Potential Energy Curves Research Articles

An Intruder-Free Fock Space Coupled-Cluster Study of the Potential Energy Curves of LiMg+ within the (2,0) Sector

The potential energy curves (PECs) and spectroscopic constants of the ground and excited states of a LiMg+ molecular cation were investigated. We obtained accurate results for the fifteen lowest-lying states of the LiMg+ cation using the Intermediate Hamiltonian Fock Space Multireference Coupled Cluster (IH-FS-CC) method applied to the (2,0) sector. Relativistic corrections were accounted for using the third-order Douglas–Kroll method. In each instance, smooth PECs were successfully computed across the entire range of interatomic distances from equilibrium to the dissociation limit. The results are in good accordance with previous studies of this molecular cation. Notably, this study marks the first application of IH-FS-CC in investigating a mixed alkali and alkaline earth molecular cation, proving its usability in determining accurate PECs of such diatomics and their spectroscopic constants.

Theoretical Insights into the Effect of Different Numbers of Thiophene Groups on Hydrogen Bond Interaction and Excited-State Intramolecular Proton-Transfer Process for Flavonoid Derivatives.

In this study, we systematically explored the impact of varying the number of thiophene groups on the hydrogen bond interaction and excited-state intramolecular proton-transfer (ESIPT) processes in flavonoid derivatives (STF, DTF, and TTF) using the density functional theory and time-dependent density functional theory methods. Initially, a thorough analysis of the optimized geometric structures revealed that the intramolecular hydrogen bond in the S1 state is enhanced and gradually weakened as the number of thiophene groups increases. To gain a deeper understanding of the hydrogen bond interaction, topological analysis, interaction region indicator scatter plots, and isosurface plots were employed. These images provide further insights that align with the structural analysis. Additionally, we observed a red-shift in the electronic spectra (absorption and fluorescence spectra), which is primarily attributed to the narrowing of the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, as elucidated by the frontier molecular orbitals. Furthermore, a combined analysis between the hole-electron distribution and the transition density matrix heat map shows that electron excitation involves the unidirectional charge-transfer mechanism. In the end, by conducting relaxed potential energy curve scans, we found that an increase in the number of thiophene groups elevates the energy barrier for ESIPT, making it more challenging for the reaction. In summary, our study underscores the vital effect of thiophene-substituted numbers in modulating the ESIPT process, which is able to provide valuable insights for the design and synthesis of desired organic fluorescent probes in the future.

Effects of triaxial deformation on the fission barrier in the Z = 118 − 120 nuclei* *Supported by the National Natural Science Foundation of China (Grant Nos. 12205076 and 12047504), the China Postdoctoral Science Foundation (Grant No. 2020M670012), and the Launching Fund of Henan University of Technology (Grant No. 2021BS047).

By using potential energy surface (PES) calculations in the three-dimensional space (β 2, γ, β 4) within the framework of the macroscopic-microscopic model, the fission trajectory and fission barrier for Z = 118(Og), 119, 120 nuclei has been systematically investigated. The calculated PES includes macroscopic liquid-drop energy, microscopic shell correction and pairing correction. Taking the 294Og176 nucleus as an example, we discuss the next closed shell after Z = 82 and N = 126 with the calculated Woods–Saxon single-particle levels. Then, the results of PES in 294Og is illustrated from the (X, Y) scale to the (β 2, γ) scale. The γ degree of freedom reveals the shape evolution clearly during the fission process. The structure near the minimum and saddle point of the PES in the Z = 118, 119, 120 nuclei is demonstrated simultaneously. Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths are also studied. The triaxial deformation in these superheavy mass regions plays a vital role in the first fission barrier, showing a significant reduction in both triaxial paths. In addition, the model-dependent fission barriers of proton-rich nuclei 295Og, 296119, and 297120 are analyzed briefly. Our studies could be valuable for synthesizing the superheavy new elements in the forthcoming HIAF and other facilities.

