Excited State Potential Energy Curves Research Articles

Different functional groups dependent fluorescent properties for ESIPT-based ABTN derivatives: A theoretical study

On the basis of density functional theory (DFT) and time-dependent DFT (TD-DFT), 2-amino-3-(benzo[d]thiazol-2-yl)benzaldehyde derivatives (ABTN-1, ABTN-2, ABTN-3) are selected as models to theoretically explore the effect of different functional groups on the fluorescent properties and excited state intramolecular proton transfer (ESIPT) behavior. The optimized configurations, infrared vibrational frequencies and topological parameters are used to analyze the intensity of intramolecular hydrogen bond (IHB). The absorption and fluorescence emission spectra are simulated, and the frontier molecular orbital as well as electron-hole distribution are investigated. In addition, the ground state (S0) and excited state (S1) potential energy curves (PECs) are constructed. The–CN group has little effect on the absorption and fluorescence wavelengths of ABTN. The –N(CH3)2 group red-shifts the absorption and fluorescence wavelengths exceeding 100 nm. The coexistence of –CN and –N(CH3)2 groups has almost the same effect on the absorption and fluorescence peaks as the–N(CH3)2 group.

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

Learning from the 4-(dimethylamino)benzonitrile twist: Two-parameter range-separated local hybrid functional with high accuracy for triplet and charge-transfer excitations.

The recent ωLH22t range-separated local hybrid (RSLH) is shown to provide outstanding accuracy for the notorious benchmark problem of the two lowest excited-state potential energy curves for the amino group twist in 4-(dimethylamino)benzonitrile (DMABN). However, the design of ωLH22t as a general-purpose functional resulted in less convincing performance for triplet excitations, which is an important advantage of previous LHs. Furthermore, ωLH22t uses 8 empirical parameters to achieve broad accuracy. In this work, the RSLH ωLH23ct-sir is constructed with minimal empiricism by optimizing its local mixing function prefactor and range-separation parameter for only 8 excitation energies. ωLH23ct-sir maintains the excellent performance of ωLH22t for the DMABN twist and charge-transfer benchmarks but significantly improves the errors for triplet excitation energies (0.17 vs 0.24eV). Additional test calculations for the AE6BH6 thermochemistry test set and large dipole moment and static polarizability test sets confirm that the focus on excitation energies in the optimization of ωLH23ct-sir has not caused any dramatic errors for ground-state properties. Although ωLH23ct-sir cannot replace ωLH22t as a general-purpose functional, it is preferable for problems requiring a universally good description of localized and charge-transfer excitations of both singlet and triplet multiplicity. Current limitations on the application of ωLH23ct-sir and other RSLHs to the study of singlet-triplet gaps of emitters for thermally activated delayed fluorescence are discussed. This work also includes the first systematic analysis of the influence of the local mixing function prefactor and the range-separation parameter in an RSLH on different types of excitations.

An efficient adaptive variational quantum solver of the Schrödinger equation based on reduced density matrices.

Recently, adaptive variational quantum algorithms, e.g., Adaptive Derivative-Assembled Pseudo-Trotter-Variational Quantum Eigensolver (ADAPT-VQE) and Iterative Qubit-Excitation Based-Variational Quantum Eigensolver (IQEB-VQE), have been proposed to optimize the circuit depth, while a huge number of additional measurements make these algorithms highly inefficient. In this work, we reformulate the ADAPT-VQE with reduced density matrices (RDMs) to avoid additional measurement overhead. With Valdemoro's reconstruction of the three-electron RDM, we present a revised ADAPT-VQE algorithm, termed ADAPT-V, without any additional measurements but at the cost of increasing variational parameters compared to the ADAPT-VQE. Furthermore, we present an ADAPT-Vx algorithm by prescreening the anti-Hermitian operator pool with this RDM-based scheme. ADAPT-Vx requires almost the same variational parameters as ADAPT-VQE but a significantly reduced number of gradient evaluations. Numerical benchmark calculations for small molecules demonstrate that ADAPT-V and ADAPT-Vx provide an accurate description of the ground- and excited-state potential energy curves. In addition, to minimize the quantum resource demand, we generalize this RDM-based scheme to circuit-efficient IQEB-VQE algorithm and achieve significant measurement reduction.

Generalization of Block-Localized Wave Function for Constrained Optimization of Excited Determinants.

