A Phenomenological Symmetry Rule for Chemical Reactivity Under Vibrational Strong Coupling

Abstract

Symmetry is known to strongly influence the course of a chemical reaction. It has also been found to play a key role in vibrational strong coupling (VSC), where it can influence the outcome of chemical reactions or alter chemical equilibria. However, the precise nature of this effect and its extent remains elusive. To further explore the role of vibrational symmetry, we have investigated the equilibrium constants of different charge transfer complexes, in particular of isomers of trimethyl benzene belonging to different point groups from which a general symmetry rule emerges. We describe the strongly coupled system by a direct product of irreducible representations associated with the complexes and the cavity. As a consequence, the coupled vibration is associated with a new irreducible representation that projects differently on the reaction coordinate of the charge transfer complexation, reflecting the changes in the equilibrium constants. This phenomenological symmetry rule points to a general underlying framework for predicting the outcome of chemical reactivity under VSC.

A general symmetry rule emerges from the study of charge transfer complexes in cavities that points to an underlying framework to the predict the outcome of chemical reactivity under vibrational strong coupling.

Introduction

The role of symmetry in chemical reactivity has long been of interest to chemists, most notably as illustrated by the Woodward–Hoffman rules that predict the outcome of pericyclic reactions and correlate the molecular orbital symmetry of the reactant with that of the product.^{[ 1 ]} The symmetry of a molecule, given by its corresponding point group, affects spectroscopic selection rules, thermodynamic properties, and determines the irreducible representations of its vibrations.^{[ 2} , ³ , ⁴ , ⁵ , ⁶ , ⁷ , ^{8 ]} Molecular vibrations are crucial in the course of a chemical reaction and its dynamics,^{[ 6} , ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ^{16 ]} and as pointed out by Bader over 60 years ago, the symmetry correlation between the vibrations and the electronic manifold strongly affects the outcome of reactions.^{[ 6 ]}

Symmetry also plays a critical role in vibrational strong coupling (VSC), a new frontier of research where much remains to be understood.^{[ 17} , ¹⁸ , ¹⁹ , ²⁰ , ²¹ , ²² , ²³ , ²⁴ , ²⁵ , ²⁶ , ²⁷ , ²⁸ , ²⁹ , ³⁰ , ³¹ , ³² , ³³ , ³⁴ , ³⁵ , ³⁶ , ³⁷ , ³⁸ , ³⁹ , ⁴⁰ , ⁴¹ , ⁴² , ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ⁴⁸ , ⁴⁹ , ⁵⁰ , ⁵¹ , ⁵² , ⁵³ , ^{54 ]} In VSC, the electromagnetic fluctuations of an optical resonance, its zero‐point energy, is coupled to a given vibrational band of a molecule. As a consequence, it occurs in the dark and no external photons are injected inside the cavity. Typically, the molecular vibration of N identical molecules is coupled to a single optical mode of a cavity that gives rise to two bright light‐matter hybrid vibropolaritonic states, VP⁺ and VP⁻, and N‐1 dark states (DS), as illustrated in Figure 1. The strength of this collective coupling is directly proportional to the transition dipole moment of the coupled vibration and $\sqrt{N}$.^{[ 19} , ^{20 ]} To achieve the strong coupling regime, the energy splitting between VP⁺ and VP⁻, known as the Rabi splitting energy, must be larger than the full width half‐maximum of the vibrational band and the cavity mode. In other words, the coupling strength must overcome the dissipative processes. VSC can be achieved by direct coupling of the solute or the solvent, or alternatively, the solute can be coupled by cooperative coupling through a vibrational band of the solvent that overlaps with the vibrational band of the solute.^{[ 20 ]}

Figure 1.

a) Sketch of vibrational strong coupling (VSC) of a cavity mode with a vibration of 1,2,3 trimethylbenzene of point group symmetry C_2v forming a CT complex with an acceptor molecule (I₂); the red arrows symbolize the A₁ mode of the methyl groups that is under VSC and black arrows symbolize the representation of the vibropolariton. The latter, as described in the text, is given by the direct product between the A₁ irreducible representation and those of the transverse field (B₁(f) and B₂(f)) of the common subgroup of the molecule and the cavity mode. The reaction coordinate is perpendicular to the aromatic ring toward I₂. b) Schematic representation of the strong coupling of a vibrational transition with an optical mode that gives rise to vibropolaritonic states, VP⁺, VP⁻, and dark states DS.

