Analysis of depolarization ratios of ClNO(2) dissolved in methanol.

Analysis of depolarization ratios of ClNO2 dissolved in methanol Marilena Trimithioti, Alexey V. Akimov, Oleg V. Prezhdo, and Sophia C. Hayes Citation: The Journal of Chemical Physics 140, 014301 (2014); doi: 10.1063/1.4854055 View online: http://dx.doi.org/10.1063/1.4854055 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/1?ver=pdfcov Published by the AIP Publishing

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THE JOURNAL OF CHEMICAL PHYSICS 140, 014301 (2014)

Analysis of depolarization ratios of ClNO2 dissolved in methanol Marilena Trimithioti,1 Alexey V. Akimov,2,3 Oleg V. Prezhdo,2 and Sophia C. Hayes1,a) 1

Department of Chemistry, University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus Department of Chemistry, University of Rochester, Rochester, New York 14627, USA 3 Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973, USA 2

(Received 6 August 2013; accepted 5 December 2013; published online 2 January 2014) A detailed analysis of the resonance Raman depolarization ratio dispersion curve for the N–O symmetric stretch of nitryl chloride in methanol at excitation wavelengths spanning the D absorption band is presented. The depolarization ratios are modeled using the time-dependent formalism for Raman scattering with contributions from two excited states (21 A1 and 31 B1 ), which are taken as linearly dissociative along the Cl–N coordinate. The analysis focuses on the interplay between different types of broadening revealing the importance of inhomogenous broadening in determining the relative contributions of the two electronic transitions. We find that the transition dipole moment (M) for 21 A1 is greater than for 31 B1 , in agreement with gas phase calculations in the literature [A. Lesar, M. Hdoscek, M. Muhlhauser, and S. D. Peyerimhoff, Chem. Phys. Lett. 383, 84 (2004)]. However, we find that the polarity of the solvent influences the excited state energetics, leading to a reversal in the ordering of these two states with 31 B1 shifting to lower energies. Molecular dynamics simulations along with linear response and ab initio calculations support the evidence extracted from resonance Raman intensity analysis, providing insights on ClNO2 electronic structure, solvation effects in methanol, and the source of broadening, emphasizing the importance of a contribution from inhomogeneous linewidth. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4854055] I. INTRODUCTION

Nitryl chloride is one of the various atmospheric species that play an important role in the reactive chlorine reservoir both in the stratosphere and troposphere. The chlorine radicals formed via the photodissociation of ClNO2 by solar radiation participate in the catalytic ozone destruction cycle in the stratosphere,1, 2 while it has been suggested that chlorine radicals in the troposphere can affect the cycling of nitrogen oxides and the production of ozone (a tropospheric pollutant), as well as reduce the lifetime of methane, a greenhouse gas in the lower atmosphere.3–5 The photochemistry of ClNO2 has been investigated in a number of previous studies which mainly focused on the gas and solid state.6–15 It was found that the dominant reaction is the dissociation of the Cl–N bond both in the gas and solid state. In the gas phase6–9 and in argon and water clusters,11 Cl and NO2 photofragments are formed, which in argon, nitrogen, and oxygen matrices recombine to form cis and trans isomers of ClONO due to the cage effect.12–14 In the case of pure solid nitryl chloride, N2 O4 is produced while photolysis of the molecule on ice surfaces leads to the formation of nitric acid.15 It is therefore evident that different photochemical reaction paths are energetically accessible to nitryl chloride depending on the environment surrounding the molecule, with the condensed phase being the next logical step in the study of ClNO2 phase-dependent reactivity. We have recently performed the first resonance Raman intensity analysis (RRIA) of ClNO2 in solution (methanol) at excitation wavelengths within the D absorption band a) Author to whom correspondence should be addressed. Electronic mail:

[email protected] 0021-9606/2014/140(1)/014301/13/$30.00

(λmax = 200 nm).16 Resonance Raman spectroscopy provided information on solvent effects on ground state structure through RR frequencies as well as excited states through RR intensities.16, 17 It was shown that structural evolution occurs along the N–O symmetric stretch. Specifically, the observed ∼24 cm−1 up-shift of the N–O symmetric stretch frequency compared to the gas phase, suggested a solvent-induced structural change in the ground state. The strengthening of the N–O bond reflected an increase in the ground state potential curvature and a shift of the equilibrium position along the N–O coordinate. Furthermore, RRIA suggested the contribution from transitions to two nearby electronic states in the description of the D band, which are dissociative along the Cl–N coordinate with a large slope of the excited state potential energy surface (PES). The participation of two excited states in the D band transition was supported by Resonance Raman depolarization ratios, that were found to deviate significantly from 1/3, thus confirming previous ab initio calculations of the low lying excited states of gaseous ClNO2 .18 These findings demonstrated that the D band in the absorption spectrum is attributed according to the theoretical study to the X1 A1 → 31 A1 transition (7.04 eV, 176 nm, f = 0.6) and to a transition with somewhat smaller oscillator strength (f = 0.3), X1 A1 → 31 B2 , (7.25 eV, 171 nm) nearby. RRIA involves simultaneous modeling of the absorption spectrum and the Raman excitation profile (REP), using expressions from the time-dependent formalism for absorption and RR scattering, and thus constitutes a useful theoretical platform for extracting molecular information about the excited states.17 Moreover, since Raman scattering is characterized by a tensor, polarization measurements are of central significance for extracting additional information

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about a molecule especially in solution, which is considered as a randomly oriented system.19 More specifically, the depolarization ratios (DPR’s) measured at excitation energies on resonance with an electronic absorption can be used to model the theoretical depolarization ratio dispersion curve simultaneously with the REP and absorption cross sections.20–27 Jerneshoj et al. have shown that by using several different combinations of excited state parameters one can obtain a good fit of the REP, but only one set of these parameters can simultaneously describe the depolarization ratios. The sensitivity of Raman excitation profiles, when two electronic excited states contribute to the scattering, to various physical quantities such as the energy separation of the two states, the homogeneous linewidth (), the displacements of the PES minima (), and the transition dipole moments of states have been examined in detail by Shin et al.28 The general trend derived from these calculations is that the electronic excited state with the largest transition dipole moment dominates the Raman excitation profile. It was also shown that the shape of the REP is very sensitive to the displacements and .29 In this paper we analyze in detail our previously measured RR DPR’s for ClNO2 in methanol,16 in order to produce a physically acceptable description of the excited states contributing to the electronic absorption spectrum in the D band region for the molecule dissolved in methanol. We find, in agreement with earlier literature,20–27 that DPRs along with RR intensities serve as a sensitive probe of excited state structure and early-time dynamics in the Franck Condon (FC) region. This is of particular importance in the case of a dissociating molecule scattering in the short-time limit, which, due to its very diffuse absorption spectrum, makes deciphering the sources of broadening and their role a challenging task. Here we take a systematic approach to demonstrate the interplay between several parameters and their importance in the modeling of the experimental observables, focusing especially on the contributions of homogeneous and inhomogeneous broadening. Molecular dynamics (MD) simulations, linear response, and ab initio calculations complement the analysis of the experimental results, as well as provide insights on solute-solvent interactions operating in this molecular system. II. COMPUTATIONAL METHODS A. Depolarization ratios and resonance Raman intensity analysis

The Raman depolarization ratio (ρ) is calculated using Eq. (1),19, 22 ρ=

I⊥ 5 1 + 3 2 = . II I 10 0 + 4 2

(1)

This equation demonstrates the relation between the experimentally obtained DPR values through the measurement of I⊥ and III (the intensities of the scattered light detected with polarization perpendicular and parallel to that of the incident radiation, respectively) and the theoretical definition. 0 , 1 , 2 , are the rotational invariants of the Raman tensor, which are expressed in terms of the cartesian polarizability tensor el-

ements, α mn (m, n = x, y or z), in the coordinate system fixed on the molecule19 and are given as follows: 0 =

1 |αxx + αyy + αzz |2 , 3

1 {|αxy − αyx |2 + |αxz − αzx |2 + |αyz − αzy |2 }, (2) 2 1 2 = {|αxy + αyx |2 + |αxz + αzx |2 + |αyz + αzy |2 } 2 1 =

1 + {|αxx − αyy |2 + |αxx − αzz |2 + |αyy − αzz |2 }. 3 0 and 1 are the isotropic and antisymmetric parts of the scattering tensor, respectively, while 2 refers to symmetric anisotropy. In contrast to ordinary Raman scattering, in Resonance Raman the polarizability tensor is not symmetric and no upper limit exists for the depolarization ratio, while the scattering tensor may have up to nine non-zero scattering terms. In RR scattering, the measurement of the depolarization ratio dispersion curve (depolarization ratio as a function of excitation frequencies spanning the absorption band) is fundamental for the determination of the number of excited states contributing to the Raman scattering.19–21, 30–36 Specifically, on resonance with one electronic excited state the value for ρ is 1/3 as only one diagonal element is taken to be non-zero. The contribution of more than one electronic excited state in the scattering entails the existence of more than one nonvanishing tensor element and results in the deviation of the depolarization ratios from the value for a single dipole-allowed transition. On resonance with a doubly degenerate state (e.g., α xx = α yy , while all others vanish) the depolarization ratio becomes 1/8. By using the sum-over-states theory for Resonance Raman, where the Raman tensor contains a summation over all molecular states, Mortensen and Hassing have defined the state tensor for each state, as follows:19 |r Sρσ i→f ≡ f |ρ|rr|σ |i. (3) Here, ρ and σ are the Cartesian components and i, f, and r are the initial, final, and intermediate states in Raman scattering.19, 22 The general form of the state tensors determined by symmetry has been derived for most point groups by Mortensen and Hassing19 by using the method of noncommuting generators.37 In this approach the character tables are replaced by eigenvalue tables, which allow straightforward calculation of matrix elements. ClNO2 belongs to the C2v point group, with the z axis defined as oriented along the C2 rotational axis of the molecule and the x axis orthogonal to the plane of the molecule. Therefore, applying this theory to ClNO2 , the state tensor for the N–O symmetric stretch, v1 , the most intense band in the RR spectrum in methanol,16 is ⎤ ⎡ 0 B1 0 ⎥ ⎢ ⎥ (4) A1 : ⎢ ⎣ 0 B2 0 ⎦ . 0 0 A1


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In the above expression, the symmetry of the vibrational mode is indicated to the left of the tensor and the symmetry elements appearing in the state tensor are due to an intermediate state with that particular symmetry.19, 22 In contrast to the work of Lesar et al.,18 our symmetry considerations define A1 and B1 as the symmetries of the two optically accessible excited states and these will be used from this point onward. Resonance Raman DPR’s for ClNO2 in methanol within the D band were found to deviate significantly from 1/3, which suggests the contribution of two closely spaced electronic states (21 A1 and 31 B1 ) to the scattering observed.16 Thus, from Eq. (4) the polarizability tensor elements corresponding to these two states are α zz and α xx , respectively, indicating two orthogonal transitions. In the time-dependent formalism for Raman scattering developed by Lee and Heller, the Raman polarizability tensor elements can be expressed as17, 38, 39 [ai→f (EL )]ρρ =

2 ie2 Mρρ

¯

∞ ×

f |i(t) exp

i(EL + εi )t −2 t 2 e dt. ¯

0

(5) In Eq. (5), EL is the frequency of the incident light, εi is the energy of the initial vibrational state, Mρρ is the electronic transition dipole moment evaluated at the equilibrium nuclear geometry and ρ = x or z for 31 B1 and 21 A1 transition, respectively. f |i(t) is the time-dependent overlap of the final state in the Raman scattering with the initial state propagating under the influence of the excited state Hamiltonian. In condensed environments, where the molecule cannot be considered as isolated, the homogeneous linewidth () includes contributions from both population decay (lifetime of the excited state) and pure dephasing (Eq. (6)): =

1 1 1 = + ∗. T2 2T1 T2

(6)

In the above equation, T2 is the total dephasing time, T1 is the excited state lifetime, and T2∗ is the timescale for pure dephasing. In Eq. (5) a Gaussian broadening function was employed in the modeling of the experimental observables, as suggested by the underlying physics of the dephasing process. However, we show in Sec. III that this function does not satisfactorily fit the red edge of the absorption spectrum, possibly due to limiting the modeling to only two states contributing to the D band absorption. We have also evaluated the effect of a Lorentzian line-shape function on the absorption spectrum, which seems to better reproduce the absorption edge (see the supplementary material73 and discussion in Sec. III). Resonance Raman intensity analysis was performed according to our previous work,16 with the difference that the modeling required a good fit to the depolarization ratio dispersion curve in addition to the electronic absorption spectrum and the Raman excitation profile (REP). The expressions used

for the latter two quantities can be found in the supplementary material73 for easy reference.

B. Electronic structure, molecular dynamics, and linear response calculations

The ab initio electronic structure calculations were performed with the Quantum Espresso program,40 utilizing a converged plane wave basis and a pseudopotential representation of core electrons. In particular, the normconserving pseudopotential generated within the PerdewBurke-Ernzerhof (PBE)41, 42 generalized gradient approximation (GGA) was used. The valence electrons were described using the hybrid PBE0 functional. The size of the plane wave basis was chosen to satisfy the 40 Ry kinetic energy cutoff. All calculations were performed at a single k-point (gammapoint). To analyze the nature of the electronic excited states and the effect of the environment on it, we computed the projected density of states (pDOS) of the ClNO2 molecule in the gasphase (isolated) and in solution (solvated by methanol). For the isolated molecule the geometry of the ClNO2 was optimized with the computational setup described above. The simulation cell was chosen to be cubic with a cell length of 15 Å that provides sufficient vacuum region to minimize interaction of the system with its periodic replica. For the solvated molecule the geometry was taken randomly from the MD trajectories. In this case the simulation cell contained additional 59 methanol molecules and the cell length varied. A representative snapshot of the system with the solvent at a random MD step is shown in Fig. 1. To compute the pure dephasing times for the solvated ClNO2 molecule, we employed the linear response formalism43–45 previously used by Reid and Prezhdo.46 Namely, the classical molecular dynamics simulations for the system of interest were performed, giving the energy of the ground state as a function of time, E0 (t). The energy of the excited state, E1 (t), was then computed for each MD trajectory point by modifying the partial charges of the atoms – the effect associated with the electron density redistribution upon photoexcitation. By such a construction we focus only on the electrostatic origins of the dephasing. In principle, one can also include effects of the changed covalent bonding and

FIG. 1. A representative snapshot of the ClNO2 /MeOH system along an MD trajectory.


