Time-resolved resonance-enhanced Stokes and anti-Stokes Raman spectra of the thiocyanate dimer radical anion, (SCN)2•−, prepared by pulse radiolysis in water, have been obtained and interpreted in conjunction with theoretical calculations to provide detailed information on the molecular geometry and bond properties of the species. The structural properties of the radical are used to develop a molecular perspective on its thermochemistry in an aqueous solution. Twenty-nine Stokes Raman bands of the radical observed in the 120-4200 cm−1 region are assigned in terms of the strongly enhanced 220 cm−1 fundamental, weakly enhanced 721 cm−1, and moderately enhanced 2073 cm−1 fundamentals, their overtones, and combinations. Calculations by range-separated hybrid density functionals (ωB97x and LC-ωPBE) support the spectroscopic assignments of the 220 cm−1 vibration to a predominantly SS stretching mode and the features at 721 cm−1 and 2073 cm−1 to CS and CN symmetric stretching modes, respectively. The corresponding bond lengths are 2.705 (±0.036) Å, 1.663 (±0.001) Å, and 1.158 (±0.002) Å. A first order anharmonicity of 1 cm−1 determined for the SS stretching mode suggests a convergence of vibrational states at an energy of ∼1.5 eV, using the Birge-Sponer extrapolation. This value, estimated for the radical confined in solvent cage, compares well with the calculated gas-phase energy of 1.26 ± 0.04 eV required for the radical to dissociate into SCN and SCN fragments. The enthalpy of dissociation drops to 0.60 ± 0.03 eV in water when solvent dielectric effects on the radical and its dissociation products upon S–S bond scission are incorporated in the calculations. No frequency shift or spectral broadening was observed between light and heavy water solvents, indicating that the motion of solvent molecules in the hydration shell has no perceptible effect on the intramolecular dynamics of the radical. The Stokes and anti-Stokes Raman frequencies were found to be identical within the experimental uncertainty, suggesting that the frequency difference between the thermally relaxed and spontaneously created vibrational states of (SCN)2•− in water is too small to be observable.

The thiocyanate dimer radical anion, (SCN)2•−, has been, for decades, a preferred model for monitoring and elucidating transient phenomena in a host of physicochemical and biological processes.1–13 The radical is formed by oxidation of the thiocyanate anion (SCN), followed by subsequent bonding of the radical produced with the parent ion. In electron irradiated aqueous solution, the hydroxyl radical (OH) is the initial oxidant. A broad structureless optical absorption with maximum at 472 nm (εmax ∼ 7580 M−1cm−1) in water, which shifts to 490 nm in the less polar dichloromethane,11 is ascribed to the radical. This absorption is routinely used as a radiation dosimeter in electron pulse radiolysis. The decrease in the yield of (SCN)2•−, when another chemical species competes with its formation, provides valuable kinetic information on the OH reactivity with the latter.8 Formation of (SCN)2•− is also used for establishing charge transfer phenomenon occurring across semiconductor-liquid interfaces. The interfacial hole transfer from photoexcited titanium dioxide (TiO2) to an adsorbed SCN anion is believed to form the SCN radical that reacts with an adjacent surface anion to produce (SCN)2•−, again identified by its optical absorption.3–7,12 The (SCN)2•− radical also finds frequent applications as a reference system for both experimental and theoretical modelings of the two-center three-electron (2c-3e) bonded multi-atomic systems, particularly those containing a sulfur atom.1,2,13

In early studies, properties of the 2c-3e class of radicals were discussed with reference to their optical absorption spectra in aqueous media, with a general qualitative description of the electronic transition.14 The absorption energy was correlated with the relative bond strength in the ground electronic state while making comparison in a series of radicals involving a similar bonding pattern.14 So far, there has been no convincing experimental or theoretical justification for such correlations.

In recent years, the 2c-3e bonded di- and poly-atomic species have been subjected to numerous quantum chemical calculations to provide a quantitative description of their electronic structure and bond properties.1,2,13,15–17 These calculations often suffer from serious disagreements, particularly when applied to polyatomic systems. In a semi-empirical Intermediate Neglect of Differential Overlap (INDO) computation, (SCN)2•− was assumed to be SS bonded, as in its oxidized closed-shell state thiocyanogen (SCN)2,15,18 which was subsequently confirmed by more advanced calculations.1 In a simplified qualitative consideration, the p and p2 electrons located on S atoms that mostly contribute towards the 2c-3e bonding would be directed normal to the SCN moiety axis. Therefore, the SSC angles cannot be drastically different from 90°. Within that constraint, the two SCN groups can acquire any relative orientation. The INDO calculations suggest a non-planar geometry for (SCN)2 and (SCN)2•−, the SSC angles 115°-133°, and the two SCN groups making an angle of 90°(±15°) with respect to each other (torsional angle). While the INDO (SCN)2 geometry is consistent with the vibrational spectra of that molecule, a similar conclusion cannot be drawn for (SCN)2•− due to meager experimental data available for confirmation.15,18 The negative electronic charge distributed over the two SCN groups induces additional intramolecular interactions. The solute-solvent interactions can also be significant if the radical anion is embedded in a polar solvent. In contrast to the semi-empirical INDO structure, a second order Møller–Plesset (MP2) perturbation computation on (SCN)2•− predicted a molecular geometry in which the two SCN groups have a near trans configuration.1,16 Commonly used density functional theory (DFT) calculations, employing the B3LYP functional,19 for example, display severe limitations when applied to such 2c-3e-bonded systems.2,13,17 Recently, a superior description of ultraviolet/visible (UV−Vis) absorption signatures of 2c-3e-bonded transient anions by range-separated hybrid (RSH) density functionals has been provided.2,13 In particular the RSH functional LC-ωPBE20 has been successfully applied to predict the UV-Vis spectra, harmonic frequencies, and dissociation energies of a series of 2c-3e dihalide radical anions (X2•−).17 On the other hand, the merits of another RSH functional, ωB97x,21 have been illustrated by the example of (H2O–OH2)+.22 We have extended the computational studies on (SCN)2•− in water using these two RSH DFT methods in this work.

As stated earlier, experimental information available to date for testing the validity and efficacy of various calculation methods for 2c-3e bonded species is insufficient. Electron paramagnetic resonance (EPR) and vibrational spectra yield far more structural content than provided by the electronic absorption spectra in solution, and are specific to the ground electronic state. On the other hand, optical spectra combine properties of the ground as well as the excited electronic states. The EPR spectral lines are broadened for sulfur containing radicals, such as (SCN)2•−, due to spin-orbit coupling, making a precise determination of hyperfine constants difficult. Thus far, an EPR study of the radical in liquid water has not been reported, even though there have been studies in aqueous glasses.23 The Raman scattering spectra, on the other hand, do not suffer from such limitations and should give a clear picture of the molecular geometry and bonding. An early resonance Raman study on this radical has provided very limited information due to experimental limitations related to poor signal-to-noise ratio in the spectra. We have undertaken an in-depth investigation of the resonance Raman spectra of (SCN)2•− in an aqueous solution, with more than an order of magnitude better signal-to-noise ratio than reported previously.18 Therefore, very weakly enhanced Raman bands, previously obscured by noise, are now revealed. Complemented with appropriate theoretical calculations, as outlined above, these new experimental data provide detailed information on the molecular geometry and bond properties of aqueous (SCN)2•−. The vibrational frequencies in the resonance Raman spectra are the characteristic of the ground electronic state and the intensity profile of the excited electronic state. We have examined the 2c-3e characteristic features in both electronic states of polyatomic (SCN)2•−, by contrasting with genuine 2c-3e diatomic systems of dihalide radical anions. The structural information deduced from the experiment and theory has been applied, for the first time, to discuss the thermochemistry of a 2c-3e bonded species in an aqueous environment.