The block-localized wave function method is useful to provide insights on chemical bonding and intermolecular interactions through energy decomposition analysis. The method relies on block localization of molecular orbitals (MOs) by constraining the orbitals to basis functions within given blocks. Here, a generalized block-localized orbital (GBLO) method is described to allow both physically localized and delocalized MOs to be constrained in orbital-block definitions. Consequently, GBLO optimization can be conveniently tailored by imposing specific constraints. The GBLO method is illustrated by three examples: (1) constrained polarization response orbitals through dipole and quadrupole perturbation in a water dimer complex, (2) the ground and first excited-state potential energy curves of ethene about its C-C bond rotation, and (3) excitation energies of double electron excited states. Multistate density functional theory is used to determine the energies of the adiabatic ground and excited states using a minimal active space (MAS) comprising specifically charge-constrained and excited determinant configurations that are variationally optimized by the GBLO method. We find that the GBLO expansion that includes delocalized MOs in configurational blocks significantly reduces computational errors in comparison with physical block localization, and the computed ground- and excited-state energies are in good accordance with experiments and results obtained from multireference configuration interaction calculations.

First-principles calculation of excited states of diatomic molecules: a benchmark for the Gutzwiller conjugate gradient minimisation method

We recently proposed the Gutzwiller conjugate gradient minimisation (GCGM) method for efficient and accurate calculation of the ground state total energy of molecular and bulk systems. The GCGM method is developed under the framework of Gutzwiller wave function but goes beyond the commonly adopted Gutzwiller approximation to improve the accuracy and flexibility in treating the correlation effects. In this conference proceeding, we benchmark the GCGM method with the calculation of excited state potential energy curves of three diatomic molecules, namely H2, N2, and O2. Our calculations demonstrate the flexibility and reasonable accuracy of the method.

Comprehending the quadruple bonding conundrum in C2 from excited state potential energy curves

The question of quadruple bonding in C2 has emerged as a hot button issue, with opinions sharply divided between the practitioners of Valence Bond (VB) and Molecular Orbital (MO) theory. Here, we have systematically studied the Potential Energy Curves (PECs) of low lying high spin sigma states of C2, N2, Be2 and HC[triple bond, length as m-dash]CH using several MO based techniques such as CASSCF, RASSCF and MRCI. The analyses of the PECs for the 2S+1Σg/u (with 2S + 1 = 1, 3, 5, 7, 9) states of C2 and comparisons with those of relevant dimers and the respective wavefunctions were conducted. We contend that unlike in the case of N2 and HC[triple bond, length as m-dash]CH, the presence of a deep minimum in the 7Σ+ state of C2 and CN+ suggests a latent quadruple bonding nature in these two dimers. Our investigations reveal that the number of bonds in the ground state can be determined for 2nd row dimers by figuring out at what value of spin symmetry a purely dissociative PEC is obtained. For N2 and HC[triple bond, length as m-dash]CH the purely dissociative PEC appears for the septet spin symmetry as compared to that for the nonet in C2. This is indicative of a higher number of bonds between the two 2nd row atoms in C2 as compared to those of N2 and HC[triple bond, length as m-dash]CH. Hence, we have struck a reconciliatory note between the MO and VB approaches. The evidence provided by us can be experimentally verified, thus providing the window so that the narrative can move beyond theoretical conjectures.

Parametrisation of the optimised effective potential method based on the Coulson–Fischer wave function for excited states

ABSTRACT This article further develops the Coulson–Fischer formalism in conjunction with the optimised effective potential method [V.N. Glushkov and S. Wilson, Molec. Phys. 110, 149 (2012)] to incorporate both exchange and static correlation effects for excited states having the same symmetry as the ground state. By using this formalism, we compute complete potential energy curves for the ground and first excited states of the molecule and the isoelectronic heteronuclear ion. Effective potentials are generated in according to a novel density functional theory [A.K. Theophilou, J. Chem. Phys. 149, 074104 (2018)] in which the Kohn–Sham (KS) like potential has spherical symmetry around each nucleus. In this way, the inconsistencies of standard density functional theory concerning the asymmetry of the KS potential are remedied. In our implementation, an effective potential which satisfies this requirement is expressed as a direct mapping of the external potential. Different approximations for the effective potentials are investigated. It is shown that applications of the proposed formalism support good agreement with the exact Coulson–Fischer theory for both the ground and first excited state potential energy curves and thus a qualitatively correct description of dissociation.