One of the surprising features of the VSC is that it can lead to very large changes in chemical rates, thermodynamics, and product ratios even though the collective Rabi splitting is only $\sim k_{B}T$ and the chemical event occurs at the molecular level. Thus, the energy perturbation induced by the Rabi splitting is not responsible for the VSC induced effects. In all these experiments, the resonant nature of VSC is a crucial aspect. First, it provides a unique way to access, by the choice of the vibration, an on‐site selectivity of chemical reactions under VSC.^{[ 17} , ¹⁸ , ¹⁹ , ²⁰ , ²¹ , ²² , ³¹ , ³² , ^{33 ]} Then, as we found serendipitously, symmetry plays a fundamental role in the change in chemical reactivity induced by VSC.^{[ 17 ]} This finding was possible precisely because VSC allows for selective coupling of molecular vibrations of a given symmetry. We exploited this unique feature in the context of the charge transfer complexation of mesitylene‐I₂ and benzene‐I₂ and observed that the modification of the equilibrium constant depends only on the symmetry of the vibrational mode of the molecule resonantly coupled to the cavity mode. The type of vibration (e.g., bending, stretching, etc.) and their energy had little, if any, influence. From this resonant symmetry selection, we further demonstrated that VSC can influence the stereoselectivity of pericyclic reactions.^{[ 18 ]}

This selection in the vibrational symmetry either favored the product or not, relative to the normal uncoupled condition. At the same time, the underlying explanation for why it leads to a change in reactivity was not understood. In this article, we extend the study on donor–acceptor charge transfer complexation by comparing three isomers of trimethyl benzene of different symmetries with various acceptors. From the results emerges a phenomenological symmetry rule for the change in charge transfer chemistry and, by extension, more generally for chemical reactivity under VSC.

Results and Discussion

The experiments were conducted both inside the cavity under VSC and outside the cavity as detailed in the Supporting Information. To achieve VSC for a selected vibrational mode, the cavity must be in resonance at normal incidence. It should be recalled that modification of molecular properties is only observed under such condition.^{[ 19} , ^{20 ]} Experimentally, the two vibro‐polaritonic modes VP⁺ and VP⁻ can be seen in the IR spectrum, as illustrated in Figure 2a, when the vibrational band at 1378 cm⁻¹ of 123TMB (1,2,3 trimethylbenzene) is coupled.

Figure 2.

a) IR spectra of 123TMB (donor D)–I₂ (acceptor A) CT complex (blue) with cavity mode (red) coupled with vibrational band of A₁ symmetry at 1378 cm⁻¹. b) UV–Vis absorbance spectrum of the reactants and the CT complex in heptane. c) Evolution of the spectrum under VSC as a function of [123TMB] in heptane. d) Benesi–Hildebrand plot under VSC and compared to that outside the cavity determined from the changes in absorbance of the CT complex at the maxima at 330 nm.

Starting from stock solutions of donor and acceptor compounds, the acceptor A concentration was kept constant, whereas that of the donor D was varied to extract the relevant data as follows. When a solution of D and A are mixed, they spontaneously form a charge transfer (CT) complex:

$$\mathrm{D}+\mathrm{A}\rightleftharpoons {\mathrm{D}}^{\delta +}{\mathrm{A}}^{\delta -}$$

$$K_{\mathrm{DA}}=\frac{[{\mathrm{D}}^{\delta +}{\mathrm{A}}^{\delta -}]}{[\mathrm{D}][\mathrm{A}]}=\frac{{\mathrm{k}}_1}{{\mathrm{k}}_{-1}}.$$ (1)

