Chemical reaction with two different elementary transition states



The phenomenon of the elementary chemical reaction with two different transition states (TSs) between reactant and product is represented. Different examples of the reaction with two transition states were reported during the last decade. In some cases, one route is dominant, in another cases the energy of the barriers is similar, but the electronic structure of TSs are different. The Valence Bond (VB) approach provides the rationalization for the phenomenon of the chemical reaction with two TSs: the reactant and product pair is based on three dominant VB structures (anchors). The VB approach provides an opportunity to distinguish between different resonance mechanisms – different TSs. The 2D-domain is based on two minima, the reactant and the product, which are connected by two different TSs and can include the electronic degeneracy. Physical consequences of the chemical reaction with dual reaction routes are discussed. © 2014 Wiley Periodicals, Inc.


Transition state (TS) is a key point of the chemical reaction model. TS theory explains the rates of elementary chemical reactions[1] by the rate-determining TS structure.[1-4] Different models of TS[5-8] are based on the two-state approximation of TS as a reactant–product hybrid. The routine procedure for the standard program suits used an average of the reactant and product structures as an initial guess of TS (e.g., GAUSSIAN suit package code QSPT for TS location). All different TS models, de facto, do not take into account the second TS. The proposition of a unique TS based on the simple physical idea clearly expressed by Eyring: “… in general more than one such pass each corresponding to a different reaction mechanism… but … one of these passes is much lower than the others, so that reaction through the higher passes is negligible by comparison.”[9] This problem was discussed by Slanina on the formal level as an isomerism of TS.[10]

Syn-anti isomerization around N[DOUBLE BOND]N or C[DOUBLE BOND]N double bond can proceed either via a perpendicular biradical TS or an in-plane inversion TS[11] (Scheme 1). In-plane H motion provides N-atom inversion without changing chemical bonds including π-bond. Torsion leads to the •N[BOND]C• biradical transition structure by coupling of the π-bond to the two orthogonal p-Atomic Orbitals (AOs). The barrier of the biradical TStorsion is considerably higher than that of the in-plane TSinversion and, consequently, only the in-plane inversion path is an operative for the thermal syn-anti isomerization.

Scheme 1.

Two different TSs for syn-anti isomerization around C[DOUBLE BOND]N double bond.

Extensive studies of conical intersections (CIs) during the last two decades have lead to the various examples of CI escorted by two isomeric TSs. Olivucci and coworkers systematically studied cis-trans isomerization in the retinal chromophore and its models. CI surrounded by two TSs was a common topological feature for all studied retinal cases. The authors[12, 13] proposed that “TS saddles controlling thermal isomerization are split in two by a CI peak. This, ultimately, leads to the appearance of the two different TSs.”

Tishchenko et al.[14] proposed two reaction paths for the intramolecular hydrogen shift—H-atom transfer (HAT) versus proton-coupled electron transfer (PCET). Various examples of chemical reactions with two TSs were reported by the Jerusalem group (see the further discussion).

MO's Models of Chemical Reaction and Indication of Two TSs Case

Modern quantum chemistry does not have a definitive answer for the electronic structure of TS of the elementary chemical reaction. The basic quantum-mechanic two state model[15] [in this case, the one state is an initial reactant (R) and the second is a final product (P)] is a natural approach to the analysis of chemical reaction.

Correlation between R and P aims to provide the classification of the elementary chemical reaction through the analysis of Molecular Orbitals (MOs) or dominant configurations, or electronic states along reaction coordinate. The orbital symmetry conservation rules of Woodward and Hoffmann[16] and the frontier orbital concept of Fukui et al.[17] classified the chemical reactions into two groups: allowed (occupied MOs of reactant correlate with occupied MOs of product), and forbidden [Highest Occupied Molecular Orbital (HOMO) reactant correlates with Lowest Unoccupied Molecular Orbital (LUMO) product and vice versa] reactions (Fig. 1a). It could also give an indirect indication about TS, because HOMO-LUMO crossing implies a high barrier, whereas correlation between occupied MOs of R and P indicate a relatively small barrier.[16] High barrier on the ground state Potential Energy Surface (PES) of forbidden reaction represented as a result of the avoided “intended” crossing between ground and doubly exited state configurations in the case of HOMO-LUMO crossing (Fig. 1a).[18]

Silver[19] presented the hierarchy of symmetry conservation rules, taking into account both kind of symmetry conservation rules—total electronic (Wigner–Witmer rules[20] and individual orbital ones (Woodward–Hoffmann rule[16]. Longuet-Higgins and Abrahamson noticed that the MO symmetry correlation must be translated to state correlation level (Figs. 1b and 1c).[21] Of course, the feasibility of a chemical reaction depends on the relative magnitude of the electronic energy barrier and reflects the orbital symmetry characteristics of R and P. A three-level classification was proposed by Silver for the chemical reactions: allowed, which conserve both total and individual orbital symmetry; forbidden conserve total, but not individual orbital, and unfeasible reactions conserve neither one of them.[19]

