A size-consistent multi-state mapping approach to surface hopping.

We develop a multi-state generalization of the recently proposed mapping approach to surface hopping (MASH) for the simulation of electronically nonadiabatic dynamics. This new approach extends the original MASH method to be able to treat systems with more than two electronic states. It differs from previous approaches in that it is size consistent and rigorously recovers the original two-state MASH in the appropriate limits. We demonstrate the accuracy of the method by applying it to a series of model systems for which exact benchmark results are available, and we find that the method is well suited to the simulation of photochemical relaxation processes.

A MASH simulation of the photoexcited dynamics of cyclobutanone.

In response to a community prediction challenge, we simulate the nonadiabatic dynamics of cyclobutanone using the mapping approach to surface hopping (MASH). We consider the first 500 fs of relaxation following photoexcitation to the S2 state and predict the corresponding time-resolved electron-diffraction signal that will be measured by the planned experiment. 397 ab initio trajectories were obtained on the fly with state-averaged complete active space self-consistent field using a (12,11) active space. To obtain an estimate of the potential systematic error, 198 of the trajectories were calculated using an aug-cc-pVDZ basis set and 199 with a 6-31+G* basis set. MASH is a recently proposed independent trajectory method for simulating nonadiabatic dynamics, originally derived for two-state problems. As there are three relevant electronic states in this system, we used a newly developed multi-state generalization of MASH for the simulation: the uncoupled spheres multi-state MASH method (unSMASH). This study, therefore, serves both as an investigation of the photodissociation dynamics of cyclobutanone, and also as a demonstration of the applicability of unSMASH to ab initio simulations. In line with previous experimental studies, we observe that the simulated dynamics is dominated by three sets of dissociation products, C3H6 + CO, C2H4 + C2H2O, and C2H4 + CH2 + CO, and we interpret our predicted electron-diffraction signal in terms of the key features of the associated dissociation pathways.

Partitioning of nutrient variation in alfalfa and corn silage by source on New York dairy farms.

Variation in feed components contributes to variation and uncertainty of diets delivered to dairy cows. Forages often have a high inclusion rate (50% to 70% of DM fed) and variable composition, and thus are an important contributor to nutrient variability of delivered diets. Our objective was to quantify the variation and identify the main sources of variability in corn silage and alfalfa-grass haylage composition at harvest (fresh forage) and feed-out (fermented forage) on New York dairy farms. Corn silage and alfalfa-grass haylage were sampled on 8 New York commercial dairy farms during harvest in the summer and fall of 2020 and during their subsequent feed-out in the winter and spring of 2021. At harvest, a composite sample of fresh chopped forage of every 8-ha section of individual fields was collected from piles delivered for silo filling. During a 16-wk feed-out period, 2 independent samples of each forage were collected 3 times per week. The fields of origin of each forage sample during feed-out were identified and recorded using silo maps created at filling. A mixed-model analysis quantified the variance of corn silage DM, NDF, and starch and haylage DM, NDF, and CP content. Fixed effects included soil type, weather conditions, and management practices during harvest and feed-out, and random effects were farm, silo unit, field, and day. At harvest, between-farm variability was the largest source of variation for both corn silage and haylage, but within-farm sources of variation exceeded farm-to-farm variation for haylage at feed-out. At feed-out, haylage DM and NDF content had higher within-farm variability than corn silage. In contrast, corn silage starch showed higher within-farm variation at feed-out than haylage CP content. For DM content at feed-out, day-to-day variation was the most relevant source of within-farm variation for both forages. However, for the nutrient components at feed-out (NDF and CP for haylage; NDF and starch for corn silage) silo-to-silo variation was the largest source of variability. Weather conditions systematically explained a proportion of the farm-to-farm variability for both forages at harvest and feed-out. We concluded that because of the high farm-to-farm variation, corn silage and haylage must be sampled on individual farms. We also concluded that due to the high silo-to-silo variability, and the still significant day-to-day and field-to-field variability within-farm, corn silage and haylage should be sampled within individual silos to better capture changes in forage components at feed-out.

