PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science.

We present an ab initio correlated approach to study molecules that interact strongly with quantum fields in an optical cavity. Quantum electrodynamics coupled cluster theory provides a nonperturbative description of cavity-induced effects in ground and excited states. Using this theory, we show how quantum fields can be used to manipulate charge transfer and photochemical properties of molecules. We propose a strategy to lift electronic degeneracies and induce modifications in the ground-state potential energy surface close to a conical intersection.

Strong light–matter interaction in cavity environments is emerging as a promising approach to control chemical reactions in a non-intrusive and efficient manner. The underlying mechanism that distinguishes between steering, accelerating, or decelerating a chemical reaction has, however, remained unclear, hampering progress in this frontier area of research. We leverage quantum-electrodynamical density-functional theory to unveil the microscopic mechanism behind the experimentally observed reduced reaction rate under cavity induced resonant vibrational strong light-matter coupling. We observe multiple resonances and obtain the thus far theoretically elusive but experimentally critical resonant feature for a single strongly coupled molecule undergoing the reaction. While we describe only a single mode and do not explicitly account for collective coupling or intermolecular interactions, the qualitative agreement with experimental measurements suggests that our conclusions can be largely abstracted towards the experimental realization. Specifically, we find that the cavity mode acts as mediator between different vibrational modes. In effect, vibrational energy localized in single bonds that are critical for the reaction is redistributed differently which ultimately inhibits the reaction.

Intermolecular bonds are weak compared to covalent bonds, but they are strong enough to influence the properties of large molecular systems. In this work, we investigate how strong light–matter coupling inside an optical cavity can modify intermolecular forces and illustrate the varying necessity of correlation in their description. The electromagnetic field inside the cavity can modulate the ground state properties of weakly bound complexes. Tuning the field polarization and cavity frequency, the interactions can be stabilized or destabilized, and electron densities, dipole moments, and polarizabilities can be altered. We demonstrate that electron–photon correlation is fundamental to describe intermolecular interactions in strong light–matter coupling. This work proposes optical cavities as a novel tool to manipulate and control ground state properties, solvent effects, and intermolecular interactions for molecules and materials.

This Perspective provides a brief introduction into the theoretical complexity of polaritonic chemistry, which emerges from the hybrid nature of strongly coupled light–matter states. To tackle this complexity, the importance of ab initio methods is highlighted. Based on those, novel ideas and research avenues are developed with respect to quantum collectivity, as well as for resonance phenomena immanent in reaction rates under vibrational strong coupling. Indeed, fundamental theoretical questions arise about the mesoscopic scale of quantum-collectively coupled molecules when considering the depolarization shift in the interpretation of experimental data. Furthermore, to rationalize recent findings based on quantum electrodynamical density-functional theory (QEDFT), a simple, but computationally efficient, Langevin framework is proposed based on well-established methods from molecular dynamics. It suggests the emergence of cavity-induced non-equilibrium nuclear dynamics, where thermal (stochastic) resonance phenomena could emerge in the absence of external periodic driving. Overall, we believe that the latest ab initio results indeed suggest a paradigmatic shift for ground-state chemical reactions under vibrational strong coupling from the collective quantum interpretation toward a more local, (semi)-classically and non-equilibrium dominated perspective. Finally, various extensions toward a refined description of cavity-modified chemistry are introduced in the context of QEDFT, and future directions of the field are sketched.

We demonstrate a robust and efficient way of controlling the optical spectra of two-dimensional materials by embedding them in a quantum cavity. The strength of the cavity light-matter coupling leads to superposition of bright and dark excitons making viable the optical observation of dark excitons. Our theoretical calculations are based on a newly developed theoretical framework that involves the ab-initio solution of the coupled quantized electron-photon Schr\"odinger equation in a quantum-electrodynamics plus Bethe-Salpeter approach. It enables the simulations of exciton-polariton states and their dispersion in a strong cavity light-matter coupling regime. We then develop a general Mott-Wannier model for this excitonic-polariton cavity problem which can be readily applied to a wider range of applications of van-der-Waals heterostructure materials in cavities.