Electronic Transition Dipole Moments Research Articles

A Chiral Propeller‐Shaped Triple Helicene Shows Multi‐Resonant Thermally Activated Delayed Fluorescence

AbstractMulti‐resonant thermally activated delayed fluorescence (MR‐TADF) helicenes show great potential as chiral emitters due to their typically high photoluminescence quantum yield and that they emit circularly polarized luminescence. Here, a new propeller‐shaped chiral MR‐TADF helicene DiKTa3, integrating three DiKTa moieties, was designed and synthesized aiming to achieve co‐parallel electronic and magnitude transition dipole moments that would lead to a high dissymmetry factor, g. It emits at λPL of 491 nm, with a full width at half maximum of 52 nm and has a moderate ΔEST value of 0.24 eV in toluene. The separated (P,P,P) enantiomer shows an absorption dissymmetry factor |gabs| of 6.8×10−4 at 450 nm, which results from a lower symmetry conformation adopted by the compound in solution than the C3‐symmetric optimized structure. This work highlights the strong influence that geometry can have on the chiroptical properties of the emitter.

Asymetrical shape of C–He lines in the ultraviolet

ABSTRACT We present the first theoretical line profile calculations of the ultraviolet spectral lines of carbon perturbed by helium using a semiclassical collision approach and high-quality ab initio potentials and electronic transition dipole moments. The temperature range is from 5000 to 8000 K. These results are important for astrophysical modelling of spectra in atmospheres of white dwarf stars showing atomic carbon in an helium atmosphere. Beyond the conventional symmetrical Lorentzian core at low He density, these lines exhibit a blue asymmetric behaviour. This blue asymmetry is a consequence of low maxima in the corresponding C–He potential energy difference curves at short internuclear distances. The collisional profiles are carefully examined and their perturber density dependence allow to understand the various line shapes of the observed carbon spectral lines in helium-rich white dwarf photosphere where the He perturber densities reach several 1021 cm−3.

Electronic structure with spin-orbit coupling effect of HfH molecule for laser cooling investigations

The electronic structure, including the spin–orbit coupling effect of the HfH molecule, has been studied to determine if it can be cooled through Doppler and Sysphus laser cooling techniques. The multi-reference configuration interaction plus Davidson correction (MRCI + Q) method has been used to calculate its potential energy curves (P.E.C.s) in the Ω(±) and 2s+1Ʌ(+/-) representation. The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment µe, and the dissociation energies De agree very well with previously published work. In addition, we present in this work twenty new doublet and quartet states in the Ω(±) representation. The electronic transition dipole moment curves (TDMCs) between the lowest-lying electronic states have been investigated for the Δ - Π, Π - ∑+ and Δ - Φ transitions among specific Ω(±) states. The Franck-Condon factors (FCFs), the Einstein coefficient of spontaneous emission Aν′ν, and the radiative lifetime τ have been computed for the investigated transitions. In addition, properties of the molecules' electronic and vibrational states, such as the static dipole moment curves (D.M.C.s), the ionic character fionic, and the rovibrational constants are calculated. We deduce from our results that the HfH molecule is indeed a laser-cooling candidate that can reach a temperature as low as the nK regime. We present a complementary scheme with suitable experimental parameters. These results can be of great interest to experimental spectroscopists interested in ultracold diatomic molecules and their applications.

Molecular factors determining brightness in fluorescence-encoded infrared vibrational spectroscopy.

Fluorescence-encoded infrared (FEIR) spectroscopy is a recently developed technique for solution-phase vibrational spectroscopy with detection sensitivity at the single-molecule level. While its spectroscopic information content and important criteria for its practical experimental optimization have been identified, a general understanding of the electronic and nuclear properties required for highly sensitive detection, i.e., what makes a molecule a "good FEIR chromophore," is lacking. This work explores the molecular factors that determine FEIR vibrational activity and assesses computational approaches for its prediction. We employ density functional theory (DFT) and its time-dependent version (TD-DFT) to compute vibrational and electronic transition dipole moments, their relative orientation, and the Franck-Condon factors involved in FEIR activity. We apply these methods to compute the FEIR activities of normal modes of chromophores from the coumarin family and compare these predictions with experimental FEIR cross sections. We discuss the extent to which we can use computational models to predict the FEIR activity of individual vibrations in a candidate molecule. The results discussed in this work provide the groundwork for computational strategies for choosing FEIR vibrational probes or informing the structure of designer chromophores for single-molecule spectroscopic applications.