DA complex has typically a new intense absorption CT band in the UV–visible, as shown in Figure 2b, for iodine (acceptor) and 1,2,3 trimethylbenzene (donor), which can be monitored to determine both the equilibrium constant (K _DA) and the absorption coefficient ε_DA of the complex by plotting the Benesi–Hildebrand Equation (2) (Figure 2d):^{[ 55} , ⁵⁶ , ⁵⁷ , ⁵⁸ , ⁵⁹ , ^{60 ]}

$$\frac{{\left[\mathrm{A}\right]}_0}{\mathrm{Abs}}=\frac{1}{{\epsilon }_{\mathrm{DA}}l}+\frac{1}{K_{\mathrm{DA}}{\epsilon }_{\mathrm{DA}}l}\left(\frac{1}{{\left[\mathrm{D}\right]}_0}\right)$$ (2)

where the [A]₀ and [D]₀ are the initial concentrations of the acceptor and donor respectively, l corresponds to the path length, Abs corresponds to the absorbance of the CT complex for varying concentrations of the donor, which is in excess compared to [A]₀. This protocol was used to analyze the consequences of VSC on the CT complexation by comparing it to the case outside the cavity as in Figure 2c,d.

Tables 1, 2 summarize the results of our study of VSC of vibrational modes of different irreducible representations for various DA complexes, using three trimethylbenzene (TMB) isomers of different point group symmetry, namely, 135, 123, and 124TMB. Clearly, patterns can be seen in how VSC affects K _DA and ε_DA. Although under normal conditions K _DA does not vary much for the three TMB isomers under complexation with I₂ (Table 1), the point group symmetry of the isomer impacts strongly the outcome of VSC experiments. For instance, upon coupling the 1378 cm⁻¹ vibrational band (─CH₃ angular deformation mode), K _DA under VSC is found to be either unchanged, increased, or decreased depending on the symmetry of the vibration of the donor. The absorption coefficient Ɛ _DA is also found to change and this is most likely related to the relative position of A and D,^{[ 17} , ^{60 ]} but this will not be discussed further as it is outside the scope of this work.

Table 1.

Complexation constants K _DA and absorption coefficients ε_DA of CT complexes of TMB isomers with I₂, measured in heptane, outside the cavity and under VSC for vibrations associated with different irreducible representations (irr. rep.).

		Outside the cavity		VSC
Acceptor	Donor	K DA	Ɛ DA	Vibr. bands (irr. rep.)	K DA	Ɛ DA
I 2	135TMB #	0.41 ± 0.02	1.44 ± 0.1	1378cm−1(A')	0.15 ± 0.02	4.70 ± 0.5
				1468cm−1(A')	0.16 ± 0.02	3.63 ± 0.4
				1609cm−1(E’ )	1.01 ± 0.1	1.52 ± 0.2
	123TMB	0.46 ± 0.05	1.05 ± 0.07	1378cm−1(A1 )	0.81 ± 0.07	0.92 ± 0.02
				1094cm−1(A1 )	0.80 ± 0.11	0.95 ± 0.05
	124TMB	0.57 ± 0.02	0.89 ± 0.01	1378cm−1(A’ )	0.52 ± 0.03	0.97 ± 0.03
				1507cm−1(A’ )	0.31 ± 0.03	1.18 ± 0.09

Absorption coefficient ε_DA 320 nm (124 TMB), 330 nm (123 TMB/135 TMB) values are given in 10⁴ mol⁻¹ L cm⁻¹. # corresponds to the results for 135 TMB and I₂ taken from Ref. 17. The point groups of the isomers are the global ones. The actual assignment of the irreducible representations for 135 TMB is based on the analysis in Ref. 61 using local symmetry. All the values are the average of 3 or more measurements.

Table 2.

Complexation constants K _DA and absorption coefficients ε_DA of 135TMB with different acceptors outside the cavity and under VSC for vibrations of both D and A and their irreducible representations (irr. rep.).

		Outside the cavity			VSC
Donor	Acceptor	K DA	Ɛ DA	D/A	Vibr. band (irr. rep.)	K DA	Ɛ DA
	# I 2	0.41 ± 0.02	1.44 ± 0.1	D	1378cm−1(A’ )	0.15 ± 0.02	4.70 ± 0.5
				D	1468cm−1(A’ )	0.16 ± 0.02	3.63 ± 0.4
				D	1609cm−1(E’ )	1.01 ± 0.1	1.52 ± 0.2
		0.26 ± 0.01	0.68 ± 0.02	D	1609cm−1(E’ )	0.38 ± 0.04	0.47 ± 0.04
				A	2253cm−1(A1 )	0.16 ± 0.01	0.81 ± 0.06
		0.23 ± 0.02	0.30 ± 0.01	A	905cm−1(B1u )	0.14 ± 0.01	0.48 ± 0.01
				D	1609cm−1(E’ )	0.29 ± 0.02	0.31 ± 0.01