Concerning for the solvent-polarity-dependent conformational equilibrium and ESIPT mechanism in Pz3HC system: A novel insight

In this report, we propose a new insight into the interaction between the solvent-polarity-dependent conformational equilibrium and excited state intramolecular proton transfer (ESIPT) behavior of Pz3HC system in four different polar solvents (polarity order: ACN > THF > TOL > CYC). Using quantum chemistry method, we first announce a coexistence mechanism between Pz3HC-1 and Pz3HC-3 in the ground state in four solvents based on the Boltzmann distribution. In particular, Pz3HC-1 is the principal configuration in non-polar solvent, but Pz3HC-3 is the principal configuration in polar solvent. In addition, the simulated fluorescence spectra interprets the negative solvatochromism effect of Pz3HC-1 and Pz3HC-3 in four solvents. The evidence from intramolecular hydrogen bonding (IHB) parameters and electronic perspective collectively confirms the light-induced IHB enhancement and intramolecular charge transfer (ICT) properties in Pz3HC-1 and Pz3HC-3, which raises the likelihood of the ESIPT process. Combining the calculation of potential energy curve (PEC) and intrinsic reaction coordinate (IRC), we demonstrate that the ESIPT ease of Pz3HC-1 in different polar solvents obeys the order of CYC > TOL > THF > ACN, while the order of ESIPT ease in Pz3HC-3 is opposite. Notably, the ESIPT process of Pz3HC-3 in CYC solvent is accompanied by the twisted intramolecular charge transfer (TICT) process. In addition, we also reveal that the enol* and keto* fluorescence peaks of Pz3HC-3 in CYC solvent are quenched by ISC and TICT process, respectively. Our work not only provides a satisfactory explanation of the novel dynamics mechanism for Pz3HC system, but also brings light to the design and application of new sensing molecules in the future.

Investigating the Photophysical Aspects of a Naphthalene-Based Excited-State Proton Transfer Dye 1-(1H-Benzo[d]imidazol-2-yl)naphthalen-2-ol: pH-Dependent Modulation of Photodynamics.

The steady state and time-resolved photophysical behavior of a proton transfer dye 1-(1H-benzo[d]imidazol-2-yl)naphthalen-2-ol (H-BINO) was investigated. The excited state intramolecular proton transfer (ESIPT) reaction in H-BINO is predominant in nonpolar solutions (toluene and DCM) with a lifetime of ∼1.0 ns. However, in polar media (DMF and MeOH), the excited state photodynamics is characterized by a complex equilibrium of emission from the locally excited state (0.1-2.3 ns), the phototautomer (0.5-1.2 ns), and the anionic emission (2.1-5.4 ns). In the solid state, emission from the various aggregated states dictates the photobehavior. Interestingly, the photodynamics in aqueous solution changes starkly as a function of pH with the anionic (2.1 ns) and phototautomeric (0.5-1.0 ns) emissions guiding the photodynamics as the pH of the medium increases. Optimized structural parameters at the proton donor and acceptor sites for the enol and keto forms and the calculated potential energy curve along the proton transfer coordinate at the density functional theory (DFT) level with the B3LYP/6-311G++(d,p) theory support a favorable and barrierless ESIPT process. The current results will surely boost the ongoing research on small molecule emissive materials.

Quantum calculation of the pressure broadening of H and K lines of Ca+ calcium ion in a gaz of ground-state He helium atoms

