Energy Curves Research Articles

Spectroscopic properties and laser cooling feasibility with the X1∏21/2↔X2∏23/2 transition for the PbX (X = F, Cl, Br, and I) molecules

The highly diagonal Frank–Condon factors (FCFs) are necessary for the laser cooling scheme, which means that only the molecules with the appropriate ground and excited electronic states can become candidates. Here, the laser cooling feasibility of the PbX (X = F, Cl, Br, and I) molecules is explored through four-component relativistic calculations. The potential energy curves and transition dipole moments of five Ω states are calculated and used to solve the Schrödinger equation of nuclear motion to obtain the rovibrational energy levels, spectroscopic parameters, the Einstein coefficients, and FCFs. Using the X1 2Π1/2 ↔ X2 2Π3/2 transition with highly diagonal FCFs, we construct optical schemes that can provide 104 ∼ 105 scattering phonons with four pumping lasers for PbX. The Doppler/recoil temperatures of PbX are 419.05 / 57.55, 9.63 / 61.20, 4.95 / 49.98, and 0.71 / 40.17 nK, respectively. Since the 10−4 s of the long spontaneous emission lifetime, the temperatures below microkelvin orders of magnitude can be achieved only if the adequate pre-cooling temperature is satisfied.

Electronic structure of ground and low-lying excited states of BaLi+ molecular ion: spin-orbit effect, radiative lifetimes and Franck-Condon factor

The study of BaLi+ and its reactivity plays a crucial role in advancing our understanding of chemical bonding or reaction mechanisms. The aim of this work is to represent a complete and extended theoretical study of BaLi+ molecular ion including ground and highly excited electronic states of 1,3Σ, 1,3Π and 1,3Δ symmetries, dissociated to the first seven dissociation limits. The corresponding potential energy curves (PECs), permanent and transition dipole moments have been investigated. These calculations were performed using the multireference configuration interaction (MRCI) method in combination with optimized basis sets and non-empirical pseudopotentials (ECP) for both Ba and Li atoms. Afterwards, the spin–orbit (SO) operator is incorporated in valence MRCI calculation using optimized relativistic spin–orbit pseudopotentials and 16 Ω states are generated and splitted into Λ-S states. The SO effect gives rise to a more complicated structure of electronic states presented in PEC and permanent and transition dipole moments. Nonadiabatic coupling matrix elements between the five lowest 1Σ+ states are also presented for the nonrelativistic results. Based on the vibrational radiative lifetime and Franck–Condon calculation, the possibilities of laser cooling of this system have been also discussed.

Photo-Induced Tautomerism of Isocytosine in Aqueous Solution when Irradiated with UVC Light

It was found that the irradiation of aqueous solution of isocytosine with UVC light provokes an oxo-hydroxy phototautomerism of the compound with a rate constant of 5.29× 10-3 min-1. It was observed a backward reaction, after removing the UV light source, with a rate constant of 0.12×10-3 min-1. Two mechanisms of the phototautomerism were investigated at the B3LYP/aug-cc-pVDZ theoretical level in water surroundings (PCM). The first one showed a consecutive dissociation and association of a proton through conical intersections S0/S1 whose structures were located at the same theoretical level in the gas phase. It occurs along the 1πσ* excited-state reaction pathway. The more probable mechanism includes an excited-state H-transfer supported by a water molecule as a catalyst. It occurs along the 1ππ* excited-state reaction pathway which we found over the IRC ground-state energy curve. The water molecule drastically reduces the energy barrier in the ground state as well in the excited state.

Revisiting the island of hexadecapole-deformation nuclei in the A ≈ 150 mass region: focusing on the model application to nuclear shapes and masses

Based on the potential-energy-surface calculation, the impact of different deformation degrees of freedom on a single-particle structure and binding energies in nuclei around 152Nd, located on one of the hexadecapole-deformation islands, is analyzed in a multi-dimensional deformation space. Various energy maps, curves and tables are presented to indicate nuclear properties. The calculated equilibrium deformations and binding energies with different potential parameters are compared with experimental data and other theories. It is found that the inclusion of the hexadecapole deformations, especially the axial one, can improve the theoretical description of both nuclear shapes and masses. In addition, our calculated potential-energy curve shows that a critical deformation-point, β 2 ≈ 0.4, exists—the triaxial (hexadecapole) deformation effect can be neglectable but the hexadecapole (triaxial) one plays an important role before (after) such a critical point.

