Isao Noda

In this paper, a new approach is proposed to construct a two-dimensional (2D) asynchronous spectrum with a much-improved signal-to-noise level.

Quantitative infrared spectroscopy of liquids often assumes linear Beer–Lambert behavior, although local-field interactions and dipole–dipole coupling introduce intrinsic nonlinearities. We investigate whether a modified Lorentz–Lorenz relation, motivated by electromagnetic theory, can reduce these deviations and restore approximate linearity in binary mixtures. Using benzene–toluene and benzene–cyclohexane as model systems, we evaluate linearity through RMSE metrics, hybrid 2D-correlation analysis, asynchronous residual sums of squares, and complex-valued classical least squares (CLS) regression. While correlation-based measures provide qualitative insights, they fail to reliably identify optimal linearization parameters. In contrast, CLS in the Lorentz–Lorenz–transformed domain, particularly with systematic-error correction, yields clear minima and substantially improves prediction accuracy, reducing mean absolute errors by more than a factor of three relative to the Beer–Lambert domain. These results demonstrate that the modified Lorentz–Lorenz transformation provides a physics-informed chemometric domain in which spectral mixing becomes more linear. The approach suggests extending inverse least square regression, principal component regression, and partial least squares regression into this domain to further enhance quantitative mixture analysis.

Mass spectrometry (MS) is a powerful chemical analysis technique and one of the leading approaches that allows the identification and quantification of thousands of different components via a highly sensitive manner. However, assignment of unknown peaks in a mass spectrum to specific fragments is still a labour-intensive and costly task. Although various approaches and numerous software platforms have been developed, the automatic assignment of unknown peaks remains an unsolved problem. Based on the self-orthogonality of the Hilbert–Noda matrix extensively used in the field of 2D correlation spectroscopy, we develop a new method to generate an auxiliary spectrum to highlight peaks for the fragments containing stable isotopes via the characteristic pattern of the peaks for the isotopologues in the mass spectra. To address the problem of coincidental orthogonality, a modified approach using the second-order Hilbert–Noda matrix is proposed. Moreover, a statistical approach is adopted to suppress the appearance of false-positively highlighted peaks in the auxiliary spectra. The effectiveness of the approach has been showcased in the analysis of the mass spectra of 1,2-dibromoethane and chloroform. Unknown peaks of fragments containing different numbers of bromine or chlorine atoms can be successfully identified.

This comprehensive survey reviews the trajectory of research dissemination in the field of two-dimensional correlation spectroscopy (2D-COS) from 1 July 2023 to 10 February 2025. It provides a systematic overview of books, reviews, tutorials, and patent applications, alongside a vast array of innovative theoretical concepts and diverse applications that had emerged during this period. Beyond reporting advancements, this review critically examines instances of improper usage or citations of 2D-COS to promote methodological rigor within the community. The survey highlights significant innovations in probe integration, chemometric data analysis, and technical methodologies. These developments underscore the expanding role of 2D-COS in materials science, environmental monitoring, and complex biological systems. By synthesizing recent literature, this review illustrates dynamic growth, increasing refinement, and multi-disciplinary diversification of 2D-COS across the global scientific landscape.

Identifying characteristic bands, those exhibiting the most distinct features (i.e., minimal correlation among themselves), is a critical step in two-dimensional correlation spectroscopy (2D-COS) analysis. This process is essential for establishing effective correlation filters to simplify congested spectral datasets. Historically, such bands were selected using subjective methods, primarily the visual inspection of correlation cross-peaks. We now propose a more systematic and objective procedure based on the sequential multiplication of horizontal slices from a 2D discrimination spectrum. This unsupervised, automatic method is potentially integrable into model-free 2D-COS analyses, making it compatible with automated, machine-based interpretation.

The growing interest in high-purity bioplastics for emerging specialized applications motivated us to investigate the crystallization of poly(3-hydroxybutyrate- co -3-hydroxyhexanoate) (PHBHx) from a chloroform solution using advanced spectroscopic techniques. Previous study of the carbonyl stretching region of time-dependent attenuated total reflection infrared (ATR-IR) spectra had revealed that solution crystallization process of PHBHx involving distinct intermediate species was markedly different from the more traditional melt crystallization. IR study of PHBHx solution crystallization is now extended to more complex C–H stretching and fingerprint regions. Characteristic IR bands of the system showing the least correlated and most independent behaviors with each other were identified using a new technique based on a two-dimensional (2D) discrimination spectrum. Correlation filters based on the characteristic bands were used to selectively attenuate interfering spectral contributions in conjunction with the hetero-mode two-dimensional correlation spectroscopy (2D-COS) analysis. Traditional classification of decreasing and increasing IR bands, respectively, during the crystallization process of PHBHx copolymers simply to the amorphous and crystalline components probably needs to be reconsidered. Dynamics of bands in the C–H stretching and fingerprint regions are not fully synchronized with the behavior of amorphous or crystalline species characterized by the carbonyl stretching region. The result strongly suggests the presence of some intermediate species appearing after the consumption of amorphous components and prior to the formation of crystals.

