Jixin Chen

Free induction decay (FID) signals in nuclear magnetic resonance (NMR) spectroscopy are commonly analyzed using the fast Fourier transform (FFT). This simulation study evaluates complementary methods for short or non-stationary FID signals in which linewidth, dephasing, or decay behavior changes during acquisition. Simulated FIDs containing exponentially damped sinusoids, Gaussian-distributed frequencies, and time-dependent broadening were analyzed using FFT, short-time Fourier transform (STFT), wavelet transform, and direct nonlinear time-domain fitting. Simulations of finite collection windows show that point-sampled FIDs can approximate window-integrated signals after amplitude and phase correction when the collection window is sufficiently sharp and reproducible. FFT remains the fastest and most reliable approach for stationary, sufficiently long, high-signal-to-noise signals. Zero filling improves spectral interpolation but does not recover frequency resolution lost through short acquisition. STFT and wavelet methods reveal time-dependent frequency and decay behavior, although with reduced frequency resolution. Direct time-domain fitting can estimate amplitudes, frequencies, phases, and decay constants from very short, relatively simple FID segments, but its reliability depends on model selection, initial estimates, the number of signal components, and avoidance of local minima. These methods therefore serve complementary roles in analyzing stationary and non-stationary NMR signals.

This report compares various simulation and data analysis methods for free induction decay (FID) signals in Nuclear Magnetic Resonance (NMR) Spectroscopy. The methods discussed include discrete fast Fourier transformation (FFT), least squares fitting (LSF), short-time Fourier transformation (STFT), and wavelet transformation. NMR is a widely used technique for elucidating the chemical composition and structure of molecules. It measures the nuclear magnetic spin frequencies of different atoms in a sample, producing signals that are waves over the time domain. This report employs Gaussian wave frequency simulations to model the interference and dephasing among adjacent frequencies of each Gaussian chemical shift. Typically, FIDs are analysed using the FFT algorithm, although least squares fitting and machine learning algorithms are also employed. The simulations indicate that STFT can generate spectrograms that are useful for further neural network training, while LSF is effective in processing signals around or even below one wave cycle.

Predicting how often molecules collide in dilute solution remains a long-standing challenge often with several orders of magnitude difference between theoretical values and experimental values also among different experimental values. Traditional frameworks from Smoluchowski and Langmuir rely on the formation of stable concentration gradients, yet such gradients rarely exist at low concentrations, under stirring, or in single-molecule settings. Here, I develop a set of diffusive association models that assume no persistent concentration gradient and instead describe encounters through the probabilistic overlap of Gaussian diffusion clouds. By analyzing collisions within nearest-neighbor layers, these models yield general expressions for both surface adsorption and bulk bimolecular association. A key result is the emergence of fractional reaction orders between 5/3 and 8/3, reflecting the combined influence of intermolecular spacing and relative diffusion rather than classical second-order behavior. When one species is rate-limiting, all models correctly reduce to quasi–first-order kinetics, consistent with all historical experimental results and recent simulations. This gradient-free formulation provides physically intuitive scaling laws for collision frequencies and clarifies why conventional models systematically overestimate rates in the dilute limit. Overall, this work offers a mechanistic alternative to empirical rate laws and aims to advance the theoretical foundation of diffusive association kinetics in low-concentration environments.

This report compares various simulation and data analysis methods for free induction decay (FID) signals in Nuclear Magnetic Resonance (NMR) Spectroscopy. The methods discussed include discrete fast Fourier transformation (FFT), least squares fitting (LSF), short-time Fourier transformation (STFT), and wavelet transformation. NMR is a widely used technique for elucidating the chemical composition and structure of molecules. It measures the nuclear magnetic spin frequencies of different atoms in a sample, producing signals that are waves over the time domain. This report employs Gaussian wave frequency simulations to model the interference and dephasing among adjacent frequencies of each Gaussian chemical shift. Typically, FIDs are analyzed using the FFT algorithm, although least squares fitting and machine learning algorithms are also employed. The simulations indicate that STFT can generate spectrograms that are useful for further neural network training, while LSF is effective in processing signals around or even below one wave cycle.

Defects in metal-organic frameworks (MOFs) have attracted significant attention in recent years due to the unique properties arising from missing linkers and/or metal nodes. In this work, we introduce mechanochemistry as a de novo synthetic strategy for incorporating extrinsic defects into MOFs by employing symmetry-reduced or defective ligands. By systematically comparing defective MOFs prepared via mechanochemical and conventional solvothermal methods, we demonstrate that mechanochemical synthesis not only enables precise incorporation of defective ligands due to its rapid reaction but also promotes their spatial aggregation, leading to the formation of locally missing domains within the lattice. These clustered defects, in turn, generate observable hierarchical porosity, a capability that surpasses that of traditional solution-based approaches. This work presents a unique example of cluster defects in MOF, analogous to the Koch-Cohen cluster observed in nonstoichiometric iron oxides, yet arising from the uneven distribution of defective ligands in the solid state─a phenomenon not previously observed in MOF chemistry.

In the summer of 2024, COVID-19 positive cases spiked in many countries, but it is no longer a deadly pandemic thanks to global herd immunity to the SARS-CoV-2 viruses. In our physical chemistry lab in spring 2024, students practice kinetic models, SIR (Susceptible, Infected, and Recovered) and SIRV (Susceptible, Infected, Recovered, Vaccinated) using COVID-19 positive cases and vaccination data from World Health Organization (WHO). In this report, we further introduce virus breakthrough to the existing model updating it the SIRVB (Susceptible, Infectious, Recovered, Vaccinated, Breakthrough) model. We believe this is the simplest model possible to explain the COVID-19 kinetics/dynamics in all countries in the past four years. Parameters obtained from such practice correlate with many indices of different countries. These models and parameters have significant value to researchers and policymakers in predicting the stages of future outbreaks of infectious diseases.

Diffusive adsorption/association is a fundamental step in almost all chemical reactions in diluted solutions, such as organic synthesis, polymerization, self-assembly, biomolecular interactions, electrode dynamics, catalysis, chromatography, air and water environmental dynamics, and social and market dynamics. However, predicting the rate of such a reaction is challenging using the equations established over 100 years ago. Several orders of magnitude differences between the theoretical predictions and experimental measurements for various systems, from self-assembled monolayers to protein-protein aggregations, make such calculations meaningless in many situations. I believe the major problem is that the time-dependent evolution curve of Fick’s gradient is an ideal assumption in most cases, and its slope is significantly overestimated. This paper digs into Fick’s gradient problem for 3D cases and provides a solution using the single-molecule diffusion probability density function discretely.

In the summer of 2024, COVID-19 positive cases spiked in many countries, but it is no longer a deadly pandemic thanks to global herd immunity to the SARS-CoV-2 viruses. In our physical chemistry lab in spring 2024, students practice kinetic models, SIR (Susceptible, Infected, and Recovered) and SIRV (Susceptible, Infected, Recovered, Vaccinated) using COVID-19 positive cases and vaccination data from World Health Organization (WHO). In this report, we further introduce virus breakthrough to the existing model updating it the SIRVB (Susceptible, Infectious, Recovered, Vaccinated, Breakthrough) model. We believe this is the simplest model possible to explain the COVID-19 kinetics in all countries in the past four years. Parameters obtained from such practice correlate with many indices of different countries. These models and parameters have significant value to researchers and policymakers in predicting the stages of future outbreaks of infectious diseases. TOC: