Nonequilibrium solvation for vertical photoemission and photoabsorption processes using the symmetry-adapted cluster–configuration interaction method in the polarizable continuum model

Photophysics of Solvated Molecules: Computational Protocol Combining Nuclear Ensemble and Nonequilibrium State-Specific Solvation Methods

Efficient calculations of the photophysical properties of molecules are essential for both understanding experimental results and accelerating materials discovery through computational simulations. However, to achieve accurate results, the effects of the surrounding medium must be taken into account. Here, we present a computational protocol that combines the nuclear ensemble method with a nonequilibrium state-specific polarizable continuum model to simulate absorption, fluorescence, phosphorescence, and intersystem crossing processes. Additionally, we introduced an extrapolation strategy that enables predictions for multiple solvents without incurring additional computational costs. We demonstrate the method's effectiveness by modeling the photophysical properties of a molecule that exhibits thermally activated delayed fluorescence, showcasing how these properties vary with solvent polarity. We also provide insight into the relationship between the solvent and photophysics by using ensemble analysis to rationalize simulation results. Furthermore, we introduce a metric for the intensity of the charge transfer character of electronic states and demonstrate how vibrations can significantly mix the electronic character of excited states. Overall, this work presents a computational approach that offers new insights into the photophysics of molecules and has the potential to advance materials discovery.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Advances, challenges and perspectives of quantum chemical approaches in molecular spectroscopy of the condensed phase

The purpose of this review is to demonstrate advances, challenges and perspectives of quantum chemical approaches in molecular spectroscopy of the condensed phase. Molecular spectroscopy, particularly vibrational spectroscopy and electronic spectroscopy, has been used extensively for a wide range of areas of chemical sciences and materials science as well as nano- and biosciences because it provides valuable information about structure, functions, and reactions of molecules. In the meantime, quantum chemical approaches play crucial roles in the spectral analysis. They also yield important knowledge about molecular and electronic structures as well as electronic transitions. The combination of spectroscopic approaches and quantum chemical calculations is a powerful tool for science, in general. Thus, our article, which treats various spectroscopy and quantum chemical approaches, should have strong implications in the wider scientific community. This review covers a wide area of molecular spectroscopy from far-ultraviolet (FUV, 120-200 nm) to far-infrared (FIR, 400-10 cm-1)/terahertz and Raman spectroscopy. As quantum chemical approaches, we introduce several anharmonic approaches such as vibrational self-consistent field (VSCF) and the combination of periodic harmonic calculations with anharmonic corrections based on finite models, grid-based techniques like the Numerov approach, the Cartesian coordinate tensor transfer (CCT) method, Symmetry-Adapted Cluster Configuration-Interaction (SAC-CI), and the ZINDO (Semi-empirical calculations at Zerner's Intermediate Neglect of Differential Overlap). One can use anharmonic approaches and grid-based approaches for both infrared (IR) and near-infrared (NIR) spectroscopy, while CCT methods are employed for Raman, Raman optical activity (ROA), FIR/terahertz and low-frequency Raman spectroscopy. Therefore, this review overviews cross relations between molecular spectroscopy and quantum chemical approaches, and provides various kinds of close-reality advanced spectral simulation for condensed phases.

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.

Photophysical properties of fluorescent imaging biological probes of nucleic acids: SAC-CI and TD-DFT Study

Recently, exciton-controlled hybridization-sensitive fluorescent oligonucleotide (ECHO) probe, which shows strong emission in the near-infrared region via hybridization to the target DNA and/or RNA strand, has been developed. In this work, photophysical properties of the chromophores of these probes and the fluorescent mechanism have been investigated by the SAC-CI and TD-DFT calculations. Three fluorescent cyanine chromophores whose excitation is challenging for TD-DFT methods, have been examined regarding the photo-absorption and emission spectra. The SAC-CI method well reproduces the experimental values with respect to transition energies, while the quantitative prediction by TD-DFT calculations is difficult for these chromophores. Some stable structures of H-aggregate system were computationally located and two of the configurations were examined for the photo-absorption. The present results support for the assumption based on experimental measurement in which strong fluorescence is due to the monomer unit in nearly planar structure and its suppression of probes is to the H-aggregates of two exciton units. Stokes shifts of these three chromophores were qualitatively reproduced by the theoretical calculations, while the energy splitting due to H-aggregate in the hybridized probe was slightly overestimated. © 2018 Wiley Periodicals, Inc.