How Plant Toxins Cause Early Larval Mortality in Herbivorous Insects: An Explanation by Modeling the Net Energy Curve.

Plants store chemical defenses that act as toxins against herbivores, such as toxic isothiocyanates (ITCs) in Brassica plants, hydrolyzed from glucosinolate (GLS) precursors. The fitness of herbivorous larvae can be strongly affected by these toxins, causing immature death. We modeled this phenomenon using a set of ordinary differential equations and established a direct relationship between feeding, toxin exposure, and the net energy of a larva, where the fitness of an organism is proportional to its net energy according to optimal foraging theory. Optimal foraging theory is widely used in ecology to model the feeding and searching behavior of organisms. Although feeding provides energy gain, plant toxins and foraging cause energy loss for the larvae. Our equations explain that toxin exposure and foraging can sharply reduce larval net energy to zero at an instar. Since herbivory needs energy, the only choice left for a larva is to stop feeding at that time point. If that is significantly earlier than the end of the last instar stage, the larva dies without food. Thus, we show that plant toxins can cause immature death in larvae from the perspective of optimal foraging theory.

Visualizing non-adiabatic quantum dynamics and photo-excitation processes on Excel

We offer two Excel modules that students can use to view the real-time spatial evolution of a diatomic molecule's nuclei when two different potential energy curves governing the nucleus motion spatially cross one another or are coupled by a light field. Module 1 comprises three spreadsheets that can be used to view non-adiabatic nuclear dynamics on two crossing nuclear potential energy curves. These curves cross because there is a value of the spatial coordinate where the two curves have the same energy, which results in a non-zero probability of the probability density crossing from one potential curve to the other. Students can view non-adiabatic nuclear dynamics involving two unbounded nuclear potential curves, pre-dissociation with a bound “ionic state” to an unbound covalent state, and quantum tunneling dynamics between two bounded potential curves. Module 2 comprises two spreadsheets that can be used to view the dynamics of the photo-excitation process, i.e., where the absorption of light leads to transitions between two nuclear potentials. Students can model the light-induced transitions between nuclear potentials when the light is provided by both a continuous wave laser and a pulsed laser. These modules are included as the supplementary material and can be run on any computer that supports Excel.

Activation entropy and enthalpy of creep in pure metals

Previously published results on the power law creep of a selection of fcc, bcc and hcp pure metals are discussed using a modified Stokes – Einstein equation originally describing Newtonian viscosity of spherical particles in a fluid. Activation energy is modified to include terms representing activation enthalpy, activation entropy and the effect of strain rate. It is similar to the Dorn equation for power law creep but with strain rate rather than stress as the independent variable. Curves of activation energy vs shear rate are linear rather than having a discontinuity as have those with stress as independent variable. All metals have linear curves of activation energy at zero rate vs temperature, the slope of which reflects the activation entropy and is similar for all metals. Intercepts which represent activation enthalpy are dependent on lattice structure.

The radiative association of PO/PH+ and the photodissociation of PH+

The potential energy curves (PECs) and transition dipole moments (TDMs) of PH+ and PO are computed with the multireference configuration interaction method, and the cross-sections for the radiative association (RA) of PH+ and PO, which is the most efficient way to form the ground states, are presented via the quantum mechanical (QM) theory and computed using ab initio molecular data. The thermal rate coefficients are also expressed and fitted with the standard formula kT=AT300αe−βT in the range of 10 K–15,000 K. Meanwhile, the photodissociation, that is the inverse process of RA for PH+, is also studied, including eight photodissociation channels for the computation of state-resolved cross-sections. Careful comparisons with the Leiden Observatory database are made. Considering the cross-sections mentioned above, the local thermodynamic equilibrium cross-sections at the temperatures of 0, 500, 1,000, and 2,000 K are also shown. We expect the results to be helpful for studies of phosphorus chemistry in the interstellar medium and planetary atmospheres.

