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The calculation of molecular excited states is critically important to decipher a plethora of molecular properties. In this paper, we develop an equation of motion formalism on top of a bi-exponentially parameterized ground state wavefunction toward the determination of excited states. While the ground state bi-exponential parameterization ensures an accurate description of the wavefunction through the inclusion of high-rank correlation effects, the excited state is parameterized by a novel linear response operator with an effective excitation rank beyond two. To treat the ground and excited states in the same footings, in addition to the conventional one- and two-body response operators, we introduced certain two-body "generalized" response operators with an effective excitation rank of one. We introduce a projective formulation for determining the perturbed amplitudes for the set of "generalized" operators. Our formulation entails a significantly small number of unknown parameters and is shown to be highly accurate compared to allied methods for several difficult chemical systems. [ABSTRACT FROM AUTHOR]

This paper presents the first implementation of a coupling between advanced wavefunction theories and molecular density functional theory (MDFT). This method enables the modeling of solvent effect into quantum mechanical (QM) calculations by incorporating an electrostatic potential generated by solvent charges into the electronic Hamiltonian. Solvent charges are deduced from the spatially and angularly dependent solvent particle density. Such a density is obtained through the minimization of the functional associated with the molecular mechanics (MM) Hamiltonian describing the interaction between the fluid particles. The introduced QM/MDFT framework belongs to QM/MM family of methods, but its originality lies in the use of MDFT as the MM solver, offering two main advantages. First, its functional formulation makes it competitive with respect to sampling-based molecular mechanics. Second, it preserves a molecular-level description lost in macroscopic continuum approaches. The excited state properties of water and formaldehyde molecules solvated into water have been computed at the selected configuration interaction (SCI) level. The excitation energies and dipole moments have been compared with experimental data and previous theoretical work. A key finding is that using the Hartree–Fock method to describe the solute allows for predicting the solvent charge around the ground state with sufficient precision for the subsequent SCI calculations of excited states. This significantly reduces the computational cost of the described procedure, paving the way for the study of more complex molecules. [ABSTRACT FROM AUTHOR]

Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus–Levich–Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane–anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes. [ABSTRACT FROM AUTHOR]

Endohedrally doped clusters form a large category of cage clusters, with unique structures, diverse elemental compositions, and highly tunable electronic structures and physisochemical properties. They have been widely achieved in laboratory and may serve as functional building blocks for assembling new supermolecular structures and devices. In this paper, for the first time, we disclosed the luminescence properties of endohedrally doped group-IV clusters by time-dependent density functional theory calculations. A total of 64 cage clusters have been explored in terms of stability, emission wavelength, and the energy difference between the first excited singlet and triplet states. The key geometric and electronic factors governing the photophysical properties of these cage clusters were unveiled, to provide crucial insights for crafting atomically precise nanoclusters for optical and optoelectronic applications. [ABSTRACT FROM AUTHOR]

Vibrational coherences in ultrafast pump–probe (PP) and 2D electronic spectroscopy (2DES) provide insights into the excited state dynamics of molecules. Femtosecond coherence spectra and 2D beat maps yield information about displacements of excited state surfaces for key vibrational modes. Half-broadband 2DES uses a PP configuration with a white light continuum probe to extend the detection range and resolve vibrational coherences in the excited state absorption (ESA). However, the interpretation of these spectra is difficult as they are strongly dependent on the spectrum of the pump laser and the relative displacement of the excited states along the vibrational coordinates. We demonstrate the impact of these convoluting factors for a model based upon cresyl violet. A careful consideration of the position of the pump spectrum can be a powerful tool in resolving the ESA coherences to gain insights into excited state displacements. This paper also highlights the need for caution in considering the spectral window of the pulse when interpreting these spectra. [ABSTRACT FROM AUTHOR]

Produced by both nature and human activities, sulfur dioxide (SO2) is an important species in the earth's atmosphere. SO2 has also been found in the atmospheres of other planets and satellites in the solar system. The photoabsorption cross sections and photodissociation of SO2 have been studied for several decades. In this paper, we reported the experimental results for photodissociation dynamics of SO2 via the G ̃ 1B1 state. By analyzing the images from the time-sliced velocity map ion imaging method, the vibrational state population distributions and anisotropy parameters were obtained for the O(1D2) + SO(X3Σ−, a1Δ, b1Σ+) and O(1S0) + SO(X3Σ−) channels, and the branching ratios for the channels O(1D2) + SO(X3Σ−), O(1D2) + SO(a1Δ), and O(1D2) + SO(b1Σ+) were determined to be ∼0.3, ∼0.6, and ∼0.1, respectively. The SO products were dominant in electronically and rovibrationally excited states, which may have yet unrecognized roles in the upper planetary atmosphere. [ABSTRACT FROM AUTHOR]

In this paper, we report on the implementation of CC2 and CC3 in the context of molecules in finite magnetic fields. The methods are applied to the investigation of atoms and molecules through spectroscopic predictions and geometry optimizations for the study of the atmosphere of highly magnetized White Dwarf stars. We show that ground-state finite-field (ff) CC2 is a reasonable alternative to CCSD for energies and, in particular, for geometrical properties. For excited states, ff-CC2 is shown to perform well for states with predominant single-excitation character. Yet, for cases in which the excited state wavefunction has double-excitation character with respect to the reference, ff-CC2 can easily lead to completely unphysical results. Ff-CC3, however, is shown to reproduce the CCSDT behavior very well and enables the treatment of larger systems at a high accuracy. [ABSTRACT FROM AUTHOR]

