Linear Response Theory and Electronic Transition Energies for a Fully Polarizable QM/Classical Hamiltonian

A Vision for the Future of Multiscale Modeling

The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.

Time-Dependent Multilevel Density Functional Theory

We present a novel three-layer approach based on multilevel density functional theory (MLDFT) and polarizable molecular mechanics to simulate the electronic excitations of chemical systems embedded in an external environment within the time-dependent DFT formalism. In our method, the electronic structure of a target system, the chromophore, is determined in the field of an embedded inactive layer, which is treated as frozen. Long-range interactions are described by employing the polarizable fluctuating charge (FQ) force field. The resulting MLDFT/FQ thus accurately describes both electrostatics (and polarization) and non-electrostatic target-environment interactions. The robustness and reliability of the approach are demonstrated by comparing our results with experimental data reported for various organic molecules in solution.

Polarizable Embedding without Artificial Boundary Polarization

We present a fully self-consistent polarizable embedding (PE) model that does not suffer from unphysical boundary polarization. This is achieved through the use of the minimum-image convention (MIC) in the induced electrostatics. It is a simple yet effective approach that includes a more physically accurate description of the polarization throughout the molecular system. Using PE with MIC (PE-MIC), we shed new light on the limitations of commonly employed cutoff models, such as the droplet model, when used in PE calculations. Specifically, we investigate the effects of the unphysical polarization at the outer boundary by comparing induced dipoles and the associated electrostatic potentials, as well as some optical properties of solute-solvent and biomolecular systems. We show that the magnitude of the inaccuracies caused by the unphysical polarization depends on multiple parameters: the nature of the quantum subsystem and of the environment, the cutoff model and distance, and the calculated property.

Induction effects on the absorption maxima of photoreceptor proteins

Multiscale simulations have been established as a powerful tool to calculate and predict excitation energies in complex systems such as photoreceptor proteins. In these simulations the chromophore is typically treated using quantum mechanical (QM) methods while the protein and surrounding environment are described by a classical molecular mechanics (MM) force field. The electrostatic interactions between these regions are often treated using electrostatic embedding where the point charges in the MM region polarize the QM region. A more sophisticated treatment accounts also for the polarization of the MM region. In this work, the effect of such a polarizable embedding on excitation energies was benchmarked and compared to electrostatic embedding. This was done for two different proteins, the lipid membrane-embedded jumping spider rhodopsin and the soluble cyanobacteriochrome Slr1393g3. It was found that the polarizable embedding scheme produces absorption maxima closer to experimental values. The polarizable embedding scheme was also benchmarked against expanded QM regions and found to be in qualitative agreement. Treating individual residues as polarizable recovered between 50% and 71% of the QM improvement in the excitation energies, depending on the system. A detailed analysis of each amino acid residue in the chromophore binding pocket revealed that aromatic residues result in the largest change in excitation energy compared to the electrostatic embedding. Furthermore, the computational efficiency of polarizable embedding allowed it to go beyond the binding pocket and describe a larger portion of the environment, further improving the results.

Understanding Charge Dynamics in Dense Electronic Manifolds in Complex Environments

Photoinduced charge transfer (CT) excited states and their relaxation mechanisms can be highly interdependent on the environment effects and the consequent changes in the electronic density. Providing a molecular interpretation of the ultrafast (subpicosecond) interplay between initial photoexcited states in such dense electronic manifolds in condensed phase is crucial for improving and understanding such phenomena. Real-time time-dependent density functional theory is here the method of choice to observe the charge density, explicitly propagated in an ultrafast time domain, along with all time-dependent properties that can be easily extracted from it. A designed protocol of analysis for real-time electronic dynamics to be applied to time evolving electronic density related properties to characterize both in time and in space CT dynamics in complex systems is here introduced and validated, proposing easy to be read cross-correlation maps. As case studies to test such tools, we present the photoinduced charge-transfer electronic dynamics of 5-benzyluracil, a mimic of nucleic acid/protein interactions, and the metal-to-ligand charge-transfer electronic dynamics in water solution of [Ru(dcbpy)2(NCS)2]4-, dcbpy = (4,4'-dicarboxy-2,2'-bipyridine), or "N34-", a dye sensitizer for solar cells. Electrostatic and explicit ab initio treatment of solvent molecules have been compared in the latter case, revealing the importance of the accurate modeling of mutual solute-solvent polarization on CT kinetics. We observed that explicit quantum mechanical treatment of solvent slowed down the charge carriers mobilities with respect to the gas-phase. When all water molecules were modeled instead as simpler embedded point charges, the electronic dynamics appeared enhanced, with a reduced hole-electron distance and higher mean velocities due to the close fixed charges and an artificially increased polarization effect. Such analysis tools and the presented case studies can help to unveil the influence of the electronic manifold, as well as of the finite temperature-induced structural distortions and the environment on the ultrafast charge motions.

Transferable Potential Function for Flexible H2O Molecules Based on the Single-Center Multipole Expansion

A potential function is presented for describing a system of flexible H₂O molecules based on the single-center multipole expansion (SCME) of the electrostatic interaction. The model, referred to as SCME/f, includes the variation of the molecular quadrupole moment as well as the dipole moment with changes in bond length and angle so as to reproduce results of high-level electronic structure calculations. The multipole expansion also includes fixed octupole and hexadecapole moments, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model contains five adjustable parameters related to the repulsive interaction and damping functions in the electrostatic and dispersion interactions. Their values are adjusted to reproduce the lowest energy isomers of small clusters, (H₂O)_n with n = 2-6, as well as measured properties of the ice Ih crystal. Subsequent calculations of the energy difference between the various isomer configurations of the clusters show that SCME/f gives good agreement with results of electronic structure calculations and represents a significant improvement over the previously presented rigid SCME potential function. Analysis of the vibrational frequencies of the clusters and structural properties of ice Ih crystal show the importance of accurately describing the variation of the quadrupole moment with molecular structures.

Conical Intersections in Solution with Polarizable Embedding: Integral-Exact Direct Reaction Field

A common strategy to exploring the properties and reactivity of complex systems is to use quantum mechanics/molecular mechanics (QM/MM) embedding, wherein a QM region is defined and treated with electronic structure theory, and the remainder of the system is treated with a force field. Important to the description of electronic excited states, especially those of charge-transfer character, is the treatment of the coupling between the QM and MM subsystems. The state of the art is to use a polarizable force field for the MM region and mutually couple the QM wavefunction and MM induced dipoles, in addition to the usual electrostatic embedding, yielding a polarizable embedding (QM/MM-Pol) approach. However, we showed previously that current popular QM/MM-Pol approaches exhibit issues of root flipping and/or incorrect descriptions of electronic crossings in multistate calculations [J. Chem. Theory Comput. 14, 2137 (2018)]. Here, we demonstrate a solution to these problems with an integral-exact reformulation of the direct reaction field approach of Thole and Van Duijnen (QM/MM-IEDRF). The resulting embedding potential includes one- and two-electron operators and many-body dipole-induced dipole interactions and thus includes a natural description of the screening of electron-electron interactions by the MM induced dipoles. Pauli repulsion from the environment is mimicked by effective core potentials on the MM atoms. Inherent to the DRF approach is the assumption that MM dipoles respond instantaneously to the positions of the QM electrons; therefore, dispersion interactions are captured approximately. All electronic states are eigenfunctions of the same Hamiltonian, while the polarization induced in the environment and the associated energetic stabilization are unique to each state. This allows for a consistent definition of transition properties and state crossings. We demonstrate QM/MM-IEDRF by exploring the influence of a (polarizable) inert xenon matrix environment on the conical intersection underlying the photoisomerization of ethylene.

