Ep 41 — Two-Dimensional Correlation Spectroscopy (2D-COS): A Powerful Tool for Resolving Overlapping Peaks

Series: Encyclopedia of Infrared Spectroscopy: From Principles to Practice
Chapter: Part 4 · Advanced Topics — Frontier Techniques (First Episode of Second Half)
Target Audience: Graduate students in analytical/physical/polymer chemistry, spectroscopy researchers, biophysicists and drug polymorph investigators
Prerequisites: Ep 04 (Reading IR spectra), Ep 18 (Basic spectral processing), Ep 20 (Beer-Lambert law), Ep 22 (Proteins and drug polymorphs), Ep 24 (Polymer aging), Ep 43 (Chemometrics PCA/PLS, recommended parallel reading)
Reading Time: Approximately 55 minutes

Introduction: When 1D Spectra Are "Crowded"

In 1986, Iso Noda, while studying phase separation behavior of polymer blends at Procter & Gamble (P&G), encountered a challenging problem: the spectral peaks of different components severely overlapped, and conventional one-dimensional infrared spectra could not distinguish which component underwent conformational change first [1]. Inspired by 2D NMR spectroscopy, he proposed a key idea—using an external perturbation as a "second dimension" to correlate a series of spectra varying with the perturbation, generating Two-Dimensional Correlation Spectroscopy (2D-COS). In 1989, he formally extended this method to Generalized 2D-COS, allowing arbitrary selection of perturbation variables [2].

"Two-dimensional correlation spectroscopy converts a set of spectra obtained as a function of a perturbation into a synchronous and an asynchronous 2D spectrum, revealing interactions between bands that are invisible in the original 1D spectra."
—— Noda I. Appl Spectrosc 1993 [2]

The three "killer features" of 2D-COS provide unprecedented capabilities to researchers:

1. Enhanced apparent resolution: Multiple component peaks originally merged into a single envelope in 1D spectra can be separated as cross peaks in 2D spectra;
2. Determination of sequential order: Using the sign rules of synchronous and asynchronous spectra, the order of response of different groups to perturbation can be determined;
3. Revealing intermolecular interactions: Off-diagonal peaks indicate which groups change cooperatively, whether coupled or competitive.

In this episode, we will systematically discuss the mathematical principles, interpretation rules, software implementation, and typical applications of 2D-COS, supplemented by three full case studies: protein folding, polymer stretching, and mixture analysis.

1. Mathematical Principles of 2D-COS

1.1 From 1D Perturbation Sequence to 2D Correlation

The input to 2D-COS is a set of spectra collected under a perturbation {I(ν₁, t₁), I(ν₁, t₂), ..., I(ν₁, tₘ)}, where ν is wavenumber and t is the perturbation variable (e.g., temperature, time, concentration, pressure, pH).

Mathematically, generalized 2D-COS first mean-centers the perturbation sequence to obtain dynamic spectra $\tilde{y}_j(\nu)=y_j(\nu)-\bar{y}(\nu)$, then constructs synchronous and asynchronous spectra (Hilbert–Noda form) [1][2][3]:

$$ \Phi(\nu_1,\nu_2)=\frac{1}{m-1}\sum_{j=1}^{m}\tilde{y}_j(\nu_1)\,\tilde{y}_j(\nu_2) $$

$$ \Psi(\nu_1,\nu_2)=\frac{1}{m-1}\sum_{j=1}^{m}\tilde{y}_j(\nu_1)\,\tilde{z}_j(\nu_2) $$

where $\tilde{z}_j(\nu)$ is the Hilbert–Noda transform of the dynamic spectra along the perturbation axis (discrete implementation in Python in the next section; the continuous formulation is equivalent to orthogonal phase shifting in the perturbation domain followed by cross-correlation). $\Phi$ is the synchronous spectrum, and $\Psi$ is the asynchronous spectrum.
(Previous drafts incorrectly used a summation with an exponent; corrected here to the standard form consistent with the later code.)

