Excited States Of Molecules Research Articles

Insights from computational analysis: Excited-state hydrogen-bonding interactions and ESIPT processes in phenothiazine derivatives

Organic materials with Mechanofluorochromism (MFC) properties have potential application value. Phenothiazine derivatives are a class of substances with MFC properties that have been synthesized and reported in experiments (Dyes and Pigments 172 (2020) 107835). Dual fluorescence of a series of phenothiazine derivatives is observed in the experiment, which proved that the ESIPT process is carried out. In this work, we choose phenothiazine derivatives (C2PAHN, C4PAHN, C8PAHN) as models to theoretically analyze the influence of different alkyl chain lengths on the excited state intramolecular proton transfer (ESIPT). In addition, the shift value of fluorescence spectrum is related to the length of alkyl chain. The fluorescence shift of C2PAHN is the largest (6.31 nm), and that of C8PAHN is the smallest (2.40 nm). The theory of density functional theory (DFT) and time-dependent density functional theory (TD-DFT) are adopted to simulate the molecular dynamics in the ground state and excited state. The analysis of the optimized molecular geometry parameters and infrared vibrational spectroscopy (IR) illustrate the stronger hydrogen bonding of the excited state molecules, which is favorable for the progress of ESIPT. Fluorescence spectroscopy reveals that the appropriate increase or decrease of alkyl chains would change the photophysical properties of the molecules. Frontier molecular orbitals (FMOs) indicate that the rearrangement of electron density from electronic level to is the driving force of the ESIPT process. Reduction density gradient (RDG) surfaces and Natural Population Analysis (NPA) tentatively lead to the conclusion that alkyl chain length is inversely proportional to hydrogen bond strength. Finally, the data are qualitatively analyzed by scanning the potential energy curves, and it is concluded that the longer the alkyl chain, the weaker the hydrogen bonding effect and the more unfavorable the ESIPT process.

Time-Dependent Second-Order Green’s Function Theory for Neutral Excitations

We develop a time-dependent second-order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation, using the second-order Born approximation for the self-energy. In the linear response regime, we recast the time-dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second-order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time-dependent Hartree-Fock (TDHF), particularly for charge-transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.

Quantifying and reducing spin contamination in algebraic diagrammatic construction theory of charged excitations.

Algebraic diagrammatic construction (ADC) theory is a computationally efficient and accurate approach for simulating electronic excitations in chemical systems. However, for the simulations of excited states in molecules with unpaired electrons, the performance of ADC methods can be affected by the spin contamination in unrestricted Hartree-Fock (UHF) reference wavefunctions. In this work, we benchmark the accuracy of ADC methods for electron attachment and ionization of open-shell molecules with the UHF reference orbitals (EA/IP-ADC/UHF) and develop an approach to quantify the spin contamination in charged excited states. Following this assessment, we demonstrate that the spin contamination can be reduced by combining EA/IP-ADC with the reference orbitals from restricted open-shell Hartree-Fock (ROHF) or orbital-optimized Møller-Plesset perturbation (OMP) theories. Our numerical results demonstrate that for open-shell systems with strong spin contamination in the UHF reference, the third-order EA/IP-ADC methods with the ROHF or OMP reference orbitals are similar in accuracy to equation-of-motion coupled cluster theory with single and double excitations.

Regulating the excited state behaviors of 2-benzooxazol-2-yl-4,6-di-tert-butyl-phenol fluorophore by solvent polarity: A theoretical simulation

• The enhanced hydrogen bonding provides the impetus to promote the ESIPT reaction. • Photo-induced increased electronic densities around N atom plays vital roles in attracting hydroxyl proton. • Non-polar solvents are more favorable for the ESIPT behavior of BDTBP compound. In view of the unique luminescent characteristics, ESIPT materials have attracted lots of eyes. Given promising highly efficient green-emitting material, 2-benzooxazol-2-yl-4,6-di- tert -butyl-phenol (BDTBP) reveals important properties in designing Schiff base optical sensors. In this work, solvent dependent excited state behavior and ESIPT process of BDTBP has been explored theoretically. Analyses of chemical structural variations and infrared (IR) vibrational spectra in both S 0 and S 1 state, the enhanced intramolecular hydrogen bonding interactions could be clearly found that promotes ESIPT tendency. Particularly, BDTBP in nonpolar solvents with stronger hydrogen bond reveals the easier PT tendency. Paying attention to the changes of HOMO and LUMO orbitals, it could be found the charge transfer happens in the excited-state molecules, the reorganization of charge densities should be conducive to promoting the ESIPT process. Simulated potential energy curves indicated the ultrafast ESIPT reaction occurs for BDTBP fluorophore, which could be regulated and controlled via solvent polarity.

