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1. An ab-initio study on the thermodynamics of disulfide, sulfide, and bisulfide incorporation into apatite and the development of a more comprehensive temperature, pressure, pH, and composition-dependent model for ionic substitution in minerals

   https://doi.org/10.2138/am-2022-8250  

   Kim, YoungJae ; Konecke, Brian ; Simon, Adam ; Fiege, Adrian ; Becker, Udo ( November 2022 , American Mineralogist)

   The mineral apatite, Ca10(PO4)6(F,OH,Cl)2, incorporates sulfur (S) during crystallization from S-bearing hydrothermal fluids and silicate melts. Our previous studies of natural and experimental apatite demonstrate that the oxidation state of S in apatite varies systematically as a function of oxygen fugacity (fO2). The S oxidation states –1 and –2 were quantitatively identified in apatite crystallized from reduced, S-bearing hydrothermal fluids and silicate melts by using sulfur K-edge X-ray absorption near-edge structure spectroscopy (S-XANES) where S 6+/ΣS in apatite increases from ~0 at FMQ-1 to ~1 at FMQ+2, where FMQ refers to the fayalite-magnetite-quartz fO2 buffer. In this study, we employ quantum-mechanical calculations to investigate the atomistic structure and energetics of S(-I) and S(-II) incorporated into apatite and elucidate incorporation mechanisms.

   One S(-I) species (disulfide, S22−) and two S(-II) species (bisulfide, HS−, and sulfide, S2−) are investigated as possible forms of reduced S species in apatite. In configuration models for the simulation, these reduced S species are positioned along the c-axis channel, originally occupied by the column anions F, Cl, and OH in the end-member apatites. In the lowest-energy configurations of S-incorporated apatite, disulfide prefers to be positioned halfway between the mirror planes at z = 1/4 and 3/4. In contrast, the energy-optimized bisulfide is located slightly away from the mirror planes by ~0.04 fractional units in the c direction. The energetic stability of these reduced S species as a function of position along the c-axis can be explained by the geometric and electrostatic constraints of the Ca and O planes that constitute the c-axis channel.

   The thermodynamics of incorporation of disulfide and bisulfide into apatite is evaluated by using solid-state reaction equations where the apatite host and a solid S-bearing source phase (pyrite and Na2S2(s) for disulfide; troilite and Na2S(s) for sulfide) are the reactants, and the S-incorporated apatite and an anion sink phase are the products. The Gibbs free energy (ΔG) is lower for incorporation with Na-bearing phases than with Fe-bearing phases, which is attributed to the higher energetic stability of the iron sulfide minerals as a source phase for S than the sodium sulfide phases. The thermodynamics of incorporation of reduced S is also evaluated by using reaction equations involving dissolved disulfide and sulfide species [HnS(aq)(2−n) and HnS(aq)(2−n); n = 0, 1, and 2] as a source phase. The ΔG of S-incorporation increases for fluorapatite and chlorapatite, and decreases for hydroxylapatite, as these species are protonated (i.e., as n changes from 0 to 2). These thermodynamic results demonstrate that the presence of reduced S in apatite is primarily controlled by the chemistry of magmatic and hydrothermal systems where apatite forms (e.g., an abundance of Fe; solution pH). Ultimately, our methodology developed for evaluating the thermodynamics of S incorporation in apatite as a function of temperature, pH, and composition is highly applicable to predicting the trace and volatile element incorporation in minerals in a variety of geological systems. In addition to solid-solid and solid-liquid equilibria treated here at different temperatures and pH, the methodology can be easily extended to different pressure conditions by just performing the quantum-mechanical calculations at elevated pressures.

    

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2. An ab-initio study on the thermodynamics of disulfide, sulfide, and bisulfide incorporation into apatite and the development of a more comprehensive temperature, pressure, pH, and composition-dependent model for ionic substitution in minerals

   Young Jae Kim, Brian Konecke ( September 2022 , The American mineralogist)