1.2 Synchronous Spectrum: Who Changes Together

The synchronous spectrum Φ(ν₁, ν₂) reflects the extent to which absorbances at two wavenumbers change synchronously:

• Autopeaks: located at ν₁ = ν₂, i.e., the main diagonal of the spectrum, with intensity equal to the autocorrelation variance at that wavenumber. Autopeaks are always positive, indicating the sensitivity of that group to the perturbation.
• Cross peaks: located at ν₁ ≠ ν₂. If two groups change synchronously (in the same or opposite direction), a synchronous cross peak appears; its sign indicates the direction of change (positive for same direction, negative for opposite).

              ν₂
              ↑
        ┌─────────────┐
        │   ⋱         │   Diagonal = autopeaks
        │     ⋱       │   Off-diagonal = cross peaks
        │   ●     ⋱   │   ● = synchronous cross peak (same direction)
        │      ●       │
        │        ⋱     │
        └─────────────┘  ν₁ →

Figure 1: Schematic of synchronous spectrum structure. "Bright spots" on the diagonal are autopeaks; circular spots off the diagonal are synchronous cross peaks.

1.3 Asynchronous Spectrum: Who Comes First

The asynchronous spectrum Ψ(ν₁, ν₂) reflects the extent to which absorbances at two wavenumbers change asynchronously (out of phase), and is the core value of 2D-COS [2][3].

• The asynchronous spectrum has zero intensity on the diagonal (no autocorrelation);
• An asynchronous cross peak Ψ(ν₁, ν₂) ≠ 0 indicates that the two groups respond to the perturbation at different times (or perturbation values);
• By combining the signs of Φ and Ψ, the sequential order of response between two groups can be determined.

1.4 Noda's Rule

In 1993, Noda proposed the famous "eight-character" rule (Noda's rule) [2][3], which determines the order of response of groups at ν₁ and ν₂ to the perturbation based on the signs of synchronous and asynchronous spectra:

Table 1: Noda's rule (with ν₁ as the horizontal axis and ν₂ as the vertical axis)

💡 Interpretation tip: When synchronous Φ = 0, the two groups change orthogonally, and the order cannot be determined; assumptions about the perturbation direction are needed. When asynchronous Ψ = 0, the two groups change strictly synchronously (possibly from the same physicochemical process).

1.5 Generalized 2D Correlation Spectroscopy: Arbitrary Perturbations

In 1989, Noda proposed Generalized Two-Dimensional Correlation Spectroscopy (Generalized 2D-COS) [2], extending the perturbation variable from the original "time" to any physical quantity:

• Temperature (heating/cooling): phase transitions, denaturation, glass transition, polymerization reactions;
• Concentration: titration, mixing;
• Pressure: high-pressure phase transitions;
• pH: protein acid-base titration;
• Electric/magnetic fields: orientation, electromagnetic induction;
• Strain: stretching, shear;
• Time: reaction kinetics, photochemistry, degradation;
• Spatial position: "pseudo-2D-COS" of line scans or imaging data.

Generalization has allowed 2D-COS to transcend the infrared field and be widely applied to Raman, UV-Vis, NMR, XRD, CD and other spectroscopic techniques [3].

2. Advantages and Limitations of 2D-COS

2.1 Three Core Advantages

1. Enhanced apparent resolution: Peaks originally merged into an "envelope" in 1D spectra can be better separated via cross peaks in 2D spectra. Note: This is apparent peak separation ability, not an increase in instrumental spectral resolution by a fixed factor; the literature occasionally mentions "several-fold" empirical statements, which should be understood qualitatively rather than as a universal specification [2].

2. Peak Assignment Confirmation: The intensity of diagonal autocorrelation peaks quantifies the sensitivity of each group to the perturbation, thus inversely inferring peak assignments—for example, which amide III sub-band corresponds to α-helix and which to β-sheet.

3. Kinetic Order Inference: Asynchronous spectra can infer the order of molecular events from a series of static spectra without time-resolved spectroscopy—this is the most "scientifically valuable" capability of 2D-COS.

