Excited Research Articles

Hückel molecular orbital theory on a quantum computer: A scalable system-agnostic variational implementation with compact encoding.

Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research.

Investigation of ultrafast intermediate states during singlet fission in lycopene H-aggregate using femtosecond stimulated Raman spectroscopy.

The singlet fission process involves the conversion of one singlet excited state into two triplet states, which has significant potential for enhancing the energy utilization efficiency of solar cells. Carotenoid, a typical π conjugated chromophore, exhibits specific aggregate morphologies known to display singlet fission behavior. In this study, we investigate the singlet fission process in lycopene H-aggregates using femtosecond stimulated Raman spectroscopy aided by quantum chemical calculation. The experimental results reveal two reaction pathways that effectively relax the S2 (11Bu+) state populations in lycopene H-aggregates: a monomer-like singlet excited state relaxation pathway through S2 (11Bu+) → 11Bu- → S1 (21Ag-) and a dominant sequential singlet fission reaction pathway involving the S2 (11Bu+) state, followed by S* state, a triplet pair state [1(TT)], eventually leading to a long lifetime triplet state T1. Importantly, the presence of both anionic and cationic fingerprint Raman peaks in the S* state is indicative of a substantial charge-transfer character.

Quasi-degenerate extension of local N-electron valence state perturbation theory with pair-natural orbital method based on localized virtual molecular orbitals.

Chemical phenomena involving near-degenerate electronic states, such as conical intersections or avoided crossing, can be properly described using quasi-degenerate perturbation theory. This study proposed a highly scalable quasi-degenerate second-order N-electron valence state perturbation theory (QD-NEVPT2) using the local pair-natural orbital (PNO) method. Our recent study showed an efficient implementation of the PNO-based state-specific NEVPT2 method using orthonormal localized virtual molecular orbitals (LVMOs) as an intermediate local basis. This study derived the state-coupling (or off-diagonal) terms to implement QD-NEVPT2 in an alternative manner to enhance efficiency based on the internally contracted basis and PNO overlap matrices between different references. To facilitate further acceleration, a local resolution-of-the-identity (RI) three-index integral generation algorithm was developed using LMOs and LVMOs. Although the NEVPT2 theory is considered to be less susceptible to the intruder-state problem (ISP), this study revealed that it can easily suffer from ISP when calculating high-lying excited states. We ameliorated this instability using the imaginary level shift technique. The PNO-QD-NEVPT2 calculations were performed on small organic molecules for the 30 lowest-lying states, as well as photoisomerization involving the conical intersection of 1,1-dimethyldibenzo[b,f] silepin with a cis-stilbene skeleton. These calculations revealed that the PNO-QD-NEVPT2 method yielded negligible errors compared to the canonical QD-NEVPT2 results. Furthermore, we tested its applicability to a large photoisomerization system using the green fluorescent protein model and the ten-state calculation of the large transition metal complex, showcasing that off-diagonal elements can be evaluated at a relatively low cost.

X marks the spot: Accurate energies from intersecting extrapolations of continuum quantum Monte Carlo data.

We explore the application of an extrapolative method that yields very accurate total and relative energies from variational and diffusion quantum Monte Carlo (VMC and DMC) results. For a trial wave function consisting of a small configuration interaction (CI) wave function obtained from full CI quantum Monte Carlo and reoptimized in the presence of a Jastrow factor and an optional backflow transformation, we find that the VMC and DMC energies are smooth functions of the sum of the squared coefficients of the initial CI wave function and that quadratic extrapolations of the non-backflow VMC and backflow DMC energies intersect within uncertainty of the exact total energy. With adequate statistical treatment of quasi-random fluctuations, the extrapolate and intersect with polynomials of order two method is shown to yield results in agreement with benchmark-quality total and relative energies for the C2, N2, CO2, and H2O molecules, as well as for the C2 molecule in its first electronic singlet excited state, using only small CI expansion sizes.

