Molecular Origins of the Optical Response of Nile Red in Model Aerosol Aqueous Ionic Environments

Abstract

Aerosol particles are ubiquitous and their physicochemical properties such as hygroscopicity, phase state, pH, and viscosity influence processes ranging from virus transmission to atmospheric light scattering and chemical reactivity. While direct in situ measurements of these properties have been experimentally challenging, fluorescence probe spectroscopy has emerged as a powerful technique for in situ aerosol analysis. The fluorophore Nile red (NR) has seen recent use in aerosol studies to indicate phase state in chemically complex environments, though open questions remain surrounding the molecular origins and influence of common aerosol chemical environments, notably high ionic strengths, on NR optical properties. Here, time-dependent density functional theory quantum mechanics/molecular mechanics calculations were employed to calculate the excitation energies of NR in aqueous environments of ionic strengths up to 1 M NaCl. The results revealed both a blueshift in the average excitation energy and a broadening of the distribution of energies with increasing ionic concentration. The relative roles of ion-induced changes in NR conformation versus solvation effects for a given NR conformation were investigated and both were found to play a substantial role in the total blueshift. Overall, this study advances molecular-level understanding of the solvatochromic behavior of NR and structurally similar fluorophores in aqueous ionic environments, supporting effective selection and application of fluorescent probes for characterizing aerosol physicochemical properties.

Graphical Abstract

1. Introduction

Aerosols are ubiquitous and intersect with human health and the environment in multiple ways. In the environment, atmospheric aerosols scatter or absorb solar radiation depending on their optical properties, ultimately affecting the Earth’s radiative balance.^1,2 Aerosol particles also play a key role in cloud nucleation thereby affecting cloud properties and behaviors and further impacting the Earth’s climate.³ Aerosols also have major direct implications for human health, with prolonged exposure to particulate matter contributing to a range of health issues and more than 6 million deaths each year.^4–6 Furthermore, aerosols that are produced via exhalation from infected individuals are implicated in the transmission of respiratory diseases.^{7, 8} The transmissibility of a virus can be impacted by environmental factors such as relative humidity and temperature, though the mechanism of these effects remains incompletely understood. Altogether, understanding the physical and chemical properties of aerosols is a fundamental step towards understanding and ultimately controlling these impacts on human health.

Despite this importance, aerosols remain challenging to study experimentally due to a range of factors including small particle sizes and low mass densities. In particular, the aerosol particles with the longest residence time in air and therefore implicated in long-range disease transmission fall in the submicron size range for which current analytical techniques are limited in their abilities for sensitive and non-perturbative physicochemical analysis.⁹ Additionally, aerosol particles frequently are not comprised of a single well-mixed phase at thermodynamic equilibrium.¹⁰ Instead, the particles can possess multiple phases and varying morphologies and often exist in metastable states which limits our ability to create representative chemical environments in bulk samples that are more amenable to study and highlights the importance of performing analyses in situ.^{11, 12} One of the few techniques capable of measuring the physicochemical properties of submicron aerosols in situ is fluorescence probe spectroscopy.^13–17

This technique involves the incorporation into the aerosol of interest of fluorescent probe molecules that exhibit changes in their optical properties depending on the properties of the surrounding medium.^{18, 19} Nile red (NR) is one such fluorophore that has seen extensive recent interest as a probe for aerosol environments.^{13, 19–21} The absorbance and fluorescence emission spectra of NR exhibit substantial shifts as a function of polarity of the surrounding media, a phenomenon known as solvatochromism.²² This shift is caused by the difference in dipole moment between the ground and excited electronic states of the molecule because the more polar excited state is preferentially solvated compared to the ground state by polar environments.^23–25 While the use of NR in life science contexts is well-established,^{26, 27} the distinct characteristics of aerosol chemical environments, in particular their high ionic strengths, are expected to influence the optical properties of NR and other structurally similar solvatochromic fluorophores in ways that are not yet fully understood. In one illustrative example, the high ionic strengths present in model inorganic aerosols were found to complicate the interpretation of the pH-dependent fluorescence of the fluorophore quinaldine red.²⁸ A thorough molecular-level understanding of how these environments influence the optical properties of NR is required to maximally and accurately interpret spectroscopic measurements as well as to guide probe selection or ultimately inform the rational design of advantageous fluorophores.

Computational studies can directly offer molecular-scale insights regarding the influence of solvation environments on optical processes that are challenging or impossible to gain from current experimental methodologies. Recent advances in excited state electronic structure methods have enabled the prediction of fluorescence spectra through excited state geometry optimization and emission calculations.^29–31 However, for situations where a substantial number of solvent molecules must be explicitly treated such as those considered here, rigorous fluorescence calculations would lead to intractable computational cost as noted by Patra et al.³² Hence, here we computationally investigate the excitation energies of NR, which have been experimentally observed to exhibit similar solvatochromism as those of emission.³³

Vertical electronic excitation energies may be obtained directly from the linear response (LR) approach at the fixed geometry of the ground state. The most successful wave function approximation in the contemporary electronic-structure theory has been the coupled cluster (CC) hierarchy of models,^34–37 as it ensures a systematic decrease of error across the hierarchy, and a rapid convergence towards the exact solution of the Schrödinger equation.³⁸ However, this high accuracy comes at a high cost as, for example, the CCSDT model,^{39, 40} which contains all single (S), double (D), and triple (T) replacements and produces excitation energies with an error as low as 0.02 eV,⁴¹ has computational complexity that scales as the eighth power with the system size.

While the lowest-order perturbative approximations to the CC hierarchy, such as the CIS(D) model⁴² scale only with the fifth-power of the system size, this scaling may still be prohibitively expensive for larger molecules or when the solvation environment must be included, as here. For such systems, time-dependent density functional theory (TD-DFT)^43–45 is routinely employed due to its formal fourth-power scaling and practical, fast implementations.⁴⁶ TD-DFT is rooted in Runge–Gross theorem⁴⁷ stating that there exists a one-to-one mapping between the time-dependent electron density for a given initial state and the time-dependent external potential which, among others, induces electronic transitions in a system. This means that DFT potentials developed for ground-state calculations may also be employed in TD-DFT excited state calculations. The time-dependent Kohn-Sham (KS) equations⁴⁷ thus employ an effective, time-dependent KS potential that consists of the external potential, the Hartree potential, and the exchange-correlation potential. The latter describes both time-independent and time-dependent electronic exchange and correlation effects. The most popular way of obtaining excitation energies within TD-DFT is via the application of response function theory to DFT.^{48, 49} In the general linear response function theory, the ground-to-excited-state excitation energies occur as poles (vanishing denominators) of the linear response function and may conveniently be obtained as eigenvalues of an algebraic eigenvalue problem.^{50, 51}

In the particular case of TD-DFT, this eigenvalue problem is known as Casida’s equation, ⁴⁸ which may be viewed as the random-phase approximation pseudo-eigenvalue problem⁵⁰ with additional terms coming from the exchange-correlation potential. While, contrary to CC theory, no systematic hierarchy of functionals exists in DFT that would allow for estimating the accuracy of a DFT result prior to comparison with experiment, DFT results for a given class of molecules and properties may be benchmarked against the CC models.^52–58 Those benchmark studies clearly show that range-separated functionals are a good choice for correct description of excited states.⁵⁷ Among range-separated hybrids, CAM-B3LYP⁵⁹ shows a good performance for excitation energies and has successfully been applied in previous studies of NR.^{60, 61}

The simplest way of incorporating solvation effects is via implicit solvation models,⁶² in which the solvent is treated as a dielectric medium and the solute molecule is placed in a molecular-shaped cavity. Continuum solvation models are widely used to incorporate bulk solvent effects into quantum chemical calculations without the computational expense of explicitly treating individual solvent molecules.⁶³ The mutual polarization between the solvent and the solute is calculated from the Poisson equation, where the quantum-mechanical charge density of the solute interacts with the potential generated by the dielectric medium, the latter represented by point charges on the cavity surface. This implicit solvent approach has mainly been realized via the polarizable continuum model (PCM)^{64, 65} and conductor-like screening model (COSMO),^{66, 67} and later extended to a model dubbed solvation model density (SMD),⁶⁸ which, in addition to the structureless bulk solvent presence, also models short-range interactions between the solute molecule and the molecules present in the first solvation shell of the solvent. The inclusion of the latter effect, yet retaining the implicit nature of the solvent, has been achieved in SMD by parametrizing it on a large training set of 2821 solvation data of varied nature, including ionic solvents.⁶⁸

In cases where details of interactions between the solute and solvent molecules become crucial for a physically meaningful description – such as hydrogen bonding, proton transfer, modeling of phase interfaces, interaction of (solvated) ions with a solute, etc. – the atomistic structure of the solvent needs to be included and necessitates the employment of molecular dynamics (MD).^69–71 As the cost of ab initio MD quickly becomes prohibitively high, one can use instead a hybrid implicit-explicit solvation scheme, in which snapshots from classical MD simulations are employed in quantum-mechanics/molecular-mechanics (QM/MM) calculations. Here, the QM region includes the solute molecule and solvent molecules of tractable size while the remainder of the solvent is treated in the MM manner.^72–74

Within this landscape of computational methods, early computational investigations into the solvatochromic optical properties of NR primarily used implicit solvent models and/or employed low-level ab initio methods (Hartree-Fock, configuration-interaction singles, second-order perturbation theory), DFT hybrid functionals without long-range correction (O3LYP⁷⁵ or B3LYP,^76–79 combined with a basis set either without diffuse functions or with only one set of diffuse functions on second-row atoms), or semi-empirical methods.^80–84 Subsequent studies (employing CAM-B3LYP or CASPT2 and a flexible basis set with diffuse functions) extended these efforts by incorporating hybrid implicit–explicit solvation schemes to better reproduce experimental excitation energies and to elucidate the roles of hydrogen bonding^{27, 60, 85–87} and, in one study, the specific influence of water on the optical response of NR.⁸⁸ Parallel investigations on other molecular fluorophores have explored solvent effects using both implicit and explicit approaches.^{72, 89–93} Previous studies specifically addressing chromophore interactions within model aerosol environments are limited. However, prior solvatochromic and ionochromic studies have demonstrated that local solvation and ionic interactions can influence the absorption properties of chromophores.^94–96 These findings motivate the present QM/MM investigation of NR in aqueous environments relevant to aerosol studies.