Conical intersections are known to play a vital role in many photochemical processes. The breakdown of the Born–Oppenheimer approximation in the vicinity of a conical intersection causes exciting phenomena, such as the ultrafast radiationless decay of excited states. The passage of a molecule through a conical intersection creates a coherent superposition of electronic states via nonadiabatic couplings. Detecting this coherent superposition may serve as a direct probe of the conical intersection. In this paper, we theoretically demonstrate the use of coherent spontaneous emission in samples with long-range order for probing the occurrence of a conical intersection in a molecule. Our simulations show that the spectrum contains clear signatures of the created coherent superposition of electronic states. We investigate the bandwidth requirements for the x-ray probes, which influence the observation of coherent superposition generated by the conical intersection. [ABSTRACT FROM AUTHOR]

This paper reports the energies and charge and spin distributions of the low-lying excited states in singlet and triplet N2V defects in diamond from direct Δ-SCF calculations based on Gaussian orbitals within the B3LYP, PBE0, and HSE06 functionals. They assign the observed absorption at 2.463 eV, first reported by Davies et al. [Proc. R. Soc. London 351, 245 (1976)], to the excitation of a N(sp3) lone-pair electron in the singlet and triplet states, respectively, with estimates of ∼1.1 eV for that of the unpaired electrons, C(sp3). In both cases, the excited states are predicted to be highly local and strongly excitonic with 81% of the C(sp3) and 87% of the N(sp3) excited charges localized at the three C atoms nearest neighbor (nn) to the excitation sites. Also reported are the higher excited gap states of both the N lone pair and C unpaired electron. Calculated excitation energies of the bonding sp3 hybrids of the C atoms nn to the four inner atoms are close to that of the bulk, which indicates that the N2V defect is largely a local defect. The present results are in broad agreement with those reported by Udvarhelyi et al. [Phys. Rev. B 96, 155211 (2017)] from plane wave HSE06 calculations, notably for the N lone pair excitation energy, for which both predict an energy of ∼2.7 eV but with a difference of ∼0.5 eV for the excitation of the unpaired electron. [ABSTRACT FROM AUTHOR]

Stimulated Raman Adiabatic Passage (STIRAP) and its variants, such as M-type chainwise-STIRAP, allow for efficiently transferring the populations in a multilevel system and have widely been used to prepare molecules in their rovibrational ground state. However, their transfer efficiencies are generally imperfect. The main obstacle is the presence of losses and the requirement to make the dynamics adiabatic. To this end, in the present paper, a new theoretical method is proposed for the efficient and robust creation and detection of deeply bound molecules in three-level Λ-type and five-level M-type systems via "Invariant-based shortcut-to-adiabaticity." In the regime of large detunings, we first reduce the dynamics of three- and five-level molecular systems to those of effective two- and three-level counterparts. By doing so, the major molecular losses from the excited states can be well suppressed. Consequently, the effective two-level counterpart can be directly compatible with two different "Invariant-based Inverse Engineering" protocols; the results show that both protocols give a comparable performance and have a good experimental feasibility. For the effective three-level counterpart, by considering a relation among the four incident pulses, we show that this model can be further generalized to an effective Λ-type one with the simplest resonant coupling. This generalized model permits us to borrow the "Invariant-based Inverse Engineering" protocol from a standard three-level Λ-type system to a five-level M-type system. Numerical calculations show that the weakly bound molecules can be efficiently transferred to their deeply bound states without strong laser pulses, and the stability against parameter variations is well preserved. Finally, the detection of ultracold deeply bound molecules is discussed. [ABSTRACT FROM AUTHOR]

Modeling excited state processes in molecular crystals is relevant for several applications. A popular approach for studying excited state molecular crystals is to use cluster models embedded in point charges. In this paper, we compare the performance of several embedding models in predicting excited states and S1–S0 optical gaps for a set of crystals from the X23 molecular crystal database. The performance of atomic charges based on ground or excited states was examined for cluster models, Ewald embedding, and self-consistent approaches. We investigated the impact of various factors, such as the level of theory, basis sets, embedding models, and the level of localization of the excitation. We consider different levels of theory, including time-dependent density functional theory and Tamm–Dancoff approximation (TDA) (DFT functionals: ωB97X-D and PBE0), CC2, complete active space self-consistent field, and CASPT2. We also explore the impact of selection of the QM region, charge leakage, and level of theory for the description of different kinds of excited states. We implemented three schemes based on distance thresholds to overcome overpolarization and charge leakage in molecular crystals. Our findings are compared against experimental data, G0W0-BSE, periodic TDA, and optimally tuned screened range-separated functionals. [ABSTRACT FROM AUTHOR]

It is known that some non-dynamic effects of electron correlation can be included in coupled cluster theory using a tailoring technique that separates the effects of non-dynamic and dynamic correlations. Recently, the simple pCCD (pair coupled cluster doubles) wavefunction was shown to provide good results for some non-dynamic correlation problems, such as bond-breaking, in a spin-adapted way with no active space selection. In this paper, we report a study of excited states using "tailored coupled cluster singles and doubles," to attempt to use pCCD as a kernel for more complete coupled-cluster singles and doubles (CCSD) results for excited states. Several excited states are explored from those primarily due to single excitations to those dominated by doubly excited states and from singlet–triplet splittings for some diradical states. For the first two situations, tailored pCCD-TCCSD offers no improvement over equation of motion-CCSD. However, when we explore the singlet–triplet gap of diradical molecules that are manifestly multi-reference, a pCCD kernel provides improved results, particularly with generalized valence bond orbitals. [ABSTRACT FROM AUTHOR]

