Two-Dimensional Moiré Polaronic Electron Crystals.

Two-dimensional moiré materials have emerged as the most versatile platform for realizing quantum phases of electrons. Here, we explore the stability origins of correlated states in WSe_{2}/WS_{2} moiré superlattices. We find that ultrafast electronic excitation leads to partial melting of the Mott states on timescales 5 times longer than predictions from the charge hopping integrals and that the melting rates are thermally activated, with activation energies of 18±3 and 13±2 meV for the one- and two-hole Mott states, respectively, suggesting significant electron-phonon coupling. A density functional theory calculation of the one-hole Mott state confirms polaron formation and yields a hole-polaron binding energy of 16 meV. These findings reveal a close interplay of electron-electron and electron-phonon interactions in stabilizing the polaronic Mott insulators at transition metal dichalcogenide moiré interfaces.

Effective Single-Mode Methodology for Strongly Coupled Multimode Molecular-Plasmon Nanosystems.

Strong coupling between molecules and quantized fields has emerged as an effective methodology to engineer molecular properties. New hybrid states are formed when molecules interact with quantized fields. Since the properties of these states can be modulated by fine-tuning the field features, an exciting and new side of chemistry can be explored. In particular, significant modifications of the molecular properties can be achieved in plasmonic nanocavities, where the field quantization volume is reduced to subnanometric volumes, thus leading to intriguing applications such as single-molecule imaging and high-resolution spectroscopy. In this work, we focus on phenomena where the simultaneous effects of multiple plasmonic modes are critical. We propose a theoretical methodology to account for many plasmonic modes simultaneously while retaining computational feasibility. Our approach is conceptually simple and allows us to accurately account for the multimode effects and rationalize the nature of the interaction between multiple plasmonic excitations and molecules.

Coupled cluster cavity Born-Oppenheimer approximation for electronic strong coupling.

Chemical and photochemical reactivity, as well as supramolecular organization and several other molecular properties, can be modified by strong interactions between light and matter. Theoretical studies of these phenomena require the separation of the Schrödinger equation into different degrees of freedom as in the Born-Oppenheimer approximation. In this paper, we analyze the electron-photon Hamiltonian within the cavity Born-Oppenheimer approximation (CBOA), where the electronic problem is solved for fixed nuclear positions and photonic parameters. In particular, we focus on intermolecular interactions in representative dimer complexes. The CBOA potential energy surfaces are compared with those obtained using a polaritonic approach, where the photonic and electronic degrees of freedom are treated at the same level. This allows us to assess the role of electron-photon correlation and the accuracy of CBOA.

On the characteristic features of ionization in QED environments.

The ionization of molecular systems is important in many chemical processes, such as electron transfer and hot electron injection. Strong coupling between molecules and quantized fields (e.g., inside optical cavities) represents a new promising way to modify molecular properties in a non-invasive way. Recently, strong light-matter coupling has shown the potential to significantly improve the rates of hot electron driven processes, for instance, in water splitting. In this paper, we demonstrate that inside an optical cavity, the residual interaction between an outgoing free electron and the vacuum field is significant. We further show that since the quantized field is also interacting with the ionized molecule, the free electron and the molecular system are correlated. We develop a theoretical framework to account for the field induced correlation and show that the interaction between the free electron and the field, free electron-field interaction, has sizable effects on the ionization potential of typical organic molecules.

A perspective on ab initio modeling of polaritonic chemistry: The role of non-equilibrium effects and quantum collectivity.

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.

Intermolecular interactions in optical cavities: An ab initio QED study.

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.

Recent developments in the PySCF program package.

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.

Cavity Control of Excitons in Two-Dimensional Materials.