Is excited state intramolecular proton transfer frustrated in 10-hydroxy-11H-benzo[b]fluoren-11-one?

Recently, Piechowska and coworker found that hydroxybenzofluorenone 10-hydroxy11H-benzo[b]fluoren-11-one (10-HHBF) does not show dual fluorescence, which is in contrast to its well-known analogue 1-hydroxy-11H-benzo[b]fluoren-11-one (1-HHBF) [Dyes Pigm. 2019, 165, 346-353.]. Based on the increased donor-acceptor distance and the lower stability of the excited state tautomer of former, they believe that different from 1-HHBF, ESIPT is not occurring in 10-HHBF. In the preset work, in order to clarify whether ESIPT would take place in 10-HHBF, we have optimized the four-state geometrical structures (ground state S0, first singlet excited state S1, transition state S1-TS and after proton transfer S1-PT), carried out the Natural Population Analysis and scanned the ground-state and excited-state potential energy curves of 1-HHBF and 10-HHBF at TD-CAM-B3LYP/6-311+g(2d,2p)/IEFPCM (cyclohexane) theory level. It is found that ESIPT should take place in both 1-HHBF and 10-HHBF and the Gibbs free energy diagram further indicates that the ESIPT process is more favorable in 10-HHBF than in 1-HHBF.

Algebraic-diagrammatic construction scheme for the polarization propagator including ground-state coupled-cluster amplitudes. I. Excitation energies.

An ad hoc modification of the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator is presented. Within this approach, all first-order Møller-Plesset correlation coefficients occurring in the second-order ADC secular matrix are replaced by amplitudes obtained from a coupled cluster doubles (CCD) calculation. This new hybrid method, denoted CCD-ADC(2), has been tested on a series of small diatomic and triatomic molecules and benchmarked with respect to Thiel's benchmark set of medium-sized organic molecules. For the latter, the calculation of 134 singlet and 71 triplet states has shown that CCD-ADC(2) exhibits a mean error and standard deviation of 0.15 ± 0.34 eV for singlet states and 0.0 ± 0.17 eV for triplet states with respect to the provided theoretical best estimates, whereas standard ADC(2) has a mean error and standard deviation of 0.22 ± 0.30 eV for singlet and 0.12 ± 0.16 eV for triplet states. The corresponding extended second-order schemes ADC(2)-x and CCD-ADC(2)-x revealed accuracies of -0.70 ± 0.32 eV and -0.76 ± 0.33 eV for singlet states and -0.55 ± 0.20 eV and -0.67 ± 0.22 eV for triplet states, respectively. Furthermore, the investigation of excited-state potential energy curves along the dissociation of the N2 molecule has shown that the higher reliability of the ground-state CCD method as compared to MP2 is also inherent to the excited states. While the curves obtained at the ADC(2) level break down at around 2 Å, the ones obtained at CCD-ADC(2) remain reasonable up to about 3.5 Å.

Photofragmentation dynamics of N,N-dimethylformamide following excitation at 193 nm.

N,N-dimethylformamide, HCON(CH3)2, is a useful model compound for investigating the peptide bond photofragmentation dynamics. We report data from a comprehensive experimental and theoretical study into the photofragmentation dynamics of N,N-dimethylformamide in the gas phase at 193 nm. Through a combination of velocity-map imaging and hydrogen atom Rydberg tagging photofragment translational spectroscopy we have identified two primary fragmentation channels, namely, fission of the N-CO "peptide" bond and N-CH3 bond fission leading to the loss of CH3. The possible fragmentation channels leading to the observed products are rationalised with recourse to CASPT2 calculations of the ground and first few excited-state potential energy curves along the relevant dissociation coordinates, and the results are compared with the data from previous experimental and theoretical studies on the same system.

Femtosecond real-time probing of reactions MMXVII: The predissociation of sodium iodide in the A 0+ state

We revisit the femtosecond transition-state spectroscopy of sodium iodide taking advantage of modern lasers and pulse-shaping to better map the low-lying electronic states, some forming predissociative wells through curve crossings. We also carry out high-level ab initio multi-reference configuration interaction calculations including spin-orbit coupling terms and using large correlation-consistent basis sets to arrive at accurate ground- and excited-state potential energy curves of NaI. Density matrix calculations employing vibrational wave functions determined from the ab initio X 0+ and A 0+ potentials are used to simulate time dependent wave packet dynamics of NaI pumped to the A 0+ state.

