Chinese Journal of Chemical Physics  2017, Vol. 30 Issue (6): 657-663

#### The article information

Si-wen Ju, Ning Zhang, Zhi-qiang Wang, Rui-ting Zhang, De-wen Zeng, Xiao-peng Shao, Ke Lin

Contacted Ion Pairs in Aqueous CuCl2 by the Combination of Ratio Spectra, Difference Spectra, Second Order Difference Spectra in the UV-Visible Spectra

Chinese Journal of Chemical Physics, 2017, 30(6): 657-663

http://dx.doi.org/10.1063/1674-0068/30/cjcp1711211

### Article history

Accepted on: December 20, 2017
Contacted Ion Pairs in Aqueous CuCl2 by the Combination of Ratio Spectra, Difference Spectra, Second Order Difference Spectra in the UV-Visible Spectra
Si-wen Jua, Ning Zhangb, Zhi-qiang Wanga, Rui-ting Zhanga, De-wen Zengc, Xiao-peng Shaoa, Ke Lina
Dated: Received on November 14, 2017; Accepted on December 20, 2017
a. School of Physics and Optoelectronic Engineering, Xidian University, Xi'an 710071, China;
b. College of Science, Central South University of Forestry and Technology, Changsha 410004, China;
c. College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China
*Author to whom correspondence should be addressed. Ke Lin, E-mail:klin@xidian.edu.cn
Abstract: The microstructure of aqueous CuCl2 has been studied through lots of technologies for many years; however, it remains a controversial subject. In this study, a new spectroscopic method has been proposed to analyze the UV-visible spectra of thin film of CuCl2/H2O solutions at different concentrations. This method is the combination of ratio spectra, difference spectra and second order difference spectra. By using this method, two new bands at ~230 and ~380 nm are obviously observed. The bands are assigned as the contacted ion pairs[CuCl3(H2O)n]- or[CuCl4(H2O)n]2-, which demonstrates that ion pairs exist in the CuCl2/H2O solution. Such finding agrees with the recent theoretical spectra obtained by time-dependent density functional theory. Furthermore, the populations of the contacted ion pairs are discussed. This study not only offers the direct spectroscopic evidence of[CuCl3(H2O)n]- or[CuCl4(H2O)n]2- in aqueous CuCl2, but also suggests that the spectroscopic analysis method is powerful to extract the weak bands in a strong overlapping spectrum.
Key words: UV-visible spectroscopy    Ratio spectra    Difference spectra    CuCl2/H2O solution    Ion pair
Ⅰ. INTRODUCTION

Ion pairing is significant to understand the properties of ionic aqueous solution. It is widely accepted that various ion pairs are formed at the high concentration of ions. The species and the microstructure of ion pairs have been studied with lots of techniques, such as X-ray diffraction [1-3], neutron diffraction [4-6], extended X-ray absorption fine structure spectroscopy [7], Raman spectroscopy [8], infrared spectroscopy [9-10], photoelectron spectroscopy [11], pump-probe ultrafast spectroscopy [12], electrochemical methods [13, 14], and molecular dynamic simulations [15].

Copper dichloride (CuCl$_2$) has attracted much attention because of its wide application in industry, chemical synthesis, biology, and so on. The ion pairs and their microstructures in aqueous CuCl$_2$ have been studied through lots of technologies [1-8, 13, 14], however some details about these ion pairs are still under debate. X-ray diffraction showed that the ion pairs with 3.3-3.6 Cl$^-$ in the first coordination sphere of the Cu$^{2+}$ existed in the high concentrated CuCl$_2$ solution (3.18-4.35 mol/L) [1], and average 1.2 Cl$^-$ occupied equatorial positions of Cu$^{2+}$ [3]. However, the Raman spectroscopy demonstrated that 4 or 6 Cl$^-$ in the first coordination sphere of Cu$^{2+}$ presented in the CuCl$_2$ solutions of 0.1-4.5 mol/L [8]. In some experiments, more Cl$^-$ ions were introduced into the Cu$^{2+}$ aqueous solution through adding other chloride salts. For example, in the solutions with 4.27-3.22 mol/L CuCl$_2$ and 4.27-6.2 mol/L HCl, X-ray diffraction demonstrated that 0.3-1.7 Cl$^-$ occupied equatorial positions of Cu$^{2+}$ [2]. In the solution with 0.1 mol/L CuCl$_2$ and 0-2.8 mol/L NaCl, extended X-ray absorption fine structure spectroscopy showed that 1.6-2 Cl$^-$ located around Cu$^{2+}$ [7]. Recently, in the solution with 5 mmol/L CuSO$_4$, 10 mmol/L HCl and 0.001-5 mol/L NaCl at 90 $^\circ$C, electrochemical methods indicated the ion pairs with 2 Cl$^-$ in the first coordination sphere of Cu$^{2+}$ were dominant in the solution [14]. In a word, the previous conclusions about the species and their micro-structure of Cu$^{2+}$-Cl$^-$ ion pairs still disagreed with each other.