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dispersion, but the electrostatic contribution is expected to be dominant due to its long-range nature. The quantities E0 (t) and E1 (t) are used to compute the dephasing function, defined as ⎛ ⎞

t

t

2 2 1 D01 (t) ≡ exp −01 t = exp ⎝− 2 dt dt

C01 (t

)⎠ , ¯ 0

0

(7) where C01 (t) = δE01 (t )δE01 (t − t )t ,

(8)

is the unnormalized autocorrelation function of the fluctuation δE01 (t) of the energy difference E01 (t) between the ground and excited states, δE01 (t) = E01 (t) − E01 (t).

(9)

The dephasing function, Eq. (7), describes a specific electronic excitation, and in general, the dephasing times are different for distinct electronic transitions. Computing all of them individually would require a detailed description of the excited state PESs that is computationally demanding. Instead, we follow the methodology previously used by Brooksby et al.46 and assume that the excited state PESs are mostly affected by the electrostatic interactions of the molecule with the surrounding medium. Therefore, the dephasing processes can be accounted for by the magnitude of the redistributed charge. Our computational approach implicitly covers a set of transitions within a limited energy range. The energy difference is defined by E01 (t) = E0 (t) − E1 (t).

(10)

One can note that the constant energy difference between the ground and excited state energy levels that arises from the electronic structure calculations on an isolated molecule does not affect the dephasing time calculations. It is sufficient to compute only the classical electrostatic contributions to the energy levels arising from the solute-solvent interactions. The homogeneous linewidth computed from Eq. (7), 01 , is related to the pure dephasing (decoherence) time T2∗ , 01 =

1 ≈ . T2∗

(11)

It is equal to the homogeneous linewidth defined above (Eq. (6)) with the assumption that the pure dephasing time is much shorter than the intrinsic electronic transition time (T2∗ T1 ). Such an assumption is supported by our calculations of the pure dephasing times, which show extremely fast dephasing. In addition to the pure dephasing rate calculations, the half-Fourier transform of the normalized autocorrelation function represents the influence spectrum. The latter contains information about the ro-vibrational modes driving electronic dephasing and relaxation processes. The molecular dynamics simulations of the solvated ClNO2 molecule are performed in the NPT ensemble under external pressure of p = 1 atm and temperature of T = 278 K. The temperature is controlled by the NoseHoover thermostat,47–52 and the pressure is controlled by

FIG. 2. Mulliken atomic charges computed at the CCSD/aug-cc-pvdz level of theory for (a) ClNO2 and (b) MeOH.

the Parrinello-Rahman barostat.51–53 The atomic positions are propagated by the velocity Verlet integration scheme.54 The equations of motion are solved for 1 ns with the time step of 1 fs and the energies E0 (t) and E1 (t) printed every 100 fs. The bonded and dispersion (non-bonded) interactions in the simulated system are described using the Universal Force Field (UFF).55 The non-bonded van der Waals (vdW) interactions are smoothly switched off in the radius between 10 and 12 Å. To describe the electrostatic interactions we employed the Ewald summation method56, 57 that is crucial in achieving good accuracy and high performance in computing the longrange interactions. The partial charges on atoms of the solvent and solute molecules are obtained from Mulliken population analysis58 of the gas-phase electronic structure calculations of these species (Fig. 2). The calculations are performed at the CCSD/aug-cc-pvdz level of theory as implemented in the Gaussian program package.59 Since the Mulliken charges are not intended to accurately reproduce the electrostatic potential, we rescaled them by different scaling parameters. The latter were found by comparing the experimental density and the evaporation enthalpy for liquid methanol with those obtained from the MD simulations that use a particular scaling factor for the partial charges. We found that reasonable agreement is found for the scaling factors in the range 1.6–1.75, in agreement with typical scaling factors found for other systems.60 Such a parameter can also be thought of as a measure of the solvent polarity, so in our calculations we used the limiting values (1.6 and 1.75) to elucidate the role of the solvent polarity on the dephasing rates. To model the electrostatic potential in the excited state of ClNO2 , the negative charge −0.625e was removed from the Cl atom and evenly redistributed among the atoms of the NO2 fragment. Keeping in mind the scaling factors for partial charges, this corresponds to a photoexcitation of a single electron from one of the occupied orbitals to one of the empty levels. Similarly to the scaling factors for the partial charges, we varied the amount of charge being redistributed across the orbitals, to understand the role of this factor in the linewidth broadening. III. RESULTS AND DISCUSSION A. Modeling of the D band and broadening effects

In solution, the interaction between molecule and solvent causes stochastic fluctuations to the molecular states. These


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fluctuations are responsible for decoherence of the resonant emission by the generation of a new population that radiates with a rate defined as the dephasing rate and given by = 1/T2 , where T2 is the total dephasing time.17, 29, 36 This process occurs when the molecule is excited to a bound excited state. Thus, the magnitude of the RR cross section is constrained by the electronic dephasing time. There is a direct dependence of the REP on : as decreases the Raman cross sections increases. However, if the excitation occurs to a dissociative excited state, the molecule is no longer trapped in the Frank Condon (FC) region where the overlap with the ground state is non-zero, which results in a shorter time-scale for the wavepacket propagation. If the excited state potential energy surface is steep enough, the constraining parameter for the intensity of the REP is no longer the dephasing time (1/), but rather the slope of the linear excited state.29 The loss of overlap caused by a dissociative normal mode in the excited state resembles the reduction caused by the homogeneous linewidth.61 However, as the homogeneous broadening imposed on the absorption cross section consists of both effects (slope and ), differentiation of the contribution of the two damping factor is difficult, as the integrated absorption is unaffected by any of them. The polarizability tensor and, consequently, the depolarization ratio, are also unaffected, in contrast to the RR cross section. Therefore, in RRIA, the value of the slope must be constrained in order to reach realistic values of that reproduce the REP. Usually, in a solvent environment, homogeneous broadening does not account for all the broadening observed in the REP and absorption cross section, and inhomogeneous broadening () must also be considered. However, the average Resonance Raman intensities and the depolarization dispersion curve (DPR) are relatively unaffected, because the inhomogeneous broadening acts at the level of the cross section and not the polarizability. Therefore, the different dependence of the absorption and Raman cross sections and DPR dispersion curve on the homogeneous linewidth (see the supplementary material73 ) helps to distinguish the role of homogeneous and inhomogeneous broadening, thus providing a more accurate measure of the total dephasing and better understanding of the factors affecting the excited state dynamics. The above discussion calls for a systematic approach for the separation of the broadening mechanisms to obtain a physically appropriate description of the contributing excited states and the experimental observables. There are various ways to disentangle the different contributions to the homogeneous linewidth. Time-resolved fluorescence or stimulated emission measurements can provide a measure for the excited state lifetime, while theoretical calculations of electronic excited state potential energy surfaces can offer insights on the slope along the dissociative coordinates. In the case of ClNO2 , time-resolved measurements have not yet been performed, so we used Lesar and co-workers’ calculated surfaces for the gaseous molecule to constrain the slope of the dissociative surface along the Cl–N coordinate. The 31 A1 (21 A1 here) potential energy surface along the Cl–N coordinate in the FC region was reproduced and depicted in Figure 3 using dimensionless coordinates. The Cartesian coordinates were converted to dimensionless displacements via Eq. (12) for a