Photoinduced C—I bond homolysis of 5-iodouracil: A singlet predissociation pathway

5-Iodouracil (5-IU) can be integrated into DNA and acts as a UV sensitive chromophore suitable for probing DNA structure and DNA-protein interactions based on the photochemical reactions of 5-IU. Here, we perform joint studies of time-resolved Fourier transform infrared (TR-FTIR) spectroscopy and ab initio calculations to examine the state-specific photochemical reaction mechanisms of the 5-IU. The fact that uracil (U) is observed in TR-FTIR spectra after 266 nm irradiation of 5-IU in acetonitrile and ascribed to the product of hydrogen abstraction by the uracil-5-yl radical (U·) provides experimental evidence for the C-I bond homolysis of 5-IU. The excited state potential energy curves are calculated with the complete active space second-order perturbation//complete active space self-consistent field method, from which a singlet predissociation mechanism is elucidated. It is shown that the initially populated 1(ππ*) state crosses with the repulsive 1(πσ*) or 1(nIσ*) state, through which 5-IU undergoes dissociation to the fragments of (U·) radical and iodine atom. In addition, the possibility of intersystem crossing (ISC) is evaluated based on the calculated vertical excitation energies. Although a probable ISC from 1(ππ*) state to 3(nOπ*) and then to the lowest triplet 3(ππ*) could occur in principal, there is little possibility for the excited state populations bifurcating to triplet manifold, given that the singlet state predissociation follows repulsive potential and should occur within dozens to hundreds of femtoseconds. Such low population of triplet states means that the contribution of triplet state to photoreactions of 5-IU should be quite minor. These results demonstrate clearly a physical picture of C-I bond homolysis of 5-IU and provide mechanistic illuminations to the interesting applications of 5-IU as photoprobes and in radiotherapy of cancer.

Theoretical insight into the excited-state intramolecular proton transfer mechanisms of three amino-type hydrogen-bonding molecules

Excited-state intramolecular proton transfer (ESIPT) dynamics of the amino-type hydrogen-bonding compound 2-(2′-aminophenyl)benzothiazole (PBT-NH2) as well as its two derivatives 2-(5′-cyano-2′-aminophenyl)benzothiazole (CN-PBT-NH2) and 2-(5′-cyano-2′-tosylaminophenyl)benzothiazole (CN-PBT-NHTs) were studied by the time-dependent density functional theory (TD-DFT) approach with the B3LYP density functional, and their absorption and emission spectra were also explored at the same level of theory. A good agreement is observed between the theoretical simulations and experimental spectra, indicating that the present calculations are reasonably reliable. In addition, it is also found that the energy barriers of the first excited singlet state of the three targeted molecules along the ESIPT reaction are computed to be 0.38, 0.34 and 0.12eV, respectively, showing the trend of gradual decrease, which implies that the introduction of the electron-withdrawing cyano or tosyl group can facilitate the occurrence of the ESIPT reaction of these amino-type H-bonding systems. Following the ESIPT, both CN-PBT-NH2 and CN-PBT-NHTs dye molecules can undergo the cis-trans isomerization reactions in the ground-state and excited-state potential energy curves along the C2-C3 bond between benzothiazole and phenyl moieties, where the energy barriers of the trans-tautomer→cis-tautomer isomerizations in the ground states are calculated to be 0.83 and 0.34eV, respectively. According to our calculations, it is plausible that there may exist the long-lived trans-tautomer species in the ground states of CN-PBT-NH2 and CN-PBT-NHTs.

A research on excited-state intramolecular proton-transfer mechanism of a new chemosensor

Based on the density functional theory (DFT) and time-dependent density functional theory (TDDFT), the excited-state intramolecular proton-transfer (ESIPT) mechanism of a new reported chromophore by Kim et al. (Sensors Actuators B Chem 206:430–434, 2015) has been investigated theoretically. The calculated results of bond lengths and bond angles of hydrogen bond O–H···N, the infrared vibrational spectra and the hydrogen bonding energies all demonstrated that the intramolecular hydrogen bond is strengthened in the first excited state. It is no denying the fact that our calculated results reproduced the experimental absorbance and fluorescence emission spectra well, which demonstrates that the TDDFT theory we adopted is reasonable and effective. From the analysis of frontier molecular orbitals, it is reasonable to suggest that the intramolecular charge-transfer nature of the excitation prompts the proton transfer giving rise to an ESPT reaction. The constructed potential energy curves of ground state and the first excited state based on keeping the O–H distance fixed from 0.993 to 2.343 A have been used to illustrate the ESIPT process. A relative lower barrier of 4.17 kcal/mol in the first excited-state potential energy curve proved the ESIPT mechanism.

