Bent Singlet Cyclobutylcarbene: Computed Geometry, Properties, and

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Bent Singlet Cyclobutylcarbene: Computed Geometry, Properties, and Product Selectivity of a Nonclassical Carbene Murray G. Rosenberg, and Udo H Brinker J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.9b01732 • Publication Date (Web): 22 Aug 2019 Downloaded from pubs.acs.org on August 26, 2019

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The Journal of Organic Chemistry

Bent Singlet Cyclobutylcarbene: Computed Geometry, Properties, and Product Selectivity of a Nonclassical Carbene Murray G. Rosenberg § and Udo H. Brinker *,†,§ † Institute of Organic Chemistry, University of Vienna, Währinger Strasse 38, A-1090 Vienna, Austria § Department of Chemistry, The State University of New York at Binghamton, P. O. Box 6000, Binghamton, NY, 13902-6000, United States

ABSTRACT: Ab initio computations of cyclobutylcarbene (c-C4H7CH) were performed using the UMP4(fc)/6-311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model. The carbene’s most striking feature is its :CH-group. It is markedly bent toward the elongated C1'–C2' bond in the singlet ground-state but not in the triplet state, which is at least 1.1 kcal/mol higher in energy. Nonclassical 3C2E bonding among the C1, C1', and C2' atoms is prominent in the HOMO{–1}. The electron-donating ability of the nonbonding HOMO is thereby enhanced. The intensified nucleophilicity of the singlet carbene is manifested in quantifiable ways. For example, its HSAB hardness, HSAB absolute electronegativity, and gas-phase proton affinity rival those of ylidestabilized N-heterocyclic carbenes. It is computed to act as a nucleophile toward alkenes with higher HSAB hardness values. Transition states from singlet cyclobutylcarbene to bicyclo[2.1.0]pentane, cyclopentene, and methylenecyclobutane were computed and confirmed by intrinsic reaction coordinate calculations. Activation energies depend on the singlet’s conformation with regard to c-C4H7 ring-puckering, :CH-group rotation, and :CH-group bending. The singlet’s bent :CH-group favors bicyclo[2.1.0]pentane and cyclopentene formation. INTRODUCTION Cyclobutylcarbene (1)1– 3 is a deceptively simple carbene.4– 17 Indeed, only a few laboratory experiments claim its intermediacy (see Supporting Information; Schemes S1–S3).18– 21 Three main C5H8 products have been attributed to thermolytically generated 1 (Scheme 1):1,2,18,19

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bicyclo[2.1.0]pentane (2; housane),22– 28 cyclopentene (3),29– 31 and methylenecyclobutane (4).32– 34 The C5H10 compounds methylcyclobutane (6) and 1-pentene (7) were also noted.18,19 The intermediacy of 1 during the UV photolysis of 2 and of 3 has been suggested as well.20,21 Regrettably, none of the methods guarantees a carbene reaction intermediate. For instance, procedures relying on the in situ formation of Bamford–Stevens reactants,35,36 such as cyclobutanecarbaldehyde p-tosylhydrazone alkali salts,19 could yield alkene 4 directly, via a Shapiro olefination,37,38 or form alkane 6 via a Wolff–Kishner–Huang 39,40 reduction.19 Furthermore, 6 and 7 likely stem from the (cyclobutyl)methyl radical (5),41 formed by tripletstate carbene 31 (Scheme 1). Yet, 5 is also accessible via the Wurtz 42,43 reaction conditions used.18 Scheme 1. Products from Cyclobutylcarbene (1)

This report presents data for carbene 1 obtained by ab initio computations, which are routinely used to model reactive intermediates.44,45 Conformations of singlet-state 11 and its intramolecular rearrangements to 2–4 are examined using the following results: (1) equilibrium geometries, (2) ring-puckering dihedral angles ( ring-puck),3,46– 49 :CH-group rotation ( rot), and :CH-group bending ( wag),3 (3) bond length (r) distortion ratios,3 (4) relative molecular energies (relE), (5) transition state (TS) geometries, and (6) activation energy (E a) values. The philicity 50– 53 of 11 is gauged from the following computed properties: (1) gas-phase singlet–triplet energy gap (E S – T),54– 56 (2) the frontier MO difference in energy gaps (E) between carbenes and alkenes,57,58 (3) hard and soft acid and base (HSAB) hardness (),59,60 and (4) gas-phase proton