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FIG. 3. Potential energy surface of the 21 A1 excited state along the Cl–N bond.18 The energy curve is linearly dissociative with slope β = 2980 cm−1 in the Frank Condon region. The displacement is given in dimensionless coordinates.

direct comparison to the results of RRIA:62 μ ω 1/2 q= (x − x0 ). (12) ¯ Here, q is the dimensionless displacement, μ is the reduced mass, ω is the frequency of the corresponding mode in cm−1 , and x0 and (x–x0 ) are the minimum of the ground state potential energy surface and the displacement of the excited state potential energy surface minimum relative to the ground state in Å, respectively. The calculated slope β was found equal to 2980 cm−1 , very close to the slope reported in our previous work and provides thus an upper limit for the excited state slope we must consider. This is exemplified in the RRIA study of ClNO in solution (another dissociative molecule) by Nyholm et al. where it was shown that excited state structural evolution following excitation is dominated by evolution along the dissociative N-Cl stretch, with a solventdependent slope.21 This slope was shown to decrease with the polarity of the solvent as a result of the weakening of the NCl bond length, with a corresponding shift of the ground state potential energy surface along this coordinate. As a consequence of the broad absorption spectrum of ClNO2 , there are several parameter sets (, , , M and excited state frequency for the NO symmetric stretch, ωe ) that can give an almost equally good fit to the absorption spectrum and the REP. Sections III A 1 and III A 2 examine the key parameters that provide the most physically realistic model for the D band, enabled by additionally considering depolarization dispersion curves. 1. Modeling of D band by considering all broadening as homogeneous

In the first case, we applied a simplification of the source of broadening, where we treated the broadening as phenomenological28 or effective33 due to the diffuse line shape of the absorption spectrum in methanol. There are a few cases in the literature for molecules in solution where this assumption was made,21, 28, 33, 63 including the study of ClNO in solution, where, as in ClNO2 , two electronic excited states contributed to the Raman scattering.21 In the latter case, inhomogeneous broadening was not included to avoid the


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FIG. 4. Experimental (solid) and calculated (dashed lines) electronic absorption spectra for ClNO2 in methanol where (a) the broadening is considered all homogeneous, (d) both homogenous and inhomogeneous broadening were included with M1 < M2 , and (g) same as (d) but with M1 > M2 . The calculated excited states are also shown (dotted lines). (b), (e), and (h) represent the corresponding Raman excitation profiles for the N–O stretch for the three cases. Points represent the experimental data, solid line represents the calculation of the REP. (c), (f), and (i) are the corresponding calculated DPR dispersion curves. The parameters employed in the calculation are presented in Table I.

assumption of correlation of the two states, which resulted in the use of large values of homogeneous broadening. However, in that case the model used to simulate the absorption spectrum and excitation profile was able to reproduce the depolarization ratios for the Raman fundamental modes. In the effective homogeneous broadening used here, both inhomogeneous broadening and the contribution of normal modes with low frequency are included (the latter applies

for all the models).28, 33 Calculated influence spectra of the ClNO2 /methanol system (see Sec. III B 1) indicate, indeed, that the low frequency modes of ClNO2 are the main mechanism for energy dissipation via electron-phonon coupling. Best fit to the absorption and REP (Figs. 4(a) and 4(b)) was accomplished with a moderate dimensionless displacement (1 ) for the ν 1 coordinate, slightly different for each excited state (2.4 vs. 2.2), while the transition moment lengths

FIG. 5. Calculation of the real and imaginary parts of the polarizability tensors. Three cases are considered: The broadening includes: (a) and (b) only ,

(a ) and (b ) and with M1 < M2 , and (a ) and (b ) and with M1 > M2 . (a), (a ), and (a ) Real parts of the polarizabilty tensor elements of state 1

(solid line) and state 2 (dashed line). (b), (b ), and (b ) Imaginary part of the polarizabilty tensor elements of state 1 (solid line) and state 2 (dashed line). The parameters employed in this calculation are presented in Table I.


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TABLE I. Excited state potential energy surface parameters for ClNO2 in methanol.a Transition

ωg (cm1 )b

v1

1291

v2 v3 v4 v5 v6

792 369 1648 408 652

v1

1291

v2 v3 v4 v5 v6

792 369 1648 408 652

ωe (cm1 )b

c

State 1 650e 570f 570g 792 369 1648 408 652

2.4e 2.2f 3.5g 0.0 0.0 0.0 0.0 0.0

State 2 650e 570f 570g 792 369 1648 408 652

2.2e 2.9f 2.5g 0.0 0.0 0.0 0.0 0.0

β (cm1 )d

2900

2900

a

Calculation performed with a Gaussian homogeneous linewidth. The refractive index was 1.328. b ωg and ωe are the ground- and excited-state harmonic frequencies, respectively. c is the dimensionless displacement of the excited state potential energy surface minimum relative to the ground state along a specific coordinate. d β is the slope of the dissociative excited state potential. e Excited states parameters employed and resulted in the graphs depicted in Figs. 4(a)–4(c) and 5(a) and 5(b). Other parameters for state 1: 1 = 1000 cm−1 , M1 = 0.409 Å, E00 = 47 600 cm−1 and for state 2: 2 = 1000 cm−1 , M2 = 0.428 Å, E00 = 49 900 cm−1 . f Excited states parameters employed and resulted in the graphs depicted in Figs. 4(d)– 4(f) and 5(a ) and 5(b ). Other parameters for state 1: 1 = 800 cm−1 , M1 = 0.360 Å, E00 = 47 000 cm−1 and for state 2: 2 = 800 cm−1 , M2 = 0.488 Å, E00 = 49 800 cm−1 . The standard deviation of inhomogeneous linewidth was = 450 cm−1 for both states. g Excited states parameters employed and resulted in the graphs depicted in Figs. 4(g)– 4(i) and 5(a