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.

Solvent effects for vertical absorption and emission processes in solution using a self-consistent state specific method based on constrained equilibrium thermodynamics

A self-consistent state specific (SS) method in the framework of TDDFT is presented to account for solvent effects on absorption and emission processes for molecules in solution. In these processes, the initial state is an equilibrium state, while the polarization of the solvent is in nonequilibrium with the electron density of the solute in the final state. Nonequilibrium solvation free energy is calculated based on a novel nonequilibrium solvation model with constrained equilibrium manipulation. The bulk solvent effects are considered using the polarizable continuum method (PCM), where the solvent-solute interaction is described with a reaction field. Molecular orbitals and orbital energies in the presence of the reaction field corresponding to the excited state are employed and the response of the solvent is not included in the TDDFT calculations. A self-consistent procedure is designed to obtain the excited state reaction field. The equations based on this new nonequilibrium solvation model in the framework of the self-consistent SS-PCM/TDDFT method for calculation of vertical absorption and emission energies are presented and implemented in the Q-Chem package. Vertical absorption and emission energies for several small molecules in solution using the newly developed code are calculated and compared with available experimental data and the results of other theoretical studies. Solvent shifts of absorption and emission energies are reasonably reproduced with this approach. The new model is a promising approach to study nonequilibrium absorption and emission processes in solution.

An EOM-CCSD-PCM Benchmark for Electronic Excitation Energies of Solvated Molecules

In this work, we benchmark the equation of motion coupled cluster with single and double excitations (EOM-CCSD) method combined with the polarizable continuum model (PCM) for the calculation of electronic excitation energies of solvated molecules. EOM-CCSD is one of the most accurate methods for computing one-electron excitation energies, and accounting for the solvent effect on this property is a key challenge. PCM is one of the most widely employed solvation models due to its adaptability to virtually any solute and its efficient implementation with density functional theory methods (DFT). Our goal in this work is to evaluate the reliability of EOM-CCSD-PCM, especially compared to time-dependent DFT-PCM (TDDFT-PCM). Comparisons between calculated and experimental excitation energies show that EOM-CCSD-PCM consistently overestimates experimental results by 0.4-0.5 eV, which is larger than the expected EOM-CCSD error in vacuo. We attribute this decrease in accuracy to the approximated solvation model. Thus, we investigate a particularly important source of error: the lack of H-bonding interactions in PCM. We show that this issue can be addressed by computing an energy shift, Δ_HB, from bare-PCM to microsolvation + PCM at DFT level. Our results show that such a shift is independent of the functional used, contrary to the absolute value of the excitation energy. Hence, we suggest an efficient protocol where the EOM-CCSD-PCM transition energy is corrected by Δ_HB(DFT), which consistently improves the agreement with the experimental measurements.

0-0 Energies Using Hybrid Schemes: Benchmarks of TD-DFT, CIS(D), ADC(2), CC2, and BSE/GW formalisms for 80 Real-Life Compounds