Pump and probe transient resonance Raman experiments were performed using a 2 MeV Van de Graaff electron accelerator providing 200-300 ns electron pulses (0.8 A peak current) with a 7.5-15 Hz repetition rate to induce water radiolysis. These enhanced repetition rates allow an efficient signal averaging which was not previously possible.18 A dye laser (Scanmate 2, Lambda Physik) pumped with a 308 nm excimer laser (CompexPro, Lambda Physik) was tuned to 480 nm and used as a Raman probe source. Significant changes were made in the existing experimental setup24 at the Notre Dame Radiation Laboratory (NDRL) to both enhance the scattered light gathering efficiency and substantially reduce radiation-induced noise in the detection system. The laser delivery line consisted of a pair of dielectric mirrors and a focusing lens. A typical laser energy used during the experiment was ∼0.4 mJ/pulse. The solution was subjected to electron pulse irradiation in the form of a jet. To sustain a stable jet, two ISCO 500D syringe pumps in a continuous flow mode were used. The position of the jet was adjusted to achieve the best overlap of the focused electron beam with the focused laser ray crossing the jet. Backscattered light was collimated by a lens adjusted to collect the Raman signal from the volume of the jet in which the laser and electron beam were overlapping. In order to avoid radiation-induced X-rays (bremsstrahlung) registering on the intensified charge-coupled device (i-CCD) camera, the detection system was placed outside of the accelerator vault. A collimated beam of scattered light was directed by three flat Al/MgF2 mirrors out of the vault through an aperture in the wall and focused onto a 850 mm spectrograph (SPEX 1402) equipped with a holographic 1800 lines/mm grating blazed at 400 nm (Richardson Gratings). A gated UV-GEN2 ICCD camera (Unigen, PI-MAX, Princeton Instruments) was used as a detector. The camera gate (80 ns) and scattered light pulse were set to overlap after the end of the electron pulse in order to observe the generated transient species at their highest concentration accessible while avoiding unwanted Cherenkov radiation associated with the electron beam, which would saturate the detector. Raman frequencies were determined from the dispersion of our instrument by reference to standard Raman bands of carbon tetrachloride, ethanol, and acetonitrile. Instrumental dispersion was better than 1 cm−1 per optical channel, and the centers of the bands were measurable with a probable error of ±1 cm−l.

The experimental details for pulse radiolysis transient absorption studies in the NDRL are described elsewhere.25 

All the calculations were performed using the Gaussian 09 program package.26 The range separated hybrid functionals, LC-ωPBE,20 LC-PBE, LC-BLYP, LC-OLYP, LC-TPSS, ωB97, and ωB97x,20 were used for calculations with default values of their respective parameters. Our objective has been to identify DFT methods that best describe our experimental findings using seven functionals that have been proven the best in prediction of UV-Vis signatures in 2c-3e systems.2,13 Post Hartree-Fock MP2 methods were also employed for comparison.27,28 Correlation consistent basis sets of the triple ζ type, augmented with diffuse functions, denoted aug-cc-pVTZ,29,30 were used throughout this study. The effect of hydration was taken into account by applying a Integral Equation Formalism variant of Polarizable Continuum Model31 (IEFPCM) with the default parameters for water. Optimized geometries and orbitals were visualized by using the GaussView program package.

The hydrated electron (e)aq and the OH radical are the dominant reactive species produced on radiolysis of oxygen-free water in near neutral aqueous solutions. The hydrated electron converts into OH in <5 ns (k ∼ 9.1 × 109 M−1s−1)8 in water saturated with N2O (∼25 mM). The OH radical reacts with SCN with a rate constant of 1.1 × 1010 M−1s−1 to oxidize it into the SCN radical.8 The formation of (SCN)2•− is complete in <100 ns, for a solution containing >1 mM SCN. The transient absorption spectrum of (SCN)2•− , prepared by OH oxidation of SCN, is displayed in Fig. 1 for reference.

FIG. 1.

Transient absorption spectrum of SCN2•− registered 20 ns after 15 ns pulsed electron irradiation of N2O-saturated 10 mM KSCN solution at neutral pH. The dashed line corresponds to the wavelength of the probing laser light used in resonance Raman experiment.

FIG. 1.

Transient absorption spectrum of SCN2•− registered 20 ns after 15 ns pulsed electron irradiation of N2O-saturated 10 mM KSCN solution at neutral pH. The dashed line corresponds to the wavelength of the probing laser light used in resonance Raman experiment.

Close modal

For Raman experiments, a jet of a 10 mM aqueous solution of KSCN bubbled with N2O for 30 min was subjected to electron pulse irradiation. Acquisition of the resonance Raman spectrum of the desired radical was performed by laser excitation at 480 nm near its optical absorption maximum (see Fig. 1). The averaged raw Raman spectrum acquired over as many as 36 000 laser pulses as required was subtracted from the identically averaged raw Raman spectrum of the same solution but recorded 100 ns after 300 ns long electron pulses. Because of fairly good dispersion of the grating used, the spectral coverage was limited to about 600 cm−1 in one setting. The closest frequency to the exciting laser line that could be usefully accessed was 160 cm−1. Several 600 cm−1 wide segments of the overlapping spectra, at different angles of diffraction grating, obtained in the 160 cm−1 to 2000 cm−1 wave number region are displayed in Fig. 2. A similarly obtained Raman spectrum in the 1600-4100 cm−1 region is presented in Fig. 3. Intensity normalization was done with reference to the overlapping Raman bands.

FIG. 2.

Lower spectral range resonance Raman spectrum of (SCN)2•− recorded 100 ns after a 300 ns electron pulse in 10 mM KSCN solution saturated with N2O at neutral pH, probed at 480 nm. Inset: Plot of vibrational frequency vs. vibrational quantum number [spectroscopic parameters of (SCN)2•−].

FIG. 2.

Lower spectral range resonance Raman spectrum of (SCN)2•− recorded 100 ns after a 300 ns electron pulse in 10 mM KSCN solution saturated with N2O at neutral pH, probed at 480 nm. Inset: Plot of vibrational frequency vs. vibrational quantum number [spectroscopic parameters of (SCN)2•−].

Close modal
FIG. 3.

Higher spectral range resonance Raman spectrum of (SCN)2•− recorded 100 ns after the 300 ns electron pulse in a 10 mM KSCN solution saturated with N2O at neutral pH, probed at 480 nm.

FIG. 3.

Higher spectral range resonance Raman spectrum of (SCN)2•− recorded 100 ns after the 300 ns electron pulse in a 10 mM KSCN solution saturated with N2O at neutral pH, probed at 480 nm.

