Simple Protocol for Capturing Both Linear-Response and State-Specific Effects in Excited-State Calculations with Continuum Solvation Models.

We present an effective computational protocol (cLR2) to describe both solvatochromism and fluorosolvatochromism. This protocol, which couples the polarizable continuum model to time-dependent density functional theory, simultaneously accounts for both linear-response and state-specific solvation effects. A series of test cases, including solvatochromic and fluorosolvatochromic compounds and excited-state intramolecular proton transfers, are used to highlight that cLR2 is especially beneficial for modeling bright excitations possessing a significant charge-transfer character, as well as cases in which an accurate balance between states of various polarities should be restored.

Exploring the Spatial Features of Electronic Transitions in Molecular and Biomolecular Systems by Swift Electrons.

We devise a new kind of experiment that extends the technology of electron energy loss spectroscopy to probe (supra-)molecular systems: by using an electron beam in a configuration that avoids molecular damage and a very recently introduced electron optics setup for the analysis of the outcoming electrons, one can obtain information on the spatial features of the investigated excitations. Physical insight into the proposed experiment is provided by means of a simple but rigorous model to obtain the transition rate and selection rule. Numerical simulations of DNA G-quadruplexes and other biomolecular systems, based on time dependent density functional theory calculations, point out that the conceived new technique can probe the multipolar components and even the chirality of molecular transitions, superseding the usual optical spectroscopies for those cases that are problematic, such as dipole-forbidden transitions, at a very high spatial resolution.

Investigating ultrafast two-pulse experiments on single DNQDI fluorophores: a stochastic quantum approach.

Ultrafast two-pulse experiments on single molecules are invaluable tools to investigate the microscopic dynamics of a fluorophore. The first pulse generates electronic or vibronic coherence and the second pulse probes the time-evolution of the coherence. A protocol that is able to simulate ultrafast experiments on single molecules is applied in this study. It is based on a coupled quantum-mechanical description of the fluorophore and real-time dynamics of the system vibronic wave packet interacting with an electric field, described by means of the stochastic Schrödinger equation within the Markovian limit. This approach is applied to the DNQDI fluorophore, previously investigated experimentally [D. Brinks et al., Nature, 2010, 465, 905-908]. We find this to be in good agreement with the experimental outcomes and provide microscopic and atomistic interpretation.

An open quantum system theory for polarizable continuum models.

The problem of a solute described by Quantum Chemistry within a solvent represented as a polarizable continuum model (PCM) is here reformulated in terms of the open quantum systems (OQS) theory. Using its stochastic Schrödinger equation formulation, we are able to provide a more comprehensive picture of the electronic energies and the coupling between solute and solvent electronic dynamics. In particular, the OQS-PCM proves to be a unifying theoretical framework naturally including polarization and dispersion interactions, the effect of solvent fluctuations, and the non-Markovian solvent response. As such, the OQS-PCM describes the interplay between the solute and the solvent typical electronic dynamical times and yields both the standard PCM and the so-called Born-Oppenheimer solvation regime, where the solvent electronic response is considered faster than any electronic dynamics taking place in the solute. In analyzing the OQS-PCM, we obtained an expression for the solute-solvent dispersion (van der Waals) interactions, which is very transparent in terms of a physical interpretation based on fluctuations and response functions. Finally, we present various numerical tests that support the theoretical findings.

First-principles investigation of the double ESIPT process in a thiophene-based dye.

The unusual emission spectrum of 2,5-bis(benzoxazol-2-yl)thiophene-3,4-diol (BBTP) is investigated. The complexity of the emission spectrum of this dye is due to the presence of two excited-state intramolecular proton transfer (ESIPT) sites that give rise to three non-equivalent tautomers. The different maxima were experimentally attributed to the initial double enol form, the single ESIPT enol-keto tautomer, and the double ESIPT structure. Our simulations, based on Time Dependent Density Functional Theory (TD-DFT) and post Hartree-Fock methods [ADC(2) and CC2] coupled to different schemes to include the solvent polarisation response, are able to reproduce the key experimental outcomes. Moreover, we prove that for solving the inconsistencies present in earlier theoretical studies, a state-specific solvation approach is needed: one should go beyond the standard linear-response scheme in polarisable dielectric models. Finally, using a validated model, we explore the impact of substitution by donor and acceptor groups.

Coupling to Charge Transfer States is the Key to Modulate the Optical Bands for Efficient Light Harvesting in Purple Bacteria.

