Cavity-Modified Unimolecular Dissociation Reactions via Intramolecular Vibrational Energy Redistribution.

While the emerging field of vibrational polariton chemistry has the potential to overcome traditional limitations of synthetic chemistry, the underlying mechanism is not yet well understood. Here, we explore how the dynamics of unimolecular dissociation reactions that are rate-limited by intramolecular vibrational energy redistribution (IVR) can be modified inside an infrared optical cavity. We study a classical model of a bent triatomic molecule, where the two outer atoms are bound by anharmonic Morse potentials to the center atom coupled to a harmonic bending mode. We show that an optical cavity resonantly coupled to particular anharmonic vibrational modes can interfere with IVR and alter unimolecular dissociation reaction rates when the cavity mode acts as a reservoir for vibrational energy. These results lay the foundation for further theoretical work toward understanding the intriguing experimental results of vibrational polaritonic chemistry within the context of IVR.

Mode-selective chemistry—exciting just a single bond in a molecule to control its chemical properties—is a long sought-after goal that would allow selective control over chemical reactivity and energy transfer.[1−6] Realization of this goal has generally been hampered, however, by intramolecular and intermolecular vibrational energy redistribution that limits the efficiency of a mode-selective excitation beyond cryogenic temperatures.[7] Interest in this field was revitalized recently with the emergence of the field of vibrational polaritonic chemistry.[8−20] Changes of reaction rates of molecules inserted into optical infrared cavities have been observed experimentally, demonstrating the influence of the resonant coupling of molecular infrared-active vibrations with the electromagnetic vacuum field of the cavity on the underlying reaction dynamics. Despite intense efforts to understand why the reaction rate changes,[21−28] the microscopic mechanisms underlying the experimental observations are still under debate. Recent studies have hinted at the role of intramolecular vibrational energy redistribution (IVR) in cavity-modified chemical reactions studied via first-principles methods[26,29] or molecular dynamics simulations.[30−33] The role of vibrational strong coupling on the chemical reactivity of 1-phenyl-2-trimethylsilylacetylene (PTA) using quantum electrodynamical density functional theory[34−36] was able to replicate some of the effects observed experimentally by Thomas et al.[37] However, due to the computational complexity, these methods still face certain limitations, such as in the number of simulated trajectories or possible reaction pathways.

Therefore, in this work, we theoretically study cavity-modified unimolecular dissociation reactions with a simple classical model of a molecule. We show that by coupling the infrared-active modes of the molecule to the de-excited cavity mode, the rate of bond dissociation in individual molecules can be selectively increased or decreased. In particular, when the cavity is initially empty, the dissociation rate decreases, while when the cavity is initially hotter than the molecule, the cavity can instead accelerate the reaction rate. We observe a change in chemical reaction rate most strongly when the cavity is tuned into resonance with particular vibrational modes, as well as a strong dependence on the cavity strength. These results help elucidate the role of IVR in vibrational polariton chemistry.

We start by discussing the setup of the model system to demonstrate the cavity-modified IVR dynamics. In this work, we use a classical triatomic model with three degrees of freedom and anharmonic potentials. This model was previously used by Karmakar et al.[38] to understand the onset of chaos in IVR processes and is itself based on the approach pioneered by Bunker and others[39−42] who studied the ozone molecule in a series of computational studies on unimolecular dissociation reactions. Importantly, this minimal model demonstrates chaotic dynamics through an interconnected Arnold web,[43,44] or network of nonlinear resonances, and therefore serves as a fundamental starting point for IVR studies of larger molecules. The Hamiltonian for the model system can be written in terms of the local vibrational modes aswhere i ∈ {1, 2, 3} corresponds to the local stretching mode between the left atom and the center atom, the local stretching mode between the center atom and the right atom, and the local bending mode, respectively. The position coordinates q for i = 1 and 2 are in units of distance, while q3 is in units of angle, and p are their respective conjugated momentum coordinates. A schematic of the model system and the coordinates is depicted in Figure a. The coupling element between momenta p and p is due to the transformation from normal mode coordinates, where we consider collective motions of nuclei, to local mode coordinates, where we focus on the movement of specific parts of the molecule.[45] To explore the effect of varying vibrational mode–mode momentum couplings, this momentum–momentum interaction is scaled by ϵ, roughly corresponding to, e.g., varying the mass of the center atom relative to the other two atoms.[39] For nonzero ϵ, the local vibrational modes q1, q2, and q3 do not correspond to normal (or eigen-) modes of the system. In addition, note that the coordinate-dependent G in the original model of Bunker[39] are approximated by their equilibrium values, , and that this model is fixed in the x–y plane with dipole activity only in the x- and y-directions, although we note that the rovibronic couplings have also been shown to impact IVR in certain circumstances.[46] For the two stretching modes i = 1, 2, the vibrational potential is approximated by a Morse potential, as shown in Figure b: where D is the dissociation energy, α controls the anharmonicity of the potential well and the number of bound vibrational states in a quantum picture, is the equilibrium atom–atom distance, and ω is the frequency of the potential well under the low-displacement or harmonic approximation. For the dissociation energies, we choose D1 = D2 = D. For the bending mode, the vibrational potential is assumed to be harmonic: The numerical values for these parameters are defined in the Supporting Information and in ref (38).