The CuTe Molecule: Theoretical investigation of the electronic structure and dipole moments of the ground and lowest excited states with rovibrational calculations

The multireference configuration interaction calculation MRSDCI (with Davidson correction) has been performed to investigate the potential energy curves, the transition electronic energies Te, the spectroscopic constants (Re, ωe and Be), the transition and permanent dipole moments, and the vibrational levels corresponding to the ground and 18 excited electronic states of the molecule CuTe in the representation 2S+1Λ(+/-) (neglecting the spin–orbit effects), whereas the PECs and the spectroscopic constants have been calculated for 27 states in the representation Ω(+/-) [including the spin–orbit (SO) effects]. The ground state equilibrium bond length and the vibrational frequency have also been investigated using the density functional theory (DFT), where different density functionals with different basis sets have been tested. This study represents the first theoretical study of the excited states of the CuTe molecule. Comparison of the present results with the available experimental ones shows an overall satisfying agreement.

MRCI Study of the Electronic Structure and Transition Properties of a Tin Dimer.

The ground and excited states of Sn2 are calculated using the multireference configuration interaction method combined with Davidson correction (MRCI+Q). The influence of the spin-orbit coupling (SOC) effect on the electronic structure is also considered by the state interaction method of Breit-Pauli Hamiltonian. In the calculations, the potential energy curves and spectroscopic constants of 23 Λ-S states and 31 Ω states of Sn2 are obtained. The prominent spectral features in the visible region, new constants, and potential energy curves are discussed. The intensity of weak magnetic and quadrupole transitions in the near IR spectra is also calculated. From a computational point of view, we predict that the weak v'(0-2)-v″(0-5) bands of the magnetic b1Σg,0++-X3Σg,1(Ms=±1)- transition may be detected experimentally; the sub-bands (0, 0), (1, 0), and (2, 0) of the a1Δg,2-X3Σg,1(Ms=±1)- transition also may be observed in experiments since they are not overlapped by the strong electric dipole transition in the same IR region. According to the SOC matrix elements and contributions of the 15Πu0+, 15Πu1 (|Σ| = 0), and 15Πu1 (|Σ| = 2) states to the predissociation line width of the 13Σu- -X3Σg1- transition, the broading and other predissociation features of the 13Σu- state are analyzed. From our calculations, it follows that the strong coupling between the bound 13Σu- state and the repulsive 15Πu state causes the predissociation of the 13Σu- state at the vibrational levels v' ≥ 8. In addition, our results suggest that the previously observed bands of Sn2 in the visible range of 19000-20000 cm-1 should be reassigned into the mixing transitions among the X3Σg,1--23Σu,0-+ and X3Σg,0+--23Σu,1+ manifold. The results are expected to provide new comprehensive information for better understanding the spectra and dynamics of the electronic excited states of the Sn2 molecule.

Spectroscopy and molecule opacity investigation on excited states of SiS

The SiS molecule, which plays a significant role in space, has attracted a great deal of attention for many years. Due to complex interactions among its low-lying electronic states, precise information regarding the molecular structure of SiS is limited. To obtain accurate information about the structure of its excited states, the high-precision multireference configuration interaction (MRCI) method has been utilized. This method is used to calculate the potential energy curves (PECs) of the 18 Λ–S states corresponding to the lowest dissociation limit of SiS. The core–valence correlation effect, Davidson’s correction and the scalar relativistic effect are also included to guarantee the precision of the MRCI calculation. Based on the calculated PECs, the spectroscopic constants of quasi-bound and bound electronic states are calculated and they are in accordance with previous experimental results. The transition dipole moments (TDMs) and dipole moments (DMs) are determined by the MRCI method. In addition, the abrupt variations of the DMs for the 15Σ+ and 25Σ+ states at the avoided crossing point are attributed to the variation of the electronic configuration. The opacity of SiS at a pressure of 100 atms is presented across a series of temperatures. With increasing temperature, the expanding population of excited states blurs the band boundaries.