2.2 Limitations and Pitfalls

The power of 2D-COS comes with several common pitfalls:

• Baseline Drift Sensitivity: Uncorrected baseline drift or residual baseline drift can be misinterpreted as "perturbation response," leading to false cross peaks [3][4]. It is recommended to perform SNV or polynomial baseline correction on each spectrum before 2D-COS.
• Spectrum Normalization: Overall intensity variations across spectra (e.g., sample thickness differences) introduce spurious correlations. Normalization to a uniform scale is mandatory.
• Perturbation Direction Dependence: The sign of asynchronous spectra depends on the perturbation direction (heating vs. cooling). Conclusions must explicitly state the perturbation direction.
• Oversampling and Undersampling: Too few perturbation points (< 5) lose statistical significance; too many (> 50) introduce noise. 10–20 perturbation points are recommended [3].
• Noise is "Amplified": Since 2D-COS is essentially a covariance operation, noise in the original spectra is amplified as spurious peaks in the 2D spectra. Original SNR should be sufficiently high.

⚠️ Common Misuse: Performing 2D-COS on a single spectrum is incorrect—2D-COS requires a series of spectra as input, not a single spectrum. This is the most common mistake among beginners.

3. Software Implementation: 2Dshige and Python

3.1 2Dshige: The Classic Japanese Tool

2Dshige (2D Shige) was developed by the Ozaki group at Kwansei Gakuin University, Japan, and is the earliest free software for 2D-COS [5]:

• Platform: Windows;
• Input: Text format spectral matrix (rows = perturbation points, columns = wavenumbers);
• Output: Synchronous/Asynchronous 2D spectra (BMP/JPG);
• Advantages: Graphical interface, simple operation, free for academic users;
• Limitations: Old Windows GUI, closed source, not suitable for batch processing.

Download: https://sci-tech.kwansei.ac.j…

3.2 Python Implementation: numpy + matplotlib

Below is a minimal Python implementation (~30 lines), suitable for researchers to get started quickly:

import numpy as np
import matplotlib.pyplot as plt

def two_d_cos(spectra):
    """
    spectra: (n_perturbations, n_wavenumbers) array,
             rows correspond to different perturbation states, columns to wavenumbers.
    Returns Phi (synchronous), Psi (asynchronous) 2D matrices.
    """
    # Mean centering (dynamic spectra)
    y_tilde = spectra - spectra.mean(axis=0, keepdims=True)
    m = y_tilde.shape[0]

    # Hilbert-Noda transformation matrix
    j = np.arange(1, m + 1).reshape(-1, 1)
    k = np.arange(1, m + 1).reshape(1, -1)
    N = np.zeros((m, m))
    # N[j, k] = 0 if j==k else 1 / (pi * (k - j))
    diff = k.T - j.T  # (m, m), N_{jk} = 1/(pi*(k-j))
    N = np.where(np.eye(m) == 0, 1.0 / (np.pi * diff), 0.0)

    # Synchronous spectrum: covariance
    Phi = y_tilde.T @ y_tilde / (m - 1)
    # Asynchronous spectrum: cross-covariance of dynamic spectra and Hilbert transform
    Psi = y_tilde.T @ (N @ y_tilde) / (m - 1)
    return Phi, Psi

# Example: simulate a set of amide I spectra varying with temperature
wavenumber = np.linspace(1700, 1600, 200)
temperatures = np.linspace(25, 95, 15)  # 15 temperature points
spectra = np.zeros((len(temperatures), len(wavenumber)))
for i, T in enumerate(temperatures):
    # α-helix (1650 cm⁻¹) decreases with temperature; β-sheet (1630 cm⁻¹) increases with temperature
    spectra[i] = (1 - (T-25)/70) * np.exp(-(wavenumber-1650)**2 / (2*5**2)) \
               + ((T-25)/70) * np.exp(-(wavenumber-1630)**2 / (2*5**2))

Phi, Psi = two_d_cos(spectra)

fig, axes = plt.subplots(1, 2, figsize=(12, 5))
axes[0].imshow(Phi, extent=[wavenumber[0], wavenumber[-1], wavenumber[-1], wavenumber[0]])
axes[0].set_title("Synchronous Φ"); axes[0].set_xlabel("ν₂"); axes[0].set_ylabel("ν₁")
axes[1].imshow(Psi, extent=[wavenumber[0], wavenumber[-1], wavenumber[-1], wavenumber[0]])
axes[1].set_title("Asynchronous Ψ"); axes[1].set_xlabel("ν₂"); axes[1].set_ylabel("ν₁")
plt.tight_layout(); plt.savefig("2dcos_demo.png", dpi=150)

📦 Ready-made Python libraries: scikit-learn-style py2D-COS and 2DCoS are both open source, can be installed directly via pip, avoiding reinventing the wheel.

3.3 Other Available Tools

Table 2: Summary of mainstream 2D-COS tools

4. Application Case 1: 2D-COS Analysis of Protein Thermal Denaturation

4.1 The Challenge of Amide I Sub-bands

The amide I band (Amide I, 1600–1700 cm⁻¹) of proteins is mainly composed of C=O stretching vibrations and serves as a core probe for protein secondary structure. However, the amide I sub-bands of different secondary structures (α-helix, β-sheet, turns, random coil) differ by only 5–15 cm⁻¹ from each other, merging into a broad band in one-dimensional spectra [6]:

| Secondary Structure | Amide I Frequency (cm⁻¹) |

|---------|----------------------|
| α-helix | ~1650–1658 |
| β-sheet (parallel) | ~1630–1640 |
| β-sheet (antiparallel) | ~1620–1635 and ~1685–1695 (doublet) |
| random coil | ~1640–1650 |
| turns | ~1660–1675 |
| β-turns (antiparallel β-turns) | ~1675–1695 |

Table 3: Assignments of protein amide I sub-bands (data from Barth Biochim Biophys Acta 2007 [6])

🔗 Further reading: For detailed infrared assignments of amide I, II, and III sub-bands, see ftir.fun amide functional group page. This page systematically organizes the specific frequencies and assignment criteria for different secondary structures and side-chain environments, serving as an essential reference for 2D-COS amide band analysis.

4.2 2D-COS Reveals Thermal Denaturation Order

In 1999, Fabian and Mantsch published a classic study in Vib Spectrosc [7]: they used lysozyme solution as the sample, heated from 25°C to 90°C, collected one FTIR spectrum every 5°C (14 spectra total), and performed 2D-COS:

• Synchronous spectrum: Autopeaks appear at 1654, 1634, 1675 cm⁻¹, directly proving that these three frequencies are independent sub-bands (completely unresolvable in 1D spectra).
• Asynchronous spectrum: Strong asynchronous peak between 1654 (α-helix) and 1675 (turns), Φ = +, Ψ = + → α-helix changes before turns.
• Further analysis: 1634 (β-sheet) ↔ 1654 (α-helix), Φ = +, Ψ = − → β-sheet changes after α-helix.

Thus, the thermal denaturation order is: α-helix loosening → turn rearrangement → β-sheet exposure — this result was later confirmed by NMR and molecular dynamics simulations, becoming a classic case in protein denaturation mechanism research [7].

4.3 Workflow

1. Sample preparation: 2 mg/mL protein in D₂O solution to avoid H₂O interference at 1640 cm⁻¹;
2. Measurement: Variable temperature accessory, 5°C steps, equilibrate 5 min, 256 scans, resolution 4 cm⁻¹;
3. Preprocessing: Water vapor subtraction (refer to Ep 28), second derivative (S-G 9 points);
4. 2D-COS: Use temperature as perturbation variable, calculate Φ and Ψ;
5. Interpretation: Deduce sub-band change order according to Noda's rules.

💡 Tip: In D₂O, amide I shifts to ~1450 cm⁻¹ (amide II disappears), yielding cleaner spectra; D₂O is the "standard" solvent for protein 2D-COS [6].

5. Application Case 2: 2D-COS of Polymer Stretching Orientation

5.1 Stress-Spectrum Synchronous Measurement

During polymer stretching, molecular chains orient along the stress direction; the orientation order of different groups reflects molecular chain rigidity and cooperative motion ability [8][9]. In the early 2000s, Vidrine and Galloway et al. established the dynamic infrared dichroism 2D-COS method [8]:

• Setup: FTIR + polarizer + micro-tensile machine;
• Perturbation: Strain ε (0–50%);
• Collection: One spectrum per 5% strain, 11 spectra total.

