arXiv subjects

Henry Krakauer

Publications and source records attributed to Henry Krakauer.

35 records · Page 2Linked to original sources

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

Finite-size correction in many-body electronic structure calculations

Finite-size (FS) effects are a major source of error in many-body (MB) electronic structure calculations of extended systems. A method is presented to correct for such errors. We show that MB FS effects can be effectively included in a modified local density approximation calculation. A parametrization for the FS exchange-correlation functional is obtained. The method is simple and gives post-processing corrections that can be applied to any MB results. Applications to a model insulator (P$_2$ in a supercell), to semiconducting Si, and to metallic Na show that the method delivers greatly improved FS corrections.

cond-mat.mtrl-sci↗

arXiv2007

Bond breaking with auxiliary-field quantum Monte Carlo

Bond stretching mimics different levels of electron correlation and provides a challenging testbed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N$_2$, and in the H$_{50}$ chain. To control the sign/phase problem, the phaseless AF QMC method constrains the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. With single Slater determinants from unrestricted Hartree-Fock (UHF) as trial wave function, the phaseless AF QMC method generally gives better overall accuracy and a more uniform behavior than the coupled cluster CCSD(T) method in mapping the potential-energy curve. In both BH and N$_2$, we also study the use of multiple-determinant trial wave functions from multi-configuration self-consistent-field (MCSCF) calculations. The increase in computational cost versus the gain in statistical and systematic accuracy are examined. With such trial wave functions, excellent results are obtained across the entire region between equilibrium and the dissociation limit.

physics.comp-ph↗

arXiv2007

A study of H+H$_2$ and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with planewave and Gaussian basis sets

We present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H$_2$ near the equilibrium geometry and in the van der Walls limit, as well as H$_2$O, OH, and H$_2$O$_2$ molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a planewave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.

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↗

arXiv2006

Auxiliary-field quantum Monte Carlo study of first- and second-row post-d elements

A series of calculations for the first- and second-row post-d elements (Ga-Br and In-I) are presented using the phaseless auxiliary-field quantum Monte Carlo (AF QMC) method. This method is formulated in a Hilbert space defined by any chosen one-particle basis, and maps the many-body problem into a linear combination of independent-particle solutions with external auxiliary fields. The phase/sign problem is handled approximately by the phaseless formalism using a trial wave function, which in our calculations was chosen to be the Hartree-Fock solution. We used the consistent correlated basis sets of Peterson and coworkers, which employ a small core relativistic pseudopotential. The AF QMC results are compared with experiment and with those from density-functional (GGA and B3LYP) and coupled-cluster CCSD(T) calculations. The AF QMC total energies agree with CCSD(T) to within a few milli-hartrees across the systems and over several basis sets. The calculated atomic electron affinities, ionization energies, and spectroscopic properties of dimers are, at large basis sets, in excellent agreement with experiment.

physics.comp-ph↗

arXiv2006

Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis

We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis, and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with system size, as a low power. A QMC approach with auxiliary fields in principle allows an exact solution of the Schrodinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few milli-Hartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled-cluster with single and double excitations and with non-iterative triples, CCSD(T). For stretched bonds in H$_2$O, our method exhibits better overall accuracy and a more uniform behavior than CCSD(T).

physics.comp-ph↗

arXiv2005

Auxiliary-field quantum Monte Carlo study of TiO and MnO molecules

Calculations of the binding energy of the transition metal oxide molecules TiO and MnO are presented, using a recently developed phaseless auxiliary field quantum Monte Carlo approach. This method maps the interacting many-body problem onto a linear combination of non-interacting problems by a complex Hubbard-Stratonovich transformation, and controls the phase/sign problem with a phaseless approximation relying on a trial wave function. It employs random walks in Slater determinant space to project the ground state of the system, and allows use of much of the same machinery as in standard density functional theory calculations, such as planewave basis and non-local pseudopotentials. The calculations used a single Slater determinant trial wave function obtained from a density functional calculation, with no further optimization. The calculated binding energies are in good agreement with experiment and with recent diffusion Monte Carlo results. Together with previous results for sp-bonded systems, the present study indicates that the phaseless auxiliary field method is a robust and promising approach for the study of correlation effects in real materials.

