Marcus Martin - Academia.edu (original) (raw)
Papers by Marcus Martin
Molecular Physics, Jul 1, 1998
Algorithms are presented to improve the e ciency for the generation of trial orientations and for... more Algorithms are presented to improve the e ciency for the generation of trial orientations and for the calculation of the Rosenbluth weight in a con® gurational-bias Monte Carlo (CBMC) simulation. These algorithms were tested for N p T and N V T simulations of n-octane, 3-methylheptane, and 3,4-dimethylhexane at di erent temperatures and densities using a preliminary version of the TraPPE united-atom representation for the CH 3 , CH 2 and CH groups. It was found that for a system of 144 molecules these algorithms speed up the calculation three times for n-octane and almost four times for 3,4-dimethylhexane, resulting in a decreased di erence in simulation time between a branched molecule and a linear isomer. For larger systems the speedup is even greater. It is shown that the excluded volume of an atom is the dominant term for the selection of a trial orientation, which leads to an improved CBMC algorithm called dual cuto con® gurational-bias Monte Carlo (DC-CBMC).
Journal of Physical Chemistry B, Aug 1, 2000
The Transferable Potentials for Phase Equilibria-United .+tom (Tra.PPE-LJ.A) force ficki for hydr... more The Transferable Potentials for Phase Equilibria-United .+tom (Tra.PPE-LJ.A) force ficki for hydrocarbons is extended to alkenes and alkylbenzenes by introducing the followins pseudo-atoms: CHZ (sp2), CH(sp2), C(sp2), CH(aro), R-C(aro) for the link to aliphatic side chains, and C (are) for the link of two benzene rings. In this united-atom force field. the nonbonded interactions of the hydrocarbon pseudo-atoms are solely governed by Lemwd-Jones 12-6 potentials, and the Lennard-Jones well depth and size parameters for the new pseudo-atoms were determined by fitting to the single-component vapor-liquid phase equilibria of a few selected model compounds. Configurational-bias Monte Carlo simulations in the .N'VT~'ersicn of the Gibbs ensemble were carried out to calculate the sillgle-co~llpol]e~lt vapor-liquid coexistence curves for ethene, propene, l-butene, tnzns-and cis-2-butene. 2methylpropene, 1..5-hexadiene, l-octene, benzene, toluene, ethylbenzene, propylbenzene, isopropylbenzene. o-, m-, and p-xylene, and naphthalene. The phase diagrams for the binary mixtures of (supercritical) ethene/n-heptane and benzene/n-pentane were determined from simulations in the NpT Gibbs ensemble. .Although the TraPPE-U.\ force field is rather simple and makes use of relatively few different pseudo-atoms, its performance. 2 %sjudged by comparisons to other popular force fields and available experimental data. k very satisfactory.
GeTe is a member of a class of materials that undergoes a very rapid phase transition between cry... more GeTe is a member of a class of materials that undergoes a very rapid phase transition between crystalline and amorphous states under the influence of optical excitation or current flow. This class of materials has found application in the rewriteable CD/DVDs and in non-volatile elecrtrical memories. While they have been studied experimentally and theoretically for over thirty years, there has
The Journal of Physical Chemistry C, 2008
We use atomistic molecular dynamics simulations to calculate the binding energy of six different ... more We use atomistic molecular dynamics simulations to calculate the binding energy of six different nucleotide monophosphates (NMPs) to a (6,0) single-wall carbon nanotube in aqueous solution. We examine two different aqueous environments, one with just two sodium counterions and a second consisting of approximately 134 mM sodium chloride solution. We find that the binding energies are generally favorable, of the order of a few kilocalories/mole. The binding energies of the different NMPs were very similar in salt solution, whereas we found a range of binding energies for NMPs in pure water. The binding energies are sensitive to the details of the association of the sodium ions with the phosphate groups and also to the average conformations of the nucleotides.
