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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Intermolecular electron transfer from intramolecular excitation and coherent acoustic phonon generation in a hydrogen-bonded charge-transfer solid

Organic materials that produce coherent lattice phonon excitations in response to external stimuli may provide next generation solutions in a wide range of applications. However, for these materials to lead to functional devices in technology, a full understanding of the possible driving forces of coherent lattice phonon generation must be attained. To facilitate the achievement of this goal, we have undertaken an optical spectroscopic study of an organic charge-transfer material formed from the ubiquitous reduction-oxidation pair hydroquinone and p-benzoquinone. Upon pumping this material, known as quinhydrone, on its intermolecular charge transfer resonance as well as an intramolecular resonance of p-benzoquinone, we find sub-cm{sup −1} oscillations whose dispersion with probe energy resembles that of a coherent acoustic phonon that we argue is coherently excited following changes in the electron density of quinhydrone. Using the dynamical information from these ultrafast pump-probe measurements, we find that the fastest process we can resolve does not change whether we pump quinhydrone at either energy. Electron-phonon coupling from both ultrafast coherent vibrational and steady-state resonance Raman spectroscopies allows us to determine that intramolecular electronic excitation of p-benzoquinone also drives the electron transfer process in quinhydrone. These results demonstrate the wide range of electronic excitations of the parent of molecules found in many functional organic materials that can drive coherent lattice phonon excitations useful for applications in electronics, photonics, and information technology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Synthesis, structural characterization, Hirshfeld surface analysis and spectroscopic studies of cadmium (II) chloride complex with 4-hydroxy-1-methylpiperidine

The chemical preparation, crystal structure, Hirshfeld surface analysis and spectroscopic characterization of the novel cadmium (II) 4-hydroxy-1-methylpiperidine complex, Cd{sub 4}Cl{sub 10}(C{sub 6}H{sub 14}NO){sub 2}·2H{sub 2}O, have been reported. The atomic arrangement can be described as built up by an anionic framework, formed by edge sharing CdCl{sub 6} and CdCl{sub 5}O octahedral linear chains spreading along the a-axis. These chains are interconnected by water molecules via O–H⋯Cl and O–H⋯O hydrogen bonds to form layers parallel to (011) plane. The organic cations are inserted between layers through C–H⋯Cl hydrogen bonds. Investigation of intermolecular interactions and crystal packing via Hirshfeld surface analysis reveals that the H{sub C}⋯Cl and H{sub C}⋯H{sub C} intermolecular interactions are the most abundant contacts of the organic cation in the crystal packing. The statistical analysis of crystal contacts reveals the driving forces in the packing formation. The {sup 13}C and {sup 15}N CP-MAS NMR spectra are in agreement with the X-ray structure. The vibrational absorption bands were identified by infrared spectroscopy. DFT calculations allowed the attribution of the NMR peaks and of the IR bands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Molecular dynamics simulation studies of 1,3-dimethyl imidazolium nitrate ionic liquid with water

The fundamental understanding of intermolecular interactions of ionic liquids (ILs) with water is essential in predicting IL–water thermodynamic properties. In this study, intermolecular or noncovalent interactions were studied for 1,3-dimethyl imidazolium [DMIM]+ cation and nitrate [NO 3 ] – anion with water, employing quantum mechanics and molecular dynamics simulations. Molecular dynamics simulations were performed using a revised multipolar polarizable force field. The effect of water on ionic liquids was evaluated in terms of thermodynamic and dynamic properties. Thermodynamic properties included liquid densities ρ, excess molar volumes ΔV E , and liquid structures g(r)⁠. Dynamic properties included self-diffusion coefficients D of mixture constituents as a function of water concentration. The density of ionic liquid–water mixtures monotonically decrease with increasing concentration of water. A negative excess volume was obtained for low and high water concentrations, demonstrating strong intermolecular interactions of water with ionic liquid components. Liquid structures of ionic liquid–water mixtures revealed a tendency for anions to interact with cations at shorter intermolecular distances when the water concentration is increased. Diffusion rates were found to increase for all mixture components with increase in the fraction of water. A significant change in the diffusion rate was found at ~0.3 weight fraction of water. However, the water self-diffusion coefficient was dominant at all concentrations. Furthermore, the ratio of water/anion and anion/cation self-diffusion coefficients was found to decrease linearly with increasing concentration of water molecules.

