MRMP2, CCSD(T), and DFT Calculations of the Isomerization Barriers

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MRMP2, CCSD(T) and DFT Calculations of the Isomerization Barriers for the Disrotatory and Conrotatory Isomerizations of 3- Aza-3-Ium-Dihydrobenzvalene, 3, 4-Diaza-3-IumDihydrobenzvalene and 3, 4-Diaza-Diium-Dihydrobenzvalene Jeffery D Veals, Kimberley N Poland, William P Earwood, Spencer M Yeager, Kari L Copeland, and Steven R Davis J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b08227 • Publication Date (Web): 31 Oct 2017 Downloaded from http://pubs.acs.org on November 4, 2017

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The Journal of Physical Chemistry

MRMP2, CCSD(T) and DFT Calculations of the Isomerization Barriers for the Disrotatory and Conrotatory Isomerizations of 3aza-3-ium-dihydrobenzvalene, 3, 4-diaza-3-ium-dihydrobenzvalene and 3, 4-diaza-diium-dihydrobenzvalene

Jeffrey D. Veals†,1, Kimberley N. Poland1, William P. Earwood1, Spencer M. Yeager††,1, Kari N. Copeland2, and Steven R. Davis1* 1

Department of Chemistry and Biochemistry, University of Mississippi, University, MS, USA 2

Division of Mathematics and Sciences, Allen University, Columbia, SC, USA

Abstract The isomerizations of 3-aza-3-ium-dihydrobenzvalene, 3,4-diaza-3-ium-dihydrobenzvalene, and 3,4-diaza-diium-dihydrobenzvalene to their respective cyclic-diene products have been studied using electronic structure methods with a multiconfigurational wavefunction and several single reference methods. Transition states for both the allowed (conrotatory) and forbidden (disrotatory) pathways were located. The conrotatory pathways of each structure all proceed through a cyclic intermediate with a trans double bond in the ring: this trans double bond destroys the aromatic stabilization of the π electrons due to poor orbital overlap between the cis and trans π bonds. The 3, 4-diaza-3-ium-dihydrobenzvalene structure has C1 symmetry, and there are four separate allowed and forbidden pathways for this structure. The 3-aza-3-iumdihydrobenzvalene structure is Cs symmetric, and there are two separate allowed and forbidden pathways for this structure. For 3, 4-diaza-3, 4-diium-benzvalene, there was a single allowed and single forbidden pathway due to the C2v symmetry. The separation of the barrier heights for all three molecules was studied, and we found the difference in activation barriers for the lowest allowed and lowest forbidden pathways in 3, 4-diaza-3-ium-dihydrobenzvalene, 3-aza-3-ium-

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dihydrobenzvalene, and 3, 4-diaza-diium-benzvalene to be 9.1, 7.4, and 3.7 kcal/mol, respectively. The allowed and forbidden barriers of 3, 4-diaza-diium-dihydrobenzvalene were separated by 3.7 kcal/mol, which is considerably less than the 12-15 kcal/mol expected based on the orbital symmetry rules. The addition of the secondary ammonium group tends to shift the conrotatory and disrotatory barriers up in energy (approximately 12-14 kcal/mol (conrotatory) and 5-10 kcal/mol (disrotatory) per secondary NH2 group) relative to the barriers of dihydrobenzvalene, but there is negligible effect on E, Z to Z, Z isomerization barriers, which remain in the expected range of > 4 kcal/mol.

†

Current address: U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005.

††

Undergraduate REU student at the University of Mississippi. Current address: Temple

University, Philadelphia, PA. E-mail

addresses:

[email protected],

[email protected], [email protected],

[email protected].

2


[email protected], [email protected],

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1. INTRODUCTION The strained tricyclic molecule, tricyclo[3.1.0.02,6]hexane (dihydrobenzvalene) has received interest for its potential use as a high energy density material.1,2,3 Previously, the isomerization of dihydrobenzvalene4 (dhb) and two of its aza-derivatives, 3-aza-dihydrobenzvalene (3-azadhb) and 3,4-diaza-dihydrobenzvalene (3,4-diaza-dhb),5 to their respective Z, Z-diene products was found to be initiated through either a Woodward-Hoffman6 allowed or disallowed pericyclic bond-breaking process. This isomerization was found to occur through rupturing of two bonds in the bicyclobutane moiety of these molecules. For dhb,4 the allowed conrotatory bond breaking process was found to occur with a barrier of 42.9 kcal/mol which was 11.4 kcal/mol lower than the forbidden disrotatory barrier. For 3-aza-dhb and 3, 4-diaza-dhb, there were more possible pathways due to the reduced symmetry of these structures. The conrotatory barriers of 3-aza-dhb and 3, 4-diaza-dhb were calculated to range from 35.6-42.2 kcal/mol and 32.0-41.6 kcal/mol, respectively. However, the disrotatory barriers of 3-aza-dhb and 3, 4-diaza-dhb ranged from 47.0-56.1 kcal/mol and 50.4-52.9, respectively. The difference in the allowed and disallowed barriers ranged from 4.8-20.5 kcal/mol for 3-aza-dhb and from 8.8-20.9 kcal/mol for 3, 4-diazadhb.5 The presence of the nitrogen heteroatom afforded a lower conrotatory ring opening barrier for both “aza” structures relative to dhb. Also, these two cases demonstrated the possibility of “tuning” the allowed-disallowed barrier gap for the pericyclic reactions in these systems. These effects were suggested to possibly be due to the presence of the lone-pair on nitrogen as well as the nitrogen atom being more electronegative than carbon. The barrier lowering effects of the lone-pair are in agreement with similar arguments for barrier lowering in benzvalene and 3, 4-

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diazabenzvalene,7 which both have π electrons that can conjugate with the orbitals of the rupturing bond in the saddle point structures associated with the pericyclic pathways. Presently, we have extended the previous work on heteroatoms5,7 to include a secondary ammonium ion group (-(NH2)+-). The effort to further understand the allowed and disallowed nature of the conrotatory and disrotatory processes in the thermal isomerization of these systems has led to the consideration of 3-aza-3-ium-tricyclo[3.1.0.02,6]hexane (3-aza-3-ium- dhb), 3,4diaza-3-ium-tricyclo[3.1.0.02,6]hexane

(3,4-diaza-3-ium-dhb)

and

3,4-diaza-diium-

tricyclo[3.1.0.02,6]hexane (3,4-diaza-diium-dhb) where the nitrogen atom lone pair is localized into a N-H bond through the NH2+ moiety. These structures should help gain insight into what effects a formally charged nitrogen will have on the isomerization barrier. Also what happens when you have an electronegative atom, but no lone pairs for resonance stabilization? These structures are isoelectronic with dhb so it will be interesting to see how far the isomerization properties and activation barriers deviate from each other. The pathways reported here are summarized in Figure 1 and include the allowed and forbidden channels for each. Also, for the allowed channel, the E,Z-diene is formed as an intermediate to the Z,Z-diene product. We performed electronic structure calculations using multi-reference wavefunction methods. Previously, this approach was found to be needed to correctly describe a number a key transition states, particularly for the disrotatory pathways and the trans to cis π-bond rotation. Since the conrotatory pathways were previously found to be well described at the QCISD(T) and CCSD(T) levels,5,7 we also performed energy calculations using several popular density functional theory methods to assess their performance for these types of isomerization reactions.