) and 5(b

). Other parameters for state 1: 1 = 850 cm−1 , M1 = 0.460 Å, E00 = 47 800 cm−1 and for state 2: 2 = 850 cm−1 , M2 = 0.330 Å, E00 = 49 600 cm−1 . The standard deviation of inhomogeneous linewidth was = 450 cm−1 for both states.

for the two excited states were taken to be of comparable magnitude (M1 = 0.409 Å and M2 = 0.428 Å). The inclusion of large values of homogeneous line width ( 1 , 2 = 1000 cm−1 ) was necessary to reproduce the Raman cross sections, along with a reduced frequency of v1 (650 cm−1 ) in both excited states. The parameters employed in the model are reported in Table I. Even though these parameters allowed a good fit to the REP, we observe that the red edge of the absorption spectrum is not well reproduced, possibly due to the existence of more than two transitions contributing to the absorption spectrum in methanol. Figure S3 (in the supplementary material73 ) demonstrates that when a Lorentzian functional form is used (whose Fourier transform is an exponential function) rather than a Gaussian, the simulation can approximate the red edge better, while the parameters used are quite similar (Table S.I). We report below similar behavior in the other two cases examined. An insight on this behavior can be gained upon observation of the time-dependent overlaps (Eq. (S5)) in the Fourier transform integrals (Eqs. (S.1) and (S.3)). Figures S5(a) and S5(b) and S6(a) and S6(b) demonstrate that both the Gaussian and exponential functions describing

the homogeneous broadening decay on longer timescales than the i|i(t) overlap along the dissociative mode, with the latter truncating the evolution of the f|i(t) and i|i(t) wavepackets along ν 1 before 10 fs, placing the dynamics in the short-time regime. Therefore, we can conclude that even though inclusion of a large homogeneous line-width is necessary to reproduce the experimental observables, the type of broadening does not appear to have an effect on the dynamics. Figures 5(a) and 5(b) present the real and imaginary parts of the tensor elements that correspond to the two excited states (α xx and α zz ). Both excited states affect the Raman scattering and their contribution to the Raman depolarization curves is similar due to the similar values of the transition dipole moment.28 The equal amplitudes and the same sign of the real and imaginary parts of the polarizabilty tensors for the two states throughout the 35 000 cm−1 –65 000 cm−1 energy range resulted in a DPR dispersion curve of 1/8 (value for two perpendicular transitions). We find that even though this approach results in a DPR dispersion curve that deviates from 1/3, the dispersion curve is underestimated by this set of parameters (Fig. 4(c)). The results of this initial analysis show that a different approach must be taken into account in order to simulate not only the absorption and REP but the DPR’s as well. In Sec. III A 2 we show that the inclusion of inhomogeneous broadening permits the consideration of more reasonable values of homogeneous linewidth and of new combinations of excited states parameters that cause insignificant differences in the absorption and REP but reproduce well the DPR experimental values. 2. Modeling of D band by considering both homogeneous and inhomogeneous broadening

A number of studies in the condensed phase have focused on the fundamental source of broadening in the absorption spectrum and the REP ( vs. or both).17, 33, 64–67 In RRIA cases where methanol was the solvent,68–72 the contribution of inhomogeneous broadening in combination with homogeneous broadening was necessary for the description of the absorption spectrum and absolute RR cross sections. In the RRIA study of benzamide68 the dramatic increase in the inhomogeneous broadening observed in methanol compared to acetonitrile was attributed to hydrogen bonding between methanol and the molecule. In the case of p-nitroalanine in these two solvents, this increase was suggested to originate from the slower time for solvation in methanol, with the part of the reorganization that is slow on the ground state vibrational time scale appearing as inhomogeneous broadening.70 In a later study of Moran et al., in which the solvent effects in the ground and excited state of a push-pull chromophore were examined, it was concluded that the model in methanol requires larger values of compared to other solvents due to the involvement of torsional modes in this solvent,71 which are usually at low frequencies. Fairly large values of were also necessary in the case of charge transfer complexes in methanol.72 As it follows from analysis of the Mulliken charges (Fig. 2), the electrostatic interactions between solute and sol-


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vent may be quite significant. One can distinguish two main types of such interactions that occur in the ClNO2 /MeOH system: (a) the orientation of positively charged chloride towards the negatively charged oxygen of the methanol hydroxyl group (e.g., see Figure 1) and (b) the hydrogen bond between the negatively charged nitryl chloride oxygen and the hydrogen of the methanol hydroxyl group. As we will discuss in Sec. III B 2, such specific interactions can break the symmetry of the electronic wavefunction of the solute and induce notable changes in its electronic structure. Experimentally, this is seen as the additional broadening, arising because of distinct response of different electronic states to the complex changes of the collective coordinate of the solvent (inhomogeneous broadening). Because the effect of the polar solvent on the electronic structure of the solute is quite strong, the inhomogeneous broadening must be taken into account in order to accurately reproduce the experimentally measured spectra with our models. For all these reasons we believe it is necessary to adopt a significantly different set of parameters that includes both homogenous and inhomogeneous broadening. The poor fit to the DPR in Sec. III A 1 may be due to the neglect of the parameter. A value of = 450 cm−1 , a reduced amount of ( 1 = 800 cm−1 and 2 = 800 cm−1 ) and always considering a steep potential along the N-Cl coordinate (β = 2900 cm−1 ), led to an overestimation of the RR cross sections, therefore a further reduction of the N–O symmetric stretch frequency (v1 = 570 cm−1 for both states) was required to depress the absolute Raman cross sections. This latter adjustment caused down shifting of the absorption spectrum. However, the DPR curve showed minimal sensitivity to this change. Therefore, the displacements and the transition dipole moments for both states were iteratively varied to obtain a good fit to the absorption bandwidth and the pattern of the RR intensities and ´ DPR’s. Best fit was achieved with 1 = 2.2 and M1 = 0.360 Å ´ for state 1 and 2 = 2.9 and M2 = 0.488 Å for state 2. In comparison to the initial simulation, larger displacements along the N–O coordinate in the excited state were required, along with larger values of M1 and M2 and particularly, a greater ratio of transition dipole moment of excited state 2 to that of state 1. The calculated fits to the absorption spectrum, REP and DPR dispersion curve are given in Figures 4(d) and 4(e), and 4(f), respectively. The parameters employed in the calculation for the second model are presented in Table I. Figures 5(a ) and 5(b ) illustrate the dependence of the DPR on the amplitude of the polarizability tensor elements and the contribution of each excited state in the DPR for this set of parameters. The DPR curve never reaches the single excited state value, 1/3, because both states contribute to the scattering, but in this case greater values than 1/8 are obtained due to the different amplitudes in the real and imaginary parts of the polarizability. State 2 has a stronger contribution to the depolarization ratio dispersion curve than state 1 in the energy range from 40 000 cm−1 to 60 000 cm−1 due to its larger transition moment length (M1 < M2 ). The Raman intensity is proportional to the fourth power of M17 and thus the REP is more strongly affected by the excited state with the larger transition dipole moment (state 2).28 However, in the case of ClNO2 the two excited states are close in energy (E00 = 2700 cm−1 )