Salem discussed the different aspects of electronic control by orbital and state symmetry.[18] In particular, it was noted that the allowedness/forbidness of the chemical reaction can be directly connected to aromatic/antiaromatic origin of TS.[22, 23] The allowed reactions with aromatic TS show strong coupling (big gap, Fig. 1b) between ground and excited state in TS region,[24, 25] whereas forbidden reactions (antiaromatic TS) have a weak coupling (small gap) (Fig. 1c).[26-28] There is no direct information about TS structure from the different reactant-product correlations. The VB method, including qualitative resonance theory,[29] declares the chemical reaction as a resonance between reactant and product. Different VB interpretations were proposed during the last 70 years.[30-32] Shaik et al. proposed avoided crossing for location of TS and presentation of electronic wave function (EWF) of TS by equivalent contributions of the reactant and product Heitler–London forms.[33]

The assumption of the unique operative TS (one reaction path) is common for all correlation models. This restriction produces dichotomy in analysis of chemical reaction: allowed or forbidden reaction[16]; feasible or nonfeasible reaction[19]; aromatic or antiaromatic TS.[22, 23] At the same time, the possibility of two different routes for the same reactant-product are rejected.

Nonetheless, the electronic state correlation can give a hint of the second TS of the chemical reaction. The crossing between ground state and first excited state is possible in the case of chemical reaction with a weak coupling in a crossing area. Small S0S1 gap creates the opportunity for the crossing along the second coordinate (Figs. 1c vs. 1d). Teller[34] discussed the general case of two state's crossing along two coordinates using perturbation theory. This approach was followed by most subsequent workers[35] who introduced various parameters to describe the interactions between the two states.

The Electronic Structure's Precondition for the Two Different TSs for the One Elementary Reaction

The PES can be partitioned into elementary two-dimensional (2D; two-or three-legged) domains[36, 37] using the elementary reaction coordinates. The dominant VB structures define not only reactant and product but also the TS structures between them.[32, 33]

This approach was applied previously for locating CI region through the analysis of the ground state PES.[38, 39] This model is based on the extension of the Longuet-Higgins sign-change theorem[40] by the use of elementary reaction coordinates.

Three different Lewis structures are the minimal number of anchor VB forms for describing 2D-domain on the PES. All anchors (A, B, and C) connected by elementary reaction coordinate through three different TSs: (AB), (AC), and (BC) (Scheme 2a). Herzberg and Longuet-Higgins used the example of (H + H2) three-legged 2D-domain as a case study for the presentation of electronic degeneracy and topological features of the EWF.[40a] Later, this approach was applied to the general molecular three-legged 2D-domain case.[38, 39]

Scheme 2.

Different types of 2D-domain describing by three-state (VB anchors) system: (a) three-legged domain—three minima (A, B, and C) connected by three elementary reaction paths; (b) two-legged domain—two different isomers (A and BC) connecting by two equivalent TSs—(AC) and (AB); and c) two-legged domain—two equivalent isomers AC and AB connecting by two different TSs—(A) and (BC). Coordinates Q+ and Q are in-phase and out-of-phase combinations of two independent reaction coordinates.

Three dominant VB structures can produce two-legged domain. For example, if one minimum is described by one anchor A and the second one by combination of B and C (Scheme 2b). Two isomeric TSs are equivalent if B and C structures contribute equivalently to the second minima (B↔C). PES's topography can be turned over. (A, C) and (A, B) combinations could be two equivalent minima, whereas two different TS are (A) and (BC) structures (Scheme 2c). Scheme 2b represents the situation, where one reaction coordinate leads to the reduction of C contribution and as a result TS AB is a resonance between A and B only, whereas AC TS annihilates the contribution of B and leads to A↔C resonance. Thus, Scheme 2b shows an example of reaction with two equivalent isomeric TSs. All reaction coordinate loops could be a phase preserving or phase inverting and, consequently, include degeneracy or not. The critical points of such 2D domain are connected to its highest point, which can be second-order saddle point or the degeneracy between the ground and first excited states.[41]

VB approach provides a lucid rationalization of the chemical reaction with two TSs phenomenon. This is a crypto three-state system—reactant and product pair based on three VB anchors. VB approach allows us to distinguish between two different TSs, because it takes into account different resonance possibilities.

