Theoretical investigation on diastereoselective [2+2] cycloaddition and Pd-catalyzed enantioselective [3+2] cycloaddition for synthesis of cis-β-lactam and exo-furobenzopyranone

: The mechanism is investigated for Wolff rearrangement/Staudinger [2+2] cycloaddition cascade and Pd-catalyzed, decarboxylative, formal [3+2] cycloaddition. Wolff rearrangement of 3-diazotetramic acid is determined to be rate-limiting step generates cyclic acyl ketene. The interaction of ketene with imine firstly results in zwitterion followed by conrotatory cyclization giving major cis-β-lactam. For synthesis of s-VECs, the epoxidation−cyclization cascade and hydrolysis give precursor of better performing exocyclic derivative. The reaction with 3-cyanochromone includes decarboxylation, nucleophilic attack and subsequent ring closure yielding 5-exo-trig furobenzopyranone. Based on the comparison between possible paths, the diastereoselectivity of cis over trans and regio-divergence of 5-exo-trig over 7-endo-trig are both kinetically controlled for [2+2] and [3+2] cycloaddition in common. The positive solvation effect is suggested by decreased absolute and activation energies in chlorobenzene and chloroform solution compared with in gas. These results are supported by Multiwfn analysis on FMO composition of specific TSs, and MBO value of vital bonding, breaking.


Introduction
As an important component of modern drug design, new heterocyclic scaffold possess attractive physical and biological profile from medicinal chemistry perspective.Among these unexplored molecular frameworks, the some spirocyclic structures are the most sought-after motifs [1].The β-Lactam also known as 2-azetidinone is privileged and well established in medicinal chemistry [2,3].Thus convenient methods for synthesis of β-lactam have attracted considerable attention with available substitution pattern.A highly worthy goal is to develop efficient synthetic methodology toward spirocyclic β-lactam frame-works.Although there is cascade Wolff rearrangement/Staudinger [2+2] cycloaddition as an active and powerful tool to produce β-lactam [4,5], few examples have been reported using cyclic diazo compound in construction of spirocyclic β-lactam [6,7].In this field of assembling pirocyclic scaffold based on diazo heterocycle transformation, Dar'in group have achieved many good results through exploring diazo tetramic acid [8][9][10].
Many advantages have been shown for Wolff rearrangement under microwave irradiation in ring expansion of aziridine [21].Furthermore, 3-diazotetramic acid has been successfully involved in approach toward Δα,β-spirobutenolide via Rh(II)-catalyzed O-H insertion into propiolic acid and Rh(II)-catalyzed condensation with nitriles delivering compound bearing a hitherto polysubstituted oxazole [22,23].A new breakthrough was Dar'in's Wolff rearrangement/Staudinger [2+2] cycloaddition cascade to access spiro bis-β-lactam involving 3-diazotetramic acid and imine [24].Another one compared this was Schreiner's Pd-catalyzed, decarboxylative, formal [3+2] cycloaddition of newly synthesized s-VECs with 3-cyanochromone [25].Although high diastereoselectivity was achieved for bis-β-lactam and excellent selectivity was provided for s-VECs synthesis, follow-up applicability, there is no report about detailed mechanistic study explaining the origin of selective cycloaddition.How three stereocenters were controlled simultaneously for novel spirocyclic bis-β-lactam?What's the mechanism of epoxidation−cyclization cascade making following exocyclic derivative overall better than endocyclic sone?To solve these mechanic problems in experiment, an in-depth theoretical study was necessary for this strategy leading to novel spiro and polyspiro heterocyclic structure with two different isomers.

Computational details
The geometry optimizations were performed at the B3LYP/BSI level with the Gaussian 09 package [26,27].The mixed basis set of LanL2DZ for Pd and 6-31G(d) for non-metal atoms [28][29][30][31][32] was denoted as BSI.Different singlet and multiplet states were clarified with B3LYP and ROB3LYP approaches including Becke's three-parameter hybrid functional combined with Lee−Yang−Parr correction for correlation [33][34][35][36][37][38][39].The nature of each structure was verified by performing harmonic vibrational frequency calculations.Intrinsic reaction coordinate (IRC) calculations were examined to confirm the right connections among key transition-states and corresponding reactants and products.Harmonic frequency calculations were carried out at the B3LYP/BSI level to gain zero-point vibrational energy (ZPVE) and thermodynamic corrections at 473 K, 363 K and 1 atm for each structure in chlorobenzene and chloroform.The solvation-corrected free energies were obtained at the B3LYP/6-311++G(d,p) (LanL2DZ for Pd) level by using integral equation formalism polarizable continuum model (IEFPCM) in Truhlar's "density" solvation model [40][41][42] on the B3LYP/BSI-optimized geometries.
As an efficient method of obtaining bond and lone pair of a molecule from modern ab initio wave functions, NBO procedure was performed with Natural bond orbital (NBO3.1) to characterize electronic properties and bonding orbital interactions [43,44].The wave function analysis was provided using Multiwfn_3.7_devpackage [45] including research on frontier molecular orbital (FMO) and Mayer bond order (MBO).