ε_DAvalues are given in 10⁴ mol⁻¹ L cm⁻¹. # corresponds to the results for 135 TMB and I₂ measured in heptane from Ref. 17. The experiment with chloranil and DDQ were carried out in acetonitrile. The point groups of the molecules are the formal ones. The actual assignment of the irreducible representations for 135 TMB is based on the analysis in Ref. 61 using local symmetry. All the values are the average of 3 or more measurements.

Table 2 compares the results of VSC for three different acceptors complexed with 135TMB. In all cases, an increase in K _DA by a factor of 1.5–3 is observed when E symmetry band of the donor is directly coupled. For the bands of A and B_1u symmetry whether of the donor or acceptor, K _DA decreases to the same value within experimental error. It should be noted that in the case of 2,3‐dichloro‐5,6‐dicyanobenzoquinone (DDQ), its A₁ band is cooperatively coupled with acetonitrile. In contrast, the K _DA of 124TMB–DDQ complex remains unchanged when the 2253 cm⁻¹ band (A₁ symmetry) is under VSC (Table S4), unlike the corresponding band for the 135TMB–DDQ complex (Table 2).

In these experiments under VSC, every coupling splits a vibrational peak into two, and therefore the vibrational degrees of freedom ν_f under VSC must increase and should be rewritten as follows:

$${\nu }_{\mathrm{f}}=3n-6+n_{\mathrm{c}}$$ (4)

where n _c corresponds to the sum of the vibrations V _c that are simultaneously coupled to the cavity times the number of Rabi splittings s per coupling so n _c = ∑V _c (2s − 1). We recall that VSC can lead to more than one Rabi splitting as in ultrastrong coupling.^{[ 29 ]} In essence, the cavity brings n _c additional degrees of freedom to the coupled molecule and will thus affect the partition function. To apprehend the nature of these additional degrees of freedom, Mulliken's initial formulation of the CT complexation is inspiring^{[ 55} , ⁵⁶ , ⁵⁷ , ⁵⁸ , ^{59 ]} Mulliken describes the wavefunction of CT complexes by the mixture of two states that define the representation basis set, a neutral DA pair, and the ionic D⁺A⁻ pair (ground and excited states):

$${\mathrm{\Psi }}_i\left(\mathrm{DA}\right)=a{\phi }_0\left(\mathrm{D},\mathrm{A}\right)+b{\phi }_1\left({\mathrm{D}}^{+}{\mathrm{A}}^{-}\right)$$

$${\mathrm{\Psi }}_f\left(\mathrm{DA}\right)=c{\phi }_0\left(\mathrm{D},\mathrm{A}\right)+d{\phi }_1\left({\mathrm{D}}^{+}{\mathrm{A}}^{-}\right)$$

where, φ₀(D,A) is the nonbond wavefunction and φ₁(D⁺A⁻) is the dative wavefunction and a, b, c, and d are the mixing coefficients. These two states (φ₀,φ₁) are taken as basis wavefunctions for the complex wavefunction Ψ whose properties are entirely given by the mixing coefficients, i.e., the components of the complex wavefunction projected on this basis. These mixing coefficients depend on the orbital symmetries involved^{[ 58 ]} and must also be vibration symmetry dependent, in agreement with Bader,^{[ 6 ]} who pointed out the importance of the vibrational symmetry in chemical reactivity. The significant change of the complexation constants under VSC must imply a modification of the degree of charge transfer in the complex reflecting in modified mixing coefficients (a, b, c, and d), manifesting the fact that the initial vibronic states have become vibropolaritonic states under VSC.

We boldly transpose this notion of projection into the realm of point group representations under VSC i) by describing VSC as a selection of irreducible representations among a set given by the molecules and the cavity, and ii) by using the fact that the CT complexation is spatially oriented along a reaction coordinate simply given by the direction of charge transfer between the donor and the acceptor (Figure 3). This leads us to “project” in the way detailed below the selected irreducible representations with respect to the reaction coordinate. Each projection corresponds to a modification of the CT complexation paths with the two extreme cases of parallel versus perpendicular projections expected to, respectively, enhance or reduce the CT reactivity.