Herein, a computational study is undertaken to understand the molecular origins of NR behavior in an aqueous solvation environment with a high concentration of ions. To balance computational efficiency and accuracy as described previously, the solvation environment is represented using classical MD simulations⁹⁷ combined with a TD-DFT based QM/MM model.⁹⁸ Sodium chloride was chosen to represent the model ionic environment as it constitutes the dominant inorganic salt in respiratory⁹⁹ (as well as sea spray) aerosols. Additionally, a neutral, unprotonated NR molecule was studied consistent with the approximate pH range of 7.5 - 11 for respiratory aerosols.^{100, 101}

2. Computational Methods

2.1. Electronic Structure Calculations

All quantum chemical calculations were performed using the Gaussian 16 software.¹⁰² Ground and excited state calculations were carried out employing DFT and TD-DFT, respectively, using the long-range-corrected hybrid functional CAM-B3LYP,⁵⁹ which, based on ample numerical evidence,^{52–58, 103} is suitable for the calculation of the one- and two-photon excitation in general, and for predictions of charge transfer excitation processes and the accurate description of excitations in NR, in particular.^{60, 61} Other range-separated functionals such as ωB97X-V¹⁰⁴ and ωB97X-D¹⁰⁵ are also expected⁵⁷ to be suitable for these purposes. To further substantiate the choice of CAM-B3LYP, we perform in Section 3.1 a comparison of NR excitation (in solution with various ionic strengths) obtained from CAM-B3LYP and CIS(D), and also benchmark CAM-B3LYP and CIS(D) gas-phase excitation energies of diethylamine (the donor moiety in the charge-transfer excitation in NR) and p-benzoquinone (the acceptor moiety model) against CC with singles and doubles excitations (CCSD).¹⁰⁶ All excitation energy calculations performed here (both TD-DFT and wave-function-based) correspond to vertical transitions and are obtained with the LR approach.

The diffuse aug-cc-pVDZ basis^107–109 set was used. The comparison of the first three excitation energies of gas-phase NR calculated with CAM-B3LYP/aug-cc-pVDZ and CAM-B3LYP/aug-cc-pVTZ shows virtually no differences (see SI, Table S1), indicating that the aug-cc-pVDZ basis is practically saturated. TD-DFT calculations involving implicit solvation effects via the SMD model were performed using the LR approach as appropriate for the excitation process studied here.¹¹⁰

2.2. Molecular Dynamics-Based Explicit Solvent Model

MD simulations were performed using the Amber 23 package.¹¹¹ Simulations were performed on a single neutral NR molecule solvated in pure water, 0.5 M NaCl, or 1 M NaCl. NR was parameterized using the generalized amber force field (GAFF2) as implemented in AmberTools23.¹²⁶ Geometry optimization of NR was performed via the Gaussian 16 software using quantum mechanical calculations at the B3LYP/6-311++G**^{112, 113} level of theory, which is expected to perform adequately for the purposes of this geometry optimization.⁸⁵ Antechamber was then used to assign GAFF2 atom types and calculate partial atomic charges with the extended Austin Model 1 – bond charge correction (AM1-BCC[X]) method.¹¹⁴ This was followed by using the parmchk2 utility to identify and assign any missing bonded or nonbonded parameters. The topology and coordinate files were then generated using the tleap module of AmberTools23.¹²⁶ An unprotonated NR molecule was studied here, though we acknowledge that protonation effects would likely become important in strongly acidic environments. While there is not a definitive widely accepted pKa value for the conjugate acid of NR, it is suggested to have a pKa of approximately 4.8¹¹⁵ which is chemically reasonable given the extended conjugation of the chromophore and the higher pKa of N,N-dimethylaniline of approximately 6.5.¹¹⁶ Experimentally, NR fluorescence has been reported to be largely independent of pH between 4.5 and 8.5,¹¹⁷ consistent with the molecule being unprotonated in the near-neutral pH range of primary interest here.

A rectangular box of 20 Å with approximately 4000 water molecules was used throughout the simulations. Periodic boundary conditions were imposed with a cut-off distance for long-range interactions of 10 Å. A total of 47 and 94 each of Na⁺ and Cl⁻ ions were included in the 0.5 and 1 M solutions, respectively. The Joung and Cheatham monovalent cation/anion TIP3P water and NaCl ion model was adopted.¹¹⁸ System minimization was conducted using the sander module, while subsequent heating, equilibration, and production steps were executed using the pmemd.cuda engine in Amber 23 package.¹¹¹ The initial minimization was performed over 2,000 steps (500 steps of steepest descent followed by 1500 steps of conjugate gradient) to remove steric clashes. The system was then heated gradually from 0 K to 300 K over 20 ps within an NVT ensemble, utilizing a Langevin thermostat for temperature regulation.¹¹⁹ Following heating, the system was equilibrated for 2 ns in the NPT ensemble with a 2 fs timestep utilizing a Berendsen barostat. The SHAKE algorithm was applied to constrain all bonds involving hydrogen atoms,¹²⁰ and a collision frequency of 1 ps⁻¹ was maintained. The production run for all systems was performed under NVT conditions, maintaining the same integration parameters as the equilibration step for a period of 5 ns.

A total of 100 snapshots of equally-spaced frames (50 ps interval) were taken from each of the solution systems for a subsequent TD-DFT QM/MM calculation. The TD-DFT calculations were performed directly on unoptimized MD snapshots to preserve the statistical fluctuations in chromophore and solvent configurations that would naturally occur in solution at room temperature. The number and type of ions included within the QM and MM regions varied between snapshots depending on the local solvent configuration at a given frame. For each QM/MM calculation, the appropriate overall region and system charges were explicitly accounted for. The placement of the QM/MM boundary is discussed below and distance cutoffs were determined using the center of mass of the ion or water molecule. Water molecules and ions in the MM region were treated using the universal force field (UFF)¹²¹ implemented in the Gaussian software. The MM region was computed by employing the charge equilibration method¹²² via the electronic embedding scheme,⁷⁴ which provides a better description of the electrostatic interactions between the two regions as it is computed at the QM level. To mitigate potential spurious charge transfer interactions,¹²³ an implicit-explicit approach was adopted in addition to using a range-separated hybrid functional CAM-B3LYP. The explicit supramolecular system was encapsulated in the cavity of an implicit water solvation environment (ε=78.35) via SMD to account for both short- and long-range polarizations emanating from the specific interaction of the explicit solvent molecules and the polarizable continuum model, respectively. The SMD continuum solvation model was chosen as for its demonstrated applicability to a wide range of charged and neutral molecular systems in different solvent environments.^{68, 124} SMD partially accounts for specific solute-solvent interactions such as hydrogen bonding through empirical solvent parametrization including solvent acidity and basicity descriptors.

