Variational and diffusion quantum Monte Carlo calculations with the CASINO code.

We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the casino program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo algorithms and software and discussing their strengths and weaknesses. We review a range of recent applications of casino.

[1]  Compression algorithm for multideterminant wave functions. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  R. Needs,et al.  Framework for constructing generic Jastrow correlation factors. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Anthony Scemama,et al.  Quantum Monte Carlo with very large multideterminant wavefunctions , 2015, J. Comput. Chem..

[4]  O. A. von Lilienfeld,et al.  Communication: Water on hexagonal boron nitride from diffusion Monte Carlo. , 2015, The Journal of chemical physics.

[5]  Takuma Tsuchiya.  Biexcitons and charged excitons in GaAs/AlAs type-II superlattices: a quantum Monte Carlo study , 2000 .

[6]  K. Burke.  Perspective on density functional theory. , 2012, The Journal of chemical physics.

[7]  G. Conduit,et al.  Direct evaluation of the force constant matrix in quantum Monte Carlo. , 2019, The Journal of chemical physics.

[8]  Ali Alavi,et al.  Unbiasing the initiator approximation in full configuration interaction quantum Monte Carlo. , 2019, The Journal of chemical physics.

[9]  Ali Alavi,et al.  Fermion Monte Carlo without fixed nodes: a game of life, death, and annihilation in Slater determinant space. , 2009, The Journal of chemical physics.

[10]  R J Needs,et al.  Inhomogeneous backflow transformations in quantum Monte Carlo calculations. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Ali Alavi,et al.  The Intricate Case of Tetramethyleneethane: A Full Configuration Interaction Quantum Monte Carlo Benchmark and Multireference Coupled Cluster Studies. , 2018, Journal of chemical theory and computation.

[12]  Phani K V V Nukala,et al.  A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations. , 2009, The Journal of chemical physics.

[13]  Bartomeu Monserrat,et al.  Dissociation of high-pressure solid molecular hydrogen: a quantum Monte Carlo and anharmonic vibrational study. , 2014, Physical review letters.

[14]  E. Giner,et al.  Quantum Monte Carlo with reoptimised perturbatively selected configuration-interaction wave functions , 2016, 1601.05915.

[15]  A. Alavi,et al.  Similarity transformation of the electronic Schrödinger equation via Jastrow factorization , 2019, The Journal of Chemical Physics.

[16]  A. Badinski,et al.  Nodal Pulay terms for accurate diffusion quantum Monte Carlo forces , 2008 .

[17]  P. L. Ríos.  Backflow and pairing wave function for quantum Monte Carlo methods , 2016 .

[18]  N. Drummond,et al.  Quantum Monte Carlo calculations of energy gaps from first principles , 2018, Physical Review B.

[19]  P. Dirac.  Quantum Mechanics of Many-Electron Systems , 1929 .

[20]  Chris J Pickard,et al.  Structure and Metallicity of Phase V of Hydrogen. , 2018, Physical review letters.

[21]  Ulli Wolff.  Monte Carlo errors with less errors , 2004 .

[22]  Chris J Pickard,et al.  Ab initio random structure searching , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[23]  Richard G. Hennig,et al.  Alleviation of the Fermion-sign problem by optimization of many-body wave functions , 2007 .

[24]  C. Melton,et al.  A new generation of effective core potentials from correlated calculations: 3d transition metal series. , 2018, The Journal of chemical physics.

[25]  C. Cheng,et al.  Van der Waals interaction in a boron nitride bilayer , 2014 .

[26]  Chris J. Pickard,et al.  Density functional theory study of phase IV of solid hydrogen , 2012, 1204.3304.

[27]  Takuma Tsuchiya.  Excitonic complexes in quantum structures: a quantum Monte Carlo study , 2004 .

[28]  G. Strinati,et al.  Evolution of the normal state of a strongly interacting Fermi gas from a pseudogap phase to a molecular Bose gas. , 2010, Physical review letters.

[29]  S. M. Rothstein,et al.  Optimal spacing and weights in diffusion monte carlo , 1986 .