The 0-0 energies of 80 medium and large molecules have been computed with a large panel of theoretical formalisms. We have used an approach computationally tractable for large molecules, that is, the structural and vibrational parameters are obtained with TD-DFT, the solvent effects are accounted for with the PCM model, whereas the total and transition energies have been determined with TD-DFT and with five wave function approaches accounting for contributions from double excitations, namely, CIS(D), ADC(2), CC2, SCS-CC2, and SOS-CC2, as well as Green's function based BSE/GW approach. Atomic basis sets including diffuse functions have been systematically applied, and several variations of the PCM have been evaluated. Using solvent corrections obtained with corrected linear-response approach, we found that three schemes, namely, ADC(2), CC2, and BSE/GW allow one to reach a mean absolute deviation smaller than 0.15 eV compared to the measurements, the two former yielding slightly better correlation with experiments than the latter. CIS(D), SCS-CC2, and SOS-CC2 provide significantly larger deviations, though the latter approach delivers highly consistent transition energies. In addition, we show that (i) ADC(2) and CC2 values are extremely close to each other but for systems absorbing at low energies; (ii) the linear-response PCM scheme tends to overestimate solvation effects; and that (iii) the average impact of nonequilibrium correction on 0-0 energies is negligible.

Synthesis and Optical Properties of Imidazole- and Benzimidazole-Based Fused π-Conjugated Compounds: Influence of Substituent, Counteranion, and π-Conjugated System

Fused π-conjugated imidazolium chlorides having hydrogen (1-Cl), octyloxy (2-Cl), N,N-dibutylamino (3-Cl), trifluoromethyl (4-Cl), and cyano (5-Cl) groups substituted on the benzene ring at the 2-position of imidazole were prepared. Counteranion exchanges from chloride to bis(trifluoromethanesulfonyl)imidate (2-TFSI) and tetrafluoroborate (2-BF4) were performed. The optical properties of these compounds (absorption and emission wavelengths, fluorescence quantum yield, and solvatochromism) were influenced by both the substituent and anion character, which was investigated by theoretical calculations using the density functional theory (DFT) and symmetry-adapted cluster-configuration interaction (SAC-CI) methods. Fused π-conjugated benzimidazolium chlorides having N,N-dibutylamino (6-Cl) and cyano (7-Cl) groups were also prepared to observe the different solvatochromic shifts.

Quantum mechanical molecular interactions for calculating the excitation energy in molecular environments: a first-order interacting space approach

Intermolecular interactions regulate the molecular properties in proteins and solutions such as solvatochromic systems. Some of the interactions have to be described at an electronic-structure level. In this study, a commutator for calculating the excitation energy is used for deriving a first-order interacting space (FOIS) to describe the environmental response to solute excitation. The FOIS wave function for a solute-in-solvent cluster is solved by second-order perturbation theory. The contributions to the excitation energy are decomposed into each interaction and for each solvent.

An efficient computational scheme for electronic excitation spectra of molecules in solution using the symmetry-adapted cluster-configuration interaction method: the accuracy of excitation energies and intuitive charge-transfer indices

Solvent effects on electronic excitation spectra are considerable in many situations; therefore, we propose an efficient and reliable computational scheme that is based on the symmetry-adapted cluster-configuration interaction (SAC-CI) method and the polarizable continuum model (PCM) for describing electronic excitations in solution. The new scheme combines the recently proposed first-order PCM SAC-CI method with the PTE (perturbation theory at the energy level) PCM SAC scheme. This is essentially equivalent to the usual SAC and SAC-CI computations with using the PCM Hartree-Fock orbital and integrals, except for the additional correction terms that represent solute-solvent interactions. The test calculations demonstrate that the present method is a very good approximation of the more costly iterative PCM SAC-CI method for excitation energies of closed-shell molecules in their equilibrium geometry. This method provides very accurate values of electric dipole moments but is insufficient for describing the charge-transfer (CT) indices in polar solvent. The present method accurately reproduces the absorption spectra and their solvatochromism of push-pull type 2,2'-bithiophene molecules. Significant solvent and substituent effects on these molecules are intuitively visualized using the CT indices. The present method is the simplest and theoretically consistent extension of SAC-CI method for including PCM environment, and therefore, it is useful for theoretical and computational spectroscopy.