36 MATERIALS SCIENCE↗
DOE OSTI2016

On interfacial properties of tetrahydrofuran: Atomistic and coarse-grained models from molecular dynamics simulation

We have determined the interfacial properties of tetrahydrofuran (THF) from direct simulation of the vapor-liquid interface. The molecules are modeled using six different molecular models, three of them based on the united-atom approach and the other three based on a coarse-grained (CG) approach. In the first case, THF is modeled using the transferable parameters potential functions approach proposed by Chandrasekhar and Jorgensen [J. Chem. Phys. 77, 5073 (1982)] and a new parametrization of the TraPPE force fields for cyclic alkanes and ethers [S. J. Keasler et al., J. Phys. Chem. B 115, 11234 (2012)]. In both cases, dispersive and coulombic intermolecular interactions are explicitly taken into account. In the second case, THF is modeled as a single sphere, a diatomic molecule, and a ring formed from three Mie monomers according to the SAFT-γ Mie top-down approach [V. Papaioannou et al., J. Chem. Phys. 140, 054107 (2014)]. Simulations were performed in the molecular dynamics canonical ensemble and the vapor-liquid surface tension is evaluated from the normal and tangential components of the pressure tensor along the simulation box. In addition to the surface tension, we have also obtained density profiles, coexistence densities, critical temperature, density, and pressure, and interfacial thickness as functions of temperature, paying special attention to the comparison between the estimations obtained from different models and literature experimental data. The simulation results obtained from the three CG models as described by the SAFT-γ Mie approach are able to predict accurately the vapor-liquid phase envelope of THF, in excellent agreement with estimations obtained from TraPPE model and experimental data in the whole range of coexistence. However, Chandrasekhar and Jorgensen model presents significant deviations from experimental results. We also compare the predictions for surface tension as obtained from simulation results for all the models with experimental data. The three CG models predict reasonably well (but only qualitatively) the surface tension of THF, as a function of temperature, from the triple point to the critical temperature. On the other hand, only the TraPPE united-atoms models are able to predict accurately the experimental surface tension of the system in the whole temperature range.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Influence of Long-Range Forces on the Transition States and Dynamics of NaCl Ion-Pair Dissociation in Water

We study NaCl ion-pair dissociation in a dilute aqueous solution using computer simulations both for the full system with long-range Coulomb interactions and for a well-chosen reference system with short-range intermolecular interactions. Analyzing results using concepts from Local Molecular Field (LMF) theory and the recently proposed AI-based analysis tool “State predictive information bottleneck” (SPIB), we show that the system with short-range interactions can accurately reproduce the transition rate for the dissociation process, the dynamics for moving between the underlying metastable states, and the transition state ensemble. Contributions from long-range interactions can be largely neglected for these processes because long-range forces from the direct interionic Coulomb interactions are almost completely canceled (>90%) by those from solvent interactions over the length scale where the transition takes place. Thus, for this important monovalent ion-pair system, short-range forces alone are able to capture detailed consequences of the collective solvent motion, allowing the use of physically suggestive and computationally efficient short-range models for the dissociation event. Here, we believe that the framework here should be applicable to disentangling mechanisms for more complex processes such as multivalent ion disassociation, where previous work has suggested that long-range contributions may be more important.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Optimization of the Reax force field for the lithium–oxygen system using a high fidelity charge model