Photo-induced structural dynamics of o-nitrophenol by ultrafast electron diffraction.

The photo-induced dynamics of o-nitrophenol, particularly its photolysis, has garnered significant scientific interest as a potential source of nitrous acid in the atmosphere. Although the photolysis products and preceding photo-induced electronic structure dynamics have been investigated extensively, the nuclear dynamics accompanying the non-radiative relaxation of o-nitrophenol on the ultrafast timescale, which include an intramolecular proton transfer step, have not been experimentally resolved. Herein, we present a direct observation of the ultrafast nuclear motions mediating photo-relaxation using ultrafast electron diffraction. This work spatiotemporally resolves the loss of planarity which enables access to a conical intersection between the first excited state and the ground state after the proton transfer step, on the femtosecond timescale and with sub-Angstrom resolution. Our observations, supported by ab initio multiple spawning simulations, provide new insights into the proton transfer mediated relaxation mechanism in o-nitrophenol.

Reductive Dynamic and Static Excited State Quenching of a Homoleptic Ruthenium Complex Bearing Aldehyde Groups.

A new homoleptic Ru polypyridyl complex bearing two aldehyde groups on each bipyridine ligand, [Ru(dab)3](PF6)2, where dab is 4,4'-dicarbaldehyde-2,2'-bipyridine, was synthesized, characterized, and utilized for iodide photo-oxidation studies. In acetonitrile (CH3CN) solution, the complex displayed an intense metal-to-ligand charge transfer (MLCT) absorbance maximum at 475 nm (ε = 22,000 M-1 cm-1) and an infrared (IR) band at 1712 cm-1 assigned to the pendent aldehyde groups. Visible light excitation in air-saturated solution resulted in room temperature photoluminescence (PL) with a maximum at 675 nm, a quantum yield, ϕPL = 0.048, and an excited state lifetime, το = 440 ns, from which radiative and nonradiative relaxation rate constants were extracted, kr = 9.1 × 104 s-1 and knr = 1.8 × 106 s-1. Pulsed visible light excitation yielded transient UV-vis and IR absorption spectra consistent with an MLCT excited state; relaxation occurred with the maintenance of two isosbestic points in the visible region, and a lifetime that agreed with that measured by time-resolved PL. Cyclic voltammetry studies in a CH3CN solution with 0.1 M TBAPF6 electrolyte revealed a quasi-reversible oxidation, E°(RuIII/II) = +1.25 V vs. Fc+/0, and three sequential one-electron reductions at -1.10, -1.25, and -1.54 V vs. Fc+/0. An excited state reduction potential of E°(Ru*2+/+) = +0.89 V vs. Fc+/0 was estimated with the Rehm-Weller expression. Titration of tetrabutylammonium iodide, TBAI, into a CD3CN solution of [Ru(dab)3](PF6)2 resulted in significant shifts in the aldehyde H atom and 3,3'-biypridyl resonances that were analyzed with a 1:1 equilibrium model, from which Keq = 460 M-1 was extracted, increasing to 5800 M-1 when the solvent was changed to acetone-d6. Iodide titrations resulted in a significant quenching of the [Ru(dab)3]*2+ lifetime and quantum yield in both CH3CN and acetone solvents. In CH3CN, the quenching was mainly dynamic and well described by the Stern-Volmer model, from which a quenching rate constant, kq, of 4.5 × 1010 M-1 s-1 and an equilibrium constant, Keq, of 8.3 × 103 M-1 were obtained. In acetone, the static quenching pathway by iodide was greatly enhanced, with a Keq of 1.2 × 104 M-1 and a higher kq of 9.2 × 1010 M-1 s-1.

Theoretical study on the mechanism of alcohol photooxidation on Nb2O5 surface.

