A time-dependent polarizable continuum model: Theory and application

Quantum dynamics of the photoinduced charge separation in a symmetric donor–acceptor–donor triad: The role of vibronic couplings, symmetry and temperature

The photoinduced charge separation in a symmetric donor–acceptor–donor (D–A–D) triad is studied quantum mechanically using a realistic diabatic vibronic coupling model. The model includes a locally excited DA*D state and two charge-transfer states D+A−D and DA−D+ and is constructed according to a procedure generally applicable to semirigid D–A–D structures and based on energies, forces, and force constants obtained by quantum chemical calculations. In this case, the electronic structure is described by time-dependent density functional theory, and the corrected linear response is used in conjunction with the polarizable continuum model to account for state-specific solvent effects. The multimode dynamics following the photoexcitation to the locally excited state are simulated by the hybrid Gaussian-multiconfigurational time-dependent Hartree method, and temperature effects are included using thermo field theory. The dynamics are connected to the transient absorption spectrum obtained in recent experiments, which is simulated and fully assigned from first principles. It is found that the charge separation is mediated by symmetry-breaking vibrations of relatively low frequency, which implies that temperature should be accounted for to obtain reliable estimates of the charge transfer rate.

Solvated Nuclear-Electronic Orbital Structure and Dynamics

Nonadiabatic dynamical processes such as proton-coupled electron transfer and excited state intramolecular proton transfer have been the subject of much research. One of the promising theoretical methods to describe these processes is the nuclear-electronic orbital (NEO) approach. This approach inherently accounts for nuclear quantum effects within quantum chemistry calculations, and it has recently been extended to directly simulate nonadiabatic processes with the development of real-time NEO methods. These processes can also be significantly dependent on the surrounding chemical environment, however, and capturing the effects of the environment is often necessary for analyzing experimentally relevant systems. This work couples the NEO density functional theory and real-time time-dependent density functional theory approaches with solvation through the polarizable continuum model. The effects of this coupling are investigated for ground state properties, solvent-dependent vibrational frequencies, and direct excited state intramolecular proton transfer dynamics.

LayerPCM: An implicit scheme for dielectric screening from layered substrates

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 modeled 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 for describing 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 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.

Density Functional Computations of Vibrational Circular Dichroism Spectra beyond the Born-Oppenheimer Approximation

Transition-metal complexes provide rich features in vibrational circular dichroism (VCD) spectra, including significant intensity enhancements, and become thus useful in structural and functional studies of molecules. Quite often, however, the vibrational spectral bands are mixed with the electronic ones, and interpretation of such experiments is difficult. In the present study, we elaborate on the theory needed to calculate the VCD intensities beyond the Born-Oppenheimer (BO) approximation. Within a perturbation approach, the coupling between the electronic and vibrational states is estimated using the harmonic approximation and simplified wave functions obtainable from common density functional theory (DFT) computations. Explicit expressions, including Slater determinants and derivatives of molecular orbitals, are given. On a model diamine complex, the implementation is tested and factors affecting spectral intensities and frequencies are investigated. For two larger molecules, the results are in a qualitative agreement with previous experimental data. Typically, the electronic-vibrational interaction Hamiltonian coupling elements are rather small (∼0 to 10 cm^-1), which provides negligible contributions to vibrational frequencies and absorption intensities. However, significant changes in VCD spectra are induced due to the large transition magnetic dipole moment associated with the d-d metal transitions. The possibility to model the spectra beyond the BO limit opens the way to further applications of chiral spectroscopy and transition-metal complexes.

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light-matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Flipping Molecules over on TiO2 Surfaces with Light and Electric Fields

Light excitation of the sensitizer [Ru(NH₃)₅(eina)](PF₆)₂, where eina is ethyl isonicotinate, anchored to anatase TiO₂ nanocrystallites interconnected in a mesoporous thin film and immersed in CH₃CN resulted in spectroscopic changes consistent with both excited-state injection and sensitizer reorientation, termed flipping. When the light irradiation was removed, the sensitizers flipped back over. Such flipping was absent when the carboxylic acid derivative of the sensitizer was utilized or when SnO₂/TiO₂ core/shell materials were employed in place of TiO₂. The flipping was attributed to the torque on the sensitizer in the electric field generated by the injected electrons. Pulsed light excitation was utilized to time-resolve flipping and charge recombination with this and the per-deuterated complex (ND₃)₅Ru^II(eina)|TiO₂. In all cases, charge recombination was more rapid when the oxidized sensitizer was flipped over, behavior consistent with stronger electronic coupling. Kinetic isotope effects of 26.7 and 0.12 were determined for charge recombination and for flipping, respectively. Spectro-electrochemical measurements showed that thermal reduction of TiO₂ with an applied potential also initiated flipping yet required much larger field strengths. The data show that the electric fields created at illuminated semiconductor interfaces are sufficient to reorientate molecules anchored to its surface.

