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• S. G. Moustafa, A. J. Schultz, “Generalized Path Integral Energy and Heat Capacity Estimators of Quantum Oscillators and Crystals Using Harmonic Mapping”, J. Chem. Theory Comput. 20, 10132-10146 (2024).
• A. J. Schultz, D. A. Kofke, “Methodical evaluation of Boyle temperatures using Mayer sampling Monte Carlo with application to polymers in implicit solvent”, J. Chem. Phys. 161, 154108 (2024).
• S. G. Moustafa, A. J. Schultz, “Harmonic Oscillator Staging Coordinates for Efficient Path Integral Simulations of Quantum Oscillators and Crystals”, J. Chem. Theory Comput. 20, 7315-7326 (2024).
• S. G. Moustafa, A. J. Schultz, J. F. Douglas, “Efficient single-run implementation of generalized Einstein relation to compute transport coefficients: A binary-based time sampling”, J. Chem. Phys. 160, 024114 (2024). PDF
• A. Bansal, A. J. Schultz, J. F. Douglas, D. A. Kofke, “Probabilistic computations of virial coefficients of polymeric structures described by rigid configurations of spherical particles: A fundamental extension of the ZENO program”, J. Chem. Phys. 157, 224801 (2022). PDF
• A. J. Schultz, D. A. Kofke, “Virial equation of state as a new frontier for computational chemistry”, J. Chem. Phys. 157, 190901 (2022). PDF
• S. G. Moustafa, A. J. Schultz, D. A. Kofke, “Reformulation of expressions for thermoelastic properties of crystals using harmonic mapping”, Phys. Rev. B 106, 104105 (2022). PDF
• N. Gokul, A. J. Schultz, D. A. Kofke, “Speed of Sound in Helium-4 from Ab Initio Acoustic Virial Coefficients”, J. Chem. Eng. Data 66, 3258-3281 (2021).
• Y. Q. Chen, A. J. Schultz, J. R. Errington, “Coupled Monte Carlo and Molecular Dynamics Simulations on Interfacial Properties of Antifouling Polymer Membranes”, J. Phys. Chem. B 125, 8193-8204 (2021).
• A. Bansal, A. J. Schultz, D. A. Kofke, “Evaluation of Osmotic Virial Coefficients via Restricted Gibbs Ensemble Simulations, with Support from Gas-Phase Mixture Coefficients”, J. Phys. Chem. B 125, 7262-7272 (2021).
• A. J. Schultz, D. A. Kofke, “Identifying and estimating bias in overlap-sampling free-energy calculations”, Mol. Simul. 47, 379-389 (2021).
• N. Gokul, A. J. Schultz, D. A. Kofke, “Properties of supercritical N2, O2, CO2, and NH3 mixtures from the virial equation of state”, AIChE J. 67, e17072 (2021). PDF supplementary info
• S. G. Moustafa, A. Purohit, A. J. Schultz, D. A. Kofke, “pyHMA: A VASP post-processor for precise measurement of crystalline anharmonic properties using harmonically mapped averaging”, Comput. Phys. Commun. 258, 107554 (2021).
• A. Purohit, A. J. Schultz, D. A. Kofke, “Implementation of harmonically mapped averaging in LAMMPS, and effect of potential truncation on anharmonic properties”, J. Chem. Phys. 152, 014107 (2020). PDF supplementary info
• R. J. Wheatley, A. J. Schultz, H. N. Do, N. Gokul, D. A. Kofke, “Cluster integrals and virial coefficients for realistic molecular models”, Phys. Rev. E 101, 051301 (2020). PDF supplementary info
• R. Messerly, N. Gokul, A. J. Schultz, D. A. Kofke, A. H. Harvey, “Molecular Calculation of the Critical Parameters of Classical Helium”, J. Chem. Eng. Data 65, 1028-1037 (2020). PDF supplementary info
• A. Trokhymchuk, A. J. Schultz, D. A. Kofke, “Alternative ensemble averages in molecular dynamics simulation of hard spheres”, Mol. Phys. 117, 3734-3753 (2019). PDF
• J. R. Elliott, A. J. Schultz, D. A. Kofke, “Combined temperature and density series for fluid-phase properties. II. Lennard-Jones spheres”, J. Chem. Phys. 151, 204501 (2019).