Results and discussion
The mechanism was explored for (a) reaction of 3-diazotetramic acid 1 with imine 2 leading to spiro bis-β-lactam 3 (b) synthesis of s-VECs exo-6 and endo-4 and Pd-catalyzed, decarboxylative-[3+2] cycloaddition with 3-cyanochromone 9 producing furobenzopyranone 10, 11 (Scheme 1).Illustrated by black arrow of Scheme 2a, Wolff rearrangement of 1 forms vital cyclic acyl ketene A, which proceeds [2+2] cycloaddition with 2 involving two steps.The interaction of ketene with 2 firstly results in β-lactam zwitterionic intermediate zi3 followed by ring closure and subsequent conrotatory cyclization giving major "cis" product denoted as c3.Shown by black arrow of Scheme 2b, the epoxidation−cyclization cascade of cyclic allylic alcohol initially gives an iminium ion intermediate 8, which is hydrolyzed in the following two steps affording carbonate.Promoted by model catalyst PdCl2, the decarboxylation intermediate of better performing exo-6 is obtained in the beginning, whose nucleophilic attack on 9 and subsequent ring closure completing [3+2] cycloaddition.The schematic structures of optimized TSs in Scheme 2 are listed in Figure 1.The activation energy was shown in Table 1 for all steps.Supplementary Table S15, Table S16 provided the relative energies of all stationary points.According to experiment, the Gibbs free energies in chlorobenzene and chloroform solution phase are discussed here.Table 1 The activation energy (in kcal mol −1 ) of all reactions in gas and solvent.

Wolff rearrangement/Staudinger [2+2] cycloaddition cascade
Wolff rearrangement proceeds via ts-1i1 as step 1 with the activation energy of 46.8 kcal mol −1 relative to the starting point 1 (black dash line of Figure 1a).The transition vector of ts-1i1 includes the cleavage of C2-N, C3-C4 bond and closing of C2 to C4 slightly later (1.69, 2.17, 2.17 Å) (Figure S1a).Once N2 leaves from the system, the five-membered ring of 1 turns to be four-membered one, which is the stable vital cyclic acyl ketene A in resultant i1 exothermic by −8.6 kcal mol −1 .The barrier is somewhat high yet still feasible to overcome considering the high temperature of 200 ℃ under microwave irradiation in experiment.
In the following [2+2] cycloaddition, although E form of imine 2 is predominating with lower relative energy, Z-2 is selected to discuss the mechanism owing to the same process and the final major "cis" product.The initial complex binding A and Z-2 denoted as zi2 is taken as the starting point of next two steps.The nucleophilic attack of Z-2 to A occurs via ts-zi2i3 with activation energy of 1.7 kcal mol −1 rather small (red dash line of Figure 1a) leading to zwitterionic intermediate zi3 continuously exothermic by −15.9 kcal mol −1 .The transition vector is simple corresponding to the N• • • C3 bonding (2.42 Å) (Figure S1b).
The introduction of strongly electron-donating p-methoxyphenyl (PMP) and benzyl (Bn) at iminium moiety disfavor direct ring closure.Thereby step 3 is required to complete fast conrotatory cyclization from diastereomeric zwitterion, which takes place via ts-zi3c3 with activation energy of 14.5 kcal mol −1 and huge heat release of −50.0 kcal mol −1 furnishing a new four-membered ring with an intersection arrangement of the previous one in final c3.The transition vector contains the approaching of C2 to C5 and concert elongation of N-C5, C2-C3 double bond to single one (2.37,1.35, 1.43 Å) (Figure S1c).The latter two steps are both readily accessible with low activation energy from kinetics and quite favorable from thermodynamics.Thus Wolff rearrangement is determined to be rate-limiting of the whole reaction.

