DFT-Calculated IR Spectrum Amide I, II, and III Band Contributions of N-Methylacetamide Fine Components.

The infrared spectrum (IR) characteristic peaks of amide I, amide II, and amide III bands are marked as amide or peptide characteristic peaks. Through the nuclear magnetic resonance study, N-methylacetamide has been determined to have six fine components, which include protonation, hydration, and hydroxy structures. Then the independent IR spectrum of every component in N-methylacetamide is calculated by using the density functional theory quantum chemistry method, and the contribution of each component to amide I, II, and III bands is analyzed. The results of this research can help to explain the formation of the amide infrared spectrum, which has positive significance in organic chemistry, analytical chemistry, and chemical biology.

Introduction

The amide is very important in organic chemistry and chemical biology.[1] The structures of proteins, enzymes, polypeptides, and many other biological molecules all have peptide bond units, which are based on the amide bond.[2] Many protein structural properties are associated with polypeptide bonds, such as functional execution, proton conduction, transcription, information reaction, and other activities related to peptide amide.[3] Therefore, the study of amide-peptide bonds has aroused great interest in chemistry and biology.

A large number of studies that included theoretical calculations and spectral methods have found that amides have some resonance structures,[4] for example, the form of enol. The absorption spectrum bands of amide infrared radiation (IR), amide I (1600–1800 cm–1), amide II (1470–1570 cm–1), amide III (1250–1350 cm–1), and amide A (3300–3500 cm–1), are peaks of infrared characterization of amide. A protein peptide bond is an amide group. A protein structure is determined by using amide I, II, III, and A IR absorption peaks.[5] The infrared spectrum and other spectra are used to study the amide, forming the infrared spectrum of amide I, II, III, and A bands. The infrared spectrum multiband of amide indicates that there are many fine components in the amide, and the structures are reported in recent research.[6] How the fine component of amide affects the biological activity of the peptide bond is being recognized.

N-Methylacetamide is a secondary amide similar to the protein peptide bond. Several fine components were found in pure N-methylacetamide. NMR (15N, 17O, 13C, 1H, and two-dimensional NMR in Figures S1–S10) confirmed the presence of six fine components in pure N-methylacetamide samples,[6] which were protonated and hydrated, but it cannot be purified as an independent component.

Then the infrared spectra of the components were calculated by using quantum chemical theory, and the contribution of each component to the infrared spectra of amide I, II, and III was analyzed. Further analysis of the contribution of the fine component–effect relationship to amide I, II, and III IR spectra is possible in future protein imaging. Fine components A-1, A-2, A-3, Im-1, D-1, and O-1 are shown in Figure , where E-1 is the structure not found.

Figure 1

Fine components in N-methylacetamide found by NMR spectra (the percent of every component was determined from the NMR integral area ratio).

Results and Discussion

Methods and Theory

ADF infrared spectroscopy can be used for molecular vibrations.[7,8] In the Born–Oppenheimer and harmonic approximations, the vibrational frequencies are determined by the normal modes corresponding to the molecular electronic ground-state potential energy surface. Various methods and basis sets have been tried for infrared calculations. The amide IR calculation test methods are Local Density Approximation (LDA) (with function -Xonly and -VWN), Generalized Gradient Approximation (GGA) (function -OPTx, -PBEx, -rPBEx, -revPBEx, -BP86, -LYP, -BLYP, and -OLYP), and the basis sets SZ, DZ, DZP, TZP, and TZ2P. Generally speaking, we can say that SZ is a single-zeta basis set, DZ is a double-zeta basis set, DZP is a double-zeta polarized basis, TZP is a core double-zeta, valence triple-zeta, polarized basis set, and finally, TZ2P is a core double-zeta, valence triple-zeta, doubly polarized basis. This explains the more intuitive names that are given for the basis sets. The infrared peaks of various methods are very close. The frequencies and intensities generally agree quite well. Improving the integration accuracy improves the agreement. The analytical frequencies are slightly more stable to changes in integration accuracy than the numerical values.

This section describes the general theory of the second analytical derivative of molecular energy where the derivative is about arbitrary parameters X and Y. The theories described in this section also apply to the DFT and Hartree–Fock theories.[9,10]

In this section, we assume that the molecular energy E is explicitly dependent on the orbital coefficient c and parameters X and Y, namely[11]

Although E is clearly dependent on the orbital coefficient, which in turn depends on the coefficient of the X and Y parameters of the standard, throughout this article, d/dX refers to X and is derived explicitly by the partial derivative, by taking the first derivative of total energy (eq ) for the parameter X(11)

Here, in the following discussion, the Greek characters are the index atomic basis functions, and Roman characters i and j are the indexes of the molecular orbit. It should also be noted that, in the instructions in this section, the first derivative of the energy is to the parameter X, and the second derivative is to the parameter Y.