The photosynthetic apparatus of purple bacteria uses exciton delocalization and static disorder to modulate the position and broadening of its absorption bands, leading to efficient light harvesting. Its main antenna complex, LH2, contains two rings of identical bacteriochlorophyll pigments, B800 and B850, absorbing at 800 and 850 nm, respectively. It has been an unsolved problem why static disorder of the strongly coupled B850 ring is several times larger than that of the B800 ring. Here we show that mixing between excitons and charge transfer states in the B850 ring is responsible for the effect. The linear absorption spectrum of the LH2 system is simulated by using a multiscale approach with an exciton Hamiltonian generalized to include the charge transfer states that involve adjacent pigment pairs, with static disorder modeled microscopically by molecular dynamics simulations. Our results show that sufficient inhomogeneous broadening of the B850 band, needed for efficient light harvesting, is only obtained by utilizing static disorder in the coupling between local excited and interpigment charge transfer states.

The Bethe-Salpeter formalism with polarisable continuum embedding: reconciling linear-response and state-specific features.

The Bethe-Salpeter equation (BSE) formalism has been recently shown to be a valuable alternative to time-dependent density functional theory (TD-DFT) with the same computing time scaling with system size. In particular, problematic transitions for TD-DFT such as charge-transfer, Rydberg and cyanine-like excitations were shown to be accurately described with BSE. We demonstrate here that combining the BSE formalism with the polarisable continuum model (PCM) allows us to include simultaneously linear-response and state-specific contributions to solvatochromism. This is confirmed by exploring transitions of various natures (local, charge-transfer, etc.) in a series of solvated molecules (acrolein, indigo, p-nitro-aniline, donor-acceptor complexes, etc.) for which we compare BSE solvatochromic shifts to those obtained by linear-response and state-specific TD-DFT implementations. Such a remarkable and unique feature is particularly valuable for the study of solvent effects on excitations presenting a hybrid localised/charge-transfer character.

Density-Dependent Formulation of Dispersion-Repulsion Interactions in Hybrid Multiscale Quantum/Molecular Mechanics (QM/MM) Models.

Mixed multiscale quantum/molecular mechanics (QM/MM) models are widely used to explore the structure, reactivity, and electronic properties of complex chemical systems. Whereas such models typically include electrostatics and potentially polarization in so-called electrostatic and polarizable embedding approaches, respectively, nonelectrostatic dispersion and repulsion interactions are instead commonly described through classical potentials despite their quantum mechanical origin. Here we present an extension of the Tkatchenko-Scheffler semiempirical van der Waals (vdWTS) scheme aimed at describing dispersion and repulsion interactions between quantum and classical regions within a QM/MM polarizable embedding framework. Starting from the vdWTS expression, we define a dispersion and a repulsion term, both of them density-dependent and consistently based on a Lennard-Jones-like potential. We explore transferable atom type-based parametrization strategies for the MM parameters, based on either vdWTS calculations performed on isolated fragments or on a direct estimation of the parameters from atomic polarizabilities taken from a polarizable force field. We investigate the performance of the implementation by computing self-consistent interaction energies for the S22 benchmark set, designed to represent typical noncovalent interactions in biological systems, in both equilibrium and out-of-equilibrium geometries. Overall, our results suggest that the present implementation is a promising strategy to include dispersion and repulsion in multiscale QM/MM models incorporating their explicit dependence on the electronic density.

EXAT: EXcitonic analysis tool.

We introduce EXcitonic Analysis Tool (EXAT), a program able to compute optical spectra of large excitonic systems directly from the output of quantum mechanical calculations performed with the popular Gaussian 16 package. The software is able to combine in an excitonic scheme the single-chromophore properties and exciton couplings to simulate energies, coefficients, and excitonic spectra (UV-vis, CD, and LD). The effect of the environment can also be included using a Polarizable Continuum Model. EXAT also presents a simple graphical user interface, which shows on-screen both site and exciton properties. To show the potential of the method, we report two applications on a a chiral perturbed BODIPY system and DNA G-quadruplexes, respectively. The program is available online at http://molecolab.dcci.unipi.it/tools/. © 2017 Wiley Periodicals, Inc.

An Ab Initio Description of the Excitonic Properties of LH2 and Their Temperature Dependence.

The spectroscopic properties of light-harvesting (LH) antennae in photosyntehtic organisms represent a fingerprint that is unique for each specific pigment-protein complex. Because of that, spectroscopic observations are generally combined with structural data from X-ray crystallography to obtain an indirect representation of the excitonic properties of the system. Here, an alternative strategy is presented which goes beyond this empirical approach and introduces an ab initio computational description of both structural and electronic properties and their dependence on the temperature. The strategy is applied to the peripheral light-harvesting antenna complex (LH2) present in purple bacteria. By comparing this model with the one based on the crystal structure, a detailed, molecular level explanation of the absorption and circular dichroism (CD) spectra and their temperature dependence is achieved. The agreement obtained with the experiments at both low and room temperature lays the groundwork for an atomistic understanding of the excitation dynamics in the LH2 system.