The Journal of Physical Chemistry B, 1999
Accurate predictions of retention times, retention indices, and partition constants are a long so... more Accurate predictions of retention times, retention indices, and partition constants are a long sought-after goal for theoretical studies in chromatography. Configurational-bias Monte Carlo (CBMC) simulations in the Gibbs ensemble using the transferable potentials for phase equilibria-united atom (TraPPE-UA) force field have been carried out to obtain a microscopic picture of the partitioning of 10 alkane isomers between a helium vapor phase and a squalane liquid phase, a prototypical gas-liquid chromatography system. The alkane solutes include some topological isomers that differ only in the arrangement of their building blocks (e.g., 2,5dimethylhexane and 3,4-dimethylhexane), for which the prediction of the retention order is particularly difficult. The Kovats retention indices, a measure of the relative retention times, are calculated directly from the partition constants and are in good agreement with experimental values. The calculated Gibbs free energies of transfer for the normal alkanes conform to Martin's equation which is the basis of linear free energy relationships used in many process modeling packages. Analysis of radial distribution functions and the corresponding energy integrals does not yield evidence for specific retention structures and shows that the internal energy of solvation is not the main driving force for the separation of topological isomers in this system.
The Journal of Physical Chemistry B, 2005
... Collin D. Wick, John M. Stubbs, § Neeraj Rai, and J. Ilja Siepmann* . Departments of... more ... Collin D. Wick, John M. Stubbs, § Neeraj Rai, and J. Ilja Siepmann* . Departments of Chemistry and of Chemical Engineering and Material Science, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota ...
Molecular Simulation, 2013
The history of the Monte Carlo for complex chemical systems Towhee open source Monte Carlo molecu... more The history of the Monte Carlo for complex chemical systems Towhee open source Monte Carlo molecular simulation tool is discussed. A proof is given that the Widom insertion method for computing the chemical potential is formally correct even when combined with the most general version of arbitrary trial distribution configurational-bias Monte Carlo. A simulation strategy for computing single component vapour–liquid phase coexistence curves is presented as a guide for inexperienced practitioners of Monte Carlo simulations. A review of papers that cite the Towhee code is presented. The paper concludes with a discussion about releasing and sustaining a simulation package that uses an open source software license.
Molecular Physics, 2006
A new formulation of configurational-bias Monte Carlo that uses arbitrary distributions to genera... more A new formulation of configurational-bias Monte Carlo that uses arbitrary distributions to generate trial bond lengths, angles and dihedrals is described and shown to provide similar acceptance rates with substantially less computational effort. Several different trial distributions are studied and a linear combination of the ideal distribution plus Gaussian distributions automatically fit to the energetic and ideal terms is found to give the best results. The use of these arbitrary trial distributions enables a new formulation of coupled-decoupled configurational bias Monte Carlo that has significantly higher acceptance rates for cyclic molecules. The chemical potential measured via a modified Widom insertion is found to be ill-defined in the case of a molecule that has flexible bond lengths due to the unbounded probability distribution that describes the distance between any two atoms. We propose a simple standard state that allows the computation of consistent chemical potentials for molecules with flexible bonds. We show that the chemical potential via Widom insertion is not computed properly for molecules with Coulombic interactions when the number of trials for any of the nonbonded selection steps is greater than one. Finally, we demonstrate the power of the new algorithms by sampling the side-chain conformations of a polypeptide.
Journal of the American Chemical Society, 1997
ABSTRACT
Journal of Physics: Conference Series, 2006
High performance computing for the application of molecular theories to biological systems. ... C... more High performance computing for the application of molecular theories to biological systems. ... Conference: Proposed for presentation at the DOE/SCIDAC Conference held June 25-29, 2006 in Denver, CO.
The Journal of Chemical Physics, 1998
An implicit solvent simulation of a neutral linear chain in a dense solvent. ... Journal Name: Pr... more An implicit solvent simulation of a neutral linear chain in a dense solvent. ... Journal Name: Proposed for publication in Physical Review Letters.