[30]  R. Needs,et al.  Pseudopotential for the electron-electron interaction , 2015, 1508.02004.

[31]  R. Needs,et al.  Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid , 2009, 1002.2122.

[32]  R. Needs,et al.  Quantum Monte Carlo study of the phase diagram of solid molecular hydrogen at extreme pressures , 2015, Nature Communications.

[33]  A. Scemama,et al.  Excitation energies from diffusion Monte Carlo using selected configuration interaction nodes. , 2018, The Journal of chemical physics.

[34]  C J Umrigar,et al.  Optimization of quantum Monte Carlo wave functions by energy minimization. , 2007, The Journal of chemical physics.

[35]  Shirley,et al.  Many-body core-valence partitioning. , 1993, Physical review. B, Condensed matter.

[36]  Gustavo E Scuseria,et al.  Computing the energy of a water molecule using multideterminants: a simple, efficient algorithm. , 2011, The Journal of chemical physics.

[37]  C. Attaccalite,et al.  Stable liquid hydrogen at high pressure by a novel Ab initio molecular-dynamics calculation. , 2008, Physical review letters.

[38]  G. Galli,et al.  Nature and strength of interlayer binding in graphite. , 2009, Physical review letters.

[39]  Bartomeu Monserrat,et al.  Lattice dynamics and electron-phonon coupling calculations using nondiagonal supercells , 2015, 1510.04418.

[40]  B. Barbiellini,et al.  Improved generalized gradient approximation for positron states in solids , 2013, 1308.5808.

[41]  V. Fal’ko,et al.  Three-particle complexes in two-dimensional semiconductors. , 2014, Physical review letters.

[42]  R. Needs,et al.  Quantum Monte Carlo study of the energetics of the rutile, anatase, brookite, and columbite TiO$_{2}$ polymorphs , 2016, 1610.08992.

[43]  Foulkes,et al.  Quantum Monte Carlo calculations for solids using special k points methods. , 1994, Physical review letters.

[44]  D. Alfé,et al.  Petascale computing opens new vistas for quantum Monte , 2011 .

[45]  M P Nightingale,et al.  Optimization of ground- and excited-state wave functions and van der Waals clusters. , 2001, Physical review letters.

[46]  Seiji Yunoki,et al.  Resonating valence bond wave function: from lattice models to realistic systems , 2005, Comput. Phys. Commun..

[47]  D. Hartree,et al.  Self-consistent field, with exchange, for beryllium , 1935 .

[48]  R. Needs,et al.  Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg. , 2005, The Journal of chemical physics.

[49]  Wilson,et al.  Optimized trial wave functions for quantum Monte Carlo calculations. , 1988, Physical review letters.

[50]  A. Badinski,et al.  Accurate forces in quantum Monte Carlo calculations with nonlocal pseudopotentials. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  M. Bajdich,et al.  Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods , 2008 .

[52]  Stefano Baroni,et al.  Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations , 1999 .

[53]  Foulkes,et al.  Variational and diffusion quantum Monte Carlo calculations at nonzero wave vectors: Theory and application to diamond-structure germanium. , 1995, Physical review. B, Condensed matter.

[54]  M. Per,et al.  Energy-based truncation of multi-determinant wavefunctions in quantum Monte Carlo. , 2017, The Journal of chemical physics.

[55]  M. Casula,et al.  Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited. , 2010, The Journal of chemical physics.

[56]  T. Gruber,et al.  Ab initio calculations of carbon and boron nitride allotropes and their structural phase transitions using periodic coupled cluster theory , 2018, Physical Review B.

[57]  D. Pines.  A Collective Description of-Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas , 1953 .

[58]  V. Fal’ko,et al.  Diffusion quantum Monte Carlo study of excitonic complexes in two-dimensional transition-metal dichalcogenides , 2017, 1706.04688.

[59]  T. Gruber,et al.  Applying the Coupled-Cluster Ansatz to Solids and Surfaces in the Thermodynamic Limit , 2018, 2004.06584.