Circularly Polarized Luminescence from Axially Chiral BODIPY DYEmers: An Experimental and Computational Study.

With our new home-built circularly polarized luminescence (CPL) instrument, we measured fluorescence and CPL spectra of the enantiomeric pairs of two quasi-isomeric BODIPY DYEmers 1 and 2, endowed with axial chirality. The electronic circular dichroism (ECD) and CPL spectra of these atropisomeric dimers are dominated by the exciton coupling between the main π-π* transitions (550-560 nm) of the two BODIPY rings. Compound 1 has strong ECD and CPL spectra (glum =4×10-3 ) well reproduced by TD-DFT and SCS-CC2 (spin-component scaled second-order approximate coupled-cluster) calculations using DFT-optimized ground- and excited-state structures. Compound 2 has weaker ECD and CPL spectra (glum =4×10-4 ), partly due to the mutual cancellation of electric-electric and electric-magnetic exciton couplings, and partly to its conformational freedom. This compound is computationally very challenging. Starting from the optimized excited-state geometries, we predicted the wrong sign for the CPL band of 2 using TD-DFT with the most recommended hybrid and range-separated functionals, whereas SCS-CC2 or a DFT functional with full exact exchange provided the correct sign.

Control of Coherences and Optical Responses of Pigment-Protein Complexes by Plasmonic Nanoantennae.

The key for light-harvesting in pigment-protein complexes are molecular excitons, delocalized excited states comprising a superposition of excitations at different molecular sites. There is experimental evidence that the optical response due to such excitons can be largely affected by plasmonic nanoantennae. Here we employ a multiscale approach combining time-dependent density functional theory and polarizable classical models to study the optical behavior of the LH2 complex present in bacteria when interacting with a gold nanorod. The simulation not only reproduces the experiments but also explains their molecular origin. By tuning the chromophoric unit and selectively switching on/off the excitonic interactions, as well as by exploring different setups, we clearly show that the dramatic enhancement in the optical response, unexpectedly, is not accompanied by changes in the coherences. Instead polarization effects are dominant. These results can be used to design an optimal control of the light-harvesting process through plasmonic nanoantennae.

Electronic Excitations in Solution: The Interplay between State Specific Approaches and a Time-Dependent Density Functional Theory Description.

We critically analyze the performances of continuum solvation models when coupled to time-dependent density functional theory (TD-DFT) to predict solvent effects on both absorption and emission energies of chromophores in solution. Different polarization schemes of the polarizable continuum model (PCM), such as linear response (LR) and three different state specific (SS) approaches, are considered and compared. We show the necessity of introducing a SS model in cases where large electron density rearrangements are involved in the excitations, such as charge-transfer transitions in both twisted and quadrupolar compounds, and underline the very delicate interplay between the selected polarization method and the chosen exchange-correlation functional. This interplay originates in the different descriptions of the transition and ground/excited state multipolar moments by the different functionals. As a result, the choice of both the DFT functional and the solvent polarization scheme has to be consistent with the nature of the studied electronic excitation.

The role of magnetic-electric coupling in exciton-coupled ECD spectra: the case of bis-phenanthrenes.

Apparent exceptions to the exciton chirality method may arise for chromophores undergoing transitions which are both electric- and magnetic-dipole allowed, for example bis-phenanthrenes. We present a computational approach to calculate exciton-coupled CD spectra based on a quantum-mechanical description of the excitonic parameters, which also includes the solvent effects.

Plasmon enhanced light harvesting: multiscale modeling of the FMO protein coupled with gold nanoparticles.

Plasmonic systems, such as metal nanoparticles, are becoming increasingly important in spectroscopies and devices because of their ability to enhance, even by several orders of magnitude, the photophysical properties of neighboring systems. In particular, it has been shown both theoretically and experimentally that combining nanoplasmonic devices with natural light-harvesting proteins substantially increases the fluorescence and absorption properties of the system. This kind of biohybrid device can have important applications in the characterization and design of efficient light-harvesting systems. In the present work, the FMO light-harvesting protein was combined with gold nanoparticles of different sizes, and its photophysical properties were characterized using a multiscale quantum-mechanical classical-polarizable and continuum model (QM/MMPol/PCM). By optimal tuning of the plasmon resonance of the metal nanoparticles, fluorescence enhancements of up to 2 orders of magnitude were observed. Orientation effects were found to be crucial: amplifications by factors of up to 300 were observed for the absorption process, while the radiative decay of the emitting state increased at most by a factor of 10, mostly as a result of poor alignment of the emitting state with the considered metal aggregates. Despite being a limiting factor for high-fluorescence-enhancement devices, the strong orientation dependence may represent an important feature of the natural light-harvesting system that could allow selective enhancement of a specific excited state of the complex.

