W. Purwanto | Old Dominion University (original) (raw)
Papers by W. Purwanto
Accurate potential energy curves are an essential ingredient in understanding chemical reactions.... more Accurate potential energy curves are an essential ingredient in understanding chemical reactions. This problem spans a wide range of correlations, with correlation effects being the most important in the bond-breaking regime. We report potential energy curves of simple molecules, including water and the carbon dimer, within the framework of the auxiliary-field quantum Monte Carlo (AFQMC) method. AFQMC projects the many-body
Physical Review A, 2005
We study the effects of many-body correlations in trapped ultracold atomic Bose gases. We calcula... more We study the effects of many-body correlations in trapped ultracold atomic Bose gases. We calculate the ground state of the gas using a ground-state auxiliary-field quantum Monte Carlo (QMC) method [Phys. Rev. E 70, 056702 (2004)]. We examine the properties of the gas, such as the energetics, condensate fraction, real-space density, and momentum distribution, as a function of the number of particles and the scattering length. We find that the mean-field Gross-Pitaevskii (GP) approach gives qualitatively incorrect result of the kinetic energy as a function of the scattering length. We present detailed QMC data for the various quantities, and discuss the behavior of GP, modified GP, and the Bogoliubov method under a local density approximation.
orbitals. Both FC and downfolding provide significant computational savings over fully correlatin... more orbitals. Both FC and downfolding provide significant computational savings over fully correlating all the electrons in full plane-wave basis, while retaining excellent transferability and accuracy. We demonstrate the approach by calculating the equation of state of crystalline MnO in antiferromagnetic and ferromagnetic phases. Twist-average boundary condition [2] and a finite-size correction [3] are employed to minimize the eect of finite simulation cell. AFQMC in this basis reproduces the results of the full plane-wave basis many-body calculations, and leads to accurate determination of the magnetic ordering.
Physical Review Letters, 2014
We investigate the stability and electronic properties of single Co atoms on graphene with near-e... more We investigate the stability and electronic properties of single Co atoms on graphene with near-exact manybody calculations. A frozen-orbital embedding scheme was combined with auxiliary-field quantum Monte Carlo to increase the reach in system sizes. Several energy minima are found as a function of the distance h between Co and graphene. Energetics only permit the Co atom to occupy the top site at h = 2.2Å in a high-spin 3d 8 4s 1 state, and the van der Waals region at h = 3.3Å in a high-spin 3d 7 4s 2 state. The findings provide an explanation for recent experimental results with Co on free-standing graphene.
Physical Review E, 2004
We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson sy... more We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson systems. The method is based on a field-theoretical approach, and is closely related to existing fermion auxiliary-field QMC methods which are applied in several fields of physics. The ground-state projection is implemented as a branching random walk in the space of permanents consisting of identical single-particle orbitals. Any singleparticle basis can be used, and the method is in principle exact. We illustrate this method with a trapped atomic boson gas, where the atoms interact via an attractive or repulsive contact two-body potential. We choose as the single-particle basis a real-space grid. We compare with exact results in small systems, and arbitrarily-sized systems of untrapped bosons with attractive interactions in one dimension, where analytical solutions exist. We also compare with the corresponding Gross-Pitaevskii (GP) mean-field calculations for trapped atoms, and discuss the close formal relation between our method and the GP approach. Our method provides a way to systematically improve upon GP while using the same framework, capturing interaction and correlation effects with a stochastic, coherent ensemble of non-interacting solutions. We discuss various algorithmic issues, including importance sampling and the back-propagation technique for computing observables, and illustrate them with numerical studies. We show results for systems with up to N ∼ 400 bosons.
Physical Review B, 2012
Many recent calculations have been performed to study a Co atom adsorbed on graphene, with signif... more Many recent calculations have been performed to study a Co atom adsorbed on graphene, with significantly varying results on the nature of the bonding. We use auxiliary-field quantum Monte Carlo (AFQMC) and a size-correction embedding scheme to accurately calculate the binding energy of Co on graphene. We find that as a function of the distance h between the Co atom and the six-fold hollow site, there are three distinct ground states corresponding to three electronic configurations of the Co atom. Two of these states provide binding and exhibit a double-well feature with nearly equal binding energy of 0.4 eV at h = 1.51 and h = 1.65Å, corresponding to low-spin 2 Co (3d 9 4s 0) and high-spin 4 Co (3d 8 4s 1), respectively.
We analyze Pion Nucleon Scattering up to 700 MeV using a simple, relativistic, unitary model. 1 T... more We analyze Pion Nucleon Scattering up to 700 MeV using a simple, relativistic, unitary model. 1 The kernel of the integral equation includes nucleon, roper, delta, D 13 as well as S 11 poles with their corresponding crossed pole terms approximated by contact interactions. The sand p-wave phase shifts are calculated from the model and shown to agree very well with the values derived from πN scattering data. 2 All parameters which involve S 11 are presented.
Physical Review B, 2007
The phaseless auxiliary-field quantum Monte Carlo ͑AF QMC͒ method ͓S. Zhang and H. Krakauer, Phys... more The phaseless auxiliary-field quantum Monte Carlo ͑AF QMC͒ method ͓S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 ͑2003͔͒ is used to carry out a systematic study of the dissociation and ionization energies of second-row group 3A-7A atoms and dimers: Al, Si, P, S, and Cl. In addition, the P 2 dimer is compared to the third-row As 2 dimer, which is also triply bonded. This method projects the many-body ground state by means of importance-sampled random walks in the space of Slater determinants. The Monte Carlo phase problem, due to the electron-electron Coulomb interaction, is controlled via the phaseless approximation, with a trial wave function ͉⌿ T ͘. As in previous calculations, a mean-field single Slater determinant is used as ͉⌿ T ͘. The method is formulated in the Hilbert space defined by any chosen one-particle basis. The present calculations use a plane wave basis under periodic boundary conditions with norm-conserving pseudopotentials. Computational details of the plane wave AF QMC method are presented. The isolated systems chosen here allow a systematic study of the various algorithmic issues. We show the accuracy of the plane wave method and discuss its convergence with respect to parameters such as the supercell size and plane wave cutoff. The use of standard norm-conserving pseudopotentials in the many-body AF QMC framework is examined.
Physical Review B, 2009
The pressure-induced structural phase transition from diamond to β-tin in silicon is an excellent... more The pressure-induced structural phase transition from diamond to β-tin in silicon is an excellent test for theoretical total energy methods. The transition pressure provides a sensitive measure of small relative energy changes between the two phases (one a semiconductor and the other a semimetal). Experimentally, the transition pressure is well characterized. Density-functional results have been unsatisfactory. Even the generally much more accurate diffusion Monte Carlo method has shown a noticeable fixed-node error. We use the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to calculate the relative energy differences in the two phases. In this method, all but the error due to the phaseless constraint can be controlled systematically and driven to zero. In both structural phases we were able to benchmark the error of the phaseless constraint by carrying out exact unconstrained AFQMC calculations for small supercells. Comparison between the two shows that the systematic error in the absolute total energies due to the phaseless constraint is well within 0.5mEh/atom. Consistent with these internal benchmarks, the transition pressure obtained by the phaseless AFQMC from large supercells is in very good agreement with experiment.
Journal of Physics: Conference Series, 2008
Over the past two decades, continuum quantum Monte Carlo (QMC) has proved to be an invaluable too... more Over the past two decades, continuum quantum Monte Carlo (QMC) has proved to be an invaluable tool for predicting of the properties of matter from fundamental principles. By solving the Schrödinger equation through a stochastic projection, it achieves the greatest accuracy and reliability of methods available for physical systems containing more than a few quantum particles. QMC enjoys scaling favorable to quantum chemical methods, with a computational effort which grows with the second or third power of system size. This accuracy and scalability has enabled scientific discovery across a broad spectrum of disciplines. The current methods perform very efficiently at the terascale. The quantum Monte Carlo Endstation project is a collaborative effort among researchers in the field to develop a new generation of algorithms, and their efficient implementations, which will take advantage of the upcoming petaflop architectures. Some aspects of these developments are discussed here. These tools will expand the accuracy, efficiency and range of QMC applicability and enable us to tackle challenges which are currently out of reach. The methods will be applied to several important problems including electronic and structural properties of water, transition metal oxides, nanosystems and ultracold atoms.
![Research paper thumbnail of Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C[sub 2] singlet states](https://attachments.academia-assets.com/55776867/thumbnails/1.jpg)
](The Journal of Chemical Physics, 2009
We show that the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method ... more We show that the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method can be used to study excited states, providing an alternative to standard quantum chemistry methods. The phaseless AFQMC approach, whose computational cost scales as M 3 -M 4 with system size M , has been shown to be among the most accurate many-body methods in ground state calculations. For excited states, prevention of collapse into the ground state and control of the Fermion sign/phase problem are accomplished by the approximate phaseless constraint with a trial wave function. Using the challenging C2 molecule as a test case, we calculate the potential energy curves of the ground and two low-lying singlet excited states. The trial wave function is obtained by truncating complete active space wave functions, with no further optimization. The phaseless AFQMC results using a small basis set are in good agreement with exact full configuration interaction calculations, while those using large basis sets are in good agreement with experimental spectroscopic constants.