Figure 1

Model of a cavity-coupled molecule. (a) Schematic of the model triatomic model in a cavity. The local vibrational degrees of freedom of the molecule are labeled q1 (stretch length between left and center atoms), q2 (stretch length between center and right atoms), and q3 (bending angle between bonds of left-center atoms and center-right atoms), while the cavity mode displacement is Qc. (b) Dipole moment function in the x-direction, or μ, when θ = 0 and the anharmonic Morse potential V1 of local stretch q1.

To incorporate the effect of light–matter coupling between the electric field of an infrared cavity and the vibrations of the molecular model, we add the classical field Hamiltonian HF,[47] which becomes the Pauli–Fierz Hamiltonian in its quantized form:[35]where ω, Q, P, and λ are the frequency, displacement, momentum, and strength of the cavity mode k; μ is the permanent dipole moment of the molecule; and ξ is the unit vector of polarization of the electric field. We note that a similar approach has been taken in classical molecular dynamics studies of polaritonic chemistry.[30,31] See the Supporting Information for a full derivation from the light–matter Lagrangian. In the following, we will consider interactions with a single cavity mode c. The permanent dipole moment of the molecule, plotted in Figure b, is defined aswhere , , ,[48] θ is the angle between the x-axis and the in-plane molecular axis through the center of the molecule, σ = 1 bohr controls the envelope width, and A = 0.4 e is such that the equilibrium permanent dipole moment μ0 in the x-direction when θ = 0 is 1 e·bohr, which is on the order of the permanent dipole moment for bent triatomic molecules such as ozone.[49,50] Importantly, the dipole moment μ approaches zero with increasing q1 and q2, physically analogous to dissociation into neutral species or screening of ionic fragments by solvent, to obviate challenges with the dipole approximation after dissociation. In the Supporting Information, however, we also study cavity-modified rates of dissociation into ionic (charged) species, where , and we find similar results.

For the full light–matter Hamiltonian in the form of H = Hmol + HF, the equations of motion can be derived with Hamilton’s equations and stably propagated given a set of initial position and momentum coordinates up to several tens of picoseconds using the eighth order Runge–Kutta method.[51] To understand the IVR dynamics of the molecule both outside and inside the cavity, we calculate the dipole moment spectrum . This expression corresponds to the one-sided Fourier transform of the permanent dipole moment μ as the displacements q and momenta p propagate under H and is directly related to the dipole moment spectrum.[52] Because the IVR dynamics are chaotic,[40,41] all results based on dynamics shown in this study are averaged over tens of thousands of initial states that are generated as described in the Supporting Information.

