arXiv subjects

Hernán R. Sánchez

Publications and source records attributed to Hernán R. Sánchez.

8 recordsLinked to original sources

arXiv2026

Chromatographic Peak Shape beyond the High-Péclet Approximation: Analytic Time-Domain Expression and Derivatives

Analytic time-domain expressions for the elution-time density and its parameter derivatives were recently derived from a stochastic model of linear isocratic chromatography incorporating advective-diffusive transport, injection dispersion, and fast and slow retention mechanisms. A Gaussian approximation, justified asymptotically at high column-scale Péclet numbers, was adopted for the distribution of the combined mobile-phase and fast-retention time, while slow retention was incorporated through a series of Gaussian-Gamma convolutions. Here, the underlying normal-inverse-Gaussian density is approximated by a finite Gaussian mixture using an existing quadrature rule. The elution-time PDF is a weighted sum of series of the previously derived Gaussian-Gamma form. Its parameter derivatives are also obtained. Newly derived recurrences reduce the cost of evaluating the coefficients of that series and their derivatives from quadratic to linear in truncation order for a fixed number of mechanisms. Through a probabilistic analysis of the series coefficients, the required number of terms is found to be small enough for rapid evaluation under usual chromatographic conditions. A relative roundoff-error estimator is derived to quantify finite-precision loss in the inherited forward recurrence for Gaussian-Gamma convolutions. For the cancellation-prone regime, a backward reconstruction is developed, initialized from an exact ratio of consecutive Gaussian-Gamma terms expressed through parabolic-cylinder functions. A highly accurate approximation is derived for rapid evaluation of this ratio. Independent high-precision calculations confirm the high accuracy of the resulting double-precision evaluation in the tested numerical case.

physics.chem-ph↗

arXiv2026

Chromatographic Peak Shape from a Stochastic-Diffusive Model with Multiple Retention Mechanisms: Analytic Time-Domain Expression and Derivatives

A time-domain analytic expression for chromatographic peak shapes is derived within a stochastic-diffusive framework that incorporates axial diffusion (molecular and multipath/Eddy), finite initial spatial variance, a retention mechanism characterized by a high rate of short-duration events, and an arbitrary number of independent slow retention mechanisms, each characterized by its own rate of infrequent, long-duration events. A highly efficient evaluation scheme is derived for this expression. In the single-slow-mechanism case, it is two to four orders of magnitude faster than the previously available analytic route. Analytical derivatives with respect to all model parameters are also obtained, and each can be evaluated at computational cost comparable to that of the peak-shape expression. Illustrative fits to three literature peaks yielded full-profile RMSE values lower than those of the exponentially modified Gaussian in all tested cases, with minima ranging from 0.03 to 0.14 percent of peak height, compared with 0.43 to 5.57 percent for the reference model. Relative to the one-slow-mechanism formulation, allowing more than one slow mechanism produced a data-dependent improvement that exceeded one order of magnitude for one of the peaks.

physics.chem-ph↗

arXiv2025

Chromatographic Peak Shape from Stochastic Model: Analytic Time-Domain Expression in Terms of Physical Parameters and Conditions under which Heterogeneity Reduces Tailing

A time-domain representation of chromatographic peak shapes is presented as an analytic expression designed for high computational efficiency, which can be used for direct time-domain peak fitting with parameters that represent physical quantities. The underlying model integrates the effects of axial diffusion (molecular and multipath/eddy), finite initial spatial variance, and two distinct retention mechanisms: one characterized by a high rate of short-duration events (fast kinetics), and another by a low rate of long-duration events (slow kinetics). Fits to experimental chromatograms yield substantially smaller residual standard error (RSE) than the standard EMG and the lowest average normalised RSE among 12 established peak-shape functions in the examined cases. The stochastic approach is reformulated using single-particle probability laws, providing a rigorous basis for future theoretical extensions. The validity of the foundational Poisson assumption is critically examined by deriving expressions for the excess variance caused by correlated microscopic retention rate fluctuations. A statistical interpretation of the HETP is presented and used to determine a lower bound on the number of microscopic retention events from chromatogram-derived macroscopic observables. This, in turn, justifies the applicability of the Gaussian limit for the mobile-plus-fast component, as established by analysis of the cumulant generating function of the closed-form benchmark derived herein. The contribution from the slow-kinetic mechanism is incorporated via a decoupling approximation, whose validity is established through a cumulant-based analysis that explicitly bounds the decoupling-induced error. Finally, the notion that mechanistic heterogeneity necessarily exacerbates peak tailing is qualified, analytically delineating parameter regions in which it leads to a reduction in peak asymmetry.