Chemical Reactions with Two Different Paths between Reactant and Product

Cis-trans isomerization around polar double bond is an important and well-documented example of the chemical reaction with two TSs. Reactant and product are differ by the covalent component C1 (cis) versus C2 (trans), whereas a third term, polar form (Z), is common to both (Scheme 3).

display math(1a)
display math(1b)
Scheme 3.

Three dominant VB contributions describing cis- and trans-isomers of molecules with a polar double bond: two covalent contributions C1 (cis), C2 (trans), and a polar form Z (common for both isomers).

Let us propose that covalent and polar forms have similar contributions to the polar double bond. It means that transition from reactant to product could be or out-of-phase combination (2a) or in-phase combination (2b) according to VB crossing model

display math(2a)
display math(2b)

Out of phase combination (2a), TS is a biradical covalent form without polar contribution. TS+ has a dominant polar contribution and can be defined as zwitterion. This kind of dual reaction routes was discovered for different molecules with C[DOUBLE BOND]C[42, 43] and C[DOUBLE BOND]N[44] polar bonds.

For example, quantum-chemical calculations of 4-cyclopentadienylidene-1,4-dihydropyridine (CPDHP)[42a] show that the polar TS and biradical TS are very different in electronic distribution (μ = 16.3D for zwitterion versus μ = 2.2D for biradical), whereas the barriers for both processes are very similar −ΔE = 47.2 kcal/mol (polar) versus ΔE = 44.8 kcal/mol (biradical). The relative contribution of covalent versus polar forms may be changed by solvent or electric field effects, which leads to extra-stabilization of zwitterionic TS up to conversion of nonpolar biradical TS to excited state.[42a] The theoretical prediction that the fluorescence lifetime is considerably shortened on lowering the polarity of the solvent due to tuning of the CI properties, was fully confirmed.[45, 46] This constitutes direct experimental evidence of a previously predicted tunable property of a CI by manipulation of TSs surrounding this CI.[42]

Two different TSs, biradical and charge-shifted control the thermal isomerization of protonated Schiff base to the all-trans isomer, were reported by Olivucci during last decade studies. Very convincing computational study[47] of 11-cis retinal protonated Schiff base show the biradical TS structure with positive charge localized in the Schiff base region. In contrast, charge transferred TS has its charge shifted to the β-ionone region. Calculations find that charge shifted TS lies 11 kcal/mol in energy below biradical TS. The reason that the barrier controlling thermal noise in rod photoreceptors correlates with the color of absorption of the photoreceptor is due to the existence of two electrically different TSs, one of which has similar electronic character to that of the vertically excited species.[47]

Chemical Reaction with Two Equivalent (Isomeric) TSs between Reactant and Product

Experimentally studied heterosubstituted bicyclo[2.1.0]pentanes exist in two forms—open and closed isomers (Fig. 2a). Closed form is more stable in the case X = O[48]; but aza-derivative X = NR[49] prefer the open ylide form (see, also an extensive discussion by Huisgen[50].

Figure 1.

One coordinate correlation (a) MO correlation; (b,c) state correlation: (b) strong coupling case/Aromatic TS, (c) weak coupling/ Antiaromatic TS; (d) weak coupling along reaction coordinate and possible crossing along second coordinate.

Figure 2.

(a) Open ylide—bicyclo[2.1.0]-pentane ring closure; (b) MO correlation diagram; (c) two reaction paths 2D domain between closed and open ylide forms (CAS calculations[51]; and (d) three dominant VB forms—1,3-DIRADICAL and two mirror ylide (zwitterionic) forms—YLIDEL and YLIDER.

This three-membered ring cyclization is a forbidden reaction according to the Woodward–Hoffmman rules, HOMO of the open form correlates with LUMO of closed form and vice versa (Fig. 2b).

High-level ab initio calculations show that closed and open forms are separated by ∼40 kcal/mol barrier. This is asymmetric TS (two equivalent isomeric left/ right TS) with one long and one short N[BOND]C bond[51] (Fig. 2c). 1,3-Singlet diradical describes a closed form, but it contribute also to the open form—1,3-DIRADICAL.[51] In-phase combination of two mirror zwitterionic (YLIDEL + YLIDER) forms is a dominant contribution to the open form. The transition from the open to the closed isomers leads to distortion along the antisymmetric Q coordinate, the loss of effective YLIDEL↔YLIDER resonance, and asymmetric domination of one of ylide forms in corresponding TS (Figs. 2c and 2d). The EWF along two reaction coordinates loop {Closed form → TSL → Open form → TSR → Closed form} preserves a sign, which was checked by analysis of a contribution of the leading configurations at different points on the loop.[51] No CI inside this 2D domain. Second-order saddle point inside this 2D domain connects the four structures—closed and open isomers and two TSs.

