Two-State or Non-Two-State? An Excess Spectroscopy-based Approach to Differentiate the Existing Forms of Molecules in Liquids Mixtures

Characterization/identification of the clusters/associates in liquids has long been a challenging topic. In this paper, we report a method to identify molecules with two different existing forms in a binary liquid solution. In this so-called two-state situation, the excess infrared spectra of a vibration mode of the respective molecule will show identical band shape if the other component is transparent in the region. More conveniently, the positions of the positive peak, negative peak, and zero-value will be seen to be fixed with varying compositions of the binary system. In the case of non-two-state mixtures, for example the mere solvation of solute by solvent, those positions will be variable. The conclusions are supported/demonstrated by computational simulation and experiments on two binary systems, D2O−H2O and C6F5I−cyclo-C6H12.

It should be stressed that not all the excess peaks behave like this. The positions can be concentration-dependent as shown in Fig. 1(c) for ν(C ≡ N) stretching in CD 3 CN− CCl 4 system. Intuitively, the fixed position of an excess band should mean something, most likely a reflection of identical configuration of the concerned bond, plus the same or close solvent environment to the respective vibrational mode. In this paper, we will show that this is true under certain conditions, particularly when there are only two existing forms of the concerned molecules. By changing the concentration of the mixtures, the amount of the two forms will change. This is regarded as a two-state transformation.
The significance of the present work lies also on its correlation to the in-situ identification of molecular clusters in liquids. Up to date, there have been some experimental methods to investigate molecular clusters 14 . But they are almost all for gas phase identification. For liquid state samples, for example water, their clusters have been studied by spraying the samples into inert solvent such as liquid helium 15,16 . Molecular clusters identified by these methods cannot reflect the real situations in liquids. Recently, Ben-Amotz and co-workers proposed that solvent molecules in a solution can be classified as bulk and solvation-shell molecules [17][18][19] . They used a multivariate curve fitting method to extract the spectrum of the latter. In principle, the idea can be used to extract the spectra of molecular clusters, while the detailed information of those clusters, including their types and spectroscopic properties, is required to be known. As a matter of fact, we have to accept that unambiguous in-situ identification of molecular clusters in pure liquids and liquid mixtures is an unsolved problem. The method proposed in this work gives a solution to the case when there are two existing forms of the target molecule in a binary system. The two forms can be two types molecular clusters or one type cluster plus monomer of the concerned component.

Results and Discussion
Theory. We consider a binary system. For each of the two components, the absorbance at a selected wavenumber is described in the form of Beer-Lambert Law: where ε i * and C i * are the molar absorption coefficient and the molarity of the compound i in pure form, redspectively, d the light path. In the case of the binary mixtures, we assume the form of Beer-Lambert Law is still applicable: where C = C 1 + C 2 . Generally speaking, absorption coefficient ε of the mixture is not a constant, but a function of wavelength and concentrations. We define the absorption coefficient of an ideal mixture as: where x 1 and x 2 are mole fractions of the two components. Then, the excess infrared spectrum, in the form of excess absorption coefficient, is defined as follows: Now we purposely identify an absorption band of component 2 (solute, M), which is not overlapped with absorption bands from the other component (solvent, S). This means that the respective wavenumber range is transparent to the solvent. We assume that there are two existing forms of the solute, for example with and without forming complex with solvent (M 1 and M 2 ), over the entire or part of the concentration range. Their molar absorptivities are denoted as ε 21 and ε 22 , which are independent on concentrations. The amounts of the two forms of the solute, however, are variable. The fraction of form 1 is denoted as δ over the two forms of the solute. In the absence of solvent, the fraction is δ 0 . With these parameters, Equation (3) turns to be Molar absorptivity of the real binary mixture is, Then, based on Equation (4), excess molar absorptivity of a real binary mixture is, It is thus clear that the term ε ε ( − ) 21 22 defines the shape of an excess spectrum band, which is independent of the apparent concentration of the binary system. Only when the molar absorptivities of the two forms of the solute equal to each other, the excess function can be zero. Thus we conclude that the peak positions and zero-intensity frequency of the excess spectroscopic bands are all fixed in a series of binary mixtures, if there are only two existing forms of the solute and the solvent is transparent over the examined wavenumber range.
Digital simulation. With the above theoretical analysis, we have performed some digital simulation of excess infrared spectra to show the ideal appearance of the excess infrared spectra. Here, a single absorption band is expressed by the Lorentzian function as follows, where w represents the full width at half-height, ν 0 the center position of band, and ε 0 , the molar absorptivity when ν = ν 0 . When there are two forms of the solute molecules in the binary system, the spectral function is expressed as follows, , ,  Fig. 2. As can be seen in Fig. 2(a), the absorption peak looks like singular and it shifts gradually to higher wavenumber with increasing solvent concentration. Apparently, the blue shift would have been caused by solvation effect. The excess infrared spectra shown in Fig. 2(b) provide correct insights of the system. Apart from showing a positive peak at the higher wavenumber side and a negative peak at the lower wavenumber side in each curve, which is the same with solvation effect, the spectra give fixed positions of positive and negative peaks at 3314 and 3264 cm −1 , respectively. Meanwhile, the zero-value points of the four excess spectra appear at identical position. Different values of the parameters generate excess infrared spectra with different shapes. When there is significant difference between the two w values, namely one broad peak overlaps with a very narrow peak, two zero-value points can be seen. Shown in Fig. 2(c,d)  The simulated infrared spectra as shown in Fig. 3(a) are quite similar to those in Fig. 2(a). The simulated excess infrared spectra, however, show completely different results. The positions of both positive and negative peaks, as well as the position of the zero-value point, are not fixed. If two distinct states and solvent effects are combined, or there are more than two distinct states of the solute, the Equation (7) will not hold anymore. More or less, the positions of the positive and negative peaks will subject to changes. Nevertheless, our simulation indicates that, depending on the extent of hydration or the relative separation of the multi-state peaks, positions of part or all of the peaks in the excess spectra can be relatively fixed (see Supplementary Information). We, therefore, conclude that if the position of an excess peak is relatively fixed, most likely it represents a distinct species.  Fig. 4. Normal water has no absorptions in the wavenumber region. The absorption band in Fig. 4(a) is assigned to ν (O− D) according to literature 20 . In Fig. 4(b), the excess spectra show two fixed-position negative peaks, one fixed positive peak, and two fixed zero-value points, which are the  Fig. 2(d). This demonstrates that, in the binary system with two-state transformation, both the excess peaks and zero-value points are fixed. C 6 F 5 I−cyclo-C 6 H 12 system. The C 6 F 5 I-cyclo-C 6 H 12 system was also studied by ATR-FTIR technique.
The IR and excess infrared spectra of the C 6 F 5 I-cyclo-C 6 H 12 system in the C-I stretching region are shown in Fig. 5. The band at 805 cm −1 is attributed to the C− I stretching vibration 22 . In Fig. 5(a), from top to bottom, the peak position is blue-shifted. In Fig. 5(b), the excess spectra show fixed positions of positive peak, negative peak, and zero-value points, which are in consistent with the simulation results shown in Fig. 2(b). This strongly suggests that C 6 F 5 I-cyclo-C 6 H 12 system exists in two distinct states upon dilution with cyclo-C 6 H 12 . For C 6 F 5 I, cyclo-C 6 H 12 is an inert solvent. So the two states may be attributed to the absorptions of monomer and self-aggregated C 6 F 5 I 12 . Most likely, the self-aggregated C 6 F 5 I is the dimer of the molecule. Quantum chemical calculations were performed to find the optimized structure of the C 6 F 5 I dimer, which is shown in the inset of Fig. 5(a). As can be seen, the two molecules form a displaced π − π stacking interaction pair. The distance of the two planes is 0.303 nm. The interaction energy is − 100.25 kJ/mol, suggesting the dimer is quite stable. Furthermore, the calculated frequencies of v(C− I) indicate that there is a redshift upon formation of dimer. Thus the negative peak at lower wavenumber is assigned to dimer and the positive one to monomer.  They are readily assigned to that from D 2 O and DOH. In C 6 F 5 I-cyclo-C 6 H 12 system, the excess infrared spectra in the C− I stretching region suggest that there are two forms of C 6 F 5 I during the mixing process. They are most likely self-aggregated and non-aggregated C 6 F 5 I. The aggregation is believed to be in the form of displaced π − π stacking. For more complicated situations such as the coexistence of three or more forms of the concerned component, the feature/shape of the excess spectra will be concentration-dependent. But if the position of a positive peak or negative peak in a series of excess spectra is relatively fixed, most likely it indicates a distinct species.