The other usual technology to study the aqueous CuCl$_2$ is UV-visible spectroscopy [16-25], as the different ion species present different color. However, such spectroscopy is usually invalid for this solution at the high concentration, as the absorption spectrum is saturated. To avoid the saturation effect, traditionally, more Cl$^-$ were added into solution through mixing XCl (X: H, Li, Na) with the dilute CuCl$_2$ aqueous solution [19-24]. Recently, thin film of the CuCl$_2$ aqueous solution was also used [25]. Previously, the ion pairs in XCl/CuCl$_2$/H$_2$O were identified through the UV-visible absorption spectroscopy [20-22]. The band at ~180 nm was regarded as [Cu(H$_2$O)$_n$]$^{2+}$. The band at ~250 nm was assigned as [CuCl(H$_2$O)$_n$]$^+$. The band at ~275 nm was attributed to [CuCl$_2$(H$_2$O)$_n$]$^0$. Three absorption bands at ~230, 270-284, and 370-384 nm were all regarded as [CuCl$_3$(H$_2$O)$_n$]$^-$ [20, 22] or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ [20, 22]. One band above 400 nm was assigned as [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ [19, 21]. The bands at ~256, 352-364 and ~389 nm were regarded as [CuCl$_5$(H$_2$O)$_n$]$^{3-}$ [20]. Most of these assignments agreed with the recent theoretical spectra obtained by time-dependent density functional theory (TD-DFT) [26-28]. Although the absorption spectra of ion pairs were recorded, the structure and spectra of these ion pairs are affected by other cations [23]. In order to avoid the effect, recently, thin solution film technology was employed to measure the UV absorption spectroscopy of the CuCl$_2$ aqueous solution [25]. In the spectra of the concentrated CuCl$_2$ aqueous solutions, the absorption bands at ~230 and ~380 nm were not observed. It was concluded that none or few [CuCl$_3$(H$_2$O)$_n$]$^-$ and [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ existed in the solution [25]. This is inconsistent with the results of X-ray diffraction [1] and Raman spectroscopy [8].

The absence of the bands at ~230 and ~380 nm may be due to the fact that the absorption bands of [CuCl$_3$(H$_2$O)$_n$]$^-$ and [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ are weak and they are overlapped by the strong bands at 250-280 nm. The spectral overlapping is also obvious in other spectra, such as the Raman spectra. Recently, a novel method called ratio spectra was employed to successfully extract the small components in the overlapping Raman spectra [29-31]. For instance, using the Raman Ratio spectrum, the small free OH vibration band was distinguished from the spectrum of water [29], the small amide A band (N-H stretching band) of protein was directly extracted from the spectrum of water [30], the small Raman bands of the hydration shell of ions and organic compound were extracted [31].

In this study, the ratio spectra are developed in the UV-visible spectra. Furthermore, we propose difference spectra and second order difference spectra. Three novel spectra are united to extract the small components in the overlapping spectra. The validity of this method is supported by the numerical simulations. Using this method, the absorption band at ~230 and ~380 nm are distinguished obviously from the UV-visible spectra of aqueous CuCl$_2$. The novel method indicates that the ion pairs [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ exist in aqueous CuCl$_2$ solutions. The population ratio of [CuCl(H$_2$O)$_n$]$^+$ to other contacted ion pairs is about 1.5 at the highest concentration.

Ⅱ. EXPERIMENT AND NUMERICAL SIMULATION

CuCl$_2\cdot$(H$_2$O)$_2$ was purchased from Sinopharm Chemical Reagent Co. Ltd. The salts were twice re-crystallized. Triple-distilled water was employed. Aqueous CuCl$_2$ were prepared with the concentration from ~0.5 mol/L to ~5 mol/L. The UV-visible absorption spectra of the film of the solutions were recorded with a commercial UV-Vis spectrometer (UV-2550, Shimadzu). The details about the experiment were described in our previous study [25].

We use numerical simulation to analyze the ratio spectra, the difference spectra and the second order difference spectra. In the simulation, five Gaussian functions are employed to simulate the overlapping spectrum, according to the following equation,

 $\begin{eqnarray} A\left( \lambda \right) = \sum\limits_{i = 1}^5 {{C_i}{\textrm{e}^{ - {{\left( {\frac{{\lambda - {\lambda _0}_i}}{{{\omega _i}}}} \right)}^2}}}} \end{eqnarray}$ (1)

Where $A(\lambda)$ is the simulated spectrum, $\lambda_0$ is the position of the center of the Gaussian band, $\omega$ controls the width of the band. C is the weighting factor of the Gaussian component. The parameters of the five Gaussian bands and the corresponding weighting factors are listed in Table Ⅰ. It's necessary to note that the number or parameters of the Gaussian functions is inessential for the result of our method. Here, these parameters were employed, as the simulated spectra are similar to the experimental UV-visible spectra of CuCl$_2$ aqueous solutions. In the numerical simulation, Lorentz functions or Voigt functions can also be used to simulate the overlapping spectrum.

Table Ⅰ Parameters of the Gaussian functions.
Ⅲ. RESULTS AND DISCUSSIONS A. UV-visible absorption spectra of CuCl$_2$ thin-film aqueous solutions

The UV-visible absorption spectra of CuCl$_2$/H$_2$O thin film at various concentrations from 0.5 mol/L to 5 mol/L are recorded and plotted in FIG. 1. All the spectra mainly consist of two bands, the one locates below 220 nm and the other locates at 250-260 nm. According to previous UV absorption spectroscopy [20, 22, 25] and TD-DFT [26-28], the band below 220 nm is assigned to the d-d electron transition of Cu$^{2+}$, and the band at 250-260 nm is assigned to various ion pairs.

 FIG. 1 UV-visible absorption spectra of CuCl$_2$ thin film aqueous solutions with the concentration of 0.5, 1, 1.5, 2, 2.5, 3, 3.6, and 5 mol/L.

As shown in FIG. 1, the band at ~250 nm shifts to ~260 nm with increasing the concentration of CuCl$_2$ from 0.5 mol/L to 5 mol/L. The red shift indicates that more than one Cl$^-$ appears in the first coordination sphere of Cu$^{2+}$, as the spectral band of [CuCl$_2$(H$_2$O)$_n$]$^0$ locates at ~275 nm [20, 22]. At the lowest concentration (0.5 mol/L), the band at ~250 nm is weaker than that below 220 nm, which suggests that few contacted ion pairs exist in the diluted solution. When increasing the concentration of CuCl$_2$, the band at 250-260 nm becomes stronger, which demonstrates that more contacted ion pairs exist in the concentrated CuCl$_2$/H$_2$O solution.

Different from the two bands in the spectra of thin film of CuCl$_2$/H$_2$O, more bands were recorded in the UV-visible absorption spectra of the XCl/CuCl$_2$/H$_2$O (X: Li, Na) solution. Two new absorption bands at ~230 nm and ~380 nm were recorded, and both are assigned to be [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ [20]. This assignment agrees with the recent TD-DFT [28]. However, both bands are not observed in the spectra of thin film of CuCl$_2$/H$_2$O (FIG. 1), thus it was concluded [CuCl$_3$(H$_2$O)$_n$]$^-$ and [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ hardly existed in the CuCl$_2$/H$_2$O solution [25]. This conclusion disagrees with those from X-ray diffraction [1] and Raman spectroscopy [8]. This disagreement may be due to the strong spectral overlapping among the bands in the UV-visible spectra.

B. Ratio spectra, difference spectra and second order difference spectra of simulated spectra

The strong spectral overlapping not only exists in UV-visible spectra, but also presents in all the other spectra. Taking Raman spectra as an example, multivariate curve resolution method [32, 33], factor analysis [34, 35], fitting analysis [36] were used to extract the spectral components in the overlapping spectra. Recently, a new method called Raman ratio spectrum was proposed, and it was successfully employed to extract small Raman bands which were overlapped seriously with a strong band [29-31]. The ratio spectrum is obtained by dividing one spectrum by another spectrum at different conditions. These previous studies demonstrate that the ratio spectrum is different from the spectrum. The spectrum denotes the absolute amount of the chemical species, and the ratio spectrum reflects the rate of the amount change. For example, a spectrum is constituted by a big and a weak band. In a particular condition, the intensity of the big band and the weak band is 100 and 1, respectively. In the other condition, the intensity of the big and the weak band is changed to 110 and 2, respectively. Thus, in the traditional spectra, the dominate band is the big band. However, in the ratio spectra, the dominate band is the weak band. Hence then, when a small band is overlapped by the other large bands, and when its rate of the change is different from those of the other large bands, it may be directly distinguished in the ratio spectrum.