3. Results and Discussion

3.1. TD-DFT Benchmarking with CIS(D) and CCSD Calculations

To substantiate the choice of TD-DFT with the functional CAM-B3LYP for the QM calculations performed here, a two-step comparison was carried out. First, CAM-B3LYP and CIS(D) are compared against CCSD in gas phase. Due to an inability to experimentally isolate the specific molecular-scale interactions between a fluorophore and the surrounding solvation environment that are the main focus of this paper, comparison against electronic structure methods such as CCSD provides a practical reference for assessing the performance of TD-DFT in our case. In a benchmark study involving 52 small organic molecules (including aromatic rings), CCSD vertical excitation energies showed a mean absolute error of 0.071 eV with respect to the CC singles-doubles-triples-and-quadruples (CCSDTQ) results for 31 excitation energies of varied character (valence, charge-transfer, Rydberg, singlet, triplet, including double-replacement component), whereas CCSDTQ itself had an error of 0.003 eV compared to a full-quintuples benchmark, CCSDTQP in aug-cc-pVTZ basis.⁴¹

CIS(D) has recently been shown to be formally (and hence also numerically) identical to a model dubbed CPS(D-2).¹²⁵ The latter is a second-order member of a perturbation series, CPS(D-n), that at zeroth order is identical to CIS and at infinite order becomes formally identical to the CCSD target (in practice, the CCSD quality is obtained already at the third order). Not only does CIS(D) significantly improve over CIS for single-replacement-dominated excitation energies,¹²⁵ but it was also shown, in a study involving 463 transitions of highly varied types of the QUEST database, that CAM-B3LYP and CIS(D) have comparable quality for excitation energies (except for radical species were CIS(D) performs worse).⁵⁷ While CIS(D) per se is not a high-level benchmark method, the agreement between CAM-B3LYP and the inexpensive wave-function-based CIS(D) may therefore serve as a measure of a good performance of (the even less expensive) CAM-B3LYP for the studied transitions.

As excitation energy calculations are intractable for a full NR molecule (Figure 1a) at the CCSD level with its standard implementation, calculations are instead performed in the first step of comparisons on the smaller representative molecules of diethylamine and p-benzoquinone. The diethylamino group is the moiety of NR that acts as a donor in the intramolecular charge-transfer excitation, while p-benzoquinone models the acceptor group of NR. The results of comparing the first three excitation energies of diethylamine and p-benzoquinone obtained with CAM-B3LYP and CIS(D) against CCSD are shown in Table S2.

Figure 1.

(a) Chemical structure of Nile red (9-(diethylamino)-5H-benzo[α]phenoxazine-5-one) with labeled atoms and dihedral angles. The quinone oxygen, phenoxazine nitrogen, phenoxazine oxygen, and nitrogen of the diethylamino group are labeled as O1, N2, O2, and N1, respectively. The numbers 1 to 6 represent atoms that make up dihedral angles. (b) A representative QM/MM model with a 4 Å QM and a 4 Å MM region used for excited state calculations. Purple and green spheres represent Na⁺ and Cl⁻ ions, respectively.

CAM-B3LYP excitation energies of diethylamine exhibited errors of magnitudes ~0.1 eV with respect to the CCSD benchmark, while the error of CIS(D) ranged between 0.55 and 0.89 eV. For p-benzoquinone, the opposite was true with CIS(D) performing substantially better than CAM-B3LYP. This was attributed to the importance of including CC double excitations for properly describing delocalized electrons and conjugated double bonds. As NR contains four such conjugated aromatic rings, it is expected that CIS(D) would overall perform better for NR than CAM-B3LYP, albeit at greater computational cost. Agreement between CAM-B3LYP and CIS(D) excitation energies may therefore be used as a measure of adequacy of CAM-B3LYP for NR excitation energy calculations in a solvated environment where CIS(D) is not computationally feasible, as investigated in the second step of comparisons.

In that second step, to assess the applicability of CAM-B3LYP for predicting excitation energies of the static structures of NR produced in the different solvent environments generated in the MD simulations, TD-DFT CAM-B3LYP results were compared to CIS(D) calculations, as shown in Figure S1. The comparison reveals a strong linear correlation, with R² = 0.76, 0.84, and 0.79 for pure water, 0.5, and 1 M NaCl solutions, respectively. CAM-B3LYP was found to systematically overestimate λ_max relative to CIS(D). The mean absolute error (MAE) was found to be 0.15 eV, 0.22 eV, and 0.21 eV for the pure water, 0.5 and 1 M NaCl solutions respectively. The reported MAE values are referenced to CIS(D) calculations rather than experimental measurements and therefore reflect the differences between computational methods rather than direct deviations from experiment. Overall, this comparison was found to support the use of TD-DFT CAM-B3LYP as a computationally efficient method that is able to capture essential trends in excited-state behavior of NR, in line with previously reported results.^{52–58, 103} The observed correlation with the CIS(D) calculations further justifies the use of CAM-B3LYP-predicted spectral shifts to interpret solvatochromic behavior of NR in varying salt concentrations, even if these shifts are of the same rough magnitude as the error associated with calculating absolute excitation energies using this approach compared to those calculated via other higher accuracy computational methodologies for a given molecular structure.