The Journal of Chemical Physics, 2011
Weak H2 physisorption energies present a significant challenge to even the best correlated theore... more Weak H2 physisorption energies present a significant challenge to even the best correlated theoretical manybody methods. We use the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to accurately predict the binding energy of Ca + -4H2. Attention has recently focused on this model chemistry to test the reliability of electronic structure methods for H2 binding on dispersed alkaline earth metal centers. A modified Cholesky decomposition is implemented to realize the Hubbard-Stratonovich transformation efficiently with large Gaussian basis sets. We employ the largest correlation-consistent Gaussian type basis sets available, up to cc-pCV5Z for Ca, to accurately extrapolate to the complete basis limit. The calculated potential energy curve exhibits binding with a double-well structure.
The Journal of Chemical Physics, 2008
The use of an approximate reference state wave function mid R:Phi(r) in electronic many-body meth... more The use of an approximate reference state wave function mid R:Phi(r) in electronic many-body methods can break the spin symmetry of Born-Oppenheimer spin-independent Hamiltonians. This can result in significant errors, especially when bonds are stretched or broken. A simple spin-projection method is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations, which yields spin-contamination-free results, even with a spin-contaminated mid R:Phi(r). The method is applied to the difficult F(2) molecule, which is unbound within unrestricted Hartree-Fock (UHF). With a UHF mid R:Phi(r), spin contamination causes large systematic errors and long equilibration times in AFQMC in the intermediate, bond-breaking region. The spin-projection method eliminates these problems and delivers an accurate potential energy curve from equilibrium to the dissociation limit using the UHF mid R:Phi(r). Realistic potential energy curves are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are in excellent agreement with experiment.
The accurate determination of potential energy curves (PECs) and excited states represents two di... more The accurate determination of potential energy curves (PECs) and excited states represents two difficult problems in electronic structure calculations. We present AFQMC PECs of the challenging C2 molecule, focusing on the ground state and two singlet low-lying excited states. AFQMC calculates a target many-body wave function (WF) by means of random walks in the space of Slater determinants. We employ
Accurate potential energy curves are an essential ingredient in understanding chemical reactions.... more Accurate potential energy curves are an essential ingredient in understanding chemical reactions. This problem spans a wide range of correlations, with correlation effects being the most important in the bond-breaking regime. We report potential energy curves of simple molecules, including water and the carbon dimer, within the framework of the auxiliary-field quantum Monte Carlo (AFQMC) method. AFQMC projects the many-body
Physical Review A, 2005
We study the effects of many-body correlations in trapped ultracold atomic Bose gases. We calcula... more We study the effects of many-body correlations in trapped ultracold atomic Bose gases. We calculate the ground state of the gas using a ground-state auxiliary-field quantum Monte Carlo (QMC) method [Phys. Rev. E 70, 056702 (2004)]. We examine the properties of the gas, such as the energetics, condensate fraction, real-space density, and momentum distribution, as a function of the number of particles and the scattering length. We find that the mean-field Gross-Pitaevskii (GP) approach gives qualitatively incorrect result of the kinetic energy as a function of the scattering length. We present detailed QMC data for the various quantities, and discuss the behavior of GP, modified GP, and the Bogoliubov method under a local density approximation.
orbitals. Both FC and downfolding provide significant computational savings over fully correlatin... more orbitals. Both FC and downfolding provide significant computational savings over fully correlating all the electrons in full plane-wave basis, while retaining excellent transferability and accuracy. We demonstrate the approach by calculating the equation of state of crystalline MnO in antiferromagnetic and ferromagnetic phases. Twist-average boundary condition [2] and a finite-size correction [3] are employed to minimize the eect of finite simulation cell. AFQMC in this basis reproduces the results of the full plane-wave basis many-body calculations, and leads to accurate determination of the magnetic ordering.
Physical Review Letters, 2014
We investigate the stability and electronic properties of single Co atoms on graphene with near-e... more We investigate the stability and electronic properties of single Co atoms on graphene with near-exact manybody calculations. A frozen-orbital embedding scheme was combined with auxiliary-field quantum Monte Carlo to increase the reach in system sizes. Several energy minima are found as a function of the distance h between Co and graphene. Energetics only permit the Co atom to occupy the top site at h = 2.2Å in a high-spin 3d 8 4s 1 state, and the van der Waals region at h = 3.3Å in a high-spin 3d 7 4s 2 state. The findings provide an explanation for recent experimental results with Co on free-standing graphene.
