Two-dimensional asynchronous spectrum with auxiliary cross peaks in probing intermolecular interactions

Abstract

A new approach called “asynchronous spectrum with auxiliary peaks (ASAP)” is proposed for generating a 2D asynchronous spectrum to investigate the intermolecular interaction between two solutes (P and Q) dissolved in the same solution. In the ASAP approach, a virtual substance S with an isolated peak assumed to be at ν_S is introduced, while the characteristic peaks of P and Q are actually observed at ν_P and ν_Q. The concentrations series of P, Q and S are specifically designed so that a spectral portion that has nothing to do with the intermolecular interaction between P and Q is completely removed from the 2D asynchronous spectrum. Auxiliary cross peaks around (ν_P, ν_S) and (ν_Q, ν_S) can be used to reveal spectral variation caused by intermolecular interaction, which cannot be observed on conventional cross peaks appearing around the spectral coordinates (ν_P, ν_P), (ν_P, ν_Q), (ν_Q, ν_P), (ν_Q, ν_Q). For example, variation of the absorptivity of P caused by an intermolecular interaction between P and Q can be probed from the auxiliary cross peaks around (ν_P, ν_S) when Q does not even have any characteristic peak in the observed spectral range.

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1. Introduction

Intermolecular interaction, which occurs ubiquitously in nature, is of the utmost importance with regard to basic science as well as to applications in organic, biological, medicinal and materials chemistry.^1–10 Investigation of the intermolecular interaction has become one of the most active topics in the past two decades.^11–22 For example, non-covalent interactions are at the root of the whole field of supra-molecular chemistry that leads to the formation of highly complex and fascinating structures.²³ In catalysis, the impact of a weak interaction between ligand and substrate on controlling the reactivity has been recognized.²⁴ In the field of pharmaceuticals, a key step is to rationalize and optimize the interactions between a potential drug and a relevant receptor.²⁵ In protein chemistry, the exploration and comprehension of noncovalent bond interactions are key to predicting the pathways of protein folding and quantifying the relative thermodynamic stability of intermediate and final states.²⁶ In comparison to a plethora of theoretical calculations of the intermolecular interactions, experimental studies on these intriguing intermolecular interactions are still quite limited.

Two-dimensional (2D) correlation spectroscopy is a powerful spectroscopic technique proposed by Noda in the late 1980s^27–30 and has attracted extensive application in a variety of research fields for the past 25 years.^31–47 In 2D correlation spectroscopy, some forms of perturbation are applied to the sample, which imparts variations of spectral signals (called dynamic spectra). Based on cross-correlation analysis, the dynamic spectra are then transformed into a spectrum with two independent spectral variable axes (2D correlation spectrum). In general, 2D correlation spectra are classified into two types: synchronous correlation spectra and asynchronous correlation spectra obtained by using different cross-correlation methods. Owing to the enhancement of the spectral resolution by spreading the peaks over the second dimension, subtle changes of the sample, not readily seen in the original data set, can be visualized in terms of cross peaks in the 2D correlation spectra.

One of the most important features of 2D correlation spectra is that cross peaks in 2D correlation spectra can potentially be used to characterize intermolecular interactions.^27,28 However, this approach suffers from the following problem: interfering cross peaks due to other sources of correlation may also arise even if there are no intermolecular interactions. This makes the mere appearance of cross peaks in 2D correlation spectra difficult to use as a reliable tool to characterize intermolecular interactions.

To address the problem, we proposed an orthogonal sample design scheme (OSD) approach in our previous work.^48–53 The brief description of the OSD approach by Noda in his recent review⁴³ is given as follows: the basic concept of OSD is to use a well-designed set of concentration series for two different constituents in solution mixtures, such that patterns of concentration variations of the two species will become mathematically orthogonal to each other. The imposed orthogonality will break down when the apparent deviation from the Beers–Lambert law, often associated with the presence of specific intermolecular interactions, is observed. Thus, the OSD technique becomes a very sensitive probe for the possible presence of specific molecular interactions. It should also be pointed out that OSD may be viewed as a form of multiple perturbation 2D correlation method, since two separate concentration variations are simultaneously imposed as perturbations. The unique feature of OSD is to proactively design the selective perturbation conditions to maximize the information content of the resulting 2D correlation spectra.