However, for the derivatives of the available coefficients, other quantities of derivatives can also be calculated, such as the kernel derivatives of the density, d/dRA, which can be used to calculate the dipole derivatives, such as[11]where l is the dipole component, l, and ZA is the nuclear charge of atom A, and the dipole derivative can be used to calculate the infrared absorption intensity and dipole strength. It is worth repeating that dc/dY is not usually calculated explicitly but directly using μ (eq ).This section discusses the basis of a second derivation theory for arbitrary parameters X and Y, and the following sections discuss a second derivation theory for ADF whose parameters are nuclear coordinates.

Calculating the vibrational frequency of a molecule requires a second derivative of the molecular energy. They were also asked to calculate the hessian, from which a fixed point could be described as a maximum, minimum, or saddle point.

Calculated IR Spectra

Amide infrared radiation (IR) absorption spectral amide I (1600–1800 cm–1), II (1470–1570 cm–1), III (1250–1350 cm–1), and A (3300–3500 cm–1) bands are the famous IR characterizations of amide. Protein peptide bonds are amide groups. The amide I, II, III, and A band IR absorption spectral peaks were used to determine the protein structures.[12,13] Fine components were protonation and hydration structures, and these were impossible to be purified to the independent component. Then the quantum chemical software was used to calculate independently the IR spectrum of every component to analyze the contribution of every component to the IR spectra. Further analysis of the amide I, II, and III for the fine component–effect relationships’ contributions might be realized for protein imaging.[14] Fine components A-1, A-2, A-3, Im-1, D-1, and O-1, excluding E-1, calculated IR spectra are shown in Figures –7.

Figure 2

Calculated IR spectrum of N-methylacetamide (A-1) component by DFT methods. The amide I 1630 cm–1 (C=O ν-s with molecular bond δ ). Amide II 1518 cm–1 (C=O connected carbon chain ν-s). 546 cm–1 (N–H γ, with molecular bond δ).

Figure 7

Calculated IR spectrum of O-1 component by DFT methods. 2795 cm–1 (CH3 hydrogen ν-s). 1444 cm–1 (CH3 hydroxygen γ). 1082 cm–1 (O–H β with bond ν). 509 cm–1 (N–H γ-s).

Calculated IR spectrum of N-methylacetimidic acid (Im-1) component by DFT methods. 1700 cm–1 (C=N ν-s). 1395 cm–1 (CH3-ν-s). 1109 cm–1 (molecular bond β-s). 464 cm–1 (O–H γ).

Calculated IR spectrum of 1-(methyl-azanyl)ethan-1-one (A-2) component by DFT methods. 1600 cm–1 (C–N ν-s). 1499 cm–1 (C–N–C=O ν-s). 1409, 1388 cm–1 (C–H β), 4076 cm–1(N–2H ν-s).

Calculated IR spectrum of 1-(methyl-amino)ethan-1,1-diol (D-1) component by DFT methods. 1210 cm–1 (molecular bond ν-s). 1190 cm–1 (molecular bond γ). 519, 224, −913 cm–1 (C–O–H γ-as). The result calculated the negative IR absorption peak, which will be analyzed in another research.

Calculated IR spectrum of A-3 component by DFT methods. 1390 cm–1 (C–C ν-s). 1215 cm–1 (C–N ν-s). 638 cm–1 (N–H γ). 2676 cm–1 (O–H ν-s).

IR Calculations

The infrared spectrum is calculated by using the density functional theory (DFT) method of ADF[15] software. Based on NMR (Figures S1–S10) fine component data, the molecule structure of each fine component has been determined.[6] Structural optimization and frequency calculation were conducted to obtain the infrared spectrum of each fine component (Figures –7).

IR bands I, II, III, and A of N-methylacetamide were analyzed, and each fine component should contribute to the final IR spectrum.[16,17] Each chemical group has independent contributions to amide I, II, III, and A bands. The contributions of each component to amide I, II, III, and A bands were different. The infrared spectrum calculation results are based on chemical bond vibration information of chemical functional groups, so the calculation error can be received, and the results reflect the real information of each independent fine component. This means that determining the structure then determines the chemical groups and bonds and then the infrared spectrum vibrational position or wavenumber. Therefore, the ADF DFT method is accurate and feasible for infrared spectrum calculation.