Figure 3.

Illustration of the relationship of the principal axis (blue dotted line) of the molecule and the CT reaction coordinate (red dashed line) of a) 135TMB and b) 123TMB with I₂.

In more detail, we first set the reference frame to represent the different point groups involved. In the context of VSC and longitudinal modes of the cavity at normal incidence with respect to the mirrors (with degenerate TE (transverse electric) versus TM (transverse magnetic) modes), a natural frame is set by the intracavity optical mode with the longitudinal z axis of the cavity (Figure 1a) and the transverse xy plane of the electric field polarization.

When reaching the strong coupling regime, the eigenstates of the system become hybridized, incorporating both light and matter components. This leads to a symmetry relation between both components, which engages the common subgroups of both the molecular system and the cavity. These common subgroups share a rotational symmetry axis (the cavity z axis) within a unique spatial representation given by the transverse plane of polarization. From this shared representation, we then describe the overall symmetry associated with the hybridization from direct products performed within the set of irreducible representations of the common subgroups. To understand how the symmetry of the coupled vibration is modified by hybridization with the optical mode, and its chemical consequences, we first assign a point group to the electromagnetic mode in the cavity. We then see how the direct product of the mode representation with that of the molecular vibration leads to a new irreducible representation corresponding to the hybrid vibropolariton. Finally, as all irreducible representations are orthogonal, the resulting change in projection on the reaction coordinate is analyzed to explain the favorable or unfavorable modification in the charge transfer complexation reaction.

Let us take as a first example the case of 135TMB with I₂ under VSC.

As the optical mode forms a standing wave along the z axis (Figure 1), degenerate in x and y, it can be analyzed in the D_∞h point group. The 135TMB isomer, strictly speaking of the D_3h point group, is typically assumed with the lower C_3v symmetry to explain the presence of the IR active bands such as CH₃ angular deformation mode.^{[ 61 ]} We choose the C_3v as the simplest common subgroup of the cavity and the molecule and we represent it within the frame set by the intracavity field. The corresponding character table for the C_3v common subgroup is given in Table 3.^{[ 62 ]}

Table 3.

Character table for C_3v point group.

C3v	E	2C 3 (z)	3 σ v
A1	+1	+1	+1	z
A2	+1	+1	−1	R z
E	+2	−1	0	(x, y) (R x, R y)

From the character table, as per the explanation given above, the electric field f transforms as the E irreducible representation (noted as E(f)) being degenerate in x and y. Next, we do the direct products of the representations E(f) with A' (A' now A₁ in the subgroup) when vibration A' of the 135TMB is strongly coupled, or with E when vibration E of the 135TMB is strongly coupled. The direct products can be reduced into A ₁⊗E(f)  =  E and the linear combination $E\otimes E(f)=A_1\oplus A_2\oplus E$, as shown in Table 4.

Table 4.

Direct product of the irreducible representations

C3v	E	2C 3 (z)	3σ v
A 1⊗E(f)  =  E	+2	−1	0
$E\otimes E(f)=A_1\oplus A_2\oplus E$	+4	1	0

This change in symmetry representation under VSC has immediate consequences. For the charge transfer complexation of 135TMB, when an A₁ symmetry vibration is coupled to the cavity mode, we see a decrease in K _DA (Table 1). This is because under VSC, the vibrational A₁ symmetry state is changed into a vibropolariton that transforms as the E representation, as shown above by the direct product. Looking at the complexation, the reaction coordinate transforms as A₁ . The mode now in the E representation under VSC is now orthogonal with respect to the charge density displacement along the reaction coordinate of the CT complex. In other words, the projection of the vibropolariton on the reaction coordinate is null (Figure 3). As a consequence, K _DA decreases.

On the contrary, when coupling the E symmetry vibration of 135TMB with the optical field, the CT complexation is favored. Here, we see that the direct product of this vibration representation with the cavity mode (E⊗E(f)) yields elements of the irreducible representations A₁ and A₂ to which correspond both the principal axis and the reaction coordinate of the charge transfer, explaining the increase in K _DA.