In this theoretical study, we have conducted calculations to investigate the pressure broadening of the H ( 4 s 2 S 1 / 2 − 4 p 2 P 1 / 2 ) and the K ( 4 s 2 S 1 / 2 − 4 p 2 P 3 / 2 ) lines of the Ca + calcium ion in a gas of ground-state He helium atoms. The focus of our work is to determine the profiles of the pressure-broadened resonance lines and analyse their behaviour under the influence of binary collisions between Ca + ions and He atoms. To achieve this, we constructed accurate potential energy curves for the ground X 2 Σ 1 / 2 + and the excited D 2 Π 1 / 2 , D 2 Π 3 / 2 and E 2 Σ 1 / 2 + states. Additionally, we constructed the corresponding transition dipole moments based on the data obtained through high-level ab initio methods, including SA-CASSCF, MRCI, and SO coupling, with Davidson and BSSE corrections. The study spans a range of temperatures from 4000 K to 12,000 K and wavelengths from 200 nm to 500 nm . The theoretical profile is characterised by dominant free-free transitions. In the vicinity of the 436 nm wavelength position, there is a satellite peak in the red wing, attributed to the contribution of D 2 Π 1 / 2 ⟵ X 2 Σ 1 / 2 + and D 2 Π 3 / 2 ⟵ X 2 Σ 1 / 2 + transitions. Our findings are in good agreement with previous theoretical results.

Influence of atomic electronegativity on ESIPT behaviour for the BTDI and its derivatives: Theoretical exploration

In this work, we theoretically explored the influence of atomic electronegativity on excited-state intramolecular proton transfer (ESIPT) behavior among novel fluorescent probes BTDI and its derivatives (BODI and BSeDI). A thorough examination of the optimized structural parameters and infrared vibrational spectra reveals an enhancement in intramolecular hydrogen bonding within BTDI and its derivatives upon light excitation. This finding is further reinforced by topological analysis and interaction region indicator scatter plots, which underscores the sensitivity of atomic electronegativity to variations in hydrogen bonding strength. With regards to absorption and fluorescence spectra, the decrease in atomic electronegativity leads to a pronounced redshift, primarily attributed to the narrowing of the energy gap. Additionally, an analysis of potential energy curves and the exploration of intrinsic reaction coordinate paths based on transition state structures afford a deeper understanding of the mechanism underlying ESIPT and being modulated through the manipulation of atomic electronegativity. We anticipate that this work on atomic electronegativity regulating ESIPT behavior will serve as a catalyst for novel fluorescent probes in the future, offering fresh perspectives and insights.

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".

Electronic structure, spectroscopy and photophysics of rubidium mono-sulphide

We investigated the nineteen first electronic states of the RbS diatomic using post Hartree-Fock configuration interaction methods at the internally contracted multi-reference configuration interaction (MRCI+(Q)) level. We thus mapped their respective potential energy curves with and without considering spin-orbit effects. After nuclear motion treatments, we derived their equilibrium distances, rotational and vibrational constants, and dissociation and electronic excitation energies. Moreover, an evaluation of the dipole moments of RbS was conducted, which in turn were used to evaluate the radiative lifetimes of the vibrational levels of RbS (X2П and A2Σ+) states. Computations show that spin-orbit interactions are important and cannot be omitted. Afterwards, and utilizing the sum rule approximation and the Franck–Condon factors, we computed both the bound-bound contributions and the bound-free terms. Our findings suggest that RbS exhibits intriguing characteristics suitable for laser cooling experiments. In sum, this work contributes to the understanding in-depth of the spectroscopy of RbS and predicts its use as a promising molecular system for laser cooling applications.

The C[formula omitted] state of potassium dimer revisited: An extensive study by polarisation labelling spectroscopy method

The polarisation labelling spectroscopy technique was applied to study the C1Πu← X1Σg+ band system in potassium dimer. About 1100 new rotationally resolved molecular lines were measured in the 22100–24100 cm−1 spectral range. Perturbations of the lowest vibrational levels of the C state were localised and their origin discussed. A set of Dunham coefficients was deduced to fit the unperturbed levels of the C1Πu state with 0≤v≤38 and 18≤J≤101 and the potential energy curve of the state was constructed.

Ab Initio Study on Electronic Excited States of Monochlorosilylene.

We perform a high-level ab initio study on 20 electronic states of monochlorosilylene (HSiCl) using an internally contracted multireference configuration interaction method including Davidson correction (icMRCI+Q). The spin-orbit coupling (SOC) effect is investigated, leading to splitting of the 20 spin-orbit-free states into 50 spin-orbit-coupled states. Vertical transition energies, oscillator strengths, and potential energy curves are presented with and without considering the SOC effect. Analysis indicates that the SOC effect plays an important role, especially for the high-lying excited states of HSiCl. The state interaction and the dynamics of the electronic states of HSiCl in the ultraviolet region are discussed based on our calculation results. Our study paves the way to understanding the behavior of electronic excited states of monochlorosilylene.