Homogeneous Dephasing in Photosynthetic Bacterial Reaction Centers: Time Correlation Function Approach.

A new tractable linear electronic transition dipole moment time correlation function (ETDMTCF) that accurately accounts for electronic dephasing, asymmetry, and width of 1-phonon profile, which the zero-phonon line (ZPL) contributes to it, in Rhodopseudomonas viridis bacterial reaction center is derived. This time correlation function proves to be superior to other frequency-domain expressions in case of strong electron-phonon coupling (which is often the case in bacterial RCs and pigment-protein complexes), many vibrational modes involved, and high temperature, whereby more vibronic and electronic (sequence) transitions would arise. The Fourier transform of this ETDMTCF leads to asymmetric multiphonon profiles composed of Lorentzian distribution and Gaussian distribution on the high- and low-energy sides, respectively, whereby the overtone widths fold themselves with that of the one-phonon profile. This ETDMTCF also features expedient computation in large systems using asymmetric phonon profiles to account correctly for dephasing and pigment-protein interaction (electron-phonon coupling). The derived ETDMTCF allows computing all nonlinear optical signals in both time and frequency domains, through the nonlinear dipole moment time correlation functions (as guided by nonlinear optical response theory) in line with the eight Liouville space pathways. The linear transition dipole moment time correlation function is of a central value as the nonlinear transition dipole moment time correlation function is expressed in terms of the linear transition dipole moment time correlation function, derived herein. One of the great advantages of presenting this ETDMTCF is its applicability to nonlinear transition dipole moment time correlation functions in line with the eight Liouville space pathways needed in computing nonlinear signals. As such, there is more to the utility and applicability of the presented ETDMTCF besides computational expediency and efficiency. Results show good agreement with the reported literature. The intimate connection between a one-phonon profile and the corresponding bath spectral density in photosynthetic complexes is discussed.

Breaking the Condon Approximation for Light Emission from Metal Halide Perovskite Nanocrystals.

The idea that the electronic transition dipole moment does not depend upon nuclear excursions is the Condon approximation and is central to most spectroscopy, especially in the solid state. We show a strong breakdown of the Condon approximation in the time-resolved photoluminescence from CsPbBr3 metal halide perovskite semiconductor nanocrystals. Experiments reveal that the electronic transition dipole moment increases on the 30 ps time scale due to structural dynamics in the lattice. Ab initio molecular dynamics calculations quantitatively reproduce experiments by considering excitation-induced structural dynamics.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. I. Response function theory.

Fluorescence-encoded infrared (FEIR) spectroscopy is an emerging technique for performing vibrational spectroscopy in solution with detection sensitivity down to single molecules. FEIR experiments use ultrashort pulses to excite a fluorescent molecule's vibrational and electronic transitions in a sequential, time-resolved manner, and are therefore sensitive to intervening vibrational dynamics on the ground state, vibronic coupling, and the relative orientation of vibrational and electronic transition dipole moments. This series of papers presents a theoretical treatment of FEIR spectroscopy that describes these phenomena and examines their manifestation in experimental data. This first paper develops a nonlinear response function description of Fourier-transform FEIR experiments for a two-level electronic system coupled to multiple vibrations, which is then applied to interpret experimental measurements in the second paper [L. Whaley-Mayda et al., J. Chem. Phys. 159, 194202 (2023)]. Vibrational coherence between pairs of modes produce oscillatory features that interfere with the vibrations' population response in a manner dependent on the relative signs of their respective Franck-Condon wavefunction overlaps, leading to time-dependent distortions in FEIR spectra. The orientational response of population and coherence contributions are analyzed and the ability of polarization-dependent experiments to extract relative transition dipole angles is discussed. Overall, this work presents a framework for understanding the full spectroscopic information content of FEIR measurements to aid data interpretation and inform optimal experimental design.

Chiral Iron Oxide Supraparticles Enable Enantiomer-Dependent Tumor-Targeted Magnetic Resonance Imaging.