2. COMPUTATIONAL DETAILS

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To determine the pathways of both the conrotatory and disrotatory channels, it was necessary to use a multiconfigurational wavefunction. These MCSCF calculations were performed using the GAMESS quantum chemistry program.8 The active space consisted of the σ and σ* orbitals in the bicyclobutane moiety of the reactant comprising 5 occupied and 5 virtual orbitals, making a MCSCF(10,10) subset for the complete active space calculation. The orbitals were chosen for inclusion into the active space by localizing the Hartree–Fock orbitals using the Edmiston– Ruedenberg9 method or Boys10 criteria. Virtual orbitals were constructed using the valence virtual orbitals method in GAMESS. These orbitals are constructed by projecting atomic and valence orbitals onto the Hartree–Fock orbitals so the resulting orbitals are valence in character.11,12 When difficulties arose choosing virtual orbitals, when the localization methods did not produce distinct virtuals relating to specific C–C bonds, appropriate virtual orbitals were constructed from the occupied orbitals by changing the appropriate signs of the primitive orbital expansion coefficients. Since the transition states each belong to the C1 point group, we were not concerned with constructing virtuals that belonged to the proper symmetry point group of the parent molecule, so this made the construction easier. During the course of the isomerization, two C–C σ bonds break, and two C=C π bonds are formed, and these orbitals naturally stayed in the active space. Geometry optimizations to locate stationary points were performed at the MCSCF(10,10) level using the cc-pVDZ13 basis set, and harmonic frequencies were calculated at the same level to confirm the nature of the stationary points and to obtain ZPE corrections. Analytic gradients were used for the geometry optimization searches and the harmonic frequencies. All transition states had only one imaginary harmonic frequency. Dynamic electron correlation was included by performing single point energies at the single state second-order MRMP level (MRMP2)14,15

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at the MCSCF optimized geometries. The cc-pVDZ13 and cc-pVTZ16 basis sets were both used for the single point MRMP2 calculations at the minima and transition states. Intrinsic reaction coordinates17 were calculated for each pathway to verify that saddle points connected the expected reactant and product structures. They were also used to follow the geometries of the reactants through the isomerization pathways to help understand the differences in barrier heights and strain energy release. Energies at the CCSD(T) level were computed for each structure and transition state at the MSCSF optimized geometries. Broken spin symmetry wavefunctions were used and energies calculated at the unrestricted UCCSD(T) level to better describe singlet biradical character of the transition states. Activation barriers at both the CCSD(T) and UCCSD(T) levels were calculated using the restricted CCSD(T) energies for the reactants. Single point energies were calculated using DFT including the M06, M062X, B3LYP, B3LYP-D3, BMK, and PBEPBE-D3 functionals and the cc-pVTZ basis set using GAMESS8 or Gaussian 09.18 These were performed at the MCSCF optimized geometries. For the disrotatory transition states with substantial singlet biradical character, unrestricted calculations were performed with the functionals using a broken spin symmetry wavefunction. The activation energies were calculated using the energy from the restricted wavefunction for the reactants.

3. RESULTS AND DISCUSSION The structures discussed here progress naturally from those of 3-aza-dihydro-benzvalene and 3, 4-diaza-dhb, which themselves were natural extensions of their all carbon analogue dhb. We can study trends associated with the nitrogen atoms by analyzing these structures. It will allow a view of what happens when there are polarized bonds in the system but in the absence of the lone

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pair. The polarization of the bonds may have an effect on the activation barriers. This could be due to inductive electron withdrawing effects of the ammonium nitrogen. For the following discussion, all reaction pathways considered were initiated by C-C bond rupture of a C-C σ-bond of the bicyclobutane moiety. The initial bond cleavage can occur through conrotatory (allowed) or disrotatory (forbidden) channels. Because the bonds break in a nonsynchronous manner, this leads to four pathways in each channel that are determined by which bond pair breaks and in which order the two bonds in the pairs cleave. There can be up to four unique pathways if the reactant possesses no symmetry or as few as one unique pathway for high symmetry reactants. For consistency, we have used the same numbering scheme of previous work.5 3.1 3-Aza-3-ium-dihydrobenzvalene The molecular structures of 3-aza-3-ium- dhb (1) and its Z, Z-cyclic product, 3-aza-3-ium-Z, Zproduct (2), along with their respective numbering schemes are shown in Figure 2. Structure 1 is similar to the 3-aza-dhb structure; however, the secondary NH group is replaced with a secondary NH2+ group as shown in Figure 2. This removes the lone pair that was able to potentially conjugate with one of the orbitals of the rupturing C1-C2 or C2-C3 sigma bonds as the conrotatory or disrotatory saddle points were formed in 3-aza-dhb, and it lends to inductive electron withdrawing effects through the sigma framework. This effect is likely to be most pronounced when the initial C-C bond breaks near the nitrogen (i.e. bond C1-C2 or bond C2C3). A schematic diagram for the reaction pathways is shown in Figure 3. 3.1.1 Conrotatory Pathways. Due to Cs symmetry, there are two unique conrotatory pathways of 3-aza-3-ium-dhb. One pathway is initiated by bond rupture of a C-C bond in the bicyclobutane moiety near atom N1 (either C1-C2 or C2-C3) and the other is initiated by a C-C

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bond rupture near atom C5 (either C1-C4 or C3-C4) as shown in Figure 2. The conrotatory saddle point structures, E, Z-intermediates, and E, Z to Z, Z saddle point structures as well as their respective numbering schemes are shown in Figure 2. The activation barriers for the conrotatory, disrotatory, and E, Z to Z, Z saddle points are presented in Table 1. The conrotatory barriers in 3-aza-3-ium- dhb range from 52.1-54.4 kcal/mol at the MRMP2 level. This indicates that there are no barrier lowering affects due to conjugation relative to dhb where the conrotatory barrier is 42.9 kcal/mol. The presence of the secondary ammonium group in the 3position of the ring has caused an increase of over 10 kcal/mol in the conrotatory barrier compared to dhb. The geometries of TSconA and TSconB are closely related as shown in Figure 4. The C1-C2 bond that is ruptured first in TSconA has a length of 2.431 Å, while the C1-C4 bond in TSconB has a length of 2.433 Å. The second bond that ruptures (C3-C4 in TSconA and C2-C3 in TSconB) has lengths of 1.804 Å and 1.838 Å in TSconA and TSconB, respectively. The bonds that will become double bonds (C2-C3 and C1-C4 in TSconB; C2-C3 and C1-C4 in TSconA) are slightly shorter in TSconB. This is indicative of TSconB being a slightly later (more productlike) transition state than TSconA, which can help explain the slightly lower barrier of TSconA (earlier transition states tend to have lower barriers). The conrotatory transition states lead to the E, Z diene intermediates EZA and EZB as shown in Figure 4. These structures are unique because of the strained trans-double bond in the cyclic ring. It was shown previously4 that because of the excess ring strain these type π bonds only require a small amount of energy to rupture (i.e. on the order of a few kcal/mol). The EZ saddle point structures are shown in Figure 4. TSezA and TSezB have activation barriers of 1.3 kcal/mol and 3.0 kcal/mol relative to their respective intermediates, EZA and EZB. These

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activation barriers are in agreement with previous work on related structures. From this, we see that the ammonium group does not seem to have any noticeable effect on this barrier. This could possibly be due to the π-bond not being affected to any noticeable degree by inductive electron withdrawing effects, which are expected to primarily occur through the sigma bond framework. 3.1.2 Disrotatory Pathways. There are two unique disrotatory pathways for this structure, and similar to the conrotatory pathways, they depend on which bond ruptures first. The saddle point structures for the concerted disrotatory pathways are shown in Figure 4. One pathway will be initiated by bond rupture of a C-C bond in the bicyclobutane moiety near atom N1 (either C1C2 or C2-C3) and the other will be initiated by a C-C bond rupture near atom C5 (either C1-C4 or C3-C4). The initial rupture of bond C1-C2 leads to TSdisA. This pathway has a barrier of 62.3 kcal/mol at the MRMP2 level. Similarly, the saddle point, TSdisB, has a barrier of 61.2 kcal/mol. Although these saddle points are nearly isoenergetic, saddle point TSdisB is slightly favored. When compared to the disrotatory pathway of dhb, these saddle point structures require 6.9-8.0 kcal/mol more energy. So similar to the conrotatory cases the presence of the secondary ammonium group tends to raise the activation barrier for the disrotatory pathways relative to dhb. The key geometric features of both these saddle points are similar. The initially ruptured bond has a length of 2.529 Å and 2.555 Å in TSdisA and TSdisB, respectively. The secondary bond has a length of 1.563 Å and 1.558 Å in TSdisA and TSdisB respectively. There is no clear indication of either structure being an earlier or later transition state. It was previously reported4 that the lengths of the primary and secondary rupturing bonds of the disrotatory saddle point of dhb were 2.544 Å and 1.563 Å, respectively. Our values for this present structure are very close

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to the values reported for dhb, and this suggest that the relative energetic differences of the current structure with respect to dhb are likely not due to simple geometric differences between the respective saddle points. 3.1.3 Natural Orbital Occupation Numbers. We get an idea of the multiconfigurational nature of the structures by examining the NOONs of the active space which consists of orbitals 18-27. The minimum energy structures 1 and 2 are not multi-configurational. The intermediates EZA and EZB (Figure 4) have a moderate degree of multiconfigurational character due to the strained trans double bond in the ring. For EZA, the NOONs are 1.782 and 0.226 for orbitals 22 and 23, respectively; for EZB they are 1.805 and 0.199. TSconA and TSconB are also moderately multiconfigurational with a NOON for MO 22 of 1.786 for TSconA and 1.819 for TSconB. In contrast, the TSezA and TSezB E, Z to Z, Z saddle points are significantly more multiconfigurational. The NOONs for MO22 range in value from 1.364-1.390 for these transition states. This is due to the rotation of the π-bond and the reduced orbital overlap in these saddle points as shown in Figure 4. The NOONs for the disrotatory saddle points are even more multiconfigurational with NOONs for MO22 and MO23 ranging in value from 1.007-1.051 and 0.966-1.005. This indicates that each of these disrotatory saddle points is a nearly perfect singlet biradical. 3.1.4 Coupled Cluster Energies. The activation barriers calculated at the CCSD(T) are close to the MRMP2 results for TSconA and TSconB being less than 3 kcal/mol higher. However, for TSdisA it is 7 kcal/mol higher and for TSdisB it is 46 kcal/mol higher. Using a spin symmetry broken wavefunction brings the results much more in line with the MRMP2 values being only 1 kcal/mol higher for both TSdisA and TSdisB. The UCCSD(T) values make the barrier deviate more for TSconA rising an additional 5 kcal/mol (10 kcal/mol absolute) above the MRMP2

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value. The UCCSD(T) values align with the energy ordering of the MRMP2 values for the TSdis and TSez transition states, but not for the two TScon saddle points. The restricted CCSD(T) energies do give the correct ordering, though as predicted by the moderate level of multiconfigurational character for the two TScon saddle points.

3.2 3, 4-Diaza-3-ium-dihydrobenzvalene The Structures and numbering scheme of 3, 4-diaza-3-ium-dihydrobenzvalene (3) and its ZZproduct (4) are shown in Figure 6. Structure 3 is similar to that of both the 3, 4-diaza-dhb and structure 1, but it has a secondary ammonium atom at the 3-position of the ring and a secondary amino nitrogen at the 4-position in the ring. It can be seen that this structure lacks symmetry and therefore will not have any degenerate conrotatory or disrotatory pathways. Thus, there are both four unique conrotatory and four unique disrotatory possibilities. The saddle points and intermediates associated with the isomerization of 3 to 4 have been denoted with a prime symbol (′) to distinguish them from the structures associated with the isomerization of 1 to 2. A schematic diagram for the reaction pathways is shown in Figure 7. 3.2.1 Conrotatory Pathways. The four conrotatory saddle points, EZ intermediates, and E, Z to Z, Z-saddle points along with numbering schemes are shown in Figure 8. The conrotatory saddle points range in energy from 50.9 to 55.0 kcal/mol at the MRMP2 level as shown in Table 3. The conrotatory saddle point, TSconC′ has the lowest activation barrier of 50.9 kcal/mol. TSconD′ is slightly higher in energy than TSconC′ followed by TSconA′ and TSconB′. Interestingly, saddle point TSconC (where the initial bond rupture occurs in the same orientation relative to the nitrogen lone pair, but two bonds removed) was also found to be the most favorable conrotatory saddle point for both the 3-aza-dhb and the 3, 4-diaza-dhb structures as

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reported previously5. This further suggest that breaking the C1-C4 bond first is more favorable in the structures having a sp3-hybridized nitrogen with a lone pair at the 3-position (N5 in Figure 6). Also, the energy range of the conrotatory transition states of 3, 4-diaza-3-ium-dhb is only 4.1 kcal/mol at the MRMP2 level, and the lowest activation barrier is over 50.9 kcal/mol. The presence of the ammonium group seems to decrease the gap between the individual conrotatory activation barriers relative to those of the 3-aza-dhb (6.4 kcal/mol) and 3,4-diaza-dhb (9.6 kcal/mol) structures5, and similar to the 3-aza-3-ium-dhb structure, the activation barriers of the aza–ium structures are higher than in their aza-amine analog (in this case 3,4-diaza-dhb). The geometries of the conrotatory saddle points are closely related, and they differ mainly in how the bond rupture of the bicyclobutane moiety occurs relative to the lone pair and the ammonium group (see Figure 8). For example, in TSconC′, the C1-C4 bond is 2.394 Å, the C2C3 bond is 1.808 Å, and the H-C1-C2-H dihedral angle is 161.4°. The TSconD′ structure, which is the next lowest in energy, has a C2-C3 bond length of 2.437 Å and a C1-C4 bond length of 1.849 Å. The H-C3-C4-H dihedral angle is 167.2° in TSconD′. Interestingly, the values of these key parameters are the largest for the conrotatory saddle point, TSconD′. This seemingly suggest that TSconD′ is a slightly later transition state and that it should not be more stable than TSconA′ or TSconB′ (later transition states tend to have larger barriers). One possible explanation is stabilization through lone pair resonance with the orbital on C2, as the C2-C3 bond of the reactant starts to break. It may be more favorable to have the lone pair oriented away from the bond that is breaking. This could help explain why TSconC′ is lower in energy than TSconA′. Analogously, TSconB′ may be the least favored because it would appear that the lone pair cannot effectively interact with either bond that is breaking as shown in Figure 8.

