Free Energy State Research Articles

Assembly mechanism of surface-functionalized nanocubes.

Faceted nanoparticles can be used as building blocks to assemble nanomaterials with exceptional optical and catalytic properties. Recent studies have shown that surface functionalization of such nanoparticles with organic molecules, polymer chains, or DNA can be used to control the separation distance and orientation of particles within their assemblies. In this study, we computationally investigate the mechanism of assembly of nanocubes grafted with short-chain molecules. Our approach involves computing the interaction free energy landscape of a pair of such nanocubes via Monte Carlo simulations and using the Dijkstra algorithm to determine the minimum free energy pathway connecting key states in the landscape. We find that the assembly pathway of nanocubes is very rugged involving multiple energy barriers and metastable states. Analysis of nanocube configurations along the pathway reveals that the assembly mechanism is dominated by sliding motion of nanocubes relative to each other punctuated by their local dissociation at grafting points involving lineal separation and rolling motions. The height of energy barriers between metastable states depends on factors such as the interaction strength and surface roughness of the nanocubes and the steric repulsion from the grafts. These results imply that the observed assembly configuration of nanocubes depends not only on their globally stable minimum free energy state but also on the assembly pathway leading to this state. The free energy landscapes and assembly pathways presented in this study along with the proposed guidelines for engineering such pathways should be useful to researchers aiming to achieve uniform nanostructures from self-assembly of faceted nanoparticles.

All-Atom Molecular Dynamics Simulation Methods for the Aggregation of Protein and Peptides: Replica Exchange/Permutation and Nonequilibrium Simulations.

Protein aggregates are associated with more than 40 serious human diseases. To understand the formation mechanism of protein aggregates at atomic level, all-atom molecular dynamics (MD) simulation is a powerful computational tool. In this chapter, we review the all-atom MD simulation methods that are useful for study on the protein aggregation. We first explain conventional MD simulation methods in physical statistical ensembles, such as the canonical and isothermal-isobaric ensembles. We then describe the generalized-ensemble algorithms such as replica-exchange and replica-permutation MD methods. These methods can overcome a difficulty, in which simulations tend to get trapped in local-minimum free-energy states. Finally we explain the nonequilibrium MD method. Some simulation results based on these methods are also presented.

Microstructure and Time-Dependent Behavior of STx-1b Calcium Montmorillonite Suspensions

CaMnt is much less important than NaMnt due to its limited commercial applications. The time-dependent property of NaMnt gel has been studied extensively as it is exploited in many applications such as drilling mud and viscosity-modifier applications. In contrast, the time-dependent property of CaMnt suspension and the factors affecting it are largely unknown. The speciation of Ca2+ ions is one such factor to be evaluated. In the current study, pH and solids concentration were examined and then used to validate a recent theory on clay gel time dependency. The results supported the theory that a strong electrostatic double layer (EDL) repulsion in the 3-D network is needed to reorganize the structure and drive it toward the state of minimum free energy. The 12 wt.% CaMnt (STx-1b) gel displayed time-dependent behavior at pH 5 but not at its natural pH of 8.4. At pH 5, the interlayer Ca2+ ions became fully hydrated and desorbed from the platelet surface. This enhanced the EDL repulsion between the platelets. At pH >6.5, the positively charged hydrolysis product Ca(OH)+ began to form and was adsorbed, partially neutralizing the permanent layer charge and weakening the repulsion. However, at 19.4 wt.% solids, the gel displayed pronounced time-dependent behavior despite the high natural pH of 8. The platelets were much closer together, allowing the EDL force to operate and effect structural reorganization. The microstructure of these CaMnt gels showed high platelet concentrations interacting to form a relatively open structure. The microstructure of a kaolin (KGa-2) suspension which showed no time-dependent behavior even after 1 day of ageing revealed the importance of particle morphology and layer charge on time dependency. Its 3-D structure was formed by relatively thick, layered platelets with a low layer charge.