[60]  R. Needs,et al.  Correlated electron pseudopotentials for 3d-transition metals. , 2015, The Journal of chemical physics.

[61]  Ali Alavi,et al.  Combining the Complete Active Space Self-Consistent Field Method and the Full Configuration Interaction Quantum Monte Carlo within a Super-CI Framework, with Application to Challenging Metal-Porphyrins. , 2016, Journal of chemical theory and computation.

[62]  Hiroshi Nakatsuji,et al.  Solving the Schrodinger equation for helium atom and its isoelectronic ions with the free iterative complement interaction (ICI) method. , 2007, The Journal of chemical physics.

[63]  Kwon,et al.  Quantum Monte Carlo calculation of the Fermi-liquid parameters in the two-dimensional electron gas. , 1994, Physical review. B, Condensed matter.

[64]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[65]  Measurements of the density-dependent many-body electron mass in two dimensional GaAs/AlGaAs heterostructures. , 2004, Physical review letters.

[66]  M. Caffarel,et al.  Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces , 2003, physics/0310035.

[67]  M. Jonsson.  Standard error estimation by an automated blocking method , 2018, Physical Review E.

[68]  Richard Phillips Feynman,et al.  Energy Spectrum of the Excitations in Liquid Helium , 1956 .

[69]  R. Needs,et al.  Diffusion quantum Monte Carlo calculation of the quasiparticle effective mass of the two-dimensional homogeneous electron gas , 2012, 1208.6317.

[70]  R. Martin,et al.  Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study , 1998, cond-mat/9803092.

[71]  George H. Booth,et al.  A comparison between quantum chemistry and quantum Monte Carlo techniques for the adsorption of water on the (001) LiH surface , 2017, The Journal of chemical physics.

[72]  Markus Holzmann,et al.  Iterative backflow renormalization procedure for many-body ground-state wave functions of strongly interacting normal Fermi liquids , 2015, 1501.02199.

[73]  H. Mao,et al.  Vibron frequencies of solid H2 and D2 to 200 GPa and implications for the P-T phase diagram. , 2011, The Journal of chemical physics.

[74]  Vitaly A. Rassolov,et al.  A geminal model chemistry , 2002 .

[75]  R. Needs,et al.  Trion formation in a two-dimensional hole-doped electron gas , 2015, 1505.07411.

[76]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[77]  P. P. Ewald.  Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .

[78]  A. Michaelides,et al.  A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: Improving reproducibility and reducing the trial-wave-function bias. , 2019, The Journal of chemical physics.

[79]  A. Alavi,et al.  Combining the Transcorrelated Method with Full Configuration Interaction Quantum Monte Carlo: Application to the Homogeneous Electron Gas. , 2017, Journal of chemical theory and computation.

[80]  Kenji Watanabe,et al.  Strongly Enhanced Tunneling at Total Charge Neutrality in Double-Bilayer Graphene-WSe_{2} Heterostructures. , 2018, Physical review letters.

[81]  R. Needs,et al.  All-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[82]  M. Boninsegni,et al.  Population size bias in diffusion Monte Carlo. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[83]  R. Needs,et al.  Jastrow correlation factor for atoms, molecules, and solids , 2004, 0801.0378.

[84]  D. Ceperley.  Ground state of the fermion one-component plasma: A Monte Carlo study in two and three dimensions , 1978 .

[85]  A. Sorouri,et al.  Finite-size errors in continuum quantum Monte Carlo calculations , 2008, 0806.0957.

[86]  C. Umrigar,et al.  A diffusion Monte Carlo algorithm with very small time-step errors , 1993 .

[87]  N. Drummond,et al.  Binding energies of excitonic complexes in type-II quantum rings from diffusion quantum Monte Carlo calculations , 2018, Physical Review B.

[88]  Norbert Nemec,et al.  Diffusion Monte Carlo: Exponential scaling of computational cost for large systems , 2009, 0906.0501.

[89]  S. Katayama,et al.  A quantum Monte Carlo study on excitonic molecules in type-II superlattices , 1998 .

[90]  A. J. Coleman.  THE STRUCTURE OF FERMION DENSITY MATRICES , 1963 .