High efficiency light harvesting by carotenoids in the LH2 complex from photosynthetic bacteria: unique adaptation to growth under low-light conditions

Rhodopin, rhodopinal, and their glucoside derivatives are carotenoids that accumulate in different amounts in the photosynthetic bacterium, Rhodoblastus (Rbl.) acidophilus strain 7050, depending on the intensity of the light under which the organism is grown. The different growth conditions also have a profound effect on the spectra of the bacteriochlorophyll (BChl) pigments that assemble in the major LH2 light-harvesting pigment-protein complex. Under high-light conditions the well-characterized B800-850 LH2 complex is formed and accumulates rhodopin and rhodopin glucoside as the primary carotenoids. Under low-light conditions, a variant LH2, denoted B800-820, is formed, and rhodopinal and rhodopinal glucoside are the most abundant carotenoids. The present investigation compares and contrasts the spectral properties and dynamics of the excited states of rhodopin and rhodopinal in solution. In addition, the systematic differences in pigment composition and structure of the chromophores in the LH2 complexes provide an opportunity to explore the effect of these factors on the rate and efficiency of carotenoid-to-BChl energy transfer. It is found that the enzymatic conversion of rhodopin to rhodopinal by Rbl. acidophilus 7050 grown under low-light conditions results in nearly 100% carotenoid-to-BChl energy transfer efficiency in the LH2 complex. This comparative analysis provides insight into how photosynthetic systems are able to adapt and survive under challenging environmental conditions.

Vertical Electronic Excitations in Solution with the EOM-CCSD Method Combined with a Polarizable Explicit/Implicit Solvent Model

The accurate calculation of electronic transition energies and properties of isolated chromophores is not sufficient to provide a realistic simulation of their excited states in solution. In fact, the solvent influences the solute geometry, electronic structure, and response to external fields. Therefore, a proper description of the solvent effect is fundamental. This can be achieved by combining polarizable explicit and implicit representations of the solvent. The former provides a realistic description of solvent molecules around the solute, while the latter introduces the electrostatic effect of the bulk solution and reduces the need of too large a number of explicit solvent molecules. This strategy is particularly appealing when an accurate method such as equation of motion coupled cluster singles and doubles (EOM-CCSD) is employed for the treatment of the chromophore. In this contribution, we present the coupling of EOM-CCSD with a fluctuating charges (FQ) model and polarizable continuum model (PCM) of solvation for vertical excitations in a state-specific framework. The theory, implementation, and prototypical applications of the method are presented. Numerical tests on small solute-water clusters show very good agreement between full EOM-CCSD and EOM-CCSD-FQ calculations, with and without PCM, with differences ≤ 0.1 eV. Additionally, approximated schemes that further reduce the computational cost of the method are introduced and showed to perform well compared to the full method (errors ≤ 0.1 eV).

The nature of the intramolecular charge transfer state in peridinin

Experimental and theoretical evidence is presented that supports the theory that the intramolecular charge transfer (ICT) state of peridinin is an evolved state formed via excited-state bond-order reversal and solvent reorganization in polar media. The ICT state evolves in <100 fs and is characterized by a large dipole moment (~35 D). The charge transfer character involves a shift of electron density within the polyene chain, and it does not involve participation of molecular orbitals localized in either of the β-rings. Charge is moved from the allenic side of the polyene into the furanic ring region and is accompanied by bond-order reversal in the central portion of the polyene chain. The electronic properties of the ICT state are generated via mixing of the "1(1)Bu(+)" ionic state and the lowest-lying "2(1)Ag(-)" covalent state. The resulting ICT state is primarily (1)Bu(+)-like in character and exhibits not only a large oscillator strength but an unusually large doubly excited character. In most solvents, two populations exist in equilibrium, one with a lowest-lying ICT ionic state and a second with a lowest-lying "2(1)Ag(-)" covalent state. The two populations are separated by a small barrier associated with solvent relaxation and cavity formation.

Energetics and dynamics of the low-lying electronic states of constrained polyenes: implications for infinite polyenes

Steady-state and ultrafast transient absorption spectra were obtained for a series of conformationally constrained, isomerically pure polyenes with 5-23 conjugated double bonds (N). These data and fluorescence spectra of the shorter polyenes reveal the N dependence of the energies of six (1)B(u)(+) and two (1)A(g)(-) excited states. The (1)B(u)(+) states converge to a common infinite polyene limit of 15,900 ± 100 cm(-1). The two excited (1)A(g)(-) states, however, exhibit a large (~9000 cm(-1)) energy difference in the infinite polyene limit, in contrast to the common value previously predicted by theory. EOM-CCSD ab initio and MNDO-PSDCI semiempirical MO theories account for the experimental transition energies and intensities. The complex, multistep dynamics of the 1(1)B(u)(+) → 2(1)A(g)(-) → 1(1)A(g)(-) excited state decay pathways as a function of N are compared with kinetic data from several natural and synthetic carotenoids. Distinctive transient absorption signals in the visible region, previously identified with S* states in carotenoids, also are observed for the longer polyenes. Analysis of the lifetimes of the 2(1)A(g)(-) states, using the energy gap law for nonradiative decay, reveals remarkable similarities in the N dependence of the 2(1)A(g)(-) decay kinetics of the carotenoid and polyene systems. These findings are important for understanding the mechanisms by which carotenoids carry out their roles as light-harvesting molecules and photoprotective agents in biological systems.

Aqueous Redox Chemistry and the Electronic Band Structure of Liquid Water

The electronic states of aqueous species can mix with the extended states of the solvent if they are close in energy to the band edges of water. Using density functional theory-based molecular dynamics simulation, we show that this is the case for OH(-) and Cl(-). The effect is, however, badly exaggerated by the generalized gradient approximation leading to systematic underestimation of redox potentials and spurious nonlinearity in the solvent reorganization. Drawing a parallel to charged defects in wide gap solid oxides, we conclude that misalignment of the valence band of water is the main source of error turning the redox levels of OH(-) and Cl(-) in resonant impurity states. On the other hand, the accuracy of energies of levels corresponding to strongly negative redox potentials is acceptable. We therefore predict that mixing of the vertical attachment level of CO2 and the unoccupied states of water is a real effect.

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.

Effect of Molecular Symmetry on the Spectra and Dynamics of the Intramolecular Charge Transfer (ICT) state of peridinin

The spectroscopic properties and dynamics of the excited states of two different synthetic analogues of peridinin were investigated as a function of solvent polarity using steady-state absorption, fluorescence, and ultrafast time-resolved optical spectroscopy. The analogues are denoted S-1- and S-2-peridinin and differ from naturally occurring peridinin in the location of the lactone ring and its associated carbonyl group, known to be obligatory for the observation of a solvent dependence of the lifetime of the S(1) state of carotenoids. Relative to peridinin, S-1- and S-2-peridinin have their lactone rings two and four carbons more toward the center of the π-electron system of conjugated carbon-carbon double bonds, respectively. The present experimental results show that as the polarity of the solvent increases, the steady-state spectra of the molecules broaden, and the lowest excited state lifetime of S-1-peridinin changes from ∼155 to ∼17 ps which is similar to the magnitude of the effect reported for peridinin. The solvent-induced change in the lowest excited state lifetime of S-2-peridinin is much smaller and changes only from ∼90 to ∼67 ps as the solvent polarity is increased. These results are interpreted in terms of an intramolecular charge transfer (ICT) state that is formed readily in peridinin and S-1-peridinin, but not in S-2-peridinin. Quantum mechanical computations reveal the critical factors required for the formation of the ICT state and the associated solvent-modulated effects on the spectra and dynamics of these molecules and other carbonyl-containing carotenoids and polyenes. The factors are the magnitude and orientation of the ground- and excited-state dipole moments which must be suitable to generate sufficient mixing of the lowest two excited singlet states.