• A. Purohit, A. J. Schultz, D. A. Kofke, “Force-sampling methods for density distributions as instances of mapped averaging”, Mol. Phys. 117, 2822-2829 (2019). PDF
• M. A. F. Afzal, A. Sonpal, M. Haghighatlari, A. J. Schultz, J. Hachmann, “A deep neural network model for packing density predictions and its application in the study of 1.5 million organic molecules”, Chem. Sci. 10, 8374-8383 (2019).
• A. J. Schultz, D. A. Kofke, “Virial Coefficients of Helium-4 from Ab initio-Based Molecular Models”, J. Chem. Eng. Data 64, 3742-3754 (2019). PDF supplementary info
• K. Jain, A. J. Schultz, J. R. Errington, “Construction of the interface potential from a series of canonical ensemble simulations”, J. Chem. Phys. 151, 044103 (2019).
• K. Jain, A. J. Schultz, J. R. Errington, “Application of the interface potential approach for studying wetting behavior within a molecular dynamics framework”, J. Chem. Phys. 150, 204118 (2019).
• A. J. Schultz, D. A. Kofke, “Alternatives to conventional ensemble averages for thermodynamic properties”, Curr. Opin. Chem. Eng. 23, 70-76 (2019). PDF
• A. Purohit, A. J. Schultz, S. G. Moustafa, J. R. Errington, D. A. Kofke, “Free energy and concentration of crystalline vacancies by molecular simulation”, Mol. Phys. 116, 3027-3041 (2018). PDF
• A. Grossfield, P. N. Patrone, D. R. Roe, A. J. Schultz, D. Siderius, D. M. Zuckerman, “Best Practices for Quantification of Uncertainty and Sampling Quality in Molecular Simulations”, Living Journal of Computational Molecular Science 1, 5067 (2018).
• A. J. Schultz, D. A. Kofke, “Comprehensive high-precision high-accuracy equation of state and coexistence properties for classical Lennard-Jones crystals and low-temperature fluid phases”, J. Chem. Phys. 149, 204508 (2018). PDF supplementary info erratum erratum PDF
• S. G. Moustafa, A. J. Schultz, D. A. Kofke, “Effects of thermostatting in molecular dynamics on anharmonic properties of crystals: Application to fcc Al at high pressure and temperature”, J. Chem. Phys. 149, 124109 (2018). PDF
• W. S. Lin, A. J. Schultz, D. A. Kofke, “Electric-field mapped averaging for the dielectric constant”, Fluid Phase Equilib. 470, 17-24 (2018). PDF
• A. J. Schultz, S. G. Moustafa, D. A. Kofke, “No system-size anomalies in entropy of bcc iron at Earth's inner-core conditions”, Sci. Rep. 8, 7295 (2018). PDF
• S. G. Moustafa, A. J. Schultz, E. Zurek, D. A. Kofke, “Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure”, Phys. Rev. B 96, 014117 (2017). PDF supplementary info
• M. E. Irrgang, M. Engel, A. J. Schultz, D. A. Kofke, S. C. Glotzer, “Virial Coefficients and Equations of State for Hard Polyhedron Fluids”, Langmuir 33, 11788-11796 (2017). PDF supplementary info
• S. Yang, A. J. Schultz, D. A. Kofke, “Evaluation of second and third dielectric virial coefficients for non-polarisable molecular models”, Mol. Phys. 115, 991-1003 (2017). PDF supplementary info