Following this original idea, we have introduced asynchronous orthogonal sample design (AOSD),^54–56 double orthogonal sample design (DOSD)⁵⁷ and double asynchronous orthogonal sample design (DAOSD)^58–66 schemes to further enhance the ability of 2D correlation spectroscopy to reveal spectral variations of the characteristic peaks of solutes caused by intermolecular interactions.

The chemical systems applicable for the OSD and related approaches are solutions containing two solutes (P and Q). The spectral coordinate of a characteristic peak from P is given by ν_P, and that from Q is ν_Q. Cross-peaks around (ν_P, ν_Q) in the 2D correlation spectrum are used to reflect intermolecular interactions between P and Q. That is to say, both P and Q possessing characteristic peaks is the prerequisite to apply OSD and relevant techniques to probe the intermolecular interactions between P and Q. In many cases, however, only one solute possesses a characteristic peak, while another solute does not have any characteristic peak within the observed spectral region. Consequently, the OSD and related approaches cannot be used directly to probe intermolecular interactions between two solutes in these chemical systems.

In our recent paper,⁶⁷ we developed a new approach to probe intermolecular interactions between P and Q dissolved in the same solutions. In the system, only P possesses a characteristic peak at spectral coordinate ν_P, while Q does not possess any characteristic peak. Based on mathematical analysis, computer simulation and experiments on a real chemical system, we demonstrated that cross peaks around the spectral coordinate (ν_P, ν_P) in asynchronous correlation spectra can also be used to reflect intermolecular interactions between P and Q. Moreover, the patterns of cross peaks around the coordinate (ν_P, ν_P) can be used to reveal subtle variations of peak position and bandwidth of the characteristic peak of P caused by intermolecular interactions. Unfortunately, variations on absorptivity of the characteristic peak of P cannot be reflected by the pattern of cross peaks around the coordinate (ν_P, ν_P).

The fact that the patterns of cross peaks fail to reflect variation of absorptivity brings about the following two problems: (1) the failure prevents us from obtaining comprehensive information on the spectroscopic behavior of the characteristic peak of P under intermolecular interactions. (2) The inability to reflect the variation of absorptivity means the approach is at risk of making incorrect conclusions concerning whether intermolecular interactions occur or not in some special cases. If intermolecular interactions only bring about changes on the absorptivity of the characteristic peak of P, no cross peaks can be observed around the coordinate (ν_P, ν_P) in the asynchronous correlation spectrum.

In order to solve this problem, a new method, called the “asynchronous spectrum with auxiliary peaks” (ASAP) approach, is proposed. In the ASAP approach, a virtual substance (denoted as S) with an isolated characteristic peak at coordinate ν_S is introduced. The cross peaks around (ν_S, ν_P) and (ν_S, ν_Q) are called auxiliary cross peaks. Mathematical analysis, computer simulation and experiment on a real chemical system were carried out. The results demonstrate that variations on absorptivity of the characteristic peak of P can be reflected by the auxiliary cross peaks around (ν_S, ν_P) when only P possesses a characteristic peak.

2. Experimental

2.1 Description of the model system used in the ASAP approach

The chemical system considered here consists of n solutions containing two solutes (P and Q). Variable concentrations are used as an external perturbation to construct 2D asynchronous correlation spectra. In addition, a virtual solute denoted as S is also introduced in association with each solution. The initial concentrations of P, Q and S are denoted as:C^i(init)_P, C^i(init)_Q and C^i(init)_S are the initial concentrations of P, Q and S in the i^th solution.

When there are intermolecular interactions between P and Q, part of P undergoes subtle structural variation and converts to U and part of Q converts to V. This inter-conversion can be expressed by the following equilibrium where K is the equilibrium constant. The so-called solute S is a virtual substance, and it does not interact with either P or Q.

For the i^th solution, the corresponding spectrum is given by eqn (3).

Aⁱ(ν) = f_P(ν)C^i(eq)_P + f_Q(ν)C^i(eq)_Q + f_U(ν)C^i(eq)_U + f_V(ν)C^i(eq)_V + f_S(ν)C^i(eq)_S (3)

where ν is the wavelength. f_P(ν), f_Q(ν), f_U(ν), f_V(ν) and f_S(ν) are the spectral functions of P, Q, U, V and S. C^i(eq)_P, C^i(eq)_Q, C^i(eq)_U, C^i(eq)_V and C^i(eq)_S are the equilibrium concentrations of P, Q, U, V and S in the i^th solution. The path length is set as 1 for convenience.