   The mineral apatite, Ca10(PO4)6(F,OH,Cl)2, incorporates sulfur (S) during crystallization from S-bearing hydrothermal fluids and silicate melts. Our previous studies of natural and experimental apatite demonstrate that the oxidation state of S in apatite varies systematically as a function of oxygen fugacity (fO2). The S oxidation states –1 and –2 were quantitatively identified in apatite crystallized from reduced, S-bearing hydrothermal fluids and silicate melts by using sulfur K-edge X‑ray absorption near-edge structure spectroscopy (S-XANES) where S6+/ΣS in apatite increases from ~0 at FMQ-1 to ~1 at FMQ+2, where FMQ refers to the fayalite-magnetite-quartz fO2 buffer. In this study, we employ quantum-mechanical calculations to investigate the atomistic structure and energetics of S(-I) and S(-II) incorporated into apatite and elucidate incorporation mechanisms. One S(-I) species (disulfide, S22−) and two S(-II) species (bisulfide, HS−, and sulfide, S2−) are investigated as possible forms of reduced S species in apatite. In configuration models for the simulation, these reduced S species are positioned along the c-axis channel, originally occupied by the column anions F, Cl, and OH in the end-member apatites. In the lowest-energy configurations of S-incorporated apatite, disulfide prefers to be positioned halfway between the mirror planes at z = 1/4 and 3/4. In contrast, the energy-optimized bisulfide is located slightly away from the mirror planes by ~0.04 fractional units in the c direction. The energetic stability of these reduced S species as a function of position along the c-axis can be explained by the geometric and electrostatic constraints of the Ca and O planes that constitute the c-axis channel. The thermodynamics of incorporation of disulfide and bisulfide into apatite are evaluated by using solid-state reaction equations where the apatite host and a solid S-bearing source phase (pyrite and Na2S2(s) for disulfide; troilite and Na2S(s) for sulfide) are the reactants, and the S-incorporated apatite and an anion sink phase are the products. The Gibbs free energy (ΔG) is lower for incorporation with Na-bearing phases than with Fe-bearing phases, which is attributed to the higher energetic stability of the iron sulfide minerals as a source phase for S than the sodium sulfide phases. The thermodynamics of incorporation of reduced S are also evaluated by using reaction equations involving dissolved disulfide and sulfide species [HnS2(aq)(2–n) and HnS(aq)(2–n); n = 0, 1, and 2] as a source phase. The ΔG of S-incorporation increases for fluorapatite and chlorapatite and decreases for hydroxylapatite as these species are protonated (i.e., as n changes from 0 to 2). These thermodynamic results demonstrate that the presence of reduced S in apatite is primarily controlled by the chemistry of magmatic and hydrothermal systems where apatite forms (e.g., an abundance of Fe; solution pH). Ultimately, our methodology developed for evaluating the thermodynamics of S incorporation in apatite as a function of temperature, pH, and composition is highly applicable to predicting the trace and volatile element incorporation in minerals in a variety of geological systems. In addition to solid-solid and solid-liquid equilibria treated here at different temperatures and pH, the methodology can be easily extended also to different pressure conditions by just performing the quantum-mechanical calculations at elevated pressures. 

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3. Simulation Data for Design of Peptides that Fold and Self-Assemble on Graphite

   https://doi.org/10.5281/zenodo.6426152  

   Comer, Jeffrey ; Thakkar, Ravindra ; Velásquez-Silva, Astrid ; Miranda-Carvajal, Ingrid ( January 2022 , Zenodo)

   This data set for the manuscript entitled "Design of Peptides that Fold and Self-Assemble on Graphite" includes all files needed to run and analyze the simulations described in the this manuscript in the molecular dynamics software NAMD, as well as the output of the simulations. The files are organized into directories corresponding to the figures of the main text and supporting information. They include molecular model structure files (NAMD psf or Amber prmtop format), force field parameter files (in CHARMM format), initial atomic coordinates (pdb format), NAMD configuration files, Colvars configuration files, NAMD log files, and NAMD output including restart files (in binary NAMD format) and trajectories in dcd format (downsampled to 10 ns per frame). Analysis is controlled by shell scripts (Bash-compatible) that call VMD Tcl scripts or python scripts. These scripts and their output are also included.

   Version: 2.0

   Changes versus version 1.0 are the addition of the free energy of folding, adsorption, and pairing calculations (Sim_Figure-7) and shifting of the figure numbers to accommodate this addition.

   
   Conventions Used in These Files
   ===============================

   Structure Files
   ----------------
   - graph_*.psf or sol_*.psf (original NAMD (XPLOR?) format psf file including atom details (type, charge, mass), as well as definitions of bonds, angles, dihedrals, and impropers for each dipeptide.)