We first describe the molecule outside of the cavity. In the simplest case, shown in the top plot of Figure , there is no mode–mode momentum coupling, i.e., ϵ = 0 in eq , and the initial energy of 1 kcal/mol is low compared to the dissociation energy D = 24 kcal/mol of the local stretching modes and of the same order of magnitude as their harmonic frequencies. Therefore, the Hamiltonian effectively corresponds to three decoupled local vibrations. Notably, the local bending peak at 632 cm–1 is sharper and brighter, while the local stretches at 1040 and 1112 cm–1 are broader and darker. The difference in peak widths is a result of the anharmonic local stretching potentials. In the second plot of Figure , we turn on the vibrational mode–mode momentum coupling by setting ϵ = 1. As expected, we find that the local vibrational modes are no longer the normal modes of the system—the normal modes are now delocalized over the three local modes, shifting the three center frequencies (ω1, ω2, ω3) of the normal bending, normal symmetric stretching, and normal antisymmetric stretching modes to (1197, 1003, 528) cm–1 from (1112, 1040, 632) cm–1 in the case of ϵ = 0. As the energy of the initial state is increased to 10 kcal/mol in the third plot of Figure , such that q1 and q2 can explore more of the anharmonic Morse potential, we observe the emergence of additional and broadened peaks corresponding to anharmonic resonances. Nonetheless, we can still identify peaks with frequencies below or above ∼800 cm–1 with the normal bending mode or normal stretching modes, respectively. As the energy of the initial states is increased to 23.9 kcal/mol in Figure , just below the dissociation energy D = 24 kcal/mol, the frequency spectra of the local stretching modes q1 and q2 have largely delocalized across the entire frequency spectrum with a broad peak near ∼500 cm–1 still corresponding to normal bending mode-like character.

Figure 2

Dipole moment spectrum of the molecule outside and inside the cavity with varying vibrational mode–mode coupling ϵ and initial energy in the molecule Emol relative to the dissociation energy D. The size and direction of the arrows indicate the relative magnitude and phase of local bond displacement in the normal modes. As the energy increases and more of the anharmonic Morse potentials can be explored, the peaks broaden. We couple the cavity mode to the bending-like modes with the highest intensity and observe Rabi splitting indicative of strong interactions between them.

For the spectra including the optical cavity mode in Figure , we couple the molecule to a single cavity mode c that we assume is x-polarized. The photon mode is then initialized with vanishingly small energy. We resonantly tune the cavity mode to the frequency with the largest intensity in the spectrum that corresponds to a bending mode and choose the cavity strength λc = 0.05 au leading to an estimated Rabi splitting ΩR = 45 cm–1 or 1.35 THz. This Rabi splitting is the border between the strong and ultrastrong coupling regimes. (We describe how the Rabi splitting can be estimated in the low-energy harmonic case in the Supporting Information.) Note that this cavity strength implies a much smaller mode volume V than experimental values to compensate for the lack of N molecules in this single-molecule model, since . The peak splitting is clear evidence of interactions between the cavity mode and vibrations, suggesting energy can be transferred between the cavity mode and vibrational modes, and the magnitude of the splitting is similar regardless of ϵ and Emol.

Dissociation Dynamics. Next, we study the dissociation dynamics of the molecular system. The molecule can dissociate when it is initialized with energy exceeding the dissociation energy D = 24 kcal/mol. We define successful dissociation when either q1 or q2 exceeds a bond length of 5 bohr from the equilibrium value or . Setting Emol = 34 kcal/mol, we show an example trajectory that leads to dissociation of the molecule inside a cavity in Figure a, where we plot the deviation of the molecular coordinates q from their equilibrium positions . The trajectory exhibits anharmonic oscillations of the internal coordinates of the molecule resulting finally in the divergence of the bond length q1 and, therefore, dissociation of the molecule.

Figure 3

IVR-mediated dissociation. (a) Single trajectory of a molecule initialized with energy of 34 kcal/mol that is greater than the dissociation energy D = 24 kcal/mol. Local mode displacements are in atomic units. The molecule dissociates at ∼3.4 ps, marked by the green region, when exceeds dissociation length rdis = 5 bohr. (b) Dipole moment spectrum of short-lived (dissociation time tdis < 0.5 ps) and long-lived (tdis > 4 ps) trajectories of the molecule outside the cavity. Long-lived trajectories exhibit sharp resonances, suggesting that strongly coupling the cavity mode to these particular modes can influence dissociation dynamics.

We generate a statistical understanding of the dissociation dynamics by studying tens of thousands of trajectories with identical energies. In Figure b, we plot the dipole moment spectrum for molecules initialized with energy 34 kcal/mol > D = 24 kcal/mol, sufficient to dissociate the bond. Binning trajectories by their lifetimes, we compare the dipole moment spectra of short-lived trajectories (tdis < 0.5 ps) and long-lived trajectories (tdis > 4 ps). For the short-lived trajectories we observe uniform spectral densities that hint at statistical decay dynamics in which the many anharmonic resonances of the local vibrational modes are explored quickly and at random. In contrast, the Fourier spectra of the long-lived trajectories feature a number of peaks; especially prominent ones are at ∼520 and ∼580 cm–1. These peaks represent modes robust against dissociation, where the molecular energy is largely stored in the local bending motion and not local stretches prone to dissociation. Therefore, we suggest to alter the dynamics of IVR-mediated dissociation by coupling the cavity to these resonances.