For each of P, Q, U, V and S, the spectral function is a single peak function that is represented by a Gaussian function as shown in eqn (4).

where j is the index of the five chemical species, i.e., P, Q, U, V and S. ε_j, ν_j, and w_j are the corresponding molar absorptivity, peak position and bandwidth (half-width at half-height, HWHH) of the characteristic band of the j^th chemical species. g_j(ν) is the peak shape function.

Since S does not interact with other solutes, we have:

C^i(init)_S = C^i(eq)_S (5)

Based on eqn (2), the following two expressions can be obtained.

C^i(eq)_P = C^i(init)_P − C^i(eq)_U (6a)

C^i(eq)_Q = C^i(init)_Q − C^i(eq)_V (6b)

Thus, eqn (3) also can be expressed as:

Aⁱ(ν) = f_P(ν)C^i(init)_P + [f_U(ν) − f_P(ν)]C^i(eq)_U + f_Q(ν)C^i(init)_Q + [f_V(ν) − f_Q(ν)]C^i(eq)_V + f_S(ν)C^i(init)_S (7)

After removing the average value over all solution samples at each wavelength, the dynamic spectrum of the i^th solution can be expressed as eqn (8).

Ãⁱ(ν) = f_P(ν)C̃^i(init)_P + [f_U(ν) − f_P(ν)]C̃^i(eq)_U + f_Q(ν)C̃^i(init)_Q + [f_V(ν) − f_Q(ν)]C̃^i(eq)_V + f_S(ν)C̃^i(init)_S (8)

where

C̃^i(init)_P = C^i(init)_P − C^init(av)_P (9a)

C̃^i(init)_Q = C^i(init)_Q − C^init(av)_Q (9b)

C̃^i(eq)_U = C^i(eq)_U − C^eq(av)_U (9c)

C̃^i(eq)_V = C^i(eq)_V − C^eq(av)_V (9d)

C̃^i(init)_S = C^i(init)_S − C^init(av)_S (9e)

C̃^i(init)_P, C̃^i(init)_Q and C̃^i(init)_S are the dynamic initial concentrations of P, Q and S in the i^th solution. C̃^i(eq)_U and C̃^i(eq)_V are the dynamic equilibrium concentrations of U and V in the i^th solution.

Asynchronous correlation spectra can be constructed based on eqn (8) and (11)

where and are the dynamic spectral vector at the spectral coordination ν₁ and ν₂, respectively.

In the computer simulation on the model system, the simulated 1D spectra were generated via a program written in our lab with the MATLAB software. All asynchronous correlation spectra were calculated based on the algorithm by Noda³⁰ using the software of MATLAB.

2.2 Experiment on a real chemical system

2.2.1. Materials. Benzo-15-crown-5 (98%) was purchased from Aladdin. Lithium chloride and methanol were of AR grade and purchased from the Beijing Chemical Company.

2.2.2. Instrument. FT-IR spectra were collected on a Thermo-Fischer Nicolet 6700 spectrometer by using a pair of BaF₂ cells with a fix spacing (100 μm). All the spectra were recorded at a resolution of 2 cm⁻¹ and 32 scans were co-added.

3. Results and discussion

Scheme 1 illustrates the 1D spectra used in constructing the asynchronous correlation spectrum. Since S is a virtual substance, the characteristic peak of S appears as gray lines. In principle, the molar absorptivity, peak position and bandwidth of the characteristic peak of S can be arbitrary. In the experiment, the peak of S does not overlap the characteristic peaks of P and Q.

Scheme 1 Schematic diagram of the simulated 1D spectra used in constructing an asynchronous correlation spectrum. S is a virtual substance, and its characteristic peak appears as gray lines. It should be pointed out that the spectral region between 200 cm⁻¹ and 0 cm⁻¹ in this scheme is a virtual frequency region.