Ultrasensitive molecularly imprinted electrochemiluminescence sensor based on highly-conductive rGO-COOH synergically amplify TCPP luminophor signal in aqueous phase system for “switches-controlled” detection of tryptamine

An efficient and innovative molecularly imprinted electrochemiluminescence sensor (MIECLS) based on the reduced carboxylated graphene oxide (rGO-COOH) amplifying aqueous phase meso-tetra(4-carboxyphenyl)porphyrin (TCPP) signal was constructed for “switches-controlled” detection of tryptamine (Tryp). The conductive rGO-COOH uninterruptedly accelerated the high-energy electrons injection into the aqueous co-reaction system of green metal-free TCPP, and more excited state molecules (TCPP*) were generated to obtain excellent ECL signal. Benefiting from the large specific surface area provided by rGO-COOH, molecularly imprinted polymer (MIP) with specific recognition cavities can be firmly electropolymerized on the surface of rGO-COOH/glassy carbon electrode (GCE), which regulated electrons transfer rate to realize “switches-controlled” detection by elution and recombination of Tryp. Under optimal conditions, the MIECLS exhibited a favorable linear relationship with Tryp in the concentration range of 1 × 10−9–1 × 10−4 mol L−1 and the limit of detection (LOD) was 0.25 × 10−9 mol L−1. The MIECLS was used for Tryp detection in actual samples with the satisfactory results (recovery rate, 83.19–91.32%) and consistent with that of HPLC. The dual application of TCPP and MIP/rGO-COOH/GCE can create nicely synergistic effect for the Tryp detection, making a novel avenue to the rapid analysis of other food hazards.

Theoretical study on aggregation-induced emission of new multi-layer 3D chiral molecules

ABSTRACT Multilayer three-dimensional (3D) chiral molecules have potential application in luminescent material fields, but the mechanism of their AIE effect is not clear. In this work, the theoretical mechanism of the aggregation-induced emission (AIE) effect has been studied for three 3D molecules of 2-X-1,3-bis(8-(4-Y-phenyl)naphthalen-1-yl)-1,3-dihydrobenzo[d][1,3,2] diazapho-sphole-2-oxie (A. X = NH2, Y = H; B. X = i-Pr, Y = H; C. X = NH2, Y = OMe). The geometrical structures and spectral properties in solution, crystal and aggregation are discussed using the combined approach of molecular dynamics (MD), DFT/TD-DFT and ONIOM QM/MM calculations. The S0 and S1 structural changes of 3D molecules show that the variation of the naphthalene and benzene rings is reduced in aggregation. Huang-Rhys (HR) factor and reorganisation energy are smaller in aggregation than in solution, especially in low-frequency vibration modes. It suggests that aggregation restricts the rotation of benzene and naphthalene rings and constrains the low-frequency vibration modes, which allows the radiated channel of the excited state molecule to be opened and glow when aggregated. This study provides an excellent explanation for the AIE phenomenon of 3D chiral molecules in experiments.

A detailed CO2(1B2) chemiluminescence chemical kinetics model for carbon monoxide and hydrocarbon oxidation

