please see this work > https://www.researchgate.net/publication/233961732_Competition_between_the_one-step_and_two-step_zwitterionic_mechanisms_in_the_23_cycloaddition_of_gem-dinitroethene_with_%28Z%29-CN-diphenylnitrone_a_DFT_computational_study

Article Competition between the one-step and two-step, zwitterionic ...

Mr. Nash,

I do not know what type of 7-membered rings you have visualized, but if your interest is focused on the lactams or lactons (attachment), than please find below known reaction pathways. Most of them have involved, however organometallic adducts. In this respect for lactams, there has study on the reaction mechanism (Reaction 2, ref. [4]). 

For lactons, a known quantum chemical study, has involved only prediction of NMR (reactions 2 and 3, ref. [7]).

Reaction governed by the acid-base experimental condition is only reaction 3, but there has not quantum chemical treatment   

,,,,refs and reactions discussed:

REACTION pathway 1

Caprolactam

1. Amoros, Daniel; Leconte, Philippe; Coqueret, Pierre

Patent: US2004/14965 A1, 2004

Conditions:

A medium resulting from the cyclizing hydrolysis of an aminocapronitrile obtained by hemihydrogenation of adiponitrile was treated by hydrogenation before distillation (stripping) of the ammonia. The resulting medium was treated by passing through an ion-exchange resin. The conditions for carrying out these treatments are disclosed in the abovementioned patents or patent applications and in particular in Patent Applications WO 98/05636 and FR 2 786 180. [0074] This medium comprises approximately 65percent by weight of caprolactam and exhibits the following purity characteristics [0075] Permanganate number (PNMnO4): 35 [0076] Content of volatile bases (NVB): 1.8 meq/kg [0077] UV number (NUV): 0.5 [0078] These characteristics are determined according to standardized procedures disclosed in Standard ISO 8660 for the permanganate number (PNMnO4), Standard ISO 8661 for the content of volatile bases (NVB) and Standard ISO 7059 for the UV number (NUV). With reference to FIG. 1, this medium is, in accordance with the invention, fed via the pipe 1 to the first distillation column 2, after addition, via the pipe 3, of 0.6 g of pure sodium hydroxide, in the form of a concentrated solution, per kg of caprolactam. [0079] The column 2 has a bottom temperature of less than 130° C. and a pressure of 70 mbar. [0080] The top fraction 4 is composed of water. [0081] The distillation bottom product 5 comprises an amount of water of less than 0.5percent by weight. [0082] This distillation bottom product 5 is fed to a second column 6 operating under reflux 7, 8. [0083] The top fraction 9, composed essentially of caprolactam and of compounds with a lower boiling point than that of caprolactam, is removed. The amount of caprolactam removed represents 0.5percent by weight of the caprolactam fed in. The distillation bottom product 10, comprising the caprolactam, is fed to a third column 11 also operating under reflux 12, 13. [0084] The top fraction 14 is composed of caprolactam of conformable purity. [0085] The purity characteristics are: [0086] Permanganate number (PNMnO4): 1.5 [0087] Content of volatile bases (NVB): 0.28 meq/kg [0088] UV number (NUV): 0.025 [0089] The distillation bottom product 15, composed predominantly of caprolactam and comprising, as impurities, compounds with a higher boiling point than that of caprolactam, is fed to a scraped-film evaporator 16 operating under a pressure of 10 mbar and a temperature of 150° C. [0090] The evaporated caprolactam is recycled via the pipe 17 to the third column 11. [0091] The non-evaporated products are removed via the pipe 18. [0092] The balance by weight of the caprolactam fed to the first column 2 and that produced at the top 14 of the third column 11 shows that 99.1percent of the participating caprolactam is recovered with a high and suitable degree of purity.

2. With water; aluminum oxide

T=260 - 312°C; P=760.051 Torr; 7 - 8 h; Five-stage reactor system; Product distribution / selectivity;

Invista North America S.A.R.L.