Perturbatively corrected ring-polymer instanton theory for accurate tunneling splittings.

We introduce an approach for calculating perturbative corrections to the ring-polymer instanton approximation to tunneling splittings (RPI+PC) by computing higher-order terms in the asymptotic expansion in ℏ. The resulting method goes beyond standard instanton theory by using information on the third and fourth derivatives of the potential along the tunneling path to include additional anharmonic effects. This leads to significant improvements both in systems with low barriers and in systems with anharmonic modes. We demonstrate the applicability of RPI+PC to molecular systems by computing the tunneling splitting in full-dimensional malonaldehyde and a deuterated derivative. Comparing to both experiment and recent quantum mechanical benchmark results, we find that our perturbative correction reduces the error from -11% to 2% for hydrogen transfer and performs even better for the deuterated case. This makes our approach more accurate than previous calculations using diffusion Monte Carlo and path-integral molecular dynamics while being more computationally efficient.

Vibrational strong coupling in liquid water from cavity molecular dynamics.

We assess the cavity molecular dynamics method for the calculation of vibrational polariton spectra using liquid water as a specific example. We begin by disputing a recent suggestion that nuclear quantum effects may lead to a broadening of polariton bands, finding instead that they merely result in anharmonic red shifts in the polariton frequencies. We go on to show that our simulated cavity spectra can be reproduced to graphical accuracy with a harmonic model that uses just the cavity-free spectrum and the geometry of the cavity as input. We end by showing that this harmonic model can be combined with the experimental cavity-free spectrum to give results in good agreement with optical cavity measurements. Since the input to our harmonic model is equivalent to the input to the transfer matrix method of applied optics, we conclude that cavity molecular dynamics cannot provide any more insight into the effect of vibrational strong coupling on the absorption spectrum than this transfer matrix method, which is already widely used by experimentalists to corroborate their cavity results.

Myxococcus CsgA, Drosophila Sniffer, and human HSD10 are cardiolipin phospholipases.

Myxococcus xanthus development requires CsgA, a member of the short-chain alcohol dehydrogenase (SCAD) family of proteins. We show that CsgA and SocA, a protein that can replace CsgA function in vivo, oxidize the 2'-OH glycerol moiety on cardiolipin and phosphatidylglycerol to produce diacylglycerol (DAG), dihydroxyacetone, and orthophosphate. A lipid extract enriched in DAGs from wild-type cells initiates development and lipid body production in a csgA mutant to bypass the mutational block. This novel phospholipase C-like reaction is widespread. SCADs that prevent neurodegenerative disorders, such as Drosophila Sniffer and human HSD10, oxidize cardiolipin with similar kinetic parameters. HSD10 exhibits a strong preference for cardiolipin with oxidized fatty acids. This activity is inhibited in the presence of the amyloid ß peptide. Three HSD10 variants associated with neurodegenerative disorders are inactive with cardiolipin. We suggest that HSD10 protects humans from reactive oxygen species by removing damaged cardiolipin before it induces apoptosis.

Improved microcanonical instanton theory.

Canonical (thermal) instanton theory is now routinely applicable to complex gas-phase reactions and allows for the accurate description of tunnelling in highly non-separable systems. Microcanonical instanton theory is by contrast far less well established. Here, we demonstrate that the best established microcanonical theory [S. Chapman, B. C. Garrett and W. H. Miller, J. Chem. Phys., 1975, 63, 2710-2716], fails to accurately describe the deep-tunnelling regime for systems where the frequencies of the orthogonal modes change rapidly along the instanton path. By taking a first principles approach to the derivation of microcanonical instanton theory, we obtain an improved method, which accurately recovers the thermal instanton rate when integrated over energy. The resulting theory also correctly recovers the separable limit and can be thought of as an instanton generalisation of Rice-Ramsperger-Kassel-Marcus (RRKM) theory. When combined with the density-of-states approach [W. Fang, P. Winter and J. O. Richardson, J. Chem. Theory Comput., 2021, 17, 40-55], this new method can be straightforwardly applied to real molecular systems.