Theoretical modeling of the solid-state photocatalysis is one of the important issues as various useful photocatalysts have been developed to date. In this work, we investigated the mechanism of the alcohol photooxidation on niobium oxide (Nb2O5) which was experimentally developed, using the density functional theory (DFT)/time-dependent (TD)DFT calculations based on the cluster model. The alcohol adsorption and the first hydrogen transfer from hydroxy group to surface occur in the ground state, while the second hydrogen transfer from CH proceeds in the excited states during the photoirradiation of UV or visible light. The spin crossing was identified and the low-lying triplet states were solved for the reaction pathway. The photoabsorption in the visible light region was characterized as the charge transfer transition from O 2p of alcohol to Nb 4d of the Nb2O5 surface. The spin density and the natural population analysis indicated the generation of spin density in the moiety of carbonyl compound and its dissipation to the interface of the surface, which partly explains the electron paramagnetic resonance measurement. It was confirmed that the rate determining step is the desorption of carbonyl compound and water molecule in agreement with the experimental rate equation analysis. The present findings with the theoretical modeling will provide useful information for the further studies of the solid-state photocatalysis.

Photoisomerization of Spiropyran in Solution: A Surface Hopping Investigation.

We performed a computational investigation of the photoisomerization of an unsubstituted spiropyran in solution using surface hopping molecular dynamics simulations in a semiempirical framework. To bring out the solvent effects on the excited state dynamics, we have run simulations in three different environments: chloroform, methanol, and ethylene glycol. We show that the interaction with a moderately polar solvent such as chloroform has little effect on the dynamics when compared to vacuum results previously obtained by our group. At variance, the interaction with the protic solvents considered considerably affects the reaction mechanism, the quantum yield, and the excited state lifetimes.

Core-Alkynylated Fluorescent Flippers: Altered Ultrafast Photophysics to Track Thick Membranes.

Fluorescent flippers have been introduced as small-molecule probes to image membrane tension in living systems. This study describes the design, synthesis, spectroscopic and imaging properties of flippers that are elongated by one and two alkynes inserted between the push and the pull dithienothiophene domains. The resulting mechanophores combine characteristics of flippers, reporting on physical compression in the ground state, and molecular rotors, reporting on torsional motion in the excited state, to take their photophysics to new level of sophistication. Intensity ratios in broadened excitation bands from differently twisted conformers of core-alkynylated flippers thus report on mechanical compression. Lifetime boosts from ultrafast excited-state planarization and lifetime drops from competitive intersystem crossing into triplet states report on viscosity. In standard lipid bilayer membranes, core-alkynylated flippers are too long for one leaflet and tilt or extend into disordered interleaflet space, which preserves rotor-like torsional disorder and thus weak, blue-shifted fluorescence. Flipper-like planarization occurs only in highly ordered membranes of matching leaflet thickness, where they light up and selectively report on these thick membranes with red-shifted, sharpened excitation maxima, high intensity and long lifetime.

Monitoring Density Redistribution at the Excited State in a Dual Emitting Molecule: An Analysis Based on Real-Time Density Functional Theory and Density Descriptors.

In this work, we computed and analyzed, by means of density-based descriptors, the real-time evolution of both the locally excited (LE) and charge-transfer (CT) excited states for the planar and twisted conformations of the DMABN (4-(N,N-dimethylamino)benzonitrile) molecule using real-time time-dependent density functional theory (DFT) and three different exchange-correlation energy functionals (EXC) belonging to the same family (the PBE one). Our results based on the analysis of density-based descriptors show that the underlying EXC modifies the evolution in time of the density. In particular, comparing the frequency of density reorganization computed with the three functionals (PBE, PBE0, and LC-PBE), we found that the frequency of electronic interconversion of the individual determinants involved during the dynamics increases from PBE to PBE0 and to LC-PBE. This allows us to show that there is a correlation between the delocalization of the electronic density and the frequency of reorganization. In particular, the greater the mean hole-electron distance during the dynamics, the lower is the frequency of density reorganization.

Substitution effects on the photoinduced excited state dynamics of perylenemonoimides in solution and thin films.