The CO2(1B2) - CO2(X1Σ+g) transition is a source of chemiluminescence from CO and hydrocarbon premixed flames and can be used as a diagnostic; however, its chemistry is not well known due to its broadband nature. Although several attempts have been made to model CO2(1B2) chemiluminescence, none performs well in hydrocarbon flames. We propose a new detailed kinetic model for CO2(1B2) chemiluminescence, based on shock tube experiments in the literature and on opposed flame data presented here. The mechanism consists of 26 reactions which describe the formation of the lower excited state molecule CO2(3B2) (R1), the inter-system crossing reaction between CO2(3B2) and CO2(1B2) (R2), CO2(1B2), the formatting reaction path in hydrocarbon flames (R3), CO2(1B2) radiative quenching (R4) and collisional quenching of CO2(3B2) and CO2(1B2) (R5-R26). The reaction rates constants of R1 and R3 within ± 60% and ± 32% uncertainty, respectively, were determined as follows:CO + O + M = CO2(3B2) + M.k1 = 1 × 1013exp(-10/RT) cm6 mol2 s−1, KJ mol−1.CH + O2 = CO2(1B2) + H.k3 = 8 × 1010 cm3 mol−1 s−1.The mechanism was evaluated against several shock tube experiments at low and elevated pressures and also the CO2(1B2)/OH* chemiluminescent intensity ratio for premixed CH4-air and C3H8-air opposed flames measured in the current study. The comparison showed good agreement for CO2(1B2) temporal profiles for CO-based, CH4-based and C2H4-based mixtures. The prediction of temperature dependence of the CO2(1B2) peak intensity for the CH4-based mixture at both low and elevated pressures was much improved relative to previous models. The CO2(1B2)/OH* chemiluminescent intensity ratio for premixed CH4-air flames predicted by the new model agrees quite well with experiment data, while a small discrepancy remains for C3H8-air flames. Overall, the developed CO2(1B2) chemiluminescence model reproduces, a wide range of experimental data and extends knowledge of CO2(1B2) chemistry.

The regulation mechanism of the excited-state behaviour of 3-Hydroxy-2-(1-ethyl-1H-pyrazol-3-yl)-4H-chromen-4-one fluorophore by solvent polarity: a computational study

Given the unique spectral properties of exhibiting dual-band fluorescence, excited-state intramolecular proton transfer (ESIPT) materials have attracted wide attention. In light of a promising, highly efficient fluorescent probe with potential ratiometric emission detection, in this work, 3-Hydroxy-2-(1-ethyl-1H-pyrazol-3-yl)-4H-chromen-4-one (3ePz3HC) has been explored its photo-induced excited-state behaviours. In analyses of structural variations and infrared (IR) vibrational spectra between S0 and S1 states, the enhanced hydrogen-bonding interactions could reveale that promote the ESIPT tendency. Particularly, 3ePz3HC in aprotic nonpolar solvents with stronger hydrogen bonds shows an easier proton-transfer tendency. Paying attention to the changes of primarily related frontier molecular orbitals, we find that the charge transfer process occurs in excited-state molecules, and the reorganisation of charge densities should be conducive to promoting the ESIPT process. Simulated potential energy curves indicate that the ultrafast ESIPT reaction occurs for 3ePz3HC with low barriers, which could be further regulated and controlled by solvent polarity. HIGHLIGHTS Photo-induced, enhanced hydrogen bonding provides the tendency for ESIPT reaction of the 3ePz3HC fluorophore. Increased electronic densities around the O3 moiety of 3ePz3HC play vital roles in facilitating the ESIPT process. Aprotic nonpolar solvents are more favourable for accelerating the ESIPT behaviour for the 3ePz3HC compound.

Elastic and inelastic collision dynamics between soliton molecules and a single soliton.

Dissipative systems form various self-organized states owing to the abundant attractor structures. The study of the response of different self-organized states under collision perturbation is of great significance for understanding the dissipative nonlinear systems. The collision dynamics of single soliton and soliton molecules can not only assist the stability analysis of attractors, but also reveal the rich physical connotations of soliton interactions. Here, for the first time, the collision processes of single soliton and soliton molecules in different excited states are detected using the dispersive Fourier transform technology. The collision processes include the disintegration and rebuilding of soliton molecules as well as chaotic oscillating evolution, accompanied by the emergence of transition states such as triple binding state, soliton fusion and acceleration. According to whether the soliton molecule can return to its initial excited state, the collisions are classified as elastic and inelastic. The different interaction strength between solitons is an important condition for rebuilding stable soliton molecules. Numerical simulations show that the gain dynamics are the main physical origin of collisions. Our research will stimulate in-depth research on the interaction of self-organized states in nonlinear systems such as chemical molecules, and have potential applications in optical logic gates.

