@article {36576, title = {Atmospheric ethylene (C2H4) observations from the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS)}, journal = {Journal of Quantitative Spectroscopy and Radiative Transfer}, volume = {346}, year = {2025}, pages = {109603}, author = {Randika Dodangodage and Peter Bernath and Chris Boone and Mike Lecours and Matthew Schmidt} } @article {35490, title = {The first satellite measurements of HFC-125 by the ACE-FTS: Long-term trends and distribution in the Earth\’s upper troposphere and lower stratosphere}, journal = {Journal of Quantitative Spectroscopy and Radiative Transfer}, volume = {330}, year = {2025}, pages = {109218}, author = {Randika Dodangodage and Peter F Bernath and Chris Boone and Jeremy J Harrison and Mike Lecours and Matthew Schmidt and Stephen A Montzka and Isaac Vimont and Molly Crotwell} } @database {36661, title = {Global Satellite-Based Atmospheric Profiles from Atmospheric Chemistry Experiment SciSat Level 2 Processed Data, v5.2, 2004-2024}, journal = {Federated Research Data Repository}, year = {2025}, author = {Peter F. Bernath and Chris D. Boone and Michael J. Lecours and Jeffrey Crouse and Johnathan Steffen and Matthew Schmidt} } @article {35842, title = {HFC-23 from updated Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) retrievals}, journal = {Journal of Quantitative Spectroscopy and Radiative Transfer}, volume = {338}, year = {2025}, pages = {109416}, author = {Randika Dodangodage and Peter F. Bernath and Chris Boone and Mike Lecours and Matthew Schmidt} } @database {35493, title = {Atmospheric Chemistry Experiment SciSat Level 2 Processed Data, v4.1/v4.2}, journal = {Federated Research Data Repository}, year = {2024}, author = {Peter F. Bernath and Chris D. Boone and Dennis Cok and Scott C. Jones and Johnathan Steffen and Michael J. Lecours and Matthew Schmidt} } @article {35342, title = {Trends in atmospheric composition between 2004\–2023 using version 5 ACE-FTS data}, journal = {Journal of Quantitative Spectroscopy and Radiative Transfer}, volume = {325}, year = {2024}, pages = {109088}, abstract = {The Atmospheric Chemistry Experiment (ACE) is a satellite mission that has been in orbit since 2003. The primary instrument on ACE is a Fourier transform spectrometer (FTS) that records infrared atmospheric transmittance spectra in the limb geometry using the Sun as a light source. Version 5 of ACE-FTS data processing contains improved volume mixing ratio (VMR) profiles for 46 molecules and 24 isotopologues, including HFC-32 (CH2F2) and HOCl as new routine data products. VMR trends for each of the 46 molecules are reported for regions of atmospheric interest. Specifically, the longevity of the ACE mission has provided an opportunity to monitor the effectiveness of the Montreal Protocol on Substances that Deplete the Ozone Layer. It is observed that chlorofluorocarbons (CFCs) are declining, hydrochlorofluorocarbons (HCFCs) are no longer increasing, but hydrofluorocarbons (HFCs) are still increasing rapidly. Greenhouse gases such as carbon dioxide are also monitored and comparisons with National Oceanic and Atmospheric Administration (NOAA) and Advanced Global Atmospheric Gases Experiment (AGAGE) measurements are made.}, author = {Matthew Schmidt and Peter Bernath and Chris Boone and Michael Lecours and Johnathan Steffen} } @article {30075, title = {On the accuracy and efficiency of different methods to calculate Raman vibrational shifts of parahydrogen clusters}, journal = {Journal of Chemical Physics}, volume = {156}, year = {2022}, pages = {084102}, abstract = {The Raman vibrational frequency shifts of pure parahydrogen and orthodeuterium clusters of sizes\ N\ = 4{\textendash}9 are calculated using the Langevin equation path integral ground state method. The shifts are calculated using three different methods; the results obtained from each are compared to experiment and variance properties are assessed. The first method requires the direct calculation of energies from two simulations: one when the cluster is in the\ v\ = 0 vibrational state and one when the cluster has\ v\ = 1 total quantum of vibration. The shift is directly calculated from the difference in those two energies. The second method requires only a\ v\ = 0 simulation to be performed. The ground state energy is calculated as usual and the excited state energy is calculated by using the distribution of the\ v\ = 0 simulation and the ratio of the density matrices between the\ v\ = 1 state and the\ v\ = 0 state. The shift is calculated from the difference in those two energies. These first two are both exact methods. The final method is based on perturbation theory where the shift is calculated by averaging the pairwise difference potential over the pair distribution function. However, this is an approximate approach. It is found that for large enough system sizes, despite the approximations, the perturbation theory method has the strongest balance between accuracy and precision when weighing against computational cost.}, author = {Matthew Schmidt and Pierre-Nicholas Roy} } @article {30073, title = {Ground state chemical potential of parahydrogen clusters of size N=21-40}, journal = {Journal of Chemical Physics}, volume = {156}, year = {2022}, pages = {016101}, abstract = {We report the ground state chemical potential of parahydrogen clusters between N = 21{\textendash}40 calculated using the Langevin equation Path Integral Ground State method. There has been much debate in the past whether the chemical potential size evolution in this region is jagged (indicating magic number cluster sizes) or if it is smooth (indicating some quantum melting below 1\ K). We compare to previous diffusion Monte Carlo and Path Integral Ground State (PIGS) results, including very recent Variational Path Integral Molecular Dynamics (VPIMD) calculations [S. Miura, J. Chem. Phys.\ 148, 102333 (2018)]. We find that the ground state chemical potential is not a smooth curve and that magic number clusters are present, consistent with VPIMD and PIGS Monte Carlo results.