Perylene monoimide (PMI) derivatives are attracting significant attention due to their strong absorption in the visible range, thermal stability, and synthetic accessibility. These properties make them promising for application in various areas such as optoelectronic devices, photosensitizers, etc. In this work, the photophysical properties and excited state dynamics of four different PMI derivatives (PMIB, BrPMITB, PMITB, and APITB) were studied in solution and thin films utilizing steady-state and time-resolved spectroscopic techniques. Among the four PMI derivatives, APITB is designed as a donor-acceptor dyad, with thianthrene as a donor and PMI as an acceptor. The activation of the triplet state through the spin-orbit charge transfer intersystem crossing (SOCT-ISC) process in THF was observed upon substitution with the thianthrene group at the peri position of the PMI moiety. The SOCT-ISC process facilitates triplet formation in the APITB dyad within 423 ps. Meanwhile, other PMI derivatives showed fluorescence within the femtosecond timescale in THF. The PMI derivatives in thin films displayed different photo physical properties to those in THF. This discrepancy arises due to the effective intermolecular coupling between the PMI derivatives in thin films.

(Invited) Luminescent InP Quantum Dots: They're Not Just Like CdSe

There are significant similarities and differences in the spectroscopy and photophysics between CdSe-based and InP-based quantum dots. One of the more important differences is the presence of reversibly populated hole traps in InP/ZnSe quantum dots (QDs). These traps affect many aspects of the overall excited state dynamics. In this paper we elucidate the hole relaxation dynamics in high quality InP/ZnSe/ZnS QDs at room temperature and focus on the role of these traps. Specifically, we show that the presence of transiently populated traps results in extremely slow (tens of picoseconds to nanoseconds) hole cooling as evidenced by a significant fraction of the photoluminescence exhibiting a slow risetime following photoexcitation. Through a combination of chemical derivatization studies and density functional theory calculations, they are assigned to substitutional indium adjacent to a zinc vacancy, In3+/VZn 2-, in the ZnSe shell.

Excited Charge Separation in a π-Interacting Phenothiazine-Zinc Porphyrin-Fullerene Donor-Acceptor Conjugate.

We have designed, synthesized, and characterized a donor-acceptor triad, SPS-PPY-C60, that consists of a π-interacting phenothiazine-linked porphyrin as a donor and sensitizer and fullerene as an acceptor to seek charge separation upon photoexcitation. The optical absorption spectrum revealed red-shifted Soret and Q-bands of porphyrin due to charge transfer-type interactions involving the two ethynyl bridges carrying electron-rich and electron-poor substituents. The redox properties suggested that the phenothiazine-porphyrin part of the molecule is easier to oxidize and the fullerene part is easier to reduce. DFT calculations supported the redox properties wherein the electron density of the highest molecular orbital (HOMO) was distributed over the donor phenothiazine-porphyrin entity while the lowest unoccupied molecular orbital (LUMO) was distributed over the fullerene acceptor. TD-DFT studies suggested the involvement of both the S2 and S1 states in the charge transfer process. The steady-state emission spectrum, when excited either at porphyrin Soret or visible band absorption maxima, revealed quenched emission both in nonpolar and polar solvents, suggesting the occurrence of excited state events. Finally, femtosecond transient absorption spectral studies were performed to witness the charge separation by utilizing solvents of different polarities. The transient data was further analyzed by GloTarAn by fitting the data with appropriate models to describe photochemical events. From this, the average lifetime of the charge-separated state calculated was found to be 169 ps in benzonitrile, 319 ps in dichlorobenzene, 1.7 ns in toluene for Soret band excitation, and ∼320 ps for Q-band excitation in benzonitrile.

Spectrally Resolved Exciton Polarizability for Understanding Charge Generation in Organic Bulk Hetero-Junction Diodes.

