arXiv subjects

Wirawan Purwanto

Publications and source records attributed to Wirawan Purwanto.

16 recordsLinked to original sources

arXiv2025

3-Dimensional Adaptive Unstructured Tessellated Look-up Tables for the Approximation of Compton Form Factors

We describe an iterative algorithm to construct an unstructured tessellation of simplices (irregular tetrahedra in 3-dimensions) to approximate an arbitrary function to a desired precision by interpolation. The method is applied to the generation of Compton Form Factors for simulation and analysis of nuclear femtography, as enabled by high energy exclusive processes such as electron-proton scattering producing just an electron, proton, and gamma-ray in the final state. While producing tessellations with only a 1% mean interpolation error, our results show that the use of such tessellations can significantly decrease the computation time for Monte Carlo event generation by $\sim23$ times for $10^{7}$ events (and using extrapolation, by $\sim955$ times for $10^{10}$ events).

math.NA↗

arXiv2020

Recent developments in the PySCF program package

PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows. The present paper explains the design and philosophy behind PYSCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PYSCF as a development environment. We then summarize the capabilities of PYSCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PYSCF across the domains of quantum chemistry, materials science, machine learning and quantum information science.

physics.chem-ph↗

arXiv2016

Auxiliary-field quantum Monte Carlo calculations of the molybdenum dimer

Chemical accuracy is difficult to achieve for systems with transition metal atoms. Third row transition metal atoms are particularly challenging due to strong electron-electron correlation in localized d-orbitals. The Cr2 molecule is an outstanding example, which we previously treated with highly accurate auxiliary-field quantum Monte Carlo (AFQMC) calculations [Purwanto et al., J. Chem. Phys. 142, 064302 (2015)]. Somewhat surprisingly, computational description of the isoelectronic Mo2 dimer has also, to date, been scattered and less than satisfactory. We present high-level theoretical benchmarks of the Mo2 singlet ground state ($X ^1Σ_g^+$) and first triplet excited state ($a ^3Σ_u^+$), using the phaseless AFQMC calculations. Extrapolation to the complete basis set limit is performed. Excellent agreement with experimental spectroscopic constants is obtained. We also present a comparison of the correlation effects in Cr2 and Mo2.

physics.chem-ph↗

arXiv2014

Quantum Monte Carlo calculations in solids with downfolded Hamiltonians

We present a systematic downfolding many-body approach for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using a frozen-core treatment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. We use the auxiliary-field quantum Monte Carlo (AFQMC) method to solve the downfolded Hamiltonian. Excellent accuracy is achieved for a range of solids, including semiconductors, ionic insulators, and metals. We further test the method by determining the spin gap in NiO, a challenging prototypical material with strong electron correlation effects. This approach greatly extends the reach of general, ab initio many-body calculations in materials.

cond-mat.mtrl-sci↗

arXiv2014

An Auxiliary-Field Quantum Monte Carlo Study of the Chromium Dimer

The chromium dimer (Cr2) presents an outstanding challenge for many-body electronic structure methods. Its complicated nature of binding, with a formal sextuple bond and an unusual potential energy curve, is emblematic of the competing tendencies and delicate balance found in many strongly correlated materials. We present a near-exact calculation of the potential energy curve (PEC) and ground state properties of Cr2, using the auxiliary-field quantum Monte Carlo (AFQMC) method. Unconstrained, exact AFQMC calculations are first carried out for a medium-sized but realistic basis set. Elimination of the remaining finite-basis errors and extrapolation to the complete basis set (CBS) limit is then achieved with a combination of phaseless and exact AFQMC calculations. Final results for the PEC and spectroscopic constants are in excellent agreement with experiment.

physics.comp-ph↗

arXiv2014

The Stability, Energetics, and Magnetic States of Cobalt Adatoms on Graphene

We investigate the stability and electronic properties of single Co atoms on graphene with near-exact many-body 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 $h = 2.2$ Å in a high-spin $3d^{8}4s^{1}$ state, and the van der Waals region at $h = 3.3$ Å in a high-spin $3d^{7}4s^{2}$ state. The findings provide an explanation for recent experimental results with Co on free-standing graphene.