Unraveling the Complex Composition of Produced Water by Specialized Extraction Methodologies.

Produced water (PW), a waste byproduct of oil and gas extraction, is a complex mixture containing numerous organic solubles and elemental species; these constituents range from polycyclic aromatic hydrocarbons to naturally occurring radioactive materials. Identification of these compounds is critical in developing reuse and disposal protocols to minimize environmental contamination and health risks. In this study, versatile extraction methodologies were investigated for the untargeted analysis of PW. Thin-film solid-phase microextraction with hydrophilic-lipophilic balance particles was utilized for the extraction of organic solubles from eight PW samples from the Permian Basin and Eagle Ford formation in Texas. Gas chromatography-mass spectrometry analysis found a total of 266 different organic constituents including 1,4-dioxane, atrazine, pyridine, and PAHs. The elemental composition of PW was evaluated using dispersive solid-phase extraction followed by inductively coupled plasma-mass spectrometry, utilizing a new coordinating sorbent, poly(pyrrole-1-carboxylic acid). This confirmed the presence of 29 elements including rare earth elements, as well as hazardous metals such as Cr, Cd, Pb, and U. Utilizing chemometric analysis, both approaches facilitated the discrimination of each PW sample based on their geochemical origin with a prediction accuracy above 90% using partial least-squares-discriminant analysis, paving the way for PW origin tracing in the environment.

Fast quasi-centroid molecular dynamics.

We describe a fast implementation of the quasi-centroid molecular dynamics (QCMD) method in which the quasi-centroid potential of mean force is approximated as a separable correction to the classical interaction potential. This correction is obtained by first calculating quasi-centroid radial and angular distribution functions in a short path integral molecular dynamics simulation and then using iterative Boltzmann inversion to obtain an effective classical potential that reproduces these distribution functions in a classical NVT simulation. We illustrate this approach with example applications to the vibrational spectra of gas phase molecules, obtaining excellent agreement with QCMD reference calculations for water and ammonia and good agreement with the quantum mechanical vibrational spectrum of methane.

A general non-adiabatic quantum instanton approximation.

We present a general quantum instanton approach to calculating reaction rates for systems with two electronic states and arbitrary values of the electronic coupling. This new approach, which we call the non-adiabatic quantum instanton (NAQI) approximation, reduces to Wolynes theory in the golden rule limit and to a recently proposed projected quantum instanton method in the adiabatic limit. As in both of these earlier theories, the NAQI approach is based on making a saddle point approximation to the time integral of a reactive flux autocorrelation function, although with a generalized definition of the projection operator onto the product states. We illustrate the accuracy of the approach by comparison with exact rates for one dimensional scattering problems and discuss its applicability to more complex reactions.

Confirming the role of nuclear tunneling in aqueous ferrous-ferric electron transfer.

We revisit the well-known aqueous ferrous-ferric electron transfer reaction in order to address recent suggestions that nuclear tunneling can lead to significant deviation from the linear response assumption inherent in the Marcus picture of electron transfer. A recent study of this reaction by Richardson and co-workers [Phys. Chem. Chem. Phys. 22, 10687 (2020)] has found a large difference between their new path-integral method, golden-rule quantum transition state theory (GR-QTST), and the saddle point approximation of Wolynes (Wolynes theory). They suggested that this difference could be attributed to the existence of multiple tunneling pathways, leading Wolynes theory to significantly overestimate the rate. This was used to argue that the linear response assumptions of Marcus theory may break down for liquid systems when tunneling is important. If true, this would imply that the commonly used method for studying such systems, where the problem is mapped onto a spin-boson model, is invalid. However, we have recently shown that size inconsistency in GR-QTST can lead to poor predictions of the rate in systems with many degrees of freedom. We have also suggested an improved method, the path-integral linear golden-rule (LGR) approximation, which fixes this problem. Here, we demonstrate that the GR-QTST results for ferrous-ferric electron transfer are indeed dominated by its size consistency error. Furthermore, by comparing the LGR and Wolynes theory results, we confirm the established picture of nuclear tunneling in this system. Finally, by comparing our path-integral results to those obtained by mapping onto the spin-boson model, we reassess the importance of anharmonic effects and the accuracy of this commonly used mapping approach.