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and the transition dipole moments are within the same order of magnitude. Thus, although the contribution of excited state 1 is smaller, it cannot be ignored. Consequently, this analysis demonstrated that best fit to the experimental depolarization ratio dispersion curve is not achieved by the variation of the homogeneous and inhomogeneous broadening, but these parameters permit the variation of M, , and the v1 excited state frequency, which act at the level of the polarizability and affect not only the REP and absorption cross sections but also the DPR’s. A third possibility to explore is the case where transition to state 1 is stronger than transition to state 2 (M1 > M2 ). We examine this by alternating the transition dipole moments, which required 1 > 2 to reproduce the observed overall width of the absorption spectrum and the increasing trend of the DPR with increasing excitation energies. We chose to vary the displacements and not readjusting to reproduce the experimental electronic absorption spectrum, because changes in the displacements affect both the absorption spectrum and DPR in contrast to , which affects only the absorption spectrum. Furthermore, a small reduction of the excited state frequency along the N–O stretch and a small increase of the homogeneous linewidth was necessary. The excited state parameters were varied iteratively to obtain the best fit to all the observables, which are depicted in Figs. 4(g) and 4(h), and 4(i). The behavior of the real and imaginary parts of the polarizability tensors α zz and α xx are depicted in Figs. 5(a

) and 5(b

), respectively. As in the previous example, both states contribute to the scattering with the difference that here excited state 1 has a stronger contribution to the depolarization ratio dispersion curve than excited state 2 in the energy range from 40 000 cm−1 to 60 000 cm−1 due to its larger transition dipole moment (M1 > M2 ). The imaginary parts of both excited states exhibit a maximum after ∼50 000 cm−1 in contrast to the previous case where only state 2 reaches a maximum after this energy value, leading to overestimation of the Raman cross section at 50 600 cm−1 . In addition, the shift of the maximum of state 1 after 50 000 cm−1 is due to the relatively large value of 1 (1 = 3.5). The set of parameters employed in this case led to a less good fit of the red edge of the electronic absorption spectrum in contrast to the previous set of parameters. This observation for the experimentally well-defined edge of the spectrum puts a limit on the magnitude of the homogeneous broadening. In the first example, the red edge of the spectrum was well reproduced due to the large value of the homogeneous broadening. In the two latter sets of calculations the standard deviation of the inhomogeneous broadening, , was kept the same and the homogeneous broadening was varied. Consequently, an upper limit for the homogeneous broadening emerged with = 800 cm−1 for both excited states. B. Insights from the atomistic modeling

1. Molecular dynamics and linear response calculations (mechanism of the homogeneous broadening)

The homogeneous linewidth used in the modeling of the depolarization and absorption spectra has been considered as


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TABLE II. Homogeneous linewidths (cm−1 ) and decoherence times (given in parentheses, fs) for the ClNO2 /MeOH system as a function of its polarity and polarization of the solute. Scaling factor (polarity) Charge redistribution (polarizability) 0.625 1.0 1.6

1.6 Linewidth (cm−1 ) (dephasing time, fs)

1.75 Linewidth (cm−1 ) (dephasing time, fs)

843 (6.3) 1292 (4.1) 1940 (2.7)

792 (6.7) 1223 (4.3) 1811 (2.9)

an adjustable parameter so far. In order to get an estimate of this parameter from the atomistic point of view and to get further insight into the physical origin of the homogeneous broadening, we performed MD simulations and linear response calculations of the ClNO2 /MeOH system as described in Sec. II B. The effect of solvent polarity is accounted for by considering two scaling factors that convert Mulliken charges of the atoms to charges utilized for the electrostatic potential calculation. As noted in Sec. II B these two values represent the range of scaling factors that are capable of reproducing evaporation enthalpy and mass density of liquid methanol. Thus, they mainly serve the purpose of elucidating the role of polarity, rather than providing an exact answer. For each value of the scaling factor we systematically varied the amount of charge density being redistributed across the solute molecule (from Cl to NO2 group). This type of variation helps us elucidate the role of solute polarizability in determining the homogeneous linewidth, ∗ . The results of these calculations are presented in Table II. From Table II one can observe that the increased polarizability of the solute reduces the pure dephasing time and, equivalently, increases the homogeneous linewidth. Qualitatively, larger polarizability of solute often implies large magnitude of the transition dipole moments. Therefore, the data presented in Table II also suggest that excitations with the largest transition dipole moment lead to larger broadening. In the case of multiple electronic states involved in the photodynamics, the most important contribution is associated with the transition that has the largest oscillator strength, in agreement with the discussion presented in Secs. III A 1 and III A 2. For the gas-phase ClNO2 such a transition is σ → σ ∗ (Cl–N). Thus, the factors affecting this transition should have the most significant impact on the experimentally measured spectra. In Sec. III B 2 we shall discuss how this transition is affected by a solvent and what this implies. The other factor affecting the homogeneous broadening is the polarity. In contrast to the polarizability, it has an opposite effect – the dephasing slows down in more polar solvents. This observation has a clear physical interpretation. In general, as the solvent polarity increases, its reorganization requires more energy. Therefore, it becomes more difficult for the solute molecule to change its local environment than in less polar or non-polar solvents. The cage-effects become more pronounced, effectively keeping the system in a local minimum on the free energy surface (FES), which is similar for both ground and excited states. Because of such a similar-

ity of the FES slopes, the wavepackets evolving on the ground and excited states decohere more slowly. As mentioned earlier, the excited state PES of gas-phase ClNO2 has an unbound character along the Cl–N coordinate, providing a natural reason for fast dephasing. However, in the solvent environment the excited state FES may have a local minimum and a barrier for dissociation along the N-Cl coordinate. This barrier can increase in highly polar solvents, leading to longer dephasing times and to narrower line widths by the mechanisms discussed above. Among different polarity/polarizability parameter sets used (Table II), the one corresponding to transfer of 0.625e Mulliken charge and the scaling factor of 1.75 predicts the homogeneous linewidth broadening parameter = 792 cm−1 – the value close to the one used in the modeling described in Sec. III A 2 ( 1 and 2 = 800 cm−1 ). Thus, our atomistic simulations ensure that the homogeneous broadening effects should be described with the value of taken in a relatively narrow range. This re-emphasizes the role of inhomogeneous broadening as the next important factor contributing to the overall broadening. In addition to the linewidth calculations, we computed the influence spectra for the ClNO2 /MeOH system with different polarity (given by the scaling factors) of the solvent (Fig. 6). Our calculations show that the electronic transitions are driven by the low-frequency modes spanning a range from 84 to 210 cm−1 . These phonon modes correspond to collective “lattice” vibrations of the solute and solvent molecule. In addition, the low-frequency modes can also be associated with the motion of the heavy atoms, such as chlorine. In this case, the mode may even include stretching or bending of intramolecular bonds and angles. As the solvent polarity increases, the higher-frequency modes at ∼460 cm−1 start playing a more significant role. One may associate such type of motions with the specific electrostatic interactions, such as hydrogen bonding or “saltbridge”-like electrostatic interactions. As it follows from the analysis of the partial charges, the hydrogen bonds are more likely to form between O atoms in NO2 group and the H atom of the MeOH hydroxyl. As the charge on both H and O atoms increases, the interaction strength increases, opening an effective pathway for energy dissipation from ClNO2 into the solvent bath.