Trajectory Surface Hopping for a Polarizable Embedding QM/MM Formulation

We present the implementation of trajectory surface-hopping nonadiabatic dynamics for a polarizable embedding QM/MM formulation. Time-dependent density functional theory was used at the quantum mechanical level of theory, whereas the molecular mechanics description involved the polarizable AMOEBA force field. This implementation has been obtained by integrating the surface-hopping program Newton-X NS with an interface between the Gaussian 16 and the Tinker suites of codes to calculate QM/AMOEBA energies and forces. The implementation has been tested on a photoinduced electron-driven proton-transfer reaction involving pyrimidine and a hydrogen-bonded water surrounded by a small cluster of water molecules and within a large water droplet.

Development, Validation, and Pilot Application of a Generalized Fluctuating Charge Model for Computational Spectroscopy in Solution

A general approach enforcing nonperiodic boundary conditions for the computation of spectroscopic properties in solution has been improved including an effective description of charge-transfer contributions and coordination number adjustment for explicit solvent molecules. Both contributions are obtained from a continuous description of intermolecular hydrogen bonds, which has been employed also for an effective clustering of molecular dynamics trajectories. Fine tuning of the model has been performed for several water clusters, and then its efficiency and reliability have been demonstrated by computing the absorption spectra of different creatinine tautomers in aqueous solution.

Absorption Properties of Large Complex Molecular Systems: The DFTB/Fluctuating Charge Approach

We report on the first formulation of a novel polarizable QM/MM approach, where the density functional tight binding (DFTB) is coupled to the fluctuating charge (FQ) force field. The resulting method (DFTB/FQ) is then extended to the linear response within the TD-DFTB framework and challenged to study absorption spectra of large condensed-phase systems.

Fast Approximate but Accurate QM/MM Interactions for Polarizable Embedding

The coupling between the quantum (QM) and classical (MM) regions is often one of the computational bottlenecks when applying polarizable QM/MM to computational spectroscopy. In this Article, we explore three strategies to approximate the QM/MM coupling based on multipole expansion techniques. The implementations of these approximations are benchmarked in terms of both accuracy and computational efficiency and are furthermore applied to the calculation of spectroscopic properties including both one- and two-photon absorption strengths. We show that the proposed strategies provide significant computational savings without compromising the accuracy of the calculated spectroscopic properties.

Quantum Mechanics/Fluctuating Charge Protocol to Compute Solvatochromic Shifts

Despite the potentialities of the quantum mechanics (QM)/fluctuating charge (FQ) approach to model the spectral properties of solvated systems, its extensive use has been hampered by the lack of reliable parametrizations of solvents other than water. In this paper, we substantially extend the applicability of QM/FQ to solvating environments of different polarities and hydrogen-bonding capabilities. The reliability and robustness of the approach are demonstrated by challenging the model to simulate solvatochromic shifts of four organic chromophores, which display large shifts when dissolved in apolar, aprotic or polar, protic solvents.