Cavity-Modified Dissociation. We explore whether coupling the molecule to the cavity can modify reaction dynamics. In our model, we initialize the molecule with Emol = 34 kcal/mol and couple it to a single cavity mode initialized such that the total field energy EF resulting from eq is 0. Again, θ = 0 and the cavity is x-polarized with frequency ωc and cavity strength λc.

First, we calculate the change in reaction rate for varying cavity strength λc. To set ωc and θ, we note that is largest around 520 cm–1 in Figure b. Therefore, we presume the strength of light–matter coupling for a given λc can be maximized by polarizing the cavity field along the x-direction and setting ωc = 520 cm–1. We vary the cavity strength λc and plot the (natural logarithm of) the survival probability S(t), or the proportion of initial states that have not dissociated as a function of time in Figure a, as well as the time required for 95% of the molecules to dissociate in Figure b. A lower survival probability S(t) corresponds to a faster reaction rate. Importantly, the dissociation slows monotonically with increasing λc, even toward the ultrastrong coupling where λc ≳ 0.05 au.

Figure 4

Cavity-modified unimolecular dissociation rate with survival probability as a function of time (top) and time required for 95% of molecules with initial energy of 34 kcal/mol (bottom) for an initially empty cavity. In (a) and (b), we vary the cavity strength λc for ωc = 520 cm–1 and the x-polarized cavity mode, resulting in the dissociation rate slowing down with increasing λc. In (c) and (d), the cavity frequency ωc is varied for λc = 0.02 au and the x-polarized cavity mode; the dissociation rate slows down between ωc ∼ 520 and ∼600 cm–1, close to the same frequencies of the peaks in in Figure b.

We further explore the cavity-coupled triatomic model by varying cavity frequency ωc from 100 to 1100 cm–1 with constant cavity strength λc = 0.01 au. From Figure c, we see that for much of this frequency range, the survival probability S(t) curves are nearly identical to the case of λc = 0 in Figure a. Around 500 cm–1, however, the reaction dynamics are strongly changed. To study them with a finer frequency resolution in this range, we plot the time required for 95% dissociation t in Figure d, where we observe peaks at ∼520 and ∼600 cm–1, close to the frequencies of the peaks in Figure b and therefore serving as direct evidence of a resonant effect. In the Supporting Information, we sweep the cavity frequency at higher cavity strengths as well and notice that the two peaks broaden and shift in frequency. We also show results for the cases of molecules with weak vibrational mode–mode coupling ϵ, where we observe rate acceleration for low ϵ, and molecules initialized with different energies Emol, where we observe qualitatively similar results.

To develop a qualitative understanding of how the cavity changes the reaction rate, we study the change in the form of the decay curves as the reaction time t increases for both varying λc and ωc. For λc = 0 corresponding to complete decoupling between the molecule and the cavity, the survival probability S(t) can be described with a monoexponential decay process,[38] corresponding to statistical distribution of vibrational energy where the space of nonlinear frequency resonances between vibrational modes is widely explored before the molecule dissociates. The reaction slows as a secondary, slower decay channel becomes more dominant, veering the survival probability S(t) away from monoexponential statistical decay. This slower decay channel has been shown to correspond to IVR-limited dissociation, where the molecule vibrates along particular modes—a bending mode in this case—before dissociating,[38] as shown by the dipole moment spectrum of short- vs long-lived trajectories in Figure b.

We demonstrate that the cavity increases the number of trajectories that decay via the IVR-limited decay channel by serving as a sink for vibrational energy, lowering the probability that one of the stretch bonds acquires enough energy to break. In Figure , for different cavity strength λc ∈ {0, 0.02, 0.05} au, we plot the time-dependent energy distribution up to the first 0.5 ps in the molecule–cavity system for shorter-lived (0.5 < tdis < 1 ps) and longer-lived (tdis > 4 ps) trajectories inside and outside the cavity averaged over ∼200 000 initial states. The distribution comprises energy in the entire molecule as Hmol, the field HF (including matter-photon coupling), and each of the local vibrational modes i as . Note that for clarity, we do not show the vibrational mode–mode coupling, which is generally unaltered by the presence of the cavity.