The dual exponential coupled cluster theory proposed by Tribedi et al.[J. Chem. Theory Comput. 16, 10, 6317–6328 (2020)] performs significantly better for a wide range of weakly correlated systems than the coupled cluster theory with singles and doubles excitations due to the implicit inclusion of high-rank excitations. The high-rank excitations are included through the action of a set of vacuum annihilating scattering operators that act non-trivially on certain correlated wavefunctions and are determined via a set of local denominators involving the energy difference between certain excited states. This often leads the theory to be prone to instabilities. In this paper, we show that restricting the correlated wavefunction, on which the scattering operators act, to be spanned by only the singlet-paired determinants can avoid catastrophic breakdown. For the first time, we present two nonequivalent approaches to arrive at the working equations, viz., the projective approach with sufficiency conditions and the amplitude form with many-body expansion. Although the effect of the triple excitation is quite small around molecular equilibrium geometry, this scheme leads to a better qualitative description of the energetics in the regions of strong correlation. With many pilot numerical applications, we have demonstrated the performance of the dual-exponential scheme with both the proposed solution strategies while restricting the excitation subspaces coupled to the corresponding lowest spin channels. [ABSTRACT FROM AUTHOR]

Multiple ERI (Electron Repulsion Integral) tensor contractions (METC) with several matrices are ubiquitous in quantum chemistry. In response theories, the contraction operation, rather than ERI computations, can be the major bottleneck, as its computational demands are proportional to the multiplicatively combined contributions of the number of excited states and the kernel pre-factors. This paper presents several high-performance strategies for METC. Optimal approaches involve either the data layout reformations of interim density and Fock matrices, the introduction of intermediate ERI quartet buffer, and loop-reordering optimization for a higher cache hit rate. The combined strategies remarkably improve the performance of the MRSF (mixed reference spin flip)-TDDFT (time-dependent density functional theory) by nearly 300%. The results of this study are not limited to the MRSF-TDDFT method and can be applied to other METC scenarios. [ABSTRACT FROM AUTHOR]

This paper reports the energies and charge and spin distributions of both the vertically excited and fully relaxed GR1 states of the neutral singlet vacancy in diamond obtained from direct Δ-SCF calculations used previously to describe the low-lying excited states in AFII NiO and α-Al2O3. The calculations are based on the B3LYP functional in its standard form, with a C basis set that is identical to that which was used previously in numerous calculations of the ground state properties of defective diamond. Both the vertically excited and thermally relaxed GR1 states are predicted to be excitonic and insulating, with extensive re-distribution of charge and spin density and back-donation to the donor site. The present calculations suggest that the triplet state makes no contribution to the GR1 excitation. The predicted energy of the zero phonon line (1.57 eV) compares with the observed value of 1.67 eV, which also suggests that the GR1 state is neutral. The bandgaps lead to an estimate of the next higher (GR2) excited state energy, which is close to that found in the observed spectra. Similar calculations are used to predict the energies of the higher gap states at (5.0–5.5) eV, including the bulk value of 7.3 eV, which compares with the experimental value of (7.3–7.4) eV. An explanation is suggested as to why only the GR1 luminescence is observed. This paper also suggests an alternative channel for the recovery of the ground state in photoluminescence studies. [ABSTRACT FROM AUTHOR]

Efficient energy transport in photosynthetic antenna is a long-standing source of inspiration for artificial light harvesting materials. However, characterizing the excited states of the constituent chromophores poses a considerable challenge to mainstream quantum chemical and semiempirical excited state methods due to their size and complexity and the accuracy required to describe small but functionally important changes in their properties. In this paper, we explore an alternative approach to calculating the excited states of large biochromophores, exemplified by a specific method for calculating the Qy transition of bacteriochlorophyll a, which we name Chl-xTB. Using a diagonally dominant approximation to the Casida equation and a bespoke parameterization scheme, Chl-xTB can match time-dependent density functional theory's accuracy and semiempirical speed for calculating the potential energy surfaces and absorption spectra of chlorophylls. We demonstrate that Chl-xTB (and other prospective realizations of our protocol) can be integrated into multiscale models, including concurrent excitonic and point-charge embedding frameworks, enabling the analysis of biochromophore networks in a native environment. We exploit this capability to probe the low-frequency spectral densities of excitonic energies and interchromophore interactions in the light harvesting antenna protein LH2 (light harvesting complex 2). The impact of low-frequency protein motion on interchromophore coupling and exciton transport has routinely been ignored due to the prohibitive costs of including it in simulations. Our results provide a more rigorous basis for continued use of this approximation by demonstrating that exciton transition energies are unaffected by low-frequency vibrational coupling to exciton interaction energies. [ABSTRACT FROM AUTHOR]

Some diarylethene molecular switches have a low quantum yield for cycloreversion when excited by a single photon, but react more efficiently following sequential two-photon excitation. The increase in reaction efficiency depends on both the relative time delay and the wavelength of the second photon. This paper examines the wavelength-dependent mechanism for sequential excitation using excited-state resonance Raman spectroscopy to probe the ultrafast (sub-30 fs) dynamics on the upper electronic state following secondary excitation. The approach uses femtosecond stimulated Raman scattering (FSRS) to measure the time-gated, excited-state resonance Raman spectrum in resonance with two different excited-state absorption bands. The relative intensities of the Raman bands reveal the initial dynamics in the higher-lying states, Sn, by providing information on the relative gradients of the potential energy surfaces that are accessed via secondary excitation. The excited-state resonance Raman spectra reveal specific modes that become enhanced depending on the Raman excitation wavelength, 750 or 400 nm. Many of the modes that become enhanced in the 750 nm FSRS spectrum are assigned as vibrational motions localized on the central cyclohexadiene ring. Many of the modes that become enhanced in the 400 nm FSRS spectrum are assigned as motions along the conjugated backbone and peripheral phenyl rings. These observations are consistent with earlier measurements that showed higher efficiency following secondary excitation into the lower excited-state absorption band and illustrate a powerful new way to probe the ultrafast dynamics of higher-lying excited states immediately following sequential two-photon excitation. [ABSTRACT FROM AUTHOR]