N2 vibrational excitation in atmospheric pressure ns pulse and RF plasma jets

Time-resolved N2 vibrational temperature and translational–rotational temperature in quasi-two-dimensional atmospheric pressure plasma jets sustained by ns pulse and RF discharges in nitrogen/noble gas mixtures are measured by the broadband vibrational Coherent Anti-Stokes Raman Scattering (CARS) . The results indicate a much stronger vibrational excitation in the RF plasma jet, due to the lower reduced electric field and higher discharge power. In a ns pulse discharge in N2/He, N2 vibrational temperature is significantly lower compared to that in N2/Ar, due to the more rapid vibration–translation (V–T) relaxation of nitrogen by helium atoms. In the RF plasma jets in N2/Ne and N2/Ar, the vibrational excitation increases considerably as the nitrogen fraction in the mixture is reduced. The experimental data in the RF plasma jet in N2/Ar jet are compared with the kinetic modeling predictions. The results indicate that nitrogen vibrational excitation in N2/Ar plasma jets with a small N2 fraction in the mixture (several percent) is controlled primarily by electron impact, anharmonic vibration–vibration (V–V) pumping, and V–T relaxation by N atoms. In comparison, V–V energy transfer from the vibrationally excited molecules in the first excited electronic state, N2(A3Σu +, v), which are generated primarily by the energy transfer from the metastable Ar atoms, has a minor effect on the vibrational populations of the ground electronic state, N2(X1Σg +, v). Although the discharge energy fraction going to electronic excitation is significant, the predicted quasi-steady-state N2(A3Σu +) number density, controlled by the energy pooling and quenching by N atoms, remains relatively low. Because of this, the net rate of N2(X1Σg +) vibrational excitation by the V–V energy transfer from N2(A3Σu +) is much lower compared to that by the direct electron impact. The results show that atmospheric pressure RF plasma jets can be used as sources of highly vibrationally excited N2 molecules and N atoms.

Excited-state intramolecular double proton transfer mechanism associated with solvent polarity for 9,9-dimethyl-3,6-dihydroxy-2,7-bis(4,5-dihydro-4,4-dimethyl-2-oxazolyl)fluorene compound

Excited-state intramolecular proton transfer (ESIPT) has been well investigated in recent years, whereas we investigated the system containing double hydrogen bonds. We explore the influence of solvent polarity on the proton transfer mechanism for 9,9-dimethyl-3,6-dihydroxy-2,7-bis(4,5-dihydro-4,4-dimethyl-2-oxazolyl)fluorene compound ((Oxa-OH)2). We consider three solvents with different polarities: cyclohexane, chloroform and acetonitrile. Various analytical methods indicate that hydrogen bonding is enhanced in the first excited state, which facilitates the proton transfer within the excited-state molecule. The frontier molecular orbital theory is employed to demonstrate that the system is subjected to photoexcitation to generate charge density redistribution. Three-dimensional potential energy surfaces are also constructed along the direction of hydrogen bond elongated, and their corresponding projection in the X-axis and Y-axis planes are plotted. The comparison of the potential barriers and the transition state structures of each proton transfer path reveals the excited-state intramolecular single proton transfer mechanism of the system. By comparing the potential barriers in different solvents, we also propose a mechanism that can modulate the excited-state proton transfer by changing the solvent polarity.

A new strategy for selective fluorescence detection of benzaldehyde and nitrobenzene

Low-cost and high-efficiency detection of benzene series in water and atmosphere is necessary for environmental detection. In this contribution, inspired by the design of hybrid local charge transfer (HLCT) excited state molecules, a small organic molecule fluorescent probe TPMCN was reported for the selective detection of benzaldehyde and nitrobenzene. The response of TPMCN to benzaldehyde showed obvious fluorescence enhancement and redshift and the limit of detection (LOD) was calculated to be 2.17 μM. In addition, the fluorescence response of TPMCN to gaseous and liquid nitrobenzene showed obvious fluorescence quenching within 5 s, and the low-cost TPMCN test strips exhibited a low LOD of 0.16 ppm for nitrobenzene and have excellent recovery properties.

Theoretical Determination of Rate Constants from Excited States: Application to Benzophenone.