An Investigation of Excited-State Intramolecular Proton Transfer Mechanism of New Chromophore

Based on the time-dependent density functional theory (TDDFT), the excited state intramolecular proton transfer (ESIPT) mechanism of a new compound 1 chromophore synthesized and designed by Liu et al. [Journal of Photochemistry and Photobiology B: Biology., 138 (2014), 75-79] has been investigated theoretically. The calculations of primary bond lengths, angles and the IR vibrational spectra verified the intramolecular hydrogen bond was strengthened. The fact that reproducing the experimental absorbance and fluorescence emission spectra well theoretically demonstrates that the TDDFT theory we adopted is reasonable and effective. In addition, intramolecular charge transfer based on the frontier molecular orbitals demonstrated the indication of the ESIPT reaction. The constructed potential energy curves of ground state and the first excited state based on keeping the O-H distance fixed at a serious of values have been used to illustrate the ESIPT process. A little barrier of 2.45 kcal/mol in the first excited state potential energy curve provided the transfer mechanism. Further, the phenomenon of fluorescence quenching has been explained reasonably based on the ESIPT mechanism. PACS: 31.25.Jf; 82.39.Jn

Extended Møller-Plesset perturbation theory for dynamical and static correlations

We present a novel method that appropriately handles both dynamical and static electron correlations in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order Møller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter.

Stilbene photoisomerization driving force as revealed by the topology of the electron density and QTAIM properties

The photoisomerization of stilbene (C14H12) has become an archetype for the study of cis-trans isomerizations induced by light. Despite the many electronic structure calculations performed to gain understanding about this important process, no insight about this reaction has been obtained by means of the exploitation of topological quantum chemical methods. This contribution addresses the changes of the topology of the electron density along with those of the properties of atoms in molecules undergone throughout this photochemical transformation. By considering the phenyl rings and the CHCH bridge of stilbene separately, we found that both groups in the ground state are destabilized when the system evolves from either the cis or trans isomer towards the conical intersection connecting the S0 and S1 states. Nonetheless, the energy of the C6H5 moieties across the excited state potential energy curve is reduced along the same change in configuration of C14H12, thereby providing the driving force for the reaction to occur. The analysis of the atomic charges reveals that the carbon atoms of the CHCH bridge withdraw electron density from their interatomic region between them and the phenyl groups. This flow of charge density might be related with the occupation of the CHCH π★ orbital which allows the reaction to take place. Finally, an examination of the electronegativity of the groups CHCH and C6H5 indicates that the phenyl rings drastically change their electronegative nature upon photoexcitation, enabling the system to undergo the photoisomerization. Overall, it is shown how the topological analysis of the electron density can provide important insights about chemical reactions carried out in excited states.

Low valency in lanthanides: a theoretical study of NdF and LuF.

The ground and low-lying excited state potential energy curves of neodymium monofluoride were calculated using multireference (CASSCF) and single reference (EOM-CR-CCSD(T)) methods. Optimized bond lengths were obtained and accurate bond dissociation energies were computed. The EOM-CR-CCSD(T) method was used to determine the bond dissociation energy of lutetium monofluoride, and it is shown that core correlation is required to produce bond dissociation energies in agreement with experiment.

MR-ccCA: A route for accurate ground and excited state potential energy curves and spectroscopic properties for third-row diatomic molecules

The potential energy curves for diatomic molecules containing third-row elements were examined using the multi-reference correlation consistent composite approach (MR-ccCA) to determine the applicability of the new approach for these systems. Remarkably smooth potential energy curves resulted, though the methodology was not designed, per se, for potential energy curves, particularly due to the additive nature of the methodology. A number of properties have been considered including the dissociation energy Do, well depth De, equilibrium bond length re, vibrational constants (ωe, ωexe) and rotational constants (Be, αe) and these properties have been compared with the experimental values for the ground state diatomics. Additionally, potential energy curves and spectroscopic properties of several of the lowest excited states of As2 have been determined, with the addition of transition energies Te and the determinations have been compared to experimental and theoretical values.