Experimental demonstrations of polarization-selection two-dimensional Vibrational-Electronic (2D VE) and 2D Electronic-Vibrational (2D EV) spectroscopies aim to map the magnitudes and spatial orientations of coupled electronic and vibrational coordinates in complex systems. The realization of that goal depends on our ability to connect spectroscopic observables with molecular structural parameters. In this paper, we use a model Hamiltonian consisting of two anharmonically coupled vibrational modes in electronic ground and excited states with linear and bilinear vibronic coupling terms to simulate polarization-selective 2D EV and 2D VE spectra. We discuss the relationships between the linear vibronic coupling and two-dimensional Huang–Rhys parameters and between the bilinear vibronic coupling term and Duschinsky mixing. We develop a description of the vibronic transition dipoles and explore how the Hamiltonian parameters and non-Condon effects impact their amplitudes and orientations. Using simulated polarization-selective 2D EV and 2D VE spectra, we show how 2D peak positions, amplitudes, and anisotropy can be used to measure parameters of the vibronic Hamiltonian and non-Condon effects. This paper, along with the first in the series, provides the reader with a detailed description of reading, simulating, and analyzing multimode, polarization-selective 2D EV and 2D VE spectra with an emphasis on extracting vibronic coupling parameters from complex spectra. [ABSTRACT FROM AUTHOR]

This paper reports the first variationally based predictions of the lowest excited state in diamond (Γ25′ → Γ15) in the unrelaxed (optical) and structurally relaxed (thermal) configurations, from direct Δ-self-consistent-field (SCF) calculations based on B3LYP, PBE0, HSE06, and GGA functionals. For the B3LYP functional, which has the best overall performance, the energy of the optical state, 7.27 eV, is within the observed range of (7.2–7.4) eV and is predicted to be insulating, with indirect bandgaps of (5.6–5.8) eV. Mulliken analyses of the excited state wavefunction indicate extensive redistributions of charge and spin resulting in a strongly excitonic state with a central charge of −0.8ǀeǀ surrounded by charges of +0.12ǀeǀ at the four nearest neighbor sites. The thermally relaxed state is predicted to be similarly excitonic, with comparable bandgaps and atomic charges. Calculations of the ground and excited state relaxations lead to a Stokes shift of 0.47 eV and predicted Γ-point luminescence energy of 6.89 eV. Assuming a similar shift at the band edge (X1), an estimate of 5.29 eV is predicted for the luminescence energy, which compares with the observed value of 5.27 eV. Excited state vibrational spectra show marked differences from the ground state, with the introduction of an infrared peak at 1150 cm−1 and a modest shift of 2 cm−1 in the TO(X) Raman mode at 1340 cm−1. Similar calculations of the lowest energy bi- and triexcitons predict these to be bound states in both optical and thermal configurations and plausible precursors to exciton condensation. Estimates of bi- and triexciton luminescence energies predict red shifts with respect to the single exciton line, which are compared to the recently reported values. [ABSTRACT FROM AUTHOR]

Eigenvectors of the reduced Bardeen–Cooper–Schrieffer (BCS) Hamiltonian, Richardson–Gaudin (RG) states, are used as a variational wavefunction ansatz for strongly correlated electronic systems. These states are geminal products whose coefficients are solutions of non-linear equations. Previous results showed an un-physical apparent avoided crossing in ground state dissociation curves for hydrogen chains. In this paper, it is shown that each seniority-zero state of the molecular Coulomb Hamiltonian corresponds directly to an RG state. However, the seniority-zero ground state does not correspond to the ground state of a reduced BCS Hamiltonian. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice, and we expect that it should always be possible to reason physically which state to choose. [ABSTRACT FROM AUTHOR]

With a He– H 3 + interaction potential obtained from advanced electronic structure calculations, we computed the vibration-rotation-tunneling (VRT) states of this complex for total angular momenta J from 0 to 9, both for the vibrational ground state and for the twofold degenerate v2 = 1 excited state of H 3 + . The potential has three equivalent global minima with depth De = 455.3 cm−1 for He in the plane of H 3 + , three equatorial saddle points that separate these minima with barriers of 159.5 cm−1, and two axial saddle points with energies of 243.1 cm−1 above the minima. The dissociation energies calculated for the complexes of He with ortho- H 3 + (o H 3 + ) and para- H 3 + (p H 3 + ) are D0 = 234.5 and 236.3 cm−1, respectively. Wave function plots of the VRT states show that they may be characterized as weakly hindered internal rotor states, delocalized over the three minima in the potential and with considerable amplitude at the barriers. Most of them are dominated by the jk = 10 and 11 rotational ground states of o H 3 + and p H 3 + , with the intermolecular stretching mode excited up to v = 4 inclusive. However, we also found excited internal rotor states: 33 in He–o H 3 + , and 22 and 21 in He–p H 3 + . The VRT levels and wave functions were used to calculate the frequencies and line strengths of all allowed v2 = 0 → 1 rovibrational transitions in the complex. Theoretical spectra generated with these results are compared with the experimental spectra in Paper II [Salomon et al., J. Chem. Phys. 156, 144308 (2022)] and are extremely helpful in assigning these spectra. This comparison shows that the theoretical energy levels and spectra agree very well with the measured ones, which confirms the high accuracy of our ab initio He– H 3 + interaction potential and of the ensuing calculations of the VRT states. [ABSTRACT FROM AUTHOR]

