Accurate quantum-mechanical rate constants for a linear response Azzouz-Borgis proton transfer model employing the multilayer multiconfiguration time-dependent Hartree approach

Quantum dynamical effects of vibrational strong coupling in chemical reactivity

Recent experiments suggest that ground state chemical reactivity can be modified when placing molecular systems inside infrared cavities where molecular vibrations are strongly coupled to electromagnetic radiation. This phenomenon lacks a firm theoretical explanation. Here, we employ an exact quantum dynamics approach to investigate a model of cavity-modified chemical reactions in the condensed phase. The model contains the coupling of the reaction coordinate to a generic solvent, cavity coupling to either the reaction coordinate or a non-reactive mode, and the coupling of the cavity to lossy modes. Thus, many of the most important features needed for realistic modeling of the cavity modification of chemical reactions are included. We find that when a molecule is coupled to an optical cavity it is essential to treat the problem quantum mechanically to obtain a quantitative account of alterations to reactivity. We find sizable and sharp changes in the rate constant that are associated with quantum mechanical state splittings and resonances. The features that emerge from our simulations are closer to those observed in experiments than are previous calculations, even for realistically small values of coupling and cavity loss. This work highlights the importance of a fully quantum treatment of vibrational polariton chemistry.

Theory of vibrational polariton chemistry in the collective coupling regime

We theoretically demonstrate that the chemical reaction rate constant can be significantly suppressed by coupling molecular vibrations with an optical cavity, exhibiting both the collective coupling effect and the cavity frequency modification of the rate constant. When a reaction coordinate is strongly coupled to the solvent molecules, the reaction rate constant is reduced due to the dynamical caging effect. We demonstrate that collectively coupling the solvent to the cavity can further enhance this dynamical caging effect, leading to additional suppression of the chemical kinetics. This effect is further amplified when cavity loss is considered.

Time evolution of ML-MCTDH wavefunctions. II. Application of the projector splitting integrator

The multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach can suffer from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of regularization of the EOMs. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here, we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to 10⁶ bath modes and find that for these problems, the PSI requires roughly 3-4 orders of magnitude fewer Hamiltonian evaluations and 2-3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH and 2-3/1-2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to ∼1.3×10⁹ parameters to obtain accurate dynamics.

Time evolution of ML-MCTDH wavefunctions. I. Gauge conditions, basis functions, and singularities

We derive a family of equations-of-motion (EOMs) for evolving multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) wavefunctions that, unlike the standard ML-MCTDH EOMs, never require the evaluation of the inverse of singular matrices. All members of this family of EOMs make use of alternative static gauge conditions than those used for standard ML-MCTDH. These alternative conditions result in an expansion of the wavefunction in terms of a set of potentially arbitrary orthonormal functions, rather than in terms of a set of non-orthonormal and potentially linearly dependent functions, as is the case for standard ML-MCTDH. We show that the EOMs used in the projector splitting integrator (PSI) and the invariant EOM approaches are two special cases of this family obtained from different choices for the dynamic gauge condition, with the invariant EOMs making use of a choice that introduces potentially unbounded operators into the EOMs. As a consequence, all arguments for the existence of parallelizable integration schemes for the invariant EOMs can also be applied to the PSI EOMs.

Symmetries in the multi-configurational time-dependent Hartree wavefunction representation and propagation

In multi-configurational time-dependent Hartree (MCTDH) approaches, different multi-layered wavefunction representations can be used to represent the same physical wavefunction. Transformations between different equivalent representations of a physical wavefunction that alter the tree structure used in the multi-layer MCTDH wavefunction representation interchange the role of single-particle functions (SPFs) and single-hole functions (SHFs) in the MCTDH formalism. While the physical wavefunction is invariant under these transformations, this invariance does not hold for the standard multi-layer MCTDH equations of motion. Introducing transformed SPFs, which obey normalization conditions typically associated with SHFs, revised equations of motion are derived. These equations do not show the singularities resulting from the inverse single-particle density matrix and are invariant under tree transformations. Based on the revised equations of motion, a new integration scheme is introduced. The scheme combines the advantages of the constant mean-field approach of Beck and Meyer [Z. Phys. D 42, 113 (1997)] and the singularity-free integrator suggested by Lubich [Appl. Math. Res. Express 2015, 311]. Numerical calculations studying the spin boson model in high dimensionality confirm the favorable properties of the new integration scheme.

Revisiting nuclear tunnelling in the aqueous ferrous–ferric electron transfer

We find that golden-rule quantum transition-state theory predicts nearly an order of magnitude less tunnelling than some of the previous estimates. This may indicate that the spin-boson model of electron transfer is not valid in the quantum regime.

Kinetic isotope effects and how to describe them

We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved.

Wavepacket dynamics and the multi-configurational time-dependent Hartree approach

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.

Quantum dynamical simulation of photoinduced electron transfer processes in dye-semiconductor systems: theory and application to coumarin 343 at TiO₂

A recently developed methodology to simulate photoinduced electron transfer processes at dye-semiconductor interfaces is outlined. The methodology employs a first-principles-based model Hamiltonian and accurate quantum dynamics simulations using the multilayer multiconfiguration time-dependent Hartree approach. This method is applied to study electron injection in the dye-semiconductor system coumarin 343-TiO2. Specifically, the influence of electronic-vibrational coupling is analyzed. Extending previous work, we consider the influence of Dushinsky rotation of the normal modes as well as anharmonicities of the potential energy surfaces on the electron transfer dynamics.