An improved path-integral method for golden-rule rates.

We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunneling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang, and Richardson [J. Chem. Phys. 150, 104107 (2019)]. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and co-workers. We then study a multidimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretization of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime without the need for the analytic continuation required by Wolynes theory.

Reversible chelating polymer for determination of heavy metals by dispersive micro solid-phase extraction with ICP-MS.

N-functionalization of pyrrole with carbon disulfide and subsequent chemical polymerization resulted in the development of a new sorbent material for the extraction of metals. The synthesized polymer, poly(pyrrole-N-carbodithioic acid) (PPy-CS2), is an air-stable, granular powder that is insoluble in water. PPy-CS2 combines pH-dependent chelation, extraction, and desorption sorbent properties that are exploited for the selective extraction and sensitive determination of heavy metals in water matrices using ultrasound-assisted dispersive micro solid-phase extraction and inductively coupled plasma mass spectrometry. Excellent removal and recovery of Cd(II), Co(II), Cu(II), Ni(II), Pb(II), and Zn(II) were achieved and compared with unfunctionalized polypyrrole, which demonstrated extraction resulted from chelation of the metal ions. The extraction efficiency of the PPy-CS2 sorbent as a function of pH, amount of sorbent, extraction time, and flow rate of the desorption solution were evaluated. Limits of detection ranged from 0.3 for cadmium to 11.2 ng/L for zinc with linear dynamic ranges from 0.1 to 500 µg/L and relative standard deviations from 2.2 to 6.3%. The sample preparation method was successfully applied for determination of the target metals in raw well water, treated well water, and river water. Validation was performed by analysis of a certified reference standard for trace metals in drinking water. Graphical abstract Schematic representation of the ultrasound-assisted micro solid-phase extraction protocol for the removal and recovery of heavy metals by the air-stable, granular, and reversible chelating polymer, poly (pyrrole-N-carbodithioic acid).

Path integral methods for reaction rates in complex systems.

We shall use this introduction to the Faraday Discussion on quantum effects in complex systems to review the recent progress that has been made in using imaginary time path integral methods to calculate chemical reaction rates. As a result of this progress, it is now routinely possible to calculate accurate rate constants including quantum mechanical zero point energy and tunnelling effects for arbitrarily complex (anharmonic and multi-dimensional) systems. This is true in the adiabatic (Born-Oppenheimer) limit, in the non-adiabatic (Fermi Golden Rule) limit, and everywhere between these two limits in the normal Marcus regime. Quantum mechanical effects on reaction rates can be enormous, even at room temperature, and the problem of including these effects in simulations of a wide variety of chemical reactions in complex systems has now effectively been solved.

Peripheral blood smear findings in a kidney transplant recipient with disseminated histoplasmosis and elevated Aspergillus galactomannan.

We report a case of disseminated histoplasmosis in a renal transplant recipient who presented with a nodular pulmonary lesion and elevated serum and bronchoalveolar lavage (BAL) Aspergillus galatomannan. This almost led to an erroneous diagnosis of invasive aspergillosis since the donor respiratory tract was known to be colonized with Aspergillus terreus. However, distinctive intracelluar Histoplasma yeasts on peripheral blood smear led to early diagnosis and appropriate treatment. The cross-reactivity between Aspergillus galactomannan and Histoplasma antigen is discussed further.

An analysis of isomorphic RPMD in the golden rule limit.