Extended improved multiparameter exponential‐type potential energy function for diatomic molecules

AbstractBased on the improved multiparameter exponential‐type potential (IMPET), an extended IMPET (EIMPET) potential has been suggested to reduce the discrepancy between the calculated and experimental values, improving the accuracy near the equilibrium and in the asymptotic region. The average fitting deviation δav and Root‐Mean‐Square (RMS) error is used to evaluate the performance of the potential which generates potential energy curves (PECs) and vibrational energy levels for ClF‐A(3Π1), CP‐X2Σ+, ICl‐X1Σ+, IBr‐X1Σ+, CO‐X1Σ+, and 6Li2‐X1Σ+ molecules that agree better with the Rydberg‐Klein‐Rees (RKR) data than Morse, Huxley‐Murrell (HM) and IMPET potentials. This work provides a reference for the construction and improvement of potential energy functions for diatomic molecules.

Dual-Channel Imine-Amine Photoisomerization in a Benzoimidazole and Benzothiazole Coupled System: Photophysics and Applications.

A molecule, namely 2-(1H-benzo[d]imidazol-2-yl)-6-(benzo[d]thiazol-2-yl)-4-bromophenol (BIBTB), having a two-way proton transfer unit of thiazole and imidazole moieties was synthesized and characterized by NMR, electrospray ionization mass spectrometry (ESI-MS), and single-crystal diffraction studies. Steady state and time-resolved spectral studies of BIBTB support excited state intramolecular proton transfer (ESIPT), causing imine-amine tautomerization through a two-way 6-membered H-bonded ring, where the N atoms of benzothiazole and the benzoimidazole unit are involved as proton acceptor sites. Interestingly, in a nonpolar and moderately polar solvent, photoisomerization in BIBTB is found to be favored toward the thiazole ring, whereas in a highly polar solvent, it is favored toward the imidazole ring. A spectral comparison of BIBTB with judicially designed molecules 2-(benzo[d]thiazol-2-yl)-4-bromophenol (HBT) and 2-(1H-benzo[d]imidazol-2-yl)-4-bromophenol (BIB) supports these inferences. Theoretical calculation using the Density Functional Theory (DFT) at CAM-B3LYP/6-311+G(d,p) level supports the existence of two low-energy 6-membered hydrogen-bonded planar conformers in the ground state in the gas phase and in solvents of different dielectrics. The potential energy curves (PECs) calculated along the proton transfer (PT) coordinate are found to have a high energy barrier in the ground state and to be barrierless or have a low energy barrier in the excited state for both the forms. The calculated vertical excitation and the emission energy from the relaxed excited and PT states show good correlation with the experimental spectral data. Aggregation of BIBTB in water with red shifted emission was established from X-ray single-crystal structure analysis, solid state emission, and Dynamic Light Scattering (DLS) measurement. The molecule BIBTB also acts as a fluorescence probe for sensing the explosive picric acid in the subnano scale and can be used to determine the proportion of water in dimethyl sulfoxide (DMSO) solvent.

Transition probabilities and radiative lifetimes of C[formula omitted]: A high level theoretical investigation