Nonequilibrium Environment Dynamics in a Frequency-Dependent Polarizable Embedding Model

Hybrid quantum mechanical/molecular mechanical (QM/MM) models are some of the most powerful and computationally feasible approaches to account for solvent effects or more general environmental perturbations on quantum chemical systems. In their more recent formulations (known as polarizable embedding) they can account for electrostatic and mutual polarization effects between the QM and the MM subsystems. In this paper, a polarizable embedding scheme based on induced dipoles that is able both to describe electron evolution of the embedded QM system in an efficient manner as well as to capture the frequency dependent behavior of the solvent is proposed, namely, ωMMPol. The effects of this frequency-dependent solvent on a time-dependent model system-the Rabi oscillations of H₂⁺ in a resonant field-are considered. The solvent is shown to introduce only mild perturbations when the excitation frequencies of the solvent and the solute are off-resonant. However, the dynamics of the H₂⁺ are fundamentally changed in the presence of a near-resonant excitation solvent. The effectiveness of ωMMPol to simulating realistic chemical systems is demonstrated by capturing charge transfer dynamics within a solvated system.

Vibrational Properties of the Phosphate Group Investigated by Molecular Dynamics and Density Functional Theory

The phosphate group (PO2(-)) is an important building block occurring in many components of living matter including nucleic acids. It provides distinct features in vibrational spectra and is useful as a local probe of NA conformation and interactions with the environment. For this purpose, it is desirable to explore in detail various factors influencing spectral shapes of characteristic phosphate vibrations. In the present study, effects of the solvent and conformational averaging are analyzed for simple model molecules, dimethylphosphate, ethylmethylphosphate, and ethylmethylthiophosphate. Infrared absorption (IR) and Raman spectra were measured and calculated using a combination of molecular dynamics (MD) and density functional theory (DFT). To fully understand the link between the structure and the spectra, the solvent has to be explicitly included in the computational modeling. The results indicate that vibrational properties of the phosphate moiety are very sensitive to its conformation and interactions with the aqueous environment indeed. Polarizable continuum solvent models without explicit water molecules provided significantly worse agreement with the experiment. The combined MD/DFT approach captures well spectral characteristics for the model systems and constitutes the most reliable basis for exploration of phosphate vibrational properties in biomolecular structural studies.

Control of optical response of a supported cluster on different dielectric substrates

We develop a computational method for optical response of a supported cluster on a dielectric substrate. The substrate is approximated by a dielectric continuum with a frequency-dependent dielectric function. The computational approach is based on our recently developed first-principles simulation method for photoinduced electron dynamics in real-time and real-space. The approach allows us to treat optical response of an adsorbate explicitly taking account of interactions at an interface between an adsorbate and a substrate. We calculate optical absorption spectra of supported Agn (n = 2, 54) clusters, changing the dielectric function of a substrate. By analyzing electron dynamics in real-time and real-space, we clarify the mechanisms for variations in absorption spectra, such as peak shifts and intensity changes, relating to various experimental results for optical absorption of supported clusters. Attractive and repulsive interactions between an adsorbate and a substrate result in red and blue shifts, respectively, and the intensity decreases by energy dissipation into a substrate. We demonstrate that optical properties can be controlled by varying the dielectric function of a substrate.

Multi-scale modeling of electronic spectra of three aromatic amino acids: importance of conformational averaging and explicit solute-solvent interactions