Ageing behaviour spanning months of NaMt, hectorite and Laponite gels: Surface forces and microstructure – A comprehensive analysis

Recent “artifact-free” microstructure information enabled the development of a more credible model for explaining the ageing time-dependent rheological behavior of NaMt, hectorite and Laponite gels. These gels displayed pronounced ageing behavior lasting months. The platelet morphology and the localised nature of the negative and positive charges produced the essential forces and interaction configurations to form the time-dependent structure. This structure is composed of nano-sized flexible platelets interacting both attractively to form the network junctions and repulsively to open up the structure. These junctions were formed by heterogeneous charge and van der Waals attractions between the jagged and curled edges, and the face of the interacting platelets. The force that is responsible for the time-dependent behaviour is the EDL repulsive force. This force governs the development of the 3-D network structure and drives it towards a minimum free energy state. This process takes a long time to complete. The resultant microstructure is completely interpenetrated with interconnected nanopores trapping as much as 99% of water in volume. At high ionic strength or 0.3 M KCl, the NaMt or bentonite gels became time independent as the van der Waals force formed the structure. The Leong model described the initial ageing behavior well. For the nanodiscotic Laponite gels, the 3-D structure is formed from sheets instead of primarily disks contradicting prevailing model. With the latest microstructure information, new mechanisms were proposed to account for the high yield stress at low solids, low permeability, intercalation behavior, layer stacking and enlarged dried platelets.

Comparative evaluation of liquid–liquid equilibria for extraction of 2,2,3,3‐tetrafluoro‐1‐propanol from water by a ZIF‐8‐porous ionic liquid

AbstractBACKGROUND2,2,3,3‐Tetrafluoro‐1‐propanol (TFP) is a benign solvent and widely used in the electronics industry as a cleaning agent. Because water and TFP can form an azeotropic mixture, it consumes energy to separate TFP from its aqueous mixtures using conventional distillation.RESULTSIn this work, the zeolitic imidazolate framework‐8 porous ionic liquid (ZIF‐8‐PIL) and the ionic liquid (IL) N‐butyl pyridinium bis(trifluoromethyl sulfonyl) imide ([Bpy][NTf2]) are used as extractants to extract TFP from its aqueous solution. ZIF‐8‐PIL was synthesized by ZIF‐8 and IL [Bpy][NTf2]. The liquid–liquid equilibrium (LLE) data for the two systems (water + TFP + ZIF‐8‐PIL/IL) were determined at 298.15, 308.15 and 318.15 K under 101.3 kPa. The selectivity (S) and distribution coefficient (D) were examined to assess the extractive performance of ZIF‐8‐PIL and IL. The non‐random two‐liquid (NRTL) model was applied to fit the tie‐line data of the investigated mixtures.CONCLUSIONThe results demonstrate that ZIF‐8‐PIL is a suitable extractant to separate TFP with values of S and D greater than unity. The NRTL model has better correlation performance for the ternary systems with root mean square deviation lower than 0.01. The obtained parameters satisfy the minimum state of the mixed Gibbs free energy, which indicated that the model parameters are reliable. © 2021 Society of Chemical Industry (SCI).

Research on the Mathematical Model of Local Equilibrium in the Top-Blown Smelting Process of Electronic Waste

In the present study, the local equilibrium modeling and division method of the multiphase non-equilibrium for the top-blowing smelting process of electronic waste was investigated based on the local equilibrium hypothesis. And the mathematical description of the multi-phase equilibrium of each local area and the correlation method between the local areas were studied by analysis of relationships among the valence state, phase, composition, and Gibbs free energy of each element. Afterward, the reaction characteristic data such as melting material, product phase, composition, temperature, atmosphere, etc. were obtained via industrial measurement experiments. Based on these, a mathematical model of local equilibrium for the top-blowing smelting process of electronic waste was established. Finally, the thermodynamic digital simulation system was developed via the calculation of metallurgical process and online control platform MetCal Desk (v7.00, MetCal, Ganzhou, China), which can investigate the element distribution behavior during the smelting process and provide theoretical guidance for the industrial production practice.