}, author = {Matthew Schmidt and Pierre-Nicholas Roy} } @article {30074, title = {Path integral simulations of confined parahydrogen molecules within clathrate hydrates: merging low temperature dynamics with the zero temperature limit}, journal = {Journal of Chemical Physics}, volume = {156}, year = {2022}, pages = {014303}, abstract = {Clathrate hydrates, or cages comprised solely of water molecules, have long been investigated as a clean storage facility for hydrogen molecules. A breakthrough occurred when hydrogen molecules were experimentally placed within a structure-II clathrate hydrate, which sparked much interest to determine their feasibility for energy storage [Mao\ et al., Science\ 297, 2247{\textendash}2249 (2002)]. We use Path Integral Molecular Dynamics (PIMD) and Langevin equation Path Integral Ground State (LePIGS) for finite temperature and zero-temperature studies, respectively, to determine parahydrogen occupancy properties in the small dodecahedral (512) and large hexakaidecahedral (51264) sized cages that comprise the structure-II unit cell. We look at energetic and structural properties of small clusters of hydrogen, treated as point-like particles, confined within each of the different sized clathrates, and treated as rigid, to determine energetic and structural properties in the zero-temperature limit. Our predicted hydrogen occupancy within these two cage sizes is consistent with previous literature values. We then calculate the energies as a function of temperature and merge the low temperature results calculated using finite temperature PIMD with the zero-temperature results using LePIGS, demonstrating that the two methods are compatible.}, author = {Matthew Schmidt and Jayme Millar and Pierre-Nicholas Roy} } @mastersthesis {14537, title = {Path integral ground state approaches for the study of weakly bound clusters and confined molecules}, year = {2018}, type = {PhD thesis}, abstract = {This thesis presents the study of weakly bound clusters in the ground state (or the zero-temperature limit) using path integral molecular dynamics. Specifically, we look individually at the quantum properties of small clusters of hydrogen and water molecules and confined hydrogen within water cages, known as clathrate hydrates, which serves as a more practical application. Clathrate hydrates have been extensively studied as a clean storage container for molecular hydrogen and there have been discrepancies on the hydrogen occupancy number between various theoretical and experimental studies. It has been shown that the occupancy number is sensitive to the potential energy surfaces and models of the hydrogen and water systems. A preliminary study of hydrogen contained in clathrates is performed using a traditional hydrogen pair potential and water-hydrogen interaction potential. Hydrogen occupancy and structural distributions are compared to literature values.\ Small clusters of the individual molecules themselves are then focused on. The molecular hydrogen pair potentials are evaluated by calculating the Raman vibrational shift, a property that is very sensitive to the interaction potential, and comparing to experimental measurements. These shifts are calculated using first order perturbation theory based on pair distribution functions generated from Langevin equation path integral ground state (LePIGS) simulations for all bosonic isotopologues. It is determined that the shifts calculated using the Hinde pair potential give better agreement to experimental results than the traditional hydrogen potentials that we have been using in the past. The perturbation theory approach is then compared with two exact methods to calculate the shifts. For the application of hydrogen clusters, it is determined that perturbation theory is the best choice when balancing accuracy and precision. In the literature, there has been a discrepancy in the shape of the chemical potential at low temperature and in the ground state. We calculate the ground state chemical potential using LePIGS and find agreement with other PIGS results. We then extend our LePIGS code to simulate flexible molecules by investigating the water dimer. Ground state energies, dissociation energies, and structural properties are calculated using two empirically based interaction potentials and one ab initio potential, MB-pol, that includes polarizability and many-body effects which has been shown to reproduce experimental dissociation energies. We further demonstrate that imaginary time correlation functions generated from LePIGS can be used to calculate accurate vibrational transition energies. This work serves as a demonstration of the effectiveness of the LePIGS method towards calculating ground state properties of small clusters and provides useful information on the interaction potentials that should be used for systems containing hydrogen or water, specifically hydrogen contained in a flexible clathrate hydrate. An analytic form of the 1-D Hinde pair potential for molecular hydrogen is also contained for general use.}, author = {Matthew D.G. Schmidt} } @article {9817, title = {Path integral Molecular dynamic simulation of flexible molecular systems in their ground state: application to the water dimer}, journal = {Journal of Chemical Physics}, volume = {148}, year = {2018}, pages = {124116}, abstract = {
We extend the Langevin equation Path Integral Ground State (LePIGS), a ground state quantum molecular dynamics method, to simulate flexible molecular systems and calculate both energetic and structural properties. We test the approach with the H2O and D2O monomers and dimers. We systematically optimize all simulation parameters and use a unity trial wavefunction. We report ground state energies, dissociation energies, and structural properties using three different water models, two of which are empirically based, q-TIP4P/F and q-SPC/Fw, and one which is
ab initio, MB-pol. We demonstrate that our energies calculated from LePIGS can be merged seamlessly with low temperature path integral molecular dynamics calculations and note the similarities between the two methods. We also benchmark our energies against previous diffusion Monte Carlo calculations using the same potentials and compare to experimental results. We further demonstrate that accurate vibrational
energies of the H2O and D2O monomer can be calculated from imaginary time correlation functions generated from the LePIGS simulations using solely the unity trial wavefunction.
}, author = {Matthew Schmidt and Pierre-Nicholas Roy} } @article {6441, title = {Raman Vibrational Shifts of Small Clusters of Hydrogen Isotopologues}, journal = {Journal of Physical Chemistry A}, volume = {119}, year = {2015}, pages = {12551}, abstract = {

Raman vibrational shifts of small parahydrogen (pH2), orthodeuterium (oD2), and paratritium (pT2) clusters with respect to the free molecules are calculated by combining a first order perturbation theory approach with Langevin equation Path Integral Ground State (LePIGS) simulations [\ J. Phys. Chem. A\ 2013,\ 117,\ 7461]. Our theoretical predictions are compared to existing cryogenic free jet expansion results for pure (pH2)N\ clusters [\ Phys. Rev. Lett.\ 2004,\ 92,\ 223401] and to new measurements for (oD2)N\ clusters reported here. This method has been successfully used before to predict the Raman vibrational shifts of (pH2)N\ clusters [\ J. Chem. Phys.\ 2014,\ 141,\ 014310]. The 6-D interaction potential of Hinde [\ J. Chem. Phys.\ 2008,\ 128,\ 154308] is reduced to 1-D using the Adiabatic Hindered Rotor approximation to yield effective pair potentials for both molecules being in the ground vibrational state, and for one of them carrying one quantum of vibrational excitation. These reduced 1-D potentials are fitted to a Morse Long Range analytic form for later convenience. Good agreement between experiment and theory is found for the smaller clusters, but significant deviations remain for the larger ones.

}, author = {Matthew Schmidt and Jos{\'e} M. Fern{\'a}ndez and Nabil Faruk and Marcel Nooijen and Robert J. Le Roy and Juan H. Morilla and Guzm{\'a}n Tejeda and Salvador Montero and Pierre-Nicholas Roy} } @mastersthesis {6438, title = {Developing a Method to Study Ground State Properties of Hydrogen Clusters}, year = {2014}, type = {MSc thesis}, abstract = {