Atomistic Polarizable Embeddings: Energy, Dynamics, Spectroscopy, and Reactivity

The computational modeling of realistic extended systems, relevant in, e.g., Chemistry and Biophysics, is a fundamental problem of paramount importance in contemporary research. Enzymatic catalysis and photoinduced processes in pigment-protein complexes are typical problems targeted by computer-aided approaches, to complement experiments as interpretative tools at a molecular scale. The daunting complexity of this task lies in between the opposite stringent requirements of results' reliability for structural/dynamical properties and related intermolecular interactions, and a mandatory principle of realism in the modeling strategy. Therefore, in practice, a truly realistic computational model of a biologically relevant system can easily fail to meet the accuracy requirement, in order to balance the excessive computational cost necessary to reach the desired precision.To address such an "accuracy vs reality" dualistic requirement, mixed quantum mechanics/classical mechanics approaches within Atomistic (i.e., preserving the discrete particle configuration) Polarizable Embeddings (QM/APEs) methods have been proposed over the years. In this Account, we review recent developments in the design and application of general QM/APE methods, targeting situations where a local intrinsically quantum behavior is coupled to a large molecular system (i.e., an environment), often involving processes with different dynamical time scales, in order to avoid brute-force, unpractical quantum chemistry calculations on the complete system.In the first place, our interest is devoted to the available APEs models presently implemented in computational software, highlighting the quantum chemistry methods that can be used to treat the QM subsystem. We review the coupling strategy between the QM subsystem and the APE, which requires to examine the way the QM/MM mutual interactions are accounted for and how the polarization of the classical environment is considered with respect to (wrt) the quantum variables. Because of the need of reliable molecular and macromolecular structures, a pivotal aspect to address here is the handling of the system dynamics (i.e., gradients wrt nuclear positions are required), especially for large molecular assemblies composed by an overwhelming number of atoms, exploring many conformations on a complex energy landscape.Alongside, we highlight our views on the necessary steps to take toward more accurate general-purposes and transferable explicit embeddings. The main objective to achieve here is to design a more physically grounded multiscale approach. To do so, one should apply advanced new generation classical models to account for refined induction effects that are able to (i) improve the quality of QM/MM interaction energies; (ii) enhance transferability by avoiding the compulsory partial (or total) reparameterization of the classical model. Moreover, the extension of recent developments originating from the field of advanced classical molecular dynamics (MD) to the realm of QM/APE methods is a key direction to improve both speed and efficiency for the phase space exploration of systems of growing size and complexity.Lastly, we point out specific research topics where an advanced QM/APE dynamics can certainly shed some light. For example, we discuss chemical reactions in "harsh" environments and the case of spectroscopic theoretical modeling where the inclusion of refined environment effects is often mandatory.

On the Transition from a Biomimetic Molecular Switch to a Rotary Molecular Motor

The experimental investigation of the unidirectional motion characterizing the photoisomerization of single-molecule rotary motors requires accessible lab prototypes featuring an electronic circular dichroism (ECD) signal that is sensitive to the geometrical and electronic changes occurring during an ultrafast reactive process. Here we report a combined experimental/computational study of a candidate obtained via the asymmetrization of a light-driven biomimetic molecular switch. We show that the achieved motor has an ECD band that is remarkably sensitive to the isomerization motion, and it is therefore suitable for time-resolved ECD studies. However, we also find that, unexpectedly, the synthesized motor isomerizes on a time scale longer than the subpicosecond time measured for the achiral parent, a result that points to alternative candidates conserving a high reaction speed.

A polarizable three-layer frozen density embedding/molecular mechanics approach

We present a novel multilayer polarizable embedding approach in which the system is divided into three portions, two of which are treated using density functional theory and their interaction is based on frozen density embedding (FDE) theory, and both also mutually interact with a polarizable classical layer described using an atomistic model based on fluctuating charges (FQ). The efficacy of the model is demonstrated by extending the formalism to linear response properties and applying it to the simulation of the excitation energies of organic molecules in aqueous solution, where the solute and the first solvation shell are treated using FDE, while the rest of the solvent is modeled using FQ charges.

Multiscale Models for Light-Driven Processes

Multiscale models combining quantum mechanical and classical descriptions are a very popular strategy to simulate properties and processes of complex systems. Many alternative formulations have been developed, and they are now available in all of the most widely used quantum chemistry packages. Their application to the study of light-driven processes, however, is more recent, and some methodological and numerical problems have yet to be solved. This is especially the case for the polarizable formulation of these models, the recent advances in which we review here. Specifically, we identify and describe the most important specificities that the polarizable formulation introduces into both the simulation of excited-state dynamics and the modeling of excitation energy and electron transfer processes.

Combining multilevel Hartree–Fock and multilevel coupled cluster approaches with molecular mechanics: a study of electronic excitations in solutions

We present the coupling of different quantum-embedding approaches with a third molecular-mechanics layer, which can be either polarizable or non-polarizable.

Simulating Absorption Spectra of Flavonoids in Aqueous Solution: A Polarizable QM/MM Study

We present a detailed computational study of the UV/Vis spectra of four relevant flavonoids in aqueous solution, namely luteolin, kaempferol, quercetin, and myricetin. The absorption spectra are simulated by exploiting a fully polarizable quantum mechanical (QM)/molecular mechanics (MM) model, based on the fluctuating charge (FQ) force field. Such a model is coupled with configurational sampling obtained by performing classical molecular dynamics (MD) simulations. The calculated QM/FQ spectra are compared with the experiments. We show that an accurate reproduction of the UV/Vis spectra of the selected flavonoids can be obtained by appropriately taking into account the role of configurational sampling, polarization, and hydrogen bonding interactions.