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The conrotatory transition states lead to the E, Z diene intermediates EZA′, EZB′, EZC′, and EZD′ as shown in Figure 8. These E, Z – dienes can then isomerize to 4 through rotation of the trans double bond. The E, Z intermediates range in energy from 60.5-67.5 kcal/mol relative to the ZZ product (see Table 3). Intermediate EZD′ is the most stable conformation followed closely by EZA′ and EZC′. These three structures are separated by less than 3 kcal/mol. The EZB′ structure may be more strained do to steric hindrance between the nitrogen lone pair and the H-atom bonded to C2 as shown in Figure 8. The isomerization of each EZ intermediate proceeds through a trans-to-cis saddle point structure. The isomerization barriers range from 0.7 – 3.1 kcal/mol at the MRMP2 level. The TSezB′ saddle point has the lowest barrier relative to its respective intermediate, EZB′. This supports the evidence that EZB′ is more strained than the other EZ intermediates. 3.2.2 Disrotatory Pathways. The disrotatory pathways for this 3, 4-diaza-3-ium-dhb structure are quite interesting as well. The disrotatory saddle points are shown in Figure 9. The disrotatory transition state barriers range in value from 58.3–64.7 kcal/mol (see Table 3). Similar to the conrotatory barriers, the disrotatory activation barriers have a fairly small energy range. Also, several of the disrotatory paths have activation barriers that are competitive with the conrotatory saddle points (see Table 3). TSdisA′ has the lowest activation barrier of 58.3 kcal/mol at the MRMP2 level, and TSdisD′ is nearly isoenergetic with an activation barrier of 58.8 kcal/mol. This is significant because these barriers are only ~3 kcal/mol higher than the largest conrotatory barrier as shown in Table 3. We will now look at the key geometric features. The initial C-C bond that breaks in TSdisA′, C1-C2, has a value of 2.517 Å. This structure has the shortest initial rupturing bond length of all the disrotatory transition states; however, for TSdisD′, the bond length of C2-C3 is 2.581 Å. So it

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seems to not follow the earlier transition state trend. TSdisB′, which has the largest activation barrier, has a C3-C4 bond length of 2.549 Å (this value is intermediate that of TSdisA′ and TSdisD′). One clue in support of lone pair resonance is that the C2-N1 bond is 1.428 Å in both TSdisA′ and TSdisD′. The analogous bond in TSdisB′ and TSdisC′ is 1.453 Å and 1.455 Å, respectively. The Bond is slightly shorter in TSdisA′ and TSdisD′ because the lone pair can interact better with the orbital on C2 in those structures as shown in Figure 9. 3.2.3 Natural Orbital Occupation Numbers. Based on the NOONs, TSconB′ is the most multi-configurational conrotatory transition state with MO 22 having an occupancy of 1.799. Regardless, the conrotatory transition states are only moderately multiconfigurational. In contrast, the E, Z to Z, Z saddle points are significantly more multiconfigurational. The NOONs for MO22 range in value from 1.357-1.426 for these saddle points. The NOONs for the disrotatory saddle points are even more multiconfigurational with NOONs for MO22 and MO23 ranging in value from 1.023-1.106 and 0.897-0.979. This indicates that each of these disrotatory saddle points is a nearly perfect singlet biradical. Saddle point TSdisA′ has similar multiconfigurational character as TSdisD′; however, TSdisB′ and TSdisC′ are the most multiconfigurational, and this also supports why they have the larger disrotatory activation barriers. 3.2.4 Coupled Cluster Energies. Using a restricted wavefunction, the CCSD(T) energies are close to the MRMP2 results for the four TSconA′-D′ transition states, being only 3.4 – 4.6 kcal/mol higher in activation barrier and being in the correct energetic order with TSconC′ having the lowest barrier and TSconB′ having the highest. Going to the UCCSD(T) energies, for the TSconA′-D′ saddle points, the energies get farther away from the MRMP2 results rising an additional 5 kcal/mol for each. For the four TSdisA′-D′ transition states, the UCCSD(T) energies go 10 kcal/mol too low for TSdisA′ and 18 kcal/mol too low for TSdisB′. For TSdisC′ and

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TSdisD′, the values are about 7 kcal/mol too high.

So for this set of saddle points, the

UCCSD(T) did not do as well as for the 3-aza-3-ium-dhb pathways described above. 3.3 3, 4-Diaza-diium-dihydrobenzvalene The geometry and numbering scheme of 3, 4-diaza-diium-dhb (5) and its ZZ-product (6) are shown in Figure 10. This tricyclic structure has two secondary ammonium groups and no lone pairs. The polarized bonds in this structure and the absence of lone pairs is expected to have a significant effect on the barriers relative to dhb, 3-aza-3-ium-dhb and 34-diaza-3-ium-dhb. Similar to dhb, there is only one symmetry unique conrotatory and disrotatory pathway for structure 5. Again, the saddle points and intermediates associated with the isomerization of 5 to 6 have been denoted with a double prime symbol (″) to distinguish them from the structures associated with the isomerization of either 1 to 2 or 3 to 4. A schematic diagram for the reaction pathways is shown in Figure 11. 3.3.1 Conrotatory Pathway. The conrotatory saddle point, E, Z intermediate, and the E, Z to Z, Z saddle point are shown in Figure 12a. The conrotatory pathway has an activation barrier of 67.2 kcal/mol at the MRMP2 level of theory as shown in Table 5. This is the largest conrotatory activation barrier encountered in all of the structures studied. This is significant because the same barrier in dhb is only 42.2 kcal/mol at a similar level of theory with a similar size basis set. The change in the electronic environment due to two ammonium groups being present has caused the activation barrier to be over 25 kcal/mol larger. In fact, the largest conrotatory barrier located for the 3-aza-3-ium-dhb structure was 55.0 kcal/mol (see Table 1) 12.2 kcal/mol lower. Another interesting point is that for TSconB′ of the 3, 4-diaza-3-ium-dhb structure the barrier is 12.8 kcal/mol larger than the barrier found for the conrotatory isomerization of dhb. So one trend is

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that for certain conrotatory pathways the barrier goes up by ~12 kcal/mol as you add a secondary ammonium group to the tricyclic ring system. The rupturing bond, C1-C2, has a length of 2.408 Å at the transition state. The second bond to break, C3-C4, is 1.842 Å at the transition state. The H-C1-C4-H dihedral angle is 160.0°. These values are all within the range of values that have been encountered previously. This further suggest that geometrical differences are not likely to play a large role in the increase of the conrotatory activation barrier for this structure. This conrotatory barrier leads to the EZ intermediate, EZA″. The EZA″ structure is shown in Figure 12a. This structure is 64.2 kcal/mol less stable than the ZZ-product, 6, at the MRMP2 level. This falls within the range of values seen for the EZ intermediates of structures 1 and 3 (see Tables 2 and 4). EZA″ can isomerize to structure 6 through TSezA″, and this process only requires 1.9 kcal/mol. This barrier is consistent with previous E, Z to Z, Z isomerization barriers. This further suggest that the ammonium groups have little to no effect on the barrier of this isomerization step.