Methods
Chemicals. D 2 O (>99%) was purchased from Armar Chemicals. C 6 F 5 I (>98%) was purchased from J&K Scientific. Cyclo-C 6 H 12 (>99%) was from Beijing Chemical Plant (Beijing, China). The samples were used without further purification. FTIR spectroscopy. FTIR spectra over the range from 4000 to 650 cm −1 were collected at room temperature (~25 °C) using a Nicolet 5700 FTIR spectrometer, equipped with an MCT detector. Two ATR cells made of trapezoidal ZnSe/Ge crystals were used in the experiments. A ZnSe crystal with an incident angle of 45° and 12 reflections was used to examine the stretching bands of O− D in D 2 O− H 2 O system. A Ge crystal with an angle of 60° and 7 reflections was used to examine the strong stretching bands of C− I in C 6 F 5 I-cyclo-C 6 H 12 system. Spectra were recorded with a resolution of 2 cm −1 , a zero filling factor of 2, and 32 parallel scans. The refractive indexes of solutions were measured with a refractometer at 25 °C. The formulas suggested by Hansen 23 , were used to do the ATR corrections.

Sample preparation.
Excess infrared spectroscopy. The theory of excess infrared spectroscopy has been described in detail elsewhere 9,10 . Briefly, an excess infrared spectrum is defined as the difference between the spectrum of a real solution and that of the respective ideal solution under identical conditions. The working equation in calculating the excess infrared spectrum is as follows:  Figure 5. Infrared spectra (a) and excess infrared spectra (b) of the C 6 F 5 I-cyclo-C 6 H 12 system at different mole fraction of C 6 F 5 I in the wavenumber range of the C-I stretching vibration. The dashed and dash-dot dotted lines in (a) depict spectra of pure C 6 F 5 I and cyclo-C 6 H 12 , respectively. where A is the absorbance of the mixture, d is the light path length, C 1 and C 2 are molarities of the two components, x 1 and x 2 are mole fractions of components 1 and 2, and ε 1 * and ε 2 * are molar absorption coefficients of the two components in their pure states, respectively. The calculation of the excess infrared spectra was programmed using Matlab 7.0 (Math Works Inc., Natick, MA).
Quantum chemical calculations. Quantum chemical calculations were performed by employing second-order many-body perturbation theory (MP2) at mixed basis sets with the Gaussian 09 program 24 . The molecular geometry were fully optimized with the LANL2DZ 25 , basis set for iodine atom and the aug-cc-pVDZ 26 , basis set for hydrogen, carbon, and fluorine atoms. All the optimized geometries were recognized as local minima with no imaginary frequency.