A Many-Body, Fully Polarizable Approach to QM/MM Simulations

We present a new development in quantum mechanics/molecular mechanics (QM/MM) methods by replacing conventional MM models with data-driven many-body (MB) representations rigorously derived from high-level QM calculations. The new QM/MM approach builds on top of mutually polarizable QM/MM schemes developed for polarizable force fields with inducible dipoles and uses permutationally invariant polynomials to effectively account for quantum-mechanical contributions (e.g., exchange-repulsion and charge transfer and penetration) that are difficult to describe by classical expressions adopted by conventional MM models. Using the many-body MB-pol and MB-DFT potential energy functions for water, which include explicit two-body and three-body terms fitted to reproduce the corresponding CCSD(T) and PBE0 two-body and three-body energies for water, we demonstrate a smooth energetic transition as molecules are transferred between QM and MM regions, without the need of a transition layer. By effectively elevating the accuracy of both the MM region and the QM/MM interface to that of the QM region, the new QM/MB-MM approach achieves an accuracy comparable to that obtained with a fully QM treatment of the entire system.

Calculation of Linear and Non-linear Electric Response Properties of Systems in Aqueous Solution: A Polarizable Quantum/Classical Approach with Quantum Repulsion Effects

We present a computational study of polarizabilities and hyperpolarizabilities of organic molecules in aqueous solutions, focusing on solute-water interactions and the way they affect a molecule's linear and non-linear electric response properties. We employ a polarizable quantum mechanics/molecular mechanics (QM/MM) computational model that treats the solute at the QM level while the solvent is treated classically using a force field that includes polarizable charges and dipoles, which dynamically respond to the solute's quantum-mechanical electron density. Quantum confinement effects are also treated by means of a recently implemented method that endows solvent molecules with a parametric electron density, which exerts Pauli repulsion forces upon the solute. By applying the method to a set of aromatic molecules in solution we show that, for both polarizabilities and first hyperpolarizabilities, observed solution values are the result of a delicate balance between electrostatics, hydrogen-bonding, and non-electrostatic solute solvent interactions.

Theory and algorithms for chiroptical properties and spectroscopies of aqueous systems

Chiroptical properties and spectroscopies are valuable tools to study chiral molecules and assign absolute configurations. The spectra that result from chiroptical measurements may be very rich and complex, and hide much of their information content. For this reason, the interplay between experiments and calculations is especially useful, provided that all relevant physico-chemical interactions that are present in the experimental sample are accurately modelled. The inherent difficulty associated to the calculation of chiral signals of systems in aqueous solutions requires the development of specific tools, able to account for the peculiarities of water-solute interactions, and especially its ability to form hydrogen bonds. In this perspective we discuss a multiscale approach, which we have developed and challenged to model the most used chiroptical techniques.

eT 1.0: An open source electronic structure program with emphasis on coupled cluster and multilevel methods

The e^T program is an open source electronic structure package with emphasis on coupled cluster and multilevel methods. It includes efficient spin adapted implementations of ground and excited singlet states, as well as equation of motion oscillator strengths, for CCS, CC2, CCSD, and CC3. Furthermore, e^T provides unique capabilities such as multilevel Hartree-Fock and multilevel CC2, real-time propagation for CCS and CCSD, and efficient CC3 oscillator strengths. With a coupled cluster code based on an efficient Cholesky decomposition algorithm for the electronic repulsion integrals, e^T has similar advantages as codes using density fitting, but with strict error control. Here, we present the main features of the program and demonstrate its performance through example calculations. Because of its availability, performance, and unique capabilities, we expect e^T to become a valuable resource to the electronic structure community.