3.3.2 Disrotatory Pathway. The structure of the disrotatory pathway is shown in Figure 12b. The disrotatory saddle point, TSdisA″, has an activation barrier of 70.9 kcal/mol at the MRMP2 level of theory as shown in Table 5. So it is only slightly larger (3.7 kcal/mol) than the TSconA″ at the MRMP2 level. We can look at the geometrical features to see how TSdisA″ compares with disrotatory transition states of the previous studies (see Figure 12b). The C1-C2 bond, which is the only bond broken at the transition state, has a bond length of 2.563 Å. The C3-C4 bond has a length of 1.559 Å. So it has only changed slightly from its value in the reactant structure of 1.496 Å. The

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H-C1-C4-H dihedral has an angle of 2.7°. Similar to the conrotatory transition state, the key geometrical features are close to those found in previously studied disrotatory structures. The disrotatory activation barrier is 17.0 kcal/mol higher in energy than the analogous barrier in dhb. The activation barrier for TSdisA″ is 6.2 kcal/mol larger than the activation barrier for TSdisB′ of 3, 4-diaza-3-ium-dhb. Similar to the conrotatory pathways, a trend can be seen where the activation barrier becomes progressively larger as secondary ammonium groups are added to the ring. 3.3.3 Natural Orbital Occupation Numbers. The conrotatory saddle point is only slightly multiconfigurational with NOON’s for MO 22 = 1.772 and MO23 = 0.237, and this is similar to previous results. The E, Z to Z, Z saddle point is more multiconfigurational with the NOON for MO22 being 1.405. TSdisA′′ is the most multiconfigurational species with the NOON for MO22 having a value of 1.03 and MO23 = 0.972. This again follows from the previous discussion where the disrotatory saddle point is the most multiconfigurational. The NOON values are in agreement with the NOONs of the previously studied structures. The intermediate EZA′′ is also moderately multiconfigurational due to the strained trans double bond with NOON’s for MO22 = 1.776 and MO23 = 0.229. 3.3.4 Coupled Cluster Energies. The CCSD(T) energy is within 5 kcal/mol of the MRMP2 value for TSconA′′ and the UCCSD(T) value is within 0.5 kcal/mol for the TSdisA′′ MRMP2 value. Using the unrestricted wavefunction brought the TSdisA′′ barrier down from 127.8 kcal/mol to 71.6 kcal/mol illustrating the necessity of using the unrestricted methodology for describing the singlet biradical character. 3.4 Density Functional Calculations. Six different density functionals were used to calculate the activation barriers for both the conrotatory and disrotatory transition states resulting from the

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isomerizations for all three reactants (1, 3, and 5). Single point energies were determined at the MCSCF optimized geometries since optimizations for the distrotatory transition states were unfeasible due to their singlet biradical nature. The values are listed in Table 7 and are compared to the MRMP2 values. Using a broken spin symmetric wavefunction for the conrotatory transitions states made only minor differences (a few kcal/mol) but made a large difference for the disrotatory transition states similar to the behavior of the coupled cluster energies where the UCCSD(T) values were much close to the MRMP2 values for the TSdis saddle points. For example, the TSdisA barrier went from 99.7 to 64.5 kcal/mol for the M06 functional and from 93.2 to 63.2 kcal/mol for the BMK functional. The M06 functional tended to be higher than the MRMP2 values by 10 kcal/mol for the TScon barriers as did M06-2X. However, for the TSdis barriers, both the M06 and M06-2X functionals were higher only a few kcal/mol. The one exception was for the TSdisB′ barrier where M06 was 4 kcal/mol lower than the MRMP2 value. The BMK functional followed the same trend as M06 and M06-2X. The PBEPBE-D3 functional was consistently close to the MRMP2 values. In fact, the absolute average deviation was only 2.2 kcal/mol. This is notable considering the use of the restricted wavefunction for the TScon structures and an unrestricted wavefunction for the TSdis structures for the DFT calculations. This is much closer to the MRMP2 values than even the UCCSD(T) values (Tables 1, 3, 5) with an absolute average deviation of 5.7 kcal/mol. The coupled cluster calculations recover more correlation energy than MRMP2, but the description of the wavefunction is better for the multireference method due to the single biradical character of many of the transition states, so it is pleasing that the PBEPBE-D3 functional was consistently close to the CCSD(T), UCCSD(T) and MRMP2 results.

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3.5 Reaction Characterization Considerations. While the activation barriers in the present study reflect an appropriate level of theory, molecular orbital basis, and dynamic correlation inclusion, the interpretation of the mechanism(s) which govern the differences in activation energies is, to some degree, equivocal. The traditional Woodward-Hoffman analysis, based on the conservation of orbital symmetry, suggests that the correlation of frontier orbital symmetry is the predominant factor which contributes to the noted differences in activation energy between different reaction pathways.19 In the event that a reaction proceeds with little symmetry, this distinction becomes less important. Also, while frontier molecular orbitals typically constitute the predominant interactions in electronic reorganization, other orbitals of course contribute to the nature of the reaction. Furthermore, the orbital symmetry approach looks at isolated reagents and, therefore, doesn’t invoke steric factors. Aside from these considerations, proponents of the so-called “Conceptual DFT (CDFT)” approach have argued the following: electron density is observable, in contrast to orbitals, and that the conceptual utility of an orbital scheme decreases with respect to accuracy.20 Recent literature has shown that a one particle theory, such as DFT, can provide insight into chemical reactions, which are typically treated via multireference expansions. This is due to what has been referred to as “Chemical Reactivity Theory (CRT).” It is beyond the scope of this work to treat the present systems within the context of CRT, but it is worthwhile to consider a few of the important concepts. The Woodward-Hoffman rules have recently been reinterpreted within a CDFT context.20-22 Use of the dual descriptor function20,22 and initial hardness response21,22 have both been able to recover the predictions stemming from the Woodward-Hoffman rules, using only

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DFT.