3.2. TD-DFT QM/MM Calculations of Solvated NR

TD-DFT QM/MM calculations were next employed to understand how the excitation energy of NR was impacted by the local solvation environment. The QM/MM method was first evaluated for the dependence of calculated excitation energy as a function of the number of solvent layers included in order to adequately balance computational cost and accuracy. Figure S2a shows a plot of the excitation wavelength λ_max versus QM region radius. The normalized computational cost associated with each calculation is also shown. The QM region radius was varied from 1 to 5 Å while the outer MM region radius was fixed at 4 Å. The computational cost, as indicated by the normalized elapsed time, more than doubled upon increasing the QM cutoff from 4 Å to 5 Å. At the same time, the λ_max only shifted by 2 nm, compared to a shift of 12 nm between a 1 Å to 4 Å cutoff. Thus, a cutoff of 4 Å for the QM region was selected as representing a reasonable balance between computational cost and accuracy. Figure S2b illustrates the effect of the MM region radius on λ_max convergence. Increasing the thickness of the MM region at a fixed QM radius of 4 Å had no substantial impact on the λ_max and only a minor impact on the overall computational cost. Therefore, a cutoff of 4 Å thickness for the MM region was selected. On average, the snapshots contained approximately 60 water molecules in the QM region and 186 water molecules in the MM region. A representative snapshot showing the regions defined as QM/MM is shown in Figure 1b.

For each of the 0, 0.5, and 1 M NaCl solutions, QM/MM excited state calculations were performed on 100 individual snapshots. For pure NaCl aerosols, these salt concentrations correspond to equilibrium RH values of 98.3% and 96.7%, respectively, at 1 atm and 298 K, representing highly humid aerosol conditions. Although ambient RH is often lower than these values, non-polarizable force fields have been shown to fail to accurately simulate highly concentrated ionic solutions. Thus, 1 M NaCl was highest concentration investigated here.^{126, 127} Figure 2a shows a histogram of the calculated λ_max from each snapshot in each of the different NaCl concentrations. At 0 M, longer λ_max were more prevalent, indicating a higher frequency of these low-energy transitions compared to 0.5 and 1 M NaCl cases. Overall, the distribution was found to shift towards shorter λ_max values as the ionic concentration increased. The shift of the average solvated NR excitation energy as a function of salt concentration with respect to the average excitation energy in pure water is shown in Figure 2b, indeed showing that an increase in NaCl concentration resulted in an increase in average excitation energy. Additionally, the introduction of ions was found to increase the standard deviation across the 100 individual frames. For pure water, the excitation standard deviation was 25 nm, while it increased to 30 and 32 nm for the 0.5 and 1 M salt solutions, respectively. To further assess the statistical significance of the observed spectral shifts, two sample Welch’s t-tests were performed on the absorption energy distributions yielding two-tailed p-values of 0.026 for the comparison between pure water and 0.5 M NaCl and 3.23 x 10⁻⁵ for pure water and 1 M NaCl, indicating that these shifts were statistically significant. This finding suggests that the addition of ions creates a more heterogeneous environment around the NR molecule, subsequently introducing variability into the electronic excitation energy.

Figure 2.

(a) Calculated λ_max for each of the 100 snapshots of NR in pure water, 0.5 and 1 M NaCl solutions. (b) Change in the average excitation energy as a function of NaCl concentration, referenced to pure water. NR-solvated represents the fully solvated NR while NR-Vacuum represents the static structures of NR stripped of their solvation environment and calculated in the vacuum-phase.

The shift observed in Figure 2b for the solvated NR could be due to multiple interrelated factors, including the solvent environment inducing a change in NR conformation or the solvent environment directly influencing the NR electronic energy levels for a given NR conformation. To isolate and assess the relative contributions of these two factors, a comparison was made between calculated excitation energy values for the fully solvated QM/MM NR molecules and the same static NR structures in the gas phase. These gas-phase NR excitation energy values were calculated after the removal of all solvent molecules without optimization of the NR molecular structures for each of the 100 snapshots obtained from the simulations. Figure 2b shows that the shift in average excitation energy for the gas-phase NR accounts for 79% and 62% of the total shift observed in the fully solvated environment for 0.5 M and 1M NaCl, respectively. This finding suggests that under these conditions, the conformation of the NR molecule induced by a given solvation environment plays a major role in determining molecular optical behavior, though further direct solvation effects on the electronic energy levels cannot be entirely ignored. The next sections constitute an analysis of each of these factors.

3.3. Direct Effects of Solvation on NR Excitation Energy

To gain insights into the role of the solvent environment acting on a fixed NR structure in the observed solvatochromic shift, individual factors such as the individual interactions of the fluorophore with water molecules and ions were examined in isolation to assess the specific contributions of each to resulting λ_max values.

3.3.1. Effects of Hydrogen Bonding

The number of hydrogen bonds (H-bonds) between NR and solvent molecules was calculated for each of the 100 snapshots for the three solutions simulated. Analysis of H-bonds was carried out from the MD trajectories using CPPTRAJ¹²⁸ in AmberTools23.¹¹¹ H-bonds were defined using the default geometric cutoff distance of 3 Å and cutoff angle of 135° from the four heteroatomic sites (O1, N1, O2, and N2) of NR shown in Figure 1a. Figure S3 shows the percentage of frames that contained a H-bond at each site for each of the three solution conditions. A substantial percentage of H-bonds were observed for each solution system, with the exact percentage varying between sites. The site with the largest percentage of frames containing H-bonds was O1, followed by N2, O2, and N1 in decreasing order. The reduced percentage of H-bonds at the N1 site compared to the other sites can be attributed to the shielding effect of the two ethyl moieties, which hinder direct H-bonding interactions with the nitrogen (N1 as labeled in Figure 1a) of the diethylamino group. In contrast, the quinone oxygen (O1 as labeled in Figure 1a) was found to form substantially more H-bonds due to its high exposure to the solvent environment.