Journal of Physical Chemistry B, 2000
The Transferable Potentials for Phase Equilibria-United Atom (TraPPE-UA) force field for hydrocar... more The Transferable Potentials for Phase Equilibria-United Atom (TraPPE-UA) force field for hydrocarbons is extended to alkenes and alkylbenzenes by introducing the following pseudo-atoms: CHâ(sp²), CH(sp²), CH(aro), R-C(aro) for the link to aliphatic side chains, and C(aro) for the link of two benzene rings. In this united-atom force field, the nonbonded interactions of the hydrocarbon pseudo-atoms are solely governed by Lennard-Jones
Abstract: this paper we discuss a seriesof configurational-bias Monte-Carlo (CBMC) simulations th... more Abstract: this paper we discuss a seriesof configurational-bias Monte-Carlo (CBMC) simulations that use a rigorousmolecular theory based implicit solvent to achieve e#cient sampling of a chainmolecule in a dense liquid solvent. The molecular theory captures solvent packingaround the chain molecule as well as the energetic e#ects of solvent-polymerinteractions. It also accounts for entropic e#ects in the solvent
Public reporting burden for this collection of information is estimated to average 1 hour per res... more Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188),
The Journal of Physical Chemistry B
We present the results of molecular dynamics simulations of n-butane and isobutane in silicalite.... more We present the results of molecular dynamics simulations of n-butane and isobutane in silicalite. We begin with a comparison of the bulk adsorption and diffusion properties for two different parameterizations of the interaction potential between the hydrocarbon species, both of which have been shown to reproduce experimental gas-liquid coexistence curves. We examine diffusion as a function of the loading of the zeolite, as well as the temperature dependence of the diffusion constant at loading and for infinite dilution. We continue with simulations in which interfaces are formed between single component gases and the zeolite. After reaching equilibrium, we examine the dynamics of exchange between the bulk gas and the zeolite. Finally, we calculate the permeability of the zeolite for n-butane and isobutane as a function of pressure. Our simulations are performed for a number of different gas temperatures and pressures, covering a wide range of state points.
Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), 1998
This report describes progress made under the CSRF project Current Topics in Density Functional T... more This report describes progress made under the CSRF project Current Topics in Density Functional Theory. Density functional theory (DFT) is a technique for computing the energetics of molecules and materials. DFT is unique among atomistic simulation techniques in combining a high accuracy approximation to the quantum mechanics describing the chemical bonding in materials with computationally tractible solutions. This combination makes it particularly important and relevant for Sandia's stockpile stewardship mission, a large part of which involves insuring material performance without nuclear testing. DFT techniques have already made important contributions to Sandia's DP programs. However, to have greater and wider impact at Sandia, DFT techniques need to have increased accuracy, they need to provide this accuracy with increased speed, and they need to have increased range as to the problems and conditions they can contribute to. The goal of this project is to achieve these improvements to DFT.
National Laboratories-Recent synthetic activities involving hydrogen clathrate hydrates raised th... more National Laboratories-Recent synthetic activities involving hydrogen clathrate hydrates raised the prospect of utilizing them as an alternative storage material for hydrogen fuel. The current work is a starting point for future studies of hydrogen occupancy of hydrogen clathrate hydrate and its stability. We present studies of the structural and thermal properties of a hydrogen molecule dissolved in liquid water and their possible implication for the hydrogen storage in clathrate hydrates. The radial distribution function, coordination number and coordination number distribution are calculated using different representations of the interatomic forces within molecular dynamics, Monte Carlo and ab initio molecular dynamics simulation frameworks. Although structural details differ in the radial distribution functions generated from the different force fields, all approaches agree that the average and most probable number of water molecules occupying the inner hydration sphere around hydrogen is 16. Furthermore, we estimate the hydrogen hydration free energy. In addition, we will present the quantum mechanical studies of the hydrogen occupancy in single clathrate hydrate cages.
Issuedby Sandia NationalLaboratories,operatedfor the United States Department of Energyby Sandia ... more Issuedby Sandia NationalLaboratories,operatedfor the United States Department of Energyby Sandia Corporation. NOTICE This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness,or usefulnessof any information,apparatus,product, or process disclosed, otirepresentthat its use would not infringe privately owned rights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government,any agency thereof, or any of their contractorsor subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors.