FIG. 6. Influence spectra for the ClNO2 /MeOH system showing the vibrational modes causing the homogeneous linewidth broadening.


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FIG. 7. Partial density of states of ClNO2 , computed with the hybrid PBE0 functional: (a) isolated molecule, note that HOMO–1 and HOMO–2 are almost degenerate but are of substantially different composition. For this reason the dot-and-line representation is used to show the density of Cl states in the isolated molecule; (b) in MeOH solvent. EF indicates the Fermi energy of the system. The DOS is normalized to the total number of states available to given molecule.

2. Electronic structure calculations (mechanism of the inhomogeneous broadening)

As it has been shown in Secs. III A 1 and III A 2, the contribution of the inhomogeneous broadening to the linewidth cannot be neglected, if a consistent and accurate description of the RR DPR’s and the electronic absorption spectra is to be obtained. One can expect that the inhomogeneous broadening effects are due to specific solvent-solute interactions that differently affect the electronic energy levels involved in the photodynamics. To uncover the effects associated with the solvent, we computed the pDOS for gas-phase ClNO2 (Fig. 7(a)) and for ClNO2 in methanol (Fig. 7(b)). The occupied orbitals of the gas-phase ClNO2 are formed by O and Cl 2p states, while the unoccupied molecular orbitals contain a notable fraction of N 2p states. This means that upon a photoexcitation, the electronic charge density is partially redistributed from the Cl end of the molecule making it more positive, to the NO2 end making it more negative. This leads to solute polarization, the extent of which can be modeled by assigning different partial atomic charges, as we used in our linear response calculations. The nature of the orbitals changes drastically in the presence of the solvent. In particular, the LUMO and LUMO + 1 states change their composition, resulting in reversal of their order. The shift of the Cl 2p states to lower energy constitutes another pronounced effect of the solvent, which alters the composition of the HOMO to HOMO–2 orbitals to primarily O 2p states, with negligible contributions from the Cl 2p orbitals. The computed frontier orbitals of the gas-phase system are visualized in Fig. 8, from where one can deduce the bonding character of the states. A detailed analysis of the molecular orbitals shows that the HOMO of ClNO2 is formed by equal amounts of the non-hybridized 2p O and 2p Cl states (Fig. 8(d)), while HOMO–1 is formed exclusively by the 2px Cl orbital (Fig. 8(c)). HOMO–2 is a mixture of the 2pz O and 2pz Cl states, forming together a state of σ symmetry (Fig. 8(b)). HOMO–3 is almost exclusively composed of the hybridized 2px O states, forming together a state of π symmetry (Fig. 8(a)). The charge density of the LUMO and LUMO + 1 orbitals (Figs. 8(e) and 8(f)) resembles that of the HOMO–2 and HOMO–3 orbitals, respectively.

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FIG. 8. Visualization of the charge density of frontier molecular orbitals in the gas-phase ClNO2 computed at the PBE0 level: (a) HOMO–3, π (O2 );(b) HOMO–2, σ (Cl–N); (c) HOMO–1, n(Cl); (d) HOMO, n(Cl) + n(O); (e) LUMO, σ ∗ (Cl–N); and (f) LUMO + 1, π ∗ (NO2 ). The isosurface value is 0.02 a.u.

The resulting assignment is in good agreement with the previous calculations18 with a few minor variations. In particular, the order of the HOMO–1 (Fig. 8(c)) and HOMO–2 orbitals (Fig. 8(b)) is reversed with respect to that reported previously. However the energy difference between these states is rather small (∼0.14 eV) and can be attributed to the methodological differences between PBE0 and MR-CI approaches. The energies for all possible electronic transitions between the occupied and unoccupied frontier orbitals are summarized in Table III. They are in reasonable agreement with the previous calculations: σ → σ ∗ (Cl–N), E = 6.9 eV (Lesar’s value 7.04 eV); π (O2 ) → π ∗ (NO2 ), E = 8.09 eV (Lesar’s value 7.25); n(Cl) → π ∗ (NO2 ), E = 7.28 or 6.67 eV (Lesar’s value 5.77 eV). Thus, the computational method (PBE0 functional with the pseudopotentials) is sufficiently accurate for description of the electronic energy levels in the system of interest and, therefore, is expected to be accurate for the extended solvent-solute system. The computed pDOSs for the extended system (Fig. 7(b)) and the visualization of the frontier orbitals shown in Fig. 9 clearly indicate that the solvent has a significant impact on the electronic structure of ClNO2 . Although one can identify the counterpart of nearly each orbital of solvated ClNO2 in the corresponding vacuum setup in terms of symmetry, the order of such orbitals is different. The fraction of atomic orbital contributions to the molecular orbitals may also vary. The energies of different orbitals are affected differently by solvent – some orbitals lower their energy much more than others. This leads to the alteration of the ordering of the orbitals in the solvent with respect to the gas-phase (Table IV). TABLE III. Transition energies (eV) for select transitions in the gas-phase ClNO2 .

HOMO–3, π (O2 ) HOMO–2, σ (Cl–N) HOMO–1, n(Cl) HOMO, n(Cl) + n(O)

LUMO, σ ∗ (Cl–N)

LUMO + 1, π ∗ (NO2 )

7.57 6.9 6.76 6.15

8.09 7.42 7.28 6.67


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less important, if not negligible. On the contrary, one should keep in mind that not only solvents capable of forming hydrogen bonds will introduce notable inhomogeneous broadening. Such effects will be expected for any solvent/solute pair in which specific interactions may be established (lock-and-key allosteric interactions, complexation, etc.) or when either has notable spatial anisotropy (e.g., macromolecular systems).

C. Assignment of electronic transitions

FIG. 9. Visualization of the charge density of frontier molecular orbitals in the gas-phase ClNO2 computed at PBE0 level: (a) HOMO–3, n(Cl), doubly degenerate; (b) HOMO–2, σ (Cl–N), doubly degenerate, isosurface value 0.002 a.u.; (c) HOMO–1, π (O2 ); (d) HOMO, n(O); (e) LUMO, π ∗ (NO2 ); and (f) LUMO + 1, σ ∗ (Cl–N). Isosurface value is 0.02 a.u.