physics.chem-ph↗

arXiv2024

Evaluating the Uncertainty in Mean Residual Times: Estimators Based on Residence Times from Discrete Time Processes

In this work, we propose estimators for the uncertainty in mean residual times that require, for their evaluation, statistically independent individual residence times obtained from a discrete time process. We examine their performance through numerical experiments involving well-known probability distributions, and an application example using molecular dynamics simulation results, from an aqueous NaCl solution, is provided. These computationally inexpensive estimators, capable of achieving very accurate outcomes, serve as useful tools for assessing and reporting uncertainties in mean residual times across a wide range of simulations.

stat.ME↗

arXiv2020

Seven derivations of the Lambert-Beer law

Seven derivations of the Lambert-Beer law are proposed in this paper. They were designed to be simple and intuitive. Most of them are suitable for the classroom. Readers can also benefit from them by looking at the phenomenon from different perspectives, which gives valuable resources when explaining it in class.

physics.class-ph↗

arXiv2019

Prediction of the inner-shell contribution to the correlation energy through DLPNO-CEPA/1 and Scaled same-spin second order Møller-Plesset perturbation theory

The use of two low cost methods for the prediction of the inner-shells contribution to the correlation energy is analyzed. The Spin-Component-Scaled second order Møller-Plesset perturbation theory (SCS-MP2) was reparameterized for the prediction of such contributions. The best results are found when only the same spin term is considered (SSS-MP2). The Coupled Electron Pair Approximation (CEPA) using the domain based local pair natural orbital approximation (DLPNO) was also studied for the same purpose. The methods were tested on the W4-11 test set using basis sets up to quadruple zeta quality. The SSS-MP2 proved to be a marked improvement upon MP2 decreasing the root-mean-square-error (RMSE) from 0.443 to 0.302 kcal/mol. The RMSE of DLPNO-CEPA/1 in the test set is only 0.147 kcal/mol and its computational cost is very low considering the intended applications. Furthermore, a linear combination of both methods decreased the RMSE to 0.118 kcal/mol.

physics.chem-ph↗

arXiv2019

Uncertainties in the Static Dielectric Constants computed from Molecular Dynamics Simulations

In this work, the uncertainties in the dielectric constants of polar liquids, computed using molecular dynamics (MD) simulations, are compared for two different calculations schemes. Expressions of the uncertainty are derived for the external field method, and compared with those of the fluctuation method. Significant differences on their the system size dependence were found. In addition, alternative calculation procedures are proposed. The individual contributions of different parts of the system to the electric susceptibility, and their corresponding uncertainties, are also studied. Additionally, the effects of the sampling frequency on the uncertainties are analyzed. MD simulations of pure liquid water (SPC/E) at 298.15 K and 1 bar were performed in order to corroborate the obtained results. In such conditions, the best estimate of the dielectric constant obtained in this study is 70.46$\pm$0.31.

physics.chem-ph↗

arXiv2018

Uncertainties in permittivities computed from molecular dynamics simulations and temperature correction of dielectric properties of condensed polar systems

A robust, simple and fast procedure for the calculation of uncertainties in relative static dielectric permittivity ($\varepsilon_s$) computed via molecular dynamics (MD) is proposed. It arises as a direct application of well founded statistical methods for auto-correlated variables. Also, in order to deal with the lack of experimental data about $\varepsilon_s$ and relaxation times ($τ$) at different temperatures, a method for their prediction is suggested. It requires one experimental value and at least two MD simulations. In the case of relaxation times, a theoretical justification is provided.

physics.chem-ph↗