The cross peaks in the asynchronous correlation spectrum based on the ASAP approach can be divided into three spectral domains, as shown in Scheme 2. Domain I contains the cross peaks around the spectral coordinates (ν_P, ν_P), (ν_Q, ν_Q), (ν_P, ν_Q) and (ν_Q, ν_P). These cross peaks are conventional cross peaks in an asynchronous correlation spectrum. Cross peaks located around (ν_S, ν_P) and (ν_S, ν_Q) in domain II and cross peaks around (ν_P, ν_S) and (ν_Q, ν_S) in domain III are auxiliary cross peaks. According to the basic properties of asynchronous correlation spectra, the auxiliary cross peaks in domain III are anti-symmetric to those in domain II with respect to the diagonal. Thus, we focus on the auxiliary cross peaks in domain II in the following part.

Scheme 2 Asynchronous correlation spectrum generated by using the ASAP approach. Cross peaks can be classified into three domains. Domain I contains the conventional cross peaks in an asynchronous correlation spectrum. Both domain II and domain III contain auxiliary cross peaks. Since cross peaks in domain III are anti-symmetric to the cross peaks in domain II with respect to diagonal, only auxiliary cross peaks in domain II are discussed.

3.1 Basic properties of the ASAP approach

It is assumed that S does not interact with P or Q since it is a virtual substance. We try to use the auxiliary cross peaks around (ν_S, ν_P) and (ν_S, ν_Q) to reflect the intermolecular interactions between P and Q. In an ideal asynchronous correlation spectrum generated by using the ASAP approach, the auxiliary cross peaks should possess the following two properties: (I): no auxiliary cross peak can be produced around (ν_S, ν_P) and (ν_S, ν_Q) when there are no intermolecular interactions between P and Q. (II): when intermolecular interactions occur between P and Q, auxiliary cross peaks around (ν_S, ν_P) or (ν_S, ν_Q) should be present. Moreover, the variations of spectral function caused by the conversion from P to U and from Q to V can be manifested by the auxiliary cross peaks around (ν_S, ν_P) or (ν_S, ν_Q).

To achieve the above goals, mathematical analysis on the auxiliary cross peaks around (ν_S, ν_P) or (ν_S, ν_Q) is carried out. Herein, ν₁ is in the spectral region of the characteristic peak of S, while ν₂ is in the spectral region of the characteristic peaks of P, Q, U and V. Ψ(ν₁, ν₂) is calculated by combining eqn (8) and (11) and its expression can be expressed as eqn (12). The expressions of the twenty-five terms in eqn (12) are given in the appendix.

Since the characteristic peak of S is intentionally set not to overlap with characteristic peaks of P, Q, U, V, we have:

Based on eqn (13), the values of R₁ ∼ R₂₀ and R₂₅ in eqn (12) are all zero, and thus only four terms R₂₁ ∼ R₂₄ are left.

When there are no intermolecular interactions between P and Q, the equilibrium concentrations of U and V, which are the products of intermolecular interactions between P and Q, should be zero. Thus we have:

According to eqn (14), the values of R₂₃ and R₂₄ are zero when there are no intermolecular interactions between P and Q.

The corresponding Ψ(ν₁, ν₂) changes into eqn (16).

Since no intermolecular interactions occur between P and Q, Ψ(ν₁, ν₂) should be zero. To make Ψ(ν₁, ν₂) be zero, a feasible way is to make both R₂₁(ν₁,ν₂) and R₂₂(ν₁,ν₂) be zero. This can be achieved by setting the initial concentrations of S to be linearly proportional to the initial concentrations of P and Q simultaneously (eqn (17a) and (17b)). Mathematical analysis to support this statement is given in detail in the appendix.

aC^i(init)_S + bC^i(init)_Q = c (17a)

mC^i(init)_S + hC^i(init)_P = d (17b)

where a, b, c, m, h and d are preset constants.

Thus, property I is achieved if the concentration series of P, Q and S satisfy eqn (17a) and (17b). That is to say, no auxiliary cross peaks are produced around (ν_S, ν_P) and (ν_S, ν_Q) when there are no intermolecular interactions between P and Q.

By selecting the concentration series P, Q and S based on eqn (17a) and (17b), the auxiliary cross peaks can be expressed as eqn (18) for the chemical system where intermolecular interactions occur between P and Q.