cond-mat.mtrl-sci↗

arXiv2013

Frozen-orbital and downfolding calculations with auxiliary-field quantum Monte Carlo

We describe the implementation of the frozen-orbital and downfolding approximations in the auxiliary-field quantum Monte Carlo (AFQMC) method. These approaches can provide significant computational savings compared to fully correlating all the electrons. While the many-body wave function is never explicit in AFQMC, its random walkers are Slater determinants, whose orbitals may be expressed in terms of any one-particle orbital basis. It is therefore straightforward to partition the full N-particle Hilbert space into active and inactive parts to implement the frozen-orbital method. In the frozen-core approximation, for example, the core electrons can be eliminated in the correlated part of the calculations, greatly increasing the computational efficiency, especially for heavy atoms. Scalar relativistic effects are easily included using the Douglas-Kroll-Hess theory. Using this method, we obtain a way to effectively eliminate the error due to single-projector, norm-conserving pseudopotentials in AFQMC. We also illustrate a generalization of the frozen-orbital approach that downfolds high-energy basis states to a physically relevant low-energy sector, which allows a systematic approach to produce realistic model Hamiltonians to further increase efficiency for extended systems.

physics.comp-ph↗

arXiv2012

Ab Initio Many-body Study of Cobalt Adatoms Adsorbed on Graphene

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 = 1.65 angstroms, corresponding to low-spin $^2$Co (3d9 4s0) and high-spin $^4$Co (3d8 4s1), respectively.

cond-mat.mtrl-sci↗

arXiv2011

Assessing weak hydrogen binding on Ca+ centers: An accurate many-body study with large basis sets

Weak H2 physisorption energies present a significant challenge to even the best correlated theoretical many-body 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.

physics.comp-ph↗

arXiv2009

Pressure-induced diamond to beta-tin transition in bulk silicon: a near-exact quantum Monte Carlo study

The pressure-induced structural phase transition from diamond to beta-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 0.5 mHa/atom. Consistent with these internal benchmarks, the transition pressure obtained by the phaseless AFQMC from large supercells is in very good agreement with experiment.

cond-mat.mtrl-sci↗

arXiv2008

Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: potential energy curves of low lying C2 singlet states

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.

physics.comp-ph↗

arXiv2007

Eliminating spin contamination in auxiliary-field quantum Monte Carlo: realistic potential energy curve of F2

The use of an approximate reference state wave function |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 |Phi_r>. The method is applied to the difficult F2 molecule, which is unbound within unrestricted Hartree-Fock (UHF). With a UHF |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 |Phi_r>. Realistic potential energy curves are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are in excellent agreement with experiment.

physics.comp-ph↗

arXiv2007

Phaseless auxiliary-field quantum Monte Carlo calculations with planewaves and pseudopotentials--applications to atoms and molecules

The phaseless auxiliary-field quantum Monte Carlo (AF QMC) method [S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003)] 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, 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 |Psi_T>. As in previous calculations, a mean-field single Slater determinant is used as |Psi_T>. The method is formulated in the Hilbert space defined by any chosen one-particle basis. The present calculations use a planewave basis under periodic boundary conditions with norm-conserving pseudopotentials. Computational details of the planewave 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 planewave method and discuss its convergence with respect to parameters such as the supercell size and planewave cutoff. The use of standard norm-conserving pseudopotentials in the many-body AF QMC framework is examined.

cond-mat.mtrl-sci↗

arXiv2005

Correlation effects in the ground state of trapped atomic Bose gases

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.

cond-mat.other↗

arXiv2004

Quantum Monte Carlo method for the ground state of many-boson systems

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. 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.

physics.comp-ph↗

arXiv1999

The role of S_11 resonance in pi N Scattering

We analyze Pion Nucleon Scattering up to 700 MeV using a simple, relativistic, unitary model\cite{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 s- and p- wave phase shifts are calculated from the model and shown to agree very well with the values derived from pi N scattering data \cite {2}. All parameters which involve S_{11} are presented.

nucl-th↗