• S. G. Moustafa, A. J. Schultz, D. A. Kofke, “Harmonically Assisted Methods for Computing the Free Energy of Classical Crystals by Molecular Simulation: A Comparative Study”, J. Chem. Theory Comput. 13, 825-834 (2017). PDF
• R. Subramanian, A. J. Schultz, D. A. Kofke, “Direct orientation sampling of diatomic molecules for path integral Monte Carlo calculation of fully quantum virial coefficients”, J. Chem. Phys. 146, 094105 (2017). PDF supplementary info
• R. Subramanian, A. J. Schultz, D. A. Kofke, “Quantum virial coefficients of molecular nitrogen”, Mol. Phys. 115, 869-878 (2017). PDF supplementary info
• S. Yang, A. J. Schultz, D. A. Kofke, “Thermodynamic Properties of Supercritical CO2/CH4 Mixtures from the Virial Equation of State”, J. Chem. Eng. Data 61, 4296-4312 (2016). PDF supplementary info
• H. Do, C. Feng, A. J. Schultz, D. A. Kofke, R. J. Wheatley, “Calculation high-order virial coefficients for the square-well potential”, Phys. Rev. E 94, 013301 (2016). PDF supplementary info
• A. J. Schultz, S. G. Moustafa, W. S. Lin, S. J. Weinstein, D. A. Kofke, “Reformulation of Ensemble Averages via Coordinate Mapping”, J. Chem. Theory Comput. 12, 1491-1498 (2016). PDF supplementary info
• A. J. Schultz, D. A. Kofke, “Vapor-phase metastability and condensation via the virial equation of state with extrapolated coefficients”, Fluid Phase Equilib. 409, 12-18 (2016). PDF
• S. G. Moustafa, A. J. Schultz, D. A. Kofke, “Very fast averaging of thermal properties of crystals by molecular simulation”, Phys. Rev. E 92, 043303 (2015). PDF
• J. R. Elliott, A. J. Schultz, D. A. Kofke, “Combined temperature and density series for fluid-phase properties. I. Square-well spheres”, J. Chem. Phys. 143, 114110 (2015). PDF supplementary info
• N. S. Barlow, A. J. Schultz, S. J. Weinstein, D. A. Kofke, “Communication: Analytic continuation of the virial series through the critical point using parametric approximants”, J. Chem. Phys. 143, 071103 (2015). PDF
• C. Feng, A. J. Schultz, V. Chaudhary, D. A. Kofke, “Eighth to sixteenth virial coefficients of the Lennard-Jones model”, J. Chem. Phys. 143, 044504 (2015). PDF supplementary info
• A. J. Schultz, D. A. Kofke, A. H. Harvey, “Molecular-based virial coefficients of CO2-H2O mixtures”, AIChE J. 61, 3029-3037 (2015). PDF supplementary info
• J. H. Yang, A. J. Schultz, J. R. Errington, D. A. Kofke, “The rate of convergence of the virial series in confined systems”, Mol. Phys. 113, 1179-1189 (2015). PDF
• S. G. Moustafa, A. J. Schultz, D. A. Kofke, “Effects of Finite Size and Proton Disorder on Lattice-Dynamics Estimates of the Free Energy of Clathrate Hydrates”, Ind. Eng. Chem. Res. 54, 4487-4496 (2015). PDF supplementary info
• A. J. Schultz, D. A. Kofke, “Etomica: An Object-Oriented Framework for Molecular Simulation”, J. Comput. Chem. 36, 573-583 (2015). PDF
• A. J. Schultz, D. A. Kofke, “Quantifying Computational Effort Required for Stochastic Averages”, J. Chem. Theory Comput. 10, 5229-5234 (2014). PDF
• S. Yang, A. J. Schultz, D. A. Kofke, A. H. Harvey, “Interpreting Gas-Saturation Vapor-Pressure Measurements Using Virial Coefficients Derived from Molecular Models”, J. Chem. Eng. Data 59, 3183-3192 (2014). supplementary info
• N. S. Barlow, A. J. Schultz, D. A. Kofke, S. J. Weinstein, “Critical Isotherms from Virial Series Using Asymptotically Consistent Approximants”, AIChE J. 60, 3336-3349 (2014). PDF
• A. J. Schultz, D. A. Kofke, “Fifth to eleventh virial coefficients of hard spheres”, Phys. Rev. E 90, 023301 (2014). PDF
• S. G. Moustafa, A. J. Schultz, D. A. Kofke, “A comparative study of methods to compute the free energy of an ordered assembly by molecular simulation”, J. Chem. Phys. 139, 084105 (2013). PDF
• H. M. Kim, A. J. Schultz, D. A. Kofke, “Second through fifth virial coefficients for model methane-ethane mixtures”, Fluid Phase Equilib. 351, 69-73 (2013). PDF
• J. H. Yang, A. J. Schultz, J. R. Errington, D. A. Kofke, “Calculation of inhomogeneous-fluid cluster expansions with application to the hard-sphere/hard-wall system”, J. Chem. Phys. 138, 134706 (2013). PDF
• A. J. Schultz, N. S. Barlow, V. Chaudhary, D. A. Kofke, “Mayer Sampling Monte Carlo calculation of virial coefficients on graphics processors”, Mol. Phys. 111, 535-543 (2013). PDF
• N. S. Barlow, A. J. Schultz, S. J. Weinstein, D. A. Kofke, “An asymptotically consistent approximant method with application to soft- and hard-sphere fluids”, J. Chem. Phys. 137, 204102 (2012). PDF
• H. M. Kim, A. J. Schultz, D. A. Kofke, “Virial Equation of State of Water Based on Wertheim's Association Theory”, J. Phys. Chem. B 116, 14078-14088 (2012).
• K. R. S. Shaul, A. J. Schultz, D. A. Kofke, “Path-integral Mayer-sampling calculations of the quantum Boltzmann contribution to virial coefficients of helium-4”, J. Chem. Phys. 137, 184101 (2012). PDF supplementary info
• K. R. S. Shaul, A. J. Schultz, D. A. Kofke, M. R. Moldover, “Semiclassical fifth virial coefficients for improved ab initio helium-4 standards”, Chem. Phys. Lett. 531, 11-17 (2012). PDF
• M. S. Sellers, A. J. Schultz, D. A. Kofke, C. Basaran, “Solute Effects on β-Sn Grain Boundary Energy and Shear Stress”, J. Nanomechanics and Micromechanics 1, 41-50 (2011).
• K. R. S. Shaul, A. J. Schultz, A. Perera, D. A. Kofke, “Integral-equation theories and Mayer-sampling Monte Carlo: a tandem approach for computing virial coefficients of simple fluids”, Mol. Phys. 109, 2395-2406 (2011).
• K. R. S. Shaul, A. J. Schultz, D. A. Kofke, “Mayer-sampling Monte Carlo calculations of uniquely flexible contributions to virial coefficients”, J. Chem. Phys. 135, 124101 (2011). PDF supplementary info
• A. J. Schultz, D. A. Kofke, “Algorithm for constant-pressure Monte Carlo simulation of crystalline solids”, Phys. Rev. E 84, 046712 (2011). PDF
• T. B. Tan, A. J. Schultz, D. A. Kofke, “Virial coefficients, equation of state, and solid-fluid coexistence for the soft sphere model”, Mol. Phys. 109, 123-132 (2011).