Figure 5

Time-dependent energy distribution of the first 0.5 ps in the molecule–cavity system for short-lived (0.5 < tdis < 1 ps) and long-lived (tdis > 4 ps) trajectories where λc ∈ {0, 0.02, 0.05} au. The resonantly tuned cavity mode couples efficiently to molecules with highly excited local bending modes and functions as a reservoir of molecular vibrational energy.

At λc = 0 corresponding to the molecule being outside the cavity, for the shorter-lived trajectories, energy is initially distributed approximately evenly between the local bending and local stretching modes and is gradually redistributed from the local bending to the local stretching modes. In sharp contrast, for the longer-lived trajectories the initial states are more highly excited in the local bending mode. Importantly, the energy oscillations indicate localization in frequency space within the sharp resonances of the x-polarized dipole moment spectra around 500–600 cm–1.

Inside the cavity with λc = 0.02 au, for both shorter- and longer-lived trajectories, we see that the cavity mode strongly couples to the local bending mode, as the field energy increases while the molecular energy decreases. Notably, the local bending mode is more excited for the longer-lived trajectories. The strongly coupled cavity mode is then able to absorb more energy from both the local bending mode and local stretching modes, in turn extending the average lifetime of the molecule. With larger cavity strength λc = 0.05 au, the reaction slows down further because the cavity couples more strongly to the molecule and is better able to absorb vibrational energy.

The cavity mode, initially vanishingly empty in Figure and Figure , appears to slow down the dissociation rate by absorbing energy from the vibrationally excited molecule. In the case of chemical reactions at thermal equilibrium, however, the cavity mode is likely to be thermally occupied. Therefore, in Figure , we present the effect of a “hot” cavity on dissociation dynamics, where the total molecule–cavity energy is 34·4/3 ∼ 45 kcal/mol and the initial states are sampled from the microcanonical ensemble. The factor of 4/3 takes into account the additional degree of freedom by the cavity mode such that the average energy per degree of freedom is the same for the molecule inside and outside the cavity.

Figure 6

Dissociation time t inside a hot cavity with varying (a) cavity frequency ωc and (b) cavity strength λc at the resonant cavity frequency ωc = 520 cm–1. The total molecule–cavity energy is 34·4/3 ∼ 45 kcal/mol, where the factor of 4/3 accounts for the additional degree of freedom by the cavity mode. As a guide to the eye, we also plot t for the bare molecule with 34 kcal/mol (segmented yellow). The resonance is broader for the hot cavity than for the empty cavity in Figure , and the reaction rate for a given λc is fastest at the resonance. The reaction rate decreases toward a plateau that is faster than the rate outside the cavity beyond λc = 0.05 au. At off-resonant cavity frequencies and when cavity–molecule interactions are weak, energy localized in the cavity cannot be efficiently transported to the molecule.

Below the cavity strength λc < 0.05 au, the reaction rate is slower inside the cavity for all cavity frequencies, reaching its fastest rate close to the resonant frequency found in Figure d. As the cavity strength λc increases beyond 0.05 au toward the ultrastrong coupling regime, the reaction can be even faster inside the cavity than outside. These results can be understood as follows: off-resonant and weak cavity–molecule interactions can prevent energy localized in the cavity from transporting to the molecule. To control for the effects of initial states where the molecule energy is too low to dissociate, in the Supporting Information, we fix the energy of the molecule to be the same as it is outside the cavity and study how increasing cavity energy affects the reaction rate. We find that hotter cavities generally increase the reaction rate, although the exact phase of the cavity state relative to the molecule’s can drastically affect the reaction rate.

In summary, we study the dissociation dynamics of a classical model of a triatomic molecule in an optical cavity based on a Bunker model, where the potential of the two local stretches are anharmonic Morse potentials and the local bending mode is harmonic. We extend this model by resonantly coupling the vibrational states with large optical dipole moments to a single electromagnetic mode of an infrared cavity. Importantly, we observe that the effect of the cavity is strongest when it is tuned into resonance with the frequencies of dissociation-resistant vibrational modes. In addition, we find that the reaction rate monotonically decreases even as the molecule–cavity system enters the ultrastrong coupling regime. The reaction is maximally slowed down when the cavity is able to absorb energy from the molecule without returning it too quickly to the molecule, lowering the probability that one of the stretch bonds acquires enough energy to break.