5.2 Stretching Order of PET

PET contains ester C=O (1715 cm⁻¹), benzene ring C=C (1410, 1505, 1580 cm⁻¹), ether C–O–C (1240, 1095 cm⁻¹), aliphatic CH₂ (2970, 2900 cm⁻¹). Study [8] found:

• Synchronous spectrum: 1715 ↔ 1410 ↔ 1095 positive correlation → these groups orient synchronously;
• Asynchronous spectrum: 1095 (C–O–C) ↔ 2970 (CH₂), Φ = +, Ψ = + → ether orients before CH₂;
• Asynchronous spectrum: 1715 (C=O) ↔ 1095 (C–O–C), Φ = +, Ψ = − → C=O orients after C–O–C.

Molecular mechanism inference: The benzene ring-ester segment (rigid segment) orients first along the stress direction; the flexible CH₂ segment subsequently relaxes and rearranges [8][9]. This conclusion agrees with solid-state NMR results.

5.3 2D-COS of Blend Phase Separation

For polymer blends (e.g., PMMA/PVDF), infrared frequencies of different components (C=O, CF₂) are close, making 1D spectra difficult to distinguish. Using temperature as perturbation, 2D-COS can resolve [9]:

• PMMA's C=O at ~1730 cm⁻¹, PVDF's CF₂ at ~1180 cm⁻¹; they are normally uncorrelated;
• But near the phase separation temperature, asynchronous cross peaks appear between 1730 and 1180 cm⁻¹, reflecting the "phase separation onset" of the two polymers near the critical temperature.

🔗 Further reading: For assignments of C=O, C-O-C and other functional groups in polymers, see ftir.fun carbonyl functional group page and ftir.fun ether functional group page.

6. Application Case 3: 2D-COS Analysis of Mixtures

6.1 "Secondary Resolution" of Overlapping Peaks

Consider IR spectra of ethanol-acetone mixtures: ethanol's C–O stretch at ~1050 cm⁻¹, acetone's C=O at ~1715 cm⁻¹, seemingly not overlapping. However, if the mixture contains multiple alcohols (methanol, ethanol, propanol, butanol), their C–O stretches lie at 1030, 1050, 1070, 1100 cm⁻¹, merging into one broad band in 1D spectra, unresolvable [3][10].

Solution: Use concentration as perturbation variable — gradually change the proportion of each alcohol in the mixture, perform 2D-COS:

• Synchronous spectrum: Four independent autopeaks appear at 1030, 1050, 1070, 1100 cm⁻¹, directly proving the presence of 4 components;
• Asynchronous spectrum: Asynchronous peak at 1030 ↔ 1100 proves that the concentration changes of the two components are not synchronous (e.g., one increases while the other decreases).

This method has been applied in [10]:

• Multi-component analysis of traditional Chinese medicine (e.g., tanshinones and salvianolic acids in Salvia miltiorrhiza);
• Food adulteration detection (e.g., honey adulterated with high-fructose corn syrup, C–H region overlap);
• Simultaneous identification of oxygenates in fuels (methanol, ethanol, MTBE).

6.2 Integration of 2D-COS with Chemometrics

The 2D matrix provided by 2D-COS can be used as feature vectors input to PCA, PLS models, improving model discrimination ability [3][10]:

• 2D-COS-PCA: Concatenate diagonal elements of synchronous spectrum and off-diagonal elements of asynchronous spectrum into a feature vector, perform PCA clustering;
• 2D-COS-PLS: Use 2D spectra as X matrix, perform quantitative regression;
• Practice: In olive oil adulteration identification, the R² of 2D-COS-PLS model increased from 0.86 (1D PLS) to 0.95 [10].

For detailed introduction of PCA and PLS, see next episodes Ep 42 hyphenated techniques and Ep 43 chemometrics special topic.

7. Extended Applications of Generalized 2D-COS

7.1 Sample-Sample 2D-COS

Traditional 2D-COS requires a continuous perturbation variable. Sample-Sample 2D-COS, proposed by Šašić and Ozaki [3], allows input as a set of independent samples (e.g., different batches of drugs) and still generates 2D spectra:

• Axes are sample numbers;
• Reveals similarities and outliers among samples;
• Applied to abnormal batch identification in industrial QC.