A cost-effective method of theoretically predicting electronic-transition rate constants from the excited states of molecules is reported. This method is based on density functional theory calculations of electronic states and quantitative rate constant determination with the Fermi golden rule. The method is applied to the theoretical determination of the excited-state decay mechanism of photoexcited benzophenone, a representative molecule in photochemistry and biochemistry. Calculated rate constants for benzophenone are quantitatively consistent with experimental ones, which validates the reliability of our rate constant calculation. The calculated population kinetics indicate that S1 → T2 → T1 → S0 is the predominant decay pathway.

Influence of intramolecular hydrogen bond formation sites on fluorescence mechanism

The fluorescence mechanism of HBT-HBZ is investigated in this work. A fluorescent probe is used to detect HClO content in living cells and tap water, and its structure after oxidation by HClO (HBT-ClO) is discussed based on the density functional theory (DFT) and time-dependent density functional theory (TDDFT). At the same time, the influence of the probe conformation and the proton transfer site within the excited state molecule on the fluorescence mechanism are revealed. Combined with infrared vibrational spectra and atoms-in-molecules theory, the strength of intramolecular hydrogen bonds in HBT-HBZ and HBT-ClO and their isomers are demonstrated qualitatively. The relationship between the strength of intramolecular hydrogen bonds and dipole moments is discussed. The potential energy curves demonstrate the feasibility of intramolecular proton transfer. The weak fluorescence phenomenon of HBT-HBZ in solution is quantitatively explained by analyzing the frontier molecular orbital and hole electron caused by charge separation. Moreover, when strong cyan fluorescence occurs in solution, the corresponding molecular structure should be HBT-ClO(T). The influence of the intramolecular hydrogen bond formation site on the molecule as a whole is also investigated by electrostatic potential analysis.

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis.

The ARL Spectral Fitting application provides a free, publicly accessible, and fully transparent method for performing Franck-Condon Lineshape Analysis (FCLSA) on spectral data, in addition to CIE color coordinate determination and basic spectral processing. While some of the features may be found in commercial software or in programs made byacademic research groups, we believe that ARL Spectral Fitting is the only application that possesses all three of the aforementioned attributes. This program is intended as a standalone, GUI-based application for use by an average laboratory researcher without requiring any coding knowledge or proprietary software. In addition to the standalone executable hosted on ARL GitHub, the associated MATLAB files are available for use and further development. FCLSA augments the information found in luminescence spectra, providing meaningful insight into the relationship between the ground and excited states of a photoluminescent species. This insight is achieved by modeling spectra with two versions (modes) of an equation that are characterized by either four or six parameters, depending on which mode is used. Once optimized, the value of each of these parameters can be used to gain insight into the molecule, as well as to perform further analysis (for example, the free energy content of the excited-state molecule). This application provides tools for easy by-hand fitting of imported data, as well as two methods for optimizing this fit-damped least-squares fitting, powered by the Levenberg-Marquardt algorithm, and derivative-free fitting utilizing the Nelder-Mead simplex algorithm. Furthermore, estimations of sample color can be performed and reported in CIE and RGB coordinates.

Measurements of Metastable Molecules in Nonequilibrium Supersonic Flows

Nonintrusive laser diagnostics are used for the measurements of metastable nitrogen molecules in the lowest excited electronic state, , in a nonequilibrium flow, blowdown supersonic wind tunnel. The tunnel is operated with nitrogen at plenum pressures of Torr, with the flow expanding through a two-dimensional contoured nozzle to the Mach number of . The steady-state run time of the tunnel is approximately 10 s. The flow is excited by a repetitive nanosecond pulse discharge operated in the plenum or in the nozzle throat. Time-resolved absolute populations in the plenum are measured by single-pass, continuous wave tunable diode laser absorption spectroscopy (TDLAS). In the supersonic test section, absolute populations are measured by cavity ring down spectroscopy (CRDS), using a tunable pulsed laser system operated at 10 Hz. During each run, 50 single-shot ring down traces are acquired, demonstrating good shot-to-shot reproducibility. The results demonstrate that the cavity ring down time is not affected by the supersonic flow. populations and the flow temperature are inferred from the single-shot CRDS data. At the conditions when the flow is excited by the discharge in the nozzle throat, population in the supersonic test section is measured by both CRDS and TDLAS diagnostics. The two diagnostic techniques are complementary and can be used for characterization of nonequilibrium reacting flows over a wide range of pressures, including short-run-time high-enthalpy flow facilities.