The chemical, physical and biological effects of chiral nanomaterials have inspired general interest and demonstrated important advantages in fundamental science. Here, chiral iron oxide supraparticles (Fe3 O4 SPs) modified by chiral penicillamine (Pen) molecules with g-factor of ≈2 × 10-3 at 415nm are fabricated, and these SPs act as high-quality magnetic resonance imaging (MRI) contrast agents. Therein, the transverse relaxation efficiency and T2 -MRI results demonstrated chiral Fe3 O4 SPs have a r2 relaxivity of 157.39 ± 2.34 mM-1 ·S-1 for D-Fe3 O4 SPs and 136.21 ± 1.26 mM-1 ·S-1 for L-Fe3 O4 SPs due to enhanced electronic transition dipole moment for D-Fe3 O4 SPs compared with L-Fe3 O4 SPs. The in vivo MRI results show that D-Fe3 O4 SPs exhibit two-fold lower contrast ratio than L-Fe3 O4 SPs, which enhances targeted enrichment in tumor tissue, such as prostate cancer, melanoma and brain glioma tumors. Notably, it is found that D-Fe3 O4 SPs have 7.7-fold higher affinity for the tumor cell surface receptor cluster-of-differentiation 47 (CD47) than L-Fe3 O4 SPs. These findings uncover that chiral Fe3 O4 SPs act as a highly effective MRI contrast agent for targeting and imaging broad tumors, thus accelerating the practical application of chiral nanomaterials and deepening the understanding of chirality in biological and non-biological environments.

Photophysical Exploration of Alectinib and Rilpivirine: Insights from Theory and Experiment.

Due to the excellent characteristics of fluorescence-based imaging, such as non-invasive detection of biomarkers in vitro and in vivo with high sensitivity, good spatio-temporal resolution and fast response times, it has shown significant prospects in various applications. Compounds with both biological activities and fluorescent properties have the potential for integrated diagnosis and treatment application. Alectinib and Rilpivirine are two excellent drugs on sale that represent a clinically approved targeted therapy for ALK-rearranged NSCLC and have exhibited more favorable safety and tolerance profiles in Phase III clinical trials, ECHO and THRIVE, respectively. The optical properties of these two drugs, Alectinib and Rilpivirine, were deeply explored, firstly through the simulation of molecular structures, electrostatic potential, OPA/TPA and emission spectral properties and experiments on UV-vis spectra, fluorescence and cell imaging. It was found that Alectinib exhibited 7.8% of fluorescence quantum yield at the 450 nm excited wavelength, due to a larger electronic transition dipole moment (8.41 Debye), bigger charge transition quantity (0.682 e) and smaller reorganization energy (2821.6 cm-1). The stronger UV-vis spectra of Rilpivirine were due to a larger electron-hole overlap index (Sr: 0.733) and were also seen in CDD plots. Furthermore, Alectinib possessed obvious active two-photon absorption properties (δmaxTPA* ϕ = 201.75 GM), which have potential TPA imaging applications in bio-systems. Lastly, Alectinib and Rilpivirine displayed green fluorescence in HeLa cells, suggesting the potential ability for biological imaging. Investigation using theoretical and experimental methods is certainly encouraged, given the particular significance of developing integrated diagnosis and treatment.

Electronic transition dipole moments from time-independent excited-state density-functional tight-binding.

Computationally inspired design of organic electronic materials requires robust models of not only the ground and excited electronic states but also of transitions between these states. In this work, we introduce a strategy for obtaining electronic transition dipole moments for the lowest-lying singlet-singlet transition in organic chromophores from time-independent excited-state density-functional tight-binding (ΔDFTB) calculations. Through small-molecule benchmarks and applications to larger chromophores, we explore the accuracy, potential, and limitations of this semiempirical strategy. While more accurate methods are recommended for small systems, we find some evidence for the method's potential in high-throughput molecular screening applications and in the analysis of molecular dynamics simulations.

Theoretical Insights on the Sensing Performance for Newly-synthesized Two-photon Fluorescent N2H4 Probes Based on Spirobifluorence.