Despite decades of research, the dominant charge generation mechanism in organic bulk heterojunction (BHJ) devices is not completely understood. While the local dielectric environments of the photoexcited molecules are important for exciton dissociation, conventional characterizations cannot separately measure the polarizability of electron-donor and electron-acceptor, respectively, in their blends, making it difficult to decipher the spectrally different charge generation efficiencies in organic BHJ devices. Here, by spectrally resolved electroabsorption spectroscopy, we report extraction of the excited state polarizability for individual donors and acceptors in a series of organic blend films. Regardless of the donor and acceptor, we discovered that larger exciton polarizability is linked to larger π-π coherence length and faster charge transfer across the heterojunction, which fundamentally explains the origin of the higher charge generation efficiency near 100% in the BHJ photodiodes. We also show that the molecular packing of the donor and acceptor influence each other, resulting in a synergetic enhancement in the exciton polarizability.

Photodetachment and Tunneling Dissociation of Cryogenic Double-Rydberg Anions NH4.

The Rydberg radical NH4 and the double Rydberg anion (DRA) NH4- have long aroused researchers' interests due to their potential for exploring the reaction dynamics of the H + NH3 → H2 + NH2 reaction, a prototypical penta-atomic system. In this study, we present high-resolution photodetachment spectroscopy of DRA NH4- and ion-molecule complex H-(NH3). We observed multiple new photodetachment channels of DRA NH4-. The energy level of the excited state (3p 2T2) of the Rydberg radical NH4 was determined to be 15052(94) cm-1, in excellent agreement with the principal Schüler band (15061.61 cm-1). Additionally, we observed the tunneling dissociation of NH4- in a cryogenic ion trap with its dissociation lifetime determined to be 19(2) ms.

A Thorough Examination of the Variables Affecting the Quantum Efficiency of Radiative Decay of Trichlorotriphenylmethyl Radicals.

Fluorescence quantum efficiency is determined by the competition between radiation and nonradiation processes of the excited states. Understanding the factors affecting the radiation and nonradiative decay rates is of great significance for the design of luminescent materials. The excitation state deactivation mechanisms of singlet and triplet states have been extensively studied, providing a comprehensive understanding of the processes involved in the relaxation of these states. However, research on free radical systems involving doublet states is relatively scarce. Therefore, in this study, radiation and nonradiative decay rates and the mechanism of a series of trichlorotriphenylmethyl-based radicals were investigated theoretically. The results indicate that the relative rotations of electron donor and acceptor, as well as the internal rotations of trichlorotriphenylmethyl moiety, play important roles in energy dissipation through nonradiative channels. The effect of a solid-state environment on the radiation and nonradiative decay rates of radicals was investigated using a combination of quantum mechanics and molecular mechanics methods. The results indicate that the solid-state environment restricts the expansion of the conjugated system in the excited state of radicals, leading to a slight decrease in radiative decay rate. In addition, the solid-state environment reduces the reorganization energy and also affects the adiabatic excitation energy of radicals. The reduction in reorganization energy results in a decrease in nonradiative rate, while the opposite effect is observed for adiabatic excitation energy. The nonradiative rate of radicals in a solid-state environment is thus inflected by a combination of molecular geometric structure relaxation and ground-excited state energy gap.

Protein Effects on the Excitation Energies and Exciton Dynamics of the CP24 Antenna Complex.

In this study, the site energy fluctuations, energy transfer dynamics, and some spectroscopic properties of the minor light-harvesting complex CP24 in a membrane environment were determined. For this purpose, a 3 μs-long classical molecular dynamics simulation was performed for the CP24 complex. Furthermore, using the density functional tight binding/molecular mechanics molecular dynamics (DFTB/MM MD) approach, we performed excited state calculations for the chlorophyll a and chlorophyll b molecules in the complex starting from five different positions of the MD trajectory. During the extended simulations, we observed variations in the site energies of the different sets as a result of the fluctuating protein environment. In particular, a water coordination to Chl-b 608 occurred only after about 1 μs in the simulations, demonstrating dynamic changes in the environment of this pigment. From the classical and the DFTB/MM MD simulations, spectral densities and the (time-dependent) Hamiltonian of the complex were determined. Based on these results, three independent strongly coupled chlorophyll clusters were revealed within the complex. In addition, absorption and fluorescence spectra were determined together with the exciton relaxation dynamics, which reasonably well agrees with experimental time scales.