We analyze the golden rule limit of the recently proposed isomorphic ring polymer (iso-RP) method. This method aims to combine an exact expression for the quantum mechanical partition function of a system with multiple electronic states with a pre-existing mixed quantum-classical (MQC) dynamics approximation, such as fewest switches surface hopping. Since the choice of the MQC method adds a degree of flexibility, we simplify the analysis by assuming that the dynamics used correctly reproduces the exact golden rule rate for a nonadiabatic (e.g., electron transfer) reaction in the high temperature limit. Having made this assumption, we obtain an expression for the iso-RP rate in the golden rule limit that is valid at any temperature. We then compare this rate with the exact rate for a series of simple spin-boson models. We find that the iso-RP method does not correctly predict how nuclear quantum effects affect the reaction rate in the golden rule limit. Most notably, it does not capture the quantum asymmetry in a conventional (Marcus) plot of the logarithm of the reaction rate against the thermodynamic driving force, and it also significantly overestimates the correct quantum mechanical golden rule rate for activationless electron transfer reactions. These results are analyzed and their implications discussed for the applicability of the iso-RP method to more general nonadiabatic reactions.

On the calculation of quantum mechanical electron transfer rates.

We present a simple interpolation formula for the rate of an electron transfer reaction as a function of the electronic coupling strength. The formula only requires the calculation of Fermi golden rule and Born-Oppenheimer rates and so can be combined with any methods that are able to calculate these rates. We first demonstrate the accuracy of the formula by applying it to a one dimensional scattering problem for which the exact quantum mechanical, Fermi golden rule, and Born-Oppenheimer rates are readily calculated. We then describe how the formula can be combined with the Wolynes theory approximation to the golden rule rate, and the ring polymer molecular dynamics (RPMD) approximation to the Born-Oppenheimer rate, and used to capture the effects of nuclear tunneling, zero point energy, and solvent friction on condensed phase electron transfer reactions. Comparison with exact hierarchical equations of motion results for a demanding set of spin-boson models shows that the interpolation formula has an error comparable to that of RPMD rate theory in the adiabatic limit, and that of Wolynes theory in the nonadiabatic limit, and is therefore as accurate as any method could possibly be that attempts to generalize these methods to arbitrary electronic coupling strengths.

Analytic continuation of Wolynes theory into the Marcus inverted regime.

The Wolynes theory of electronically nonadiabatic reaction rates [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] is based on a saddle point approximation to the time integral of a reactive flux autocorrelation function in the nonadiabatic (golden rule) limit. The dominant saddle point is on the imaginary time axis at tsp=iλspℏ, and provided λsp lies in the range -ß/2≤λsp≤ß/2, it is straightforward to evaluate the rate constant using information obtained from an imaginary time path integral calculation. However, if λsp lies outside this range, as it does in the Marcus inverted regime, the path integral diverges. This has led to claims in the literature that Wolynes theory cannot describe the correct behaviour in the inverted regime. Here we show how the imaginary time correlation function obtained from a path integral calculation can be analytically continued to λsp<-ß/2, and the continuation used to evaluate the rate in the inverted regime. Comparison with exact golden rule results for a spin-boson model and a more demanding (asymmetric and anharmonic) model of electronic predissociation shows that the theory is just as accurate in the inverted regime as it is in the normal regime.

Highly directional pressure sensing using the phase gradient.

Many methods of two-microphone directional sensing have limited bandwidth. For active intensity, finite-difference error can be removed by using the phase and amplitude gradient estimator method. Using similar principles, a directional pressure sensor based on the phase gradient is developed that is accurate up to the spatial Nyquist frequency, and beyond if phase unwrapping is applied. A highly directional frequency-independent array response of arbitrary order can be achieved with two microphones. The method is compared against beamforming and traditional gradient sensing for single and multiple sources and is found to have improved localization capabilities and increased bandwidth.

Three-microphone probe bias errors for acoustic intensity and specific acoustic impedance.

In acoustic intensity estimation, adding a microphone at the probe center removes errors associated with pressure averaging. Analytical bias errors are presented for a one-dimensional, three-microphone probe for active intensity, reactive intensity, and specific acoustic impedance in a monopole field. Traditional estimation is compared with the Phase and Amplitude Gradient Estimator (PAGE) method; the PAGE method shows an increased bandwidth for all three quantities. The two- and three-microphone methods are compared experimentally, showing reduced bias errors with three-microphone PAGE for active and reactive intensity, whereas using two microphones is preferred for specific acoustic impedance.