The development of fluorescent probe for hydrazine (N2H4) detection has attracted much attention due to the important role of N2H4 plays in the fields of medicine, agriculture, biology and environments. In this paper, the optical properties and water solubility of two novel two-photon fluorescent molecular probes (Probe1 and Probe2) before and after the reaction with N2H4 are studied by using the density function theory. The results show that electronic distribution and transition dipole moment of the probes are obviously changed after the reaction with N2H4, thus the optical properties of the molecules are influenced and the detection of N2H4 are realized. In addition, photoinduced electron transfer processes for Probe1 and Probe2 in the presence of N2H4 are theoretically characterized, which explains the experimental observations from the microscopic mechanism. Special attention has been paid on the analysis of the two-photon absorption for the probes with the absence and presence of N2H4 by the response theory method. Both probes with good water solubility show large variation on the two-photon absorption cross section when reacts with N2H4. In particular, the two-photon absorption response of Probe2 is more obvious, so it possesses preferable two-photon fluorescence microscopic imaging ability. More importantly, the receptor effect on the sensing performances of the probes are demonstrated, providing a theoretical reference for the design and synthesis on more efficient two-photon fluorescence N2H4 probes. Our study provides necessary information on the response mechanism of the studied chemosensors and helps to establish the relationship between the structure and optical properties of two-photon fluorescence N2H4 probes.

Optical–optical double resonance study of the H' 1 (1D2) ion-pair state of I35Cl: Rovibrational structure and electronic transition dipole moment function

The H' 1 (1D2) ion-pair state of I35Cl, which correlates to the I+ (1D2) + Cl− (1S0) dissociation limit, was analyzed spectroscopically by H' 1 (1D2) ← A3Π1 ← X1Σ+ optical–optical double resonance excitation. In total, 751 transitions covering 0 ≤ vH' ≤ 20 and 10 ≤ JH' ≤ 41 were observed. An e/f-parity splitting (Ω-type doubling) in the H' 1 (1D2) state was observed. By fitting 656 transitions to Dunham type expansion, Dunham coefficients for the H' 1 (1D2) state were determined to be Y00 = 51615.194(14), Y10 = 184.2440(59), Y20 = −0.63083(67), Y30 = 0.001400(21), Y01 = 0.05780468(82), Y11 = −2.2465(19) × 10−4, and Y21 = −2.227(88) × 10−7 cm−1. The vibration-dependent Ω-type doubling constants were determined to be q0 = 1.97(17) × 10−5, q1 = 8.76(38) × 10−6, and q2 = −3.498(18) × 10−7 cm−1. The electronic transition dipole moment function of the H' 1 (1D2) – A3Π1 transition in the range of 2.977–3.683 Å was determined experimentally by analyzing the dispersed ultraviolet (UV) fluorescence spectra combined with the fluorescence lifetime of the H' 1 (1D2) state.

Nanoimaging of the Edge-Dependent Optical Polarization Anisotropy of Black Phosphorus.

The electronic structure and functionality of 2D materials is highly sensitive to structural morphology, not only opening the possibility for manipulating material properties but also making predictable and reproducible functionality challenging. Black phosphorus (BP), a corrugated orthorhombic 2D material, has in-plane optical absorption anisotropy critical for applications, such as directional photonics, plasmonics, and waveguides. Here, we use polarization-dependent photoemission electron microscopy to visualize the anisotropic optical absorption of BP with 54 nm spatial resolution. We find the edges of BP flakes have a shift in their optical polarization anisotropy from the flake interior due to the 1D confinement and symmetry reduction at flake edges that alter the electronic charge distributions and transition dipole moments of edge electronic states, confirmed with first-principles calculations. These results uncover previously hidden modification of the polarization-dependent absorbance at the edges of BP, highlighting the opportunity for selective excitation of edge states of 2D materials with polarized light.

Collision-induced satellite in the blue wing of the Balmer-β line and consequences on the Balmer series

In this paper we emphasize the non-Lorentzian behavior of the Balmer series in helium-dominated DBA white dwarf stars for which the decades-old problem exists for the determination of the hydrogen abundance. In a very recent work, we have shown that quasi-molecular line satellites due to H-He and H-H collisions are responsible for the asymmetrical shape of the Lyman-α lines observed with the Cosmic Origin Spectrograph and that a similar asymmetry exists for the Balmer-α line profiles. In continuation with very recent work, where the n = 2, 3 potential energies and transition dipole moments from the ground state were determined, here, we present accurate H-He potential energies and electronic transition dipole moments concerning the molecular states correlated with H(n = 4)+He and their transition dipole moments with the states correlated with H(n = 2)+He. Those new data are used to provide a theoretical investigation of the collisional effects in the blue wing of the Balmer-β line of H perturbed by He. Because of the general trend characterizing the repulsive Σ states of the potential energies involved in the Balmer series, the amplitude in the core of the line is decreasing very fast with the order of the series when the helium density gets as large as 1021 cm−3. This study is undertaken by applying a unified theory of spectral line broadening that is valid at very high helium densities found in DZA white dwarf stars. The treatment includes collision-induced line satellites due to asymptotically forbidden transitions, and it explains the asymmetry observed in their spectra.