The hydration structure of cellulose is very important for understanding the hydrolysis of cellulose at the molecular level. In this paper, we report a joint experimental and theoretical study on x-ray absorption spectroscopy (XAS) of aqueous cellobiose, a disaccharide unit of cellulose. In the experimental part, high resolution measurements of the carbon K-edge XAS spectra were taken. In the theoretical part, ab initio molecular dynamics simulations and ensemble calculations of electronic excited states were performed to obtain the continuous XAS spectra. The XAS spectra were found to have three characteristic peaks at 289.3, 290.7, and 293.6 eV, each representing the absorption by carbon atoms of the alcohol group, the hemiacetal group, and both of these functional groups. It was found that the peak heights in the spectrum change considerably over the temperature range of 25–60 °C, which is a reflection of the number of hydrogen bonds between cellobiose and water. We suggest that this spectral change could be useful information for identifying the hydration of cellulose in various environments. [ABSTRACT FROM AUTHOR]

Incorporation of fluorescent proteins into biochemical systems has revolutionized the field of bioimaging. In a bottom-up approach, understanding the photophysics of fluorescent proteins requires detailed investigations of the light-absorbing chromophore, which can be achieved by studying the chromophore in isolation. This paper reports a photodissociation action spectroscopy study on the deprotonated anion of the red Kaede fluorescent protein chromophore, demonstrating that at least three isomers–assigned to deprotomers–are generated in the gas phase. Deprotomer-selected action spectra are recorded over the S1 ← S0 band using an instrument with differential mobility spectrometry coupled with photodissociation spectroscopy. The spectrum for the principal phenoxide deprotomer spans the 480–660 nm range with a maximum response at ≈610 nm. The imidazolate deprotomer has a blue-shifted action spectrum with a maximum response at ≈545 nm. The action spectra are consistent with excited state coupled-cluster calculations of excitation wavelengths for the deprotomers. A third gas-phase species with a distinct action spectrum is tentatively assigned to an imidazole tautomer of the principal phenoxide deprotomer. This study highlights the need for isomer-selective methods when studying the photophysics of biochromophores possessing several deprotonation sites. [ABSTRACT FROM AUTHOR]

Two-dimensional electronic–vibrational spectroscopy (2DEVS) is an emerging spectroscopic technique which exploits two different frequency ranges for the excitation (visible) and detection (infrared) axes of a 2D spectrum. In contrast to degenerate 2D techniques, such as 2D electronic or 2D infrared spectroscopy, the spectral features of a 2DEV spectrum report cross correlations between fluctuating electronic and vibrational energy gaps rather than autocorrelations as in the degenerate spectroscopies. The center line slope of the spectral features reports on this cross correlation function directly and can reveal specific electronic–vibrational couplings and rapid changes in the electronic structure, for example. The involvement of the two types of transition moments, visible and infrared, makes 2DEVS very sensitive to electronic and vibronic mixing. 2DEV spectra also feature improved spectral resolution, making the method valuable for unraveling the highly congested spectra of molecular complexes. The unique features of 2DEVS are illustrated in this paper with specific examples and their origin described at an intuitive level with references to formal derivations provided. Although early in its development and far from fully explored, 2DEVS has already proven to be a valuable addition to the tool box of ultrafast nonlinear optical spectroscopy and is of promising potential in future efforts to explore the intricate connection between electronic and vibrational nuclear degrees of freedom in energy and charge transport applications. [ABSTRACT FROM AUTHOR]

The effective design of dyes optimized for thermally activated delayed fluorescence (TADF) requires the precise control of two tiny energies: the singlet–triplet gap, which has to be maintained within thermal energy, and the strength of spin–orbit coupling. A subtle interplay among low-energy excited states having dominant charge-transfer and local character then governs TADF efficiency, making models for environmental effects both crucial and challenging. The main message of this paper is a warning to the community of chemists, physicists, and material scientists working in the field: the adiabatic approximation implicitly imposed to the treatment of fast environmental degrees of freedom in quantum–classical and continuum solvation models leads to uncontrolled results. Several approximation schemes were proposed to mitigate the issue, but we underline that the adiabatic approximation to fast solvation is inadequate and cannot be improved; rather, it must be abandoned in favor of an antiadiabatic approach. [ABSTRACT FROM AUTHOR]

Photo-induced relaxation processes leading to excimer formations or other traps are in the focus of many investigations of optoelectronic materials because they severely affect the efficiencies of corresponding devices. Such relaxation effects comprise inter-monomer distortions in which the orientations of the monomer change with respect to each other, whereas intra-monomer distortions are variations in the geometry of single monomers. Such distortions are generally neglected in quantum chemical investigations of organic dye aggregates due to the accompanied high computational costs. In the present study, we investigate their relevance using perylene-bisimide dimers and diindenoperylene tetramers as model systems. Our calculations underline the importance of intra-monomer distortions on the shape of the potential energy surfaces as a function of the coupling between the monomers. The latter is shown to depend strongly on the electronic state under consideration. In particular, it differs between the first and second excited state of the aggregate. Additionally, the magnitude of the geometrical relaxation decreases if the exciton is delocalized over an increasing number of monomers. For the interpretation of the vibronic coupling model, pseudo-Jahn–Teller or Marcus theory can be employed. In the first part of this paper, we establish the accuracy of density functional theory-based approaches for the prediction of vibrationally resolved absorption spectra of organic semiconductors. These investigations underline the accuracy of those approaches although shortcomings become obvious as well. These calculations also indicate the strength of intra-monomer relaxation effects. [ABSTRACT FROM AUTHOR]