Analysis of unsteady MHD fluid flow across two parallel discs with uniform fluctuation subject to modified Hall and activation energy

This study intends to examine the consequences of the externally applied magnetic field and modified Hall effect on nanofluid flow across two symmetrically spinning and extending discs, where continuously the upper disc moves upward and downward. The lower disc is vertically fixed. The discs rotate and move vertically, generating a 3D flow. The mass density, heat transfer and flow motion have been evaluated and modeled in the form of the system of partial differential equations (PDEs) with an additional influence of activation energy, heat source and chemical reaction. The system of PDEs is modified to an ordinary set of differential equations by employing the resemblance substitution method. The obtained system of ODEs is further solved through the numerical approach (bvp4c). The results are compared to the bvp4c package and published work for validity purposes. In the case of downward displacement of the upper disc, magnetic and Hall characteristics have a significant impact on the velocity curve. The energy curve elevates with the upward movement of the disc, while it reduces with the downward fluctuation. Furthermore, the mass transmission rate enhances with the influence of hall current, while diminishing with the impact of chemical reaction rate.

Correlations between Energy Dissipation Characteristics and the Rheological Property Degradation of Asphalt Binders

Fatigue failure in asphalt pavements, caused by continuous loading, primarily occurs at the interface between the asphalt binder and the aggregate (adhesive failure) or within the asphalt binder itself (cohesive failure). This study conducted variable stress fatigue tests on asphalt binders to investigate the fatigue damage evolution mechanism that aligns most closely with actual road conditions. By altering test conditions such as stress amplitude and loading frequency, the study summarized the patterns of change in the fatigue performance parameters of binder samples and analyzed their fatigue life. The research methods employed are of significant value for refining the existing asphalt fatigue evaluation systems. Indicators such as dissipated energy ratio, cumulative dissipated energy ratio, rate of change in dissipated energy, and the G-R constant n × Gn* were used as criteria for fatigue failure. The fatigue life of samples under different stress levels was calculated, and the applicability of each dissipated energy fatigue indicator was evaluated. The evaluation indicators, like dissipated energy ratio and cumulative dissipated energy ratio, failed under large stress outside the non-linear viscoelastic range, whereas the rate of change in dissipated energy and the G-R constant n × Gn* accurately determined the fatigue life of samples in fatigue tests at all stress levels, covering a broader range of applicable stresses. In variable stress fatigue tests, the rate of change in dissipated energy and the G-R constant were used as indicators for determining fatigue failure. Under a small-to-large loading mode, the second stage of the sample’s fatigue life was too short, causing the G-R constant curve to not reach its peak, and hence it could not accurately determine the sample’s fatigue life. Under a large-to-small loading mode, there are sufficient loading cycles before fatigue failure occurs, allowing the G-R constant curve to reach its peak, demonstrating that the G-R constant remains applicable in this loading mode. Under both small-to-large and large-to-small loading modes, the fatigue failure point of the samples could be determined based on the rate of change in dissipated energy curve. It is recommended to use the rate of change in dissipated energy as the failure criterion for samples in variable stress fatigue tests on asphalt binders.

An Off-Grid Compressive Sensing Algorithm Based on Sparse Bayesian Learning for RFPA Radar

In the application of Compressive Sensing (CS) theory for sidelobe suppression in Random Frequency and Pulse Repetition Interval Agile (RFPA) radar, the off−grid issues affect the performance of target parameter estimation in RFPA radar. Therefore, to address this issue, this paper presents an off−grid CS algorithm named Refinement and Generalized Double Pareto (GDP) distribution based on Sparse Bayesian Learning (RGDP−SBL) for RFPA radar that utilizes a coarse−to−fine grid refinement approach, allowing precise and cost−effective signal recovery while mitigating the impact of off−grid issues on target parameter estimation. To obtain a high-precision signal recovery, especially in scenarios involving closely spaced targets, the RGDP−SBL algorithm makes use of a three−level hierarchical prior model. Furthermore, the RGDP−SBL algorithm efficiently utilizes diagonal elements during the coarse search and exploits the convexity of the grid energy curve during the fine search, therefore significantly reducing computational complexity. Simulation results demonstrate that the RGDP−SBL algorithm significantly improves signal recovery performance while maintaining low computational complexity in multiple scenarios for RFPA radar.