Model-free analysis of molecular orientation in amorphous organic semiconductor films for understanding its formation dynamics: Methods and systematic investigation

To achieve high-performance organic light-emitting diodes (OLEDs), various amorphous organic semiconductor materials were developed, and the higher-order structure of their films and their formation dynamics were investigated. In particular, their molecular orientations were widely analyzed because it significantly affects optical and electrical properties of the OLEDs. However, conventional methods of the analysis of the orientation order parameter ( S ) need the construction of an anisotropic optical model, which brings a certain degree of analytical error and thus makes it difficult to assess the slight changes in S values arising from differences in experimental conditions. In this study, we present a simple model-free analytical method to estimate S values, named "QACIOS", that avoids the significant analytical errors and applies to various OLED materials, including materials that easily crystallize. In applying the method to UV/visible and IR spectral regions, the S values of electronic and vibrational transition dipole moments in the films can be simply estimated. The orientations of functional groups in single-layer and multilayer samples are obtainable separately, and in situ measurements are also demonstrated. Furthermore, we present a systematic analysis of the dependence of S on experimental conditions during sample fabrication such as deposition rate, substrate temperature, and substrate surface. From this analysis, the difference in formation dynamics of the molecular orientation of two structural isomers of OLED materials is quantitatively clarified, further demonstrating the usefulness of the method. A model-free simple analytical method by quantitative absorbance comparison with an isotropically oriented standard (QACIOS) is applied to systematic investigation of orientations of long molecular axis and functional groups in amorphous organic semiconductor films and their formation dynamics. • A model-free simple analytical method for reliable estimation of orientation order parameter is proposed and applied to many kinds of amorphous OLED materials. • Orientation analysis of functional groups in single-layer and multilayer samples are performed. • The difference in formation dynamics of molecular orientation of two OLED isomers is clarified quantitatively. • The method can be a commonly-used standard method for orientation analysis of OLED films.

Relative molecular orientations in organic optoelectronic films probed via polarization-selected UV/IR mixed frequency ultrafast spectroscopy

Molecular packing patterns are crucial factors determining electron/energy transfer processes that are critical for the optoelectronic properties of organic thin film devices. Herein, the polarization-selective ultraviolet/infrared (UV/IR) mixed frequency ultrafast spectroscopy is applied to investigate the relative molecular orientations in two organic thin films of 7-(diethylamino)coumarin-3-carboxylic acid (DEAC) and perylene. The signal anisotropy changes caused by intermolecular energy/electron transfers are utilized to calculate the cross angles between the electronic transition dipole moment of the donor and the vibrational transition dipole moments of the acceptor, yielding the relative orientation between two adjacent molecules. Using this method, the relative orientation angle in DEAC film is determined to be 53.4°, close to 60° of its single crystalline structure, and that of the perylene film is determined to be 6.2°, also close to −0.2° of its single crystalline structure. Besides experimental uncertainties, the small difference between the angles determined by this method and those of single crystals also results from the fact that the thin film samples are polycrystalline where some of the molecules are amorphous.

Collisional effects in the blue wing of the Balmer-α line

In order to investigate the near wing of the Lyman-α line, accurate line profile calculations and molecular data are both required due to the existence of a close line satellite responsible for its asymmetrical shape. Lyman-α lines observed with the Cosmic Origin Spectograph on the Hubble Space Telescope show this peculiarity in the spectra of DBA and DA white dwarf stars. A similar asymmetrical shape in the blue wing can be predicted in the Balmer-α line of H perturbed by He and H atoms. In continuation with a very recent work on the Lyman-α line, where the n = 2 potential energies and transition dipole moments from the ground state were determined, we present new accurate H-He potential energies and electronic transition dipole moments involving the molecular states correlated with H(n = 3)+He and their transition dipole moments with the states correlated with H(n = 2)+He. Those new data and existing molecular data for H(n = 2,3)-H are used to provide a theoretical investigation of the collisional effects in the blue wing of the Balmer-α line of H perturbed by He and H atoms. We note the consequences for the Balmer-α line shape in the physical conditions found in the cool atmosphere of DZA white dwarfs where helium densities may be as high as 1021 cm−3. This study is undertaken with a unified theory of spectral line broadening valid at very high helium densities.