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In addition, other CDFT indices such as global hardness, electrophilicity, and

polarizability have been utilized, as well as a number of local reactivity descriptors.23 Aside from CDFT reactivity indices, other approaches can be found in the recent literature24, such as the electron localization function (ELF)25 and stress tensor trajectories26. The latter directly incorporates directional parameters and was shown to correlate real space stress tensor trajectories with the lowest total energy barrier. In the event that symmetry dominates, the traditional conservation of orbital symmetry is capable of generalizing particular orientations. On the contrary, measures which incorporate directional parameters (e.g., the QTAIM/stress tensor approach)26 offer more promise in the limit of low symmetry, highly directional chemistries. Our study used the concept of the Woodward-Hoffman rules to define an allowed conrotatory and a forbidden disrotatory pathway even though the transition states belong to the C1 point group. For structure 1, the forbidden pathway is 10.2 kcal/mol above the allowed pathway, in line with the average 12-15 kcal/mol difference found through orbital symmetry analysis. However, for structure 2, the difference between allowed and forbidden pathways is only 3.7 kcal/mol (TSconA′ and TSdisA′) and 6.5 kcal/mol (TSconD′ and TSdisD′) where the initial bond cleavage is further removed from the NH2+ group, but 9.7 (TSconB′ and TSdisB′) and 13.3 kcal/mol (TSconC′ and TSdisC′) when the initial bond breaks adjacent to the NH2+ group. One explanation is the possibility of electron delocalization of the nitrogen lone pair into the two singly occupied orbitals on the carbon atoms comprising the cleaved bond (pathways A′ and D′) lowering the barrier of the disrotatory transition state. For pathways B′ and C′, there is no lone pair available since it is being used for a N-H bond in the NH2+ group and so the

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difference in the allowed and forbidden barriers is more in line with orbital symmetry considerations. For structure 3, there is only one allowed and one forbidden pathway due to the C2v symmetry of the reactant. The energy difference between the allowed and forbidden pathways is only 3.7 kcal/mol even though there is no lone pair for delocalization. One explanation is that destabilization of the transition states occurs through the charge of the two NH2+ groups withdrawing electron density from the reacting part of the molecule, so the allowed barrier is raised relative to the forbidden barrier. This is consistent with the allowed barrier being 70.9 kcal/mol as opposed to the 54.6 and 52.3 kcal/mol allowed barriers for structure 2.

4. CONCLUSIONS The minima and saddle points associated with the isomerization the three strained tricyclic structures, 3-aza-3-ium-dihydrobenzvalene, 3, 4-diaza-3-ium-dihydrobenzvalene, and 3, 4-diazadiium-dihydrobenzvalene to their respective cyclic ZZ-products were studied at the MRMP2/ccpVTZ//MCSCF(10, 10)/cc-pVDZ level. Single point calculations were also performed at the QCISD(T)/cc-pVTZ and CCSD(T)/cc-pVTZ levels and using several popular DFT methods. The primary conclusions are as follows. • The 3-aza-3-ium-dihydrobenzvalene structure has two unique conrotatory and two unique disrotatory pathways due to Cs symmetry. The activation barriers for the conrotatory pathways range from 52.1-54.4 kcal/mol at the MRMP2/cc-pVTZ level, while the disrotatory barriers range from 61.2-62.3 kcal/mol at this level. The presence of the secondary ammonium group in the 3-position of the ring caused an increase of over 10 kcal/mol in the conrotatory barriers and an increase of over 7 kcal/mol in the disrotatory barriers of 3-aza-3-ium-dhb compared to dhb. These increases in barrier heights could be due to inductive electron withdrawing effects. The

21



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secondary ammonium had little effect on the π-bond rotation barriers, which ranged from 1.33.0 kcal/mol at the MRMP2/cc-pVTZ level. This energy range is in agreement with previous calculated results for this class of strained saddle points. • The 3, 4-diaza-3-ium-dihydrobenzvalene structure has four unique conrotatory and four unique disrotatory pathways due to C1 symmetry. The activation barriers for the conrotatory pathways range from 50.9-55.0 kcal/mol at the MRMP2/cc-pVTZ level, while the disrotatory barriers range from 58.8-64.7 kcal/mol at this level. The presence of the secondary ammonium group in the 3-position of the ring caused an increase of 8 kcal/mol in the conrotatory barriers and an increase of 5-11 kcal/mol in the disrotatory barriers of 3,4-diaza-3-ium-dhb compared to dhb. Just as for the 3-aza-3-ium-dhb, the secondary ammonium had little to no effect on the π-bond rotation barriers, which ranged from 0.7-3.1 kcal/mol at the MRMP2/cc-pVTZ level. • The 3, 4-diaza-diium-dihydrobenzvalene structure has only one unique conrotatory and disrotatory pathway due to C2v symmetry. The activation barriers for the conrotatory pathway, disrotatory, and E, Z to Z, Z-saddle points were 67.2, 70.7, and 1.9 kcal/mol, respectively, at the MRMP2/cc-pVTZ level. The presence of two secondary ammonium groups caused an increase of 24 kcal/mol and 17 kcal/mol for the conrotatory barrier and disrotatory barrier, respectively, relative to the analogous barriers of dhb. Similar to the other two cases there is negligible effect on the trans to cis activation barrier. • There was a clear increase in activation barriers with the addition of secondary ammonium groups. The presence of the ammonium groups also tends to draw activation barriers closer in energy. The energy difference between lowest energy conrotatory and disrotatory barriers were 9.1, 7.4, 3.7 kcal/mol, respectively for 3-aza-3-ium-dihydrobenzvalene, 3, 4-diaza-3-iumdihydrobenzvalene, and 3, 4-diaza-diium-dihydrobenzvalene. However, considering the energy

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difference between the least favorable allowed barrier and most favorable disallowed barrier, the energy differences were as small as 6.8, 3.3, and 3.7 for 3-aza-3-ium-dihydrobenzvalene, 3, 4-diaza-3-ium-dihydrobenzvalene, and 3,4-diaza-diium-dihydrobenzvalene, respectively. • Comparisons of ZPE-corrected energies computed using MRMP2 to those obtained using CCSD(T) shows that the higher correlation method is robust enough to overcome the mild multiconfigurational character of the EZ intermediates and the conrotatory saddle points. We found that the disrotatory pathways are quite challenging to describe at the single reference level and CCSD(T) cannot overcome the deficiencies of the RHF reference for these saddle points. However, we find that by using a broken symmetry wave function one can improve the results considerably. • The activation barriers computed using the PBEPBE-D3 functional, at the restricted level for the conrotatory pathways and the unrestricted level for the disrotatory pathways reproduced the MRMP2 values remarkably well.

ACKNOWLEDGMENTS The authors acknowledge partial financial support from the Army Research Office through an STIR grant and computer time from the Mississippi Center for Supercomputing Research. We also wish to acknowledge the Ole Miss Physical Chemistry Summer Research Program, and this material is based upon work supported by the National Science Foundation under grant no. CHE-1460568.

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Supporting Information. Cartesian coordinates for each structure, IRC plots for each transition state, Imaginary frequencies for each transition state, Natural orbital occupation numbers for the active space for each structure, Electronic energies (hartrees) for each structure for each method, zero point energies, values for the unrestricted density functional energies.

