Quantum Field Approaches to Chemical Systems

Abstract

Quantum-matter theory (QMT), based on the Schrödinger or Dirac equations, is firmly established for both intra- and intermolecular interactions. However, there are two key issues with QMT. First, its applicability to large molecular complexes is hindered by the relatively high computational cost of the calculations required to achieve high accuracy. Second, fields are also quantum objects that produce many intriguing effects beyond standard QMT approaches to molecular systems. This review focuses on recent developments in quantum-field theory (QFT) approaches to both covalent and non-covalent interactions for molecules in vacuum and subject to environments such as cavities and solvents. QFT provides a rich playground for novel chemical theories and insights. For example, chemical reactions and van der Waals interactions can be manipulated by cavities, boundaries, and optical excitations; novel interactions emerge when molecules interact with quantized fields; systems with millions of atoms could soon be treated with coarse-grained QFT formalisms; and unexpected scaling laws for atomic and molecular properties can emerge when QFT is applied to sets of chemical systems. This review sets the stage for an exciting QFT-driven path for further development of chemical theory.

Figures (3)

• Figure 1: Molecular Interactions from a Quantum Field Theoretical Perspective.(a) Molecular interactions between two polarizable entities and their corresponding QED Feynman diagrams (up to the fourth-order perturbation theory) in the minimal-coupling formalism. Here, $\widehat{H}_{\rm f}$ is the Hamiltonian of the fluctuating electromagnetic field (EMF), $\widehat{H}_{\rm mol}$ denotes the atomic/molecular Hamiltonians, $V_{dd}$ is the dipolar Coulomb coupling, and the remaining sum describes atom–field interactions (see appendix \ref{['sec:Appendix_B']} for more details about the Hamiltonian of a system of intercting matter and a quantized electromagnetic field). The diagrams represent processes up to fourth order in perturbation theory. (b) The well-known effects of the vacuum EMF on atoms/molecules, dispersive macroscopic bodies, or the combination of both. The presence of macroscopic bodies and boundaries alters EMF fluctuations, thereby influencing molecular interactions. In macroscopic QED, electric, magnetic, and geometric properties of the boundaries and macroscopic bodies or the bulk materials are encoded into classical Green functions, and the EMF is expressed in terms of that. (c) Inside optical cavities and resonators, strong matter-field couplings are reachable. In such situations, strong coupling between matter and the cavity EMF gives rise to hybrid states that combine properties of molecular and field states, known as polaritons. (d) A quantum-field-theoretical description of matter as a field interacting with other fields (e.g. EMF) allows for the full account of the many-body nature of molecular interactions under the influence of external fields and boundaries and enables the development of computational methods scalable from simple atomic dimers to complex biological macromolecules.
• Figure 2: Applications of QFT-based methods to atomic and molecular systems.(a) Single-orbital entanglement (quantum relative entropy) in the Complete Active Space calculations correlating 10 electrons in 10 $\pi$ orbitals for C$_{10}$H$_{12}$. The orbital numbering follows the upper panel (canonical from self consistent Hartree-Fock/ from Pipek-Mezey (PM) localizationpipek1989fast/ atomic by Jacobi-rotation of PM $\pi$- orbitalskoridon2021orbital). Colors indicate no Superselection Rules (SSR) (all colors), Parity-SSR (black/dark grey), and Number-SSR (black). Adapted from ding2022quantum. (b) Bonding/antibonding characterization in H$_2$-like dimers via eigenvalues and flow lines of the electronic stress tensor $\overleftrightarrow{\tau}_e(\bm r)$: the $1s\sigma$ state exhibits tensile stress ($>0$) at the bond midpoint and a spindle structure in the stress lines, whereas $1s\sigma^\ast$ shows compressive stress ($<0$) and a disrupted stress topology consistent with antibonding character. Adapted from tachibana2019new. (c) Second Quantized Many-Body (SQ-MBD) decomposition of the Many-Body dispersion energy into intra-fragment ($U_{\mathrm{MBD}}$), inter-fragment pair ($V_{\mathrm{MBD}}$), and per-fragment ($E^{\rm frag}_{\rm MBD}$) contributions, shown per residue and secondary-structure element in crambin (meV). Adapted from gori2023second. (d) Reference van der Waals radii $R_{\rm vdW}^{\rm ref}$gobre2016efficient versus electromagnetic field (EMF)-dressed radii for 72 elements, and corresponding polarizabilities (in atomic units); noble gases (red), transition metals (open symbols), and other elements (green). The plot illustrates the scaling relation between static polarizability $\mathcal{A}$ and the EMF-dressed van der Waals radius $R_{\rm f}$, with a prefactor involving the fine-structure constant $\alpha$. Adapted from tkatchenko2021fine.
• Figure 3: Atoms and Molecules Coupled with Quantum Electromagnetic Field (EMF): (a) Interplay between molecular forces induced by an external static field and dispersion force due to the vacuum EMF in two configurations of a benzene dimer demonstrates the possibility of tailoring molecular forces through external fields. Many-body characteristics of dispersion and field-induced polarization forces (taken into account using the MBD method DiStasio-2014-MBD-Review) result in an intricate interplay between these forces and the field-induced electrostatic force. Adapted from Reza_JPCL2022. (b) Electronic strong-coupling of molecules with the cavity EMF yields the matter-field hybridization and formation of upper and lower polaritons that are spectroscopically observable. Adapted from Ebbesen2016-Perspective-Hybrid-Light-Matter. (c) Vibrational strong-coupling of molecules with the cavity EMF: (1) Formation of vibrational polariton states $|\pm\rangle$ from hybridization of molecular and cavity excitations. (2) Suppression of reaction rates as a function of cavity photon frequency inside and outside the cavity, with the IR spectrum of the uncoupled molecule. (3) Enhancement of reaction rates under vibrational strong coupling. (4) Cavity-induced mode selectivity in a reaction with two competing products. Adapted from Huo2023-Review-PolaritonChemistry.