Next, let us consider the CT complexes of the 123TMB isomer with I₂. The 123TMB isomer belongs to the point group C_2v and has its principal axis in the plane of the benzene ring; in other words, orthogonal to the reaction coordinate as illustrated in Figure 3b. As a consequence, we expect the opposite response to VSC as compared to 135TMB, as observed. The common subgroup with the optical field is also C_2v with the character Table 5.

Table 5.

Character table for C_2v point group.

C2v	E	C 2 (z)	σ v (xz)	σ v (yz)	Linear functions, rotations
A1	+1	+1	+1	+1	z
A2	+1	+1	−1	−1	R z
B1	+1	−1	+1	−1	x, R y
B2	+1	−1	−1	+1	y, R x

In the C_2v subgroup, the cavity field transforms as the B₁ and B₂ irreducible representations, noted B₁(f) and B₂(f) representations along x and y. From the direct product in Table 6, the A₁ vibration now transforms as B₁ or B₂ both orthogonal to the principal axis C₂, thus now along the charge transfer axis, i.e., its reaction coordinate (see Figure 3b), leading to an increase in K _DA, as observed.

Table 6.

Direct product of the irreducible representations

C2v	E	C 2 (z)	σ v (xz)	σ v (yz)
A1 ⊗ B1(f) = B1	+1	−1	+1	−1
A1 ⊗ B2(f) = B2	+1	−1	−1	+1

Finally, for the least symmetric isomer, 124TMB, the corresponding C_s point group has no well‐defined principal axis. As a consequence, the changes under VSC are much smaller relative to the other two other isomers, consistent with the model.

We can apply the same analysis to explain all the increases and decreases K _DA in Tables 1 and 2, as shown in Table 7. In the latter, we have added results for a complex with two CT bands (spatial isomers) where the changes in the equilibrium constant can again be understood by the symmetry representation of the vibropolariton relative to the reaction coordinate. The modified K _DA under VSC reflect relative changes in the reaction rates of the charge transfer complexation (Equation 1). Within the same symmetry‐based approach, it should be possible to rationalize other modifications of reaction rates under VSC, for instance, the silyl deprotection reaction reported in 2016 and more recently for alcoholysis reaction.^{[ 21} , ^{31 ]} These small molecule reactants have well defined symmetry and their reactions are well‐known high‐yield ones where most likely the vibronic overlap is already favorable.^{[ 6 ]} Therefore, it is not surprising that when VSC induces changes in symmetry representation of key vibrations so that they become orthogonal to the reaction coordinate, it decreases the rate as observed, reflecting a higher activation energy (see Table 7).

Table 7.

Summary of reactions under VSC and agreement with symmetry predictions: reaction type (CT: charge transfer), point group of the molecule under VSC, irreducible representation of vibration in the common subgroup with the optical field, symmetry product, prediction, and experimental observation.

Reaction	Point group	Vibration irreducible represent.	Symmetry product with cavity mode	Prediction	Observation
135TMB→I2 CT	D3h donor	E (in C3v)	E ⊗ E(f) = A1 + A2 + E	K DA increases	K DA increases for donor E symmetry vibrations
135TMB→DDQ CT
135TMB→Chloranil CT
135TMB→I2 CT	D3h donor	A1 (in C3v)	A1 ⊗ E(f) = E	K DA decreases	K DA decreases for donor E symmetry vibrations
123TMB→I2 CT	C 2v donor	A1	A1 ⊗ B1(f) = B1 A1 ⊗ B2(f) = B2	K DA increases	K DA increases for donor E symmetry vibrations
135TMB→Chloranil CT	D2h acceptor	B1 (in C2v)	B1 ⊗B1(f) = A1 B1 ⊗B2(f) = A2	K DA decreases	K DA decreases for acceptor B1u symmetry vibrations
Anisole→TCNE a) CT 2 CT isomers	D2h acceptor	A1 (in C2v)	A1 ⊗ B1(f) = B1 A1 ⊗ B2(f) = B2	K DA increases	K DA increases for both CT complexes
Anisole→TCNE a) CT 2 CT isomers	C 2v donor	B2	B1 ⊗B1(f) = A1 B1 ⊗B2(f) = A2	K DA decreases	K DA decreases for isomer 1
Silyl deprotection[ 21 ]	C 2v	A	A1 ⊗ B2(f) = B2 A1 ⊗ B1(f) = B1	Deceleration	Reaction rate decelerated
Alcoholysis of phenyl isocyanate[ 31 ]	C 2v	A	A1 ⊗ B2(f) = B2 A1 ⊗ B1(f) = B1	Deceleration	Reaction rate decelerated