Studies using molecular dynamics (MD) have long struggled to simulate the failure modes of materials, predicting unrealistically high ductility and failing to capture brittle fracture. The primary cause of this shortcoming is an inadequate description of bond breaking. While reactive force fields such as ReaxFF show improvements compared to traditional force fields, the charge models used yield unphysical partial charges, especially during dissociation of ionic bonds. This flaw may be remedied by using the atom-condensed Kohn–Sham density functional theory (DFT) approximated to a second order (ACKS2) charge model for determining partial charges. In this work, we present a new ACKS2-enabled Reax force field for fracture simulations of lithium oxide systems, which was obtained by training against an extensive set of DFT, multireference configuration interaction (MRCI), and MRCI+Q reference data using genetic optimization techniques. This new force field significantly improves the bond breaking behavior, but still cannot fully capture the brittle fracture in MD simulations, suggesting more research is needed to improve simulation of brittle fracture.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Impact of Rigidity on Molecular Self-Assembly

Rigid, cage-like molecules, like diamondoids, show unique self-assembly behavior, such as templating 1-D nanomaterial assembly via pathways that are typically blocked for such bulky substituents. We investigate molecular forces between diamondoids to explore why molecules with high structural rigidity exhibit these novel assembly pathways. The rigid nature of diamondoids significantly lowers configurational entropy, and we hypothesize that this influences molecular interaction forces. To test this concept, we calculated the distance-dependent impact of entropy on assembly using molecular dynamics simulations. To isolate pairwise entropic and enthalpic contributions to assembly, we considered pairs of molecules in a thermal bath, fixed at set intermolecular separations but otherwise allowed to freely move. By comparing diamondoids to linear alkanes, we draw out the impact of rigidity on the entropy and enthalpy of pairwise interactions. We find that linear alkanes actually exhibit stronger van der Waals interactions than diamondoids at contact, because the bulky structure of diamondoids induces larger net atomic separations. Yet, we also find that diamondoids pay lower entropic penalties when assembling into contact pairs. Thus, the cage-like shape of diamondoids introduces an enthalpic penalty at contact, but the penalty is counterbalanced by entropic effects. Investigating the distance dependence of entropic forces provides a mechanism to explore how rigidity influences molecular assembly. Our results show that low entropic penalties paid by diamondoids can explain the effectiveness of diamondoids in templating nanomaterial assembly. Hence, tuning molecular rigidity can be an effective strategy for controlling the assembly of functional materials, such as biomimetic surfaces and nanoscale materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A Simple Kinetic Model for the Phase Transition of the van der Waals Fluid

A simple kinetic model, which is presumably minimum, for the phase transition of the van der Waals fluid is presented. In the model, intermolecular collisions for a dense gas has not been treated faithfully. Instead, the expected interactions as the non-ideal gas effect are confined in a self-consistent force term. Collision term plays just a role of thermal bath. Accordingly, it conserves neither momentum nor energy, even globally. It is demonstrated that (i) by a natural separation of the mean-field self-consistent potential, the potential for the non-ideal gas effect is determined from the equation of state for the van der Waals fluid, with the aid of the balance equation of momentum, (ii) a functional which monotonically decreases in time is identified by the H theorem and is found to have a close relation to the Helmholtz free energy in thermodynamics, and (iii) the Cahn–Hilliard type equation is obtained in the continuum limit of the present kinetic model. Numerical simulations based on the Cahn–Hilliard type equation are also performed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Thermodynamics of Small Alkali Metal Halide Cluster Ions: Comparison of Classical Molecular Simulations with Experiment and Quantum Chemistry

We evaluate the ability of selected classical molecular models to describe the thermodynamic and structural aspects of gas-phase hydration of alkali halide ions and the formation of small water clusters. To understand the effect of many-body interactions (polarization) and charge penetration effects on the accuracy of a force field, we perform Monte Carlo simulations with three rigid water models using different functional forms to account for these effects: (i) point charge non-polarizable SPC/E, (ii) Drude point charge polarizable SWM4- DP, and (iii) Drude Gaussian charge polarizable BK3. Model predictions are compared with experimental Gibbs free energies and enthalpies of ion hydration, and with microscopic structural properties obtained from quantum DFT calculations. We find that all three models provide comparable predictions for pure water clusters and cation hydration, but differ significantly in their description of anion hydration. None of the investigated classical force fields can consistently and quantitatively reproduce the experimental gas phase hydration thermodynamics. The outcome of this study highlights the relation between the functional form that describes the effective intermolecular interactions and the accuracy of the resulting ion hydration properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Deconstructing the Local Intermolecular Ordering and Dynamics of Liquid Chloroform and Bromoform