Physical Review E, 2004
We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson sy... more We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson systems. The method is based on a field-theoretical approach, and is closely related to existing fermion auxiliary-field QMC methods which are applied in several fields of physics. The ground-state projection is implemented as a branching random walk in the space of permanents consisting of identical single-particle orbitals. Any singleparticle basis can be used, and the method is in principle exact. We illustrate this method with a trapped atomic boson gas, where the atoms interact via an attractive or repulsive contact two-body potential. We choose as the single-particle basis a real-space grid. We compare with exact results in small systems, and arbitrarily-sized systems of untrapped bosons with attractive interactions in one dimension, where analytical solutions exist. We also compare with the corresponding Gross-Pitaevskii (GP) mean-field calculations for trapped atoms, and discuss the close formal relation between our method and the GP approach. Our method provides a way to systematically improve upon GP while using the same framework, capturing interaction and correlation effects with a stochastic, coherent ensemble of non-interacting solutions. We discuss various algorithmic issues, including importance sampling and the back-propagation technique for computing observables, and illustrate them with numerical studies. We show results for systems with up to N ∼ 400 bosons.
Physical Review B, 2012
Many recent calculations have been performed to study a Co atom adsorbed on graphene, with signif... more Many recent calculations have been performed to study a Co atom adsorbed on graphene, with significantly varying results on the nature of the bonding. We use auxiliary-field quantum Monte Carlo (AFQMC) and a size-correction embedding scheme to accurately calculate the binding energy of Co on graphene. We find that as a function of the distance h between the Co atom and the six-fold hollow site, there are three distinct ground states corresponding to three electronic configurations of the Co atom. Two of these states provide binding and exhibit a double-well feature with nearly equal binding energy of 0.4 eV at h = 1.51 and h = 1.65Å, corresponding to low-spin 2 Co (3d 9 4s 0) and high-spin 4 Co (3d 8 4s 1), respectively.
We analyze Pion Nucleon Scattering up to 700 MeV using a simple, relativistic, unitary model. 1 T... more We analyze Pion Nucleon Scattering up to 700 MeV using a simple, relativistic, unitary model. 1 The kernel of the integral equation includes nucleon, roper, delta, D 13 as well as S 11 poles with their corresponding crossed pole terms approximated by contact interactions. The sand p-wave phase shifts are calculated from the model and shown to agree very well with the values derived from πN scattering data. 2 All parameters which involve S 11 are presented.
Physical Review B, 2007
The phaseless auxiliary-field quantum Monte Carlo ͑AF QMC͒ method ͓S. Zhang and H. Krakauer, Phys... more The phaseless auxiliary-field quantum Monte Carlo ͑AF QMC͒ method ͓S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 ͑2003͔͒ is used to carry out a systematic study of the dissociation and ionization energies of second-row group 3A-7A atoms and dimers: Al, Si, P, S, and Cl. In addition, the P 2 dimer is compared to the third-row As 2 dimer, which is also triply bonded. This method projects the many-body ground state by means of importance-sampled random walks in the space of Slater determinants. The Monte Carlo phase problem, due to the electron-electron Coulomb interaction, is controlled via the phaseless approximation, with a trial wave function ͉⌿ T ͘. As in previous calculations, a mean-field single Slater determinant is used as ͉⌿ T ͘. The method is formulated in the Hilbert space defined by any chosen one-particle basis. The present calculations use a plane wave basis under periodic boundary conditions with norm-conserving pseudopotentials. Computational details of the plane wave AF QMC method are presented. The isolated systems chosen here allow a systematic study of the various algorithmic issues. We show the accuracy of the plane wave method and discuss its convergence with respect to parameters such as the supercell size and plane wave cutoff. The use of standard norm-conserving pseudopotentials in the many-body AF QMC framework is examined.