cond-mat.str-el↗

arXiv2004

Kinetic Monte Carlo Simulations of Crystal Growth in Ferroelectric Alloys

The growth rates and chemical ordering of ferroelectric alloys are studied with kinetic Monte Carlo (KMC) simulations using an electrostatic model with long-range Coulomb interactions, as a function of temperature, chemical composition, and substrate orientation. Crystal growth is characterized by thermodynamic processes involving adsorption and evaporation, with solid-on-solid restrictions and excluding diffusion. A KMC algorithm is formulated to simulate this model efficiently in the presence of long-range interactions. Simulations were carried out on Ba(Mg_{1/3}Nb_{2/3})O_3 (BMN) type materials. Compared to the simple rocksalt ordered structures, ordered BMN grows only at very low temperatures and only under finely tuned conditions. For materials with tetravalent compositions, such as (1-x)Ba(Mg_{1/3}Nb_{2/3})O_3 + xBaZrO_3 (BMN-BZ), the model does not incorporate tetravalent ions at low-temperature, exhibiting a phase-separated ground state instead. At higher temperatures, tetravalent ions can be incorporated, but the resulting crystals show no chemical ordering in the absence of diffusive mechanisms.

cond-mat.mtrl-sci↗

arXiv2002

Quantum Monte Carlo method using phase-free random walks with Slater determinants

We develop a quantum Monte Carlo method for many fermions that allows the use of any one-particle basis. It projects out the ground state by random walks in the space of Slater determinants. An approximate approach is formulated to control the phase problem with a trial wave function $|Ψ_T>$. Using plane-wave basis and non-local pseudopotentials, we apply the method to Si atom, dimer, and 2, 16, 54 atom (216 electrons) bulk supercells. Single Slater determinant wave functions from density functional theory calculations were used as $|Ψ_T>$ with no additional optimization. The calculated binding energy of Si2 and cohesive energy of bulk Si are in excellent agreement with experiments and are comparable to the best existing theoretical results.

cond-mat↗

arXiv2000

Charge transfer electrostatic model of compositional order in perovskite alloys

We introduce an electrostatic model including charge transfer, which is shown to account for the observed B-site ordering in Pb-based perovskite alloys. The model allows charge transfer between A-sites and is a generalization of Bellaiche and Vanderbilt's purely electrostatic model. The large covalency of Pb^{2+} compared to Ba^{2+} is modeled by an environment dependent effective A-site charge. Monte Carlo simulations of this model successfully reproduce the long range compositional order of both Pb-based and Ba-based complex A(BB^{'}B^{''})O_3 perovskite alloys. The models are also extended to study systems with A-site and B-site doping, such as (Na_{1/2}La_{1/2})(Mg_{1/3}Nb_{2/3})O_3, (Ba_{1-x}La_{x})(Mg_{(1+x)/3}Nb_{(2-x)/3})O_3 and (Pb_{1-x}La_{x})(Mg_{(1+x)/3}Ta_{(2-x)/3})O_3. General trends are reproduced by purely electrostatic interactions, and charge transfer effects indicate that local structural relaxations can tip the balance between different B-site orderings in Pb based materials.

cond-mat.mtrl-sci↗

arXiv1998

First-Principles Studies of Local Order in Relaxor Ferroelectrics

A key to optimizing the growth of the new single-crystal relaxor ferroelectrics is resolving basic questions concerning their structural properties and energetics. We report on initial first-principles total energy and force calculations, examining the energetics of local order in PZN type relaxors.

cond-mat.mtrl-sci↗

arXiv1997

Ab Initio Linear Response Study of SrTiO3

The lattice instabilities of perovskite structure oxides are responsible for many of their interesting properties, such as temperature-dependent ferroelectric phase transitions. First-principles calculations using linear response theory provide an accurate means to determine the lattice dynamics throughout the entire Brillouin zone (BZ). Using the LAPW linear response method, we have previously carried out such a study on ferroelectric KNbO3. We present here the results of a similar investigation for cubic SrTiO3. While KNbO3 has only ferroelectric-type instabilities, SrTiO3 exhibits both ferroelectric (FE) and antiferrodistortive (AFD) instabilities. We correctly predict the known instability at the R-point in the BZ, which is responsible for the AFD phase transition to the tetragonal structure at about 105 K. Furthermore, the phase space of the ferroelectric instability is greatly reduced compared to KNbO3. Antiferrodistortive instabilities exist in one-dimensional cylindrical tubes extending along the entire R-M-R line in the BZ. The essentially 1-D character of these tubes corresponds to real space planar instabilities characterized by rotations of oxygen octahedra.