The allyl-cyclopropyl pair is an analog of ylide-bicyclo[2.1.0]pentane system. Both reactions have a two equivalent low-symmetry TSs. The principal difference is that allyl-cyclopropyl 2D domain includes CI in contrast with above discussed ylide—bicyclo[2.1.0]-pentane case. Allyl-cyclopropyl cyclization was proposed by Longuet-Higgins and Abrahamson[21] as a case study to show the limitation of MO correlation and the necessity to use the state correlation approach. In particular, allyl-cyclopropyl electronic state correlation shows the crossing between reactant and product EWF along the symmetric coordinate keeping two C[BOND]C bonds equivalent. Moreover, the crossing occurs in both cases, conrotatory as disrotatory one, in undoubted contradiction to the Woodward–Hoffmann rules.[16] Quantum-chemical calculations of allyl-cyclopropyl cyclization show nonsymmetric TSs with one long and one short C[BOND]C bond.[52]

Two Different Reaction Routes between Reactant and Product: Two Different Resonance Schemes

Propane cation-radical C3 math formula was studied by ESR spectroscopy. Experimental data and quantum-chemical calculations agree with a localization of positive charge on the elongated one-electron C[BOND]C bond.[53, 54] The lowest charge-transfer TS between two minima I and II involves three electrons on three centers (3e/3c resonance) (ΔE = 4.7kcal/mol). It describes as an anticombination of the reactant I and product II VB forms. VB structure with charge localized on the C[BOND]H (III) bond is not realized as a ground state minima, but this is a dominant contribution for the alternative charge shift TS (ΔE = 13.0 kcal/mol). Second, TS is result of two resonances between III and I and III and II. So, this interaction includes conjugated pair of 3e-3centers resonances—five electrons on four centers (5e/4c resonance). Two different TSs for the charge shift in the case of propane radical cation is a relic of three state system covering 2D domain between two propane cation radical minima I and II (Fig. 3).[54]

Figure 3.

Propane cation radical [H3CCH2CH3]+ 2D domain on the PES. This system is described by three dominant VB structures I, II, and III. Two different routes are connected two ground state minima I and II.[54]

Singularity of the Chemical Reaction with Two TSs

Thermal chemical reaction with two different TSs does not differ from the usual (one TS) ground state reaction with one dominant route. This is a case when both processes, thermochemical and photochemical, lead to the same result (single product). It was shown earlier on the computational level[12, 13, 42, 43, 47] and verified experimentally.[45, 46] Both of the routes, a photochemical as thermal reaction, can be manipulated by the solvent. Solvent tuning of a CI process is a direct result of effective influence on a zwitterion TS. Lowering of the zwitterion TS barrier means the accelerating of thermal reaction, but it leads to the opening S0S1 gap and consequent delay of photochemical reaction. Of course, solvent effect can change also the preferable thermal reaction mechanism by changing the relative barrier heights as was proposed earlier.[42] Both processes, the thermal versus photochemical routes, are possible. No dichotomy in this case.


Various examples of the reaction with two TSs were reported during the last decade: cis-trans isomerization around a polar double bond; charge shift processes; HAT vs. PCET reactions; and so forth. Intensive studies of the photochemical reaction going through the CI led to discovery of some examples of chemical reactions with two different TSs. Usually, the computational study of the chemical reaction is restricted by the search of a single TS only. The key problem is identification of the chemical reaction with two reaction paths. Traditional approaches to the electronic structure analysis of chemical reactions (such as correlation diagrams, symmetry selection rules, aromatic vs. antiaromatic TS, etc.) cannot provide an indication for the chemical reaction with two TSs. VB analysis, which can select the dominant VB forms (anchors) on the PES, can provide the criteria for the chemical reaction with two elementary routes. Chemical reaction with two TSs described by the crypto three-state system—reactant and product pair based on three VB anchors. The VB approach allows selection of the chemical reactions with a possible dual reaction path and distinguishing between two different TSs, because it takes into account different resonance possibilities.

The obvious feature of the dual reaction path is a connection between thermal and photochemical routes. Their common basis is the 2D origin of these reactions. The competition between two thermal routes can provide the manipulation of the reaction mechanism by different physical factors.


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    Shmuel Zilberg studied chemistry at the Lomonosov Moscow State University. He received PhD in the Zelinsky Organic Chemistry Institute (Moscow, Academy of Sciences) in 1983. In 1994, he went to the Hebrew University of Jerusalem, where he is currently researcher associated with the Lise-Meitner-Minerva Center of Computational Quantum Chemistry. His research interests lie in the theoretical photochemistry, electronic structure of excited states, non-Lewis molecules, charge transfer, and VB interpretation of chemical processes. [Color figure can be viewed in the online issue, which is available at]