Effective electron displacements: a tool for time-dependent density functional theory computational spectroscopy.

We extend our previous definition of the metric Δr for electronic excitations in the framework of the time-dependent density functional theory [C. A. Guido, P. Cortona, B. Mennucci, and C. Adamo, J. Chem. Theory Comput. 9, 3118 (2013)], by including a measure of the difference of electronic position variances in passing from occupied to virtual orbitals. This new definition, called Γ, permits applications in those situations where the Δr-index is not helpful: transitions in centrosymmetric systems and Rydberg excitations. The Γ-metric is then extended by using the Natural Transition Orbitals, thus providing an intuitive picture of how locally the electron density changes during the electronic transitions. Furthermore, the Γ values give insight about the functional performances in reproducing different type of transitions, and allow one to define a "confidence radius" for GGA and hybrid functionals.

Communication: one third: a new recipe for the PBE0 paradigm.

We analyze the performances of the parameter-free hybrid density functional PBE0-1/3 obtained combining the PBE generalized-gradient functional with a predefined amount of exact exchange of 1/3, as recently discussed by Cortona [J. Chem. Phys. 136, 086101 (2012)]. The numerical results that we have obtained for various properties, such as atomization energies (G2-148 dataset), weak interactions (NCB31 dataset), hydrogen-bond length optimizations, and dissociation energies (HB10 dataset), and vertical excitation energies, show an increased performance of PBE0-1/3 with respect to the widely used PBE0. We therefore propose to use one third as the mixing coefficient for the PBE-based hybrid functional.

Benchmarking Time-Dependent Density Functional Theory for Excited State Geometries of Organic Molecules in Gas-Phase and in Solution.

We analyze potentials and limits of the Time-Dependent Density Functional Theory (TD-DFT) approach for the determination of excited-state geometries of organic molecules in gas-phase and in solution. Three very popular DFT exchange-correlation functionals, two hybrids (B3LYP and PBE0) and one long-range corrected (CAM-B3LYP), are here investigated, and the results are compared to the correlated RI-CC2 wave function approach. Solvent effects are further analyzed by means of a polarizable continuum model. A total of 15 organic chromophores (including both small molecules and larger push-pull systems) are considered as prototypes of n → π* and π → π* singlet excitations. Our analysis allows to point out specific correlations between the accuracy of the various functionals and the type of excitation and/or the type of chemical bonds involved. We find that while the best ground-state geometries are obtained with PBE0 and B3LYP, CAM-B3LYP yields the most accurate description of electronic and geometrical characteristics of excited states, both in gas-phase and in solution.

On the Metric of Charge Transfer Molecular Excitations: A Simple Chemical Descriptor.

A new index is defined with the aim of further exploring the metric of excited electronic states in the framework of the time-dependent density functional theory. This descriptor, called Δr, is based on the charge centroids of the orbitals involved in the excitations and can be interpreted in term of the hole-electron distance. The tests carried out on a set of molecules characterized by a significant number of charge-transfer excitations well illustrate its ability in discriminating between short (Δr ≤ 1.5 Å) and long-range (Δr ≥ 2.0 Å) excitations. On the basis of the well-known pitfalls of TD-DFT, its values can be then associated to the functional performances in reproducing different type of transitions and allow for the definition of a "trust radius" for GGA and hybrid functionals. The study of other systems, including some well-known difficult cases for other metric descriptors, gives further evidence of the high discrimination power of the proposed index. The combined use with other density or orbital-based descriptors is finally suggested to have a reliable diagnostic test of TD-DFT transitions.

The Fate of a Zwitterion in Water from ab Initio Molecular Dynamics: Monoethanolamine (MEA)-CO2.

Understanding the fundamental reactions accompanying the capture of carbon dioxide in amine solutions is critical for the design of high-performance solvents and requires an accurate modeling of the solute-solvent interaction. As a first step toward this goal, using ab initio molecular dynamics (Car-Parrinello) simulations, we investigate a zwitterionic carbamate, a species long proposed as intermediate in the formation of a stable carbamate, in a dilute aqueous solution. CO2 release and deprotonation are competitive routes for its dissociation and are both characterized by free-energy barriers of 6-8 kcal/mol. Water molecules play a crucial role in both pathways, resulting in large entropic effects. This is especially true in the case of CO2 release, which is accompanied by a strong reorganization of the solvent beyond the first coordination shell, leading to the formation of a water cage entrapping the solute (hydrophobic effect). Our results contrast with the assumptions of implicit solvent models.