Absorption spectra of xanthines in aqueous solution: a computational study

We present a detailed computational analysis of the UV/Vis spectra of caffeine, paraxanthine and theophylline in aqueous solution. A hierarchy of solvation approaches for modeling the aqueous environment have been tested, ranging from the continuum model to the non-polarizable and polarizable quantum mechanical (QM)/molecular mechanics (MM) models, with and without the explicit inclusion of water molecules in the QM portion. The computed results are directly compared with the experimental data, thus highlighting the role of electrostatic, polarization and hydrogen boding solute-solvent interactions.

Polarizable Embedding with a Transferable H2O Potential Function II: Application to (H2O)n Clusters and Liquid Water

The incorporation of polarization in multiscale quantum-mechanics/molecular-mechanics (QM/MM) simulations is important for a variety of applications, for example, charge-transfer reactions. A recently developed formalism based on a density functional theory description of the QM region and a potential energy function for H₂O molecules that includes quadrupole as well as dipole polarizability of the MM region is used to simulate liquid water and water clusters. Analysis of the energy, atomic forces, MM polarization, and structure is presented. A quantitative assessment of the QM/MM-MM/MM interaction energy differences of all possible QM/MM configurations of (H₂O)_n clusters shows that the interquartile range of the distributions of the QM/MM binding energies is never more than 20 meV/molecule higher or lower than the binding energies produced with either of the single-model results. Comparing these interaction energy differences with the QM/MM induction differences show that they are not systematically caused by the induced MM moments of our polarizable embedding scheme. Optimized hexamer geometries as well as the liquid water structure are shown to be improved in comparison with results obtained using point-charge based embedding models neglecting polarization.

Polarizable Embedding with a Transferable H2O Potential Function I: Formulation and Tests on Dimer

The incorporation of mutual polarization in multiscale simulations where different regions of the system are treated at different level of theory is important in studies of, for example, electronic excitations and charge transfer processes. We present here an energy functional for describing a quantum mechanics/molecular mechanics (QM/MM) scheme that includes reciprocal polarization between the two subsystems. The inclusion of polarization alleviates shortcomings inherent in electrostatic embedding QM/MM models based on point-charge force fields. A density functional theory (DFT) description of the QM subsystem is coupled to a single center multipole expansion (SCME) description of H₂O molecules in the MM subsystem that includes anisotropic dipole and quadrupole polarizability as well as static multipoles up to and including the hexadecapole. The energy functional and the coupling scheme is general and can be extended to arbitrary order in terms of both the static and induced moments. Tests of the energy surface for the H₂O dimer show that the QM/MM results lie in between the pure DFT and pure SCME values. The consistency of the many-body contributions to the energy and analytical forces is demonstrated for an H₂O pentamer.

Electronic transitions for a fully polarizable QM/MM approach based on fluctuating charges and fluctuating dipoles: Linear and corrected linear response regimes

The fully polarizable Quantum Mechanics/Molecular Mechanics (QM/MM) approach based on fluctuating charges and fluctuating dipoles, named QM/FQFμ [T. Giovannini et al., J. Chem. Theory Comput. 15, 2233 (2019)], is extended to the calculation of vertical excitation energies of solvated molecular systems. Excitation energies are defined within two different solvation regimes, i.e., linear response (LR), where the response of the MM portion is adjusted to the QM transition density, and corrected-Linear Response (cLR) in which the MM response is adjusted to the relaxed QM density, thus being able to account for charge equilibration in the excited state. The model, which is specified in terms of three physical parameters (electronegativity, chemical hardness, and polarizability) is applied to vacuo-to-water solvatochromic shifts of aqueous solutions of para-nitroaniline, pyridine, and pyrimidine. The results show a good agreement with their experimental counterparts, thus highlighting the potentialities of this approach.