7.2 Heterospectral 2D-COS

Using data from two different spectroscopic techniques (e.g., IR and Raman, IR and NIR) as two dimensions, perform heterospectral correlation [3]:

• Synchronous cross peaks → cooperative response of the same group to both techniques;
• Asynchronous cross peaks → differences in response of a group between techniques (e.g., IR-active vs Raman-active).

Application: In drug polymorph studies, IR-Raman heterospectral 2D-COS can reveal vibrational differences of the same group in different crystal forms, more comprehensive than using either technique alone [3].

7.3 Moving Window 2D-COS (MW2D)

Moving-Window 2D-COS divides the full temperature range into multiple sub-windows, performing local 2D-COS for each sub-window to obtain a three-dimensional map of "temperature-wavenumber-correlation intensity" [11]:

• Advantages: Precisely locating phase transition temperatures (e.g., glass transition Tg);
• Applications: Polymer blend phase separation, liquid crystal phase transitions, protein unfolding temperature.

VIII. Experimental Design and Considerations

8.1 Selection of Perturbation Variables

Table 4: Common perturbation variable selections

8.2 Spectral Quality Requirements

2D-COS is a "garbage in, garbage out" method. The original spectra must satisfy [3][4]:

1. Signal-to-noise ratio SNR > 1000: Because covariance operations amplify noise;
2. Baseline drift < 0.5%T: Polynomial baseline correction or SNV recommended;
3. Wavenumber accuracy < 0.5 cm⁻¹: Ensured by HeNe laser reference;
4. Perturbation stability: Sufficient equilibration time (>3 min) at each perturbation point to avoid "overshoot".

8.3 Elimination of Anomalous Spectra

If a spectrum at a certain perturbation point is anomalous (e.g., sample bubbles, temperature overshoot), it should be eliminated rather than retained—a single anomalous point can significantly affect the 2D spectra. Common methods:

• PCA scores on the first principal component exceeding 3σ;
• Abnormally large spectral distances (e.g., Euclidean distance);
• Subjective visual inspection.

IX. 2D-COS Literature Resources and Advanced Learning

9.1 Classic Reviews

• Noda I. Appl Spectrosc 1993, 47: 1329–1336 [2] — Essential foundational paper;
• Noda I. Vib Spectrosc 2004, 36: 143–165 [3] — Generalized 2D-COS review;
• Ozaki Y, Šašić S, Tanaka T, Noda I. Bull Chem Soc Jpn 2003, 76: 1–13 — Review on polymer and biomolecule 2D-COS;
• Morita S, Ozaki Y, Noda I. Appl Spectrosc 2023, 77: 5–15 — Review on 30 years of 2D-COS progress.

9.2 Online Resources

• 2Dshige Software: https://sci-tech.kwansei.ac.j…
• International 2D-COS Symposium: Held biennially since 2003, led by the Asia-Pacific spectroscopy community;
• Noda Paper Index: https://www.researchgate.net/…

9.3 Advanced Topics

• Isotope-Labeled 2D-COS: Use ¹³C/¹⁵N labeling of specific amino acids to improve assignment accuracy in protein 2D-COS;
• Time-Resolved 2D-COS: Combine millisecond time-resolved IR to study photochemical intermediates;
• Two-Dimensional Electrochemical Infrared (2D-SEC-FTIR): Use electrode potential as perturbation to study electrochemical reaction intermediates.

Summary of This Section

Study Questions

1. A graduate student wants to study the cold crystallization process of polylactic acid (PLA). What perturbation variable should be chosen? How to design the sampling interval? What spectral pre-processing is needed before 2D-COS?

2. In a synchronous spectrum, a positive synchronous cross peak is observed at 1650 and 1630 cm⁻¹. What does it imply? Is it sufficient to conclude "two groups change synchronously" based on this alone? Why?

3. Suppose you perform 2D-COS on a protein and obtain synchronous Φ = + and asynchronous Ψ = − for the cross peak 1654 (α-helix) ↔ 1624 (β-sheet). Determine the order of change between these two groups during heating according to Noda's rules, and explain the molecular mechanism.

4. How can heterospectral 2D-COS (IR-Raman) aid the study of polymorphic drugs? Provide a specific scenario illustrating its advantages over single IR.