Close modal

The spectra in Figs. 2 and 3 are examined for their 2c-3e characteristics, as (SCN)2•− is often referred to as a pseudo-dihalide radical anion (X2•−) in the literature.11 The strongest Raman band in Fig. 2 appears at 220 cm−1 and compares well with the radical frequency reported previously.15,18 We confirm, as discussed later, the suggested assignment of this frequency to the SS stretching mode, based on purely spectroscopic arguments. The excellent signal-to-noise ratio in our spectra allows the observation of more than six overtones of this vibration and a reasonably accurate estimation of the first order anharmonicity constant, a valuable structural parameter, which has not been known previously. In addition, we have been able to recognize new spectral features in the low frequency region. A weak shoulder band at 721 cm−1 can be clearly seen in Fig. 2, which is not explainable as an overtone of the 220 cm−1 fundamental. It is relatively sharper than the nearby overtones. The 721 cm−1 frequency combines with the 220 cm−1 mode and its overtones to give rise to bands at 941 cm−1, 1159 cm−1, and 1375 cm−1 (Fig. 2). A Raman transition originating from the thermally populated 220 cm−1 vibrational state and terminating at 721 cm−1 appears as a very weak and poorly resolved shoulder band at 501 cm−1. The first overtone of the 721 cm−1 vibration appears at 1442 cm−1. The fact that the 721 cm−1 frequency combines with the 220 cm−1 fundamental and its overtones is a clear indication that the both vibrations belong to the same chemical species and not to any impurity or other transient reaction product.

The Raman spectrum in the 1800-4200 cm−1 region (Fig. 3) shows the strongest band at 2073 cm −1. This band has about 20%-25% the intensity of the 220 cm−1 Raman band in Fig. 2. The 2073 cm−1 frequency combines with not only the 220 cm−1 and 721 cm−1 fundamentals but also several of their overtones and combinations, in an additive and subtractive fashion as indicated by the abundance of combination bands in the high frequency spectral region shown in Fig. 3. Assignment of the observed peaks is summarized in Table I. In spite of the exceptional signal-to-noise ratio (260/1 when necessary to develop very weak signals) in our spectra, and our capability to detect a band even if it is only ∼1% as intense as the strongest 220 cm−1 band, we could identify only three fundamentals. It is obvious that the negligible resonance Raman enhancement of the other fundamentals reflects on the nature of the species and not on the limitation of the experiments.

TABLE I.

Raman frequencies (cm−1) of (SCN)2•− and their assignment.

This workTheoretical predictions ωB97x/aug-cc-pVTZ in PCM water (harmonic)Previous studies18 Assignment
220 221 218 ν(SS) 
438  439 2ν(SS) 
501   ν(CS)−ν(SS) 
654  657 3ν(SS) 
721 738  ν(CS) 
868   4ν(SS) 
941   ν(CS)+ν(SS) 
1080   5ν(SS) 
1159   ν(CS)+2ν(SS) 
1290   6ν(SS) 
1375   ν(CS)+3ν(SS) 
1442   2ν(CS) 
1589   ν(CS)+4ν(SS) 
1635   ν(CN)−2ν(SS) 
1662   2ν(CS)+ν(SS) 
1853  1849 ν(CN)−ν(SS) 
2073 2230 2067 ν(CN) 
2293  2285 ν(CN)+ν(SS) 
2511  2512 ν(CN)+2ν(SS) 
2727   ν(CN)+3ν(SS) 
2794   ν(CN)+ν(CS) 
2941   ν(CN)+4ν(SS) 
3014   ν(CN)+ν(SS)+ν(CS) 
3153   ν(CN)+5ν(SS) 
3232   ν(CN)+2ν(SS)+ν(CS) 
3363   ν(CN)+6ν(SS) 
3480   Water 
3708   2ν(CN)−2ν(SS) 
3926   2ν(CN)−ν(SS) 
4146   2ν(CN) 
This workTheoretical predictions ωB97x/aug-cc-pVTZ in PCM water (harmonic)Previous studies18 Assignment
220 221 218 ν(SS) 
438  439 2ν(SS) 
501   ν(CS)−ν(SS) 
654  657 3ν(SS) 
721 738  ν(CS) 
868   4ν(SS) 
941   ν(CS)+ν(SS) 
1080   5ν(SS) 
1159   ν(CS)+2ν(SS) 
1290   6ν(SS) 
1375   ν(CS)+3ν(SS) 
1442   2ν(CS) 
1589   ν(CS)+4ν(SS) 
1635   ν(CN)−2ν(SS) 
1662   2ν(CS)+ν(SS) 
1853  1849 ν(CN)−ν(SS) 
2073 2230 2067 ν(CN) 
2293  2285 ν(CN)+ν(SS) 
2511  2512 ν(CN)+2ν(SS) 
2727   ν(CN)+3ν(SS) 
2794   ν(CN)+ν(CS) 
2941   ν(CN)+4ν(SS) 
3014   ν(CN)+ν(SS)+ν(CS) 
3153   ν(CN)+5ν(SS) 
3232   ν(CN)+2ν(SS)+ν(CS) 
3363   ν(CN)+6ν(SS) 
3480   Water 
3708   2ν(CN)−2ν(SS) 
3926   2ν(CN)−ν(SS) 
4146   2ν(CN) 

The vibrational mode assignment of the 721 cm−1 and 2073 cm−1 vibrational frequencies is straightforward, based on the earlier studies of analogous molecules and radicals. The (SCN)2•− radical with 6 atoms can have only 12 fundamental vibrations. Since the 472 nm electronic transition of the radical is quite strong, only totally symmetric vibrations would have favorable Raman Franck-Condon factors necessary for their significant resonance enhancement.32 The observation of only three fundamental vibrations in resonance Raman spectra suggest that the radical geometry is either highly symmetric or the symmetric vibrations in a molecular configuration of low symmetry do not involve an appreciable change in the nuclear coordinates from the ground to the excited electronic state (negligible Raman Franck-Condon factor). The observed vibrations that must be totally symmetric with respect to the molecular geometry can be readily attributed to the stretching motions of the SS, CS, and CN bonds. The CS and CN bonds are single and triple bonds in the parent anion, and a drastic change in their nature is not expected due to bonding involving an unpaired electron located on the sulfur atom in SCN with the non-bonding electron pair on the sulfur atom of SCN. The respective stretching frequencies cannot be drastically different and, therefore, a minimal effect of mixing of the atomic displacements or mechanical coupling is expected. The CS symmetric stretch frequency in the gas phase thiocyanogen, (SCN)2, has been measured in the range of 668-673 cm−1.33,34 In aqueous SCN, the CS frequency is found at 75235 cm−1, and is obviously affected by the hydrogen bonding and the solvent dielectric effect of water.36 Those effects are expected to be relatively smaller in (SCN)2•−, as the negative charge is distributed over two SCN moieties and the dimer radical is larger in size. The CS stretching frequency of 721 cm−1 in (SCN)2•− is of intermediate magnitude, which is as expected. The CN frequency in SCN,37,38 SCN,35,37,39 and (SCN)234,40 occurs in the 2070-2100 cm−1 region. The observed vibration at 2073 cm−1 in (SCN)2•− is thus readily assignable to the CN stretching motion.

