apssamp.bib

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@article{Irving-Kirwood,
author = {Yang,Jerry Zhijian  and Wu,Xiaojie  and Li,Xiantao },
title = {A generalized Irving–Kirkwood formula for the calculation of stress in molecular dynamics models},
journal = {The Journal of Chemical Physics},
volume = {137},
number = {13},
pages = {134104},
year = {2012},
doi = {10.1063/1.4755946},

URL = { 
        https://doi.org/10.1063/1.4755946
    
},
eprint = { 
        https://doi.org/10.1063/1.4755946
    
}

}

@article{Broido2007,
abstract = {We present an ab initio theoretical approach to accurately describe phonon thermal transport in semiconductors and insulators free of adjustable parameters. This technique combines a Boltzmann formalism with density functional calculations of harmonic and anharmonic interatomic force constants. Without any fitting parameters, we obtain excellent agreement ({\textless}5{\%} difference at room temperature) between the calculated and measured intrinsic lattice thermal conductivities of silicon and germanium. As such, this method may provide predictive theoretical guidance to experimental thermal transport studies of bulk and nanomaterials as well as facilitating the design of new materials. {\textcopyright} 2007 American Institute of Physics.},
author = {Broido, D. A. and Malorny, M. and Birner, G. and Mingo, Natalio and Stewart, D. A.},
doi = {10.1063/1.2822891},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Broido et al/Intrinsic lattice thermal conductivity of semiconductors from first principles/Broido et al. - Intrinsic lattice thermal conductivity of semiconductors from first principles.pdf:pdf},
issn = {0003-6951},
journal = {Applied Physics Letters},
month = {dec},
number = {23},
pages = {231922},
title = {{Intrinsic lattice thermal conductivity of semiconductors from first principles}},
url = {http://aip.scitation.org/doi/10.1063/1.2822891},
volume = {91},
year = {2007}
}
@article{Zhou2014,
abstract = {First-principles prediction of lattice thermal conductivity $\kappa$L of strongly anharmonic crystals is a long-standing challenge in solid-state physics. Making use of recent advances in information science, we propose a systematic and rigorous approach to this problem, compressive sensing lattice dynamics. Compressive sensing is used to select the physically important terms in the lattice dynamics model and determine their values in one shot. Nonintuitively, high accuracy is achieved when the model is trained on first-principles forces in quasirandom atomic configurations. The method is demonstrated for Si, NaCl, and Cu12Sb4S13, an earth-abundant thermoelectric with strong phonon-phonon interactions that limit the room-temperature $\kappa$L to values near the amorphous limit.},
archivePrefix = {arXiv},
arxivId = {1404.5923},
author = {Zhou, Fei and Nielson, Weston and Xia, Yi and Ozoliņ{\v{s}}, Vidvuds},
doi = {10.1103/PhysRevLett.113.185501},
eprint = {1404.5923},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Zhou/Lattice Anharmonicity and Thermal Conductivity from Compressive Sensing of First-Principles Calculations/Zhou - Lattice Anharmonicity and Thermal Conductivity from Compressive Sensing of First-Principles Calculations.pdf:pdf},
issn = {10797114},
journal = {Physical Review Letters},
number = {18},
pages = {1--5},
title = {{Lattice anharmonicity and thermal conductivity from compressive sensing of first-principles calculations}},
volume = {113},
year = {2014}
}
@article{Tenenbaum1982,
abstract = {We have developed a technique to produce stationary nonequilibrium states in a molecular-dynamics system; this method is based on the introduction of stochastic boundary conditions to simulate the contact with a thermal wall. The relaxation times involved in such contact are short enough (10-11 sec) to make the technique suitable for computer experiments. The method allows the simulation of bulk properties in a system coupled with a heat reservoir and the study of the local thermodynamical equilibrium. Furthermore, it gives a physical description of the heat transfer near a thermal wall. The method has been applied to simulate high thermal gradients in a region of dense fluids ranging from the gas-liquid coexistence line to the freezing line, to check the validity of the linear thermal response (Fourier's law). We have found that the linear region extends at least up to gradients of the order of 1.8×109 K/cm for argon. In the bulk region where boundary effects are negligible we have verified the validity of the local equilibrium hypothesis for all simulated gradients. {\textcopyright} 1982 The American Physical Society.},
author = {Tenenbaum, Alexander and Ciccotti, Giovanni and Gallico, Renato},
doi = {10.1103/PhysRevA.25.2778},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Tenenbaum, Ciccotti, Gallico/Stationary nonequilibrium states by molecular dynamics. Fourier's law/Tenenbaum, Ciccotti, Gallico - Stationary nonequilibrium states by molecular dynamics. Fourier's law.pdf:pdf},
issn = {0556-2791},
journal = {Physical Review A},
month = {may},
number = {5},
pages = {2778--2787},
title = {{Stationary nonequilibrium states by molecular dynamics. Fourier's law}},
url = {https://link.aps.org/doi/10.1103/PhysRevA.25.2778},
volume = {25},
year = {1982}
}
@incollection{Klemens1958,
author = {Klemens, P.G.},
booktitle = {Solid State Physics - Advances in Research and Applications},
doi = {10.1016/S0081-1947(08)60551-2},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Klemens/Thermal Conductivity and Lattice Vibrational Modes/Klemens - Thermal Conductivity and Lattice Vibrational Modes.pdf:pdf},
issn = {00811947},
number = {C},
pages = {1--98},
title = {{Thermal Conductivity and Lattice Vibrational Modes}},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0081194708605512},
volume = {7},
year = {1958}
}
@book{Allen2017,
abstract = {Computer simulation is an essential tool in studying the chemistry and physics of liquids. Simulations allow us to develop models and to test them against experimental data. They can be used to evaluate approximate theories of liquids, and to provide detailed information on the structure and dynamics of model liquids at the molecular level. This book is an introduction and practical guide to the molecular dynamics and Monte Carlo methods. The first four chapters describe these methods in detail, and provide the essential background in intermolecular forces and statistical mechanics. Chapters 5 and 6 emphasize the practical aspects of writing efficient programs and analysing the simulation results. The remaining chapters cover advanced techniques, non-equilibrium methods, Brownian dynamics, quantum simulations, and some important applications. FORTRAN code is presented in the text.},
author = {Allen, Michael P. and Tildesley, Dominic J.},
booktitle = {Mathematics of Computation},
doi = {10.1093/oso/9780198803195.001.0001},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Allen, Tildesley/Computer Simulation of Liquids/Allen, Tildesley - Computer Simulation of Liquids.pdf:pdf},
isbn = {9780198803195},
issn = {00255718},
month = {nov},
number = {195},
pages = {442},
publisher = {Oxford University Press},
title = {{Computer Simulation of Liquids}},
url = {http://www.oxfordscholarship.com/view/10.1093/oso/9780198803195.001.0001/oso-9780198803195},
volume = {1},
year = {2017}
}