Local intermolecular structure and dynamics of the polar molecular liquids chloroform and bromoform are studied by molecular dynamics simulation. Structural distribution functions, including 1- and 2-D pair correlations and dipole contour plots allow direct comparison and show agreement with recent analyses of diffraction experiments. Studies of the haloforms’ reorientational dynamics and longevity of structural features resulting from intermolecular interaction extend previous work toward deeper understanding of the factors controlling these features. Analyses of ensemble average structures and dynamical properties isolate mass, electrostatics, and steric packing as driving forces or contributing factors for the observed ordering and dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Self-assembling of formic acid on the partially oxidized p (2×1) Cu(110) surface reconstruction at low coverages

Carbon dioxide (CO 2 ) reduction for synthetic fuel generation could be an integral part of a sustainable energy future. Copper (Cu) is the leading electrocatalyst for CO 2 reduction to produce multiple C-containing products such as C1 and C2 hydrocarbons and oxygenates. Understanding the mechanisms leading to their production could help optimize these pathways further. Adsorption studies of the many possible intermediates on well-characterized surfaces are crucial to elucidating these mechanisms. In this work, we explore the adsorption configurations of formic acid (HCOOH) on the surface of the partially oxidized p (2 × 1) reconstruction of the Cu(110) surface, using low-temperature scanning tunneling and atomic force microscopy, in conjunction with density functional theory modeling. We find that HCOOH adsorbs favorably on the CuO chain comprising the reconstruction. The adsorption interactions involve dative bonding of the carbonyl O to the oxidized Cu and hydrogen bonding of the OH group to the surface O or to an adjacently adsorbed HCOOH molecule. Furthermore, cooperative adsorption of the molecules occurs, forming two- to three-molecule-long oligomer chains, facilitated by intermolecular hydrogen bonding and mutual polarization of the CuO acid-base adsorption sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Chiral assembly of weakly curled hard rods: Effect of steric chirality and polarity

We theoretically investigate the pitch of lyotropic cholesteric phases composed of slender rods with steric chirality transmitted via a weak helical deformation of the backbone. In this limit, the model is amenable to analytical treatment within Onsager theory and a closed expression for the pitch versus concentration and helical shape can be derived. Within the same framework, we also briefly review the possibility of alternative types of chiral order, such as twist-bend or screw-like nematic phases, finding that cholesteric order dominates for weakly helical distortions. While long-ranged or “soft” chiral forces usually lead to a pitch decreasing linearly with concentration, steric chirality leads to a much steeper decrease of quadratic nature. This reveals a subtle link between the range of chiral intermolecular interaction and the pitch sensitivity with concentration. A much richer dependence on the thermodynamic state is revealed for polar helices where parallel and anti-parallel pair alignments along the local director are no longer equivalent. It is found that weak temperature variations may lead to dramatic changes in the pitch, despite the lyotropic nature of the assembly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Spectroscopic identification of ethanol-water conformers by large-amplitude hydrogen bond librational modes