SS bonding in (SCN)2•− can be compared to 2c-3e bonding in diatomic radical anions (X2•−). The stretching frequency in aqueous Cl2•− has been observed at 273 cm−1.41 Considering only the masses of Cl and S atoms, and assuming similar force constants, the 2c-3e SS bond stretch in a hypothetical hemibonded S2•− molecule would be at ∼287 cm−1. With the Br2•− frequency of 167 cm−1 as a reference,41 the SS frequency is expected at ∼264 cm−1, and with I2•− as a reference41 at 229 cm−1. Of course, the SS frequency in (SCN)2•− can be slightly lower, if the reduced mass of S atoms in the SCN moieties is taken into consideration. The observed frequency 220 cm−1 in SCN2•− is thus in the expected range. Therefore, (SCN)2•− behaves as a genuine 2c-3e bonded multi-atomic radical species or as a pseudo-diatomic-dihalide radical anion (X2•−) in water in its ground electronic state.

In an isolated three-electron bonded diatomic (X2•−) system, the lowest excited electronic state is dissociative.42,43 A relatively high intensity of the 220 cm−1 band in the spectra, along with the appearance of a number of overtones (Figs. 2 and 3), suggests a drastic change in the SS bond length in the resonant excited electronic state, as in X2•− radicals. In an analogous polyatomic system, one would expect to observe only one very strongly enhanced vibration and its overtones, and other vibrations which do not mechanically couple with that vibration should have far less intensity. It is clear that (SCN)2•− does not fulfill that criterion. The strongly enhanced CN fundamental band and observably enhanced CS fundamental in resonance Raman spectra (Figs. 2 and 3) are indicative of a resonant excited electronic state that involves a significant nuclear displacement along all atomic coordinates in the excited state, particularly along the CN bond. Figure 4 illustrates computed natural transition orbitals of (SCN)2•−. We can clearly see that upon excitation, molecule experiences a change in the electron density over all bonds which should translate to the consequential nuclear displacements. The excited electronic states in 2c-3e polyatomic radicals, such as (SCN)2•−, do not necessarily parallel their ground electronic state or retain analogy with X2•−.

FIG. 4.

Natural transition orbitals of (SCN)2•− computed at the IEFPCM-ωB97x/aug-cc-pVTZ level. Upon excitation, there is a large change in the electron distribution around the SS bond (bonding to antibonding), additionally apparent π-bonding between C and N shifts towards C and S.

FIG. 4.

Natural transition orbitals of (SCN)2•− computed at the IEFPCM-ωB97x/aug-cc-pVTZ level. Upon excitation, there is a large change in the electron distribution around the SS bond (bonding to antibonding), additionally apparent π-bonding between C and N shifts towards C and S.

Close modal

The computational procedure that best predicts the experimental vibrational frequencies, in accord with their qualitative spectroscopic interpretation,44 should well describe its molecular geometry. A group of seven different RSH functionals, based on their performance in the previous studies,2 namely, LC-ωPBE, LC-PBE, LC-OLYP, LC-BLYP, LC-TPSS, ωB97, and ωB97x, were selected to compute vibrational frequencies of (SCN)2•− in water. Of these, the results of geometry optimization of (SCN)2•− with Dunning’s augmented triple-ζ basis set (aug-cc-pVTZ) are summarized in Table II. All of the methods were able to predict harmonic frequencies very close to the observed experimental anharmonic values. In contrast, the SS frequency calculated by most often used DFT functional, B3LYP, is reported as 160 cm−1 which is a 32% underestimation.1 We determined frequency scaling factors for each tested RSH method using an arithmetic average of individual corrections applied to best match experimental and computed frequencies of SS, CS, and CN bonds (Table II). Applying these scaling factors, one can predict experimental frequencies of (SCN)2•− using either of the RSH methods within several percent of accuracy. Since most commonly used RSH functionals, LC-ωPBE or ωB97x, are capable of predicting experimental frequencies of (SCN)2•− normal modes within average 3% error, we decided to extend our further computational studies using only these two methods.

TABLE II.

Comparison of optimized geometries of (SCN)2•− calculated with MP2 and selected range-separated hybrid functionals in PCM water using aug-cc-pVTZ basis set. Vibrational frequencies adjusted by scaling factors are given in parentheses (see text).

ExperimentMP2LC-ωPBEωB97xLC-PBELC-BLYPLC-OLYPLC-TPSSωB97
SS stretching (cm−1220 248 239 (223) 221 (214) 256 (231) 240 (223) 241 (223) 253 (229) 225 (216) 
SC stretching (cm−1721 728 747 (693) 738 (716) 767 (691) 745 (693) 754 (697) 762 (691) 746 (716) 
CN stretching (cm−12073 2560 2266 (2148) 2230 (2164) 2318 (2087) 2310 (2148) 2316 (2140) 2316 (2099) 2240 (2149) 
Scale factor   0.9350 0.9704 0.9005 0.9301 0.9242 0.9062 0.9595 
r(SS) (Å)  2.707 2.669 2.742 2.621 2.685 2.671 2.635 2.729 
r(SC) (Å)  1.673 1.662 1.664 1.652 1.660 1.655 1.654 1.665 
r(CN) (Å)  1.174 1.156 1.160 1.149 1.147 1.148 1.148 1.161 
α(SSC) (deg)  84 96 94 94 95 95 94 94 
Tors. angle (CSSC) (deg)  180 83 56 56 75 75 79 54 
ExperimentMP2LC-ωPBEωB97xLC-PBELC-BLYPLC-OLYPLC-TPSSωB97
SS stretching (cm−1220 248 239 (223) 221 (214) 256 (231) 240 (223) 241 (223) 253 (229) 225 (216) 
SC stretching (cm−1721 728 747 (693) 738 (716) 767 (691) 745 (693) 754 (697) 762 (691) 746 (716) 
CN stretching (cm−12073 2560 2266 (2148) 2230 (2164) 2318 (2087) 2310 (2148) 2316 (2140) 2316 (2099) 2240 (2149) 
Scale factor   0.9350 0.9704 0.9005 0.9301 0.9242 0.9062 0.9595 
r(SS) (Å)  2.707 2.669 2.742 2.621 2.685 2.671 2.635 2.729 
r(SC) (Å)  1.673 1.662 1.664 1.652 1.660 1.655 1.654 1.665 
r(CN) (Å)  1.174 1.156 1.160 1.149 1.147 1.148 1.148 1.161 
α(SSC) (deg)  84 96 94 94 95 95 94 94 
Tors. angle (CSSC) (deg)  180 83 56 56 75 75 79 54 

The SS, CS, and CN bond distances in an isolated molecule by the RSH functional ωB97x, 2.760 Å, 1.668 Å, and 1.160 Å compare well with the literature MP2 values of 2.752 Å, 1.679 Å, and 1.174 Å, respectively.1 Reported MP2/6-311++G(d,p) SS stretching frequency,1 230 cm−1, is close to the ωB97x frequency of 220 cm−1 (experimental harmonic frequency—222 cm−1). However when aug-cc-pVTZ basis set is used with the MP2 method, the geometry/frequency changes noticeably (Table II) suggesting that MP2 approach strongly depends on the basis set.27,45 The experimental vibrational spectroscopic data are not adequate to make a preference between the structural predictions by the LC-ωPBE and ωB97x functionals. Giving both of them equal weights, we estimate the SS bond lengths in PCM water as 2.705 (±0.035) Å, CS bond lengths as 1.663 (±0.001) Å, and CN bond lengths as 1.158 (±0.002) Å. Although the torsional angle is predicted to be about the same, i.e., 180° for the isolated radical, both methods predict relatively shallow potential minimum which agrees well with MP2 predictions reported earlier1 as well as with our own MP2 calculations (Fig. 5). The effect of polarizable continuum is quite dramatic in RSH methods as it causes a decrease of the CSSC dihedral angle to 83° and 56°, respectively (Fig. 5). Interestingly, polarizable continuum does not affect dihedral angle as vividly in MP2/aug-cc-pVTZ method as the global minimum remains at 180° but the molecule gains additional local minimum near 75°, which can be reached via a low energy barrier (Fig. 5). The SSC angle is close to 90° ± 6° for all the methods explored (Table II). None of the bending vibrations expected in the low frequency region, as in (SCN)2, are observably resonance enhanced in (SCN)2•−. In a molecular geometry lacking symmetry, the SSC bending normal mode would be totally symmetric (Raman Franck-Condon allowed) and may contain a small SS displacement and, for that reason, could be seen in resonance Raman spectrum. However, for a molecular geometry with SSC angle close to 90°, the SS displacement component would be negligible, and that may be the reason why the bending modes are not observed. A bending frequency (of SCN) calculated at about ∼440 cm−1 (446 cm−1) is degenerate with the overtone of the experimental 220 cm−1 frequency, but there is no evidence that such a vibration is in Fermi resonance with the overtone frequency. It appears that the RSH molecular geometry is not lost on reduction of (SCN)2 to (SCN)2•−. In the section on Bond dissociation energy, we discuss thermochemical dissociation of (SCN)2•− in water and make a rough estimation of its relative size.

FIG. 5.

Relaxed scan of potential energy of (SCN)2•− in vacuum (red) and PCM water (blue) determined using MP2 (solid) or DFT methods [ωB97x/(dotted) and LC-ωPBE (dashed)] with aug-cc-pVTZ basis set. All plots are offset to 0 kJ/mol at their respective minimum energy angles for easier comparison.

FIG. 5.

Relaxed scan of potential energy of (SCN)2•− in vacuum (red) and PCM water (blue) determined using MP2 (solid) or DFT methods [ωB97x/(dotted) and LC-ωPBE (dashed)] with aug-cc-pVTZ basis set. All plots are offset to 0 kJ/mol at their respective minimum energy angles for easier comparison.

Close modal

Figure 5 presents the variation of the total energy of the radical with respect to the torsional angle for illustration. It can be seen that a significant change in energy does not occur for a wide variation in the torsional angles of solvated intermediate. It is likely that the radical explores this potential energy surface, with breath of torsional angles around a mean value of ∼90°, but all differing in vibrational energies by <5 cm−1, i.e., within the Raman band widths.

As noted earlier, the SS stretching vibration 220 cm−1 is anharmonic. The band positions in Fig. 2 were fitted (inset) with the relationship, ν = (ωe − ωeχe)v − ωeχev2 (ν—observed frequency, ωe—harmonic frequency, ωeχe—anharmonicity constant, v—vibrational quantum number), to obtain ωe = 222 cm−1, ωeχe = 1 cm−1. Assuming a first order anharmonicity in the stretching motion (Morse potential) and Birge-Sponer extrapolation,46 we estimate that a convergence in vibrational states will be reached for an energy of (De) ∼ 1.5 eV (De = ωe2/4ωeχe), which for a diatomic molecule is approximated as the bond dissociation energy. The dissociation energy thus estimated may have a large uncertainty due to the crude diatomic approximation of pseudohalide (SCN)2•− radical anion and the neglect of higher anharmonicity terms. However, the observation of vibrational frequencies as high as ∼4000 cm−1 (∼0.5 eV) and no evidence of any significant change in the frequency of the SS fundamental 220 cm−1 and its overtones superimposed over the CN vibration 2073 cm−1 (Fig. 3) is a clear indication that a De of ∼1.5 eV for the radical is not unreasonable. The bond dissociation energy thus estimated is comparable to that of diatomic dihalide anion radicals, such as Cl2•− or Br2•− in water which are 1.6 and 1.3 eV, respectively.41 

The bond dissociation energy (De) of (SCN)2•− was computed in two ways: (1) for the isolated radical by stretching the S–S bond from optimized geometry up to 1000 Å with otherwise constrained geometry; (2) in PCM water by the difference in the absolute energies of (SCN)2•− and the sum of energies of SCN and SCN. Applying the ωB97x/aug-cc-pVTZ method, the De determined by the first approach was ∼1.22 eV (Fig. 6). This value agrees reasonably well with the extrapolated De from the experimental SS vibrational frequency and anharmonicity. The De of (SCN)2•− calculated applying the LC-ωPBE/aug-cc-pVTZ method gave ∼1.29 eV (Fig. 6) (averaged value of 1.26 ± 0.04 eV). It has been previously reported that using LC-ωPBE estimation of the potential energy curve for dihalide radical anions, and determination of De from that, was in excellent agreement with the experimental values.17,41 By comparison MP2/aug-cc-pVTZ computation gave us 1.61 eV.

FIG. 6.

Potential energy curves of (SCN)2•− calculated with ωB97x/aug-cc-pVTZ and LC-ωPBE/aug-cc-pVTZ methods.

FIG. 6.

Potential energy curves of (SCN)2•− calculated with ωB97x/aug-cc-pVTZ and LC-ωPBE/aug-cc-pVTZ methods.

Close modal

The fact that the calculated De for the isolated radical compares well with the spectroscopically estimated value in water points towards an interesting aspect of the solvation dynamics. The Raman scattering process is extremely fast (<10−15 s) and a significant motion of the solvent molecules may not occur on the vibrational time scale. The dissociation energy extrapolated from the anharmonicty is that of the encaged (SCN)2•−, which can be equal to or slightly higher than that of the isolated molecule. Bond dissociation occurs with the fragments still in cage, and the cage escape and individual solvation follows later. That has also been observed for dihalide anions in water.41 

The thermochemical dissociation relates to the slow process when the solvent has enough time to reorient and solvate the fragments. The solution De(sol) or enthalpy of reaction is related to the equilibrium constant of reaction (1),

SCN2aqSCNaq+SCNaq.
(1)

The difference between the ωB97x(or LC-ωPBE)/aug-cc-pVTZ optimized energies of dimer product and respective substrates in water (Table III) resulted in the calculated enthalpy of reaction of 0.63 (or 0.56) eV (0.60 ± 0.03). Interestingly MP2/aug-cc-pVTZ gave 0.98 eV which is about 60% higher value for the enthalpy of this reaction in relation to the mentioned DFT methods. There have been a few experimental studies examining the temperature dependence of reaction (1) equilibrium constant.47–49 Based on van’t Hoff plot parameters for reaction (1), the S–S bond dissociation enthalpy has been determined in the range of 0.28-0.46 eV.47,48 The most recent studies by Chin and Wine gave the averaged value of 0.38 eV.47 The difference with the calculated RSH values of ∼0.60 is not as significant as it appears. A computational value is a difference of two large calculated numbers and therefore can bear a substantial probable error.

TABLE III.

Comparison of optimized geometries of SCN, SCN, and (SCN)2•− calculated with ωB97x (LC-ωPBE in parentheses) functional in vacuum and PCM water using aug-cc-pVTZ basis set.

PropertyExp.SCN VacuumPCMExp.SCN VacuumPCM(SCN)2•− VacuumPCM
SS stretching (cm−1… … … … … … 220 (243) 221 (239) 
SCN in phase … … … … … … 447 (457) 440 (446) 
bending (cm−1        
SC stretching (cm−1750a, 745b 750 (760) 755 (764) 735c 760 (755) 748 (744) 738 (746) 738 (747) 
CN stretching (cm−12066d2212 (2243) 2200 (2231) 1942c2066 (2100) 2086 (2124) 2239 (2271) 2230 (2266) 
 2069a   1930c     
r(SS) (Å)  … …  … … 2.760 (2.700) 2.742 (2.669) 
r(SC) (Å)  1.666 (1.661) 1.661 (1.656)  1.636 (1.636) 1.639 (1.640) 1.668 (1.664) 1.664 (1.662) 
r(CN) (Å)  1.165 (1.162) 1.164 (1.161)  1.165 (1.161) 1.164 (1.159) 1.160 (1.156) 1.160 (1.156) 
α(SSC) (deg) … … … … … … 95 (94) 94 (96) 
δ(CSSC) (deg) … … … … … … 180 (180) 56 (83) 
Energy (eV)  −13364.35 −13366.83  −13360.84 −13360.96 −26726.42 −26728.42 
  (−13360.04) (−13362.53)  (−13356.50) (−13356.63) (−26717.71) (−26719.72) 
Hydration enthalpy −2.48 −0.12 −2.00 
(eV) (−2.49) (−0.13) (−2.01) 
PropertyExp.SCN VacuumPCMExp.SCN VacuumPCM(SCN)2•− VacuumPCM
SS stretching (cm−1… … … … … … 220 (243) 221 (239) 
SCN in phase … … … … … … 447 (457) 440 (446) 
bending (cm−1        
SC stretching (cm−1750a, 745b 750 (760) 755 (764) 735c 760 (755) 748 (744) 738 (746) 738 (747) 
CN stretching (cm−12066d2212 (2243) 2200 (2231) 1942c2066 (2100) 2086 (2124) 2239 (2271) 2230 (2266) 
 2069a   1930c     
r(SS) (Å)  … …  … … 2.760 (2.700) 2.742 (2.669) 
r(SC) (Å)  1.666 (1.661) 1.661 (1.656)  1.636 (1.636) 1.639 (1.640) 1.668 (1.664) 1.664 (1.662) 
r(CN) (Å)  1.165 (1.162) 1.164 (1.161)  1.165 (1.161) 1.164 (1.159) 1.160 (1.156) 1.160 (1.156) 
α(SSC) (deg) … … … … … … 95 (94) 94 (96) 
δ(CSSC) (deg) … … … … … … 180 (180) 56 (83) 
Energy (eV)  −13364.35 −13366.83  −13360.84 −13360.96 −26726.42 −26728.42 
  (−13360.04) (−13362.53)  (−13356.50) (−13356.63) (−26717.71) (−26719.72) 
Hydration enthalpy −2.48 −0.12 −2.00 
(eV) (−2.49) (−0.13) (−2.01) 
a

Aqueous solutions.35 

b

CsI matrix.39 

c

Gas phase.38,53,54

d

Gas phase.37 

The total energy of a solvated ion can be expressed as the sum of gas phase De and solvation energy. In view of the hydration energy of −3.2 eV for SCN50 and assuming −0.18 eV for the SCN radical,18 the total hydration energy of the two fragments is −3.38 eV. The total energy of solvated (SCN)2•− is lower by about 0.38 eV,47 i.e., in the range −3.76 eV. Of this, ∼1.5 eV is gas phase De (see Fig. 7). The remaining energy, −2.25 eV, can be attributed to the hydration energy of (SCN)2•−. Hence we can estimate that the Born effective radius of (SCN)2•− in water can be roughly −3.2 eV/−2.26 eV = 1.42 times larger than that of SCN.51 Comparison of computational hydration energies (Table III) obtained with either of the applied methods gives ∼1.24 times larger Born effective radius of (SCN)2•− than SCN. We find the mentioned discrepancy between the roughly estimated experimental value and computation quite satisfactory considering possible errors in both types of analysis.

FIG. 7.

Illustration of thermochemical transformations of (SCN)2•− in water. Comparison of S–S bond dissociation energetics obtained by our resonance Raman experiment (dissociation products pair still in the solvation cage) and van’t Hoff analysis47 experiment (products solvated and in thermal equilibrium with solvent).

FIG. 7.

Illustration of thermochemical transformations of (SCN)2•− in water. Comparison of S–S bond dissociation energetics obtained by our resonance Raman experiment (dissociation products pair still in the solvation cage) and van’t Hoff analysis47 experiment (products solvated and in thermal equilibrium with solvent).

Close modal

It has been known for more than a century that the instantaneously created excited electronic states of a molecule by absorption of light have higher energy than the relaxed electronic states when a solvent has sufficient time to adjust to the equilibrium nuclear configuration of the excited electronic state. Emission occurs from the relaxed state and the energy (or wavelength) shift from the absorption is termed as the Stokes shift. The vibrational states in Stokes Raman are instantaneously created, while the Raman transitions in anti-Stokes Raman originate from the thermally relaxed vibrational states. However, the frequency difference in a vibration in Stokes and anti-Stokes Raman has never been observed. In the former type of states, the solvent has little time to respond to the vibrational excitation while in latter it has plenty. The potential energy well for the Stokes vibrations can be relatively deeper, and its effect may be detectable if the solute molecule has low De, as in 2c-3e systems. Due to the Boltzmann factor, only low frequency vibrations can be observed in anti-Stokes Raman of a 2c-3e radical, overlapped by strong Rayleigh scattering, making a very accurate determination of frequency quite challenging. Also, contamination of the thermally relaxed states from the spontaneously created states can occur. In the thiocyanate dimer radical anion, the high intensity of the CN stretch allows the observation of thermally relaxed and spontaneously created vibrational states away from the Rayleigh scattering. In Fig. 8 (inset), the Raman band at 1853 cm−1 represents a transition from the thermally relaxed SS stretch to the spontaneously created CN stretch at 2073 cm−1 and the frequency difference is 220 cm−1. The frequency difference between the spontaneously created CN stretch and the similarly created CN + SS stretch at 2293 cm−1 is still 220 cm−1. There was no effect of replacing light water with heavy water as solvent (Fig. 8). We also measured the anti-Stokes and Stokes Raman shifts of the SS symmetric stretch from the exciting laser line (Fig. 9) with the same result. We conclude that there is no observable difference between the thermally relaxed and spontaneously created vibrational states within the limit of our experimental uncertainty (±0.4 cm−1) as opposed to the previously reported data.18 This result on (SCN)2•−, although negative, is quite important as it could help us to rationalize a definite small frequency shift that we have observed in an aqueous triatomic anion in which solvent induced symmetry breaking has been previously reported.52 

FIG. 8.