Dicarbon species are of particular interest within the physical chemistry community. However, contrary to neutral C2, the theory of electronic structure and spectra concerning C2− ions is not well-established. To address this gap in information, high-level multireference configuration interaction (MRCI) calculations have been performed, and new potential energy curves for fourteen low-lying states of C2− are reported. The best estimate for the ground dissociation energy is 64,720 cm−1 at the MRCI+Q/AV5Z level of theory. The first excited state, A2Πu, lies at 3,836 cm−1 (Re = 2.4829 a0 and ωe = 1649 cm−1). The infrared A2Πu − X2Σg+ transition has Einstein coefficients of the order of 103–104 s−1. The lifetime of the A2Πu state is given in microseconds. For the B2Σu+ state, it was calculated τ0≈ 78 ns in good accord with the experimental value of 77 ± 8 ns. The a4Σu+ state is placed at an excitation energy of 32,369 cm−1, much higher than expected by experimentalists (19,448 cm−1). The spin-forbidden transitions a4Σu+ − X2Σg+ are strong enough to be detected experimentally (A04≈ 3 × 106 s−1). The 14Πg − a4Σu+ transitions are more concentrated in the IR region. The radiative lifetime of 14Πg is computed to be 12μs. There is no doubt that the current data considerably enhance our understanding of the spectroscopy of C2−.

High-Resolution Rovibronic Cross Sections of the MgH+ Molecular Cation.

The high-resolution rovibronic line lists of the MgH+ molecular cation are presented in our work. The potential energy curves are calculated by the method of multireference configuration interaction and Davidson correction (MRCI+Q) with the spin-orbit coupling (SOC) effect. Spectroscopy constants are fitted and the results are in good agreement with experiments, ensuring the accuracy of the electronic structure. On account of potential energy curves and transition dipole moments, the Franck-Condon factors and Einstein coefficients of transition are obtained. These calculations are used to obtain an accurate partition functions and line lists for molecules. Using the partition functions and line lists, the absorption cross-sections under different temperatures and pressures were simulated. Our work could provide some theoretical insights into solar and cold planet spectrum.

Calculating Potential Energy Surfaces with Quantum Computers by Measuring Only the Density Along Adiabatic Transitions.

We show that chemically accurate potential energy surfaces (PESs) can be generated from quantum computers by measuring only the density along an adiabatic transition between different molecular geometries. In lieu of using phase estimation, the energy is evaluated by performing line-integration using the inverted real-space time-dependent density functional theory Kohn-Sham (KS) potential obtained from the geometry-varying densities of the full wave function. The accuracy of this method depends on the validity of the adiabatic evolution itself and the potential inversion process (which is theoretically exact but can be numerically unstable), whereas the total evolution time is the defining factor for the precision of phase estimation. We examine the method with a one-dimensional system of two electrons for both the ground and first triplet states in first quantization, as well as the ground state of three- and four-electron systems in second quantization. It is shown that few accurate measurements can be utilized to obtain chemical accuracy across the full potential energy curve, with a shorter propagation time than may be required using phase estimation for a similar accuracy. We also show that an accurate potential energy curve can be calculated by making many imprecise density measurements (using a few shots) along the time evolution and smoothing the resulting density evolution. Finally, it is important to note that the method is able to classically provide a check of its own accuracy by comparing the density resulting from a time-independent KS calculation using the inverted potential with the measured density. This can be used to determine whether longer adiabatic evolution times are required to satisfy the adiabatic theorem.

Predissociation dynamics of the hydroxyl radical (OH) based on a five-state spectroscopic model.

Multi-reference configuration interaction potential energy curves (PECs) and spin-orbit couplings for the X 2Π, A 2Σ+, 1 2Σ-, 1 4Σ-, and 1 4Π states of OH are computed and refined against empirical energy levels and transitions to produce a spectroscopic model. Predissociation lifetimes are determined by discretizing continuum states in the variational method nuclear motion calculation by restricting the calculation to a finite range of internuclear separations. Varying this range gives a series of avoided crossings between quasi-bound states associated with the A 2Σ+ and continuum states, from which predissociation lifetimes are extracted. 424 quasi-bound A 2Σ+ state rovibronic energy levels are analyzed, and 374 predissociation lifetimes are produced, offering good coverage of the predissociation region. Agreement with measured lifetimes is satisfactory, and a majority of computed results were within experimental uncertainty. A previously unreported A 2Σ+ state predissociation channel that goes via X 2Π is identified in the calculations. A Python package, binSLT, produced to calculate predissociation lifetimes, associated line broadening parameters, and lifetime uncertainties is made available. The PECs and other curves from this work will be used to produce a rovibronic ExoMol line list and temperature-dependent photodissociation cross sections for the hydroxyl radical.