The far-infrared absorption spectra have been recorded for hydrogen-bonded complexes of water with ethanol embedded in cryogenic neon matrices at 2.8 K. The partial isotopic H/D-substitution of the ethanol subunit enabled by a dual inlet deposition procedure enables the observation and unambiguous assignment of the intermolecular high-frequency out-of-plane and the low-frequency in-plane donor OH librational modes for two different conformations of the mixed binary ethanol/water complex. The resolved donor OH librational bands confirm directly previous experimental evidence that ethanol acts as the O⋯HO hydrogen bond acceptor in the two most stable conformations. In the most stable conformation, the water subunit forces the ethanol molecule into its less stable gauche configuration upon dimerization owing to a cooperative secondary weak O⋯HC hydrogen bond interaction evidenced by a significantly blue-shift of the low-frequency in-plane donor OH librational band origin. The strong correlation between the low-frequency in-plane donor OH librational motion and the secondary intermolecular O⋯HC hydrogen bond is demonstrated by electronic structure calculations. The experimental findings are further supported by CCSD(T)-F12/aug-cc-pVQZ calculations of the conformational energy differences together with second-order vibrational perturbation theory calculations of the large-amplitude donor OH librational band origins.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Realizing nearly-free-electron like conduction band in a molecular film through mediating intermolecular van der Waals interactions

Collective molecular physical properties can be enhanced from their intrinsic characteristics by templating at material interfaces. Here we report how a black phosphorous (BP) substrate concatenates a nearly-free-electron (NFE) like conduction band of a C 60 monolayer. Scanning tunneling microscopy reveals the C 60 lowest unoccupied molecular orbital (LUMO) band is strongly delocalized in two-dimensions, which is unprecedented for a molecular semiconductor. Experiment and theory show van der Waals forces between C 60 and BP reduce the inter-C 60 distance and cause mutual orientation, thereby optimizing the π-π wave function overlap and forming the NFE-like band. Electronic structure and carrier mobility calculations predict that the NFE band of C 60 acquires an effective mass of 0.53–0.70 m e ( m e is the mass of free electrons), and has carrier mobility of ~200 to 440 cm 2 V -1 s -1 . The substrate-mediated intermolecular van der Waals interactions provide a route to enhance charge delocalization in fullerenes and other organic semiconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Theoretical Study of C-H Bond Cleavage via Concerted Proton-Coupled Electron Transfer in Fluorenyl-Benzoates

Developing new strategies to activate and cleave C-H bonds is important for a broad range of applications. Recently a new approach for C-H bond activation using multi-site concerted proton-coupled electron transfer (PCET) involving intermolecular electron transfer to an oxidant coupled to intramolecular proton transfer was reported. For a series of oxidants reacting with 2-(9H-fluoren-9-yl)benzoate, experimental studies revealed an atypical Brønsted a, defined as the slope of the logarithm of the PCET rate constant versus the logarithm of the equilibrium constant or the scaled driving force. Herein this reaction is modeled with a vibronically nonadiabatic PCET theory. Hydrogen tunneling, thermal sampling of the proton donor-acceptor mode, solute and solvent reorganization, and contributions from excited vibronic states are found to play important roles. The calculations qualitatively reproduce the experimental observation of a Brønsted a significantly less than 0.5 and explain this shallow slope in terms of exoergic processes between pairs of electron-proton vibronic states. These fundamental mechanistic insights may guide the design of more effective strategies for C-H bond activation and cleavage.