@book{Evans2007,
abstract = {This graduate level book charts the development and theoretical analysis of molecular dynamics as applied to equilibrium and non-equilibrium systems.},
author = {Evans, Denis J. and Morriss, Gary P.},
booktitle = {Statistical Mechanics of Nonequilibrium Liquids},
doi = {10.22459/smnl.08.2007},
title = {{Statistical Mechanics of Nonequilibrium Liquids}},
year = {2007}
}
@article{Muller-Plathe1997,
abstract = {A nonequilibrium molecular dynamics method for calculating the thermal conductivity is presented. It reverses the usual cause and effect picture. The “effect,” the heat flux, is imposed on the system and the “cause,” the temperature gradient is obtained from the simulation. Besides being very simple to implement, the scheme offers several advantages such as compatibility with periodic boundary conditions, conservation of total energy and total linear momentum, and the sampling of a rapidly converging quantity (temperature gradient) rather than a slowly converging one (heat flux). The scheme is tested on the Lennard-Jones fluid.},
author = {M{\"{u}}ller-Plathe, Florian},
doi = {10.1063/1.473271},
file = {:Users/davidetisi/Documents/Mendeley Desktop/M{\"{u}}ller-Plathe/A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity/M{\"{u}}ller-Plathe - A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity.pdf:pdf},
issn = {0021-9606},
journal = {The Journal of Chemical Physics},
month = {apr},
number = {14},
pages = {6082--6085},
title = {{A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity}},
url = {http://aip.scitation.org/doi/10.1063/1.473271},
volume = {106},
year = {1997}
}




@article{Ramires1995,
abstract = {New experimental data on the thermal conductivity of liquid water along the saturation line have been obtained recently, using the bare and coated transient hot wire technique, with high accuracy. ...},
author = {Ramires, Maria L. V. and {Nieto de Castro}, Carlos A. and Nagasaka, Yuchi and Nagashima, Akira and Assael, Marc J. and Wakeham, William A.},
doi = {10.1063/1.555963},
issn = {0047-2689},
journal = {Journal of Physical and Chemical Reference Data},
keywords = {1070,1180,CORRELATIONS,DATA COMPILATION,EXPERIMENTAL DATA,REFERENCE SYSTEMS,STANDARDS,THERMAL CONDUCTIVITY,WATER},
month = {may},
number = {3},
pages = {1377--1381},
publisher = {American Institute of Physics for the National Institute of Standards and Technology},
title = {{Standard Reference Data for the Thermal Conductivity of Water}},
url = {http://aip.scitation.org/doi/10.1063/1.555963},
volume = {24},
year = {1995}
}