An analysis on the effect of H-bonding on λ_max values was performed by systematically isolating and removing the water molecule participating in the H-bond of interest and subsequently performing a second QM/MM calculation with that molecule removed, similar to the analysis performed by Shedge et al.⁹⁴ in their study of the effect of ions on the absorption spectrum of green fluorescent protein (GFP). The analysis was performed on snapshots derived from the 1 M NaCl solution and no optimization was performed upon removal of the water molecule. Figure 3 shows a scatter plot of Δλ_max values representing the difference in calculated λ_max with the removed H-bond and with the H-bond present. The presence of a H-bonded water molecule at the O1, O2, and N2 sites was found to result in a redshift, whereas a H-bond at the N1 site caused a blueshift. Notably, the magnitude of the redshift was found to be larger at the O1 and N2 sites compared to the O2 site. These trends in the λ_max shift can be rationalized in terms of the intramolecular charge transfer (ICT) that NR undergoes upon excitation. In the ICT process, charge density is transferred from an electron-rich donor group to an electron-accepting group. In the case of NR, the N1 functions as the donor, while the O1 serves as the charge acceptor. The shift of electron density from the diethylamino group towards the O1 can be observed through visualization of a representative calculated HOMO and LUMO, as shown in Figure S4.⁶¹ H-bonds at the N1 stabilize the ground state by reducing the electron density at the donor site. This stabilization affects the ICT process by increasing the energy gap between the ground and excited states, resulting in an observed redshift. In contrast, H-bonds at the O1 as well as the phenoxazine oxygen (O2) and phenoxazine nitrogen (N2) as labeled in Figure 1a, stabilize the electronic excited state by lowering the electron density at the acceptor sites. This stabilization facilitates the ICT process by decreasing the energy gap, resulting in an observed blueshift.

Figure 3.

A scatter plot of the Δλ_max values caused by the presence of hydrogen bonds at the four heteroatomic sites of the molecular dye. The analysis was performed on snapshots obtained from the 1 M NaCl solution.

3.3.2. Effects of Ion Pairing

Next, the ion pairing of Na⁺ and Cl⁻ ions at the four heteroatomic sites was analyzed for the 0.5 M and 1.0 M NaCl solutions. Ion pairing in this context refers to any ion either Na⁺ or Cl⁻ pairing with the NR heteroatoms consistent with terminology previously used by Shedge et al.⁹⁴ CPPTRAJ¹²⁸ in AmberTools23¹¹¹ was used to analyze the ion pairing from the MD trajectories. The distance cutoffs of contact ion pairs (CIP; < 3 Å) and solvent separated ion pairs (SSIP; between 3 and 5.5 Å) were adopted from Shedge et al.⁹⁴ Figure S5 shows the percentage of frames containing CIPs and SSIPs at the heteroatomic sites of the molecular dye across the NaCl solution simulations. An increase in NaCl concentration resulted in a consistent increase in SSIP formation at the four heteroatomic sites. Notably, CIP formation was observed only for Na⁺ at the O1, with no CIP formation observed for Cl⁻ at any of the heteroatomic sites. The radial distribution function (RDF) with respect to any of the NR atoms is shown in Figure S6 and demonstrates that Na⁺ tended to be found closer to the NR molecule, while Cl⁻ was generally located farther away. The RDF of the individual heteroatomic sites is also shown in Figure S7. Here, each site showed a close H atom peak representative of H-bonding while only the O1 showed a Na⁺ peak representative of CIP formation, as discussed previously. Among the heteroatomic sites, SSIP formation was most prominent at O1 followed by N2, O2, and N1. As in the H-bond case, the reduced percentage of SSIP formation at the N1 is attributed to the steric shielding provided by the two ethyl groups, which limits its exposure to the solvent environment.

The effect of the ions on the calculated λ_max values was next investigated. First, as a rough test, either all the Na⁺ ions or all the Cl⁻ ions within the QM region were removed and the λ_max value was recalculated. Snapshots were randomly selected from frames containing either Na⁺, Cl⁻, or both within the QM region irrespective of the spatial orientation or distance of the ion from the NR molecule. Figure 4a shows a scatter plot of the Δλ_max values of Na⁺ and Cl⁻ IPs, where Δλ_max represents the difference between the λ_max following ion removal and that of the corresponding fully solvated NR molecule. The presence of either ion generally resulted in a shift in λ_max, with the direction of the shift dependent on the type of ion present. The Na⁺ ions predominantly resulted in a redshift, while the presence of Cl⁻ resulted in either a minimal shift or a blueshift. The spread in magnitude of the effect of ion suggested that the ion-induced shift depends on the spatial location and distance of the ion to the NR molecule. Thus, to further investigate the influence of ion pairing on λ_max, additional analyses were conducted to isolate the effects of IPs at each of the four heteroatoms sites of the NR molecule.

Figure 4.

(a) A scatter plot of the Δλ_max values resulting from the presence of Na⁺ and Cl⁻ ions in the QM region. The analysis was performed on snapshots obtained from the 1 M NaCl solution. (b) A scatter plot of the Δλ_max values resulting from the presence of CIP and SSIP at the heteroatomic sites of the molecular dye. The analysis was performed on snapshots obtained from the 1 M NaCl solution.