Accelerating molecular property calculations with semiempirical preconditioning.

Computing ab initio molecular linear response properties, e.g., electronic excitation energies and transition dipole moments, requires the solution of large eigenvalue problems or large systems of equations. These large eigenvalue problems or large systems of equations are commonly solved iteratively using Krylov space algorithms, such as the Davidson algorithm for eigenvalue problems. A critical ingredient in Krylov space algorithms is the preconditioner, which is used to generate optimal update vectors in each iteration. We propose to use semiempirical approximations as preconditioners to accelerate the calculation of ab initio properties. The crucial advantage to improving the preconditioner is that the converged result is unchanged, so there is no trade-off between accuracy and speedup. We demonstrate our approach by accelerating the calculation of electronic excitation energies and electric polarizabilities from linear response time-dependent density functional theory using the simplified time-dependent density functional theory semiempirical model. For excitation energies, the semiempirical preconditioner reduces the number of iterations on average by 37% and up to 70%. The semiempirical preconditioner reduces the number of iterations for computing the polarizability by 15% on average and up to 33%. Moreover, we show that the preconditioner can be further improved by tuning the empirical parameters that define the semiempirical model, leading to an additional reduction in the number of iterations by about 20%. Our approach bridges the gap between semiempirical models and ab initio methods and charts a path toward combining the speed of semiempirical models with the accuracy of ab initio methods.

Electronic dephasing in mixed quantum–classical molecular systems using the spin-boson model

Pure electronic dephasing is investigated using the spin-boson Hamiltonian in mixed quantum–classical environment. The spin-boson model used here is a composite system made up of a quantum subsystem, an electronic 2-level subsystem linearly coupled to harmonic vibrations, interacting with a classical bath. Experimental results for a multitude of molecular systems indicate that the zero-phonon line (ZPL) profile is determined by electronic dephasing, which is not accounted for in the multimode Brownian oscillator (MBO) model due to the unphysical contribution from the MBO bath modes to the ZPL profile. Mixed quantum–classical dynamics formalism of non-equilibrium systems is employed to assess the contribution of the bath modes to pure electronic dephasing by probing the ZPL profile when coupled to a classical bath in the mixed quantum–classical condensed systems. Pure electronic dephasing is discussed in the context of mixed quantum–classical dynamics formalism which starts with mixed quantum–classical Liouville equation in a mixed quantum–classical environment. It is noteworthy, however, that the fundamental difference between the fully quantum MBO model and the mixed quantum–classical Brownian oscillator, is that the zero-phonon line calculated by the former shows unphysical asymmetry on the low-energy side as it has not been observed in real systems, whereas the ZPL reported herein eliminates this asymmetry. A systematic approach using matrix mechanics is developed to treat this phenomenon. To this end, a closed-form expression of linear and nonlinear optical electronic transition dipole moment time correlation functions in a dissipative media are derived. Linear absorption spectra and 4-wave mixing signals at various temperatures showing a sound thermal broadening, temporal decay, and accurate pure dephasing further ratify the applicability and correctness of the mixed quantum–classical dynamics approach to spectroscopy and dynamics are computed.

Excited state distribution function for probing Herzberg–Teller vibronic coupling using linear optical response theory: Application to glassy pheophytin a

The goal of the present work is to develop an excited-state distribution function that can be used to calculate electronic transition dipole moment time correlation functions at a considerably low computational cost. An additional merit of the distribution function is its capability to probe the Hertzberg-Teller vibronic coupling effect in terms of the previously reported Condon correlation functions in the literature without having to start from the equilibrium density operator to probe spectral non-Condon effects, thereby exploring Hertzberg-Teller vibronic coupling by building on the Condon regime. It is easily extendable to anharmonic systems. Model calculations are reported to show the high degree of accuracy and computational efficiency of the presented approach. Application to a photosynthetic system such as pheophytin a in triethylamine is provided.