cond-mat.mtrl-sci↗

arXiv1996

Prediction of Phase Transition in CaSiO$_3$ Perovskite and Implications for Lower Mantle Structure

First principles linear response calculations are used to investigate the lattice dynamics of what is thought to be the third most abundant phase in the lower mantle, CaSiO_3 perovskite. The commonly assumed cubic structure (Pm3m) is found to be dynamically unstable at all pressures, exhibiting unstable modes along the Brillouin zone edge from the M-point to the R-point. Based on these results, we predict that the ground state structure of CaSiO_3 perovskite is a distorted phase with lower than cubic symmetry. We predict that a phase transition occurs in CaSiO_3 perovskite within the earth's lower mantle from the low temperature distorted phase to the cubic phase at high temperature. The predicted phase transition provides a possible explanation of some of the seismological observations of reflective features within the lower mantle.

physics.geo-ph↗

arXiv1996

Polarization Dependence of Born Effective Charge and Dielectric Constant in KNbO$_3$

The Born effective charge Z^{*} and dielectric tensor ε_{\infty} of KNbO_3 are found to be very sensitive to the atomic geometry, changing by as much as 27% between the paraelectric cubic and ferroelectric tetragonal and rhombohedral phases. Subtracting the bare ionic contribution reveals changes of the dynamic component of Z^{*} as large as 50%, for atomic displacements that are typically only a few percent of the lattice constant. Z^{*}, ε_{\infty} and all phonon frequencies at the Brillouin zone center were calculated using the {\it ab initio} linearized augmented plane-wave linear response method with respect to the reference cubic, experimental tetragonal, and theoretically determined rhombohedral ground state structures. The ground state rhombohedral structure of KNbO_3 was determined by minimizing the forces on the relaxed atoms. By contrast with the cubic structure, all zone center phonon modes of the rhombohedral structure are stable and their frequencies are in good agreement with experiment. In the tetragonal phase, one of the soft zone center modes in the cubic phase is stablized. In view of the small atomic displacements involved in the ferroelectric transitions, it is evident that not only the soft mode frequencies but also the Born effective charge and dielectric constants are very sensitive to the atomic geometry.

cond-mat.soft↗

arXiv1995

Pressure Dependence of Born Effective Charges, Dielectric Constant and Lattice Dynamics in SiC

The pressure dependence of the Born effective charge, dielectric constant and zone-center LO and TO phonons have been determined for $3C$-SiC by a linear response method based on the linearized augmented plane wave calculations within the local density approximation. The Born effective charges are found to increase nearly linearly with decreasing volume down to the smallest volume studied, $V/V_0=0.78$, corresponding to a pressure of about 0.8 Mbar. This seems to be in contradiction with the conclusion of the turnover behavior recently reported by Liu and Vohra [Phys.\ Rev.\ Lett.\ {\bf 72}, 4105 (1994)] for $6H$-SiC. Reanalyzing their procedure to extract the pressure dependence of the Born effective charges, we suggest that the turnover behavior they obtained is due to approximations in the assumed pressure dependence of the dielectric constant $\varepsilon_\infty$, the use of a singular set of experimental data for the equation of state, and the uncertainty in measured phonon frequencies, especially at high pressure.

mtrl-th↗

arXiv1994

First-Principles Determination of Chain-Structure Instability in KNbO$_3$

A complete mapping in the Brillouin zone of the structural instability associated with the ferroelectric phase transitions of KNbO$_3$ has been obtained by first-principles calculations using an LAPW linear response approach. The wavevector dependence of the instability reveals pronounced two-dimensional character, which corresponds to chains oriented along $\left<100\right>$\ directions of displaced Nb atoms. The results are discussed in relation to models of the ferroelectric phase transitions.

mtrl-th↗