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REFERENCES (1) Christl, M.; Brüntrup, G. Reaktionen am Benzvalen: Reduktion mit Diimin und Ozonolyse, Chem. Ber. 1974, 107, 3908–3914. (2) Christl, M.; Heinemann, U; Kristof, W. Thermal Rearrangement of some endo–endo′-bridged Bicyclo[1.1.0]butanes, J. Am. Soc. 1975, 97, 2299–2301. (3) Davis, S. R.; Tan, P. L. Theoretical and Experimental Study of the Structure, Vibrational Frequencies, and Strain Energy of tricyclo[3.1.0.02,6]hexane, J.Phys. Chem. 1994, 98, 12236–12241. (4) Davis, S. R.; Nguyen, K. A.; Lammertsma, K.; Mattern, D. L.; Walker, J. E. Ab Initio Study of the Thermal Isomerization of Tricyclo[3.1.0.02,6]hexane to (Z,Z)-1,3-Cyclohexadiene through the (E,Z)-1,3-Cyclohexadiene Intermediate, J. Phys. Chem. 2003, 107, 198–203. (5) Veals, J. D.; Davis, S, R. Isomerization Barriers for the Conrotatory and Disrotatory Isomerizations of 3-aza-dihydrobenzvalene to 1,2-dihydropyridine and 3,4-diazadihydrobenzvalene to 1,2-dihydropyridazine, Comput. Theor. Chem. 2013, 1020, 127-135. (6) Woodward, R. B.; Hoffmann, R. The Conservation of Orbital Symmetry, Verlag Chemie, Weinheim, Germany, 1970, pp. 75–78. (7) Veals, J. D.; Davis, S. R. Isomerization Barriers for the Disrotatory and Conrotatory Isomerizations of 3-aza-benzvalene and 3,4-diaza-benzvalene to Pyridine and Pyridazine, Phys. Chem. Chem. Phys, 2013, 15, 13593-13600. (8) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J. et al. General Atomic and Molecular Electronic Structure System. J. Comp. Chem. 1993, 14, 1347–1363. (9) Edmiston, C.; Ruedenberg, K. Localized Atomic and Molecular Orbitals, Rev. Mod. Phys., 1963, 35, 457–464. (10) Boys, S. F. Quantum Science of Atoms, Molecules, and Solids, Academic Press, NY 1966, 253–262. (11) Lu, W. C; Wang, C. Z.; Schmidt, M. W.; Bytautas, L.; Ho, K. M.; Ruedenberg, K. Molecule Intrinsic Minimal Basis Sets. I. Exact Resolution of ab initio Optimized

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Molecular Orbitals in Terms of Deformed Atomic Minimal-Basis Orbitals, J. Chem. Phys. 2004, 120, 2629–2637. (12) Lu, W. C.; Wang, C. Z.; Chan, T. L.; Ruedenberg, K.; Ho, K. M. Representation of Electronic Structures in Crystals in terms of Highly Localized Quasiatomic Minimal Basis Orbitals, Phys. Rev. B 2004, 70, 041101-1/4. (13) Woon, D. E.; J. Thom, J; Dunning, H. Gaussian Basis sets for use in Correlated Molecular Calculations. III. The Atoms Aluminum through Argon Revisited, J. Chem. Phys. 1993, 98, 1358–1371. (14) Hirao, K. Multireference Moller-Plesset Method, Chem. Phys. Lett. 1992, 190, 374–380. (15) Hirao, K. Chem. Phys. Lett. 1992, 196, 397–403. (16) Kendall, R. A.; Thom, J.; Dunning, H.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions, J. Chem. Phys. 1992, 96, 6796–6806. (17) Gonzalez, C.; Schlegel, H. B. An Improved Algorithm for Reaction Path Following, J. Chem. Phys. 1989, 90, 2154–2161. (18) Gaussian 09, Revision D.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et. al. Gaussian, Inc., Wallingford CT, 2013. (19) Woodward, R. B.; Hoffmann, R. The Conservation of Orbital Symmetry, Angew. Chem. Int. Ed. 1969, 8 (11), 781–853. (20) Ayers, P. W.; Morell, C.; De Proft, F.; Geerlings, P. Understanding the Woodward– Hoffmann Rules by Using Changes in Electron Density, Chem. Eur. J. 2007, 13, 8240-8247. (21) De Proft, F; Chattaraj, P. K.; Ayers, P. W.; Torrent-Sucarrat, M.; Subramanian, M. E.; Girl, S.; Geerlings, P. Initial Hardness Response and Hardness Profiles in the Study of WoodwardHoffmann Rules for Electrocyclizations, J. Chem. Theory Comp., 2008, 4, 595-602. (22) Geerlings, P.; Ayers, P. W.; Toro-Labbe, A.; Chattaraj, P. K.; De Proft, F. The WoodwardHoffmann Rules Reinterpreted by Conceptual Density Functional Theory, Acc. Chem. Res., 2012, 45, 683-695. (23) Morales-Bayuelo, A. Analyzing Torquoselectivity in Electrocyclic Ring Opening Reactions

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of trans-3,4-dimethylcyclobutene and 3-formylcyclobutene through Electronic Structure Principles. Phys. Chem. Chem. Phys. 2015, 17, 23104-23111. (24) Morales-Bayuelo, A. Understanding the Electronic Reorganization in the Thermal Isomerization Reaction of trans-3,4-dimethylcyclobutene. Origins of Outward Pseudodiradical {2n +2π} Torquoselectivity. Int. J. Quantum Chem. 2013, 113, 1534-1543. (25) Becke, A. D; Edgecombe, K. E. A Simple Measure of Electron Localization in Atomic and Molecular Systems, J Chem. Phys., 1990, 92, 5397-5403. (26) Guo, H.; Morales-Bayuelo A.; Xu, T.; Momen, R.; Wang, L.; Yang, P.; Kirk, SR.; Jenkins, S. Distinguishing and Quantifying the Torquoselectivity in Competitive Ring-opening Reactions Using the Stress Tensor and QTAIM. J. Comput.Chem. 2016, 37, 2722-2733.

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Tables Table 1. Activation Barriers, Ea, for each Pathway (kcal/mol) Including ZPE Correction. Reactiona TSa

MCSCFb MRMP2c CCSD(T)d UCCSD(T)e ()

1→EZA

TSconA 54.8

52.1

57.1

62.3 (0.827)

1→EZB

TSconB

55.9

54.4

58.6

58.6 (0.782)

1→2

TSdisA

59.3

62.3

69.3

63.0 (1.013)

1→2

TSdisB

58.5

61.2

104.4

62.2 (0.847)

EZA→2

TSezA

2.6

1.3

4.4

4.5 (1.133)

EZB→2

TSezB

4.5

3.0

8.1

6.4 (1.129)

a

All geometries were optimized at the MCSCF(10,10)/cc-pVDZ level.

b

The energies are calculated at the MCSCF/cc-pVTZ level.

c

The energies are calculated at the MRMP2/cc-pVTZ//MCSCF/cc-pVDZ level.

d

The energies are calculated at the CCSD(T)/cc-pVTZ//MCSCF/cc-pVDZ level.

e

The energies of the TS are calculated at the UCCSD(T)/cc-pVTZ//MCSCF/cc-pVDZ level. The

expectation value of S2 operator is given in parenthesis.