According to eqn (4) and (18) changes into eqn (19)

Eqn (19) can be expressed as a summation of four parts. The first term contains g_U(ν₁) − g_P(ν₁). That is to say, it reflects variations of bandwidth and peak position of P. The second term contains (ε_V − ε_Q), demonstrating that it is relevant to the variations of absorptivity of P. Similarly, the third term reflects the variations of bandwidth and peak position of Q and the fourth term is relevant to the variation of absorptivity of Q. Thus, the auxiliary cross peaks in the ASAP approach do reflect the variation of spectral function of P and Q caused by intermolecular interaction. Therefore, property II of the auxiliary cross peak is also achieved.

3.2 The application of the ASAP approach in reflecting the variation of absorptivity when only one substance involving intermolecular interactions possesses characteristic peaks

Equipped with the ASAP approach, we try to establish a method to reveal the variation of absorptivity of P when Q does not possess any characteristic peak in the spectral region.

Considering a chemical system where P possesses a characteristic peak at ν_P but Q has no characteristic peak, we have proved that cross peaks around the coordinate (ν_P, ν_P) near the main diagonal in an asynchronous correlation spectrum can be used to characterize the intermolecular interactions between P and Q. In our previous work,⁶⁷ we demonstrated that the cross peaks around the coordinate (ν_P, ν_P) can be expressed as eqn (20).

where x and y are in a spectral region around ν_P.

Based on the mathematical property of the Hilbert–Noda transformation, matrix N in eqn (21), H₁(x, y) and H₂(x, y) can be combined into one term.

where A⃑ and B⃑ can be arbitrary n-dimensional vectors.

Eqn (20) can be expressed as eqn (22).

As shown in eqn (22), the pattern of cross peaks around (ν_P1, ν_P2) can reflect the variations of g(ν) that are relevant to peak position and bandwidth. Although the variation of absorptivity is related to the intensity of cross peak, it is hard to retrieve information on the variations of absorptivity from the intensity of the cross peak, since the intensity of a cross peak is affected by a variety of factors. These factors are difficult to measure accurately.

To solve the problem, the ASAP approach is adopted, and we try to obtain the variation of the absorptivity of the characteristic peak of P from the auxiliary cross peak. Since both Q and V do not show any characteristic peak, we have f_Q(ν₁) = 0 and f_V(ν₁) = 0. Thus, the R₂₄ term in eqn (18) is zero. Consequently, the auxiliary cross peaks can be expressed as eqn (23).

As shown in eqn (23), the auxiliary cross peak is composed of two parts. We notice that the second part contains (ε_U − ε_P) term, which reflects the variation of absorptivity of the characteristic peak of P under intermolecular interactions. Therefore, the problem that a variation of the absorptivity of the characteristic peak of P cannot be reflected when Q does not possess any characteristic peak is addressed by using the ASAP approach. Information on the variation of absorptivity can be retrieved from the pattern of auxiliary cross peaks around (ν_S, ν_P).

First, we carry out a computer simulation on a model chemical system to show how variation of the absorptivity can be obtained by using the ASAP approach. In this simulated system, intermolecular interactions between P and Q only cause the variation of absorptivity of P, and the corresponding K value is arbitrarily set as 0.01 here. The spectral parameters of P, U and S are given in Table 1. The concentrations of P, Q and S are listed in Table 2.

Table 1 Peak parameters of the chemical species P, U and S in the model system when only P possesses a characteristic peak

Spectral variable	Peak position	Bandwidth	Absorptivity
a It should be pointed out that S is in the virtual frequency region.
P	350.00	20.00	1.00
U	350.00	20.00	1.03
S^a	100.00	20.00	1.00

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Table 2 Initial concentrations of the chemical species P, Q and S in the model systems

Number	CP	CQ	CS
1	2.00	5.00	10.00
2	0.00	3.00	12.00
3	4.00	7.00	8.00
4	7.00	10.00	5.00