Poly(3-hydrxybutyrate- co -3-hydroxyhexanoate) (PHBHx) is a biopolymer that is produced and degraded by microbes. Because of the potential to replace polymers derived from petrochemicals with these materials, there is a high level of expectation for its commercial uses if its physical and chemical properties can be understood and controlled. Among other things these properties are determined by the polymer’s morphology – that is its crystallinity, and orientation of both crystalline and amorphous phases. The focus on the Raman characteristics of the crystalline phase enables elucidation of the characteristics of the polymer experiencing dynamic crystallization under various conditions. In this article we will start by reviewing the changes in the Raman spectrum from an amorphous to a crystalline material in an isothermal crystallization study. In that study a correlation field splitting between a CH stretching band that interacts with the carbonyl group on the opposite chain in the unit cell was identified. Then we will show the polarized Raman spectra of single crystals which enable an explanation of the residual amorphous material seen in the spectra of single crystals. Using the information from the single crystal measurements we can then study the Raman behavior of spherulites and confirm the model that proposes an explanation for the appearance of rings in the polarized light microscope (PLM) images of some spherulites. The polarized Raman studies confirm that the crystal ribbons that grow along the radii are twisting about the growth direction. The two-dimensional correlation spectroscopy (2D-COS) analysis of the polarized spectra of spherulites suggest the presence of strain that has been proposed to induce the twisting.

Due to the growing interest in high-purity bioplastics for emerging applications, we investigated the solution crystallization of poly(3-hydroxybutyrate- co -3-hydroxyhexanoate) (PHBHx) from a chloroform solution using advanced spectroscopic techniques. Compared to melt crystallization, solution crystallization proved to be a more complex process. Solvent evaporation led to the formation of amorphous PHBHx and less-ordered crystallites. Subsequently, a distinct intermediate species of slightly disordered crystals formed, eventually transforming into more ordered crystalline structures. To analyze the time-dependent attenuated total reflection infrared (ATR-IR) spectra during crystallization, we employed two-dimensional correlation spectroscopy (2D-COS) and codistribution spectroscopy (2D-CDS). To streamline the 2D analysis of this complex dynamic system, we utilized a correlation filter (CF) technique to attenuate interfering contributions from overlapping peaks.

This comprehensive survey review offers the trajectory of research dissemination in the field of two-dimensional correlation spectroscopy (2D-COS) from 1 July 2022 to 17 June 2024. It covers books, reviews, tutorials, innovative concepts and theories, patents applications, and diverse applications that emerged during this period, as well as instances of improper usage or citations of 2D-COS. Innovations in probe integration, data analysis, and technical methodologies highlight the expanding role of 2D-COS in materials science, environmental monitoring, and biological system. This review shows the dynamic growth and diversification of 2D-COS across in many scientific fields.

Cross-peak signature patterns in two-dimensional (2D) asynchronous spectra are a useful tool for revealing the deeper physicochemical characteristics of intermolecular interactions. Various interferences such as noise can cause problems in recognizing the correct type of cross-peaks. The symmetrical characteristics of the cross-peaks may offer an intrinsic criterion for distinguishing between different types of cross-peaks. When intermolecular interaction only brings about a shift in the characteristic peak of a solute, we found that the resultant cross-peaks possess a mirror symmetry. However, such a symmetry may not be directly observable in the 2D asynchronous spectrum covered by severe noise. To solve this problem, a comprehensive approach to identify the symmetry is developed. Firstly, a method to locate the mirror is proposed. Then, the Kolmogorov–Smirnov test and Bayesian analysis are used to obtain the probability of the existence of mirror symmetry in the cross-peak group. The approach is showcased in three model systems and a real-world example (the benzene/I₂ system), which demonstrates that the approach is helpful in assigning the correct type of cross-peak under difficult situations.