Electronic transitions in the ultraviolet and visible spectral range can reveal a wealth of information about biomolecular geometry and interactions, such as those involved in protein folding. However, the modeling that provides the necessary link between spectral shapes and the structure is often difficult even for seemingly simple systems. To understand as to how conformational equilibria and solute-solvent interaction influence spectral intensities, we collected absorption (UV-vis), electronic circular dichroism (ECD), and magnetic circular dichroism (MCD) spectra of phenylalanine (Phe), tyrosine (Tyr) and tryptophan (Trp) zwitterions in aqueous solutions, and compared them with quantum-chemical simulations. These aromatic amino acids provide a relatively strong signal in the accessible wavelength range. At the same time, they allow for a relatively accurate modeling. Energies and intensities of spectral bands were reproduced by the time-dependent density functional theory (TD DFT). The solvent was approximated by a continuum as well as clusters containing solvent molecules from the first hydration sphere. The ECD signal was found to be strongly dependent on molecular conformation, and the dependence was much weaker in UV-vis and MCD spectra. All spectral intensities, however, were significantly affected by the solvent approximation; especially for ECD and MCD the usual polarizable continuum solvent model did not yield satisfactory spectral shapes. On the other hand, averaging of the clusters obtained from molecular dynamics simulations provided an unprecedented agreement with the experiment. Proper modeling of the interactions with the environment thus makes the information about the molecular structure, as obtained from the electronic spectra, more accurate and reliable.

Stereoelectronic explanations for the mechanistic details of transimination and HF elimination reactions

The β-fluoroamines are commonly used as substrate analogs to determine the mechanistic details of enzymatic reactions. Presence of fluorine atom gives rise to the alterations in the electronic profile and the pKa of molecules which results in mechanistic deviations. The fluorine-substituted mechanism-based substrate analogs are widely used in the inactivation of pyridoxal 5'-phosphate (PLP)-dependent enzymes. The presence of fluorine atom also alters the sequence of reactions taking place in PLP-dependent enzymes where the HF elimination reaction appears in between the transimination and inactivation reactions. Despite the amount of the works on β-fluoroamines, the effect of stereoelectronic differences on the transimination and HF elimination reactions taking place in PLP-dependent enzymes has not been investigated yet. A density functional theory study is conducted to elucidate mechanistic details of the reactions occurring in PLP-dependent enzymes. In order to understand the mechanistic insights of different isomers and the effect of the fluorine atom, 4-amino-3-fluorobutanoic acid (3-F-GABA) enantiomers are chosen to be investigated besides 4-aminobutanoic acid (GABA), which is the natural substrate for γ-aminobutyric acid aminotransferase (GABA-AT). The investigated β-fluoroamines are the experimentally proposed potential inhibitors of PLP-dependent enzyme GABA-AT.

Absorption and Emission Spectra of Solvated Molecules with the EOM-CCSD-PCM Method

The accurate calculation of transition energies and properties of isolated molecules is not enough for realistic simulations of their absorption and emission spectra in solution. In fact, the solvent influences the solute geometry, electronic structure, and response to external fields, and a proper description of the solvent effect is fundamental. However, the computational cost of including explicit solvent molecules around the solute becomes rather onerous when an accurate method such as the equation of motion coupled cluster singles and doubles (EOM-CCSD) is employed. The polarizable continuum model of solvation (PCM) may provide an efficient alternative to explicit models, since the sampling of solvent configurations is implicit and the solute-solvent mutual polarization is naturally accounted for. In this contribution, the absorption and emission spectra of molecules in solution are modeled through the EOM-CCSD-PCM method. The equilibrium solvation regime is employed for the geometry optimization of the solute molecule in the ground and excited states, while the nonequilibrium solvation regime is employed for vertical transitions. The theory, implementation, and prototypical applications of the method are presented. The numerical tests involve solvents that are particularly challenging for PCM: low-polar and protic polar solvents. Nonetheless, the experimental trends are well reproduced, and the overall agreement with the measured data is remarkable.

Theoretical study on HF elimination and aromatization mechanisms: a case of pyridoxal 5' phosphate-dependent enzyme

Pyridoxal 5-phosphate (PLP), the phosphorylated and the oxidized form of vitamin B6 is an organic cofactor. PLP forms a Schiff base with the ϵ-amino group of a lysine residue of PLP-dependent enzymes. γ-Aminobutyric acid (GABA) aminotransferase is a PLP-dependent enzyme that degrades GABA to succinic semialdehyde, while reduction of GABA concentration in the brain causes convolution besides several neurological diseases. The fluorine-containing substrate analogues for the inactivation of the GABA-AT are synthesized extensively in cases where the inactivation mechanisms involve HF elimination. Although two proposed mechanisms are present for the HF elimination, the details of the base-induced HF elimination are not well identified. In this density functional theory (DFT) study, fluorine-containing substrate analogue, 5-amino-2-fluorocyclohex-3-enecarboxylic acid, is particularly chosen in order to explain the details of the HF elimination reactions. On the other hand, the experimental studies revealed that aromatization competes with Michael addition mechanism in the presence of 5-amino-2-fluorocyclohex-3-enecarboxylic acid. The results allowed us to draw a conclusion for the nature of HF elimination, besides the elucidation of the mechanism preference for the inactivation mechanism. Furthermore, the solvent phase calculations carried out in this study ensure that the proton transfer steps should be assisted either by a water molecule or a base for lower activation energy barriers.