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As shown in Fig. 1, no cross peak in domain I is observed, indicating that a variation of absorptivity of the characteristic peak of P cannot be reflected by the conventional cross peaks in an asynchronous correlation spectrum. Furthermore, this result demonstrates that conventional cross peaks fail to detect intermolecular interaction between P and Q. However, a single auxiliary cross peak can be clearly observed around (100, 350) in domain II of Fig. 1. This result demonstrates that intermolecular interactions between P and Q can be manifested by the presence of an auxiliary cross peak. Moreover, the pattern of auxiliary cross peaks is also helpful to reveal the variation of absorptivity. As shown in domain I of Fig. 1, no cross peak around (350, 350) is observable, indicating that intermolecular interactions do not produce variations in either peak position or bandwidth of the characteristic peak of P. Thus, the first term in eqn (23) is zero and the second term relevant to the variation of absorptivity is left. According to eqn (23), the second term will produce a single auxiliary cross peak. As shown in domain II of Fig. 1, a single auxiliary cross peak is observed, confirming that the variation of absorptivity is revealed.

Fig. 1 Asynchronous correlation spectrum based on the ASAP approach when just P possesses a characteristic peak and intermolecular interactions induce a variation in the absorptivity of P. It should be pointed out that the spectral region between 200 cm⁻¹ and 0 cm⁻¹ in this figure is a virtual frequency region.

Then we apply the ASAP approach on a real chemical system. In the real chemical system, coordination between Li⁺ and benzo-15-crown-5 is probed. First, a series of methanol solutions containing lithium chloride (denoted as LC) and benzo-15-crown-5 (denoted as BC) was prepared. The concentrations of benzo-15-crown-5 and lithium chloride are listed in Table 3. The concentrations of S in the four solutions listed in Table 3 are 0.00, 0.08, 0.19 and 0.30 mol L⁻¹ respectively. The peak position, bandwidth and absorptivity of the characteristic peak of the virtual substance (S) are set to be 1450.00, 10.00 and 1.00 respectively. FT-IR spectra of the solutions were recorded and are shown in Fig. 2A. The band located at around 1597 cm⁻¹ is assigned to vibration of the skeleton of the aromatic ring and used as a characteristic peak of benzo-15-crown-5. In the FTIR spectra, spectral data below 1500 cm⁻¹ are truncated and spectra of a virtual substance S are put in the spectral region between 1500 and 1400 cm⁻¹. The peaks shown in gray refer to the virtual substance S. Li⁺ does not exhibit any absorption peak in the FTIR spectrum. The asynchronous correlation spectrum based on the ASAP approach is constructed by using the 1D spectra of Fig. 2A and is shown in Fig. 2B. A pair of cross peaks in domain I can be clearly observed in Fig. 2B.

Table 3 The concentrations of benzo-15-crown-5 and lithium chloride in solutions

Number	CBC (mol L^−1)	CLC (mol L^−1)
1	0.30	0.00
2	0.22	0.08
3	0.11	0.19
4	0.00	0.30

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Fig. 2 (A) FT-IR spectra of the benzo-15-crown-5 of the solutions; (B) 2D asynchronous correlation spectrum generated by using the 1D spectra in (A) based on the ASAP approach. The spectral region between 1500 cm⁻¹ and 1400 cm⁻¹ is a virtual frequency region. In (B), the absolute intensity of the positive peak is larger than that of the negative peak (this is manifested by the fact that the number of contours in the positive auxiliary peak is larger than that in the negative auxiliary peak).

According to our previous work,^48–67 the following experiment is performed: benzo-15-crown-5 is dissolved in methanol alone. A good linear relationship between the absorbance of the 1597 cm⁻¹ band and the concentration of benzo-15-crown-5 can be obtained when the concentration range of benzo-15-crown-5 is between 0.00 mol L⁻¹ and 0.30 mol L⁻¹ (ESI†). Since the concentrations of benzo-15-crown-5, listed in Table 3, are within the above concentration range, the possibility that the conventional cross peaks in domain I of Fig. 2B are caused by the interaction between benzo-15-crown-5 and methanol can be safely precluded. That is to say, it is the coordination between Li⁺ and benzo-15-crown-5 that brings about the structural variation on the aromatic ring and produces the cross peaks in the corresponding asynchronous correlation spectrum. This spectral pattern suggests that coordination between Li⁺ and benzo-15-crown-5 brings about a blue shift of the 1597 cm⁻¹ band. The result obtained from the conventional cross peak in domain I is consistent with that shown in Fig. 2A.