Influential mechanism of water occurrence states of waste-activated sludge: specifically focusing on the roles of EPS micro-spatial distribution and cation-dominated interfacial properties

The highly hydrated colloidal structure of waste-activated sludge (WAS) is the main obstacle of enhanced dewatering for sludge volume minimization. Extracellular polymeric substances (EPS) maintain the colloidal stability of bio-flocs in a three-dimensional matrix due to bindings with bivalent cations (i.e., Ca2+ and Mg2+) and hydrophobic interactions. However, few studies specifically focused on the quantitative relationships among spatial distribution of EPS, microstructure of bio-flocs and fractions of bound water (e.g. vicinal water and interstitial water). Thus, there may be still some debates on whether and what extent of the lysis or flocculation of sludge flocs is optimal for the dewaterability improvement. This study applied the gradient addition of cation exchange resin (CER) to remove EPS-complexed cations and loosen the spatial distribution of EPS. Consequently, how the spatial extension of EPS layers with relief of complex cations influenced the particle size distribution, fractal dimension, interfacial free energy and water occurrence states of WAS was systematically investigated. The quartz crystal microbalance with dissipation (QCM-D) was also applied to analyze the water-EPS interactions with and without the presence of Ca2+ and Mg2+. All the results confirmed that the dispersed EPS adhering layers led to the higher fractal dimension (Df) but the lower space filling degree of bio-flocs. Also, the 4-fold reduction in the polar/acid-based interfacial free energy could be induced by the removal of cations from EPS matrix, which indicated the significant increase in hydrophobicity. Predictably, the fractions of vicinal water and interstitial water were dominated by the polar/acid-based interfacial free energy and pore structure of microbial aggregates, respectively, which were confirmed by the strong Pearson correlation (Rp>0.80, p-value<0.04). These findings are expected to provide the improved mechanistic insights into the relationship between water occurrence states and colloidal structure of WAS, and can serve as the basis for the optimal combination of various sludge conditioning approaches towards regulating aggregation states of bio-flocs.

Intrinsic Nucleophilicity of Inverting and Retaining Glycoside Hydrolases Revealed Using Carbasugar Glyco-Tools

Hydrolyses of cyclohexenyl-based carbasugars that mimic either α-d-glucose or α-d-galactose were explored with two Bacteroides thetaiotaomicron enzymes from glycoside hydrolase family 97: an inverting α-glucosidase (BtGH97a) and a retaining α-galactosidase (BtGH97b). Both enzymes yield nucleophilic substitutions at the pseudo-anomeric center of the carbasugar substrates, giving significantly different linear energy relationships for the catalytic rate constant as a function of the leaving group ability. Specifically, the kinetic data for the inverting α-glucosidase is consistent with the reaction giving a hydrolyzed inverted carbaglucose product by a mechanism that proceeds with little nucleophilic participation by the bound water molecule at the reaction transition state. In contrast, the reaction of carbagalactose substrates with the retaining GH97 enzyme involves a rate-limiting nonchemical step, likely a conformational change, followed by rapid substitution involving a nucleophilic amino acid residue to give a covalently bound intermediate. Considering the structural similarities between these two GH97 enzymes, the kinetic data nonetheless reveal a significant (>106) difference in the rates of nucleophilic attack between the unique enzymatic nucleophiles─with the less nucleophilic species being H2O in the inverting α-glucosidase and the better nucleophile being a carboxylate in the retaining α-galactosidase. The enzymatic rate constant ratio for the phenyl carbasugars contrasts with the corresponding kinetic data obtained using natural substrate phenyl glycopyranosides. Last, for the galactocarbasugar with a phenol leaving group, the second-order rate constant for alkylation of the GH97 α-galactosidase is only ∼10-fold lower than that for glycosylation of this enzyme by the parent carbohydrate phenyl α-d-galactopyranoside. This modest difference in rate constants underscores our conclusion that retaining glycoside hydrolases may not have optimized the nucleophilicity of their active site nucleophiles with the result that the transition state free energies for formation and hydrolysis of the covalent enzyme intermediate are matched.

An enhanced sampling QM/AMOEBA approach: The case of the excited state intramolecular proton transfer in solvated 3-hydroxyflavone.

We present an extension of the polarizable quantum mechanical (QM)/AMOEBA approach to enhanced sampling techniques. This is achieved by connecting the enhanced sampling PLUMED library to the machinery based on the interface of Gaussian and Tinker to perform QM/AMOEBA molecular dynamics. As an application, we study the excited state intramolecular proton transfer of 3-hydroxyflavone in two solvents: methanol and methylcyclohexane. By using a combination of molecular dynamics and umbrella sampling, we find an ultrafast component of the transfer, which is common to the two solvents, and a much slower component, which is active in the protic solvent only. The mechanisms of the two components are explained in terms of intramolecular vibrational redistribution and intermolecular hydrogen-bonding, respectively. Ground and excited state free energies along an effective reaction coordinate are finally obtained allowing for a detailed analysis of the solvent mediated mechanism.

Thermodynamic properties ofε-Fe with thermal electronic excitation effects on vibrational spectra

The thermodynamic properties of hcp-iron ({\epsilon}-Fe) are essential for investigating planetary cores' internal structure and dynamic properties. Despite their importance to planetary sciences, experimental investigations of {\epsilon}-Fe at relevant conditions are still challenging. Therefore, ab initio calculations are crucial to elucidating the thermodynamic properties of this system. Here we use a free energy calculation scheme based on the phonon gas model compatible with temperature-dependent phonon frequencies. We investigate the effects of electronic thermal excitations, which introduces a temperature dependence on phonon frequencies, and the implication for the thermodynamic properties of {\epsilon}-Fe at extreme pressure (P) and temperature (T) conditions. We disregard phonon-phonon interactions, i.e., anharmonicity and their effect on phonon frequencies. Nevertheless, the current scheme is also applicable to T-dependent anharmonic frequencies. We conclude that the impact of thermal electronic excitations on vibrational properties is not significant up to ~ 4,000 K at 200 GPa but should not be ignored at higher temperatures or pressures. However, the static free energy, Fst, must always include the effect of thermal excitation fully in a continuum of Ts. Our results for isentropic equations of state show good agreement with data from recent ramp compression experiments up to 1,400 GPa conducted at the National Ignition Facility (NIF).

Electrostatic Control of Photoisomerization in Channelrhodopsin 2.

Channelrhodopsin 2 (ChR2) is the most commonly used tool in optogenetics. Because of its faster photocycle compared to wild-type (WT) ChR2, the E123T mutant of ChR2 is a useful optogenetic tool when fast neuronal stimulation is needed. Interestingly, in spite of its faster photocycle, the initial step of the photocycle in E123T (photoisomerization of retinal protonated Schiff base or RPSB) was found experimentally to be much slower than that of WT ChR2. The E123T mutant replaces the negatively charged E123 residue with a neutral T123 residue, perturbing the electric field around the RPSB. Understanding the RPSB photoisomerization mechanism in ChR2 mutants will provide molecular-level insights into how ChR2 photochemical reactivity can be controlled, which will lay the foundation for improving the design of optogenetic tools. In this work, we combine ab initio nonadiabatic dynamics simulation, excited state free energy calculation, and reaction path search to comprehensively characterize the RPSB photoisomerization mechanism in the E123T mutant of ChR2. Our simulation agrees with previous experiments in predicting a red-shifted absorption spectrum and significant slowdown of photoisomerization in the E123T mutant. Interestingly, our simulations predict similar photoisomerization quantum yields for the mutant and WT despite the differences in excited-state lifetime and absorption maximum. Upon mutation, the neutralization of the negative charge on the E123 residue increases the isomerization barrier, alters the reaction pathway, and changes the relative stability of two fluorescent states. Our findings provide new insight into the intricate role of the electrostatic environment on the RPSB photoisomerization mechanism in microbial rhodopsins.

The study of oxygen reduction reaction on Ge‐doped MoS 2 monolayer based on first principle

Rational design of electrocatalyst for air cathode with high oxygen reduction reaction (ORR) performance is highly demanded. However, current low performance of electrocatalyst remains a big challenge. Herein, the possibility of germanium (Ge)-doped molybdenum disulfide (MoS2) monolayer as a novel electrocatalyst for ORR in alkaline solution was studied based on first principle calculation. The results indicate that oxygen is strongly adsorbed on the surface of Ge-doped MoS2 monolayer. Moreover, a high barrier should be overcome during H2O molecular dissociation and the barrier of dissociation decreases with the number of doped Ge atoms increasing. Based on the calculation of transition state and Gibbs free energy, the triple Ge atoms-doped MoS2 monolayer shows the best activity toward ORR with the lowest rate-determine step barrier of 0.23 eV. Our study may provide a meaningful method for the design of novel MoS2-based electrocatalyst for ORR.

Step by Step Strecker Amino Acid Synthesis from Ab Initio Prebiotic Chemistry.

The amino acids synthesis from elementary precursors in abiotic conditions is traditionally described according to the Strecker reaction, thoroughly invoked to justify the observation of amino acids in extraterrestrial samples and their emergence in the primordial Earth. To this day, however, a quantitative microscopic description of the mechanism, thermodynamics, and kinetics of the multistep Strecker reaction is still lacking. In the present work we tackle this study by adopting a state-of-the-art ab initio computational approach, combining an efficient scheme of exploration of the relevant chemical networks with a rigorous determination of the underlying free energy and transition states. We determine the step-by-step chemical pathway from "Strecker precursors" to glycine in solution and calculate the corresponding full free energy landscape. Our results agree well with the scarce available experimental data and complete them, thus providing the first end-to-end study of this complex reaction, a crucial bottleneck for the emergence of life.

Energy Storage and Reuse in Negative Capacitance

In this article, we analyze how a ferroelectric (FE) acts as a rechargeable energy storage medium which stores, releases, and retrieves energy, and helps the gate achieve a desired charge density with reduced energy (voltage) from the external gate drive. During transistor turn-on, the FE releases energy, while the whole system is absorbing energy, and during turn-off, the FE retrieves energy, while the whole system is releasing energy. Capacitor energy is analyzed using two different approaches: static material free energy integrals and transient circuit power integrals. The two results agree within 1%. Energy analysis is also performed for a metal–oxide–semiconductor field-effect transistor structure for two gate lengths, 20 nm and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2~\mu \text{m}$ </tex-math></inline-formula> , in an inverter circuit. At 2- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> gate length, the values of energy match under these two different approaches with less than a 6% difference. The difference is larger in the 20-nm gate length case due to larger parasitic capacitances, such as gate-to-drain and gate-to-source capacitance, affecting the transient circuit analysis. Even so, most of the energy storage and retrieval benefit is retained even in small size negative capacitance transistors.

Conformational Landscapes of Ligand-Gated Ion Channel GLIC from Markov State Modeling

Ligand-gated ion channels (LGICs) are responsible for propagating electrochemical signals in neurons and other excitable cells, by rapidly cycling between functional states upon appropriate chemical stimuli. However, few LGICs have been characterized in both open and closed conformations, and the timescales of the gating transitions, initiated by ligand-binding, are typically too slow for classical molecular dynamics simulations. Consequently, the precise landscape of LGIC transitions is poorly understood. We have utilized enhanced sampling to run unbiased molecular dynamics simulations in a massively parallel fashion, and construct Markov state models of a structurally rich, pH-gated bacterial LGIC, GLIC from Gloeobacter violaceus. We then tested the ability of these models to recapitulate functional effects of protonation and mutagenesis on channel opening. Consistent with functional recordings, our models reveal deepening of the open state free energy well upon protonation in the extracellular domain or mutation (I233T) of the transmembrane gate, with relatively low maximal open probability. Analysis of states along the main reaction coordinate confirms multiple previously suggested mechanisms, but we note that the blooming and twisting motions of the extracellular domain mainly depend on pH and not the conformational state of the channel. Additionally, analysis of the conformational symmetries reveals a highly asymmetric intermediate and symmetric open state, while the closed states display mixed asymmetric extracellular and symmetric transmembrane domains. This work demonstrates the construction of plausible Markov state models from limited sampling of LGIC variants, capable of predicting allosteric effects from chemical perturbation, and identifying geometric variables in functional transitions. Such statistical tools constitute a promising approach to elucidate LGIC gating mechanisms, with practical implications for modeling neuronal function and the development of state-selective drugs.

A speciated, conventional Pitzer ion-interaction model for the aqueous Nd3+–H+–Na+–K+–Ca2+–Cl−–OH− system at 298 K and 0.1 MPa

A conventional, speciated Pitzer ion-interaction model at 298 K and 0.1 MPa is presented for the NdCl3 + H2O system and mixtures containing HCl, NaCl, KCl, and CaCl2. The model uses Nd3+, NdOH2+, Nd(OH)2+, Nd(OH)30, NdCl2+, and NdCl2+ solute species and was fitted to isopiestic, electromotive force (emf), and NdCl3·6H2O solubility data. The model was then extended to pH values at which Nd(OH)3, Nd(OH)2Cl, and a speculative double salt, Nd(OH)3·NdCl3, are stable. The two hydroxychloride salts enabled the model to join the stability fields of NdCl3·6H2O and Nd(OH)3 ensuring continuity in the range 2 < pH < 13. The activity coefficient model developed from the low pH [NdCl3 + NaCl](aq) system reproduces the solubility of solid Nd(OH)3(s) in water and NaCl(aq) with only the addition of standard state free energy terms for crystalline (cr) and amorphous (am) NdOH3(s) and the Nd(OH)2+ and Nd(OH)30 solute species. No Pitzer parameters involving NdOH2+, Nd(OH)2+ and Nd(OH)30 were necessary to reproduce the full body of thermodynamic data over an ionic strength range from infinite dilution to the solubility limits of NaCl, KCl, CaCl2·6H2O, Nd(OH)3(s), the hydroxychloride salts, and for mixtures containing up to 4.5 molal HCl(aq). The model adds only five ‘binary’ and three ‘ternary’ Pitzer ion-interaction parameters to the H-Na-K-Ca-Cl-OH parameters in Harvie et al. (1984; hereafter HMW). The model is simpler, compositionally broader, and more accurate than previously published Pitzer ion-interaction models for aqueous neodymium-chloride and -hydroxide solutions containing HCl, NaCl, KCl or CaCl2. The model has ramifications for geochemical modeling and uncertainty quantification of An(III) solubilities used to support certification of evaporite hosted nuclear waste repositories.

Visualizing free-energy landscapes for four hard disks.

We present a simple model system with four hard disks moving in a circular region for which free-energy landscapes can be directly calculated and visualized in two and three dimensions. We construct several energy landscapes for our system, and we explore the strengths and limitations of each in terms of understanding system dynamics, in particular the relationship between state transitions and free-energy barriers. We also demonstrate the importance of distinguishing between system dynamics in real space and those in landscape coordinates, and we show that care must be taken to appropriately combine dynamics with barrier properties to understand the transition rates. This simple model provides an intuitive way to understand free-energy landscapes, and it illustrates the benefits that free-energy landscapes can have over potential energy landscapes.

Expectation maximized molecular dynamics: Toward efficient learning of rarely sampled features in free energy surfaces from unbiased simulations.

Biophysical processes often encounter high energy transition states that lie in regions of the free energy landscape (FEL) inaccesible to conventional molecular dynamics simulations. Various enhanced sampling methods have been developed to handle the inherent quasi-nonergodicity, either by adding a biasing potential to the underlying Hamiltonian or by forcing the transitions with parallel tempering. However, when attempting to probe systems of increasing complexity with limited computational resources, there arises an imminent need for fast and efficient FEL exploration with sufficient accuracy. Herein, we present a computationally efficient algorithm based on statistical inference for fast estimation of key features in the two-dimensional FEL. Unlike conventional enhanced sampling methods, this newly developed method avoids direct sampling of high free energy states. Rather, the transition states connecting metastable regions of comparable free energies are estimated using Bayesian likelihood maximization. Furthermore, the method incorporates a tunable self-feedback mechanism with classical molecular dynamics for preventing unnecessary sampling that no more effectively contributes to the underlying distributions of metastable states. We have applied this novel protocol in three independent case studies and compared the results against a conventional method. We conclude with the scope of further developments for improved accuracy of the new method and its generalization toward estimation of features in more complex FELs.

DNA barcoding coupled with secondary structure information enhances Achyranthes species resolution

Species of the genus Achyranthes are known to possess immense medicinal value leading to its inclusion in Ayurveda. A. aspera has been widely used in all the traditional Indian systems of medicine, while A. bidentata is mentioned in Chinese, Japanese and Korean pharmacopoeias. Molecular authentication of any medicinal plant species is a prerequisite for the success of its herbal business. Presently, DNA barcoding provides a successful tool for controlling the quality of medicinal plant materials in the trade. Here, we have evaluated four different barcode loci and their efficiency in delineating the Achyranthes species. The internal transcribed spacer 2 (ITS2) barcode proved to be the best performing marker analyzed through barcode gap estimation, BOLD and Bayesian analysis. The inter- and intra-specific genetic divergence observed among and within the Achyranthes species was validated through the Wilcoxon signed-rank test. Further secondary structure modeling of the ITS2 region was performed for better resolution at the species level. The secondary structure was generated based on the lowest free energy state deduced through the mfold web server followed by structure alignment through LocARNA web server. Analysis showed that the helix III and IV possess the maximum variability along with the central ring in differentiating the species. A total of fourteen single-nucleotide polymorphisms (SNPs) identified in the 200 aligned ITS2 dataset could be useful for the development of species-specific marker(s) in future. Through this study we recommend the use of a combination of secondary structure information with DNA barcoding for significantly improving the species identification resolution.

Theory of radio-frequency spectroscopy of impurities in quantum gases

We present a theory of radio-frequency spectroscopy of impurities interacting with a quantum gas at finite temperature. By working in the canonical ensemble of a single impurity, we show that the impurity spectral response is directly connected to the finite-temperature equation of state (free energy) of the impurity. We consider two different response protocols: "injection", where the impurity is introduced into the medium from an initially non-interacting state; and "ejection", where the impurity is ejected from an initially interacting state with the medium. We show that there is a simple mapping between injection and ejection spectra, which is connected to the detailed balance condition in thermal equilibrium. To illustrate the power of our approach, we specialize to the case of the Fermi polaron, corresponding to an impurity atom that is immersed in a non-interacting Fermi gas. For a mobile impurity with a mass equal to the fermion mass, we employ a finite-temperature variational approach to obtain the impurity spectral response. We find a striking non-monotonic dependence on temperature in the impurity free energy, the contact, and the radio-frequency spectra. For the case of an infinitely heavy Fermi polaron, we derive exact results for the finite-temperature free energy, thus generalizing Fumi's theorem to arbitrary temperature. We also determine the exact dynamics of the contact after a quench of the impurity-fermion interactions. Finally, we show that the injection and ejection spectra obtained from the variational approach compare well with the exact spectra, thus demonstrating the accuracy of our approximate method.