[91]  A. Scemama,et al.  Perturbatively Selected Configuration-Interaction Wave Functions for Efficient Geometry Optimization in Quantum Monte Carlo , 2018, Journal of chemical theory and computation.

[92]  E. Neuscamman.  Subtractive manufacturing with geminal powers:making good use of a bad wave function , 2016 .

[93]  D. Ceperley.  The statistical error of green's function Monte Carlo , 1986 .

[94]  Risto M. Nieminen,et al.  Theory of Positrons in Solids and on Solid Surfaces , 1994 .

[95]  M. J. Gillan,et al.  LETTER TO THE EDITOR: Linear-scaling quantum Monte Carlo technique with non-orthogonal localized orbitals , 2004 .

[96]  A. Michaelides,et al.  Evidence for stable square ice from quantum Monte Carlo , 2016, 1611.06718.

[97]  M. Gillan,et al.  Boosting the accuracy and speed of quantum Monte Carlo: Size consistency and time step , 2016, 1605.08706.

[98]  H. Tamura,et al.  Measurement of photoluminescence spectral linewidth of a GaAs quantum well in perpendicular electric fields: Evidence of a crossover from trions to an electron-hole gas , 2013 .

[99]  Michele Casula.  Beyond the locality approximation in the standard diffusion Monte Carlo method , 2006 .

[100]  E. Hylleraas,et al.  Binding Energy of the Positronium Molecule , 1947 .

[101]  E. Hylleraas,et al.  Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium , 1929 .

[102]  R J Needs,et al.  Norm-conserving Hartree-Fock pseudopotentials and their asymptotic behavior. , 2009, The Journal of chemical physics.

[103]  N. Tubman,et al.  Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids , 2016, 1603.03957.

[104]  H. G. Petersen,et al.  Error estimates on averages of correlated data , 1989 .

[105]  W. Foulkes,et al.  Nature of the metallization transition in solid hydrogen , 2016, 1608.00754.

[106]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[107]  John C. Slater,et al.  Note on Hartree's Method , 1930 .

[108]  D. Ceperley,et al.  New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field. , 1993, Physical review letters.

[109]  V. Fal’ko,et al.  Binding energies of trions and biexcitons in two-dimensional semiconductors from diffusion quantum Monte Carlo calculations (vol 95, 081301, 2017) , 2017, 1701.07407.

[110]  R. Assaraf,et al.  Optimizing the Energy with Quantum Monte Carlo: A Lower Numerical Scaling for Jastrow-Slater Expansions. , 2017, Journal of chemical theory and computation.

[111]  J. Grossman,et al.  Linear-scaling quantum Monte Carlo calculations. , 2001, Physical review letters.

[112]  T. Gaskell.  The Collective Treatment of a Fermi Gas: II , 1961 .

[113]  R. Needs,et al.  Pseudopotentials for correlated electron systems. , 2013, Journal of Chemical Physics.

[114]  R. Needs,et al.  Finite size errors in quantum many-body simulations of extended systems , 1998, cond-mat/9810243.

[115]  Verena A. Neufeld,et al.  A study of the dense uniform electron gas with high orders of coupled cluster. , 2017, The Journal of chemical physics.

[116]  R. Needs,et al.  Continuum variational and diffusion quantum Monte Carlo calculations , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[117]  M. Atatüre,et al.  Charge-tuneable biexciton complexes in monolayer WSe2 , 2018, Nature Communications.

[118]  I. Bar-Joseph.  Excitons in two-dimensional electron gas , 2005 .

[119]  Ki-ichi Nakamura.  Two-Body Correlation of Interacting Fermions , 1959 .

[120]  Paul R. C. Kent,et al.  Monte Carlo energy and variance-minimization techniques for optimizing many-body wave functions , 1999 .

[121]  Kenji Watanabe,et al.  Tuning of impurity-bound interlayer complexes in a van der Waals heterobilayer , 2019, 2D Materials.

[122]  C. Lambert,et al.  Quasiparticle and excitonic gaps of one-dimensional carbon chains. , 2016, Physical chemistry chemical physics : PCCP.