The numerical simulation is performed to show whether the ratio spectrum can also be used to extract the small spectral components in the UV-visible spectra. The spectra were simulated with the sum of some Gaussian functions. Using three kinds of weighting factors (Table Ⅰ), we obtained three different spectra, which are shown in FIG. 2. The first spectrum (spectrum Ⅰ) is obtained through adding two strong Gaussian bands at 180 and 260 nm, as shown in FIG. 2(a). Another Gaussian band at 275 nm was added into spectrum Ⅰ to simulate an overlapping spectrum (spectrum Ⅱ), as shown in FIG. 2(b). Furthermore, two small Gaussian bands at 230 and 380 nm were added into spectrum Ⅱ to simulate the spectrum that consisted of weak spectral bands (spectrum Ⅲ), as shown in FIG. 2(c).

 FIG. 2 Three simulated spectra with different weighting factors. (a) spectrum Ⅰ, (b) Ⅱ, and (c) Ⅲ, which consist of two, three, and five Gaussian bands, respectively. The weak bands at 230 and 380 nm were multiplied by ten times to be directly shown.
 $\begin{eqnarray} R\left( \lambda \right) = \frac{{{A_x}\left( \lambda \right)}}{{{A_\textrm{I}}\left( \lambda \right)}}\end{eqnarray}$ (2)

All the three simulated spectra are similar (FIG. 3(a)). We can only observe the band below 200 nm and the band at 260-270 nm in these simulated spectra. The small bands at 230 and 380 nm are not observed, because these bands are overlapped seriously with the strong bands at 180 and 260-270 nm. Here, ratio spectra are employed to extract the weak spectral components from the spectra. Using Eq.(2), the ratio spectra ($R(\lambda)$) are obtained through dividing spectrum Ⅱ and spectrum Ⅲ by spectrum Ⅰ, as shown in FIG. 3(b). Obviously, the ratio spectra are much different from the spectra. In ratio spectrum of spectrum Ⅱ, a band at ~280 nm is observed, which is because a new band at 275 nm is added in the spectrum Ⅱ. In the ratio spectrum of spectrum Ⅲ (FIG. 3(b)), three bands at ~230, ~280, and ~420 nm are observed, which is because three spectral components are added in the spectrum Ⅲ. Although the band at ~230 nm is very small (FIG. 3(b)), it is really observed in the ratio spectrum (FIG. 3(c)). Hence then, the small spectral component can be observed in the ratio spectra although it is overlapped seriously with large spectral band in the spectra. However, the position of the small band in ratio spectra is a little different from that of the corresponding band list in Table Ⅰ. The difference may be caused by the serious spectral overlapping. Here, in order to determine the accurate position of the small band, another method should be employed to analyze the spectra and the ratio spectra. We call this method as difference spectra.

 FIG. 3 (a) Three simulated spectra, (b) the corresponding ratio spectra, and (c) magnification of the ratio spectrum of spectrum Ⅲ.

Using an obvious characteristic in the ratio spectra, the difference spectra can be obtained easily. In ratio spectra (FIG. 3 (b) and (c)), a constant exists below 220 nm. This is because only one spectral component locates in this spectral region, other bands hardly contribute to this region. Using the constant in the ratio spectra and the following equation, the spectral component below 220 nm can be removed from spectrum Ⅱ and spectrum Ⅲ.

 $\begin{eqnarray} A_x'\left( \lambda \right) = {A_x}\left( \lambda \right) - c{A_\textrm{I}}\left( \lambda \right) \end{eqnarray}$ (3)

Where $A'_x(\lambda)$ and $A_x(\lambda)$ is the difference spectrum and spectrum, respectively. c is the constant below 220 nm in corresponding ratio spectra. The difference spectra are shown in FIG. 4(a). In the difference spectrum of spectrum Ⅱ, one band at 271 nm is observed. In the difference spectrum of spectrum Ⅲ, three bands at 230, 271, and 380 nm are observed. Except the band at 271 nm, the positions of these bands agree well with the positions listed in Table Ⅰ. Previously, the ratio Raman spectrum and the difference Raman spectrum were successfully used to extract the small spectral band of the hydration shell in aqueous solutions [31]. Here, the simulation demonstrates the ratio spectra and the difference spectra can also be employed to extract the small bands in the UV-Vis spectra.