   - graph_*.pdb or sol_*.pdb (initial coordinates before equilibration)
   - repart_*.psf (same as the above psf files, but the masses of non-water hydrogen atoms have been repartitioned by VMD script repartitionMass.tcl)
   - freeTop_*.pdb (same as the above pdb files, but the carbons of the lower graphene layer have been placed at a single z value and marked for restraints in NAMD)
   - amber_*.prmtop (combined topology and parameter files for Amber force field simulations)
   - repart_amber_*.prmtop (same as the above prmtop files, but the masses of non-water hydrogen atoms have been repartitioned by ParmEd)

   Force Field Parameters
   ----------------------
   CHARMM format parameter files:
   - par_all36m_prot.prm (CHARMM36m FF for proteins)
   - par_all36_cgenff_no_nbfix.prm (CGenFF v4.4 for graphene) The NBFIX parameters are commented out since they are only needed for aromatic halogens and we use only the CG2R61 type for graphene.
   - toppar_water_ions_prot_cgenff.str (CHARMM water and ions with NBFIX parameters needed for protein and CGenFF included and others commented out)

   Template NAMD Configuration Files
   ---------------------------------
   These contain the most commonly used simulation parameters. They are called by the other NAMD configuration files (which are in the namd/ subdirectory):
   - template_min.namd (minimization)
   - template_eq.namd (NPT equilibration with lower graphene fixed)
   - template_abf.namd (for adaptive biasing force)

   Minimization
   -------------
   - namd/min_*.0.namd

   Equilibration
   -------------
   - namd/eq_*.0.namd

   Adaptive biasing force calculations
   -----------------------------------
   - namd/eabfZRest7_graph_chp1404.0.namd
   - namd/eabfZRest7_graph_chp1404.1.namd (continuation of eabfZRest7_graph_chp1404.0.namd)

   Log Files
   ---------
   For each NAMD configuration file given in the last two sections, there is a log file with the same prefix, which gives the text output of NAMD. For instance, the output of namd/eabfZRest7_graph_chp1404.0.namd is eabfZRest7_graph_chp1404.0.log.

   Simulation Output
   -----------------
   The simulation output files (which match the names of the NAMD configuration files) are in the output/ directory. Files with the extensions .coor, .vel, and .xsc are coordinates in NAMD binary format, velocities in NAMD binary format, and extended system information (including cell size) in text format. Files with the extension .dcd give the trajectory of the atomic coorinates over time (and also include system cell information). Due to storage limitations, large DCD files have been omitted or replaced with new DCD files having the prefix stride50_ including only every 50 frames. The time between frames in these files is 50 * 50000 steps/frame * 4 fs/step = 10 ns. The system cell trajectory is also included for the NPT runs are output/eq_*.xst.

   Scripts
   -------
   Files with the .sh extension can be found throughout. These usually provide the highest level control for submission of simulations and analysis. Look to these as a guide to what is happening. If there are scripts with step1_*.sh and step2_*.sh, they are intended to be run in order, with step1_*.sh first.

   
   CONTENTS
   ========

   The directory contents are as follows. The directories Sim_Figure-1 and Sim_Figure-8 include README.txt files that describe the files and naming conventions used throughout this data set.

   Sim_Figure-1: Simulations of N-acetylated C-amidated amino acids (Ac-X-NHMe) at the graphite–water interface.

   Sim_Figure-2: Simulations of different peptide designs (including acyclic, disulfide cyclized, and N-to-C cyclized) at the graphite–water interface.

   Sim_Figure-3: MM-GBSA calculations of different peptide sequences for a folded conformation and 5 misfolded/unfolded conformations.

   Sim_Figure-4: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 370 K.

   Sim_Figure-5: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 295 K.

   Sim_Figure-5_replica: Temperature replica exchange molecular dynamics simulations for the peptide cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) with 20 replicas for temperatures from 295 to 454 K.

   Sim_Figure-6: Simulation of the peptide molecule cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) in free solution (no graphite).