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affinity (PA).61,62 The structural and electronic results are used to explain why 11 is nucleophilic even though carbenes are electron-deficient (i.e., lack a Lewis octet).. RESULTS AND DISCUSSION Cyclobutylcarbene Conformers: Geometric Definitions and Stereodescriptors Carbene 1 can assume various conformations with different dimensions, including bond lengths (r)s, bond angles ( )s, and dihedral angles ( )s.3 Important descriptors defining aspects of 1 are shown in Figure 1. Moreover, 1 can adopt two spin-multiplicities. The dominant electron configurations of the divalent C atoms of 11 and 31 are depicted in Figure 1a. Related properties, such as the E S – T,54 are discussed below. The ring-puckering dihedral angle ( ring3 puck) of 1 is defined by eq 1. The “puckered-down” carbene 1a and “puckered-up” carbene 1b conformers are depicted in Figure 1b. Note, a similar scheme was used for the dual-ring carbene spiro[3.3]hept-1-ylidene,46 which exhibits both cyclobutylidene and cyclobutylcarbene behavior. A transverse ring-puckering dihedral angle ( ' ring-puck) is also defined (eq 2). Dihedral angles  ring-puck and  ' ring-puck have opposite algebraic signs unless the four-membered ring is flat (i.e.,  ring-puck =  ' ring-puck = 0 deg). In that case, the equatorial (eq) and axial (ax) positions within 1 become isoclinic. The rotational dihedral angle ( rot) relates the H1' and H1 atoms of 1 (Figure 1c) and is defined by eq 3.3 The endocyclic and exocyclic rotamers of 1 are designated as endo-1 and exo-1, respectively (Figure 1c). The respective designations anti-1 and syn-1 have also been employed, allowing for additional demarcations, such as anticlinal (±ac) and synclinal (±sc).3,46 (a)

1

1

3

1

(b)

1a

1b

endo-1

exo-1

(c)



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(d)

1

ent-1

Figure 1. Carbene 1 has many forms due to (a) spin-multiplicity, (b) ring-puckering conformerism, (c) rotamerism, and (d) auto-enantiomerism.

 ring-puck = 180 deg – | (C1'–C2'–C4'–C3')|

(1)

 ' ring-puck = 180 deg – | (C2'–C3'–C1'–C4')|

(2)

 rot =  (H1'–C1'–C1–H1)

(3)

 wag =  (cis-H3'–C3'–C1'–C1)

(4)

The bending dihedral angle ( wag) is shown in Figure 1d and defined in eq 4.3 Essentially,  wag is the amount of :CH-group deflection in 1 from the ring’s C1'···C3' axis toward the C1'– C2' bond (Figure 1d). The phenomenon can also be gauged using eq 5.3 The ring distortion ratio contrasts the elongated C1'–C2' bond with the unperturbed C1'–C4' bond. r(C1'–C2') distortion = {[ ] – 1} × 100% r(C1'–C4')

(5)

Computed Models of Carbene 1 Structural Dimensions and Relative Energies The UMP4(fc)/6-311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model was ultimately chosen, based on preliminary tests of various theoretical models (see Supporting Information), to compute the equilibrium geometries, zero-point vibrational energies (ZPVE)s, and singlepoint energies of carbene 1 isomers (Figure 2). Its singlet ground state has two conformations (Table 1): (a) endo-11a and (b) endo-11b. The higher-energy triplet state of 1 has five conformations (Table 1): (a) endo-31b, (b) exo-31b, (c) endo-31a, (d) exo-31a, and (e) (±sc)-31a. The smallest gas-phase E S – T of 1 is computed to be –1.1 kcal/mol, based on endo-11bendo3 1b (Table 1). Hence, 31 will not be thermally populated in a cryogenic matrix (e.g., T = –265 °C; vide infra). However, the total population of 31 could reach 22% at T = 25 °C and 46% at T = 195 °C (see Supporting Information). This is more likely if 11 decays slowly, the E S – T gap remains small, and intersystem crossing (isc) 63 via spin-orbit coupling is rapid (Scheme 1). The enthalpies of the three main products of 1 were also computed using the G3(UMP2) thermochemical recipe (Table 2). The results matched accepted heats of formation for hydrocarbons 2–4.


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(a)

(b)

endo-11a (relE = [0] kcal/mol) (c)

endo-11b (relE = 0.5 kcal/mol) (d)

endo-31a (relE = 3.1 kcal/mol)

endo-31b (relE = 1.6 kcal/mol)

Figure 2. Equilibrium geometries and relative energies of cyclobutylcarbene isomers: (a) endo1 1a (puckered-down), (b) endo-11b (puckered-up), (c) endo-31a (puckered-down), and (d) endo1 1b (puckered-up). [UMP4(fc)/6-311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model; 50% ellipsoids] Table 1. Cyclobutylcarbene (1) and (Cyclobutyl)methylium Ion (1H+) Measurements Molecule

a

c-C4H8 3 (± sc)- 1a 3 endo- 1a 3 exo- 1a 3 endo- 1b 3 exo- 1b 1 endo- 1a 1 endo- 1b + 1aH + 1bH

relE  carbene (kcal/ mol) (deg) — — 3.1 132.3 3.1 132.1 3.2 133.0 1.6 131.0 1.9 133.9 [0] 107.9 0.5 107.7 — — — —

b

r(C1' –C2') r(C1' –C4') Distortion (Å) (Å) (%) 1.548 1.565 1.566 1.563 1.562 1.559 1.668 1.679 1.906 1.874

1.548 1.558 1.566 1.563 1.562 1.559 1.544 1.539 1.508 1.493

c

0.0 0.4 0.0 0.0 0.0 0.0 8.0 9.1 26.4 25.5

a

 ring-puck d  ' ring-puck e (deg) (deg) +32.4 –30.5 –29.8 +32.4 +32.4 +32.4 –5.7 +19.7 –12.5 +26.4