Amide I band IR absorption ranges from 1600 to 1800 cm–1. Based on the calculated IR spectra of fine components in N-methylacetamide, the A-1, A-2, and Im-1 have IR absorption peaks in the amide I band. A-1 has C=O and gave symmetry vibration, while molecular bond scissoring vibration produces IR absorption at 1630 cm–1. A-2 has C–N symmetry vibration producing IR absorption at 1600 cm–1. Im-1 has C=N symmetry vibration producing IR absorption at 1700 cm–1. So, the fine components A-1, A-2, and Im-1 have contributions to the amide I band.

Amide II band IR absorption ranges from 1470 to 1570 cm–1. The fine component A-1 has C=O connected carbon giving symmetry vibration that produces IR absorption at the 1518 cm–1 peak. A-2 C–N–C=O has symmetry vibration that produces IR absorption at the 1499 cm–1peak. A-2 C–H in-plane bending vibration produces IR absorption at the 1409 cm–1peak. A-3 C–C symmetry vibration produces IR absorption at the 1390 cm–1 peak. O-1 CH3 hydroxygen has out-of-plane bending vibration that produces IR absorption at the 1444 cm–1 peak. Im-1 C-H3 symmetry vibration produces IR absorption at the 1395 cm–1 peak. So, the A-1, A-2, A-3, O-1, and Im-1 have contributions to the amide II band.

The amide III band has a range of 1250–1350 cm–1. A-2 C–H has in-plane bending vibration that produces IR absorption at the 1388 cm–1 peak. A-3 C–N symmetry vibration produces IR absorption at the 1215 cm–1 peak. The D-1 molecular bond has symmetry vibration that produces IR absorption at the 1210 cm–1 peak. The D-1 molecular bond out-of-plane bending vibration produces IR absorption at the 1190 cm–1 peak. O-1 O–H has in-plane bending vibration with molecular bond vibration that produces IR absorption at the 1082 cm–1 peak. Im-1 molecular bond in-plane bending symmetry vibration produces IR absorption at the 1109 cm–1 peak. So, the fine components A-2, A-3, D-1, O-1, and Im-1 have contributions to the amide III band.

The amide A band ranges 3300–3500 cm–1. A-2 N–2H has symmetry vibration that produces IR absorption at the 4076 cm–1 peak. A-3 O–H symmetry vibration produces IR absorption at the 2676 cm–1 peak. O-1 CH3 hydroxygen symmetry vibration produces IR absorption at the 2795 cm–1 peak. So, the fine components A-2, A-3, and O-1 have contributions to the amide A band. The other IR absorption peaks and the fine component calculated IR absorption peaks that contributed to the amide I, II, III, and A bands are listed in Table .

Table 1

Contribution of the DFT-Calculated Infrared (IR) Absorption Peaks of the N-Methylacetamide Fine Components to Amide I, II, III, and A Bandsa

Asymmetry, as; symmetry, s; vibration, ν; in-plane bending vibration, β; scissoring vibration, δ; rocking vibration, ρ; out-of-plane bending vibration, γ; wagging vibration, ω; twisting vibration ,τ; symmetrical deformation vibration, δs; asymmetrical deformation vibration, δas.

A summary is shown in Figures –8. The A-1, Im-1, and A-2 have contributions to the amide I band. The amide I was from the double bond (C=O, C=N) stretch vibration. The components A-1 and A-2 have carbonyl bond N–(C=O)–CH3 stretch vibration, which shows that the amide II was from the carbonyl (C=O)-related carbon chain bond stretch vibration. Amide III was mainly from the methyl-related C–H or C–C stretch vibrations. Amide A was about 3500 cm–1, mainly from the H-N stretch/bend vibration or hydroxyl H-O- stretch/bend vibration.

Figure 8

Calculated IR spectrum of 1-(methyl-amino)ethan-1-ol (E-1) component by DFT methods. This E-1 was a reference component not found in N-methylacetamide. 2838 cm–1 (CH3-ν-s). 1390 cm–1 (C–C ν-s with C–H β). 1151 cm–1 (C–N ν-s) 1019 cm–1 (O–H β) 786 cm–1 (C–O ν-s), 599 cm–1 (N–H γ). 328 cm–1 (O–H γ).

