reactions are found to be advantageous over the other alternative methods such as homodesmotic and isodesmic reactions in determining the strain energies.128 In principle, group equivalence reactions are both isodesmic and homodesmotic, and are capable of separating resonance from the destabilization due to strain.129 For constructing a group equivalence reaction,72,103 the following criteria have been considered: (i) Pairing (each individual equivalent group in the cyclic molecule must be paired with an equivalent group with a short acyclic counterpart) (ii) Heavy atoms (at least three heavy atoms should be part of each molecular fragment that can be considered as product) (iii) Balancing (each atom/fragments in the product should be balanced for the type and numbers of bonds and also the hybridization). Indeed, this method can work only when the reactions containing rings only on the reactant side. Due to the absence of ring in the product side, the group equivalence reactions cancel out the effect of resonance.128 Using these group equivalent reactions, the ring strain energies for the parent and their respective isomeric radicals have been estimated at (U)B3LYP/cc-pVTZ and (U)M06-2X/cc-pVTZ levels of theory (Table S10 in the supporting information). If the enthalpy change accompanying the group equivalence reactions is more negative, it indicates that the ring strain will be more. Upon creating a radical center by homolysis of C-H or X-H (X = B, CH, N, O, P and S) bonds, the


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resulting species gather more strain relative to their respective parent. The only exception is 1a, which possesses 2.7 kcal/mol lower strain energy than its parent 1. The B-centered 1a and Pcentered 5a radicals are found to be less strained among their isomeric radicals, whereas the Ccentered 2a and N-centered 3a are the most strained among their respective isomeric radicals. In general, we observed that the -centered radicals are found to be the least strained radicals among each set of heterocyclic/carbocyclic isomeric radicals.

Scheme 2. Group Equivalence Reactions Used for the Estimation of Ring Strain of (a) Parent Heterocycle (b) Heteroatom-Centered (c) -Centered and (d) -Centered Radical Isomers. As previously reported by Bach et al., the estimated strain energies of -centered and centered radicals correlate very well with C-H BDE’s, indicating that the strain energy increases as the BDE values increase.75 Recently, Alabugin et al. reported that %s character has a very good correlation with the strain energy. In order to understand the effect of heteroatom in the influence of strain energy, we correlated the %s character of the heteroatom (based on the NBO hybridization analysis) with that of strain energy of the individual radicals relative to their respective parent. The plots are included in the Supporting Information as Figure S3. Except for boron based radicals, we found out that all of the radical isomers showed a linear correlation.


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Presumably, the presence of an empty orbital and a slight electropositive nature of boron might be responsible for the deviation from the linearity. Apart from these, we have also considered various geometrical and molecular parameters such as internuclear distances, bond angles, Mulliken and NBO charges and hybridization (Figure 4, Table S2, S8 and S9 in the supporting information). Priority has been given to the role of heteroatom and their relative position with respect to the radical center in this regard. Based on the relationships, we obtained the following general trends: (1) The strain energy decreases as the internuclear distance increases between the radical center and the heteroatom, except in the case of B-centered radical 1a. (2) Upon creating a radical center, the radical species undergo a maximum distortion at the radical center, however, this typically counterbalanced by the adjacent atoms. We observed that if the adjacent atom is one of the heteroatoms or CH2 (in -centered radicals), the compensation of those atoms is relatively less compared to C3 center (Table S7 in the supporting information). This may be one of the reasons for higher ring strains in the case of -centered radicals. In the same line, the change in the ∠CXC (X=heteroatom) angle at the heteroatom junction (relative to their respective parent) is a clear indicator of the estimated strain in the molecule. If the bond angle at heteroatom increases, the strain energy decreases and vice versa (Figure 4a and Table S10 in the supporting information). (3) The strain energies of the parent molecules change in the following order: B > C > O > P > N > S. However, this trend changes upon introducing the radical centers, viz, for -centered radicals, it is a slightly varied (B > C > P > O > N > S). Whereas the changes are more pronounced in the case of -centered radicals (B > P > C > O > N > S) and heteroatom centered radicals (C > B > N > P). Apparently, the interactions of the heteroatoms with the radical centers play a significant role in the strain energies of the radicals.


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Figure 4: Correlation charts of ring strain energies with (a) bond angle at ∠CXC, where X=heteroatom or CH2; (Black – Parent; Blue – X-centered radicals; Red – -centered radicals; Green – -centered radicals) (b) Internuclear distance between radical center and the X. For understanding such interactions, NBO charges have been considered. These revealed that all of the -centered radicals were found to have zwitterionic character, whereas only 2c, 3c and


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4c among all of the -centered radicals exhibiting it. Despite the presence of more strain energy in destabilizing the C- and N-centered radicals than their respective isomers, both of them are found to be more stable. On the other hand, B- and P-centered radicals have lesser ring strains relative to their respective radical analogues. In all of the cases, the - delocalization could be responsible for the higher stability of the heteroatom- or C-centered radicals. Similarly, due to the dominating -delocalization and/or low ring strain, the -centered radicals are found to be more stable relative to their -centered analogues. It is evident that the delocalization (stabilizing effect) competes with the strain energy (destabilizing effect) in all of the radical isomers. Eventually the heteroatom- and -centered radical isomers are stabilized on the basis of dominating radical delocalization. 5. Conclusions In summary, sixteen heterocyclic and carbocylic radical isomers have been extensively studied, out of which, four are heteroatom centered and the remaining are C-centered radicals. All of the heteroatom radicals and 2a were found to be -centered, however, singly occupied molecular orbitals (SOMO) and their spin density values demonstrate a variable amount of −character in the B- and P-centered radicals. On the basis of high localization of spin values, all of the - and -centered radicals are found to be -radicals. Among all of the radicals that we investigated, the -centered radicals are found to be the most stable. On the other hand, the centered radicals are relatively more stabilized relative to their corresponding -centered radicals. Particularly the estimated C-H BDE’s fit very well with the trend shown in the stability of -centered and -centered radicals. Various factors like spin density, SOMO, strain energy, resonance energy and aromaticity have been accounted for their stability. Except for boron based radicals, we found out that all of the radical isomers showed linear correlation between the


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relative strain energy and the %s character of the hetero and carbon atoms. Despite the higher ring strain, the dominating -delocalization of the radical electron leading to higher stabilization of all the heteroatom centered and 2a radicals. Similarly, more delocalization and lower ring strain can be accounted for relatively higher stability of -centered over -centered radical isomers. Interestingly, the delocalization of radical electron in -centered radicals leads to a quasi-antiaromatic system. Overall, a competition between delocalization of radical electron or spin and the ring strain exists that dictates the overall stability of the five membered heterocyclic/carbocyclic radicals.

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ASSOCIATED CONTENT

*S Supporting Information See supporting information for Table S1, S2, S3, S4, S5, S6, S7, S8, S9 and S10 which provides computational data on the thermodynamic parameters, relative energies, BDE’s, RSE’s, NBO analysis, NICS results, bond angle deviation, Mulliken charges, hybridization and the results on ring strain for the various isomeric radicals and their respective parent molecules. Figure S1, S2 and S3 depicts the complete molecular orbital picture from CASSCF calculations, Electrostatic potential surfaces and the relationship between the relative strain energy and the %s character. Cartesian coordinates of optimized geometries as Appendix S1 are also included. (PDF)

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AUTHOR INFORMATION

Corresponding Author *Sugumar Venkataramani. Mob. +91-9915323141


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E-mail:[email protected] ORCID Sugumar Venkataramani: 0000-0002-6465-3655

▪ ‡

Author Contributions

C.S. and A.K.Y. contributed equally.

Notes The authors declare no competing financial interest. Acknowledgements: We are thankful to IISER Mohali for the start-up grant and providing research facilities including computational facilities. C.S. thanks IISER Mohali for Junior and Senior Research Fellowships. A.K.Y. thank INSPIRE for the fellowships. We would like to acknowledge Dr. K. R. Shamasundar and Mr. Satyam Ravi for their help in MCSCF calculations and stimulating discussions. We thank Ms. Lilit Jacob for her valuable discussions and contributions.

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120. Alabugin, I. V.; Bresch, S.; Gomes, G. D. P. Orbital Hybridization: A Key Electronic Factor in Control of Structure and Reactivity. J. Phys. Org. Chem. 2015, 28, 147–162. 121. During our investigations, the default optimization of the radicals 3a and 5a led to centered radicals. However, we tried to optimize them by swapping the orbitals to attain -centered radicals. Although it worked for 3a at lower basis set (ST0-3G), we could not optimize the -centered radical at higher basis sets. Similarly, the orbital swapping strategy failed in the case of 5a as well. At this juncture, we expect the delocalization of radical electron in the -orbital governs more stability than the availability of it in the orbital, irrespective of the stabilization through aromaticity. 122. Considering the fact that the energy differences at different levels are too small, it will be difficult to find the exact reason for this discrepancy. However, the amount of dispersive forces involved between the radical center and oxygen lone pair could be responsible in the furanyl radical isomers 4b and 4c. 123. This is in line with our earlier work, where the thermodynamic relative stability order is in the same trend as the BDEs. (For example, see references 67 and 68) 124. Izgorodina, E. I.; Coote, M. L.; Radom, L. Trends in R-X Bond Dissociation Energies (R = Me, Et, i-Pr, t-Bu; X = H, CH3, OCH3, OH, F): A Surprising Shortcoming of Density Functional Theory. J. Phys. Chem. A. 2005, 109(33), 7558–7566. 125. In the case of 1a, a competition between the configurations 01 and 10 leading to a slightly dominating -character with a spin density value of 0.63 at B-center. By achieving this, not only the ring strain gets relieved in 1a, but also the molecule attains


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non-planarity (as a consequence of Jahn-Teller distortion) that overcomes the antiaromaticity. 126. Alabugin, I. V. Stereoelectronic Effects: A Bridge Between Structure and Reactivity; John Wiley & Sons, Ltd.: Chichester, UK, 2016. 127. Alabugin, I. V.

Stereoelectronic Interactions in Cyclohexane, 1,3-Dioxane, 1,3-

Oxathiane, and 1,3-Dithiane: W-Effect, σC-X ↔ σ*C-H Interactions, Anomeric Effect What is Really Important? J. Org. Chem. 2000, 65 (13), 3910–3919. 128. Bachrach, S. M. Computational Organic Chemistry; John Wiley & Sons, Inc: New Jersey, 2014. 129. Steven M. Bachrach. On the Destabilization (Strain) Energy of Biphenylene. J. Phys. Chem. A 2008, 112, 7750–7754.


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TOC Graphic


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Deciphering Stability of Five-Membered Heterocyclic Radicals

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