@article{Lu2008,
abstract = {We present a first-principles study of the static dielectric properties of ice and liquid water. The eigenmodes of the dielectric matrix E are analyzed in terms of maximally localized dielectric functions similar, in their definition, to maximally localized Wannier orbitals obtained from Bloch eigenstates of the electronic Hamiltonian. We show that the lowest eigenmodes of E (-1) are localized in real space and can be separated into groups related to the screening of lone pairs, intra-, and intermolecular bonds, respectively. The local properties of the dielectric matrix can be conveniently exploited to build approximate dielectric matrices for efficient, yet accurate calculations of quasiparticle energies.},
author = {Lu, Deyu and Gygi, Fran{\c{c}}ois and Galli, Giulia},
doi = {10.1103/PhysRevLett.100.147601},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Lu, Gygi, Galli/Dielectric Properties of Ice and Liquid Water from First-Principles Calculations/Lu, Gygi, Galli - Dielectric Properties of Ice and Liquid Water from First-Principles Calculations.pdf:pdf},
issn = {0031-9007},
journal = {Physical Review Letters},
month = {apr},
number = {14},
pages = {147601},
title = {{Dielectric Properties of Ice and Liquid Water from First-Principles Calculations}},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.100.147601},
volume = {100},
year = {2008}
}
@article{Galli2008,
author = {Galli, G.A. and Galli, Giulia},
doi = {10.1107/S0108767308099893},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Galli, Galli/Quantum simulations of liquids and solids under pressure synergy between theory and experiment/Galli, Galli - Quantum simulations of liquids and solids under pressure synergy between theory and experiment.pdf:pdf},
issn = {0108-7673},
journal = {Acta Crystallographica Section A Foundations of Crystallography},
keywords = {protein structures,synchrotron radiation},
month = {aug},
number = {a1},
pages = {C4--C4},
title = {{Quantum simulations of liquids and solids under pressure: synergy between theory and experiment}},
url = {http://scripts.iucr.org/cgi-bin/paper?S0108767308099893},
volume = {64},
year = {2008}
}
@article{Gillan2016,
abstract = {Kohn-Sham density functional theory (DFT) has become established as an indispensable tool for investigating aqueous systems of all kinds, including those important in chemistry, surface science, biology and the earth sciences. Nevertheless, many widely used approximations for the exchange-correlation (XC) functional describe the properties of pure water systems with an accuracy that is not fully satisfactory. The explicit inclusion of dispersion interactions generally improves the description, but there remain large disagreements between the predictions of different dispersion-inclusive methods. We present here a review of DFT work on water clusters, ice structures and liquid water, with the aim of elucidating how the strengths and weaknesses of different XC approximations manifest themselves across this variety of water systems. Our review highlights the crucial role of dispersion in describing the delicate balance between compact and extended structures of many different water systems, including the liquid. By referring to a wide range of published work, we argue that the correct description of exchange-overlap interactions is also extremely important, so that the choice of semi-local or hybrid functional employed in dispersion-inclusive methods is crucial. The origins and consequences of beyond-2-body errors of approximate XC functionals are noted, and we also discuss the substantial differences between different representations of dispersion. We propose a simple numerical scoring system that rates the performance of different XC functionals in describing water systems, and we suggest possible future developments.},
author = {Gillan, Michael J. and Alf{\`{e}}, Dario and Michaelides, Angelos},
doi = {10.1063/1.4944633},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Gillan, Alf{\`{e}}, Michaelides/Perspective How good is DFT for water/Gillan, Alf{\`{e}}, Michaelides - Perspective How good is DFT for water.pdf:pdf},
issn = {0021-9606},
journal = {The Journal of Chemical Physics},
month = {apr},
number = {13},
pages = {130901},
title = {{Perspective: How good is DFT for water?}},
url = {http://aip.scitation.org/doi/10.1063/1.4944633},
volume = {144},
year = {2016}
}
@article{Sit2005,
abstract = {The static and dynamical properties of heavy water have been studied at ambient conditions with extensive Car-Parrinello molecular-dynamics simulations in the canonical ensemble, with temperatures ranging between 325 K and 400 K. Density-functional theory, paired with a modern exchange-correlation functional (PBE), provides an excellent agreement for the structural properties and binding energy of the water monomer and dimer. On the other hand, the structural and dynamical properties of the bulk liquid show a clear enhancement of the local structure compared to experimental results; a distinctive transition to liquid-like diffusion occurs in the simulations only at the elevated temperature of 400 K. Extensive runs of up to 50 picoseconds are needed to obtain well-converged thermal averages; the use of ultrasoft or norm-conserving pseudopotentials and the larger plane-wave sets associated with the latter choice had, as expected, only negligible effects on the final result. Finite-size effects in the liquid state are found to be mostly negligible for systems as small as 32 molecules per unit cell.},
author = {Sit, P. H.-L. and Marzari, Nicola},
doi = {10.1063/1.1908913},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Sit, Marzari/Static and dynamical properties of heavy water at ambient conditions from first-principles molecular dynamics/Sit, Marzari - Static and dynamical properties of heavy water at ambient conditions from first-principles molecular dynamics.pdf:pdf},
issn = {0021-9606},
journal = {The Journal of Chemical Physics},
month = {may},
number = {20},
pages = {204510},
title = {{Static and dynamical properties of heavy water at ambient conditions from first-principles molecular dynamics}},
url = {http://aip.scitation.org/doi/10.1063/1.1908913},
volume = {122},
year = {2005}
}

@article{Grossman2004,
author = {Grossman, Jeffrey C and Schwegler, Eric and Draeger, Erik W and Gygi, Fran{\c{c}}ois and Galli, Giulia},
doi = {10.1063/1.1630560},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Grossman et al/Towards an assessment of the accuracy of density functional theory for first principles simulations of water/Grossman et al. - Towards an assessment of the accuracy of density functional theory for first principles simulations of water.pdf:pdf},
issn = {0021-9606},
journal = {The Journal of Chemical Physics},
month = {jan},
number = {1},
pages = {300--311},
title = {{Towards an assessment of the accuracy of density functional theory for first principles simulations of water}},
url = {http://aip.scitation.org/doi/10.1063/1.1630560},
volume = {120},
year = {2004}
}

@InProceedings{He_2016_CVPR,
author = {He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian},
title = {Deep Residual Learning for Image Recognition},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2016}
}