Free energy curves for the Volmer reaction obtained from molecular dynamics simulation based on quantum chemistry

Hydrogen desorption from Au(111) at a constant electrode charge has been studied by a DFT-based tight binding theory (DFTB). Free energy curves have been obtained from molecular dynamics with umbrella sampling. The activation energy increases linearly with the applied negative charge and decreases with temperature, so that the Butler-Volmer law does not hold in its strict form. The activation energy is determined by the reorganization of the accepting water molecule and its surroundings, which becomes more facile with temperature. A separation of the free energy curves into a constant chemical part and an electrostatic part, which varies with the charge, does not hold. Because of its speed DFTB is very suitable for the investigation of electrochemical reactions, but is presently hampered by a lack of sets of interaction parameters.

High Accuracy Ab Initio Potential Energy Curves and Dipole Moment Functions for the X1Σ+ and a3Π Spin States of the CF+ Diatomic Molecule.

Potential energy curves and dipole moment functions constructed using high-accuracy ab initio methods allow for an in-depth examination of the electronic structure of diatomic molecules. Ab initio computations serve as a valuable complement to experimental data, offering insights into the nature of short-lived molecules such as those encountered within the interstellar medium (ISM). While laboratory experiments provide critical groundwork, the ISM's conditions often permit longer lifetimes for lower stability molecules, enabling unique observations. The CF+ diatomic molecule is one such molecule that has been observed spectroscopically in the ISM. Previous experimental and theoretical work have examined different spectroscopic aspects of the CF+ molecule, but the development of newer, more complete potential energy curves and dipole moment functions allows for even greater insight. We constructed both potential energy curves and dipole moment functions for the ground X1Σ+ and first excited a3Π states of CF+ for both the 12C and 13C isotopologues. The potential energy curves were constructed using coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) at the complete basis set limit with corrections from full triple, quadruple, quintuple, and hextuple excitations within a finite-basis coupled cluster wave function as well as corrections from full configuration interaction and relativistic effects. Rovibrational wave functions were calculated using a vibrational Hamiltonian matrix, which moves beyond the harmonic oscillator approximation. The equilibrium bond length, vibrational constant, and rotational constant were reproduced to within 0.00013 Å, 0.28 cm-1, and 0.00045 cm-1, respectively, of experimental values. Experimental transition energies from rovibrational spectra were reproduced with an error of no larger than 0.63 cm-1. The triplet excited state (a3Π) was found to have a longer equilibrium bond length at 1.21069 Å, a vibrational constant of 1611.29 cm-1, and a rotational constant of 1.56376 cm-1. Rovibrational line lists for the 12C and 13C isotopologues for both the X1Σ+ and the excited a3Π states were generated.

Theoretical insights into photoinduced excited‐state behaviors for the novel CHPPhl fluorophore: Effects of solvent polarity

AbstractInspired by the distinguished photochemical and photophysical properties of novel hydroxyl‐substituted tetraphenylimidazole (HPI) derivatives that could be potentially applied across various disciplines, in this work, effects of solvent polarity on excited‐state hydrogen bond effects and excited‐state intramolecular proton transfer (ESIPT) reaction of 3‐(6,9‐Diphenyl‐1H‐phenanthro[9,10‐d]imidazole‐2‐yl)‐9‐phenyl‐9H‐carbazol‐4‐ol (CHPPhl) are focused. By comparing the structural changes and infrared (IR) vibrational spectra of the E‐HBT fluorophore in polar acetone, moderate polar tetrahydrofuran and non‐polar hexane solvents, combined with the preliminary detection of hydrogen bond interaction by core–valence bifurcation (CVB) index, we can conclude that the hydrogen bond could be strengthened in S1 state, which is favorable for the occurrence of ESIPT reactions. The charge recombination behavior of hydrogen bond induced by photoexcitation also further illustrates this point. Via constructing potential energy curves (PECs) based on restrictive optimization and searching transition state (TS) form, we confirm change of surrounding solvent polarity has a regulatory effect on the ESIPT behavior for CHPPhl; that is, the lower the solvent polarity is more conducive to the ESIPT reaction.