Molecular Physics, Jul 1, 1998
Algorithms are presented to improve the e ciency for the generation of trial orientations and for... more Algorithms are presented to improve the e ciency for the generation of trial orientations and for the calculation of the Rosenbluth weight in a con® gurational-bias Monte Carlo (CBMC) simulation. These algorithms were tested for N p T and N V T simulations of n-octane, 3-methylheptane, and 3,4-dimethylhexane at di erent temperatures and densities using a preliminary version of the TraPPE united-atom representation for the CH 3 , CH 2 and CH groups. It was found that for a system of 144 molecules these algorithms speed up the calculation three times for n-octane and almost four times for 3,4-dimethylhexane, resulting in a decreased di erence in simulation time between a branched molecule and a linear isomer. For larger systems the speedup is even greater. It is shown that the excluded volume of an atom is the dominant term for the selection of a trial orientation, which leads to an improved CBMC algorithm called dual cuto con® gurational-bias Monte Carlo (DC-CBMC).
Journal of Physical Chemistry B, Aug 1, 2000
The Transferable Potentials for Phase Equilibria-United .+tom (Tra.PPE-LJ.A) force ficki for hydr... more The Transferable Potentials for Phase Equilibria-United .+tom (Tra.PPE-LJ.A) force ficki for hydrocarbons is extended to alkenes and alkylbenzenes by introducing the followins pseudo-atoms: CHZ (sp2), CH(sp2), C(sp2), CH(aro), R-C(aro) for the link to aliphatic side chains, and C (are) for the link of two benzene rings. In this united-atom force field. the nonbonded interactions of the hydrocarbon pseudo-atoms are solely governed by Lemwd-Jones 12-6 potentials, and the Lennard-Jones well depth and size parameters for the new pseudo-atoms were determined by fitting to the single-component vapor-liquid phase equilibria of a few selected model compounds. Configurational-bias Monte Carlo simulations in the .N'VT~'ersicn of the Gibbs ensemble were carried out to calculate the sillgle-co~llpol]e~lt vapor-liquid coexistence curves for ethene, propene, l-butene, tnzns-and cis-2-butene. 2methylpropene, 1..5-hexadiene, l-octene, benzene, toluene, ethylbenzene, propylbenzene, isopropylbenzene. o-, m-, and p-xylene, and naphthalene. The phase diagrams for the binary mixtures of (supercritical) ethene/n-heptane and benzene/n-pentane were determined from simulations in the NpT Gibbs ensemble. .Although the TraPPE-U.\ force field is rather simple and makes use of relatively few different pseudo-atoms, its performance. 2 %sjudged by comparisons to other popular force fields and available experimental data. k very satisfactory.
GeTe is a member of a class of materials that undergoes a very rapid phase transition between cry... more GeTe is a member of a class of materials that undergoes a very rapid phase transition between crystalline and amorphous states under the influence of optical excitation or current flow. This class of materials has found application in the rewriteable CD/DVDs and in non-volatile elecrtrical memories. While they have been studied experimentally and theoretically for over thirty years, there has
The Journal of Physical Chemistry C, 2008
We use atomistic molecular dynamics simulations to calculate the binding energy of six different ... more We use atomistic molecular dynamics simulations to calculate the binding energy of six different nucleotide monophosphates (NMPs) to a (6,0) single-wall carbon nanotube in aqueous solution. We examine two different aqueous environments, one with just two sodium counterions and a second consisting of approximately 134 mM sodium chloride solution. We find that the binding energies are generally favorable, of the order of a few kilocalories/mole. The binding energies of the different NMPs were very similar in salt solution, whereas we found a range of binding energies for NMPs in pure water. The binding energies are sensitive to the details of the association of the sodium ions with the phosphate groups and also to the average conformations of the nucleotides.