@article{Kondor2018,
abstract = {We describe N-body networks, a neural network architecture for learning the behavior and properties of complex many body physical systems. Our specific application is to learn atomic potential energy surfaces for use in molecular dynamics simulations. Our architecture is novel in that (a) it is based on a hierarchical decomposition of the many body system into subsytems, (b) the activations of the network correspond to the internal state of each subsystem, (c) the "neurons" in the network are constructed explicitly so as to guarantee that each of the activations is covariant to rotations, (d) the neurons operate entirely in Fourier space, and the nonlinearities are realized by tensor products followed by Clebsch-Gordan decompositions. As part of the description of our network, we give a characterization of what way the weights of the network may interact with the activations so as to ensure that the covariance property is maintained.},
archivePrefix = {arXiv},
arxivId = {1803.01588},
author = {Kondor, Risi},
eprint = {1803.01588},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Kondor/N-body Networks a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials/Kondor - N-body Networks a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials.pdf:pdf},
month = {mar},
pages = {1--11},
title = {{N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials}},
url = {http://arxiv.org/abs/1901.10416 http://arxiv.org/abs/1803.01588},
year = {2018}
}
@article{Bartok2010,
abstract = {We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, derived from quantum mechanical calculations. The resulting model does not have a fixed functional form and hence is capable of modeling complex potential energy landscapes. It is systematically improvable with more data. We apply the method to bulk carbon, silicon and germanium and test it by calculating properties of the crystals at high temperatures. Using the interatomic potential to generate the long molecular dynamics trajectories required for such calculations saves orders of magnitude in computational cost.},
archivePrefix = {arXiv},
arxivId = {0910.1019},
author = {Bart{\'{o}}k, Albert P. and Payne, Mike C and Kondor, Risi and Cs{\'{a}}nyi, G{\'{a}}bor},
doi = {10.1103/PhysRevLett.104.136403},
eprint = {0910.1019},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Bart{\'{o}}k et al/Gaussian Approximation Potentials the accuracy of quantum mechanics, without the electrons/Bart{\'{o}}k et al. - Gaussian Approximation Potentials the accuracy of quantum mechanics, without the electrons.pdf:pdf},
isbn = {0031-9007},
issn = {0031-9007},
journal = {Physical Review Letters},
month = {apr},
number = {13},
pages = {136403},
pmid = {20481899},
title = {{Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons}},
url = {http://arxiv.org/abs/0910.1019 http://dx.doi.org/10.1103/PhysRevLett.104.136403 https://link.aps.org/doi/10.1103/PhysRevLett.104.136403},
volume = {104},
year = {2010}
}
@article{Behler2007,
abstract = {The accurate description of chemical processes often requires the use of computationally demanding methods like density-functional theory (DFT), making long simulations of large systems unfeasible. In this Letter we introduce a new kind of neural-network representation of DFT potential-energy surfaces, which provides the energy and forces as a function of all atomic positions in systems of arbitrary size and is several orders of magnitude faster than DFT. The high accuracy of the method is demonstrated for bulk silicon and compared with empirical potentials and DFT. The method is general and can be applied to all types of periodic and nonperiodic systems. {\textcopyright} 2007 The American Physical Society.},
author = {Behler, J{\"{o}}rg and Parrinello, Michele},
doi = {10.1103/PhysRevLett.98.146401},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Behler, Parrinello/Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces/Behler, Parrinello - Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces.pdf:pdf},
issn = {0031-9007},
journal = {Physical Review Letters},
month = {apr},
number = {14},
pages = {146401},
title = {{Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces}},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.98.146401},
volume = {98},
year = {2007}
}
@article{Smith2017,
abstract = {We demonstrate how a deep neural network (NN) trained on a data set of quantum mechanical (QM) DFT calculated energies can learn an accurate and transferable atomistic potential for organic molecules containing H, C, N, and O atoms.},
archivePrefix = {arXiv},
arxivId = {1610.08935},
author = {Smith, J. S. and Isayev, O. and Roitberg, A. E.},
doi = {10.1039/C6SC05720A},
eprint = {1610.08935},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Smith, Isayev, Roitberg/ANI-1 an extensible neural network potential with DFT accuracy at force field computational cost/Smith, Isayev, Roitberg - ANI-1 an extensible neural network potential with DFT accuracy at force field computational cost.pdf:pdf},
issn = {2041-6520},
journal = {Chemical Science},
number = {4},
pages = {3192--3203},
publisher = {Royal Society of Chemistry},
title = {{ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost}},
url = {http://xlink.rsc.org/?DOI=C6SC05720A},
volume = {8},
year = {2017}
}
@article{Rupp2012,
abstract = {We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr{\"{o}}dinger equation is mapped onto a nonlinear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross validation over more than seven thousand organic molecules yields a mean absolute error of ∼10kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves. {\textcopyright} 2012 American Physical Society.},
archivePrefix = {arXiv},
arxivId = {1109.2618},
author = {Rupp, Matthias and Tkatchenko, Alexandre and M{\"{u}}ller, Klaus-Robert and von Lilienfeld, O. Anatole},
doi = {10.1103/PhysRevLett.108.058301},
eprint = {1109.2618},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Rupp et al/Fast and accurate modeling of molecular atomization energies with machine learning/Rupp et al. - Fast and accurate modeling of molecular atomization energies with machine learning.pdf:pdf},
issn = {0031-9007},
journal = {Physical Review Letters},
month = {jan},
number = {5},
pages = {058301},
pmid = {22400967},
title = {{Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning}},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.108.058301},
volume = {108},
year = {2012}
}
@article{Butler2018,
author = {Butler, Keith T. and Davies, Daniel W. and Cartwright, Hugh and Isayev, Olexandr and Walsh, Aron},
doi = {10.1038/s41586-018-0337-2},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Butler et al/Machine learning for molecular and materials science/Butler et al. - Machine learning for molecular and materials science.pdf:pdf},
issn = {0028-0836},
journal = {Nature},
month = {jul},
number = {7715},
pages = {547--555},
publisher = {Springer US},
title = {{Machine learning for molecular and materials science}},
url = {http://arxiv.org/abs/1901.10416 http://www.nature.com/articles/s41586-018-0337-2},
volume = {559},
year = {2018}
}