–32.4 +30.7 +30.0 –32.4 –32.5 –32.6 +5.6 –18.8 +12.2 –23.6

 rot f

 wag g

(deg) — ±62.9 180 0 180 0 ±169.3 ±169.6 — —

(deg) — ±0.4 0 0 0 0 ±35.2 ±39.8 ±47.1 ±52.7

Equilibrium geometries computed using the UMP2(full)/6-311++G(d,p) theoretical model. b  carbene =  (C1'–C1–H1). c Values calculated according to eq 5. d Values calculated according to



eq 1. e Values calculated according to eq 2. f Values calculated according to eq 3. g Values calculated according to eq 4. Table 2. Enthalpies of Carbene 1 and Products a Molecule 298H b f H c endo-11b d 101.2 — 3 endo- 1b 102.8 — 3 endo- 1a 104.2 — 2 38.3 37.8 e 3 8.6 8.6 f 4 29.3 29.1 g a Units in kcal/mol. b Computed using the G3(UMP2) thermochemical recipe. c Experimental enthalpy of formation. d endo-11aendo-11b upon geometry optimization. e cf. Ref. 28. f cf. Ref. 31. g cf. Ref. 34. The carbene bond angle ( carbene) is defined as  (R'–C–R). The  carbene values for 11 and 31, computed at the UMP2(full)/6-311++G(d,p) level of theory, are typical for singlet and triplet alkylcarbenes, respectively (Table 1). The nonbonding  and p orbitals of a carbene’s divalent C atom are not strictly degenerate. Nevertheless, Hund’s rule of maximum multiplicity applies and monoalkylcarbenes often have triplet ground-states with a small E S – T . Ground-state :CH2 has a 3(1p1) electron configuration and a wide bond angle of 134 deg.44,64,65 Thus, 1 is anomalous due to the stabilizing nonclassical bond in 11. In accordance with the Wigner– Witmer rules of spin conservation,63,66 singlet carbenes (e.g., 1) will be generated from closedshell precursors in the absence of triplet sensitizers. Even carbenes with triplet ground-states react from their higher-energy singlet states if the gas-phase E S – T is below ca. 5 kcal/mol.54 Triplet carbenes react orders of magnitude slower than singlet carbenes do.67,68 Thus, 31 is expected to react orders of magnitude slower than 11. Of course, isc cannot be ignored if the gas-phase E S – T is low, although a small condensed-phase E S – T tends to suggest that isc from 1 1 to 31, and vice-versa, will actually be slow.54,69,70 Molecular Orbitals of Carbene 1 A stabilizing 3-center 2-electron (3C2E) interaction can develop if there is a small energy difference between a singlet carbene’s properly aligned donor and acceptor MOs (Figure 3). The divalent C atom’s empty p orbital can accept electron density from a  bond,71 mixed / “banana” bond,72 or a  bond,73,74 which is ostensibly strained in the case of 11.


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(a)

(b)

(c)

Figure 3. Nonclassical 3C2E bonding is enabled in singlet-state carbenes if the divalent C atom’s unoccupied p orbital approaches a C–C (a)  bond, (b) / “banana” bond, or (c)  bond. The :CH-group of 11 is bent toward the C1'–C2' bond, which is elongated. This facilitates an intramolecular orbital interaction between the divalent C atom’s p orbital and the fourmembered ring’s strained C1'–C2'  bond. Delocalized 3C2E bonding is evident in the HOMO{– 1} wave function of 11 (Chart 1; cf. Figure 3c). Nonclassical C1···C2' bonds are outlined in red (Chart 1). Bending of the :CH-group is absent in 31. Its 3(1p1) electron configuration precludes 3C2E bonding because the half-filled p orbital cannot accept an electron-pair.3,72 Although the filled HOMO of 11 and half-filled HOMO{–1} of 31 feature the  orbital of the divalent C atom, the wave functions for the cyclobutane part are wholly different (Chart 1). Similarly, there is a clear difference between the unoccupied LUMO of 11 and half-filled HOMO of 31. Although the p orbital of each divalent C atom is prominent, the wave functions for the cyclobutane units are also not alike (Chart 1). It is almost misleading to call both molecules cyclobutylcarbene. Chart 1. Select Molecular Orbitals (MO)s of Cyclobutylcarbene (1) a Carbene

HOMO{–2}

HOMO{–1} b

endo-11a

endo-11b


HOMO b

LUMO


Carbene

HOMO{–2}

HOMO{–1} b

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HOMO b

LUMO

— —

endo-31b a

Molecular orbitals computed using the ROHF/6-31G(d)//UMP2(full)/6-311++G(d,p) theoretical model. Surfaces shown at their 0.055 isovalues. b Half-filled SOMO for 31. Nonclassical Singlet vs. Classical Triplet Carbenes The structural dichotomy between a nonclassical singlet carbene and its classical triplet counterpart is due to 3C2E bonding in the former.71,72 The divalent C atom of a bent :CH-group can acquire additional electron-density from the C1'–C2' bond. This is possible only with a singlet carbene, which can be viewed as a “gem-zwitterion.”75 The empty p orbital of the 1 2 0 ( p ) electron configuration is available for a stabilizing intramolecular MO interaction. The resulting C1···C2' bond is nonclassical since the C1 and C2' atoms are not adjacent in the classical Lewis bond description (Figure 4). This phenomenon is further enhanced upon carbene protonation.72 For example, the + CH2-group of 1aH+ 76, 77 is bent toward the very elongated C1···C2' “bond” by  wag = 47 deg (Table 1). (a)

(b)

Figure 4. Singlet-state cyclobutylcarbene (11) does not have a (a) C s -symmetric classical structure. Instead, the (b) C1 atom approaches the C2' atom to establish nonclassical 3C2E bonding. Singlet Cyclobutylcarbene (11): A C5H8 Nucleophile Carbene Philicity from Differences in Frontier MO Energy Gaps Almost all singlet carbenes have 1( 2p0 ) electron configurations. Thus, they are formally (±)ambiphiles. However, they are sensitive to factors that affect electron density around the divalent C atom, such as the  inductive effect of substituents. For example, electronwithdrawing group (R(EWG)) substituents will engender electrophilic carbenes while electron-


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releasing group (R(ERG)) substituents will generate nucleophilc ones.50 The difference in energy gaps (E) between the frontier MOs of carbenes and those of their substrates, like alkenes or carbonyl compounds,72 specifies which of the two possible HOMO–LUMO interactions dominates the (cyclo)addition.57,58,72 Although the intermolecular frontier MO interactions are formally bi-directional, the sign of E determines if the carbenes act as (+)-electrophiles, by 1 2 0 ( p )-directed p-approach, or as (–)-nucleophiles, by 1( 2p0 )-directed -approach.78 The philicities of 1 and some representative carbenes toward a set of 8 alkenes was evaluated by the vector quantity defined in eq 6.72 The E values are listed in Table 3. Note that CCl2 acts as an electrophile except with fumaronitrile. The negative E value implies that the electrondeficient carbene prefers to act as a nucleophile in the presence the electron-poor alkene.79 It will engage the alkene * orbital with its  orbital. In contrast, 1 acts as a nucleophile except with the electron-rich alkenes 2,3-dimethylbut-2-ene and C 2 -symmetric trans-ethene-1,2diamine, as indicated by the positive E values (Table 3). E = E( → *)nucleophilic – E(p ← )electrophilic = (E * – E ) – (E p – E )

(6)

Table 3. Frontier MO Difference in Energy Gaps (E) between Carbenes and Alkenes a – c ALKENE

CARBENE

3

4

3.40

2.61

2.07

1.93

1.38

1.18

0.19

–0.89

3.33

2.54

2.00

1.85

1.31

1.11

0.12

–0.96

1.26

0.47

–0.07

–0.22

–0.76

–0.96

–1.95

–3.03

1.21

0.41

–0.13

–0.28

–0.82

–1.01

–2.00

–3.08

0.77

–0.03

–0.57

–0.72

–1.25

–1.45

–2.44

–3.52

1

endo- 1a

1

endo- 1b

a

Computed using the UMP4(fc)/6-311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model and eq 6. b The MO energy gap is defined as Ecarbene Ý alkene. c Units in eV.



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HSAB Hardness and HSAB Absolute Electronegativity of Carbene 11 The Lewis basicity of a singlet carbene’s nonbonding  orbital can be gauged using the HSAB 59,60 principle. Carbene 11 has a HSAB hardness () value of 5.0, according to the UMP4(fc)/6-311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model and eq 7 (see Supporting Information). This is a reflection of the high-lying HOMO of 11. Indeed, the nonbonding  orbital of 11 is harder than that of CCl2 but softer than that of the N-heterocyclic carbene 2,5-dimethyl-2,5-diazacyclopent-3-en-1-ylidene (see Supporting Information). Furthermore, 11 is harder than most of the alkenes of a test set except for very electron-rich ones, such as 2,3-dimethylbut-2-ene and C 2 -symmetric trans-ethene-1,2-diamine (see Supporting Information). Moreover, 11 has a HSAB absolute electronegativity ( ) value of 4.0, according to the same theoretical model and eq 8 (see Supporting Information). The easily quantified HSAB -values are important because they are already reflected in Table 3, according to eq 9 (see Supporting Information). These data support the hypothesis that 11 is a nucleophilic carbene. A high value for the gas-phase proton affinity (PA) of 11 would further support this hypothesis. hardness () = ½(ELUMO – EHOMO)

(7)

absolute electronegativity ( ) = –½(ELUMO + EHOMO)

(8)

E = 2( )

(9)

Gas-Phase Proton Affinity (PA) of Singlet Cyclobutylcarbene (11) Singlet carbenes usually act as electron-pair acceptors (i.e., electrophiles), because their divalent C atoms are electron deficient. However, other factors can determine carbene philicity.50– 53 Thus, carbenes sometimes act as electron-pair donors (i.e., nucleophiles). Since nucleophilicity often parallels basicity, the Brønsted–Lowry basicity of such carbenes is informative. The gas-phase PA reaction of a Brønsted–Lowry base (:B) is the reverse of the protolysis reaction of the corresponding conjugate acid B–H+ (eq 10).61,62 Thus, PA = –H°. Since a H+ ion’s energy is 0 hartree, the PA of 1 is the enthalpy difference between it and 1H+ (eq 11). The gas-phase PA values for conformers 1a and 1b are listed in Table 4. The PA value of ca. 261 kcal/mol places it among the most Brønsted–Lowry basic of carbenes. In fact, the PA of 1 is as high as those of ylide-stabilized N-heterocyclic carbenes,61,80 even though its divalent C atom lacks two flanking heteroatoms. The low  value, negative E value, high gas-phase PA value, bent :CH-group, and elongated C1'–C2' bond all suggest that 11 is a nucleophilic carbene due to nonclassical 3C2E bonding. This class of carbenes can be potent nucleophiles despite being formally electron deficient molecules.72 Note that the gas-phase PA of 1 is significantly


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higher than that of 3, whose experimental value is 183.15 kcal/mol.81 Also, the gas-phase PA of 2 (/ bond) is higher than that of 3 ( bond). :B + H+  B–H+ (PA = –H°)

(10)

1 + H+  1H+ (PA = H°1 – H°1H+)

(11)

Table 4. Data for Gas-Phase Proton Affinity (PA) a Conjugate PA b,c Conjugate relE c,d Base (:B) (C5H8) Acid (B–H+) (C5H9+ ) endo-11a 261.1 1aH+ [0] 1 + endo- 1b 260.5 1bH 1.1 + 2 197.6 1aH [0] + 2 184.8 2H 12.6 + 3 180.4 C 2-3H –11.7 + 3 179.8 C s -3H –10.9 a Enthalpies computed using the UMP4(fc)/6-311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model. b Gas-phase proton affinity (PA) of conjugate base (:B). c Units in kcal/mol. d Relative energy of corresponding conjugate acid (B–H+). The Nature of Cyclobutane’s Bent C–C Bonds Cyclobutane and cyclopropane have comparable strain energies.82–84 Although their framework bond angles  (C–C–C) are small, their interorbital angles  (hC –C–hC') are typical for tetracoordinate C atoms (Table 5).83,85– 88 Consequently, their bond paths lie outside the C–C internuclear axes. One measure of this is the deviation angle  (hC –C–C), which was computed herein to be 11 deg for puckered cyclobutane (see Supporting Information). Due to its small  value, the reactivity of cyclobutane mimics that of cyclopentane more than that of cyclopropane, which is prone to electrophilic attack because its bent / bonds behave somewhat like  bonds.89 However, cyclobutane’s outward-pointing hybrid orbitals hC can interact with the empty s orbitals of H+ ions. Computations of edge-protonated cyclobutane have shown it to be more stable than corner-protonated cyclobutane.88 In the case of 11, the empty p orbital of the divalent C1 atom interacts with the cyclobutane edge (i.e., the C1'–C2'  bond) and establishes an asymmetric 3C2E bond. Table 5. Some Computed Properties of Small-Ring Cycloalkanes a Cycloalkane  (C–C–C)  (hC –C–hC ') b Hybridization of p-Character of hC  (hC –C–C) c (deg)

Cyclopropane

60.00

(deg)

104.73

Directed Orbital hC

sp

3.93


(%)

(deg)

79.7

22.36


Cycloalkane

 (C–C–C)  (hC –C–hC ') b (deg)

(deg)

Hybridization of p-Character of hC  (hC –C–C) c Directed Orbital hC (%) (deg)

Cyclobutane 87.68 109.65 sp 2.97 74.8 11.00 a b Computed using the UMP2(full)/6-311++G(d,p) theoretical model. Interorbital angle between directed hybrid orbitals hC and hC'. c Deviation angle of directed orbital hC pointing outside the C–C internuclear axis. Conformational Isomerism of Cyclobutylcarbene Rotation of Cyclobutylcarbene’s Pendant :CH-Group Nonclassical 3C2E bonding within endo-11 hinges on two structural features: (1) the :CH-group must be bent and (2) the divalent C atom’s empty p orbital must be properly aligned with the ring’s C1'–C2'  bond. This means that dihedral angles  wag and  rot are pivotal. It is clear from Table 1 that  wag is optimal at ±(35–40) deg. In addition, the H1' and H1 atoms must be essentially antiperiplanar at ±169 deg (i.e., endo). These  values ensure 3C2E bonding among the C1, C1', and C2’ atoms. Energy profiles were computed for 11a and 11b (cf. Figure 1c) in which the :CH-group was rigidly rotated without geometry optimization (Figure 5). The endo-11 rotamer is slightly preferred over the exo-11 rotamer, due its eclipsing H1' and H1 atoms. Still, exo-11 should be viable because the “other” lobe of the p orbital is now aligned with the C1'– C2' bond. However, both exo-11a and exo-11b rearranged to 3 when their starting geometries were subjected to geometry optimization.


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(a)

(b)

Figure 5. Energy profiles for rigid :CH-group rotation within carbenes (a) 11a and (b) 11b show a slight preference for the endo rotamers ( rot = –169 deg): relE = 1.5 and 3.5 kcal/mol, respectively. Ring-Puckering in Four-Membered Carbocycles Nonclassical 11 has a bent :CH-group but C s -symmetric 31 does not since it lacks a 3C2E bond. Consequently,  ring-puck of 31 is close to that of unsubstituted cyclobutane (c-C4H8),88,90– 93 whose  ring-puck is ca. 30.1–35.0 deg (cf. Table 1).47,94 This dihedral angle corresponds to a C–C–C bond angle ( CCC) of ca. 88.0–87.3 deg, according to the trigonometric relation expressed in eq 12.88 According to the UMP4(fc)/6-311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model,  ring-puck = 32.4 deg (Table 1) and  CCC = 87.68 deg. Thus, these values are within the accepted range. Ring-puckering in four-membered carbocycles relieves torsional strain due to multiple Hatom eclipsing interactions. Cyclobutane’s ring-puckering is characterized by a degenerate pair of energy minima (Figure 6). The reported energy barrier for cyclobutane ring-puckering inversion, through a flat D 4h -symmetric TS, is 1.5 kcal/mol.47,94 The E a value found here is only 1.0 kcal/mol. This is notably below the UMP2(full)/6-311++G(d,p) barrier height for c-C4H8 ringpuckering inversion graphed in Figure 6. The energy profile for 6 shows a preference for the puckered-up conformation, which has an equatorial CH3-group (Figure 6). The energy profile for nonclassical 1, with its pendant :CH-group, is flatter and shows a preference for puckered-up endo-11b (Figure 6). When ZPVE and higher-level single-point energy corrections are applied, puckered-down endo-11a becomes the preferred conformer. The energy profile for 1H+, with its



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pendant +CH2-group, is also fairly flat. However, puckered-down conformer 1aH+ is preferred (Figure 6).

Figure 6. Substituent effects on ring-puckering in four-membered carbocycles were computed using the UMP2(full)/6-311++G(d,p)//UMP2(full)/6-311++G(d,p) theoretical model.

ring-puck  tan ( CCC ) = cos ( 2 ) 2

(12)

Pendant :CH-Group Wagging The TSs for :CH-group wagging within carbene 11 were computed using the UMP4(fc)/6311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model (vide infra): (a) endo-11a  ent,endo-11a (E a = 6.6 kcal/mol) and (b) endo-11b  ent,endo-11b (E a = 7.3 kcal/mol). The high energy barriers for auto-enantiomerization of 11 help lock its bent conformation and foster 2 and 3 production (Scheme 1). On the other hand, the formation of 4 requires additional motion. The :CH-group must unbend prior to the 1,2-H atom shift. Cyclobutylcarbene’s Brønsted–Lowry Conjugate Acid: The (Cyclobutyl)methylium Ion C s -Symmetric (Cyclobutyl)methylium Ion (C s -1H+) Cyclobutane’s degenerate HOMO pair is split if the ring is substituted by an electronwithdrawing + CH2-group.95,96 Early computational models of the (cyclobutyl)methylium ion (1H+) revealed the following details: 96–99 (1) two prevalent rotamers of different energy (relE = 4,96 4.08,97 or 7.40 kcal/mol 98), (2) each one is Cs -symmetric (i.e.,  wag(cis-H3'–C3'–C1'–C1) = 0 deg), and (3) the cyclobutane plane is bisected (a) by the + CH2-group in the lower-energy form (C s -1aH+) and (b) by the + CH2-group’s p orbital in the higher-energy form (C s -1bH+). Orbital overlap between the C1 and C1' atoms of C s -1aH+ results in a stabilizing -type bond.


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Bent (Cyclobutyl)methylium Ion (1H+) and Gas-Phase PA of C5H9+ Isomers Experimental attempts to generate the (cyclobutyl)methylium ion (1H+) using the superacid ClSO2F·SbF5 at T = –90 °C are reported to give the C 2 -symmetric cyclopentylium ion (C 2 -3H+), via ring-expansion (Scheme 2).76 The B3LYP/6-311+G(d) theoretical model also supported the spontaneity of 1H+ C 2 -3H+.76 However, a local minimum for 1H+ was found at the MP2/ccpVTZ[6-31G(d)] level of theory. It represented 1aH+ as a -bridged nonclassical ion.76,77 Nonclassical distortion is more pronounced in protonated 1aH+ than in endo-11a (cf. 26.4% vs. 8.0%; Table 1). Bent carbocation 1aH+ is poised to undergo ring-expansion to give C 2 -3H+ (Scheme 2).99– 102 The computations show how the elongated C1'–C2' bond of endo-11a (r = 1.67 Å) becomes even more stretched in 1aH+ (r = 1.91 Å) until it is finally broken in C 2 -3H+ (r = 2.38 Å). Geometry optimization of symmetric carbocation C s -1H+ herein led to asymmetric carbonium ion 1H+. The + CH2-group of rotamer C s -1aH+ bends markedly toward the C1'–C2' bond in the equilibrium geometry (Scheme 2). Finally, geometry optimization of C 2 -3H+ led to C s -3H+, but the final corrected energy of C 2 -3H+ was slightly lower than that of C s -3H+. Scheme 2. Fate of the Elongated C1'–C2' Bond of Cyclobutylcarbene (1) a

a

Computed using the UMP4(fc)/6-311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model.



