Nonadiabatic Investigation of the Electronic Spectroscopy of trans-1,3-Butadiene.

Low-lying UV spectroscopy of trans-1,3-butadiene has been extensively studied by experimentalists and theorists. Though a host of techniques has been applied to understand its lowest electronic states, there are still important open questions. Among these are the positions of the two lowest valence excited states and the factors responsible for the spectral shape of the lowest allowed transitions. We present results from EOM-CC calculations in extended basis sets that are used to parametrize a three-electronic-state Koppel, Domcke, and Cederbaum (KDC) model. We test the sensitivity of the KDC model to a variety of parameters and address several outstanding questions regarding the spectrum. We find that the overall shape of the spectrum is determined primarily by the Franck-Condon envelope of the 11Bu state and that the princple impact of the doubly excited 21Ag state is to broaden the 11Bu peaks. There is only modest sensitivity to the relative position of these two states. We find that the lowest Rydberg state, the 11Bg state, has an unexpected impact on the third peak in the spectrum, and its effect is considerably more energy-dependent than that of the 21Ag state.

Cation States of Ethane: HEAT Calculations and Vibronic Simulations of the Photoelectron Spectrum of Ethane.

High-accuracy ab initio calculations have been carried out on ethane and its radical cation. With the HEAT-345(Q) scheme, adiabatic ionization potentials of 11.52 and 11.57 eV are determined for the X̃ (2)Eg and à (2)A1g states, respectively, with an uncertainty of ±0.015 eV. Also considered in this report are linear and quadratic vibronic coupling involving both states. With this simple vibronic model, the photoelectron spectrum of ethane was simulated in the 11-15 eV region using linear and full quadratic Jahn-Teller coupling Hamiltonians, and with up to 70 billion direct product basis functions in a high-performance computing environment. Although the linear vibronic coupling model adequately reproduces the spectral envelope, the quadratic vibronic treatment results in much better agreement with the observed spectrum.

A Highly-Efficient Implementation of the Doktorov Recurrence Equations for Franck-Condon Calculations.

In this paper, a new algorithm for computing Franck-Condon overlaps using the Doktorov recurrence equations is proposed. One of the major computational stresses of using the recurrence equations arises from searching data structures for overlaps that are stored in memory. The proposed algorithm alleviates this problem by tracking, throughout the algorithm, the locations in memory of overlaps that are required to use the recurrence relations. The tracking procedure helps to significantly reduce the run time of the algorithm compared to existing implementations.

Differential sensing for the regio- and stereoselective identification and quantitation of glycerides.

Glycerides are of interest to the areas of food science and medicine because they are the main component of fat. From a chemical sensing perspective, glycerides are challenging analytes because they are structurally similar to one another and lack diversity in terms of functional groups. Furthermore, because animal and plant fat consists of a number of stereo- and regioisomeric acylglycerols, their components remain challenging analytes for chromatographic and mass spectrometric determination, particularly the quantitation of species in mixtures. In this study, we demonstrated the use of an array of cross-reactive serum albumins and fluorescent indicators with chemometric analysis to differentiate a panel of mono-, di-, and triglycerides. Due to the difficulties in identifying the regio- and stereochemistry of the unsaturated glycerides, a sample pretreatment consisting of olefin cross-metathesis with an allyl fluorescein species was used before array analysis. Using this simple assay, we successfully discriminated 20 glycerides via principal component analysis and linear discriminant analysis (PCA and LDA, respectively), including stereo- and regioisomeric pairs. The resulting chemometric patterns were used as a training space for which the structural characteristics of unknown glycerides were identified. In addition, by using our array to perform a standard addition analysis on a mixture of triglycerides and using a method introduced herein, we demonstrated the ability to quantitate glyceride components in a mixture.

Parallelization strategy for large-scale vibronic coupling calculations.

The vibronic coupling model of Köppel, Domcke, and Cederbaum is a powerful means to understand, predict, and analyze electronic spectra of molecules, especially those that exhibit phenomena that involve breakdown of the Born-Oppenheimer approximation. In this work, we describe a new parallel algorithm for carrying out such calculations. The algorithm is conceptually founded upon a "stencil" representation of the required computational steps, which motivates an efficient strategy for coarse-grained parallelization. The equations involved in the direct-CI type diagonalization of the model Hamiltonian are presented, the parallelization strategy is discussed in detail, and the method is illustrated by calculations involving direct-product basis sets with as many as 17 vibrational modes and 130 billion basis functions.

Public avoidance and epidemics: insights from an economic model.

In this paper, we present a mathematical model of infectious disease transmission in which people can engage in public avoidance behavior to minimize the likelihood of acquiring an infection. The framework employs the economist's theory of utility maximization to model people's decision regarding their level of public avoidance. We derive the reproductive number of a disease which determines whether an endemic equilibrium exists or not. We show that when the contact function exhibits saturation, an endemic equilibrium must be unique. Otherwise, multiple endemic equilibria that differ in disease prevalence can coexist, and which one the population gets to depends on initial conditions. Even when a unique endemic equilibrium exists, people's preferences and the initial conditions may determine whether the disease will eventually die out or become endemic. Public health policies that increase the recovery rate or encourage self-quarantine by infected people can be beneficial to the community by lowering disease prevalence. However, it is also possible for these policies to worsen the situation and cause prevalence to rise since these measures give people less incentive to engage in public avoidance behavior. We also show that implementing policies that result in a higher level of public avoidance behavior in equilibrium does not necessarily lower prevalence and can result in more infections.