Potential-Energy Curves for the Ground and Several Electronic States of NdO and NdS.

Potential energy curves (PECs) were calculated for 21 and 18 electronic states of NdO and NdS molecules, respectively. In each case, static electron correlation effects were described by incomplete model space multiconfiguration self-consistent field wave functions based on an active space that included the most important valence orbitals. Dynamic electron correlation was included by the multireference second-order generalized Van Vleck perturbation theory method. Scalar-relativistic contributions were included by the effective core potential approach, using def2-TZVPP basis sets. Spin-dependent relativistic corrections were determined to be small and negligible for the Nd atom and so were not included in the calculations. The 21 and 18 electronic states of NdO and NdS were predicted to be in the excitation energy range of ∼3.2 and ∼2.7 eV, respectively. The ground electronic states of NdO and NdS were determined as 15H (6s4fσ4fϕ4fδ) and 15H (4fϕ4fπ4fπ6s), with spectroscopic constants: bond length Re = 1.780 and 2.325 Å, and harmonic frequency ωe = 891 and 538 cm-1, respectively.

Ion-core switching in Rydberg series of XeKr

We investigate XeKr in high Rydberg states by mass-resolved optical-optical double resonance excitation spectroscopy. We excite XeKr via two-photon absorption to the v* = 0 and v* = 2 vibrational levels of an intermediate electronically excited state of Xe*Kr correlated to Xe*6p[5/2]2 and excite Xe*Kr further via one-photon absorption to the high Rydberg states of Xe**Kr in the energy range of 93200–97400 cm−1. The potential energy curves and the quantum defects of the d-Rydberg and s-Rydberg series of Xe**Kr, converging the A 2Π3/2 state of XeKr+ are determined. From the kinetic energy release in the predissociation process, we conclude that the ion-core switching occurs by the interaction between the bound electronic states of Xe**Kr converging to the A 2Π3/2 state of XeKr+ and the repulsive electronic states of low-lying electronic states of XeKr**. Based on numerical simulations, we interpret the dependence of the yield of the ion-core switching on the excitation energy in terms of the population transfer from the bound electronic states of the high Rydberg states Xe**Kr, converging to the A 2Π3/2 state of XeKr+, to those converging to the electronic ground X2 Σ 1 / 2 + state of XeKr + .

Modulating the ESIPT Mechanism and Luminescence Characteristics of Two Reversible Fluorescent Probes by Solvent Polarity: A Novel Perspective.

As reversible fluorescent probes, HTP-1 and HTP-2 have favourable applications for the detection of Zn2+ and H2S. Herein, the impact of solvent on the excited-state intramolecular proton transfer (ESIPT) of HTP-1 and HTP-2 was comprehensively investigated. The obtained geometric parameters and infrared (IR) vibrational analysis associated with the intramolecular hydrogen bond (IHB) indicated that the strength of IHB for HTP-1 was weakened in the excited state. Moreover, structural torsion and almost no ICT behaviour indicated that the ESIPT process did not occur in HTP-1. Nevertheless, when the 7-nitro-1,2,3-benzoxadiazole (NBD) group replaced the H atom, the IHB strength of HTP-2 was enhanced after photoexcitation, which inhibited the twisting of tetraphenylethylene, thereby opening the ESIPT channel. Notably, hole-electron analysis and frontier molecular orbitals revealed that the charge decoupling effect was the reason for the fluorescence quenching of HTP-2. Furthermore, the potential energy curves (PECs) revealed that HTP-2 was more inclined to the ESIPT process in polar solvents than in nonpolar solvents. With a decrease in solvent polarity, it was more conducive to the ESIPT process. Our study systematically presents the ESIPT process and different detection mechanisms of the two reversible probe molecules regulated by solvent polarity, providing new insights into the design and development of novel fluorescent probes.