Protonation of Bicyclo[2.1.0]pentane (2) The protonation of fused bicycloalkane 2 has been the topic of computational research.99–101 The C5-protonation of 2 is reported to give the high-energy C s -symmetric carbonium ion 2H+, wherein the central C–C bond of 2 is maintained.100 The results were reproduced herein using the UMP4(fc)/6-311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model. The C1protonation of 2 is reported to give cation C 2 -3H+, in which the central C–C bond of 2 is cleaved.100,101 Another structure was reported,100,101 but it is almost certainly unoptimized C 2 3H+. Its dimensions are closer to those of carbocation C 2 -3H+ than those of carbonium ion 1H+.76 However, an energy profile computed herein simulates the endocyclic approach of a H+ ion toward the C1 atom of 2. Its minimum represents puckered-down carbonium ion 1aH+ (Figure 7). Thus, the proton-induced heterolysis of the central C1–C4 bond of 2 leading to classical carbocation C 2 -3H+ may go indirectly through nonclassical carbocation 1aH+. In any case, the Cartesian coordinates of carbonium ion 1aH+ appear here for the first time (see Supporting Information).

Figure 7. Approach of H+ toward the C1 atom of 2 proceeds along its endocyclic face to give 1aH+, prior to C 2 -3H+ (Scheme 2). [UMP2(full)/6-311++G(d,p)//UMP2(full)/6-311++G(d,p) theoretical model] Isomerization of Cyclobutylcarbene to C5H8 Products The isomerizations of 1 to 2–4 (Scheme 1) were examined by computing the TS of each elementary step and following the transformations by their intrinsic reaction coordinates (IRC)s. Data from Table 6 include pertinent dihedral angles, TS imaginary frequencies, and activation energies.


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Table 6. Elementary-Step Transition States of Carbene 1 a Transition  ring-puck_TS b  rot_TS c  wag_TS d  TS Eae Product f State (deg) (deg) (deg) (cm –1) (kcal/mol) TS-2 exo –4.3 g –158.1 h ±32.0 682i i 2.4 2 j k l TS-2 endo +1.3 +21.6 ±28.8 651i 1.8 2 g h TS-3aendo –25.9 –152.5 ±58.0 839i 9.6 3 j k TS-3bendo +24.1 +177.9 ±58.7 481i 4.6 3 g h TS-4a ac –28.4 –119.5 ±8.5 457i 8.4 4 g h TS-4a sc –27.8 –64.1 ±2.4 431i 6.4 4 j h TS-4b sc +28.6 –67.4 ±4.5 320i 5.2 4 a Computed using the UMP4(fc)/6-311++G(2df,2p)//UMP2(full)/6-311++G(d,p) theoretical model. b  ring-puck_TS =  (C1'–C2'–C4'–C3') based on 1. c  rot_TS =  (H1'–C1'–C1–H1) based on 1. d  wag_TS =  (cis-H3'–C3'–C1'–C1) based on 1. e E a = E TS = E TS – E endo-11a. f cf. Scheme 1. g Puckered-down conformer. h Endocyclic rotamer. i 1,3-C–H Bond insertion TS: endo-to-exo. j Puckered-up conformer. k Exocyclic rotamer. l 1,3-C–H Bond insertion TS: endo-to-endo. 1,3-C–H Bond Insertion Reactions Fused bicyclic 2 is formed by an intramolecular 1,3-C–H bond insertion reaction within 11 (Scheme 1). The preferred interaction is thought to involve the carbene’s empty p orbital with the CH2-group’s  CH2 group orbital and not its  CH2 group orbital.103 The elementary step 112 is facilitated by the :CH-group’s bent disposition (i.e.,  wag = 35 and 40 deg; cf. Table 1). Its equilibrium geometry pre-positions nonclassical carbene 11 to form the fused cyclopropane unit of 2. The proximity of the carbene’s reactive :CH-group to the cis-H2' atom promotes two rotameric TSs (Table 6): TS-2exo (E a = 2.4 kcal/mol) and TS-2endo (E a = 1.8 kcal/mol). In the higher-energy elementary step, the cis-H2' atom of endo-11a migrates from the endocyclic face to the exocyclic face of 2, becoming its exo-H5. In the endo-to-exo TS, the carbene’s  rot value changes by ca. 38 deg. In the lower-energy elementary step, the cis-H2' atom of exo-11b migrates from the endocyclic face to the endocyclic face of 2, becoming its endo-H5. In the endo-to-endo TS, the carbene’s  rot value changes by only ca. 3 deg. The increasing angle strain within 11, as it forms the three-membered ring in 2, is mitigated since a triangular array of C atoms already exists in 11 (Figure 4b). Structural pre-ordering within the TS has already been achieved.104– 106 [1,2]-Sigmatropic Rearrangements: 1,2-C Atom Shift Reactions Ring-expansion of 11 yields cycloalkene 3 via a 1,2-C atom shift reaction (Scheme 1). The bent :CH-group of 11 should assist the formation of 3 because the carbene’s nonclassical C1···C2' bond (Figure 4b) becomes the adjoining C1–C5 bond in 3. There are two TSs, which differ by