[123]  Cox,et al.  Bound states in optical absorption of semiconductor quantum wells containing a two-dimensional electron Gas , 2000, Physical review letters.

[124]  R. Needs,et al.  Shape and energy consistent pseudopotentials for correlated electron systems. , 2017, The Journal of chemical physics.

[125]  M. Eremets,et al.  Conductive dense hydrogen. , 2011, Nature materials.

[126]  R. Krause-Rehberg,et al.  Positron Annihilation in Semiconductors , 1999 .

[127]  M. Parrinello,et al.  A Novel Technique for the Simulation of Interacting Fermion Systems , 1989 .

[128]  Claudia Filippi,et al.  Multiconfiguration wave functions for quantum Monte Carlo calculations of first‐row diatomic molecules , 1996 .

[129]  Ali Alavi,et al.  Taming the First-Row Diatomics: A Full Configuration Interaction Quantum Monte Carlo Study. , 2012, Journal of chemical theory and computation.

[130]  B. Alder,et al.  THE GROUND STATE OF THE ELECTRON GAS BY A STOCHASTIC METHOD , 2010 .

[131]  A. Alavi,et al.  A comparative study using state-of-the-art electronic structure theories on solid hydrogen phases under high pressures , 2019, npj Computational Materials.

[132]  Sandro Sorella,et al.  Geminal wave functions with Jastrow correlation: A first application to atoms , 2003 .

[133]  Ali Alavi,et al.  Breaking the carbon dimer: the challenges of multiple bond dissociation with full configuration interaction quantum Monte Carlo methods. , 2011, The Journal of chemical physics.

[134]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[135]  N. Drummond,et al.  Ground-state properties of the one-dimensional electron liquid , 2011, 1102.3854.

[136]  R. Martin,et al.  Renormalization factor and effective mass of the two-dimensional electron gas , 2008, 0810.2450.

[137]  John Edward Lennard-Jones,et al.  The molecular orbital theory of chemical valency XVI. A theory of paired-electrons in polyatomic molecules , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[138]  E. Pajanne,et al.  Electron liquid in collective description. III. Positron annihilation , 1979 .

[139]  M. J. Gillan,et al.  Efficient localized basis set for quantum Monte Carlo calculations on condensed matter , 2004 .

[140]  A. Tkatchenko,et al.  Fast and accurate quantum Monte Carlo for molecular crystals , 2018, Proceedings of the National Academy of Sciences.

[141]  R. Needs,et al.  Quantum Monte Carlo study of a positron in an electron gas. , 2011, Physical review letters.

[142]  Lubos Mitas,et al.  QWalk: A quantum Monte Carlo program for electronic structure , 2007, J. Comput. Phys..

[143]  N. Handy,et al.  A calculation for the energies and wavefunctions for states of neon with full electronic correlation accuracy , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[144]  S. Katayama,et al.  A quantum Monte Carlo study on excitonic molecules in quantum wells , 1998 .

[145]  G. Conduit,et al.  Jastrow correlation factor for periodic systems , 2016, 1607.05921.

[146]  A. Scemama,et al.  Excited States with Selected Configuration Interaction-Quantum Monte Carlo: Chemically Accurate Excitation Energies and Geometries , 2019, Journal of chemical theory and computation.

[147]  Takuma Tsuchiya.  Biexcitons and charged excitons in quantum dots: a quantum Monte Carlo study , 2000 .

[148]  R. Needs,et al.  Evidence from Quantum Monte Carlo Simulations of Large-Gap Superfluidity and BCS-BEC Crossover in Double Electron-Hole Layers. , 2017, Physical review letters.

[149]  E. Gregoryanz,et al.  Evidence for a new phase of dense hydrogen above 325 gigapascals , 2016, Nature.

[150]  R. Needs,et al.  Exciton-exciton interaction and biexciton formation in bilayer systems , 2008, 0811.3318.

[152]  Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities , 2002, cond-mat/0206147.

[154]  Payne,et al.  Periodic boundary conditions in ab initio calculations. , 1995, Physical review. B, Condensed matter.

[155]  R. T. Pack,et al.  Cusp Conditions for Molecular Wavefunctions , 1966 .

[156]  K. West,et al.  Measurements of the density-dependent many-body electron mass in 2D GaAs/AlGaAs Heterostructures , 2004 .

[157]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[158]  Ali Alavi,et al.  Communications: Survival of the fittest: accelerating convergence in full configuration-interaction quantum Monte Carlo. , 2010, The Journal of chemical physics.

[159]  D. Ceperley,et al.  Accurate, efficient, and simple forces computed with quantum Monte Carlo methods. , 2004, Physical review letters.

[160]  R. Needs,et al.  Erratum: Density functional theory study of phase IV of solid hydrogen [Phys. Rev. B 85 , 214114 (2012)] , 2012 .

[161]  R. J. Needs,et al.  Variance-minimization scheme for optimizing Jastrow factors , 2005 .

[162]  G. Conduit,et al.  Tail-regression estimator for heavy-tailed distributions of known tail indices and its application to continuum quantum Monte Carlo data. , 2019, Physical review. E.

[163]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[164]  S. Moroni,et al.  Orbital-dependent backflow wave functions for real-space quantum Monte Carlo , 2019, Physical Review B.

[165]  Bonding, structures, and band gap closure of hydrogen at high pressures , 2012, 1209.3895.

[166]  R. Needs,et al.  Excitons and biexcitons in symmetric electron-hole bilayers. , 2013, Physical review letters.

[167]  David Pfau,et al.  Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks , 2019, Physical Review Research.

[168]  N. Drummond,et al.  Stability of trions in coupled quantum wells modeled by two-dimensional bilayers , 2017, 1707.09427.

[169]  Foulkes,et al.  Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions. , 1996, Physical review. B, Condensed matter.

[170]  E. Wang,et al.  Adsorption and diffusion of water on graphene from first principles , 2011 .

[171]  V. Fal’ko,et al.  Localized interlayer complexes in heterobilayer transition metal dichalcogenides , 2018, Physical Review B.

[172]  R J Needs,et al.  Scheme for adding electron-nucleus cusps to Gaussian orbitals. , 2005, The Journal of chemical physics.

[173]  Ying Wai Li,et al.  QMCPACK: an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids , 2018, Journal of physics. Condensed matter : an Institute of Physics journal.

[174]  James B. Anderson,et al.  Quantum chemistry by random walk. H 2P, H+3D3h1A′1, H23Σ+u, H41Σ+g, Be 1S , 1976 .

[175]  R. Needs,et al.  Quantum Monte Carlo calculation of the energy band and quasiparticle effective mass of the two-dimensional Fermi fluid , 2009, 0910.1434.

[176]  T. Gokmen,et al.  Effective mass suppression in dilute, spin-polarized two-dimensional electron systems. , 2008, Physical review letters.

[177]  A. Gross,et al.  Reaction energetics of hydrogen on Si(100) surface: A periodic many-electron theory study. , 2018, The Journal of chemical physics.

[178]  Dario Bressanini,et al.  Robust wave function optimization procedures in quantum Monte Carlo methods , 2002 .

[179]  Bartomeu Monserrat,et al.  Anharmonic vibrational properties in periodic systems: energy, electron-phonon coupling, and stress , 2013, 1303.0745.

[180]  A. Alavi,et al.  Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via nonunitary similarity transformations , 2018, Physical Review B.

[181]  V. Fal’ko,et al.  Quantum Monte Carlo calculation of the binding energy of bilayer graphene. , 2015, Physical review letters.

[182]  J. Perdew,et al.  How accurate are the parametrized correlation energies of the uniform electron gas , 2018 .

[183]  Shiwei Zhang,et al.  Finite-size correction in many-body electronic structure calculations. , 2007, Physical review letters.

[184]  W. Foulkes,et al.  Quantum Monte Carlo study of high pressure solid molecular hydrogen , 2013, 1307.1463.

[185]  Iliya Sabzevari,et al.  Improved Speed and Scaling in Orbital Space Variational Monte Carlo. , 2018, Journal of chemical theory and computation.

[186]  P. Stiles,et al.  Electron-Electron Interactions Continuously Variable in the Range2.1>rs>0.9 , 1972 .

[187]  D. Ceperley,et al.  Monte Carlo simulation of a many-fermion study , 1977 .

[188]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[189]  Umrigar,et al.  Accelerated Metropolis method. , 1993, Physical review letters.

[190]  A. Badinski,et al.  Methods for calculating forces within quantum Monte Carlo simulations , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[191]  R. Assaraf,et al.  Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo. , 2016, The Journal of chemical physics.

[192]  A. Alavi,et al.  Efficient formulation of full configuration interaction quantum Monte Carlo in a spin eigenbasis via the graphical unitary group approach. , 2019, The Journal of chemical physics.

[193]  Chris J. Pickard,et al.  Hexagonal structure of phase III of solid hydrogen , 2016, 1609.07486.

[194]  D M Ceperley,et al.  Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[195]  Iron-based superconductors: Current status of materials and pairing mechanism , 2015, 1504.04919.

[196]  Ali Alavi,et al.  A Full Configuration Interaction Perspective on the Homogeneous Electron Gas , 2011, 1109.2635.

[197]  R J Needs,et al.  Energy derivatives in quantum Monte Carlo involving the zero-variance property. , 2008, The Journal of chemical physics.

[198]  C. Melton,et al.  Spin-orbit interactions in electronic structure quantum Monte Carlo methods , 2015, 1510.08096.

[199]  M. Tan,et al.  Exciton and biexciton energies in bilayer systems , 2005, 0801.0375.

[200]  R. Needs,et al.  Perspective: Role of structure prediction in materials discovery and design , 2016 .

[201]  N. Nemec,et al.  Strategies for improving the efficiency of quantum Monte Carlo calculations. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[202]  Excitonic condensation in a symmetric electron-hole bilayer. , 2002, Physical review letters.

[203]  R. Nieminen,et al.  Electron-positron density-functional theory. , 1986, Physical review. B, Condensed matter.

[204]  D. Ceperley.  Path integrals in the theory of condensed helium , 1995 .

[205]  A. Alavi,et al.  Correlation energies of the high-density spin-polarized electron gas to meV accuracy , 2018, Physical Review B.

[206]  D. Ceperley,et al.  Backflow correlations for the electron gas and metallic hydrogen. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[207]  L. Hedin.  NEW METHOD FOR CALCULATING THE ONE-PARTICLE GREEN'S FUNCTION WITH APPLICATION TO THE ELECTRON-GAS PROBLEM , 1965 .

[208]  Timothy C. Berkelbach,et al.  Binding energies and spatial structures of small carrier complexes in monolayer transition-metal dichalcogenides via diffusion Monte Carlo , 2015, 1508.01224.

[209]  V. Fock,et al.  Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems , 1930 .

[210]  Malvin H. Kalos,et al.  Green's Function Monte Carlo Method for Liquid He 3 , 1981 .

[211]  R. Needs,et al.  Quantum Monte Carlo simulations of solids , 2001 .

[212]  Chris J. Pickard,et al.  Structure of phase III of solid hydrogen , 2007 .

[213]  T. Kuehne,et al.  Unconventional phase III of high-pressure solid hydrogen , 2019, Physical Review B.

[214]  Markus Holzmann,et al.  Finite-size error in many-body simulations with long-range interactions. , 2006, Physical review letters.

[215]  Yan Wang,et al.  Elimination of Coulomb finite-size effects in quantum many-body simulations , 1997 .

[216]  G. Ackland,et al.  The role of van der Waals and exchange interactions in high-pressure solid hydrogen. , 2017, Physical chemistry chemical physics : PCCP.

[217]  J R Trail,et al.  Heavy-tailed random error in quantum Monte Carlo. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[218]  Satoshi Nakano,et al.  Raman scattering and X-ray diffraction studies on phase III of solid hydrogen , 2017 .