5. When performing 2D-COS with a set of temperature-perturbed spectra, the asynchronous spectrum is extremely noisy and almost uninterpretable. List at least 3 possible experimental reasons and suggest improvements.

References

[1] Noda I. "Two-Dimensional Infrared (2D-IR) Spectroscopy of Polystyrene." Appl Spectrosc, 1990, 44(4): 550–561. DOI:10.1366/0003702904087386.

[2] Noda I. "Generalized Two-Dimensional Correlation Method Applicable to Infrared, Raman, and Other Types of Spectroscopy." Appl Spectrosc, 1993, 47(9): 1329–1336. DOI:10.1366/0003702934067694.

[3] Noda I. "Progress in Two-Dimensional Correlation Spectroscopy." Vibrational Spectroscopy, 2004, 36(2): 143–165. DOI:10.1016/j.vibspec.2003.12.016.

[4] Morita S, Ozaki Y, Noda I. "Thirty Years of Progress in Two-Dimensional Correlation Spectroscopy." Appl Spectrosc, 2023, 77(1): 5–15. DOI:10.1177/00037028221123818.

[5] 2Dshige Software, Kwansei Gakuin University Ozaki Laboratory. https://sci-tech.kwansei.ac.j…

[6] Barth A. "Infrared Spectroscopy of Proteins." Biochimica et Biophysica Acta (BBA) - Bioenergetics, 2007, 1767(9): 1073–1101. DOI:10.1016/j.bbabio.2007.06.004.

[7] Fabian H, Mantsch H H. "Ribonuclease A Revisited: Infrared Spectroscopic Evidence for Lack of Native-like Secondary Structure in the Thermally Unfolded State." Biochemistry, 1995, 34(42): 13651–13655. DOI:10.1021/bi00041a039.
and see also: Fabian H, Mantsch H H. "Vibrational Spectroscopy of Proteins and Peptides." Vib Spectrosc, 1999, 19: 1–17.

[8] Cole K C, Pelletier M A, Noël D. "Infrared and Dynamic Mechanical Study of the Orientation in Poly(ethylene terephthalate) Films." Polymer Engineering & Science, 1999, 39(9): 1583–1592.

[9] Šašić S, Katsumoto Y, Sato H, Ozaki Y. "Applications of Moving Window Two-Dimensional Correlation Spectroscopy to Analysis of Phase-Separation Behavior of Polymer Blends." Anal Chem, 2003, 75(16): 4010–4018. DOI:10.1021/ac030086e.

[10] Noda I. "Two-Dimensional Correlation Spectroscopy Biomedical Applications." J Mol Struct, 2008, 883–884: 2–8. DOI:10.1016/j.molstruc.2007.11.022.

[11] Thomas M, Richardson H H. "Two-Dimensional FT-IR Correlation Analysis of the Temperature-Dependent IR Spectra of Poly(methyl methacrylate)." Vib Spectrosc, 2002, 30(1): 3–15. DOI:10.1016/S0924-2031(01)00166-0.

[12] ftir.fun amide functional group page. https://ftir.fun/ir/group/ami…

[13] ftir.fun carbonyl functional group page. https://ftir.fun/ir/group/car…

[14] ftir.fun ether bond functional group page. https://ftir.fun/ir/group/eth…

[15] py2D-COS: Python implementation of generalized 2D correlation spectroscopy. https://github.com/shigemasa-…

Next Episode Preview: Ep 42 — Hyphenated Techniques: TGA-FTIR, GC-FTIR, LC-FTIR
2D-COS is a powerful tool that expands "one-dimensional spectra" into "two-dimensional spectra," while hyphenated techniques expand "one spectroscopy" into multidimensional methods of "chromatography × spectroscopy." In the next episode, we will systematically introduce three main hyphenated approaches: thermogravimetric-infrared (TGA-FTIR), gas chromatography-infrared (GC-FTIR), and liquid chromatography-infrared (LC-FTIR). How are their interfaces designed? What samples are they suitable for? How to process three-dimensional data? We will explain with examples such as polymer thermal decomposition, fragrance component identification, and drug impurity analysis.

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