 FIG. 4 (a) Difference spectra and (b) the second order difference spectrum of the simulated spectra.

However, some shortages still present in the difference spectra. For example, although the small band at 230 nm is observed in the difference spectrum of spectrum Ⅲ (FIG. 4(a)), it is still overlapped with the nearest strong band. The position of the strongest band is different from any position in Table Ⅰ. Therefore, we define the second order difference spectrum using the following equation:

 $\begin{eqnarray} A_x''\left( \lambda \right) = A_x'\left( \lambda \right) - sA_{\textrm{II}}'\left( \lambda \right)\end{eqnarray}$ (4)

Where $A"x(\lambda)$ and $A'x(\lambda)$ are the second order difference spectrum and the difference spectrum, respectively. s is a adjustable coefficient, which is chosen to avoid negative data in the second order difference spectrum. The nonnegative criteria was also used in the principal component analysis [37]. Using the difference spectrum (FIG. 4(a)), we obtain the second order difference spectrum, as shown in FIG. 4(b). Three bands at 230, 275, and 380 nm can be observed obviously in the second order difference spectrum. They all agree well with the data listed in Table Ⅰ. Consequently, the ratio spectra, difference spectra and the second order difference spectra are successfully united to distinguish the small bands that are overlapped by large spectral bands.

C. Ratio spectra, difference spectra and second order difference spectra of CuCl$_2$/H$_2$O solution

The above ratio spectra, difference spectra and second order difference spectra are employed to analyze the UV-visible spectra of aqueous CuCl$_2$ thin film solutions. Through dividing the spectra at each concentration by the spectrum at 0.5 mol/L, we obtain the corresponding ratio spectra, as shown in FIG. 5(a). In the ratio spectra, two new spectral components at ~230 and ~285 nm are obviously observed. According to the previous TD-DFT [26-28], the band at ~230 nm was assigned to [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$, and the band at ~285 nm was attributed to [CuCl$_2$(H$_2$O)$_n$]$^0$, [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$. Another characteristic band of [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ locate at ~380 nm [20, 28], however this band is not observed in the ratio spectra because of the ultra-low signal-to-noise ratio (SNR) in the $>$350 nm region. The another ratio spectra are obtained through dividing the spectrum at 5 mol/L by the spectrum at 3.6 mol/L, as shown in FIG. 5(b). The SNR in the region is high enough to present the band ~380 nm. In a word, the ratio spectra provide the direct evidence of the contacted ion pair [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ in CuCl$_2$ aqueous solution. Besides the new band at ~230 and ~380 nm in the ratio spectra, a constant is observed below 220 nm in all the ratio spectra. The constant demonstrates that the band below 220 nm can only be assigned as the d-d electron transition of Cu$^{2+}$ [26-28].

 FIG. 5 Ratio spectra of UV-visible spectra of CuCl$_2$ thin film aqueous solutions, (a) the spectra at x=1, 1.5, 2, 2.5, 3, 3.6, and 5 mol/L divided by the spectrum at 0.5 mol/L and (b) the spectrum at 5 mol/L divided by the spectrum at 3.6 mol/L.

Although the bands of [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ are observed in the ratio spectra, the corresponding spectra are not obtained quantitatively. In order to acquire the spectra of [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$, the spectra of other ion species should be removed from the UV-visible spectra of CuCl$_2$/H$_2$O solution. Based on the constant below 220 nm region in the ratio spectra, we can calculate the difference spectra between the spectrum at 0.5 mol/L and the spectrum at other concentrations. The corresponding difference spectra are shown in FIG. 6(a). At the lowest concentration (1 mol/L), only one symmetrical band at ~250 nm exists in the difference spectrum, and it is assigned as the contacted ion pair [CuCl(H$_2$O)$_n$]$^+$ [20, 27]. With increasing of the concentration of CuCl$_2$, a new band at ~270 nm is observed in the difference spectra, and it becomes the strongest band at the highest concentration (5 mol/L). This new band may be regarded as the ion pairs [CuCl$_2$(H$_2$O)$_n$]$^0$, [CuCl$_3$(H$_2$O)$_n$]$^-$, and [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ [26-28]. The bands at ~250 and ~270 nm overlap seriously with each other, thus we use the second order difference spectra to remove the spectral band of [CuCl(H$_2$O)$_n$]$^+$ at ~250 nm. Using the nonnegative criteria, the second order difference spectra are obtained and shown in FIG. 6(b). In the spectra, three bands are obviously observed. These bands locate at ~230, ~280 and ~380 nm, respectively. According to recent TD-DFT [28], the band at ~280 nm is assigned as [CuCl$_2$(H$_2$O)$_n$]$^0$, [CuCl$_3$(H$_2$O)$_n$]$^-$ and [CuCl$_4$(H$_2$O)$_n$]$^{2-}$, and it can be attributed to the charge transfer between copper and chloride atoms. The bands at ~230 and ~380 nm are assigned as [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$. Thus, it is concluded that [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ exists in CuCl$_2$ aqueous solutions.