their ring-puckering dihedral angle  ring-puck (Table 6): TS-3aendo (E a = 9.6 kcal/mol) and TS-3bendo (E a = 4.6 kcal/mol). According to the IRC of TS-3aendo, the C2' atom of endo-11a migrates away from C1' and toward C1 with concomitant H1-atom rotation from endo-to-exo, which gives the cis C–C double bond of 3. The large yield of 3,18,19 despite a high E a value of 9.6 kcal/mol, might be explained by one of the following: (1) ring-expansion of endo-11a to 3 might proliferate from quantum mechanical (QM) tunneling within 1, or (2) if 1 is chemically activated (i.e., “hot”)107 when it is generated then 1* would have enough energy to surmount the classical energy barrier (i.e., 1*[TS-3aendo]‡3). The latter argument can also be made for a chemically activated 2*, which may rearrange to 3. Indeed, 2 thermally isomerizes to 3 at T = 330 °C,22,24 though traces of adventitious transition metal catalysts can effect the rearrangement at T = 25 °C.24 The E a of TS-3bendo was found to be 5 kcal/mol lower than that of TS-3aendo. This appears to be a more favorable route to 3. However, the IRC for TS-3bendo did not support the formation of 3 and its cis C–C double bond. [1,2]-Sigmatropic Rearrangements: 1,2-H Atom Shift Reactions exo-Methylenation of 11 gives 4 via a 1,2-H shift reaction (Scheme 1). Three anticlinal/synclinal TSs were found (Table 6): TS-4aac (E a = 8.4 kcal/mol), TS-4asc (E a = 6.4 kcal/mol), and TS-4bsc (E a = 5.2 kcal/mol). Their IRCs indicate asynchronous elementary steps (see Supporting Information). The 1,2-H atom shifts from 11 to 4 require the bent :CH-group to first unbend toward the C1'···C3' line of bilateral symmetry. Indeed, the SCF wave function sometimes converged to a :CH-group wagging TS-Wag-11 (see Supporting Information). Reducing  wag within 11 breaks its stabilizing 3C2E bond, which requires energy. Next, the H1' atom must be rotated in-between its endo and exo conformations before it can bridge the C1 and C1' atoms. The 6-311++G(d,p) basis set was appropriate here because it places polarization (p) and diffuse (+) functions on the bridging H atom. After the C1' atom of 11 becomes spirocyclic in the 1,2-H atom shift TS, it remains strained in 4 because one end of the exocyclic C–C double bond is part of a four-membered ring. Comparison of Cyclobutylcarbene with Some Substituted Derivatives Substitution at C1 Absolute rate constants (k T )s for the elementary steps of “invisible” carbene reaction intermediate’s can be measured by laser flash photolysis (LFP) kinetics experiments if pyridine is used to form traceable ylides.67,108– 110 Results for cyclobutyl(fluoro)carbene (8) at T = 246– 313 K show that ring-expansion to cyclopentene 9 is noticeably slow (k 296 = 1.8 × 10 6 s– 1) despite ring-strain relief (Scheme 3).67,111 The prevailing model of a conjugative intramolecular eu –p MO interaction in a C s-symmetric (cyclobutyl)carbinyl system was used to explain this phenomenon (Figure 8; cf. endo-31b HOMO{–2} in Chart 1).96,111,112 The attenuation was not


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attributed to cyclobutylcarbene stabilization through a bent :CF-group. Indeed, -type backbonding from the F atom will obstruct 3C2E bonding in carbene 18 (Scheme 3). Although alkene 10 was reported, the formation of a bicyclo[2.1.0]pentane skeleton was not. Scheme 3. Rearrangements within Cyclobutyl(halo)carbenes 8 Were Slower Than Expected

Figure 8. Conjugative stabilization of unbent carbene 18-F via cyclobutyl–carbinyl MO interaction. Cryogenic matrix isolation techniques were used to investigate the ring-expansion of fluoro(1-methylcyclobut-1-yl)carbene (11) to cyclopentene 12 (Scheme 4).113– 117 Carbene 11 was chosen instead of 1 to study 1,2-C atom shifts for two main reasons. The CH3-group on its C1' atom avoids a potentially competitive 1,2-R group shift; CH3-groups have a low migratory aptitude.67,72 Additionally, the F atom lowers E S – T (i.e., E S – T

Bent Singlet Cyclobutylcarbene: Computed Geometry, Properties, and

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