Quantum Confinement Effects on Solvatochromic Shifts of Molecular Solutes

We demonstrate the pivotal role of quantum mechanics density confinement effects on solvatochromic shifts. In particular, by resorting to a quantum mechanics/molecular mechanics (QM/MM) approach capable of accounting for confinement effects we successfully reproduce vacuo-to-water solvatochromic shifts for dark n → π* and bright π → π* transitions of acrolein and dark n → π* transitions of pyridine and pyrimidine without the need of including explicit water molecules in the QM portion. Remarkably, our approach is also able to dissect the effects of the single forces acting on the solute-solvent couple and allows for a rationalization of the experimental findings in terms of physicochemical quantities.

Quantum Chemical Modeling of the Photoinduced Activity of Multichromophoric Biosystems

Multichromophoric biosystems represent a broad family with very diverse members, ranging from light-harvesting pigment-protein complexes to nucleic acids. The former are designed to capture, harvest, efficiently transport, and transform energy from sunlight for photosynthesis, while the latter should dissipate the absorbed radiation as quickly as possible to prevent photodamages and corruption of the carried genetic information. Because of the unique electronic and structural characteristics, the modeling of their photoinduced activity is a real challenge. Numerous approaches have been devised building on the theoretical development achieved for single chromophores and on model Hamiltonians that capture the essential features of the system. Still, a question remains: is a general strategy for the accurate modeling of multichromophoric systems possible? By using a quantum chemical point of view, here we review the advancements developed so far highlighting differences and similarities with the single chromophore treatment. Finally, we outline the important limitations and challenges that still need to be tackled to reach a complete and accurate picture of their photoinduced properties and dynamics.

General Linear Scaling Implementation of Polarizable Embedding Schemes

A general framework to treat polarizable embedding schemes in the context of QM/MM calculations is presented. Such a framework is completely general, as it allows in principle one to treat any electrostatic distribution and polarization model with minimal modifications and achieves linear scaling in computational cost and memory requirements. The performances and scaling of the new implementation are demonstrated with benchmark calculations on water clusters including up to 1146240 atoms.

Mutually polarizable QM/MM model with in situ optimized localized basis functions

We extend our recently developed quantum-mechanical/molecular mechanics (QM/MM) approach [Dziedzic et al., J. Chem. Phys. 145, 124106 (2016)] to enable in situ optimization of the localized orbitals. The quantum subsystem is described with onetep linear-scaling density functional theory and the classical subsystem - with the AMOEBA polarizable force field. The two subsystems interact via multipolar electrostatics and are fully mutually polarizable. A total energy minimization scheme is employed for the Hamiltonian of the coupled QM/MM system. We demonstrate that, compared to simpler models using fixed basis sets, the additional flexibility offered by in situ optimized basis functions improves the accuracy of the QM/MM interface, but also poses new challenges, making the QM subsystem more prone to overpolarization and unphysical charge transfer due to increased charge penetration. We show how these issues can be efficiently solved by replacing the classical repulsive van der Waals term for QM/MM interactions with an interaction of the electronic density with a fixed, repulsive MM potential that mimics Pauli repulsion, together with a modest increase in the damping of QM/MM polarization. We validate our method, with particular attention paid to the hydrogen bond, in tests on water-ion pairs, the water dimer, first solvation shells of neutral and charged species, and solute-solvent interaction energies. As a proof of principle, we determine suitable repulsive potential parameters for water, K⁺, and Cl^-. The mechanisms we employed to counteract the unphysical overpolarization of the QM subsystem are demonstrated to be adequate, and our approach is robust. We find that the inclusion of explicit polarization in the MM part of QM/MM improves agreement with fully QM calculations. Our model permits the use of minimal size QM regions and, remarkably, yields good energetics across the well-balanced QM/MM interface.