DFT/TDDFT based study to decipher the excited state intramolecular proton transfer process for 3-benzothiazol-2-yl-2-hydroxy-5-methyl-benzaldehyde-oxime

In this study, we theoretically investigate the interactions of hydrogen bonding in excited states and the mechanism of intramolecular proton transfer (ESIPT) for the novel compound 3-benzothiazol-2-yl-2-hydroxy-5-methyl-benzaldehyde-oxime (HBT-phos) theoretically. Herein, the effects of atomic electronegativity of chalcogen (O, S and Se) are also focused. Firstly, employing quantum theory of atoms-in-molecules (QTAIM) method, we confirm intrinsic quality of O-H···N within HBT-phos derivatives (HBT-phos-O, HBT-phos-S and HBT-phos-Se). By astutely examining changes in geometries and infrared (IR) spectra, we elegantly demonstrate O-H···N is remarkably strengthened in S1 state, indicating a pronounced tendency towards ESIPT. Computational hydrogen bonding energies further magnificently support this conclusion. Probing into photo-induced excitation, we discover heightened electronic densities surrounding N atom that play pivotal roles in attracting protons, thereby facilitating ESIPT. Ultimately, upon comparing potential energy curves in excited states, we deduce ESIPT process is expected to be exceptionally rapid with low atomic electronegativity (O → S → Se), which elucidates why detecting fluorescence peak of HBT-phos-S itself proves challenging in experiment. This study not only fills the void in understanding ESIPT mechanism within HBT-phos derivatives and authentically reveals its unambiguous mechanism, but also presents atomic-electronegativity-dependent ESIPT behaviour and the explanation for fluorescence quenching observed in prior experiment.

A DFT study on photodissociation of the palladium tetrachloride anion PdCl42− in solution

Photodissociation of PdCl42− in water is investigated using the time-dependent DFT method with the polarized continuum model. First, to find out the exchange–correlation functional that can well describe the present system we make following two comparisons using many functionals: (i) the DFT absorption spectrum vs. experiment; (ii) the DFT one-dimensional (1D) potential energy curves (PECs) vs. the previous MRCI 1D PECs. As a result of comparison, it is found that the range-separated hybrid functionals well reproduce the observed spectrum and, among these, the M11 functional may be the most reasonable choice. Next, using M11, we calculate ground and excited-state 1D PECs for single Cl loss in water and the ground-state two-dimensional (2D) potential energy surface (PES) for double Cl loss in water. It is revealed in the 1D PECs in water that electronic excitations to the PECs that have large transition dipole moments with the ground electronic state may easily lead to the PdCl3− + Cl− dissociation channel, which is similar to single Cl loss in the gas phase. It is also found that the ground-state 2D PES in water correlates with the PdCl2 + 2Cl− dissociation channel with no transition state on the way to it. This is different from the prediction in the gas phase; the ground-state 2D PES correlates with the PdCl2 + Cl2− dissociation channel with a transition state on the minimum energy path leading to it.

Mechanistic insights into the AIE properties of BF2 complexes of N-acetyl 2-aminobenzothiazoles as rotorless polyheteroaromatics

A series of four novel BF2 complexes of N-acetyl 2-aminobenzothiazoles featuring rigid rotorless polyheteroaromatic structures have been designed and synthesized. All of these compounds exhibited AIE properties with excellent solid-state fluorescence quantum yields up to 81.7%. Theoretical calculations revealed the characteristics of their ground-state structures and excitation processes. Their seemingly abnormal nonradiative decay in solutions was investigated from both direct vibrational relaxation and S0/S1 surface crossing perspectives by the two-channel model. The minimum energy conical intersection (MECI) located by SF-TDDFT method indicated that the CI is mainly induced by the deformation of the BF2 complex ring, leads to elevated energy level, and thus is not responsible for the fluorescence quenching. The potential energy curve (PEC) constructed along the distortion angle θ of BF2 complex ring showed that when θ reaches 50° (the dark-state region approaching MECI), the energy barrier is only 0.11 eV, suggesting that the deformed dark state could serve as an effective deactivation channel via ultrafast internal conversion (IC). Crystallographic analysis illustrated that the F atoms perpendicular to the polyheterocycle could effectively prohibit detrimental π-π stacking and enhance intermolecular interactions, thereby resulting in efficient solid-state emission.