@article{Schwegler2004,
archivePrefix = {arXiv},
arxivId = {cond-mat/0405561},
author = {Schwegler, Eric and Grossman, Jeffrey C. and Gygi, Fran{\c{c}}ois and Galli, Giulia},
doi = {10.1063/1.1782074},
eprint = {0405561},
issn = {00219606},
journal = {Journal of Chemical Physics},
number = {11},
pages = {5400--5409},
primaryClass = {cond-mat},
title = {{Towards an assessment of the accuracy of density functional theory for first principles simulations of water. II}},
volume = {121},
year = {2004}
}


@article{Kingma2014,
abstract = {We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.},
archivePrefix = {arXiv},
arxivId = {1412.6980},
author = {Kingma, Diederik P. and Ba, Jimmy},
eprint = {1412.6980},
journal = {3rd International Conference on Learning Representations, ICLR 2015 - Conference Track Proceedings},
month = {dec},
pages = {1--15},
title = {{Adam: A Method for Stochastic Optimization}},
url = {http://arxiv.org/abs/1412.6980},
year = {2014}
}

@article{Wang2017,
abstract = {Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform molecular dynamics. Potential applications of DeePMD-kit span from finite molecules to extended systems and from metallic systems to chemically bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical molecular dynamics and quantum (path-integral) molecular dynamics packages, i.e., LAMMPS and the i-PI, respectively. Thus, upon training, the potential energy and force field models can be used to perform efficient molecular simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interatomic potential energy and forces of a water model using data obtained from density functional theory. We demonstrate that the resulted molecular dynamics model reproduces accurately the structural information contained in the original model.},
archivePrefix = {arXiv},
arxivId = {1712.03641},
author = {Wang, Han and Zhang, Linfeng and Han, Jiequn and E, Weinan},
doi = {10.1016/j.cpc.2018.03.016},
eprint = {1712.03641},
issn = {00104655},
journal = {Computer Physics Communications},
keywords = {Deep neural networks,Many-body potential energy,Molecular dynamics},
month = {dec},
pages = {178--184},
title = {{DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics}},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0010465518300882 http://arxiv.org/abs/1712.03641 http://dx.doi.org/10.1016/j.cpc.2018.03.016},
volume = {228},
year = {2017}
}


@article{Hamann2013,
abstract = {Fully nonlocal two-projector norm-conserving pseudopotentials are shown to be compatible with a systematic approach to the optimization of convergence with the size of the plane-wave basis. A reformulation of the optimization is developed, including the ability to apply it to positive-energy atomic scattering states and to enforce greater continuity in the pseudopotential. The generalization of norm conservation to multiple projectors is reviewed and recast for the present purposes. Comparisons among the results of all-electron and one- and two-projector norm-conserving pseudopotential calculations of lattice constants and bulk moduli are made for a group of solids chosen to represent a variety of types of bonding and a sampling of the periodic table. {\textcopyright} 2013 American Physical Society.},
author = {Hamann, D. R.},
doi = {10.1103/PhysRevB.88.085117},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Hamann/Optimized norm-conserving Vanderbilt pseudopotentials/Hamann - Optimized norm-conserving Vanderbilt pseudopotentials.pdf:pdf},
issn = {1098-0121},
journal = {Physical Review B},
month = {aug},
number = {8},
pages = {085117},
title = {{Optimized norm-conserving Vanderbilt pseudopotentials}},
url = {https://link.aps.org/doi/10.1103/PhysRevB.88.085117},
volume = {88},
year = {2013}
}


@article{Hamann1979,
abstract = {A very simple procedure to extract pseudopotentials from ab initio atomic calculations is presented. The pseudopotentials yield exact eigenvalues and nodeless eigenfunctions which agree with atomic wave functions beyond a chosen radius rc. Moreover, logarithmic derivatives of real and pseudo wave functions and their first energy derivatives agree for r{\textgreater}rc guaranteeing excellent transferability of the pseudopotentials. {\textcopyright} 1979 The American Physical Society.},
author = {Hamann, D. R. and Schl{\"{u}}ter, M. and Chiang, C.},
doi = {10.1103/PhysRevLett.43.1494},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Hamann, Schl{\"{u}}ter, Chiang/Norm-Conserving Pseudopotentials/Hamann, Schl{\"{u}}ter, Chiang - Norm-Conserving Pseudopotentials.pdf:pdf},
issn = {0031-9007},
journal = {Physical Review Letters},
month = {nov},
number = {20},
pages = {1494--1497},
title = {{Norm-Conserving Pseudopotentials}},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.43.1494},
volume = {43},
year = {1979}
}


@ARTICLE{Cepstal_ana, 
author={D. G. {Childers} and D. P. {Skinner} and R. C. {Kemerait}}, 
journal={Proceedings of the IEEE}, 
title={The cepstrum: A guide to processing}, 
year={1977}, 
volume={65}, 
number={10}, 
pages={1428-1443}, 
keywords={Cepstrum;Cepstral analysis;Data analysis;Data processing;Wavelet analysis;Sonar detection;Frequency estimation;Speech synthesis;Signal processing;Signal analysis}, 
doi={10.1109/PROC.1977.10747}, 
ISSN={0018-9219}, 
month={Oct},}