A combined experimental and theoretical study of optical rotatory dispersion for (R)-glycidyl methyl ether in aqueous solution

The dispersive optical activity for aqueous solutions of non-rigid (R)-glycidyl methyl ether (R-GME) has been explored synergistically from experimental and theoretical perspectives. Density functional theory analyses performed with the polarizable continuum model for implicit solvation identified nine low-lying stable conformers that are interconverted by rotation about two large-amplitude torsional coordinates. The antagonistic chiroptical signatures predicted for these structural isomers were averaged under a Boltzmann-weighting ansatz to estimate the behavior expected for a thermally equilibrated ensemble. This led to optical rotatory dispersion profiles that reproduced the overall shape of observations but failed to achieve uniform agreement with measured specific-rotation values even when anharmonic vibrational corrections were applied. A mixed QM/FQ paradigm, whereby quantum-mechanical (QM) calculations of optical activity were combined with classical molecular dynamics simulations of explicit solvation that included mutual-polarization effects by means of fluctuating charges (FQ), was enlisted to elucidate the microsolvation environment and gauge its impact upon conformer distributions and response properties. Although quantitative accord with experiments remained elusive, this approach revealed strong variations in the magnitude and sign of rotatory powers for R-GME as the configuration of surrounding water molecules evolved, thereby highlighting the inherently dynamical nature of the solvated chiroptical response, calling into question the validity of "static" descriptions based on the presumption of distinct energy minima, and giving insight into the inherent complexity posed by the modeling of such properties for solvated systems.

Interplay between conformational and solvent effects in UV-visible absorption spectra: curcumin tautomers as a case study

We present a combined theoretical and experimental study on the UV-vis spectra of enol-keto (EK) and keto-keto (KK) tautomeric forms of curcumin dissolved in aqueous solution. Solvent effects have been investigated by resorting to the implicit polarizable continuum model (QM/PCM) and non-polarizable and fully polarizable QM/MM approaches, the latter based on the fluctuating charges (FQ) force-field. In particular, all methods are challenged to rationalize the contribution of conformational, electrostatic and polarization effects in the calculation of the vertical excitation spectra of curcumin tautomers. The obtained results highlight that for both tautomers specific solute-solvent hydrogen-bond interactions play a minor role with respect to conformational and electrostatic effects.

A quantum-mechanical perspective on linear response theory within polarizable embedding

We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole structures as well as residues of the individual terms are discussed. In addition to providing a thorough justification for the descriptions used in polarizable embedding models, this theoretical analysis clarifies which form of the response function to use and highlights complications in separating out subsystem contributions to molecular properties. The basic features of the presented expressions and various approximate forms are illustrated by their application to a composite model system.

Open-ended formulation of self-consistent field response theory with the polarizable continuum model for solvation

The study of high-order absorption properties of molecules is a field of growing importance. Quantum-chemical studies can help design chromophores with desirable characteristics. Given that most experiments are performed in solution, it is important to devise a cost-effective strategy to include solvation effects in quantum-chemical studies of these properties. We here present an open-ended formulation of self-consistent field (SCF) response theory for a molecular solute coupled to a polarizable continuum model (PCM) description of the solvent. Our formulation relies on the open-ended, density matrix-based quasienergy formulation of SCF response theory of Thorvaldsen, et al., [J. Chem. Phys., 2008, 129, 214108] and the variational formulation of the PCM, as presented by Lipparini et al., [J. Chem. Phys., 2010, 133, 014106]. Within the PCM approach to solvation, the mutual solute-solvent polarization is represented by means of an apparent surface charge (ASC) spread over the molecular cavity defining the solute-solvent boundary. In the variational formulation, the ASC is an independent, variational degree of freedom. This allows us to formulate response theory for molecular solutes in the fixed-cavity approximation up to arbitrary order and with arbitrary perturbation operators. For electric dipole perturbations, pole and residue analyses of the response functions naturally lead to the identification of excitation energies and transition moments. We document the implementation of this approach in the Dalton program package using a recently developed open-ended response code and the PCMSolver libraries and present results for one-, two-, three-, four- and five-photon absorption processes of three small molecules in solution.

Towards the SMART workflow system for computational spectroscopy

Is it possible to convert highly specialized research in the field of computational spectroscopy into robust and user-friendly aids to experiments and industrial applications?

Effective computational route towards vibrational optical activity spectra of chiral molecules in aqueous solution

A polarizable QM/MM approach to accurately compute the Vibrational Optical Activity (VOA) spectra of chiral systems is proposed and applied to aqueous solutions of (l)-methyl lactate and (S)-glycidol.