The direct effect of IPs on λ_max was investigated by comparing the λ_max calculated with a CIP or SSIP present at one of the four heteroatoms with the λ_max calculated after that ion of interest was removed and the rest of the frame was frozen in place. Figure 4b shows the scatter plot of the Δλ_max resulting from the presence of Na⁺ and Cl⁻ IPs at the four heteroatomic sites. The presence of Na⁺ at the O1 and N2 sites resulted in a redshift, whereas the presence of Cl⁻ at these sites led to a blueshift. At the N1 site, the opposite trend was observed with the presence of Na⁺ leading to a blueshift while the presence of Cl⁻ resulted in a redshift. At the O2 site, mixed behavior was observed, where the presence of Na⁺ and Cl⁻ caused shifts in both directions, albeit generally of a small magnitude.

These observed shifts can also be rationalized through the impact of the ion on the ICT process. Na⁺ IPs at the O1 and the N2 preferentially stabilize the excited electronic state by lowering the electron density at the electron-rich acceptor site. This stabilization reduces the energy required for excitation, thereby leading to redshift in λ_max. Conversely, Na⁺ IPs at the N1 preferentially stabilize the ground state by withdrawing electron density from the electron-rich donor site. This ground-state stabilization increases the energy gap between the ground and excited states resulting in a blueshift in λ_max. In contrast, Cl⁻ IPs exhibit the opposite stabilization behavior, with Cl⁻ IPs at the N1 preferentially stabilizing the electron-deficient excited state by contributing electron density to the donor site, resulting in a redshift, and preferentially destabilizing the electron-rich excited state at the O1 and the N2 by increasing the local electron density, resulting in a blueshift. The distance dependence of IPs on the λ_max was further analyzed by comparing the magnitude of the shift produced by CIPs, which were only observed with Na⁺ at the O1 site, to those produced by SSIPs. The CIPs on average produced a larger in magnitude shift compared to the SSIPs, which held true both for the same heteroatom (O1) and for SSIPs present at other heteroatoms. This finding is consistent with those of Shedge et al.,⁹⁴ which showed that an increased distance between the Na⁺ in an IP and the fluorophore acceptor site led to a decrease in the magnitude of the redshift produced by the IP.

3.4. Effects of Solvent-Induced NR Conformation on Excitation Energy

The fact that NR molecules structurally frozen and stripped of all surrounding solvent molecules and ions still retain a substantial fraction of the observed blueshift with increasing salt concentration, as shown in Figure 2b, underscores the necessity of also examining the impact of solvent-induced changes in molecular conformation of NR.

3.4.1. Donor Dihedral Angles Distribution

Notably, a previous study demonstrated that the dihedral angle at the donor site of NR in particular strongly impacts the ICT process.^{80, 129} This dihedral angle defines the rotation of the ethyl moieties (measured as the angle between the 1-2 and 4-5 bonds in Figure 1a) around the 2-4 bond relative to the ring system. Dihedral angles close to 0° and ±180° are termed ‘planar’ structures due to the ethyl moieties lying approximately in the plane of the conjugated ring system while ‘twisted’ structures exhibit dihedral angles close to ±90° thus contain ethyl moieties that lie roughly perpendicular to the planar ring system.⁸⁰ Due to the importance of this rotational angle, the rotational energy profiles of this group with respect to the conjugated ring system in GAFF2 and DFT were compared (Figure S8). The GAFF2 and DFT energy profiles exhibited the same minima and maxima with both methods predicting a rotational barrier centered near 90° of nearly 10 kcal mol⁻¹. Although GAFF2 slightly underestimated the magnitude of the energy maximum by approximately 10% compared to DFT, the agreement was deemed sufficiently close to indicate that the force field was adequately capturing the torsional behavior of this group in the NR molecule for the purposes of this study.

Figure 5 shows a scatter plot of calculated vacuum λ_max values for the total 300 NR structures taken from the three solution conditions versus the 1-2-4-5 dihedral angle. An analogous plot of the essentially equivalent 3-2-4-6 dihedral angle that is defined with respect to the opposing ethyl group is shown in Figure S9. Figure 5 indicates that dihedral angles close to 0 and ±180° result in lower excitation energies, corresponding to a redshifted λ_max, whereas those closer to ±90° result in higher excitation energies, corresponding to a blueshifted λ_max. This result agrees with previous studies that have found that NR undergoes planar ICT, in which the diethylamino group remaining close to planarity leads to lower-energy excitations.^{80, 130}

Figure 5.

A scatter plot of the 1-2-4-5 dihedral angles (as labeled in Figure 1a) versus vacuum phase λ_max.

Polar histograms of the 1-2-4-5 dihedral angle distributions for pure water, 0.5 M, and 1 M NaCl solutions are shown in Figure 6a, b, and c, respectively. The analogous distributions of the dihedral angles for the counter ethyl moiety, 3-2-4-6 are shown in Figure S10. Notably, in the pure water solution, the dihedral angles were primarily distributed near 0 and ±180°, indicating a near planar structure and the associated lower energies. However, the addition of NaCl was seen to result in a broadening of the distribution of dihedral angles and a marked increase in dihedral angles near ±90° that are associated with higher energy excitations. This shift in the distribution of the dihedral angles for the different solutions suggests that the addition of NaCl ions leads to the diethylamino group adopting different conformations, subsequently impacting λ_max and playing an important role in the calculated spectral shifts seen in Figure 2b.

Figure 6.

Polar histogram plot of the distribution of 1-2-4-5 dihedral angles for the pure water, 0.5 and 1 M NaCl solutions. Values close to 0 and 180° are named as ‘planar structures’ while the ‘twisted structures’ present these values near 90° and 270°.