Collisions in a dual-species magneto-optical trap of molecules and atoms

We study inelastic collisions between CaF molecules and 87Rb atoms in a dual-species magneto-optical trap. The presence of atoms increases the loss rate of molecules from the trap. By measuring the loss rates and density distributions, we determine a collisional loss rate coefficient k 2 = (1.43 ± 0.29) × 10−10 cm3 s−1 at a temperature of 2.4 mK. We show that this is not substantially changed by light-induced collisions or by varying the populations of excited-state atoms and molecules. The observed loss rate is close to the universal rate expected in the presence of fast loss at short range, and can be explained by rotation-changing collisions in the ground electronic state.

Synthesis, solvatochromism and electric dipole moment study of coumarin-fused quinoline: experimental and quantum chemical computational investigations

A new coumarin-fused quinoline push–pull fluorescent probe was designed, synthesized and characterized using $$^{\mathrm {1}}$$ H NMR, $$^{\mathrm {13}}$$ C NMR and mass spectrometry analysis. Electronic absorption and fluorescence studies of the synthesized probe were investigated in wide range of solvents of varying polarities, and the data were used to study its solvatochromic properties. The ground and excited state dipole moments of fluorescent probe were obtained from Bakhshiev’s and Bilot–Kawasaki’s equations by means of the solvatochromic shift method. The high value of dipole moment for the excited state over ground-state value was attributed to more polar excited state of molecule. Also, emission peak undergoes a bathochromic shift with an increase in the polarity of the solvent, confirming $${\varvec{\pi }} \rightarrow {\varvec{\pi }}{} \mathbf * $$ transition. The ground-state and excited-state dipole moments were calculated and compared using DFT calculations. Both experimental and computational studies revealed that excited-state dipole moment values are higher than corresponding ground-state value of studied compound. A new coumarin-fused quinoline push–pull fluorescent probe was designed, synthesized and characterized. The ground-state and excited-state dipole moments were calculated and compared using DFT calculations.

Probing Molecular Excited States by Atomic Force Microscopy.

By employing single charge injections with an atomic force microscope, we investigated redox reactions of a molecule on a multilayer insulating film. First, we charged the molecule positively by attaching a single hole. Then we neutralized it by attaching an electron and observed three channels for the neutralization. We rationalize that the three channels correspond to transitions to the neutral ground state, to the lowest energy triplet excited states and to the lowest energy singlet excited states. By single-electron tunneling spectroscopy we measured the energy differences between the transitions obtaining triplet and singlet excited state energies. The experimental values are compared with density functional theory calculations of the excited state energies. Our results show that molecules in excited states can be prepared and that energies of optical gaps can be quantified by controlled single-charge injections. Our work demonstrates the access to, and provides insight into, ubiquitous electron-attachment processes related to excited-state transitions important in electron transfer and molecular optoelectronics phenomena on surfaces.

Effect of electronic excitation on nuclear magnetic shielding as illustrated by nuclear spin optical rotation (NSOR) in liquids

Near resonance effect of NSOR generates new resonant light shift ω well separated from the ground state optical chemical shift ω 0 , from which the shielding in the excited state can be obtained. • The near resonance effect on the optical chemical shift in NSOR is theoretically studied. • The dressed state theory is employed to explore the near resonance effect. • New optical chemical shift line in NSOR spectrum due to excited state molecule is estimated. • Possibility of detecting the new optical chemical line is discussed. Conventional NMR is generally a technique for electronic ground state molecules. In this paper, the effect of electronic excitation on nuclear magnetic shielding is theoretically illustrated by Nuclear Spin Optical Rotation (NSOR) in liquids. The near-resonance effect on the optical chemical shift in NSOR is explored by using the dressed state theory. The results indicate that in the NSOR spectrum of a molecule with nucleus I = 1/2, such effect can induce a new optical chemical shift line with the circular frequency different from that of the ground state. From it the NMR shielding of a molecule in the electronic excited state can be got directly and used to analyze excited molecule structure in liquids. For multi-nuclei molecules, the result applies to each nucleus.