^a) A. Jayachandran, J. G. Ricca, M. K. Mahato, J. Wega, E. Vauthey, T. W. Ebbesen, in preparation

In summary, we have found a phenomenological link between chemical reactivity under VSC and symmetry representation. This link views VSC as generating a hybridization of a vibration and the optical field that results in a new irreducible representation for the vibropolariton, relative to the principal axis and thereby its projection on the reaction coordinate. Needless to say, however that many other factors will also modify or obscure this rule. For instance, the vibrational states of the molecules are rarely pure normal modes so that the effect of vibrational symmetry changes will not always be detected, the more so the larger the molecules. VSC has to affect the limiting step in the pathway for it to be detectable in the rates; although it could still be seen in the product yields in complex landscapes as already shown.^{[ 22} , ^{36 ]} Internal vibrational energy redistribution will also be affected by VSC as pointed out in recent theoretical studies.^{[ 37} , ³⁸ , ^{39 ]} Furthermore, external conditions such as solvation can also influence the outcome.

Although the molecules are randomly oriented, most molecules are coupled, as shown in References, ^{[ 17 ]} and ^{[ 36 ]} where phase transition like behavior is seen upon the onset of VSC as there is always some projection onto the field. Intermolecular interactions will further favor the coupling.

It is tempting to see whether the phenomenological symmetry principle identified here is also in agreement with other findings. For instance, recent results show that the conductivity of polystyrene can be boosted by 6 orders of magnitude when coupling the B₂ vibration of the styrene moiety.^{[ 26 ]} The B₂ vibration can only be changed under VSC to A₁ symmetry representation according to the C_2v symmetry of styrene, and thereby favoring the charge displacement along the principal axis of the styrene moiety. Of course, other factors are no doubt also involved such as the delocalized states associated with the collective coupling that contribute to boosting the conductivity.

As the hybridization between the optical mode and the vibrations under VSC leads to novel combinations of irreducible representations, it is highly possible that electronic strong coupling (ESC) also results in symmetry changes in the electronic wavefunctions involved. This could lead to major changes in chemical landscapes, as observed for photochemical ones^{[ 63} , ⁶⁴ , ⁶⁵ , ^{66 ]} as it would affect the mixing (configuration interaction) between the ground and excited states that define among other things the height of the reaction barrier.

Our results emphasize again the relevance of symmetry, and in particular vibrational symmetry, in chemical reactivity. Taken together with the fact that VSC induces no detectable changes in chemical shifts in the ¹H and ¹³C NMR; in other words, in the electronic density distribution in the molecules,^{[ 36 ]} it indicates that VSC acts primarily on the reaction pathways and not on the reactant electronic ground state. Thus, VSC is a unique tool to modify selectively vibrational symmetry and its projection on the reaction landscape. Such triggering of new mechanistic paths can also be combined with well demonstrated selective laser excitation of individual vibrations of reactants.^{[ 8} , ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ^{16 ]} By applying the symmetry rule identified here, it should be possible to help predict the outcome of reactions under VSC, making it a useful a tool to manipulate and control reactions and to understand their mechanism.

Conclusion

Although our phenomenological symmetry rule can account for many of the experimental findings, there is clear need for more theoretical work to understand many details. For instance, although the vibropolaritons, VP⁺ and VP⁻, are embedded in the new symmetry representation, their exact nature needs to be clarified. Furthermore, it has not escaped our attention that the origin of the normal incidence condition for seeing change in properties might be related to the fact the optical field symmetry breaks down at other angles.

Conflict of Interests

The authors declare no conflict of interest.

Supporting information

Supporting Information

Jayachandran A., Patrahau B., Ricca J. G., Mahato M. K., Pang Y., Nagarajan K., Thomas A., Genet C., Ebbesen T. W., Angew. Chem. Int. Ed. 2025, 64, e202503915. 10.1002/anie.202503915

Data Availability Statement

The data that support the findings of this study are available in the Supporting Information of this article.