3.4.2. Random Forest for Feature Importance Identification

Beyond the dihedral angle of the diethylamino group, other structural features that may substantially contribute to the calculated spectral shifts were also investigated. To identify other key structural features, feature importance scores were ranked to identify the most influential structural parameters. Specifically, a random forest regression model was implemented using Scikit-Learn,¹³¹ and feature importance scores were computed based on the mean decrease in variance (MDV). MDV is a metric that quantifies the average reduction in variance when splitting on a given feature during regression. The input feature set was comprised of forty-five intramolecular bond lengths and forty-two atomic partial charges of the NR molecule extracted from each of the 100 snapshots for all solutions. The vacuum phase excitation energies computed for each NR geometry was set as the target variable. Figure S11 shows a ranked list of the features with the highest feature importance scores. Features with high importance scores were found to include the C1-N2 bond length, the C2-C3 bond length, the C1-C4 bond length, and the partial charge on the C2 atom, in descending order. In contrast, the least important features, such as C-H bond lengths, were found to contribute negligibly to the performance of the model.

Following the ML prediction, the vacuum-phase λ_max was plotted against the most important structural feature identified by the model, which was the C1-N2 bond length, as shown in Figure 7. Consistent with its feature importance score, the scatter plot revealed a moderate correlation between λ_max and the C1-N2 bond length, with an R² value of 0.36. Specifically, an increase in the bond length from approximately 1.27 Å to 1.40 Å corresponded to a redshift in λ_max. The strength of the correlations between λ_max value the next two highest ranked structural features were substantially weaker (R² values of 0.106 and 0.0105) indicating that the C1-N2 bond length was the most important geometric feature by a substantial linked to the optical response of NR.

Figure 7.

A scatter plot of the vacuum phase λ_max versus the C1-N2 bond length, exhibiting a positive correlation with R² = 0.357.

To further analyze this phenomenon, excitation energies were calculated from NR structures with the C1-N2 bond length fixed at 1.27 Å, 1.30 Å (the bond length of the most stable vacuum-phase geometry) and 1.40 Å following optimization of the rest of the molecule. Table S3 shows the orbital populations analyzed using the electron localization of transition excitations (ELOTE). Increasing bond length led to a more narrow frontier orbital eigenvalue gap from 0.188 to 0.170 a.u, which agrees with the correlation observed in Figure 7. Furthermore, the population analysis shows that this shift is accompanied by a change in the shift in electron density upon excitation. At the shortest bond length, the contribution to the HOMO from the donor nitrogen N1 was 17.15% and this contribution decreased greatly to <1% in the LUMO. In contrast, the acceptor O1 contribution to the HOMO was 4.29% and this contribution increased to 8.52% in the LUMO. At a bond length of 1.40 Å, the magnitude of these two shifts decreased, with a shift of 12.80% to 2.4% for N1 and a shift of 6.18% to 6.71% for O1 from HOMO to LUMO, respectively. Overall, these changes suggest that elongation of the C1-N2 bond is associated with a change in the redistribution of electron density that occurs upon excitation.

4. Conclusions and Implications for Aerosol Fluorescence Probe Spectroscopy

Overall, this study provides molecular level insights into how chemically-complex aqueous ionic environments govern the solvatochromic behavior of NR. In particular, findings from this study indicate that the optical response of NR and similar fluorophores cannot be understood solely in terms of bulk ionic strength or continuum dielectric effects but rather arise from the complex interplay between ion organization, H-bond structure, ion-specific interactions, and conformational changes of the chromophore itself. The motivation for this study is ultimately to inform experimental applications of fluorescence probe spectroscopy to offer insights into the local chemical environment within aerosol particles, which are typified by high ionic strengths. The findings here can thus be discussed through this lens to offer potentially generalizable lessons within this application area to support effective selection and use of fluorescent probes for characterizing aerosol properties.

The finding that ion-induced conformational changes in NR contributed substantially to the observed change in optical response suggests that fluorophores with more rigid structures may be less impacted by the presence of high ionic strengths. This design principle may be useful for selecting fluorophores for which the presence of high ionic strengths could serve as a confounding variable that complicates the measurement of another target property. Such a confounding influence of ionic strength was previously observed in attempts to use the fluorophore quinaldine red as a probe to measure pH.²⁸ This concept of molecular rigidification has been previously identified to additionally have beneficial effects on fluorescence quantum yields of a range of fluorophores in aqueous environments.¹³²

The finding that IPs and H-bonds produced shifts in excitation energy that depended on the donor or acceptor nature of the NR heteroatoms as well as the sign of net charge on the interacting dissolved species suggests that the amount of steric hindrance around heteroatomic sites could modulate and/or suppress the impact of the solvation environment on excitation energies. Along these same lines, the finding that the net effect of interactions with cations was a redshift while the net effect of interacting with chloride ions was a blueshift suggests that, especially for asymmetric salts, ion specific properties like charge densities and steric hindrance would also play a major role in determining the overall effect of exposure of the fluorophore to a high concentration of ions. Thus, beyond the specific case of NR, this study helps to establish a broader molecular-level framework for understanding the impact of aqueous ionic solvation environments on solvatochromic fluorescence probes. These proposed design principles largely apply to fluorophores that undergo some degree of ICT, such as the established aerosol fluorophores NR¹³ and Prodan,¹⁷ and other considerations may be applicable with fluorophores that exhibit alternative excitation mechanisms.

Supplementary Material

Basis set comparison; CCSD comparison with CAM-B3LYP and CIS(D); Atomic contributions to frontier orbitals; TD-DFT comparison with CIS(D); test of solvent layers for QM/MM excitation energy convergence; frequency of occurrence of H-bonds and ion pairs; molecular orbitals involved in intramolecular charge transfer; radial distribution functions; rotational profile of NR dihedral angle distribution of dihedral angles and excitation energy dependence on dihedral angles; ranking of molecular features as predicted by random forest feature importance