Epoxidation−cyclization cascade
Shown by black dash line of Figure 1b, the epoxidation structure of cyclic allylic alcohol 7 is located and taken as starting point of epoxidation−cyclization cascade, from which the cyclization initiated from negative carbonyl O3 to epoxane positive C2 takes place via ts-i78 with activation energy of 34.2 kcal mol −1 endoergic by 31.3 kcal mol −1 affording an iminium ion intermediate 8 in step 1.The transition vector also includes the breaking of C2-O1 and shortening of C1-O3 single bond (1.66, 2.15, 1.34 Å) (Figure S1d).The destruction of epoxy structure makes the negative charge significantly transferred to epoxy O1.
With water molecule, the reactive 8 is prone to be hydrolyzed through the following two steps affording carbonate in i2.The new starting point between 8 and H2O is located as i0, from which the protonation of negative O1 is readily to undergo via ts-i01 with activation energy of 4.2 kcal mol −1 exothermic by −26.1 kcal mol −1 in step 2. In addition to the obvious indication of H1 shift from O4 of H2O to O1, the transition vector also indicates asynchronous O4 bonding to C4 (1.12, 1.33, 2.3 Å) (Figure S1e).The resultant i1 is stable with pronated O1H1 and sp3 hybrid C4.
Another H2 of H2O is provided to N1 in step 3 (1.34,1.23 Å) via ts-i12 with the activation energy of 35.6 kcal mol −1 relative to i1.Meanwhile C4-O4 single bond is contracted to double one and the dissociation of N1 from C4 causes depature of EtNH2 molecule (1.33, 1.54 Å) in stable i2.This detailed motion can be demonstrated by the transition vector of ts-i12 (Figure S1f).Thankfully, this step is continuously exothermic by −27.9 kcal mol −1 favorable thermodynamically.The barriers of step 1 and step 3 somewhat high are both capable to overcome under the experimental temperature of 90 ℃.
The complex binding 9 denoted as i5 is taken as starting point of the following two steps completing [3+2] cycloaddition.According to the transition vector (Figure S1h), the nucleophilic attack of negative aldehyde O2 to positive C4 of 9 (2.14 Å) proceeds via ts-i56 with the activation energy of 33.7 kcal mol −1 forming i6 exothermic by −6.2 kcal mol −1 in step 5. Prior to this major motion, H3 returns from C2 to C1 (1.93, 1.15 Å).It is noted that the N2-C6 bonding between cyano and terminal alkene of exo-6 favorable for stabilizing is not available for endo-4, making subsequent 5-exo-trig ring closure outcompetes 7-endo-trig one.
The five-membered ring is generated via ts-i67 with a barrier of 22.6 kcal mol −1 through concerted N2-C6 departure and C2-C5 linkage (2.14, 2.47 Å) (Figure S1i) liberating final i7 exothermic by -10.0 kcal mol −1 with recovered formal cyano and terminal alkene.PdCl2 is still bonded to negative C3 of C3-C6 double bond as the promotion of whole process.Three barriers from step 4 to step 6 are mediated in agreement with requisite slightly high temperature of 90 ℃.

Diastereoselectivity and regio-divergence
To highlight the idea of feasibility for changes in electron density and not molecular orbital interactions are responsible of the reactivity of organic molecules, quantum chemical tool Multiwfn was applied to analyze of electron density such as MBO results of bonding atoms and contribution of atomic orbital to HOMO of typical TSs (Table S17 and S18, Figure S2).These results all confirm the above analysis.

Conclusions
Our DFT calculations provide the first theoretical investigation on Wolff rearrangement/Staudinger [2+2] cycloaddition cascade and Pd-catalyzed, decarboxylative, formal [3+2] cycloaddition.Wolff rearrangement of 3-diazotetramic acid is rate-limiting step generates cyclic acyl ketene.The interaction of ketene with imine firstly results in zwitterion followed by conrotatory cyclization giving major cis-β-lactam.For synthesis of s-VECs, the epoxidation−cyclization cascade and hydrolysis give precursor of better performing exocyclic derivative.The reaction with 3-cyanochromone includes decarboxylation, nucleophilic attack and subsequent ring closure yielding 5-exo-trig furobenzopyranone.Based on the comparison between possible paths, the diastereoselectivity of cis over trans and regio-divergence of 5-exo-trig over 7-endo-trig are both kinetically controlled for [2+2] and [3+2] cycloaddition in common.The positive solvation effect is suggested by decreased absolute and activation energies in chlorobenzene and chloroform solution compared with in gas.These results are supported by Multiwfn analysis on FMO composition of specific TSs, and MBO value of vital bonding, breaking.Supplementary materials: Supplementary data available: [Computation information and coordinates of stationary points; Calculated relative energies for the ZPE-corrected Gibbs free energies (ΔGgas), and Gibbs free energies (ΔGsol) for all species in solution phase at 473 K, 363 K.].
Author contributions: Conceptualization, NL; methodology, NL; software, NL; validation, NL; formal analysis, NL; investigation, NL; resources, NL; data curation, NL; writing-original draft preparation, NL; writing-review and editing, NL; visualization, NL; supervision, CM; project administration, CM; funding acquisition, XL.All authors have read and agreed to the published version of the manuscript.