We use the pair-product approximation to the complex-time quantum mechanical propagator to obtain accurate quantum mechanical results for the symmetrized velocity autocorrelation function of a Lennard-Jones fluid at two points on the thermodynamic phase diagram. A variety of tests are performed to determine the accuracy of the method and understand its breakdown at longer times. We report quantitative results for the initial 0.3 ps of the dynamics, a time at which the correlation function has decayed to approximately one fifth of its initial value.
Forward-backward semiclassical dynamics (FBSD) provides a rigorous and powerful methodology for calculating time correlation functions in condensed phase systems characterized by substantial quantum mechanical effects associated with zero-point motion, quantum dispersion, or identical particle exchange symmetries. The efficiency of these simulations arises from the use of classical trajectories to capture all dynamical information. However, full quantization of the density operator makes these calculations rather expensive compared to fully classical molecular dynamics simulations. This article discusses the convergence properties of various correlation functions and introduces an optimal Monte Carlo sampling scheme that leads to a significant reduction of statistical error. A simple and efficient procedure for normalizing the FBSD results is also discussed. Illustrative examples on model systems are presented.
The
essentials of Monte Carlo integration are presented for use in an
upper-level physical chemistry setting. A Mathcad document that aids
in the dissemination and utilization of this information is described
and is available in the Supporting Information. A brief outline of
Monte Carlo integration is given, along with ideas and pedagogy for
optimum use of the Mathcad document in relation to application of
this technique to quantum mechanical calculations to which undergraduate
chemistry students are typically exposed.
A simple and safe procedure is proposed which allows for the collection of HCl and DCl gas produced via slow heating of an aqueous mixture of each component.
This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to undergraduate students in their third year during physical chemistry, thus providing a theoretical foundation for the subsequent introduction of such material in analytical instrumentation courses. With the reinforcement of familiar concepts such as the Heisenberg Uncertainty Principle, classical correspondence, and linear combinations in the context of both position and momentum space for a particle in a box, a better understanding of the mathematical implications of the Fourier transform is fostered. Subsequent analysis of a time-dependent function constructed via a linear combination and its transformation to the frequency domain provides a practical example relating to the Fourier processes applied in analytical spectroscopy. The final portion of the exercise returns to the position/momentum conjugate pair and explores how the construction of a narrow wavepacket via a sum of cosines illustrates the Uncertainty Principle once the probability density functions of each coordinate are analyzed. This exercise has been shown to not only reinforce fundamental concepts necessary for a true appreciation of quantum mechanics, but also help demystify the Fourier transform process for students taking analytical chemistry.
Kombucha, a popular probiotic beverage,
contains detectable concentrations
of ethyl alcohol. To be sold as a nonalcoholic product, alcohol concentrations
in kombucha must be shown to be less than 0.5% by volume. This paper
describes the use of an inexpensive, commercially available sensor
to reliably and accurately measure alcohol concentrations in kombucha
across a variety of undergraduate chemistry laboratory courses. Procedures
and assessment data are also provided for two courses: an introductory
course for nonchemistry majors and upper-division analytical chemistry.
In the case of the analytical chemistry course, results from the alcohol
sensor were compared to headspace gas chromatography as a capstone
assessment. In all cases, the alcohol content of multiple commercial
kombucha samples were determined, and students submitted final reports
using appropriate scientific writing aligned with precise learning
objectives.
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