Cavity molecular dynamics simulations of liquid water under vibrational ultrastrong coupling Tao E. Lia , Joseph E. Subotnika, and Abraham Nitzana,b,1 aDepartment of Chemistry, University of Pennsylvania, Philadelphia, PA 19104; and bSchool of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel Contributed by Abraham Nitzan, June 11, 2020 (sent for review May 11, 2020; reviewed by Angel Rubio and George C. Schatz) We simulate vibrational strong coupling (VSC) and vibrational The first step toward proving the above hypothesis is to ascer- ultrastrong coupling (V-USC) for liquid water with classical molec- tain whether or not any dynamical property of molecules is ular dynamics simulations. When the cavity modes are resonantly actually changed for a realistic experiment, a goal that forms coupled to the O−H stretch mode of liquid water, the infrared the central objective of this manuscript. In order to investi- spectrum shows asymmetric Rabi splitting. The lower polari- gate whether such modification occurs, below we will model ton (LP) may be suppressed or enhanced relative to the upper VSC and V-USC using cavity molecular dynamics (MD) sim- polariton (UP) depending on the frequency of the cavity mode. ulation, where the nuclei are evolved under a realistic elec- Moreover, although the static properties and the translational dif- tronic ground-state potential surface. Such an approach is an fusion of water are not changed under VSC or V-USC, we do find extension of the usual simplified 1D models where the mat- the modification of the orientational autocorrelation function of ter side is evolved as two-level systems (24–26) or coupled H2O molecules especially under V-USC, which could play a role in harmonic oscillators (16, 17, 27, 28). Although such simplified ground-state chemistry. models are adequate enough for studying Rabi splitting qualita- tively by fitting experimental parameters, these models usually vibrational strong coupling j ultrastrong coupling j molecular dynamics j ignore translation, rotation, and collision, as well as the intri- liquid water cate structure of molecular motion, all of which are crucial for determining the dynamic properties of molecules. There- fore, explicit cavity MD simulations become a more appropriate trong light-matter interactions between a vibrational mode of approach for studying all dynamic properties. Moreover, even Smolecules and a cavity mode have attracted great attention of though one can find a Rabi splitting from 1D models, perform- late (1). The signature of strong interactions is the formation of ing cavity MD simulations is also very helpful for providing lower polariton (LP) and upper polariton (UP), which are mani- more details about the IR spectrum, and this approach can be fested in the Rabi splitting of a vibrational peak in the molecular used to benchmark the validity of 1D models under various infrared (IR) spectrum. According to the normalized ratio (η) conditions. between the Rabi splitting frequency (ΩN ) and the original There have been a few flavors of cavity MD schemes for vibrational frequency (!0), or η = ΩN =2!0, one often classifies electronic strong coupling (29–31). For example, Luk et al. 0 < η < 0:1 as vibrational strong coupling (VSC) and η > 0:1 as (30) applied multiscale quantum mechanics/molecular mechan- vibrational ultrastrong coupling (V-USC) (2). The investigation ics simulation for studying the dynamics of electronic polaritons of VSC or V-USC in liquid phase was initially suggested by for Rhodamine molecules. By contrast, MD simulations for Ebbesen and coworkers (3–5), and it was later found experimen- VSC and V-USC, to our best knowledge, have not been exten- tally that VSC or V-USC can modify the ground-state chemical sively studied before. Therefore, below we will first establish a reaction rates of molecules even without external pumping (6). framework for cavity MD simulation including implementation This exotic catalytic effect provides a brand new way to con- trol chemical reactions remotely. As such, there has been a recent push to understand the origins and implications of VSC Significance and V-USC. While the experimental side has focused on the search for Strong coupling between a vibrational molecular peak and large catalytic effects (7–10) as well as understanding polari- a cavity mode is known to lead to interesting spectroscopic ton relaxation dynamics through two-dimensional (2D)-IR spec- features and even the modification of ground-state chem- troscopy (11, 12), on the theoretical side, the nature of VSC and istry from small molecules to enzyme. Here, we develop a V-USC remains obscured. On the one hand, Rabi splitting can simulation tool for modeling such vibrational strong (and be easily modeled by, for example, diagonalizing a model Hamil- ultrastrong) coupling at the interface between optics, chem- tonian in the singly excited manifold (13–15) or solving equations istry, and biology. With liquid water as an example, our of motion classically for a set of one-dimensional (1D) harmonic simulation not only reveals an asymmetric Rabi splitting in the oscillators (16, 17). On the other hand, a robust explanation infrared spectrum, but also captures cavity modification of the of the catalytic effect of VSC or V-USC remains elusive (18– dynamic properties of water. 21). For example, as recently shown by us and others (21–23), the classical potential of mean force along a reaction pathway Author contributions: T.E.L., J.E.S., and A.N. designed research, performed research, is not changed by usual VSC or V-USC setups for standard analyzed data, and wrote the paper.y experiments of interest. Moreover, as demonstrated below, any Reviewers: A.R., Max Planck Institute for the Structure and Dynamics of Matter; and static equilibrium property of a molecule is not changed under G.C.S., Northwestern University. y VSC or V-USC when nuclei and photons are treated classi- The authors declare no competing interest.y cally. Unfortunately, these findings show that one cannot explain Published under the PNAS license.y the observed effect under VSC or V-USC from a static and Data deposition: The code and simulation data are available on GitHub (https://github. classical point of view. From such a conclusion, one possible com/TaoELi/cavity-md-ipi).y hypothesis of the manifestations of VSC or V-USC effect on 1 To whom correspondence may be addressed. Email: [email protected] chemical rates should arise from the modification of nonequi- This article contains supporting information online at https://www.pnas.org/lookup/suppl/ librium, or dynamical, properties of molecules under VSC doi:10.1073/pnas.2009272117/-/DCSupplemental.y or V-USC. First published July 17, 2020. 18324–18331 j PNAS j August 4, 2020 j vol. 117 j no. 31 www.pnas.org/cgi/doi/10.1073/pnas.2009272117 Downloaded by guest on September 28, 2021 ^ G details, and second, we will investigate the Rabi splitting and the Here, the ground-state molecular Hamiltonian HM = dynamical properties of liquid water. D ^ E ΨGjHMjΨG depends on the nuclear degrees of freedom only The motivation for studying liquid water is twofold. 1) Among common liquids, water shows strong Rabi splitting and strong and can be expressed as catalytic effects under VSC or V-USC (8, 10, 32). More inter- N ^2 ! N esting, when the cavity mode is resonantly coupled to the O−H ^ G X X Pnj ^ (n) ^ X X ^ (nl) HM = + Vg (fRnj g) + Vinter , [2b] stretch mode, experiments (10) have observed that the intensity 2Mnj n=1 j 2n n=1 l>n of the vibrational LP peak is much smaller than the UP peak in the IR spectrum, an observation that cannot be accounted for where the capital letters P^nj , R^ nj , and Mnj denote the momen- by standard strong coupling models. 2) MD simulations of water tum operator, position operation, and mass, respectively, for outside the cavity have been extensively studied, and good agree- j n V^ (n) ment with experiments can be achieved (33–35). Extending such the th nucleus in molecule ; g denotes the intramolecular ^ (nl) simulations to include coupling to cavity modes is expected to potential for molecule n; and Vinter denotes the intermolec- show the cavity-induced spectral changes and provides numbers ular interactions between molecule n and l. The field-related that are directly comparable with experimental results. Hamiltonian becomes (21) 2 General Theory of V-USC N ! G X 1 2 2 1 X 1 H^ = ! q^ + p^k,λ − p d^ng,λ The full-quantum Hamiltonian for light-matter interactions F 2 k,λ k,λ 2 Ω k,λ n=1 0 reads (21, 36) [2c] H^ = H^ + H^ : [1a] N QED M F X X 1 D ^2 E + ng jδdng,λj ng , ^ 2Ω0 Here, QED denotes quantum electrodynamics, HM denotes k,λ n=1 the conventional (kinetic + potential) Hamiltonian for the ^ ^ molecular system where we define d ng,λ ≡ h ng jµ^ n j ng · ξλi and δd ng,λ ≡ µ^ n · ^ 2 ξλ − d ng,λ. Note that, since Coulombic interactions are mod- ^ X p^i ^ ified by proximity to dielectric boundaries in the cavity, the HM = + VCoul (f^ri g), [1b] 2mi ^ (nl) i intermolecular interactions Vinter in Eq. 2b may differ from the free-space form (40, 41). However, as we have argued before PHYSICS where mi , p^i , ^ri denote the mass, momentum operator, and (21), for standard VSC setups with a cavity length on the order position operator for the ith particle (nucleus or electron), of micrometers, V^ (nl) should be nearly identical to those in ^ inter respectively, and VCoul (f^ri g)denotes the Coulombic interaction free space. (See ref. 21 for a brief discussion of the inconsis- operator between all nuclei and electrons.