The Journal of Physical Chemistry B, 1999
Accurate predictions of retention times, retention indices, and partition constants are a long so... more Accurate predictions of retention times, retention indices, and partition constants are a long sought-after goal for theoretical studies in chromatography. Configurational-bias Monte Carlo (CBMC) simulations in the Gibbs ensemble using the transferable potentials for phase equilibria-united atom (TraPPE-UA) force field have been carried out to obtain a microscopic picture of the partitioning of 10 alkane isomers between a helium vapor phase and a squalane liquid phase, a prototypical gas-liquid chromatography system. The alkane solutes include some topological isomers that differ only in the arrangement of their building blocks (e.g., 2,5dimethylhexane and 3,4-dimethylhexane), for which the prediction of the retention order is particularly difficult. The Kovats retention indices, a measure of the relative retention times, are calculated directly from the partition constants and are in good agreement with experimental values. The calculated Gibbs free energies of transfer for the normal alkanes conform to Martin's equation which is the basis of linear free energy relationships used in many process modeling packages. Analysis of radial distribution functions and the corresponding energy integrals does not yield evidence for specific retention structures and shows that the internal energy of solvation is not the main driving force for the separation of topological isomers in this system.
The Journal of Physical Chemistry B, 2005
... Collin D. Wick, John M. Stubbs, § Neeraj Rai, and J. Ilja Siepmann* . Departments of... more ... Collin D. Wick, John M. Stubbs, § Neeraj Rai, and J. Ilja Siepmann* . Departments of Chemistry and of Chemical Engineering and Material Science, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota ...
Molecular Simulation, 2013
The history of the Monte Carlo for complex chemical systems Towhee open source Monte Carlo molecu... more The history of the Monte Carlo for complex chemical systems Towhee open source Monte Carlo molecular simulation tool is discussed. A proof is given that the Widom insertion method for computing the chemical potential is formally correct even when combined with the most general version of arbitrary trial distribution configurational-bias Monte Carlo. A simulation strategy for computing single component vapour–liquid phase coexistence curves is presented as a guide for inexperienced practitioners of Monte Carlo simulations. A review of papers that cite the Towhee code is presented. The paper concludes with a discussion about releasing and sustaining a simulation package that uses an open source software license.
Molecular Physics, 2006
A new formulation of configurational-bias Monte Carlo that uses arbitrary distributions to genera... more A new formulation of configurational-bias Monte Carlo that uses arbitrary distributions to generate trial bond lengths, angles and dihedrals is described and shown to provide similar acceptance rates with substantially less computational effort. Several different trial distributions are studied and a linear combination of the ideal distribution plus Gaussian distributions automatically fit to the energetic and ideal terms is found to give the best results. The use of these arbitrary trial distributions enables a new formulation of coupled-decoupled configurational bias Monte Carlo that has significantly higher acceptance rates for cyclic molecules. The chemical potential measured via a modified Widom insertion is found to be ill-defined in the case of a molecule that has flexible bond lengths due to the unbounded probability distribution that describes the distance between any two atoms. We propose a simple standard state that allows the computation of consistent chemical potentials for molecules with flexible bonds. We show that the chemical potential via Widom insertion is not computed properly for molecules with Coulombic interactions when the number of trials for any of the nonbonded selection steps is greater than one. Finally, we demonstrate the power of the new algorithms by sampling the side-chain conformations of a polypeptide.
Journal of the American Chemical Society, 1997
ABSTRACT
Journal of Physics: Conference Series, 2006
High performance computing for the application of molecular theories to biological systems. ... C... more High performance computing for the application of molecular theories to biological systems. ... Conference: Proposed for presentation at the DOE/SCIDAC Conference held June 25-29, 2006 in Denver, CO.
The Journal of Chemical Physics, 1998
An implicit solvent simulation of a neutral linear chain in a dense solvent. ... Journal Name: Pr... more An implicit solvent simulation of a neutral linear chain in a dense solvent. ... Journal Name: Proposed for publication in Physical Review Letters.