• M. S. Sellers, A. J. Schultz, C. Basaran, D. A. Kofke, “Effect of Cu and Ag solute segregation on beta Sn grain boundary diffusivity”, J. Appl. Phys. 110, 013528 (2011). PDF
• T. B. Tan, A. J. Schultz, D. A. Kofke, “Efficient calculation of alpha- and beta-nitrogen free energies and coexistence conditions via overlap sampling with targeted perturbation”, J. Chem. Phys. 135, 044125 (2011). PDF
• K. R. S. Shaul, A. J. Schultz, D. A. Kofke, “Mayer-sampling Monte Carlo calculations of methanol virial coefficients”, Mol. Simul. 36, 1282-1288 (2010). PDF
• K. R. S. Shaul, A. J. Schultz, D. A. Kofke, “The effect of truncation and shift on virial coefficients of Lennard-Jones potentials”, Collect. Czech. Chem. Commun. 75, 447-462 (2010). PDF
• M. S. Sellers, A. J. Schultz, C. Basaran, D. A. Kofke, “beta-Sn grain-boundary structure and self-diffusivity via molecular dynamics simulations”, Phys. Rev. B 81, 134111 (2010). PDF
• M. S. Sellers, A. J. Schultz, C. Basaran, D. A. Kofke, “Atomistic modeling of beta-Sn surface energies and adatom diffusivity”, Appl. Surf. Sci. 256, 4402-4407 (2010). PDF
• T. B. Tan, A. J. Schultz, D. A. Kofke, “Suitability of umbrella- and overlap-sampling methods for calculation of solid-phase free energies by molecular simulation”, J. Chem. Phys. 132, 214103 (2010). PDF
• H. M. Kim, A. J. Schultz, D. A. Kofke, “Molecular based modeling of associating fluids via calculation of Wertheim cluster integrals”, J. Phys. Chem. B 114, 11515-11524 (2010). PDF link
• A. J. Schultz, D. A. Kofke, “Virial coefficients of model alkanes”, J. Chem. Phys. 133, 104101 (2010). PDF supplementary info
• T. B. Tan, A. J. Schultz, D. A. Kofke, “Efficient calculation of temperature dependence of solid-phase free energies by overlap sampling coupled with harmonically targeted perturbation”, J. Chem. Phys. 133, 134104 (2010). PDF
• A. J. Schultz, K. R. S. Shaul, S. Yang, D. A. Kofke, “Modeling solubility in supercritical fluids via the virial equation of state”, J. Supercrit. Fluids 55, 479-484 (2010). PDF
• A. J. Schultz, D. A. Kofke, “Sixth, seventh and eighth virial coefficients of the Lennard-Jones model”, Mol. Phys. 107, 2309-2318 (2009).
• A. J. Schultz, D. A. Kofke, “Interpolation of virial coefficients”, Mol. Phys. 107, 1431-1436 (2009).
• S. D. Li, M. S. Sellers, C. Basaran, A. J. Schultz, D. A. Kofke, “Lattice strain due to an atomic vacancy”, Int. J. Mol. Sci. 10, 2798-2808 (2009). PDF
• K. M. Benjamin, A. J. Schultz, D. A. Kofke, “Fourth and fifth virial coefficients of polarizable water”, J. Phys. Chem. B 113, 7810-7815 (2009). PDF link erratum erratum PDF
• A. J. Schultz, D. A. Kofke, “Virial coefficients of Lennard-Jones mixtures”, J. Chem. Phys. 130, 224104 (2009). PDF supplementary info
• A. J. Schultz, C. K. Hall, J. Genzer, “Obtaining concentration profiles from computer simulation structure factors”, Macromolecules 40, 2629-2632 (2007).
• K. M. Benjamin, J. K. Singh, A. J. Schultz, D. A. Kofke, “Higher-order virial coefficients of water models”, J. Phys. Chem. B 111, 11463-11473 (2007). PDF
• K. M. Benjamin, A. J. Schultz, D. A. Kofke, “Virial coefficients of polarizable water: Applications to thermodynamic properties and molecular clustering”, J. Phys. Chem. C 111, 16021-16027 (2007). PDF
• K. M. Benjamin, A. J. Schultz, D. A. Kofke, “Gas-phase molecular clustering of TIP4P and SPC/E water models from higher-order virial coefficients”, Ind. Eng. Chem. Res. 45, 5566-5573 (2006). PDF
• A. J. Schultz, C. K. Hall, J. Genzer, “Computer simulation of block copolymer/nanoparticle composites”, Macromolecules 38, 3007-3016 (2005).
• A. J. Schultz, C. K. Hall, J. Genzer, “Box length search algorithm for molecular simulation of systems containing periodic structures”, J. Chem. Phys. 120, 2049-2055 (2004). PDF
• A. J. Schultz, C. K. Hall, J. Genzer, “Computer simulation of copolymer phase behavior”, J. Chem. Phys. 117, 10329-10338 (2002). PDF