   Sim_Figure-7: Free energy calculations for folding, adsorption, and pairing for the peptide CHP1404 (sequence: cyc(GTGSGTG-GPGG-GCGTGTG-SGPG)). For folding, we calculate the PMF as function of RMSD by replica-exchange umbrella sampling (in the subdirectory Folding_CHP1404_Graphene/). We make the same calculation in solution, which required 3 seperate replica-exchange umbrella sampling calculations (in the subdirectory Folding_CHP1404_Solution/). Both PMF of RMSD calculations for the scrambled peptide are in Folding_scram1404/. For adsorption, calculation of the PMF for the orientational restraints and the calculation of the PMF along z (the distance between the graphene sheet and the center of mass of the peptide) are in Adsorption_CHP1404/ and Adsorption_scram1404/. The actual calculation of the free energy is done by a shell script ("doRestraintEnergyError.sh") in the 1_free_energy/ subsubdirectory. Processing of the PMFs must be done first in the 0_pmf/ subsubdirectory. Finally, files for free energy calculations of pair formation for CHP1404 are found in the Pair/ subdirectory.

   Sim_Figure-8: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) where the peptides are far above the graphene–water interface in the initial configuration.

   Sim_Figure-9: Two replicates of a simulation of nine peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 370 K.

   Sim_Figure-9_scrambled: Two replicates of a simulation of nine peptide molecules with the control sequence cyc(GGTPTTGGGGGGSGGPSGTGGC) at the graphite–water interface at 370 K.

   Sim_Figure-10: Adaptive biasing for calculation of the free energy of the folded peptide as a function of the angle between its long axis and the zigzag directions of the underlying graphene sheet.

    

   This material is based upon work supported by the US National Science Foundation under grant no. DMR-1945589. A majority of the computing for this project was performed on the Beocat Research Cluster at Kansas State University, which is funded in part by NSF grants CHE-1726332, CNS-1006860, EPS-1006860, and EPS-0919443. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562, through allocation BIO200030. 

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4. Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models

   https://doi.org/10.21468/SciPostPhys.15.2.044  

   Zhang, Zhao ; Klich, Israel ( January 2023 , SciPost Physics)

   We generalize the area-law violating models of Fredkin and Motzkin spin chains into two dimensions by building quantum six- and nineteen-vertex models with correlated interactions. The Hamiltonian is frustration free, and its projectors generate ergodic dynamics within the subspace of height configuration that are non negative. The ground state is a volume- and color-weighted superposition of classical bi-color vertex configurations with non-negative heights in the bulk and zero height on the boundary. The entanglement entropy between subsystems has a phase transition as the q q -deformation parameter is tuned, which is shown to be robust in the presence of an external field acting on the color degree of freedom. The ground state undergoes a quantum phase transition between area- and volume-law entanglement phases with a critical point where entanglement entropy scales as a function L\log L L log L of the linear system size L L . Intermediate power law scalings between L\log L L log L and L^2 L 2 can be achieved with an inhomogeneous deformation parameter that approaches 1 at different rates in the thermodynamic limit. For the q>1 q > 1 phase, we construct a variational wave function that establishes an upper bound on the spectral gap that scales as q^{-L^3/8} q − L 3 / 8 . 

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5. Zentropy Theory for Positive and Negative Thermal Expansion

   https://doi.org/10.1007/s11669-022-00942-z  

   Liu, Zi-Kui ; Wang, Yi ; Shang, Shun-Li ( January 2022 , Journal of Phase Equilibria and Diffusion)

   It has been observed in both natural and man-made materials that volume sometimes decreases with increasing temperature. Though mechanistic understanding has been gained for some individual materials, a general answer to the question “Why does volume sometimes decrease with the increase of temperature?” remains lacking. Based on the thermodynamic relation that the derivative of volume with respect to temperature, i.e., thermal expansion, is equal to the negative derivative of entropy with respect to pressure, we developed a general theory in terms of multiscale entropy to understand and predict the change of volume as a function of temperature, which is termed as zentropy theory in the present work. It is shown that a phase at high temperatures is a statistical representation of the ground-state stable and multiple nonground-state metastable configurations. It is demonstrated that when the volumes of the nonground-state configurations with high probabilities are smaller than that of the ground-state configuration, the volume of the phase may decrease with the increase of temperature in certain ranges of temperature-pressure combinations, depicting the negative divergency of thermal expansion at the critical point. As examples, positive and negative divergencies of thermal expansion are predicted at the critical points of Ce and Fe3Pt, respectively, along with the temperature and pressure ranges for abnormally positive and negative thermal expansions. The authors believe that the zentropy theory is applicable to predict anomalies of other physical properties of phases because the change of entropy drives the responses of a system to external stimuli. 

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