State-Specific Coupled-Cluster Methods for Excited States.

We reexamine ΔCCSD, a state-specific coupled-cluster (CC) with single and double excitations (CCSD) approach that targets excited states through the utilization of non-Aufbau determinants. This methodology is particularly efficient when dealing with doubly excited states, a domain in which the standard equation-of-motion CCSD (EOM-CCSD) formalism falls short. Our goal here to evaluate the effectiveness of ΔCCSD when applied to other types of excited states, comparing its consistency and accuracy with EOM-CCSD. To this end, we report a benchmark on excitation energies computed with the ΔCCSD and EOM-CCSD methods for a set of molecular excited-state energies that encompasses not only doubly excited states but also doublet-doublet transitions and (singlet and triplet) singly excited states of closed-shell systems. In the latter case, we rely on a minimalist version of multireference CC known as the two-determinant CCSD method to compute the excited states. Our data set, consisting of 276 excited states stemming from the quest database [Véril et al., WIREs Comput. Mol. Sci. 2021, 11, e1517], provides a significant base to draw general conclusions concerning the accuracy of ΔCCSD. Except for the doubly excited states, we found that ΔCCSD underperforms EOM-CCSD. For doublet-doublet transitions, the difference between the mean absolute errors (MAEs) of the two methodologies (of 0.10 and 0.07 eV) is less pronounced than that obtained for singly excited states of closed-shell systems (MAEs of 0.15 and 0.08 eV). This discrepancy is largely attributed to a greater number of excited states in the latter set exhibiting multiconfigurational characters, which are more challenging for ΔCCSD. We also found typically small improvements by employing state-specific optimized orbitals.

Excited-state downfolding using ground-state formalisms

Downfolding coupled cluster (CC) techniques are powerful tools for reducing the dimensionality of many-body quantum problems. This work investigates how ground-state downfolding formalisms can target excited states using non-Aufbau reference determinants, paving the way for applications of quantum computing in excited-state chemistry. This study focuses on doubly excited states for which canonical equation-of-motion CC approaches struggle to describe unless one includes higher-than-double excitations. The downfolding technique results in state-specific effective Hamiltonians that, when diagonalized in their respective active spaces, provide ground- and excited-state total energies (and therefore excitation energies) comparable to high-level CC methods. The performance of this procedure is examined with doubly excited states of H2, Methylene, Formaldehyde, and Nitroxyl.

Semiclassical analytic theory of electronic energy transfer in 3D atomic collisions.

A previously developed semiclassical theory of nonadiabatic energy transfer is used to analyze electronic excitation and quenching in three-dimensional atomic collisions. The predicted transition probabilities, cross sections, and rate coefficients are compared with the quantum scattering calculations for O + O and N + N, for the same interaction potentials and nonadiabatic coupling, and with the experimental data where available. The theory predictions are in very good agreement with quantum scattering, at the conditions when the energy transfer is dominated by a single pair of adiabatic potentials. Closed-form analytic expressions for the cross sections and rate coefficients are obtained, for both the strongly and weakly coupled cases. The results quantify and illustrate the effect of the interaction potentials and their coupling on the energy transfer. The analytic cross sections and rate coefficients are in good agreement with the numerical predictions. The same approach has been used to predict the rate coefficients of electronic excitation and quenching in collisions of N + O atoms. The fidelity of these predictions may be improved considerably if accurate potentials for the excited electronic states of N + O and their coupling are available. The applicability of the semiclassical theory for the prediction of the rates of heavy particle impact excitation in atom-molecule collisions is discussed.