Patent: US7060820 B1, 2006 ;

Conditions:

The reactors were charged with cylindrical extrudates of γ-alumina catalyst obtained from Degussa (apparent bulk density of 0.7551 g/cm3; and BET surface area of 350 m2/g). The feed comprised 30 g/min of ACN and 30 g/min of water, WHSV of 1.0 hr-1. The system ran with inlet/exit temperatures of the five reactors at approximately 295° C./307° C., 302° C./307° C., 288° C./312° C., 296° C./300° C., and 260° C./290° C., respectively, for a total time on stream of 8 hours. The system ran at a pressure of slightly above 1 atm.The outlet from the fifth reactor was connected to the inlet of a distillation column. The vapor feed from the outlet of the fifth reactor was fed to substantially the middle of the distillation column, which was maintained at atmospheric pressure. The distillation column separated ammonia, water, and low boiling impurities from the reaction products comprising of CPL, ammonia, water, unconverted ACN, and small quantities of other low and high boiling impurities eluting from the five-stage reactor system.Ammonia, water, and low boiling impurities were condensed in a condenser attached to the top of the (Oldershaw column) and a variable portion returned to the top of the column as reflux to maintain a condenser temperature of 97° C. (reflux ratio of 0.65). The top of the condenser was connected to the vent header to discharge small quantities of non-condensible gases/vapors emanating from the distillation column.CPL, water, and other high boiling components (impurities) were collected in the reboiler (or pot) at the bottom of the Oldershaw column. The liquid product, containing CPL and approximately 25 wt. percent water, was continuously removed from the reboiler by a metering (FWI) pump and collected in a 55 gallon drum. The analyses of the liquid product showed 99.6percent selectivity to CPL and an overall ACN conversion of 95percent. The resultant 94.6percent yield of CPL remained approximately constant for the total duration of the 8-hour run. The analyses of the liquid product did not show any significant change in the impurity level compared to that at the exit of the fifth reactor.; In a manner analogous to Example 1 a second run was performed essentially under identical conditions except the feed composition was reduced to 20 g/min of ACN and 20 g/min of water. The analyses of the product collected in the reboiler/pot of the Oldershaw column showed 99.6percent selectivity to CPL and an overall ACN conversion of 98.7percent. The resultant 98.3percent yield of CPL remained approximately constant for the total duration of the 7-hour run. The analyses of the product did not show any significant change in the impurity level compared to that at the exit of the fifth reactor.

3. With water

T=120°C; chemoselective reaction;

Liu, Y.; He, L.; Wang, M.; Cao, Y.; He, H.; Fan, K. ChemSusChem, 2012, 5, 1392-1396

4. With water; dihydridotetrakis(triphenylphosphine)ruthenium(II) in ethylene glycol dimethyl ether

T=160°C; 24 h; Murahashi, S.; Naota, T.; Saito, E. Journal of the American Chemical Society, 1986, 108, 7846-7847

5. With water; aluminium, T=305°C; Du Pont de Nemours and Co.

Patent: US2357484 , 1941;

6. With zirconium, 165 h; Conversion of starting material; BASF Aktiengesellschaft, Patent: US6353101 B1, 2002

REACTION pathway 3

1. Caprolactam, J. Ritz, H. Fuchs, H. Kieczka, W. Moran, 2011 DOI: 10.1002/14356007.a05_031.pub2

Reactions 1 and 3 quantum chemistry:

7. Abraham, R.; Griffiths, L.; Perez, M. Magnetic Resonance in Chemistry, 2013, 51, 143-155

REACTION pathway 2

1. With Fe(AAEMA)3; oxygen; isobutyraldehyde in 1,2-dichloro-ethane

P=760 Torr; 36 h; Ambient temperature;

Mastrorilli, P.; Nobile, C. Tetrahedron Letters, 1994, 35, 4193-4196

2. With Na2B4O7; dihydrogen peroxide; N-benzyl-N,N,N-triethylammonium chloride in water; benzene

T=55°C; 24 h;

Pande, C.; Gupta, N. Monatshefte fuer Chemie, 1995, 126, 647-652

3. With bismuth trifluoromethanesulphonate in dichloromethane

T=20°C; Baeyer-Villiger oxidation; 0.5 h;

Alam, M.; Varala, R.; Adapa, S. Synthetic Communications, 2003, 33, 3035-3040

Reaction mechanism:

4. Miranda, M.; Deporre, Y.; Vazquez-Lima, H.; Johnson, M.; Marell, D.; Cramer, C.; Tolman, W. Inorganic Chemistry, 2013, 52, 13692-13701

Dear Nash

First, sometimes, TS approach function in gaussian 09 cannot perfectly well describe TS structure. Thus, i carefully recommend you that you may find similar reaction pathway. After that, you should build geometry by your hands. I know this is really tough things to do. Sometimes, it is very useful approach way to find TS structure.  

Second, i don't know what kind of basis set you used for TS search. Please use high level basis set with diffuse and polarization function. 

Hope this help