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Mechanical deformations, either spontaneously occurring during sample preparation or purposely induced in their nanoscale manipulation, drastically affect the electronic and optical properties of transition metal dichalcogenide monolayers. In this first-principles work based on density-functional theory, we shed light on the interplay among strain, curvature, and electronic structure of MoSe$_2$ nanowrinkles. We analyze their structural properties highlighting the effects of coexisting local domains of tensile and compressive strain in the same system. By contrasting the band structures of the nanowrinkles against counterparts obtained for flat monolayers subject to the same amount of strain, we clarify that the specific features of the former, such as the moderate variation of the band-gap size and its persisting direct nature, are ruled by curvature rather than strain. The analysis of the wave-function distribution indicates strain-dependent localization of the frontier states in the conduction region while in the valence the sensitivity to strain is much less pronounced. The discussion about transport properties, based on the inspection of the effective masses, reveals excellent perspectives for these systems as active components for (opto)electronic devices.

Organic/inorganic interfaces formed by monolayer substrates and conjugated molecular adsorbates are attractive material platforms leveraging the modularity of organic compounds together with the long-range phenomena typical of condensed matter. New quantum states are known to be generated by electronic interactions in these systems as well as by their coupling with light. However, little is still known about hybrid vibrational modes. In this work, we discover from first principles the existence of an infrared-active chiral phonon mode in a pyrene-decorated MoSe$_{2}$ monolayer given by the combination of a frustrated rotation of the molecule around its central axis and an optical mode in the substrate. Our results suggest the possibility to enable phonon chirality in molecular superlattices.

The recent development of multidimensional ultrafast spectroscopy techniques calls for the introduction of computational schemes that allow for the simulation of such experiments and the interpretation of the corresponding results from a microscopic point of view. In this work, we present a general and efficient first-principles scheme to compute two-dimensional electronic spectroscopy maps based on real-time time-dependent density-functional theory. The interface of this approach with the Ehrenfest scheme for molecular dynamics enables the inclusion of vibronic effects in the calculations based on a classical treatment of the nuclei. The computational complexity of the simulations is reduced by the application of numerical advances such as branching techniques, undersampling, and a novel reduced phase cycling scheme, applicable for systems with inversion symmetry. We demonstrate the effectiveness of this method by applying it to prototypical molecules such as benzene, pyridine, and pyrene. We discuss the role of the approximations that inevitably enter the adopted theoretical framework and set the stage for further extensions of the proposed method to more realistic systems.

The ultrafast dynamics of charge carriers in organic donor-acceptor interfaces are of primary importance to understanding the fundamental properties of these systems. In this work, we focus on a charge-transfer complex formed by quaterthiophene $p$-doped by tetrafluoro-tetracyanoquinodimethane and investigate electron dynamics and vibronic interactions also at finite temperatures by applying a femtosecond pulse in resonance with the two lowest-energy excitations of the system with perpendicular and parallel polarization with respect to the interface. The adopted \textit{ab initio} formalism based on real-time time-dependent density-functional theory coupled to Ehrenfest dynamics enables monitoring the dynamical charge transfer across the interface and assessing the role played by the nuclear motion. Our results show that the strong intermolecular interactions binding the complex already in the ground state influence the dynamics, too. The analysis of the nuclear motion involved in these processes reveals the participation of different vibrational modes depending on the electronic states stimulated by the resonant pulse. Coupled donor-acceptor modes mostly influence the excited state polarized across the interface, while intramolecular vibrations in the donor molecule dominate the excitation in the orthogonal direction. The results obtained at finite temperatures are overall consistent with this picture, although thermal disorder contributes to slightly decreasing interfacial charge transfer.