@article{Giannozzi_2009,
	doi = {10.1088/0953-8984/21/39/395502},
	url = {https://doi.org/10.1088%2F0953-8984%2F21%2F39%2F395502},
	year = 2009,
	month = {sep},
	publisher = {{IOP} Publishing},
	volume = {21},
	number = {39},
	pages = {395502},
	author = {Paolo Giannozzi and Stefano Baroni and Nicola Bonini and Matteo Calandra and Roberto Car and Carlo Cavazzoni and Davide Ceresoli and Guido L Chiarotti and Matteo Cococcioni and Ismaila Dabo and Andrea Dal Corso and Stefano de Gironcoli and Stefano Fabris and Guido Fratesi and Ralph Gebauer and Uwe Gerstmann and Christos Gougoussis and Anton Kokalj and Michele Lazzeri and Layla Martin-Samos and Nicola Marzari and Francesco Mauri and Riccardo Mazzarello and Stefano Paolini and Alfredo Pasquarello and Lorenzo Paulatto and Carlo Sbraccia and Sandro Scandolo and Gabriele Sclauzero and Ari P Seitsonen and Alexander Smogunov and Paolo Umari and Renata M Wentzcovitch},
	title = {{QUANTUM} {ESPRESSO}: a modular and open-source software project for quantum simulations of materials},
	journal = {Journal of Physics: Condensed Matter},
	abstract = {QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure
calculations and materials modeling, based on density-functional theory, plane waves, and
pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The
acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure,
Simulation, and Optimization. It is freely available to researchers around the world under
the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon
newly-restructured electronic-structure codes that have been developed and tested by some
of the original authors of novel electronic-structure algorithms and applied in the last
twenty years by some of the leading materials modeling groups worldwide. Innovation and
efficiency are still its main focus, with special attention paid to massively parallel
architectures, and a great effort being devoted to user friendliness. QUANTUM
ESPRESSO is evolving towards a distribution of independent and interoperable codes
in the spirit of an open-source project, where researchers active in the field of
electronic-structure calculations are encouraged to participate in the project by
contributing their own codes or by implementing their own ideas into existing codes.}
}

@article{Kang2017,
abstract = {We present a first-principles approach to calculate the phonon thermal conductivity based on the Green-Kubo formalism. In this approach, the density functional theory energy is distributed to each atom, and a two-step method in the molecular dynamics is introduced to avoid the atomic position R wrapping problem in a periodic system when the heat current is calculated. We show that this first-principles Green-Kubo approach is particularly suitable for disordered systems like amorphous and liquid, where the thermal conductivities are small due to strong phonon scattering but difficult to be calculated using anharmonic interaction energy. We have applied our method to liquid Ar, liquid Si, and amorphous Si. The calculated thermal conductivities agree well with previous theoretical and experimental results. We have also compared our method to previous works combining first-principles simulations with the Green-Kubo formalism.},
author = {Kang , Jun and Wang, Lin-Wang},
doi = {10.1103/PhysRevB.96.020302},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Kang, Wang/First-principles Green-Kubo method for thermal conductivity calculations/Kang, Wang - First-principles Green-Kubo method for thermal conductivity calculations.pdf:pdf},
issn = {2469-9950},
journal = {Physical Review B},
month = {jul},
number = {2},
pages = {020302},
title = {{First-principles Green-Kubo method for thermal conductivity calculations}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.96.020302},
volume = {96},
year = {2017}
}

@article{Carbogno2017,
  title = {Ab Initio Green-Kubo Approach for the Thermal Conductivity of Solids},
  author = {Carbogno, Christian and Ramprasad, Rampi and Scheffler, Matthias},
  journal = {Phys. Rev. Lett.},
  volume = {118},
  issue = {17},
  pages = {175901},
  numpages = {5},
  year = {2017},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.118.175901},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.118.175901}
}


@article{Giannozzi_2017,
	doi = {10.1088/1361-648x/aa8f79},
	url = {https://doi.org/10.1088%2F1361-648x%2Faa8f79},
	year = 2017,
	month = {oct},
	publisher = {{IOP} Publishing},
	volume = {29},
	number = {46},
	pages = {465901},
	author = {P Giannozzi and O Andreussi and T Brumme and O Bunau and M Buongiorno Nardelli and M Calandra and R Car and C Cavazzoni and D Ceresoli and M Cococcioni and N Colonna and I Carnimeo and A Dal Corso and S de Gironcoli and P Delugas and R A DiStasio and A Ferretti and A Floris and G Fratesi and G Fugallo and R Gebauer and U Gerstmann and F Giustino and T Gorni and J Jia and M Kawamura and H-Y Ko and A Kokalj and E Kü{\c{c}}ükbenli and M Lazzeri and M Marsili and N Marzari and F Mauri and N L Nguyen and H-V Nguyen and A Otero-de-la-Roza and L Paulatto and S Ponc{\'{e}} and D Rocca and R Sabatini and B Santra and M Schlipf and A P Seitsonen and A Smogunov and I Timrov and T Thonhauser and P Umari and N Vast and X Wu and S Baroni},
	title = {Advanced capabilities for materials modelling with Quantum {ESPRESSO}},
	journal = {Journal of Physics: Condensed Matter},
	abstract = {Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.}
}


@article{Linfeng2018,
abstract = {We introduce a scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is "first principle-based" in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DeePMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size.},
archivePrefix = {arXiv},
arxivId = {arXiv:1707.09571v1},
author = {Zhang, Linfeng and Han, Jiequn and Wang, Han and Car, Roberto and Weinan, E.},
doi = {10.1103/PhysRevLett.120.143001},
eprint = {arXiv:1707.09571v1},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Zhang et al/Deep Potential Molecular Dynamics A Scalable Model with the Accuracy of Quantum Mechanics/Zhang et al. - Deep Potential Molecular Dynamics A Scalable Model with the Accuracy of Quantum Mechanics.pdf:pdf},
issn = {10797114},
journal = {Physical Review Letters},
keywords = {doi:10.1103/PhysRevLett.120.143001 url:https://doi},
number = {14},
pages = {143001},
publisher = {American Physical Society},
title = {{Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics}},
url = {https://doi.org/10.1103/PhysRevLett.120.143001},
volume = {120},
year = {2018}
}



@incollection{NIPS2018_7696,
title = {End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems},
author = {Zhang, Linfeng and Han, Jiequn and Wang, Han and Saidi, Wissam and Car, Roberto and E, Weinan},
booktitle = {Advances in Neural Information Processing Systems 31},
editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
pages = {4436--4446},
year = {2018},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/7696-end-to-end-symmetry-preserving-inter-atomic-potential-energy-model-for-finite-and-extended-systems.pdf}
}

@article{Khintchine1934,
abstract = {Evaluations of individual terminology systems should be driven in part by the intended usages of such systems. Clinical interface terminologies support interactions between healthcare providers and computer-based applications. They aid practitioners in converting clinical "free text" thoughts into the structured, formal data representations used internally by application programs. Interface terminologies also serve the important role of presenting existing stored, encoded data to end users in human-understandable and actionable formats. The authors present a model for evaluating functional utility of interface terminologies based on these intended uses.},
author = {Khintchine, A.},
doi = {10.1007/BF01449156},
file = {:Users/DavideTisi/Downloads/Khintchine1934{\_}Article{\_}KorrelationstheorieDerStation{\~{A}}¤.pdf:pdf},
issn = {0025-5831},
journal = {Mathematische Annalen},
month = {dec},
number = {1},
pages = {604--615},
title = {{Korrelationstheorie der stationaren stochastischen Prozesse}},
url = {http://link.springer.com/10.1007/BF01449156},
volume = {109},
year = {1934}
}
@article{Wiener1930,
author = {Wiener, Norbert},
doi = {10.1007/BF02546511},
file = {:Users/DavideTisi/Google Drive/PhD/Baroni/euclid.acta.1485887877.pdf:pdf},
isbn = {0001-5962},
issn = {0001-5962},
journal = {Acta Mathematica},
number = {C},
pages = {117--258},
title = {{Generalized harmonic analysis}},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0065268708603635 http://projecteuclid.org/euclid.acta/1485887877},
volume = {55},
year = {1930}
}

@article{Marcolongo2016,
abstract = {Quantum simulation methods based on density-functional theory are currently deemed unfit to cope with atomic heat transport within the Green-Kubo formalism, because quantum-mechanical energy densities and currents are inherently ill-defined at the atomic scale. We show that, while this difficulty would also affect classical simulations, thermal conductivity is indeed insensitive to such ill-definedness by virtue of a sort of gauge invariance resulting from energy extensivity and conservation. Based on these findings, we derive an expression for the adiabatic energy flux from density-functional theory, which allows heat transport to be simulated using ab-initio equilibrium molecular dynamics. Our methodology is demonstrated by comparing its predictions with those of classical equilibrium and ab-initio non-equilibrium (M$\backslash$"uller-Plathe) simulations for a liquid-Argon model, and finally applied to heavy water at ambient conditions.},
author = {Marcolongo, Aris and Umari, Paolo and Baroni, Stefano},
doi = {10.1038/nphys3509},
file = {:Users/davidetisi/Documents/Mendeley Desktop/Marcolongo, Umari, Baroni/Microscopic theory and quantum simulation of atomic heat transport/Marcolongo, Umari, Baroni - Microscopic theory and quantum simulation of atomic heat transport.pdf:pdf},
issn = {1745-2473},
journal = {Nature Physics},
month = {jan},
number = {1},
pages = {80--84},
title = {{Microscopic theory and quantum simulation of atomic heat transport}},
url = {http://www.nature.com/articles/nphys3509},
volume = {12},
year = {2016}
}