Physical Review B, 2009
The pressure-induced structural phase transition from diamond to β-tin in silicon is an excellent... more The pressure-induced structural phase transition from diamond to β-tin in silicon is an excellent test for theoretical total energy methods. The transition pressure provides a sensitive measure of small relative energy changes between the two phases (one a semiconductor and the other a semimetal). Experimentally, the transition pressure is well characterized. Density-functional results have been unsatisfactory. Even the generally much more accurate diffusion Monte Carlo method has shown a noticeable fixed-node error. We use the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to calculate the relative energy differences in the two phases. In this method, all but the error due to the phaseless constraint can be controlled systematically and driven to zero. In both structural phases we were able to benchmark the error of the phaseless constraint by carrying out exact unconstrained AFQMC calculations for small supercells. Comparison between the two shows that the systematic error in the absolute total energies due to the phaseless constraint is well within 0.5mEh/atom. Consistent with these internal benchmarks, the transition pressure obtained by the phaseless AFQMC from large supercells is in very good agreement with experiment.
Journal of Physics: Conference Series, 2008
Over the past two decades, continuum quantum Monte Carlo (QMC) has proved to be an invaluable too... more Over the past two decades, continuum quantum Monte Carlo (QMC) has proved to be an invaluable tool for predicting of the properties of matter from fundamental principles. By solving the Schrödinger equation through a stochastic projection, it achieves the greatest accuracy and reliability of methods available for physical systems containing more than a few quantum particles. QMC enjoys scaling favorable to quantum chemical methods, with a computational effort which grows with the second or third power of system size. This accuracy and scalability has enabled scientific discovery across a broad spectrum of disciplines. The current methods perform very efficiently at the terascale. The quantum Monte Carlo Endstation project is a collaborative effort among researchers in the field to develop a new generation of algorithms, and their efficient implementations, which will take advantage of the upcoming petaflop architectures. Some aspects of these developments are discussed here. These tools will expand the accuracy, efficiency and range of QMC applicability and enable us to tackle challenges which are currently out of reach. The methods will be applied to several important problems including electronic and structural properties of water, transition metal oxides, nanosystems and ultracold atoms.
The Journal of Chemical Physics, 2009
We show that the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method ... more We show that the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method can be used to study excited states, providing an alternative to standard quantum chemistry methods. The phaseless AFQMC approach, whose computational cost scales as M 3 -M 4 with system size M , has been shown to be among the most accurate many-body methods in ground state calculations. For excited states, prevention of collapse into the ground state and control of the Fermion sign/phase problem are accomplished by the approximate phaseless constraint with a trial wave function. Using the challenging C2 molecule as a test case, we calculate the potential energy curves of the ground and two low-lying singlet excited states. The trial wave function is obtained by truncating complete active space wave functions, with no further optimization. The phaseless AFQMC results using a small basis set are in good agreement with exact full configuration interaction calculations, while those using large basis sets are in good agreement with experimental spectroscopic constants.
The Journal of Chemical Physics, 2011
Weak H2 physisorption energies present a significant challenge to even the best correlated theore... more Weak H2 physisorption energies present a significant challenge to even the best correlated theoretical manybody methods. We use the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to accurately predict the binding energy of Ca + -4H2. Attention has recently focused on this model chemistry to test the reliability of electronic structure methods for H2 binding on dispersed alkaline earth metal centers. A modified Cholesky decomposition is implemented to realize the Hubbard-Stratonovich transformation efficiently with large Gaussian basis sets. We employ the largest correlation-consistent Gaussian type basis sets available, up to cc-pCV5Z for Ca, to accurately extrapolate to the complete basis limit. The calculated potential energy curve exhibits binding with a double-well structure.
The Journal of Chemical Physics, 2008
The use of an approximate reference state wave function mid R:Phi(r) in electronic many-body meth... more The use of an approximate reference state wave function mid R:Phi(r) in electronic many-body methods can break the spin symmetry of Born-Oppenheimer spin-independent Hamiltonians. This can result in significant errors, especially when bonds are stretched or broken. A simple spin-projection method is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations, which yields spin-contamination-free results, even with a spin-contaminated mid R:Phi(r). The method is applied to the difficult F(2) molecule, which is unbound within unrestricted Hartree-Fock (UHF). With a UHF mid R:Phi(r), spin contamination causes large systematic errors and long equilibration times in AFQMC in the intermediate, bond-breaking region. The spin-projection method eliminates these problems and delivers an accurate potential energy curve from equilibrium to the dissociation limit using the UHF mid R:Phi(r). Realistic potential energy curves are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are in excellent agreement with experiment.
The accurate determination of potential energy curves (PECs) and excited states represents two di... more The accurate determination of potential energy curves (PECs) and excited states represents two difficult problems in electronic structure calculations. We present AFQMC PECs of the challenging C2 molecule, focusing on the ground state and two singlet low-lying excited states. AFQMC calculates a target many-body wave function (WF) by means of random walks in the space of Slater determinants. We employ