This thesis presents the benchmarking and development of a method to study ground state properties of hydrogen clusters using molecular dynamics. Benchmark studies are performed on our Path Integral Molecular Dynamics code using the Langevin equation for finite temperature studies and our Langevin equation Path Integral Ground State code to study systems in the zero-temperature limit when all particles occupy their nuclear ground state. A simulation is run on the first {\textquoteright}real{\textquoteright} system using this method, a parahydrogen molecule interacting with a fixed water molecule using a trivial unity trial wavefunction. We further develop a systematic method of optimizing the necessary parameters required for our ground state simulations and introduce more complex trial wavefunctions to study parahydrogen clusters and their isotopologues orthodeuterium and paratritium.\ The effect of energy convergence with parameters is observed using the trivial unity trial wavefunction, a Jastrow-type wavefunction that represents a liquid-like system, and a normal mode wavefunction that represents a solid-like system. Using a unity wavefunction gives slower energy convergence and is inefficient compared to the other two. Using the Lindemann criterion, the normal mode wavefunction acting on floppy systems introduces an ergodicity problem in our simulation, while the Jastrow does not. However, even for the most solid-like clusters, the Jastrow and the normal mode wavefunctions are equally efficient, therefore we choose the Jastrow trial wavefunction to look at properties of a range of cluster sizes. The energetic and structural properties obtained for parahydrogen and orthodeuterium clusters are consistent with previous studies, but to our knowledge, we may be the first to predict these properties for neutral paratritium clusters. The results of our ground state simulations of parahydrogen clusters, namely the distribution of pair distances, are used to calculate Raman vibrational shifts and compare to experiment. We investigate the accuracy of four interaction potentials over a range of cluster sizes and determine that, for the most part, the ab initio derived interaction potentials predict shifts more accurately than the empirically based potentials for cluster sizes smaller than the first solvation shell and the trend is reversed as the cluster size increases. This work can serve as a guide to simulate any system in the nuclear ground state using any trial wavefunction, in addition to providing several applications in using this ground state method.

}, author = {Matthew D.G. Schmidt} } @article {6440, title = {First-principles prediction of the Raman shifts in parahydrogen clusters}, journal = {Journal of Chemical Physics}, volume = {141}, year = {2014}, pages = {014310}, abstract = {

We report a first-principles prediction of the Raman shifts of parahydrogen (pH2)\ clusters\ of sizes\ N\ = 4{\textendash}19 and 33, based on path integral\ ground-statesimulations with an\ ab initio\ potential energy surface.\ The Raman shifts are calculated, using perturbation theory, as the average of the difference-potential energy\ surface\ between the\ potential energy surfaces\ for vibrationally excited and\ ground-state\ parahydrogen\ monomers.\ The radial distribution of the\ clusters\ is used as a weight function in this average. Very good overall agreement with experiment [G. Tejeda, J. M. Fern{\'a}ndez, S. Montero, D. Blume, and J. P. Toennies,\ Phys. Rev. Lett.\ 92, 223401 (2004)] is achieved for\ p(H2)2-8,13,33. A number of different pair potentials are employed for the calculation of the radial\ distribution functions.\ We find that the Raman shifts are sensitive to slight variations in the radial\ distribution functions.

}, author = {Nabil Faruk and Matthew Schmidt and Hui Li and Robert J. Le Roy and Pierre-Nicholas Roy} } @article {6439, title = {Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues}, journal = {Journal of Chemical Physics}, volume = {140}, year = {2014}, pages = {234101}, abstract = {

We developed and studied the implementation of trial\ wavefunctions\ in the newly proposed\ Langevin equation\ Path Integral\ Ground State\ (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy,\ J. Phys. Chem. A\ 117, 7461 (2013)]. The LePIGS method is based on the Path Integral\ Ground State(PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a\ Langevin equation\ based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial\ wavefunction,\ ψT, equal to unity. The present paper assesses the effectiveness of three different trial\ wavefunctions\ on three\ isotopes\ of hydrogen for\ cluster\ sizes\ N\ = 4, 8, and 13. The trial\ wavefunctions\ of interest are the unity trial\ wavefunction\ used in the original LePIGS work, a Jastrow trial\ wavefunction\ that includes correlations due to hard-core repulsions, and a\ normal mode\ trial\ wavefunction\ that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow\ wavefunction\ to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium\ clusters\ of size\ N= 4 - 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium\ clusters\ will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the\ ground state\ of a large variety of systems.

}, author = {Matthew Schmidt and Steve Constable and Christopher Ing and Pierre-Nicholas Roy} } @article {6413, title = {Langevin Equation Path Integral Ground State}, journal = {Journal of Physical Chemistry A}, volume = {117}, year = {2013}, pages = {7461}, abstract = {

We propose a Langevin equation path integral ground state (LePIGS) approach for the calculation of ground state (zero temperature) properties of molecular systems. The approach is based on a modification of the finite temperature path integral Langevin equation (PILE) method (J. Chem. Phys.2010,\ 133, 124104) to the case of open Feynman paths. Such open paths are necessary for a ground state formulation. We illustrate the applicability of the method using model systems and the weakly bound water{\textendash}parahydrogen dimer. We show that the method can lead to converged zero point energies and structural properties.

}, author = {Steve Constable and Matthew Schmidt and Christopher Ing and Tao Zeng and Pierre-Nicholas Roy} }