@article{Ercole2017,
abstract = {A new method is introduced to estimate transport coefficients in extended systems from optimally short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and the cepstral analysis of time series. Information from the full sample power spectrum of the relevant current for a single trajectory is leveraged to evaluate and optimally reduce the noise affecting its zero-frequency value, whose expectation is proportional to the corresponding transport coefficient. Our method is unbiased and consistent, in that both the resulting bias and statistical error can be made arbitrarily small in the long-time limit. A simple protocol to evaluate thermal conductivities is finally proposed and validated in the paradigmatic cases of elemental and molecular fluids (liquid Ar and H{\$}{\_}2{\$}O) and of crystalline and glassy solids (MgO and a-SiO{\$}{\_}2{\$}).},
author = {Ercole, Loris and Marcolongo, Aris and Baroni, Stefano},
doi = {10.1038/s41598-017-15843-2},
file = {:Users/DavideTisi/Google Drive/PhD/Baroni/s41598-017-15843-2.pdf:pdf},
issn = {2045-2322},
journal = {Scientific Reports},
month = {dec},
number = {1},
pages = {15835},
publisher = {Springer US},
title = {{Accurate thermal conductivities from optimally short molecular dynamics simulations}},
url = {http://dx.doi.org/10.1038/s41598-017-15843-2 http://www.nature.com/articles/s41598-017-15843-2},
volume = {7},
year = {2017}
}
@article{Bertossa2019,
abstract = {The thermal conductivity of classical multi-component fluids is seemingly affected by the intrinsic arbitrariness in the definition of the atomic energies and it is ill-conditioned numerically, when evaluated from the Green-Kubo theory of linear response. To cope with these two problems we introduce two new concepts: a convective invariance principle for transport coefficients, in the first case, and multi-variate cepstral analysis, in the second. A combination of these two concepts allows one to substantially reduce the noise affecting the estimate of the thermal conductivity from equilibrium molecular dynamics, even for one-component systems.},
archivePrefix = {arXiv},
arxivId = {1808.03341},
author = {Bertossa, Riccardo and Grasselli, Federico and Ercole, Loris and Baroni, Stefano},
doi = {10.1103/PhysRevLett.122.255901},
eprint = {1808.03341},
file = {:Users/DavideTisi/Google Drive/PhD/Baroni/1808.03341.pdf:pdf},
issn = {0031-9007},
journal = {Physical Review Letters},
keywords = {cepstral analysis,molecular dynamics,series,statistical analysis of time,transport properties},
month = {jun},
number = {25},
pages = {255901},
title = {{Theory and Numerical Simulation of Heat Transport in Multicomponent Systems}},
url = {http://arxiv.org/abs/1808.03341 http://dx.doi.org/10.1103/PhysRevLett.122.255901 https://link.aps.org/doi/10.1103/PhysRevLett.122.255901},
volume = {122},
year = {2019}
}



@article{OnsagerI,
  title = {Reciprocal Relations in Irreversible Processes. I.},
  author = {Onsager, Lars},
  journal = {Phys. Rev.},
  volume = {37},
  issue = {4},
  pages = {405--426},
  numpages = {0},
  year = {1931},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRev.37.405},
  url = {https://link.aps.org/doi/10.1103/PhysRev.37.405}
}


@article{OnsagerII,
  title = {Reciprocal Relations in Irreversible Processes. II.},
  author = {Onsager, Lars},
  journal = {Phys. Rev.},
  volume = {38},
  issue = {12},
  pages = {2265--2279},
  numpages = {0},
  year = {1931},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRev.38.2265},
  url = {https://link.aps.org/doi/10.1103/PhysRev.38.2265}
}





@Inbook{Baroni2018,
author="Baroni, Stefano
and Bertossa, Riccardo
and Ercole, Loris
and Grasselli, Federico
and Marcolongo, Aris",
editor="Andreoni , Wanda and Yip, Sidney",
title="Heat Transport in Insulators from Ab Initio Green-Kubo Theory",
bookTitle="Handbook of Materials Modeling: Applications: Current and Emerging Materials",
year="2018",
publisher="Springer International Publishing",
address="Cham",
pages="1--36",
abstract="The Green-Kubo theory of thermal transport has long be considered incompatible with modern simulation methods based on electronic-structure theory, because it is based on such concepts as energy density and current, which are ill-defined at the quantum-mechanical level. Besides, experience with classical simulations indicates that the estimate of heat-transport coefficients requires analysing molecular trajectories that are more than one order of magnitude longer than deemed feasible using ab initio molecular dynamics. In this paper we report on recent theoretical advances that are allowing one to overcome these two obstacles. First, a general gauge invariance principle has been established, stating that thermal conductivity is insensitive to many details of the microscopic expression for the energy density and current from which it is derived, thus permitting to establish a rigorous expression for the energy flux from Density-Functional Theory, from which the conductivity can be computed in practice. Second, a novel data analysis method based on the statistical theory of time series has been proposed, which allows one to considerably reduce the simulation time required to achieve a target accuracy on the computed conductivity. These concepts are illustrated in detail, starting from a pedagogical introduction to the Green-Kubo theory of linear response and transport, and demonstrated with a few applications done with both classical and quantum-mechanical simulation methods.",
isbn="978-3-319-50257-1",
doi="10.1007/978-3-319-50257-1_12-1",
url="https://doi.org/10.1007/978-3-319-50257-1_12-1"
}


@article{KuboRyogo,
author = {Kubo ,Ryogo and Yokota ,Mario and Nakajima ,Sadao},
title = {Statistical-Mechanical Theory of Irreversible Processes. II. Response to Thermal Disturbance},
journal = {Journal of the Physical Society of Japan},
volume = {12},
number = {11},
pages = {1203-1211},
year = {1957},
doi = {10.1143/JPSJ.12.1203},

URL = { 
        https://doi.org/10.1143/JPSJ.12.1203
    
},
eprint = { 
        https://doi.org/10.1143/JPSJ.12.1203
    
}

}



@BOOK{DeGroot,
   author       = {S. R. De Groot and P. Mazur},
   year         = 1984,
   title        = {Non-Equilibrium Thermodynamics},
   publisher    = {Dover Publications}
}



@ARTICLE{Kubo,
   author       = "R. Kubo",
   title        ="Statistical-mechanical theory of irreversible processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems",
   year         = "1957",
   journal      = "J. Phys. Soc. Jpn.",
   volume       = "12",
   pages        = "570-586",
}

@ARTICLE{Green,
   author       = "M. S. Green",
   title        ="Markoff random processes and the statistical mechanics of time-dependent phenomena, II. Irreversible processes in fluids",
   year         = "1954",
   journal      = "J. Chem. Phys.",
   volume       = "22",
   pages        = "398–413",
}