First-principles simulations of electronic properties of hybrid inorganic/organic interfaces are challenging, as common density-functional theory (DFT) approximations target specific material classes like bulk semiconductors or gas-phase molecules. Taking as a prototypical example anthracene physisorbed on monolayer MoS$_2$, we assess the ability of different \textit{ab initio} schemes to describe the electronic structure using semi-local and hybrid DFT. For the latter, an unconstrained three-parameter range-separation scheme is employed. Comparisons against many-body perturbation theory results indicate that DFT is substantially unable to make reliable predictions about interfacial properties. Hybrid functionals, while improving the accuracy of the MoS$_2$ band structure, do not systematically enhance the description of hybrid systems with respect to semi-local functionals. Neither approach provides a good starting point for $G_0W_0$, which, consequently, cannot provide much information beyond the correct energy level alignment. We show that non-empirically parametrized electrostatic screening models can accomplish the same task at negligible computational costs. Such schemes can include substrates of hybrid interfaces in good agreement with experimental data. Our results indicate that currently, fully atomistic, many-body simulations of weakly interacting hybrid systems are not worth the required computational resources. In contrast, ab-initio-parametrized effective models mimicking the environment offer a scalable alternative without compromising accuracy and predictivity.

Modeling the electronic and optical properties of organic semiconductors remains a challenge for theory, despite the remarkable progress achieved in the last three decades. The complexity of these systems, including structural (dis)order and the still debated doping mechanisms, has been engaging theorists with different backgrounds. Regardless of the common interest across the various communities active in this field, these efforts have not led so far to a truly interdisciplinary research area. In the attempt to move further in this direction, we present our perspective as solid-state theorists for the study of molecular materials in different states of matter. Considering exemplary systems belonging to well-known families of oligo-acenes and -thiophenes, we provide a quantitative description of electronic properties and optical excitations obtained with state-of-the-art first-principles methods such as density-functional theory and many-body perturbation theory. Simulating the systems as gas-phase molecules, clusters, and periodic lattices, we are able to identify short- and long-range effects in their electronic structure. While the latter are usually dominant in organic crystals, the former play an important role, too, especially in the case of donor/acceptor complexes. Furthermore, we demonstrate the viability of implicit schemes to evaluate band gaps of molecules embedded in isotropic and even anisotropic environments, in quantitative agreement with experiments. In the context of doped organic semiconductors, we show how the crystalline packing enhances the favorable characteristics of these systems for opto-electronic applications. The counter-intuitive behavior predicted for their electronic and optical properties is deciphered with the aid of a tight-binding model, which represents a connection to the most common approaches to evaluate transport properties in these materials.

The design of low-dimensional organic-inorganic interfaces for the next generation of opto-electronic applications requires an in-depth understanding of the microscopic mechanisms ruling electronic interactions in these systems. In this work, we present a first-principles study based on density-functional theory inspecting the structural, energetic, and electronic properties of five molecular donors and acceptors adsorbed on freestanding hexagonal boron nitride (hBN) and molybdenum disulfide (MoS$_2$) monolayers. All considered heterostructures are stable, due to the crucial contribution of dispersion interactions, which are maximized by the overall flat arrangement of the physisorbed molecules on both substrates. The level alignment of the hybrid systems depends on the characteristics of the constituents. On hBN, both type-I and type-II heterostructures may form, depending on the relative energies of the frontier orbitals with respect to the vacuum level. On the other hand, all MoS$_2$-based hybrid systems exhibit a type-II level alignment, with the molecular frontier orbitals positioned across the energy gap of the semiconductor. The electronic structure of the hybrid materials is further determined by the formation of interfacial dipole moments and by the wave-function hybridization between the organic and inorganic constituents. These results provide important indications for the design of novel low-dimensional hybrid materials with suitable characteristics for opto-electronics.

Understanding the fundamental mechanisms ruling laser-induced coherent charge transfer in hybrid organic/inorganic interfaces is of paramount importance to exploit these systems in next-generation opto-electronic applications. In a first-principles work based on real-time time-dependent density-functional theory, we investigate the ultrafast charge-carrier dynamics of a prototypical two-dimensional vertical nanojunction formed by a MoSe$_2$ monolayer with adsorbed pyrene molecules. The response of the system to the incident pulse, set in resonance with the frequency of the lowest-energy transition in the physisorbed moieties, is clearly nonlinear. Under weak pulses, charge transfer occurs from the molecules to the monolayer while for intensities higher than 1000 GW/cm$^{2}$, the direction of charge transfer is reverted, with electrons being transferred from MoSe$_2$ to pyrene. This finding is explained by Pauli blocking: laser-induced (de)population of (valence) conduction states saturates for intensities beyond 200 GW/cm$^{2}$. Evidence of multi-photon absorption is also provided by our results. A thorough analysis of electronic current density, excitation energy, and number of excited electrons supports the proposed rationale and suggests the possibility to create an inorganic/organic coherent optical nanojunction for ultrafast electronics.

The atomistic resolution recently achieved by ultrafast spectroscopies demands corresponding theoretical advances. Real-time time-dependent density-functional theory (RT-TDDFT) with Ehrenfest dynamics offers an optimal trade-off between accuracy and computational costs to study electronic and vibrational dynamics of laser-excited materials in the sub-picosecond regime. However, this approach is unable to account for thermal effects or zero-point energies which are crucial in the physics involved. Herein, we adopt a quantum-semiclassical method based on RT-TDDFT+Ehrenfest to simulate laser-induced electronic and vibrational coherences in condensed matter. With the example of carbon-conjugated molecules, we show that ensemble-averaging with initial configurations from a nuclear quantum distribution remedies many shortcomings of single-trajectory RT-TDDFT+Ehrenfest, damping electronic coherence and introducing ultrafast non-adiabatic coupling between excited states. As the number of sampled configurations decreases with size and rigidity of the compounds, computational costs remain moderate for large systems for which mean-field approaches shine. The explicit inclusion of a time-dependent pulse in the simulations makes this method a prime advance for first-principles studies of coherent nonlinear spectroscopy as an independent counterpart to experimental results.

Among polycyclic aromatic hydrocarbons, pyrene is widely used as an optical probe thanks to peculiar ultraviolet absorption and infrared emission features. Interestingly, this molecule is also an abundant component of the interstellar medium, where it is detected via its unique spectral fingerprints. In this work, we present a comprehensive first-principles study on the electronic and vibrational response of pyrene and its cation to ultrafast, coherent pulses in resonance with their optically active excitations in the ultraviolet region. The analysis of molecular symmetries, electronic structure, and linear optical spectra is used to interpret transient absorption spectra and kinetic energy spectral densities computed for the systems excited by ultrashort laser fields. By disentangling the effects of the electronic and vibrational dynamics via \textit{ad hoc} simulations with stationary and moving ions, and, in specific cases, with the aid of auxiliary model systems, we rationalize that the nuclear motion is mainly harmonic in the neutral species, while strong anharmonic oscillations emerge in the cation, driven by electronic coherence. Our results provide additional insight into the ultrafast vibronic dynamics of pyrene and related compounds and set the stage for future investigations on more complex carbon-conjugated molecules.

Hybridization effects play a crucial role in determining the electronic properties of hybrid inorganic/organic interfaces. To gain insight into these important interactions, we perform a first-principles study based on hybrid density-functional theory including spin-orbit coupling, focusing on eight representative systems formed by two carbon-conjugated molecules-pyrene and perylene-physisorbed on the transition-metal dichalcogenide monolayers (TMDCs) MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$. By means of band unfolding techniques, we analyze the band structures of the considered materials, identifying the contributions of the individual constituents as well as the signatures of their hybridization. Based on symmetry and energetic arguments, we derive general conditions for electronic hybridization between conjugated molecules and underlying TMDCs even when the former do not lie planar on the latter, thus providing the key to predict how their mutual arrangement affects their electronic interactions.

We present LayerPCM, an extension of the polarizable-continuum model coupled to real-time time-dependent density-functional theory for an efficient and accurate description of the electrostatic interactions between molecules and multilayered dielectric substrates on which they are physisorbed. The former are modelled quantum-mechanically, while the latter are treated as polarizable continua characterized by their dielectric constants. The proposed approach is purposely designed to simulate complex hybrid heterostructures, with nano-engineered substrates including a stack of anisotropic layers. LayerPCM is suitable to describe the polarization-induced renormalization of frontier energy levels of the adsorbates in the static regime. Moreover, it can be reliably applied to simulating laser-induced ultrafast dynamics of the molecules through the inclusion of electric fields generated by Fresnel-reflection at the substrate. Depending on the complexity of the underlying layer structure, such reflected fields can assume non-trivial shapes and profoundly affect the dynamics of the photo-excited charge carriers in the molecule. In particular, the interaction with the substrate can give rise to strong delayed fields which lead to interference effects resembling those of multi-pulse-based spectroscopy. The robustness of the implementation and the above-mentioned features are demonstrated with a number of examples, ranging from intuitive models to realistic systems.

The first-principles simulation of the electronic structure of organic semiconductors in solution poses a number of challenges that are not trivial to address simultaneously. In this work, we investigate the effects and the mutual interplay of solvation, alkylization, and doping on the structural, electronic, and optical properties of sexithiophene, a representative organic semiconductor molecule. To this end, we employ (time-dependent) density functional theory in conjunction with the polarizable-continuum model. We find that the torsion between adjacent monomer units plays a key role, as it strongly influences the electronic structure of the molecule, including energy gap, ionization potential, and band widths. Alkylization promotes delocalization of the molecular orbitals up to the first methyl unit, regardless of the chain length, leading to an overall shift of the energy levels. The alterations in the electronic structure are reflected in the optical absorption, which is additionally affected by dynamical solute-solvent interactions. Taking all these effects into account, solvents decrease the optical gap by an amount that depends on its polarity, and concomitantly increase the oscillator strength of the first excitation. The interaction with a dopant molecule promotes planarization. In such scenario, solvation and alkylization enhance charge transfer both in the ground state and in the excited state.

Hybrid interfaces formed by inorganic semiconductors and organic molecules are intriguing materials for opto-electronics. Interfacial charge transfer is primarily responsible for their peculiar electronic structure and optical response. Hence, it is essential to gain insight into this fundamental process also beyond the static picture. Ab initio methods based on real-time time-dependent density-functional theory coupled to the Ehrenfest molecular dynamics scheme are ideally suited for this problem. We investigate a laser-excited hybrid inorganic/organic interface formed by the electron acceptor molecule 2,3,5,6-tetrafluoro-7,7,8,8-tetracyano-quinodimethane (F4TCNQ) physisorbed on a hydrogenated silicon cluster, and we discuss the fundamental mechanisms of charge transfer in the ultrashort time window following the impulsive excitation. The considered interface is $p$-doped and exhibits charge transfer in the ground state. When it is excited by a resonant laser pulse, the charge transfer across the interface is additionally increased, but contrary to previous observations in all-organic donor/acceptor complexes, it is not further promoted by vibronic coupling. In the considered time window of 100~fs, the molecular vibrations are coupled to the electron dynamics and enhance intramolecular charge transfer. Our results highlight the complexity of the physics involved and demonstrate the ability of the adopted formalism to achieve a comprehensive understanding of ultrafast charge transfer in hybrid materials.

Real-time time-dependent density functional theory, in conjunction with the Ehrenfest molecular dynamics scheme, is becoming a popular methodology to investigate ultrafast phenomena on the nanoscale. Thanks to recent developments, it is also possible to explicitly include in the simulations a time-dependent laser pulse, thereby accessing the transient excitation regime. However, the complexity entailed in these calculations calls for in-depth analysis of the accessible and yet approximate (either "dressed" or "bare") quantities, in order to evaluate their ability to provide us with a realistic picture of the simulated processes. In this work, we analyze the ultrafast dynamics of three small molecules (ethylene, benzene, and thiophene) excited by a resonant laser pulse in the framework of the adiabatic local-density approximation. The electronic response to the laser perturbation in terms of induced dipole moment and excited-state population is compared to the results given by an exactly solvable two-level model. In this way, we can interpret the charge-carrier dynamics in terms of simple estimators, such as the number of excited electrons. From the computed transient absorption spectra we unravel the appearance of nonlinear effects such as excited-state absorption and vibronic coupling. In this way, we observe that the laser excitation affects the vibrational spectrum by enhancing the anharmonicities therein while the coherent vibrational motion contributes to stabilize the electronic excitation already within a few tens of femtoseconds., Comment: Supplemental information available on the journal page