Sayfutyarova, Elvira R.↗
DOE OSTI2015

Molecular and Dissociative Adsorption of Water on (TiO 2 ) n Clusters, n = 1–4

In the low energy structures of the (TiO 2 ) n (H 2 O) m (n ≤ 4, m ≤ 2n) and (TiO 2 ) 8 (H 2 O) m (m = 3, 7, 8) clusters were predicted using a global geometry optimization approach, with a number of new lowest energy isomers being found. Water can molecularly or dissociatively adsorb on pure and hydrated TiO 2 clusters. Dissociative adsorption is the dominant reaction for the first two H 2 O adsorption reactions for n = 1, 2, and 4, for the first three H 2 O adsorption reactions for n = 3, and for the first four H 2 O adsorption reactions for n = 8. As more H 2 O’s are added to the hydrated (TiO 2 )n cluster, dissociative adsorption becomes less exothermic as all the Ti centers become 4-coordinate. Furthermore two types of bonds can be formed between the molecularly adsorbed water and TiO 2 clusters: a Lewis acid–base Ti–O(H 2 ) bond or an O···H hydrogen bond. The coupled cluster CCSD(T) results show that at 0 K the H 2 O adsorption energy at a 4-coordinate Ti center is ~15 kcal/mol for the Lewis acid–base molecular adsorption and ~7 kcal/mol for the H-bond molecular adsorption, in comparison to that of 8–10 kcal/mol for the dissociative adsorption. The cluster size and geometry independent dehydration reaction energy, ED, for the general reaction 2(-TiOH) → -TiOTi– + H 2 O at 4-coordinate Ti centers was estimated from the aggregation reaction of nTi(OH) 4 to form the monocyclic ring cluster (TiO 3 H 2 ) n + nH 2 O. E D is estimated to be -8 kcal/mol, showing that intramolecular and intermolecular dehydration reactions are intrinsically thermodynamically allowed for the hydrated (TiO 2 ) n clusters with all of the Ti centers 4-coordinate, which can be hindered by cluster geometry changes caused by such processes. Finally by bending force constants for the TiOTi and OTiO bonds are determined to be 7.4 and 56.0 kcal/(mol·rad 2 ). Infrared vibrational spectra were calculated using density functional theory, and the new bands appearing upon water adsorption were assigned.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1999

Tetragonal Lysozyme Interactions Studied by Site Directed Mutagenesis

A number of recent experimental and theoretical studies have indicated that tetragonal lysozyme crystal growth proceeds by the addition of aggregates, formed by reversible self association of the solute molecules in the bulk solution. Periodic bond chain and atomic force microscopy studies have indicated that the probable growth unit is at minimum a 43 tetramer, and most likely an octamer composed of two complete turns about the 43 axis. If these results are correct, then there are intermolecular interactions which are only formed in the solution and others only formed at the joining of the growth unit to the crystal surface. We have set out to study these interactions, and the correctness of this hypothesis, using site directed mutagenesis of specific amino acid residues involved in the different bonds. We had initially expressed wild type lysozyme in S. cervasiae with yields of approximately 5 mg/L, which were eventually raised to approximately 40 mg/L. We are now moving the expression to the Pichia system, with anticipated yields of 300 to (3)500 mg/L, comparable to what can be obtained from egg whites. An additional advantage of using recombinant protein is the greater genetic homogeneity of the material obtained and the absence of any other contaminating egg proteins. The first mutation experiments are TYR 23 (Registered) PHE or ALA and ASN 113 (Registered) ALA or ASP. Both TYR 23 and ASN 113 form part of the postulated dimerization intermolecular binding site which lead to the formation of the 43 helix. Tyrosine also participates in an intermolecular hydrogen bond with ARG 114. The results of these and subsequent experiments will be discussed.

Crawford, Lisa↗
DOE OSTI2015

From hydrogen bonding to metal coordination and back: Porphyrin-based networks on Ag(111)

The self-assembly of a metal-free porphyrin bearing two pyridyl coordinating sites and two pentyl chains at trans meso positions was investigated under ultrahigh vacuum on a Ag(111) surface by scanning tunneling microscopy (STM). The STM measurements revealed a well-ordered close-packed structure with a rhombic unit cell for coverages ≤1 monolayer with their molecular plane parallel to the surface. The growth direction of the molecular islands is aligned along the step edges, which are restructured due to molecule-substrate interactions. The shorter unit cell vector of the molecular superstructure follows the 〈1-10〉 direction of the Ag(111) substrate. Hydrogen bonds between pyridyl and pyrrole groups of neighboring molecules as well as weak van der Waals forces between the pentyl chains stabilize the superstructure. Deposition of cobalt atoms onto the close-packed structure at room temperature leads to the formation of a hexagonal porous network stabilized by metal-ligand bonding between the pyridyl ligands and the cobalt atoms. Thermal annealing of the Co-coordination network at temperatures >450 K results in the transformation of the hexagonal network into a second close-packed structure. Changes in the molecule-substrate interactions due to metalation of the porphyrin core with Co as well as intermolecular interactions can explain the observed structural transformations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