The final IR spectra might be the comprehensive static results of the multicomponent, and the amide I and II changed with the ratios’ changing of fine components in an amide. The fine components may be transformed into others, which might be based on some changing environmental conditions (pH, temperature, metal ions, anions, light, heat, pressure, collision, solvents, air, wet, and so on). So, the amide final IR spectra have different states based on the ratios of fine components. These amide fine components are connected with the peptide bond IR specrta.[18,19]

IR Spectra

To compare the calculated results, the infrared absorption spectrum of pure N-methylacetamide was recorded. The results are shown in Figure . It is generally believed that the peak of 3500 cm–1 in Figure is from the infrared absorption peak of water, namely, the hydroxyl peak. In the fine component, the hydroxyl structure exists in components Im-1, O-1, D-1, and A-3. The hydroxyl −OH elastic vibration peak of IR is around 3000–4000 cm–1.This means that the hydroxyl peaks of amide 3000–4000 cm–1 in Figure come from the −OH groups or −CH3 oscillations of the amide fine resonance structure rather than from the IR absorption peaks of unpurified water. These results may correct the misunderstanding that the 3000–4000 cm–1 is not from unpurified water; it should be from the amide several fine components.

Figure 9

Experimental test IR absorption spectrum of pure N-methylacetamide liquid sample (Shanghai Aladdin Reagent. Melting point 29–31 °C). (1656, 1564, 1375, 1303, 1164, 593, 3313 cm–1).

Different components in the sample act together on the final infrared spectrum. Each component has a weight on the spectrum. Based on the integral area data of NMR, Figure shows the weight addition for the IR spectra of the six components, which are compared with the actual IR spectrum in Figure .The components based on NMR integral area added weights to the infrared spectral contribution, and there is a big difference between Figure and Figure . This means that the contribution of the fine component to the infrared spectrum may be a nonlinear weight ratio, which is subject to some mathematical functional relations and needs to be determined by mathematical methods. The result is close to but not equal to the real infrared spectrum. The comparison results are shown in Figure . The contribution of each component to the infrared spectra of amide I, II, and III bands is shown in Figure .

Figure 10

Weight addition of the calculated IR absorption spectra (Figures –7) of fine components in N-methylacetamide. Compared with Figure , the real IR spectrum. (1630, 1518, 546 cm–1).

Figure 12

Comparison of the real IR spectrum with the calculation IR spectra.

Figure 11

Unity IR spectra with the calculation of all the calculated IR spectra contributions to the amide I, II, and III bands.

Figure shows the fine components of amide I, II, and III contributions to the infrared spectrum. The contribution of each component to the infrared spectrum is seen. So, amide I has a contribution from A-1, A-2, and Im-1. The amide II band has contributions from all components. D-1 mainly contributes to amide III, and other fine components also contribute to the amide III band.

Figure shows the comparison between the actual IR spectrum of N-methylacetamide and the calculated IR spectra of the fine components. The detailed properties of amide I, II, and III were defined by the analysis of each fine component. Therefore, it is helpful to find the relationship between the amide property and the structure. The structural effect of the amide or protein peptide bond might be determined by analyzing the infrared spectra of fine components.

Conclusions

Based on 1H, 13C, 15 N, 17O, and two-dimensional NMR, it has been found that N-methylacetamide has several fine components, which include protonation, hydration, and hydroxy structures. For several fine components of pure N-methylacetamide, the infrared spectrum of every independent component is calculated by the DFT method. The results show that the IR spectra of N-methylacetamide only by single structural analysis may interfere, and it is difficult to get accurate analysis results of the peptide or protein. Therefore, the infrared spectrum or other spectra of N-methylacetamide should be more clear and accurate by basing on these amide fine components. The detailed composition makes the structure–effect relationships easier to determine than they used to be in a confined structure. The results of infrared spectrum calculation of these fine components will be helpful to the study of amide I, II, III, and A and to even clarify some experiments and theories of arguing. The significance of these results is helpful for better analysis of amide I, II, III, and A bands in different microstructure ratios. These results can enhance the characterization of protein and help to discover the contribution of amide fine components to the structure–effect relationship of the peptide and protein.

The application of the two-dimensional vibration spectrum will be the next step in the restudy of amides. The vibration spectrum is a tool widely used in the study of molecular structures and surfaces. These one-dimensional techniques include infrared reflection absorption spectroscopy,[20] Attenuated Total Reflection (ATR) spectroscopy,[21] and sum frequency generation spectroscopy.[22] More recently, multiple efforts have been made to extend the monolayer sensitivity of these techniques to vibrational spectroscopies of higher dimensionality.[23] Two-dimensional infrared (2D IR) and other multidimensional techniques contain additional features that are not easily equated between the one-dimensional spectral peaks, such as the cross-coupled oscillator and the experimental separation ability of the isomorphic inhomogeneous donor and line width. These spectra provide a wealth of information on the structure and dynamics of samples and have been proven useful in bulk system studies in chemistry and biology.[24,25] These spectral methods can help in amide component research in the future.