Table 2. Relative Energies, ∆E, for Minima Structures (kcal/mol) Including ZPE Correction. Structurea MCSCFb MRMP2c CCSD(T)d EZA

66.5

60.0

64.0

EZB

64.6

58.4

61.8

1

34.9

21.3

20.9

2

0.0

0.0

0.0

a


b


c


d


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Table 3. Activation Barriers, Ea, for each Pathway (kcal/mol) Including ZPE Correction. Reactiona TSa

MCSCFb MRMP2c CCSD(T)d UCCSD(T)e ()

3→EZA′

TSconA′ 57.4

54.6

58.7

63.6 (1.028)

3→EZB′

TSconB′ 56.9

55.0

59.5

64.8 (0.994)

3→EZC′

TSconC′ 54.2

50.9

55.5

60.4 (0.931)

3→EZD′

TSconD′ 55.5

52.3

55.7

60.6 (0.995)

3→4

TSdisA′

56.6

58.3

94.7

49.5 (0.586)

3→4

TSdisB′

60.8

64.7

93.4

46.4 (0.530)

3→4

TSdisC′

61.4

64.1

120.5

71.1 (1.026)

3→4

TSdisD′

57.3

58.8

122.0

65.2 (1.019)

EZA′→4

TSezA′

2.8

2.7

4.3

4.7 (1.245)

EZB′→4

TSezB′

1.2

0.7

4.9

3.0 (1.240)

EZC′→4

TSezC′

3.1

3.1

7.7

5.8 (1.245)

EZD′→4

TSezD′

2.2

1.2

2.8

4.3 (1.246)

a


b


c


d


e



Table 4. Relative Energies, ∆E, for Minima Structures (kcal/mol) Including ZPE Correction. Structurea MCSCFb MRMP2c CCSD(T)d EZA′

69.7

62.4

65.8

EZB′

74.0

67.5

71.1

EZC′

69.8

62.9

66.6

EZD′

68.5

60.5

63.8

3

36.3

23.0

22.3

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4

0.0

0.0

0.0

a


b


c


d


Table 5. Activation Barriers, Ea, for each Pathway (kcal/mol) Including ZPE Correction. TSa MCSCFb MRMP2c CCSD(T)d UCCSD(T)e () Reactiona 5→ EZA″ TSconA″ 69.2 67.2 72.5 77.8 (0.885) 5→6 TSdisA″ 67.0 70.9 127.8 71.6 (1.017) EZA″→6 TSezA″ 2.1 1.9 3.9 4.8 (1.133) a All geometries were optimized at the MCSCF(10,10)/cc-pVDZ level. b


c


d


e



Table 6. Relative Energies, ∆E, for Minima Structures (kcal/mol) Including ZPE Correction. Structurea MCSCFb MRMP2c CCSD(T)d 27.6 12.4 11.4 5 EZA″ 72.3 64.2 67.5 0.0 0.0 0.0 6 a All geometries were optimized at the MCSCF(10,10)/cc-pVDZ level. b The energies are calculated at the MCSCF/cc-pVTZ level. c The energies are calculated at the MRMP2/cc-pVTZ//MCSCF/cc-pVDZ level. d The energies are calculated at the CCSD(T)/cc-pVTZ//MCSCF/cc-pVDZ level .

Table 7. Activation Barriers, Ea, for Selected Transitions States Calculated using various Functionals Compared to the MRMP2 Values (kcal/mol). 30


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Structurea MRMP2c M06d M062Xd B3LYPd B3LYP-D3d

BMKd

PBEPBE-D3d

TSconA TSconB TSdisAb TSdisBb TSconA′ TSconB′

63.1 63.2 63.2 62.5 61.9 65.2

55.5 56.3 61.8 60.9 54.4 57.2

TSconC′ 50.9 61.4 64.6 53.9 53.5 60.4 TSconD′ 52.3 59.9 63.2 52.0 51.5 58.7 b TSdisA′ 58.3 60.3 61.9 53.2 53.1 59.5 TSdisB′b 64.7 60.9 62.4 54.2 53.9 60.1 b TSdisC′ 64.1 65.9 67.2 59.0 58.9 64.8 TSdisD′b 58.8 66.4 67.5 59.6 59.5 65.6 TSconA′′ 67.2 80.1 83.5 72.1 71.6 78.7 b TSdisA′′ 70.9 75.5 76.6 66.1 65.9 71.6 a All geometries were optimized at the MCSCF(10,10)/cc-pVDZ level.

52.6 50.6 57.4 57.8 62.8 63.9 70.3 72.9

b

52.1 54.4 62.3 61.2 54.6 55.0

64.2 64.4 64.5 62.7 63.1 66.3

67.2 67.3 65.4 64.5 66.4 69.2

56.6 56.7 57.7 56.3 55.5 58.4

56.1 56.2 57.5 56.1 55.2 57.8

Broken spin symmetric wavefunction: S2 expectation values close to 1.0.

c


d

The energies are calculated at the DFT/cc-pVTZ//MCSCF/cc-pVDZ level.

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Figures Figure 1. Schematic summary of the reactions reported including the three reactants (structures 1, 3, and 5), the intermediates (EZA(B, C, D)), and the products (structures 2, 4, and 6).

32


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Figure 2. The structures and numbering scheme for the 3-aza-3-ium-dihydrobenzvalene structure and its ZZ product.

Figure 3. Schematic Energy Diagram for the Reaction Pathways for Structure 1.

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! " = 62.3 kcal/mol ! " = 3.0 kcal/mol ! " = 61.2 kcal/mol

! " = 1.3 kcal/mol

! " = 54.4 kcal/mol ! " = 52.1 kcal/mol E=60.0 kcal/mol

E=58.4 kcal/mol E=21.3 kcal/mol

E=0.0 kcal/mol

Figure 4. Structures of the saddle points and intermediates and their respective numbering schemes for species along the conrotatory isomerization pathways of 3-aza-3-iumdihydrobenzvalene.

34


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Figure 5. Structures and numbering schemes of the saddle points along the disrotatory pathways of 3-aza-3-ium-dihydrobenzvalene.

Figure 6. The structures and numbering scheme for the 3,4-diaza-3-ium-dihydrobenzvalene structure and its ZZ product.

35



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=64.7 kcal/mol TSdisX’ = 58.3 kcal/mol = 58.3 kcal/mol TSconX’ = 50.9 kcal/mol TSezX’ E = 67.5 kcal/mol EZX’

= 0.7 kcal/mol = 3.1 kcal/mol

E = 60.5 kcal/mol

E = 23.0 kcal/mol

E = 0.0 kcal/mol

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Figure 8. Structures of the saddle points and intermediates and their respective numbering schemes for species along the conrotatory isomerization pathways of 3, 4-diaza-3-iumdihydrobenzvalene.

37



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Figure 9. Structures and numbering schemes of the saddle points along the disrotatory pathways of 3,4-diaza-3-ium-dihydrobenzvalene.

Figure 10. The structures and numbering scheme for the 3, 4-diaza-diium-dihydrobenzvalene structure and its ZZ product.


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! " = 70.9 kcal/mol

! " = 1.9 kcal/mol

! " = 67.2 kcal/mol

E = 64.2 kcal/mol

E = 12.4 kcal/mol

E = 0.0 kcal/mol

Figure 12. a) Structures of the saddle points and intermediates and their respective numbering schemes for species along the conrotatory isomerization pathways of 3, 4-diaza-diiumdihydrobenzvalene. b) Structure and numbering scheme of the saddle point along the disrotatory pathway of 3, 4-diaza-diium-dihydrobenzvalene. 39



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TOC Graphic

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MRMP2, CCSD(T), and DFT Calculations of the Isomerization Barriers

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