When the energy of the molecule–cavity system is increased such that the energy per degree of freedom is equivalent to that of the bare molecule, the reaction rate is generally slowed down as energy initialized in the cavity is unable to be transferred to the molecule without resonant and strong cavity–molecule interaction. To control for this localization effect, we also fix the molecule energy and study dissociation as a function of the cavity energy. We find that cavity-modified reaction rates are generally only observable when the cavity is “cooler” compared to the molecule. Nevertheless, even a “hot” cavity can slow down reaction dynamics. As an example, we show that particular cavity states are more prone to initially absorbing energy from the molecule, while others with the same initial energy are more prone to transferring energy to the molecule, both of which are a result of the initial sign of the light–matter interaction term. These results highlight the importance of dynamical effects in vibrational polariton chemistry.

Here we briefly highlight similarities to and differences from previous studies.[20,21,24,53] While earlier studies did not find a resonance effect of the optical cavity,[21,53] recent work using quantum transition-state theory has demonstrated a dynamical solvent-caging effect[24] when the photon mode is in resonance to the curvature of the reaction barrier. An extension[20] also finds a resonance effect for vibrational excitations for certain parameter regimes. In our paper, we study the effect of cavity modification on chemical reactions via intramolecular vibrational energy redistribution, which requires at least a second vibrational degree of freedom. Our work, although fully classical, finds a resonance effect when the photon mode is tuned in resonance to the vibrational excitation.

This study lays the foundation for further theoretical and experimental work toward understanding the intriguing experimental results of vibrational polariton chemistry. We emphasize that the cavity strengths necessary to substantially influence the reaction dynamics, or λc ≳ 0.01 au, are orders of magnitude larger than those in many-molecule experiments of vibrational polariton chemistry. We, however, emphasize that single-molecule strong coupling can already be reached experimentally. For instance, recent experiments in picocavity setups have demonstrated effective volumes ∼1 nm3 [55−58] that lead to sizable Rabi splittings of the same order as those in this study. Alternatively, other strategies to achieve single-molecule strong light–matter coupling in optical cavities have been proposed recently[59] that seem promising. Such setups may be able to reproduce the cavity-modified IVR pathways discussed in our manuscript. To bridge the gap between single-molecule studies and many-molecule experiments, where the latter exhibit significant dark state populations, we expect molecular dynamics studies of many molecules inside an optical cavity that also include molecular translational and rotational degrees of freedom and intramolecular interactions[30−33,60,61] with a particular focus on IVR dynamics to be fruitful. In addition, in cases when the dissociation energy becomes comparable to a quantum of vibrational energy, quantum effects can play an important role in the dissociation dynamics.[37] In such cases a quantum description, e.g., via first-principles method such as quantum electrodynamical density functional theory[26,34−36,62,63] is necessary. Because many reactions studied under vibrational strong coupling are under thermal equilibrium at ∼25 meV with activation barriers far in excess of thermal energy,[64] reactions are incredibly rare events and thus challenging to study computationally. In this study, the molecule energy is set at 30–36 kcal/mol or 1.4–1.6 eV to react in a reasonable amount of simulation time. Future studies may also include the effects of cavity loss via, for instance, Langevin approaches, additional cavity modes representing the other fundamental modes of Fabry–Pérot cavities, and line width broadening of each cavity mode by the nonzero-incidence wave vectors. While for computational feasibility and ease of interpretation, we consider only a triatomic anharmonic model that serves as a minimal viable model for chaotic dynamics, molecules studied in experiments are considerably more complex. They can contain ∼100 vibrational degrees of freedom. These many degrees of freedom may exhibit vibrational mode–mode couplings that span several orders of magnitude. Future studies should therefore determine whether the observed cavity-modified chemical reactivity in this study is robust to these factors. Finally, experimental studies that consider reactions limited by IVR that therefore do not abide by the standard assumptions of transition rate theory and where the initial states of the intramolecular vibrational and cavity degrees of freedom can be controlled will help to further clarify the role of IVR in vibrational polaritonic chemistry.