Comparison of lower and higher (inset) resonance Raman spectrum of (SCN)2•− recoded in light (black) and heavy (red) water.

FIG. 8.

Comparison of lower and higher (inset) resonance Raman spectrum of (SCN)2•− recoded in light (black) and heavy (red) water.

Close modal
FIG. 9.

Comparison of Stokes and anti-Stokes resonance Raman signals of the fundamental S–S vibration of the (SCN)2•− radical anion in water. Higher resolution (0.4 cm−1) achieved by application of i-CCD detector with smaller pixel size (13.5 μm).

FIG. 9.

Comparison of Stokes and anti-Stokes resonance Raman signals of the fundamental S–S vibration of the (SCN)2•− radical anion in water. Higher resolution (0.4 cm−1) achieved by application of i-CCD detector with smaller pixel size (13.5 μm).

Close modal

The time resolved resonance Raman spectra of the thiocyanate dimer radical anion in water obtained with high signal-to-noise ratio, ranging between 50/1 to 270/1, exhibits only three fundamentals associated with SS, CS, and CN stretches out of twelve possible modes for the radical. The 220 cm−1 SS stretching mode is most highly enhanced, but the 2073 cm−1 CN stretching mode is also very prominent in the spectra. Not only the enhanced modes but also the lack of observable resonance enhancement of low frequency modes, such as those related to SSC or SCN bends, have been valuable in discriminating among structural models that might describe the observed vibrational frequencies reasonably well.

We have applied the structural information on a solvated radical derived from a judicious combination of vibrational spectroscopy in a solution and an appropriate theory to uncover its thermochemistry for the first time. The range separated hybrid (RSH) density functionals LC-ωPBE and ωB97x both provide an adequate description of the experimental vibrational frequencies and the SS bond dissociation in the solvent cage. Both predict a radical geometry in which the SSC and torsional angles are close to 90°, which explains why only the stretching, and not the bending modes, should be resonance enhanced in Raman. It has been shown that the radical structure is flexible as far as the torsional angle is concerned, and at room temperature may present distribution of forms with various torsional angles, which however do not appreciably affect the stretching frequencies. The calculations also explain the change in enthalpy on thermochemical dissociation in water. The hydration energy of (SCN)2•− has been estimated as 2.25-2.78 eV. Comparison with the experimental hydration energy of SCN (3.2 eV) limits the Born ionic radius of the radical to <1.4 times the ionic radius of SCN, with which the geometries obtained with the RSH functional conform reasonably.

The radical ground electronic state has SS bond properties analogous to that of diatomic dihalide anions in water, and therefore is an excellent model for 2-center 3-electron bonded multiatomic systems that can be used as reference in theoretical and experimental investigations. However, transition to the excited electronic state is spread over all three bonds. The optical absorption spectrum of the radical is not appropriate to rationalize, even qualitatively, the bond properties of other 2c-3e polyatomic systems.

The Stokes and anti-Stokes Raman frequencies of (SCN)2•− in water are identical within the experimental accuracy of their measurement. Contrary to our expectations, based on an earlier study,18 the frequency difference between the spontaneously created and thermally relaxed vibrational states was unobservable.

We would like to express our thanks to the supporting staff in NDRL for their help in implementing improvements to the time-resolved Raman setup over the last year. In particular, help from our glassblower Kiva Ford and our machinist Joseph Admave is greatly appreciated. We would like to thank Chris Draves from Andor Technology for sharing their No. DH340T-25-H-83 ICCD camera for tests in experiments requiring higher resolutions. Thanks are also due to Dr. Daniel M. Chipman for helpful discussions.

The research described herein was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Basic Energy Sciences, Office of Science, United States Department of Energy (Grant No. DE-FC02-04ER15533). This is contribution number NDRL-5171 from the Notre Dame Radiation Laboratory.

1.
R.
Joshi
,
T. K.
Ghanty
, and
T.
Mukherjee
,
J. Mol. Struct.: THEOCHEM
723
,
235
(
2005
).
2.
C.
Dupont
,
E.
Dumont
, and
D.
Jacquemin
,
J. Phys. Chem. A
116
,
3237
(
2012
).
3.
X. J.
Yang
and
N.
Tamai
,
Phys. Chem. Chem. Phys.
3
,
3393
(
2001
).
4.
T.
Morishita
,
A.
Hibara
,
T.
Sawada
, and
I.
Tsuyumoto
,
J. Phys. Chem. B
103
,
5984
(
1999
).
5.
D. W.
Bahnemann
,
M.
Hilgendorff
, and
R.
Memming
,
J. Phys. Chem. B
101
,
4265
(
1997
).
6.
R. B.
Draper
and
M. A.
Fox
,
J. Phys. Chem.
94
,
4628
(
1990
).
8.
G. V.
Buxton
,
C. L.
Greenstock
,
W. P.
Helman
, and
A. B.
Ross
,
J. Phys. Chem. Ref. Data
17
,
513
(
1988
).
9.
P. E.
Mason
,
G. W.
Neilson
,
C. E.
Dempsey
,
A. C.
Barnes
, and
J. M.
Cruickshank
,
Proc. Natl. Acad. Sci. U. S. A.
100
,
4557
(
2003
).
10.
Z. B.
Alfassi
,
The Chemistry of Free Radicals: N-Centered Radicals
(
John Wiley & Sons, Ltd.
,
Chichester, England
,
1998
).
11.
R.
Michalski
,
A.
Sikora
,
J.
Adamus
, and
A.
Marcinek
,
J. Phys. Chem. A
114
,
861
(
2010
).
12.
R.
Rossetti
,
S. M.
Beck
, and
L. E.
Brus
,
J. Am. Chem. Soc.
106
,
980
(
1984
).
13.
E.
Dumont
,
A. D.
Laurent
,
X.
Assfeld
, and
D.
Jacquemin
,
Chem. Phys. Lett.
501
,
245
(
2011
).
14.
K. D.
Asmus
, in
Sulfur-Centered Reactive Intermediates in Chemistry and Biology
, edited by
C.
Chatgilialoglu
and
K. D.
Asmus
(
Plenum Press
,
New York and London
,
1990
), p.
155
.
15.
N. H.
Jensen
,
R.
Wilbrandt
,
P.
Pagsberg
,
R. E.
Hester
, and
E.
Ernstbrunner
,
J. Chem. Phys.
71
,
3326
(
1979
).
16.
A. K.
Pathak
,
T.
Mukherjee
, and
D. K.
Maity
,
J. Mol. Struct.: THEOCHEM
755
,
241
(
2005
).
17.
M.
Yamaguchi
,
J. Phys. Chem. A
115
,
14620
(
2011
).
18.
R.
Wilbrandt
,
N. H.
Jensen
,
P.
Pagsberg
,
A. H.
Sillesen
,
K. B.
Hansen
, and
R. E.
Hester
,
Chem. Phys. Lett.
60
,
315
(
1979
).
19.
A. D.
Becke
,
J. Chem. Phys.
98
,
5648
(
1993
).
20.
O. A.
Vydrov
and
G. E.
Scuseria
,
J. Chem. Phys.
125
,
234109
(
2006
).
21.
J. D.
Chai
and
M.
Head-Gordon
,
J. Chem. Phys.
128
,
084106
(
2008
).
22.
P. R.
Pan
,
Y. S.
Lin
,
M. K.
Tsai
,
J. L.
Kuo
, and
J. D.
Chai
,
Phys. Chem. Chem. Phys.
14
,
10705
(
2012
).
23.
I. S.
Ginns
and
M. C. R.
Symons
,
J. Chem. Soc., Dalton Trans.
1973
(
1
),
3
.
24.
G. N. R.
Tripathi
,
ACS Symp. Ser.
236
,
171
(
1983
).
25.
G. L.
Hug
,
Y. C.
Wang
,
C.
Schoneich
,
P. Y.
Jiang
, and
R. W.
Fessenden
,
Radiat. Phys. Chem.
54
,
559
(
1999
).
26.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
,
G. E.
Scuseria
,
M. A.
Robb
,
J. R.
Cheeseman
,
G.
Scalmani
,
V.
Barone
,
B.
Mennucci
,
G. A.
Petersson
,
H.
Nakatsuji
,
M.
Caricato
,
X.
Li
,
H. P.
Hratchian
,
A. F.
Izmaylov
,
J.
Bloino
,
G.
Zheng
,
J. L.
Sonnenberg
,
M.
Hada
,
M.
Ehara
,
K.
Toyota
,
R.
Fukuda
,
J.
Hasegawa
,
M.
Ishida
,
T.
Nakajima
,
Y.
Honda
,
O.
Kitao
,
H.
Nakai
,
T.
Vreven
,
J. A.
Montgomery
, Jr.
,
J. E.
Peralta
,
F.
Ogliaro
,
M. J.
Bearpark
,
J.
Heyd
,
E. N.
Brothers
,
K. N.
Kudin
,
V. N.
Staroverov
,
R.
Kobayashi
,
J.
Normand
,
K.
Raghavachari
,
A. P.
Rendell
,
J. C.
Burant
,
S. S.
Iyengar
,
J.
Tomasi
,
M.
Cossi
,
N.
Rega
,
N. J.
Millam
,
M.
Klene
,
J. E.
Knox
,
J. B.
Cross
,
V.
Bakken
,
C.
Adamo
,
J.
Jaramillo
,
R.
Gomperts
,
R. E.
Stratmann
,
O.
Yazyev
,
A. J.
Austin
,
R.
Cammi
,
C.
Pomelli
,
J. W.
Ochterski
,
R. L.
Martin
,
K.
Morokuma
,
V. G.
Zakrzewski
,
G. A.
Voth
,
P.
Salvador
,
J. J.
Dannenberg
,
S.
Dapprich
,
A. D.
Daniels
,
Ö.
Farkas
,
J. B.
Foresman
,
J. V.
Ortiz
,
J.
Cioslowski
, and
D. J.
Fox
, gaussian 09, Revision E.01,
Gaussian, Inc.
,
Wallingford, CT, USA
,
2009
.
27.
B.
Braida
and
P. C.
Hiberty
,
J. Phys. Chem. A
104
,
4618
(
2000
).
28.
B.
Braida
,
P. C.
Hiberty
, and
A.
Savin
,
J. Phys. Chem. A
102
,
7872
(
1998
).
29.
T. H.
Dunning
,
J. Chem. Phys.
90
,
1007
(
1989
).
30.
D. E.
Woon
and
T. H.
Dunning
,
J. Chem. Phys.
98
,
1358
(
1993
).
31.
J.
Tomasi
,
B.
Mennucci
, and
R.
Cammi
,
Chem. Rev.
105
,
2999
(
2005
).
32.
A. C.
Albrecht
,
J. Chem. Phys.
34
,
1476
(
1961
).
33.
M. J.
Nelson
and
A. D. E.
Pullin
,
J. Chem. Soc.
1960
(
2
),
604
.
34.
C. E.
Vanderzee
and
A. S.
Quist
,
Inorg. Chem.
5
,
1238
(
1966
).
35.
J. Y.
Chien
,
J. Am. Chem. Soc.
69
,
20
(
1947
).
36.
M.
Valiev
,
S. H. M.
Deng
, and
X. B.
Wang
,
J. Phys. Chem. B
120
,
1518
(
2016
).
37.
M.
Polak
,
M.
Gruebele
, and
R. J.
Saykally
,
J. Chem. Phys.
87
,
3352
(
1987
).
38.
S. E.
Bradforth
,
E. H.
Kim
,
D. W.
Arnold
, and
D. M.
Neumark
,
J. Chem. Phys.
98
,
800
(
1993
).
39.
D. J.
Gordon
and
D. F.
Smith
,
Spectrochim. Acta, Part A
30
,
1953
(
1974
).
40.
D. C.
Frost
,
C.
Kirby
,
W. M.
Lau
,
C. B.
Macdonald
,
C. A.
McDowell
, and
N. P. C.
Westwood
,
Chem. Phys. Lett.
69
,
1
(
1980
).
41.
G. N. R.
Tripathi
,
R. H.
Schuler
, and
R. W.
Fessenden
,
Chem. Phys. Lett.
113
,
563
(
1985
).
42.
T.
Clark
,
J. Comput. Chem.
2
,
261
(
1981
).
43.
T.
Clark
,
J. Am. Chem. Soc.
110
,
1672
(
1988
).
44.
G. N. R.
Tripathi
,
J. Phys. Chem. A
102
,
2388
(
1998
).
45.
T. H.
Dunning
and
K. A.
Peterson
,
J. Chem. Phys.
108
,
4761
(
1998
).
46.
G.
Herzberg
,
Molecular Spectra and Molecular Structure: Spectra of Diatomic Molecules
(
Van Nostrand
,
Princeton
,
1950
), Vol. 1.
47.
M.
Chin
and
P. H.
Wine
,
J. Photochem. Photobiol., A
69
,
17
(
1992
).
48.
J. H.
Baxendal
and
P. L. T.
Bevan
,
J. Chem. Soc. A
1969
(
15
),
2240
.
49.
A. J.
Elliot
and
F. C.
Sopchyshyn
,
Int. J. Chem. Kinet.
16
,
1247
(
1984
).
50.
Y.
Marcus
,
J. Chem. Soc., Faraday Trans. 1
83
,
339
(
1987
).
51.

Ratio of ionic radii approximated as the ratio of covalent lengths.

52.
Unpublished work from our laboratory for solvent induced symmetry breaking in triiodide anion, see
A. E.
Johnson
and
A. B.
Myers
,
J. Phys. Chem.
100
,
7778
, (
1996
).
53.
F. J.
Northrup
and
T. J.
Sears
,
Mol. Phys.
71
,
45
(
1990
).
54.
H.
Ohtoshi
,
K.
Tsukiyama
,
A.
Yanagibori
,
K.
Shibuya
,
K.
Obi
, and
K.
Tanaka
,
Chem. Phys. Lett.
111
,
136
(
1984
).