Machine learning (ML) has shown to advance the research field of quantum chemistry in almost any possible direction and has also recently been applied to investigate the multifaceted photochemistry of molecules. In this paper, we pursue two goals: (i) We show how ML can be used to model permanent dipole moments for excited states and transition dipole moments by adapting the charge model of Gastegger et al. [Chem. Sci. 8, 6924–6935 (2017)], which was originally proposed for the permanent dipole moment vector of the electronic ground state. (ii) We investigate the transferability of our excited-state ML models in chemical space, i.e., whether an ML model can predict the properties of molecules that it has never been trained on and whether it can learn the different excited states of two molecules simultaneously. To this aim, we employ and extend our previously reported SchNarc approach for excited-state ML. We calculate UV absorption spectra from excited-state energies and transition dipole moments as well as electrostatic potentials from latent charges inferred by the ML model of the permanent dipole moment vectors. We train our ML models on C H 2 N H 2 + and C2H4, while predictions are carried out for these molecules and additionally for CHNH2, CH2NH, and C 2 H 5 + . The results indicate that transferability is possible for the excited states. [ABSTRACT FROM AUTHOR]

A rigorous practically applicable theory is presented for obtaining lower bounds to eigenvalues of Hermitian operators, whether the ground state or excited states. Algorithms are presented for computing "residual energies" whose magnitude is essential for the computation of the eigenvalues. Their practical application is possible due to the usage of the Lanczos method for creating a tridiagonal representation of the operator under study. The theory is self-consistent, in the sense that a lower bound for one state may be used to improve the lower bounds for others, and this is then used self-consistently until convergence. The theory is exemplified for a toy model of a quartic oscillator, where with only five states the relative error in the lower bound for the ground state is reduced to 6 · 10−6, which is the same as the relative error of the least upper bound obtained with the same basis functions. The lower bound method presented in this paper suggests that lower bounds may become a staple of eigenvalue computations. [ABSTRACT FROM AUTHOR]

We use femtosecond optical pump-probe spectroscopy to study the Light Induced Excited Spin State Trapping (LIESST) dynamics in an FeII spin-crossover material. In these systems, LIESST derives from fast molecular switching induced by light from low (LS, S = 0) to high spin (HS, S = 2) states, as reported for molecules in solution as well as in the solid state. Since the direct LS-to-HS conversion is forbidden by selection rules, the switching dynamics involves intermediate electronic states such as metal-to-ligand charge transfer (MLCT) or ligand-field excited states of singlet or triplet nature. In addition, the HS state is structurally trapped by the elongation of the metal-ligand bond, which is accompanied by the coherent activation and damping of the molecular breathing mode. The ultrafast LIESST dynamics was mainly investigated in FeN6 ligand field systems with almost octahedral symmetry, under MLCT excitation. Our recent study on the FeII(pap-5NO2)2 spin-crossover material, with a FeIIN4O2 ligand field of C2 symmetry, has shown that in addition to MLCT bands, optical excitation, through quite intense and low-energy shifted d-d bands, can also drive LIESST. Compared to MLCT, d-d excitation involves shorter-lived intermediates, drives faster LS-to-HS switching, and enhances the coherent structural dynamics. In this paper, we present an ultrafast study of the pump wavelength dependence of LIESST and we evidence a photoselective crossover from the MLCT to the d-d pathways. [ABSTRACT FROM AUTHOR]

The structure of the hydrated electron, particularly whether it exists primarily within a cavity or encompasses interior water molecules, has been the subject of much recent debate. In Paper I [C.-C. Zho et al., J. Chem. Phys. 147, 074503 (2017)], we found that mixed quantum/classical simulations with cavity and non-cavity pseudopotentials gave different predictions for the temperature dependence of the rate of the photoexcited hydrated electron's relaxation back to the ground state. In this paper, we measure the ultrafast transient absorption spectroscopy of the photoexcited hydrated electron as a function of temperature to confront the predictions of our simulations. The ultrafast spectroscopy clearly shows faster relaxation dynamics at higher temperatures. In particular, the transient absorption data show a clear excess bleach beyond that of the equilibrium hydrated electron's ground-state absorption that can only be explained by stimulated emission. This stimulated emission component, which is consistent with the experimentally known fluorescence spectrum of the hydrated electron, decreases in both amplitude and lifetime as the temperature is increased. We use a kinetic model to globally fit the temperature-dependent transient absorption data at multiple temperatures ranging from 0 to 45 °C. We find the room-temperature lifetime of the excited-state hydrated electron to be 137±40 fs, in close agreement with recent time-resolved photoelectron spectroscopy (TRPES) experiments and in strong support of the "non-adiabatic" picture of the hydrated electron's excited-state relaxation. Moreover, we find that the excited-state lifetime is strongly temperature dependent, changing by slightly more than a factor of two over the 45 °C temperature range explored. This temperature dependence of the lifetime, along with a faster rate of ground-state cooling with increasing bulk temperature, should be directly observable by future TRPES experiments. Our data also suggest that the red side of the hydrated electron's fluorescence spectrum should significantly decrease with increasing temperature. Overall, our results are not consistent with the nearly complete lack of temperature dependence predicted by traditional cavity models of the hydrated electron but instead agree qualitatively and nearly quantitatively with the temperature-dependent structural changes predicted by the non-cavity hydrated electron model. [ABSTRACT FROM AUTHOR]

This paper presents core excitation spectra from coupled-cluster (CC) theory obtained from both a time-independent and a new time-dependent formalism. The conventional time-independent CC formulation for excited states is the equation-of-motion (EOM-CC) method whose eigenvalues and eigenvectors describe the core excited states. An alternative computational procedure is offered by a time-dependent CC description. In that case, the dipole transition operator is expressed in the CC effective Hamiltonian form and propagated with respect to time. The absorption spectrum is obtained from the CC dipole autocorrelation function via a Fourier transformation. Comparisons are made among the time-dependent results obtained from second-order perturbation theory, to coupled cluster doubles and their linearized forms (CCD and LCCD), to CC singles and doubles (CCSD) and the linearized form (LCCSD). In the time-independent case, considerations of triples (EOM-CCSDT) and quadruples (EOM-CCSDTQ) are used to approach sub-electron volt accuracy. A particular target is the allyl radical, as an example of an open-shell molecule. As the results have to ultimately be the same, the two procedures offer a complementary approach toward analyzing experimental results. [ABSTRACT FROM AUTHOR]

We propose a modification to the nonadiabatic surface hopping calculation method formulated in a paper by Yu et al. [Phys. Chem. Chem. Phys. 16, 25883 (2014)], which is a multidimensional extension of the Zhu-Nakamura theory with a practical diabatic gradient estimation algorithm. In our modification, their diabatic gradient estimation algorithm, which is based on a simple interpolation of the adiabatic potential energy surfaces, is replaced by an algorithm using the numerical derivatives of the adiabatic gradients. We then apply the algorithm to several models of nonadiabatic dynamics, both analytic and ab initio models, to numerically demonstrate that our method indeed widens the applicability and robustness of their method. We also discuss the validity and limitations of our new nonadiabatic surface hopping method while considering in mind potential applications to excited-state dynamics of biomolecules or unconventional nonadiabatic dynamics such as radiation decay processes in ultraintense X-ray fields. [ABSTRACT FROM AUTHOR]

Our paper presents the first theoretical and experimental study using single-molecule Metal-Induced Energy Transfer (smMIET) for localizing single fluorescent molecules in three dimensions. Metal-Induced Energy Transfer describes the resonant energy transfer from the excited state of a fluorescent emitter to surface plasmons in a metal nanostructure. This energy transfer is strongly distance-dependent and can be used to localize an emitter along one dimension. We have used Metal-Induced Energy Transfer in the past for localizing fluorescent emitters with nanometer accuracy along the optical axis of a microscope. The combination of smMIET with single-molecule localization based super-resolution microscopy that provides nanometer lateral localization accuracy offers the prospect of achieving isotropic nanometer localization accuracy in all three spatial dimensions. We give a thorough theoretical explanation and analysis of smMIET, describe its experimental requirements, also in its combination with lateral single-molecule localization techniques, and present first proof-of-principle experiments using dye molecules immobilized on top of a silica spacer, and of dye molecules embedded in thin polymer films. [ABSTRACT FROM AUTHOR]

When a CHD3 molecule is pumped to the C-H stretching-excited state by absorbing a linearly polarized infrared (IR) photon via the R(0) branch of the v1 = 1 ← 0 transition, the rotational angular momentum j of the prepared state |jK = |10 preferentially lies in a plane perpendicular to the IR polarization axis εIR. By way of contrast, when the Q(1) branch is used, the state of |jK = |1 ± 1 is prepared with j aligned along the direction of εIR. Reported here is a detailed study of the title reaction by actively controlling the collision geometries under these two IR-excitation schemes at collision energy Ec = 8.6 kcal mol−1, using a crossed molecular beam, product imaging approach. We found that under the R(0) excitation, the polarization-dependent differential cross sections for the HCl(v = 0) + CD3(00) channel can largely be understood by invoking dual reaction mechanisms. The forward-scattered products are most likely mediated by a time-delayed resonance mechanism--as the formation of the HCl(v = 1) + CD3(00) channel, whereas the backward/sideways scattered products are governed by a direct abstraction mechanism. Compared to the previous results at lower Ec of 3.8 kcal mol−1, the sighting of opening-up the attack angle at the transition state of the direct pathway is proposed. Results under the Q(1) excitation are, however, perplexing and bear no obvious correlation to the corresponding ones for the R(0) excitation, defying simple intuitive interpretation. Possible reasons are put forward, which call for theoretical investigations for deeper insights. The results on the alternative isotope channel, DCl + CHD2, will be reported in the following paper. [ABSTRACT FROM AUTHOR]

In the present paper, accurate optical absorption spectrum of liquid H2O is calculated in the energy range of 5-20 eV to probe the nature of water's excited states by means of many body perturbation approach. Main features of recent inelastic X-ray measurements are well reproduced, such as a bound excitonic peak at 7.9 eV with a shoulder at 9.4 eV as well as the absorption maximum at 13.9 eV, followed by a broad shoulder at 18.4 eV. The spectrum is dominated by excitonic effects impacting the structures of the spectrum at low and higher energy regimes mixed by single particle effects at high energies. The exciton distribution of the low-energy states, in particular of S1, is highly anisotropic and localized mostly on one water molecule. The S1 state is essentially a HOCO-LUCO (highest occupied crystal orbital - lowest unoccupied crystal orbital) transition and of intra-molecular type, showing a localized valence character. Once the excitation energy is increased, a significant change in the character of the electronically excited states occurs, characterized through emergence of multiple quasi-particle peaks at 7.9 eV in the quasi-particle (QP) transition profile and in the occurring delocalized exciton density distribution, spread over many more water molecules. The exciton delocalization following a change of the character of excited states at around 7.9 eV causes the blue shift of the first absorption band with respect to water monomer S1. However, due to reduction of the electronic band gap from gas to liquid phase, following enhanced screening upon condensation, the localized S1 state of liquid water is red-shifted with respect to S1 state of water monomer. For higher excitations, near vertical ionization energy (11 eV), quasi-free electrons emerge, in agreement with the conduction band electron picture. Furthermore, the occurring red and blue shift of the excited states are independent of the coupling of resonant and anti-resonant contributions to the spectrum. [ABSTRACT FROM AUTHOR]

Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schrödinger equation with N Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from O(N²) to O(N). By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing the nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems: the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-dimensional model for collinear triatomic vibrational dynamics. In all cases, the pseudospectral Gaussian method is in quantitative agreement with numerically exact calculations. The results are promising for nonadiabatic molecular dynamics in molecular systems where strongly correlated ground or excited states require expensive electronic structure calculations. [ABSTRACT FROM AUTHOR]

Auger decay is an efficient ultrafast relaxation process of core-shell or inner-shell excited atom or molecule. Generally, it occurs in femto-second or even atto-second time domain. Direct measurement of lifetimes of Auger process of single ionized and double ionized inner-shell state of an atom or molecule is an extremely difficult task. In this paper, we have applied the highly correlated complex absorbing potential-equation-of-motion coupled cluster (CAP-EOMCC) approach which is a combination of CAP and EOMCC approach to calculate the lifetime of the states arising from 2p inner-shell ionization of an Ar atom and 3d inner-shell ionization of Kr atom. We have also calculated the lifetime of Ar2+(2p-13p-1)¹D, Ar2+(2p-13p-1)¹S, and Ar2+(2p-13s-1) 1P double ionized states. The predicted results are compared with the other theoretical results as well as experimental results available in the literature. [ABSTRACT FROM AUTHOR]

Changes in the electronic structure of pigments in protein environments and of polar molecules in solution inevitably induce a re-adaption of molecular nuclear structure. Both changes of electronic and vibrational energies can be probed with visible or infrared lasers, such as two-dimensional electronic spectroscopy or vibrational spectroscopy. The extent to which the two changes are correlated remains elusive. The recent demonstration of two-dimensional electronic-vibrational (2DEV) spectroscopy potentially enables a direct measurement of this correlation experimentally. However, it has hitherto been unclear how to characterize the correlation from the spectra. In this paper, we present a theoretical formalism to demonstrate the slope of the nodal line between the excited state absorption and ground state bleach peaks in the spectra as a characterization of the correlation between electronic and vibrational transition energies. We also show the dynamics of the nodal line slope is correlated to the vibrational spectral dynamics. Additionally, we demonstrate the fundamental 2DEV spectral line-shape of a monomer with newly developed response functions. [ABSTRACT FROM AUTHOR]

1,2-diphenoxyethane (DPOE) is a flexible bichromophore whose excited states come in close-lying pairs whose splitting and vibronic coupling can be modulated by solvent. Building on the ground state infrared spectroscopy of DPOE-(H2O)n clusters with n = 2-4 from the adjoining paper [Walsh et al., J. Chem. Phys. 142, 154303 (2015)], the present work focuses on the vibronic and excited state infrared spectroscopies of the clusters. The type and degree of asymmetry of the water cluster binding to DPOE is reflected in the variation in the magnitude of the S1/S2 splitting with cluster size. Excited state resonant ion-dip infrared spectroscopy was performed at the electronic origins of the first two excited states in order to explore how the water clusters' OH stretch spectra report on the nature of the two excited states, and the interaction of the S2 state with nearby S1 vibronic levels mediated by the water clusters. The data set, when taken as a whole, provides a state-to-state view of internal conversion and the role of solvent in mediating conversion of electronic excitation between two chromophores, providing a molecular-scale view of Kasha's rule. [ABSTRACT FROM AUTHOR]

The electronic structure of eight zinc-centered porphyrin macrocyclic molecules are investigated using density functional theory for ground-state properties, time-dependent density functional theory (TDDFT) for excited states, and Franck-Condon (FC) analysis for further characterization of the UV-vis spectrum. Symmetry breaking was utilized to find the lowest energy of the excited states for many states in the spectra. To confirm the theoretical modeling, the spectroscopic result from zinc phthalocyanine (ZnPc) is used to compare to the TDDFT and FC result. After confirmation of the modeling, five more planar molecules are investigated: zinc tetrabenzoporphyrin (ZnTBP), zinc tetrabenzomonoazaporphyrin (ZnTBMAP), zinc tetrabenzocisdiazaporphyrin (ZnTBcisDAP), zinc tetrabenzotransdiazaporphyrin (ZnTBtransDAP), and zinc tetrabenzotriazaporphyrin (ZnTBTrAP). The two latter molecules are then compared to their phenylated sister molecules: zinc monophenyltetrabenzotriazaporphyrin (ZnMPTBTrAP) and zinc diphenyltetrabenzotransdiazaporphyrin (ZnDPTBtransDAP). The spectroscopic results from the synthesis of ZnMPTBTrAP and ZnDPTBtransDAP are then compared to their theoretical models and non-phenylated pairs. While the Franck-Condon results were not as illuminating for every B-band, the Q-band results were successful in all eight molecules, with a considerable amount of spectral analysis in the range of interest between 300 and 750 nm. The π-π* transitions are evident in the results for all of the Q bands, while satellite vibrations are also visible in the spectra. In particular, this investigation finds that, while ZnPc has a D4h symmetry at ground state, a C4v symmetry is predicted in the excited-state Q band region. The theoretical results for ZnPc found an excitation energy at the Q-band 0-0 transition of 1.88 eV in vacuum, which is in remarkable agreement with published gas-phase spectroscopy, as well as our own results of ZnPc in solution with Tetrahydrofuran that are provided in this paper. [ABSTRACT FROM AUTHOR]