Assuming that the transitions in the solvent involve the same type of orbitals as in the gas-phase, such a reversal agrees with the assumptions we made in the RR DPR simulations. It implies that the less intense π (O2 ) → π ∗ (NO2 ) transition occurs at the lower energy of 5.83 eV rather than the more intense σ → σ ∗ (Cl–N) transition that is characterized by a larger excitation energy. In fact, the latter consists of two nearly degenerate transitions at 6.79 and 6.65 eV, due to a near degeneracy of the σ (Cl–N) orbital. By analyzing several computational setups, differing in the geometry of the solvent-solute complex, we have found that the energies of the KS states can also notably fluctuate depending on the instantaneous configuration of the extended system. In particular, the LUMO − LUMO + 1 gap can vary from 0.5 to 1.5 eV, leading to similar fluctuations of the energies of the 31 B1 and 21 A1 states. This indicates that time (ensemble) averaging is needed for more accurate estimates of the transition energies and linewidths. Because of high computational demands of the PBE0 functional and because of the relatively large system size used in this study, such a dynamics cannot be currently computed. Still, the qualitative analysis described above elucidates possible mechanisms for the inhomogeneous line broadening of the electronic absorption spectra of ClNO2 in polar solvents, such as methanol. In closing this subsection, we want to emphasize that the inhomogeneous contribution to the line width is strongly related to the presence of specific interactions, such as hydrogen bonding. In the present system the hydrogen bonding effects tend to dominate the solvation process and may be not so important for non-polar solvents. Therefore, it is expected that in the latter systems the inhomogeneous broadening to be TABLE IV. Transition energies (eV) for select transitions in solvated ClNO2 . The quasi-degenerate energy levels are separated by commas. Orbitals HOMO–3, n(Cl) HOMO–2, σ (Cl–N) HOMO–1, π (O2 ) HOMO, n(O)

LUMO, π ∗ (NO2 )

LUMO + 1, σ ∗ (Cl–N)

7.39, 7.30 6.39, 6.26 5.83 5.21

7.79, 7.69 6.79, 6.65 6.23 5.60

Considering the experimental results and computational analysis presented here, there is no doubt that two separate transitions contribute to the scattering. However, the excited state parameters obtained from RRIA do not allow us to directly distinguish which excited state is 21 A1 and which one is 31 B1 . Theoretical calculations from literature18 have indicated that in the gas phase the vertical excitation energy to 31 B1 is higher (7.25 eV) than the vertical excitation energy to 21 A1 (7.04 eV). The theoretical calculations for the electronic structure of the isolated molecule performed in the present study also predict higher vertical excitation energy to the 31 B1 than to 21 A1 (8.09 eV vs 7.04 eV). Lesar et al.18 have calculated the oscillator strengths for transitions to all singlet states, with the transition to 21 A1 found stronger than transition to 31 B1 (f = 0.66 vs f = 0.28). Although the transition assignment for the gas-phase system is clear, there is no such assurance regarding the dominant transition in solution. The RR intensity analysis described above leads to the adoption of the second set of excited states parameters as the best combination for ClNO2 dissolved in methanol due to the better agreement between experimental and calculated results. This model presupposes that a lower energy state (state 1) has also a lower value of oscillator strength than a higher-lying excited state (state 2) (M1 < M2 ). Thus, considering the theoretical results for the gas phase one may attribute state 1 to 31 B1 (π (O2 ) → π ∗ (NO2 ) transition) and state 2 to 21 A1 (σ → σ ∗ (Cl–N) transition). However, the vertical excitation energies derived from our RR study (maxima of the calculated absorption bands for the two states) are reversed compared to theoretical results for the gas phase. The energy maximum for state 1 is 5.94 eV and the corresponding value for state 2 is 6.33 eV. Both absorption spectrum and pDOS calculations of ClNO2 in MeOH demonstrate that the solvent influences the excited state energies. Specifically, in the section above it was shown that in solution the ordering of the two transitions involved in the D band is reversed because of the notably different effect of the solvent on the orbitals involved in these transitions. In both cases the energies for the transition π (O2 ) → π ∗ (NO2 ) and σ → σ ∗ (Cl–N) shift to lower values – from 8.09 eV to 5.83 eV for the former and from 6.9 eV to 6.79 and 6.65 eV for the latter. Because the π (O2 ) → π ∗ (NO2 ) transition is affected to a larger extent – shift by 2.26 eV – than the σ → σ ∗ (Cl–N) transition for which the shift is only 0.11–0.25 eV, the overall effect of the solvent is seen as the reversal of the character of the excited states. In addition to the energy shift of the electronic levels, the solvent splits the σ → σ ∗ (Cl–N) transition into two


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energetically close states, resulting in two closely spaced peaks at 6.79 and 6.65 eV, as has been noted in Sec. III B. The energy difference of 0.14 eV is comparable with the one calculated from RRIA (0.39 eV). On the contrary, the energy difference between 21 A1 and 31 B1 states is somewhat larger – 0.96–1.07. Keeping in mind that these values correspond to instantaneous nuclear configurations one can expect that the ensemble-averaged values can provide better agreement with the values deduced from the RRIA measurements. Thus, the most important factors leading to deviation of the depolarization ratios of ClNO2 in methanol from 1/3 are: (a) involvement of both 21 A1 and 31 B1 states in the excited state dynamics and (b) additional splitting of the levels of originally degenerate excited state 21 A1 due to solvent-solute interactions.

IV. CONCLUSIONS

The analysis of the depolarization ratio dispersion curve for ClNO2 in methanol presented in this study in combination with theoretical calculations (MD, ab initio, and linear response) revealed the key role of solute–solvent interactions in this molecular system. The systematic investigation of the contributions to spectral broadening indicated clearly that inhomogeneous broadening is a limiting factor for the quantification of the broadening in dissociative molecules that scatter in the short time limit. The contribution of inhomogeneous broadening was found to stem from the solute–solvent interactions that occur in the system, and its inclusion was necessary in order to model all the experimental observables (REP, absorption spectrum and DPR’s). The solute–solvent interactions consist of both electrostatic interactions of the MeOH oxygen with the Cl and hydrogen bonding between the negatively charged ClNO2 oxygen and the OH hydrogen. Moreover, combination of pDOS calculations and RRIA revealed a number of solvent-induced changes in the electronic structure of the molecule leading to alteration of excited state energies with corresponding implications for the state contributions to the D absorption band of ClNO2 .

ACKNOWLEDGMENTS

M.T. and S.C.H. gratefully acknowledge funding from the Cyprus Research Promotion Foundation, grant PENEK/ENISX/0508/19 and KY-GA/0907/07. The funds for the grant involve contributions from the Republic of Cyprus and the European fund for regional development of the European Union. A.V.A. was funded by the Computational Materials and Chemical Sciences Network (CMCSN) project at Brookhaven National Laboratory under contract DE-AC0298CH10886 with the U.S. Department of Energy and supported by its Division of Chemical Sciences, Geosciences & Biosciences, Office of Basic Energy Sciences. O.V.P. acknowledges financial support from the U.S. Department of Energy, grant DE-SC0006527. The authors would like to acknowledge helpful discussions with Anne Myers Kelly and Søren Hassing, and would like to thank Antonjia Lesar for making available the results from electronic structure calcula-

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tions for Fig. 3, as well as Christophe Jouvet for preliminary calculations. 1 M.

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