Linking the historical and chemical definitions of diabatic states for charge and excitation energy transfer reactions in condensed phase

Marcus theory of electron transfer (ET) and Förster theory of excitation energy transfer (EET) rely on the Condon approximation and the theoretical availability of initial and final states of ET and EET reactions, often called diabatic states. Recently [Subotnik et al., J. Chem. Phys. 130, 234102 (2009)], diabatic states for practical calculations of ET and EET reactions were defined in terms of their interactions with the surrounding environment. However, from a purely theoretical standpoint, the definition of diabatic states must arise from the minimization of the dynamic couplings between the trial diabatic states. In this work, we show that if the Condon approximation is valid, then a minimization of the derived dynamic couplings leads to corresponding diabatic states for ET reactions taking place in solution by diagonalization of the dipole moment matrix, which is equivalent to a Boys localization algorithm; while for EET reactions in solution, diabatic states are found through the Edmiston-Ruedenberg localization algorithm. In the derivation, we find interesting expressions for the environmental contribution to the dynamic coupling of the adiabatic states in condensed-phase processes. In one of the cases considered, we find that such a contribution is trivially evaluable as a scalar product of the transition dipole moment with a quantity directly derivable from the geometry arrangement of the nuclei in the molecular environment. Possibly, this has applications in the evaluation of dynamic couplings for large scale simulations.

Synthesis and spectroscopic characterization of two tetrasubstituted cationic porphyrin derivatives

An imidazolium tetrasubstituted cationic porphyrin derivative (the free base and its Zn(II) complex) with five-membered heterocyclic groups in the meso-positions were synthesized using microwave irradiation, and the compounds obtained characterized by ¹H-NMR and mass spectrometry. We observed that under microwave irradiation the yield is similar to when the synthesis is performed under conventional heating, however, the time required to prepare the porphyrins decreases enormously. In order to investigate the electronic state of these compounds, we employed UV-Vis and fluorescence spectroscopy combined with quantum chemical calculations. The results reveal the presence, in both compounds, of a large number of electronic states involving the association between the Soret and a blue-shifted band. The Soret band in both compounds also shows a considerable solvent dependence. As for emission, these compounds present low quantum yield at room temperature and no solvent influence on the fluorescence spectra was observed.

Toward effective and reliable fluorescence energies in solution by a new state specific polarizable continuum model time dependent density functional theory approach

A state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of emission energies has been developed and coded in the framework of the so called polarizable continuum model (PCM). The new model allows for a rigorous and effective treatment of dynamical solvent effects in the computation of fluorescence and phosphorescence spectra in solution, and it can be used for studying different relaxation time regimes. SS and conventional linear response (LR) models have been compared by computing the emission energies for different benchmark systems (formaldehyde in water and three coumarin derivatives in ethanol). Special attention is given to the influence of dynamical solvation effects on LR geometry optimizations in solution. The results on formaldehyde point out the complementarity of LR and SS approaches and the advantages of the latter model especially for polar solvents and/or weak transitions. The computed emission energies for coumarin derivatives are very close to their experimental counterparts, pointing out the importance of a proper treatment of nonequilibrium solvent effects on both the excited and the ground state energies. The availability of SS-PCM/TD-DFT models for the study of absorption and emission processes allows for a consistent treatment of a number of different spectroscopic properties in solution.

Effective method to compute Franck-Condon integrals for optical spectra of large molecules in solution

The authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky [Acta Physicochim. URSS 7, 551 (1937)] rotation of the normal modes. The method automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a quite modest computational time, both in vacuo and in condensed phase. Starting from the rigorous time-dependent expression they discuss indeed in which limits the spectrum of a molecule embedded in a solvent, described as a polarizable continuum, can be computed in a time-independent formalism, defining both nonequilibrium and equilibrium limits. In these cases the polarizable continuum model provides a suitable description of the solvent field. By computing the absorption spectra of anthracene in gas phase and of coumarin C153 in gas phase and cyclohexane, and the phosphorescence spectrum of the unsubstituted coumarin in ethanol they show that the method is fast and efficient.