However, whether the absorptivity of the 1597 cm⁻¹ band varies or not remains unknown. Herein the auxiliary cross peak around (1450, 1597 cm⁻¹) in domain II is used to check whether the intermolecular interactions between benzo-15-crown-5 and Li⁺ cause variations of absorptivity other than peak position. According to the 1D spectra in Fig. 2A and the conventional cross peak in domain I of Fig. 2B, we learn that the interactions between benzo-15-crown-5 and Li⁺ make the characteristic peak of benzo-15-crown-5 undergo a blue-shift (Δx_U > 0). In domain II, a pair of vertical auxiliary cross peaks can be observed. One auxiliary cross peak is positive and the other is negative. The spectral pattern of the auxiliary cross peak also indicates that the 1597 cm⁻¹ band undergoes a band-shift. When we examine the auxiliary cross peaks carefully, it is noticed that the absolute intensity of the positive auxiliary cross peak is slightly larger than that of the negative auxiliary cross peak. The pattern of cross peaks around the coordinate (1597, 1597 cm⁻¹) demonstrates that coordination between the lithium ion and benzo-15-crown-5 cannot produce an observable variation in the bandwidth of the 1597 cm⁻¹ peak. If coordination only brings about band-shift of the 1597 cm⁻¹ peak, the absolute intensities of the pair of the auxiliary cross peaks should be the same. This is not the case in Fig. 2B, suggesting that the absorptivity of the 1597 cm⁻¹ peak also changes as coordination occurs between benzo-15-crown-5 and lithium ion.

Thus, we performed a computer simulation on three model systems to mimic the spectral behavior of the benzo-15-crown-5/lithium chloride system. The peak parameters of P, U and S in the three model systems are listed in Table 4. The corresponding 2D asynchronous spectra are shown in Fig. 3. It is found that the pattern of auxiliary cross peaks in Fig. 2B is quite similar to that shown in Fig. 3C. This result demonstrates that the absorptivity of the 1597 cm⁻¹ band also increases upon coordinating with lithium ion. That is to say, coordination between Li⁺ and benze-15-crown-5 not only makes the 1597 cm⁻¹ band undergo a blue shift but also brings about a slight increment of its absorptivity.

Table 4 Peak parameters for three model systems

	Model system I	Model system II	Model system III
XP (cm^−1)	1597.00	1597.00	1597.00
WP (cm^−1)	10.00	10.00	10.00
εP	1.00	1.00	1.00
XU (cm^−1)	1600.00	1600.00	1600.00
WU (cm^−1)	10.00	10.00	10.00
εU	0.97	1.00	1.03
XS (cm^−1)	1450.00	1450.00	1450.00
WS (cm^−1)	10.00	10.00	10.00
εS	1.00	1.00	1.00
XU − XP (cm^−1)	3.00	3.00	3.00
WU − WP (cm^−1)	0.00	0.00	0.00
εU − εP	−0.03	0.00	0.03

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Fig. 3 2D asynchronous correlation spectra generated by using the ASAP approach on three model systems to simulate the spectral variation of the lithium chloride/benzo-15-crown-5 system. The spectral region between 1500 cm⁻¹ and 1400 cm⁻¹ in figure is a virtual frequency region. Red contours mean the cross peaks are positive and blue contours mean the cross peaks are negative. The pattern of the auxiliary cross peak around (1450, 1597 cm⁻¹) in (C) is similar to that shown in Fig. 2B. The absolute intensity of the positive peak is larger than that of the negative peak (this is manifested by the fact that the number of contours in the positive auxiliary peak is larger than that in the auxiliary negative peak).

In summary, we propose the ASAP approach, where a virtual substance(S) is introduced into solutions containing two solutes (P and Q), is a useful technique. Under a suitable concentration series, auxiliary cross peaks around (ν_S, ν_P) and (ν_S, ν_Q) can be used to reflect intermolecular interactions between P and Q. By using the ASAP approach, variations of absorptivity of the characteristic peak of P can be retrieved when Q has no characteristic peak in the spectral region.

Acknowledgements

This project is financially supported by the National Natural Science Foundation of China (No. 51373003, 51074150, 51574213), Natural Science Foundation of Hebei Province (No. B2014205129) and the Key Project of Chinese National Programs for Fundamental Research and Development (973 Programs No. 2012CBA01203, 2013CB632602).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra16062f

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