 FIG. 6 (a) Difference spectra and (b) the second order difference spectra of the UV-visible spectra of CuCl$_2$ thin-film aqueous solutions.

The above second order difference spectra demonstrate the difference spectra could be decomposed into two spectral components, as shown in FIG. 7(a). One spectral component contains the band at ~250 nm, which is assigned as the ion pair [CuCl(H$_2$O)$_n$]$^+$. The other spectral component contains three bands at ~230, ~280 and ~380 nm, which are assigned as the ion pairs [CuCl$_2$(H$_2$O)$_n$]$^0$ or [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$. Consequently, using the two spectral components, we can estimate the amount ratio of [CuCl(H$_2$O)$_n$]$^+$ to the other ion pairs with more Cl$^-$ in the first coordination shell. Without regarding the absorption coefficient, the amount ratio can be obtained according to the following equation,

 $\begin{eqnarray} r = \frac{{I\left( {{\rm{component }}\ 1} \right)}}{{I\left( {{\rm{component }}\ 2} \right)}} \end{eqnarray}$ (5)

Where r is the amount ratio, I is the integral intensity of the corresponding spectral component. The concentration dependent amount ratios are obtained and plotted in FIG. 7(b). It is observed that the amount ratios decrease with the concentration. It demonstrates that the population of [CuCl$_2$(H$_2$O)$_n$]$^0$ and [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ increases with the concentration. In the CuCl$_2$ aqueous solution at the highest concentration (5 mol/L), the ratio is ~1.5, which demonstrates the amount of [CuCl(H$_2$O)$_n$]$^+$ is larger than the total amount of the other contacted ion pairs with more Cl$^-$ in the first coordination shell.

 FIG. 7 (a) The decomposition of the difference spectra at concentration 5 mol/L, (b) the concentration dependent amount ratio of the [CuCl(H$_2$O)$_n$]$^+$ to other contacted ion pairs.
Ⅳ. CONCLUSION

In this study, we present a novel spectroscopic analytical method to extract small spectral band from overlapping bands. The numerical simulation demonstrates the combination of ratio spectra, difference spectra and second order difference spectra can successfully be used to distinguish the overlapping weak bands. Employing this method, the UV-visible spectra of CuCl$_2$ aqueous solutions are analyzed. The small bands at ~230 and ~380 nm are observed in the ratio spectra and the second order difference spectra. The bands are assigned as the ion pairs [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$, which agrees well with the theoretical analysis of the previous TD-DFT. It is concluded the contacted ion pairs [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ exist in CuCl$_2$ aqueous solutions. Further decomposition demonstrates the population of these ion pairs is less than that of [CuCl(H$_2$O)$_n$]$^+$. This study not only offers the direct evidence of the [CuCl$_3$(H$_2$O)$_n$]$^-$ or [CuCl$_4$(H$_2$O)$_n$]$^{2-}$ in CuCl$_2$/H$_2$O, but also implies that the combination of ratio spectra, difference spectra and second order difference spectra would be a powerful method in the spectroscopic analysis method.

Ⅴ. ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China (No.21473171, No.21703164, and No.51134007), the National Basic Research Program of China (No.2014CB643401), the Fundamental Research Funds for the Central Universities (No.JB160508), and the Huashan Mountain Scholar Program and the 111 Project (No.B17035).

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a. 西安电子科技大学, 物理与光电工程学院, 西安 710071;
b. 中南林业科技大学理学院, 长沙 410004;
c. 中南大学化学化工学院, 长沙 410083