We propose a robust and efficient way of controlling the optical spectra of two-dimensional materials and van der Waals heterostructures by quantum cavity embedding. The cavity light-matter coupling leads to the formation of exciton-polaritons, a superposition of photons and excitons. Our first-principles study demonstrates a reordering and mixing of bright and dark excitons spectral features and in the case of a type II van-der-Waals heterostructure an inversion of intra- and interlayer excitonic resonances. We further show that the cavity light-matter coupling strongly depends on the dielectric environment and can be controlled by encapsulating the active two-dimensional (2D) crystal in another dielectric material. Our theoretical calculations are based on a newly developed nonperturbative many-body framework to solve the coupled electron-photon Schrödinger equation in a quantum-electrodynamical extension of the Bethe-Salpeter approach. This approach enables the ab initio simulations of exciton-polariton states and their dispersion from weak to strong cavity light-matter coupling regimes. Our method is then extended to treat van der Waals heterostructures and encapsulated 2D materials using a simplified Mott-Wannier description of the excitons that can be applied to very large systems beyond reach for fully ab initio approaches.

Chemical Bond Mechanism for Helium Revealed by Electronic Excitation.

Helium chemistry is notoriously very impervious. It is therefore certainly no surprise that, for example, beryllium and helium atoms, in their ground state, do not bind. Full configuration-interaction calculations show that the same turns out to be true, save for a long-range shallow attraction, for the Be+ + He system. However, quite astonishingly, when one electron is re-added to Be+ in an excited 2pπ or 3s orbital (Be 1P or 1S), a bound adduct with He is formed, at an interatomic separation as short as 1.5 Å. Understanding why this happens reveals an unsuspected chemical mechanism that stabilizes helium compounds at the molecular level.

Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes.

In earlier work [A. Y. Sokolov and G. K.-L. Chan, J. Chem. Phys. 144, 064102 (2016)], we introduced a time-dependent formulation of the second-order N-electron valence perturbation theory (t-NEVPT2) which (i) had a lower computational scaling than the usual internally contracted perturbation formulation and (ii) yielded the fully uncontracted NEVPT2 energy. Here, we present a combination of t-NEVPT2 with a matrix product state (MPS) reference wavefunction (t-MPS-NEVPT2) that allows us to compute uncontracted dynamic correlation energies for large active spaces and basis sets, using the time-dependent density matrix renormalization group algorithm. In addition, we report a low-scaling MPS-based implementation of strongly contracted NEVPT2 (sc-MPS-NEVPT2) that avoids computation of the four-particle reduced density matrix. We use these new methods to compute the dissociation energy of the chromium dimer and to study the low-lying excited states in all-trans polyenes (C4H6 to C24H26), incorporating dynamic correlation for reference wavefunctions with up to 24 active electrons and orbitals.

Cation-induced band-gap tuning in organohalide perovskites: interplay of spin-orbit coupling and octahedra tilting.

Organohalide lead perovskites have revolutionized the scenario of emerging photovoltaic technologies. The prototype MAPbI3 perovskite (MA = CH3NH3(+)) has dominated the field, despite only harvesting photons above 750 nm (∼1.6 eV). Intensive research efforts are being devoted to find new perovskites with red-shifted absorption onset, along with good charge transport properties. Recently, a new perovskite based on the formamidinium cation ((NH2)2CH(+) = FA) has shown potentially superior properties in terms of band gap and charge transport compared to MAPbI3. The results have been interpreted in terms of the cation size, with the larger FA cation expectedly delivering reduced band-gaps in Pb-based perovskites. To provide a full understanding of the interplay among size, structure, and organic/inorganic interactions in determining the properties of APbI3 perovskites, in view of designing new materials and fully exploiting them for solar cells applications, we report a fully first-principles investigation on APbI3 perovskites with A = Cs(+), MA, and FA. Our results evidence that the tetragonal-to-quasi cubic structural evolution observed when moving from MA to FA is due to the interplay of size effects and enhanced hydrogen bonding between the FA cations and the inorganic matrix altering the covalent/ionic character of Pb-I bonds. Most notably, the observed cation-induced structural variability promotes markedly different electronic and optical properties in the MAPbI3 and FAPbI3 perovskites, mediated by the different spin-orbit coupling, leading to improved charge transport and red-shifted absorption in FAPbI3 and in general in pseudocubic structures. Our theoretical model constitutes the basis for the rationale design of new and more efficient organohalide perovskites for solar cells applications.

A quantitative view of charge transfer in the hydrogen bond: the water dimer case.

The hydrogen bond represents a fundamental intermolecular interaction that binds molecules in vapor and liquid water. A crucial and debated aspect of its electronic structure and chemistry is the charge transfer (CT) accompanying it. Much effort has been devoted, in particular, to the study of the smallest prototype system, the water dimer, but even here results and interpretations differ widely. In this paper, we reassess CT in the water dimer by using charge-displacement analysis. Besides a reliable estimate of the amount of CT (14.6 me) that characterizes the system, our study provides an unambiguous context, and very useful bounds, within which CT effects may be evaluated, crucially including the associated energy stabilization.

Charge-displacement analysis for excited states.

We extend the Charge-Displacement (CD) analysis, already successfully employed to describe the nature of intermolecular interactions [L. Belpassi et al., J. Am. Chem. Soc. 132, 13046 (2010)] and various types of controversial chemical bonds [L. Belpassi et al., J. Am. Chem. Soc. 130, 1048 (2008); N. Salvi et al., Chem. Eur. J. 16, 7231 (2010)], to study the charge fluxes accompanying electron excitations, and in particular the all-important charge-transfer (CT) phenomena. We demonstrate the usefulness of the new approach through applications to exemplary excitations in a series of molecules, encompassing various typical situations from valence, to Rydberg, to CT excitations. The CD functions defined along various spatial directions provide a detailed and insightful quantitative picture of the electron displacements taking place.

Collective Strong Coupling Modifies Aggregation and Solvation.

Intermolecular (Coulombic) interactions are pivotal for aggregation, solvation, and crystallization. We demonstrate that the collective strong coupling of several molecules to a single optical mode results in notable changes in the molecular excitations around a single perturbed molecule, thus representing an impurity in an otherwise ordered system. A competition between short-range coulombic and long-range photonic correlations inverts the local transition density in a polaritonic state, suggesting notable changes in the polarizability of the solvation shell. Our results provide an alternative perspective on recent work in polaritonic chemistry and pave the way for the rigorous treatment of cooperative effects in aggregation, solvation, and crystallization.

Revealing charge-transfer effects in gas-phase water chemistry.

An understanding of the interactions involving water and other small hydrogenated molecules such as H(2)S and NH(3) at the molecular level is an important and elusive scientific goal with potential implications for fields ranging from biochemistry to astrochemistry. One longstanding question about water's intermolecular interactions, and notably hydrogen bonding, is the extent and importance of charge transfer (CT) , which can have important implications for the development of reliable model potentials for water chemistry, among other applications. The weakly bound adducts, commonly regarded as pure van der Waals systems, formed by H(2)O, H(2)S, and NH(3) with noble gases or simple molecules such as H(2), provide an interesting case study for these interactions. Their binding energies are approximately 1 or 2 kJ/mol at most, and CT effects in these systems are thought to be negligible. Our laboratory has performed high-resolution molecular-beam scattering experiments that probe the (absolute scale) intermolecular potential of various types of these gas-phase binary complexes with extreme sensitivity. These experiments have yielded surprising and intriguing quantitative results. The key experimental measurable is the "glory" quantum interference shift that shows a systematic, anomalous energy stabilization for the water complexes and clearly points to a significant role for CT effects. To investigate these findings, we have performed very accurate theoretical calculations and devised a simple approach to study the electron displacement that accompanies gas-phase binary intermolecular interactions in extreme detail. These calculations are based on a partial progressive integration of the electron density changes. The results unambiguously show that water's intermolecular interactions are not typical van der Waals complexes. Instead, these interactions possess a definite, strongly stereospecific CT component, even when very weak, where a water molecule may act as electron donor or acceptor depending on its orientation. CT is mediated by an asymmetric role played by the two hydrogen atoms, which causes strong orientation effects. The careful comparison of these calculations with the experimental results shows that the stabilization energy associated to CT is approximately 2-3 eV per electron transferred and may make up for a large portion of the total interaction energy. A simple electron delocalization model helps to validate and explain these findings.

Molecular van der Waals Fluids in Cavity Quantum Electrodynamics.

Intermolecular van der Waals interactions are central to chemical and physical phenomena ranging from biomolecule binding to soft-matter phase transitions. In this work, we demonstrate that strong light-matter coupling can be used to control the thermodynamic properties of many-molecule systems. Our analyses reveal orientation dependent single molecule energies and interaction energies for van der Waals molecules. For example, we find intermolecular interactions that depend on the distance between the molecules R as R-3 and R0. Moreover, we employ ab initio cavity quantum electrodynamics calculations to develop machine-learning-based interaction potentials for molecules inside optical cavities. By simulating systems ranging from 12 H2 to 144 H2 molecules, we observe varying degrees of orientational order because of cavity-modified interactions, and we explain how quantum nuclear effects, light-matter coupling strengths, number of cavity modes, molecular anisotropies, and system size all impact the extent of orientational order.

Adsorption of organic dyes on TiO2 surfaces in dye-sensitized solar cells: interplay of theory and experiment.

First-principles computer simulations can contribute to a deeper understanding of the dye/semiconductor interface lying at the heart of Dye-sensitized Solar Cells (DSCs). Here, we present the results of simulation of dye adsorption onto TiO(2) surfaces, and of their implications for the functioning of the corresponding solar cells. We propose an integrated strategy which combines FT-IR measurements with DFT calculations to individuate the energetically favorable TiO(2) adsorption mode of acetic acid, as a meaningful model for realistic organic dyes. Although we found a sizable variability in the relative stability of the considered adsorption modes with the model system and the method, a bridged bidentate structure was found to closely match the FT-IR frequency pattern, also being calculated as the most stable adsorption mode by calculations in solution. This adsorption mode was found to be the most stable binding also for realistic organic dyes bearing cyanoacrylic anchoring groups, while for a rhodanine-3-acetic acid anchoring group, an undissociated monodentate adsorption mode was found to be of comparable stability. The structural differences induced by the different anchoring groups were related to the different electron injection/recombination with oxidized dye properties which were experimentally assessed for the two classes of dyes. A stronger coupling and a possibly faster electron injection were also calculated for the bridged bidentate mode. We then investigated the adsorption mode and I(2) binding of prototype organic dyes. Car-Parrinello molecular dynamics and geometry optimizations were performed for two coumarin dyes differing by the length of the π-bridge separating the donor and acceptor moieties. We related the decreasing distance of the carbonylic oxygen from the titania to an increased I(2) concentration in proximity of the oxide surface, which might account for the different observed photovoltaic performances. The interplay between theory/simulation and experiments appears to be the key to further DSCs progress, both concerning the design of new dye sensitizers and their interaction with the semiconductor and with the solution environment and/or an electrolyte upon adsorption onto the semiconductor.

Molecular orbital theory in cavity QED environments.

Coupling between molecules and vacuum photon fields inside an optical cavity has proven to be an effective way to engineer molecular properties, in particular reactivity. To ease the rationalization of cavity induced effects we introduce an ab initio method leading to the first fully consistent molecular orbital theory for quantum electrodynamics environments. Our framework is non-perturbative and explains modifications of the electronic structure due to the interaction with the photon field. In this work, we show that the newly developed orbital theory can be used to predict cavity induced modifications of molecular reactivity and pinpoint classes of systems with significant cavity effects. We also investigate electronic cavity-induced modifications of reaction mechanisms in vibrational strong coupling regimes.

Shining light on the microscopic resonant mechanism responsible for cavity-mediated chemical reactivity.

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.

Time-Step Targeting Time-Dependent and Dynamical Density Matrix Renormalization Group Algorithms with ab Initio Hamiltonians.

We study the dynamical density matrix renormalization group (DDMRG) and time-dependent density matrix renormalization group (td-DMRG) algorithms in the ab initio context to compute dynamical correlation functions of correlated systems. We analyze the strengths and weaknesses of the two methods in small model problems and propose two simple improved formulations, DDMRG++ and td-DMRG++, that give increased accuracy at the same bond dimension at a nominal increase in cost. We apply DDMRG++ to obtain the oxygen core-excitation energy in the water molecule in a quadruple-zeta quality basis, which allows us to estimate the remaining correlation error in existing coupled cluster results. Further, we use DDMRG++ to compute the local density of states and gaps and td-DMRG++ to compute the complex polarization function, in linear hydrogen chains with up to 50 H atoms, to study metallicity and delocalization as a function of bond length.