Journal of Physical Chemistry B, 2000
The Transferable Potentials for Phase Equilibria-United Atom (TraPPE-UA) force field for hydrocar... more The Transferable Potentials for Phase Equilibria-United Atom (TraPPE-UA) force field for hydrocarbons is extended to alkenes and alkylbenzenes by introducing the following pseudo-atoms: CHâ(sp²), CH(sp²), CH(aro), R-C(aro) for the link to aliphatic side chains, and C(aro) for the link of two benzene rings. In this united-atom force field, the nonbonded interactions of the hydrocarbon pseudo-atoms are solely governed by Lennard-Jones
Abstract: this paper we discuss a seriesof configurational-bias Monte-Carlo (CBMC) simulations th... more Abstract: this paper we discuss a seriesof configurational-bias Monte-Carlo (CBMC) simulations that use a rigorousmolecular theory based implicit solvent to achieve e#cient sampling of a chainmolecule in a dense liquid solvent. The molecular theory captures solvent packingaround the chain molecule as well as the energetic e#ects of solvent-polymerinteractions. It also accounts for entropic e#ects in the solvent
Public reporting burden for this collection of information is estimated to average 1 hour per res... more Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188),
The Journal of Physical Chemistry B
We present the results of molecular dynamics simulations of n-butane and isobutane in silicalite.... more We present the results of molecular dynamics simulations of n-butane and isobutane in silicalite. We begin with a comparison of the bulk adsorption and diffusion properties for two different parameterizations of the interaction potential between the hydrocarbon species, both of which have been shown to reproduce experimental gas-liquid coexistence curves. We examine diffusion as a function of the loading of the zeolite, as well as the temperature dependence of the diffusion constant at loading and for infinite dilution. We continue with simulations in which interfaces are formed between single component gases and the zeolite. After reaching equilibrium, we examine the dynamics of exchange between the bulk gas and the zeolite. Finally, we calculate the permeability of the zeolite for n-butane and isobutane as a function of pressure. Our simulations are performed for a number of different gas temperatures and pressures, covering a wide range of state points.
Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), 1998
This report describes progress made under the CSRF project Current Topics in Density Functional T... more This report describes progress made under the CSRF project Current Topics in Density Functional Theory. Density functional theory (DFT) is a technique for computing the energetics of molecules and materials. DFT is unique among atomistic simulation techniques in combining a high accuracy approximation to the quantum mechanics describing the chemical bonding in materials with computationally tractible solutions. This combination makes it particularly important and relevant for Sandia's stockpile stewardship mission, a large part of which involves insuring material performance without nuclear testing. DFT techniques have already made important contributions to Sandia's DP programs. However, to have greater and wider impact at Sandia, DFT techniques need to have increased accuracy, they need to provide this accuracy with increased speed, and they need to have increased range as to the problems and conditions they can contribute to. The goal of this project is to achieve these improvements to DFT.
National Laboratories-Recent synthetic activities involving hydrogen clathrate hydrates raised th... more National Laboratories-Recent synthetic activities involving hydrogen clathrate hydrates raised the prospect of utilizing them as an alternative storage material for hydrogen fuel. The current work is a starting point for future studies of hydrogen occupancy of hydrogen clathrate hydrate and its stability. We present studies of the structural and thermal properties of a hydrogen molecule dissolved in liquid water and their possible implication for the hydrogen storage in clathrate hydrates. The radial distribution function, coordination number and coordination number distribution are calculated using different representations of the interatomic forces within molecular dynamics, Monte Carlo and ab initio molecular dynamics simulation frameworks. Although structural details differ in the radial distribution functions generated from the different force fields, all approaches agree that the average and most probable number of water molecules occupying the inner hydration sphere around hydrogen is 16. Furthermore, we estimate the hydrogen hydration free energy. In addition, we will present the quantum mechanical studies of the hydrogen occupancy in single clathrate hydrate cages.
Issuedby Sandia NationalLaboratories,operatedfor the United States Department of Energyby Sandia ... more Issuedby Sandia NationalLaboratories,operatedfor the United States Department of Energyby Sandia Corporation. NOTICE This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness,or usefulnessof any information,apparatus,product, or process disclosed, otirepresentthat its use would not infringe privately owned rights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government,any agency thereof, or any of their contractorsor subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors.