arXiv subjects

Henry Krakauer

Publications and source records attributed to Henry Krakauer.

At least 19 recordsLinked to original sources

arXiv2023

Non-perturbative Many-Body Treatment of Molecular Magnets

Molecular magnets have received significant attention because of their potential applications in quantum information and quantum computing. A delicate balance of electron correlation, spin-orbit coupling (SOC), ligand field splitting, and other effects produces a persistent magnetic moment within each molecular magnet unit. The discovery and design of molecular magnets with improved functionalities would be greatly aided by accurate computations. However, the competition among the different effects poses a challenge for theoretical treatments. Electron correlation plays a central role, since d-, or f-element ions, which provide the magnetic states in molecular magnets, often require explicit many-body treatments. SOC, which expands the dimensionality of the Hilbert space, can also lead to non-perturbative effects in the presence of strong interaction. Furthermore, molecular magnets are large, with tens of atoms in even the smallest systems. We show how an $\textit{ab initio}$ treatment of molecular magnets can be achieved with auxiliary-field quantum Monte Carlo (AFQMC), in which electron correlation, SOC, and material specificity are included accurately and on an equal footing. The approach is demonstrated by an application to compute the zero-field splitting of a locally-linear Co$^{2+}$ complex.

cond-mat.str-el↗

arXiv2021

Ab initio Calculations in Atoms, Molecules, and Solids, Treating Spin-Orbit Coupling and Electron Interaction on Equal Footing

We incorporate explicit, non-perturbative treatment of spin-orbit coupling into ab initio auxiliary-field quantum Monte Carlo (AFQMC) calculations. The approach allows a general computational framework for molecular and bulk systems in which materials specificity, electron correlation, and spin-orbit coupling effects can be captured accurately and on equal footing, with favorable computational scaling versus system size. We adopt relativistic effective-core potentials which have been obtained by fitting to fully relativistic data and which have demonstrated a high degree of reliability and transferability in molecular systems. This results in a 2-component spin-coupled Hamiltonian, which is then treated by generalizing the ab initio AFQMC approach. We demonstrate the method by computing the electron affinity in Pb, the bond dissociation energy in Br$_2$ and I$_2$, and solid Bi.

cond-mat.str-el↗

arXiv2018

Local embedding and effective downfolding in the auxiliary-field quantum Monte Carlo method

A local embedding and effective downfolding scheme has been developed and implemented in the auxiliary-field quantum Monte Carlo (AFQMC) method. A local cluster in which electrons are fully correlated is defined and the frozen orbital method is used on the remainder of the system to construct an effective Hamiltonian which operates within the local cluster. Local embedding, which involves only the occupied sector, has previously been employed in the context of Co/graphene. Here, the methodology is extended in order to allow for effective downfolding of the virtual sector thus allowing for significant reduction in the computational effort required for AFQMC calculations. The system size which can be feasibly treated with AFQMC is therefore greatly extended as only a single local cluster is explicitly correlated at the AFQMC level of theory. The approximation is controlled by the separate choice of the spatial size of the active occupied region, $R_o$, and of the active virtual region, $R_v$. The systematic dependence of the AFQMC energy on $R_o$ and $R_v$ is investigated and it is found that relative AFQMC energies of physical and chemical interest converge rapidly to the full AFQMC treatment (i.e. using no embedding or downfolding).

cond-mat.str-el↗

arXiv2016

Auxiliary-field quantum Monte Carlo calculations with multiple-projector pseudopotentials

We have implemented recently developed multiple-projector pseudopotentials into the planewave based auxiliary-field quantum Monte Carlo (pw-AFQMC) method. Multiple-projector pseudopotentials can yield smaller planewave cut-offs while maintaining or improving transferability. This reduces the computational cost of pw-AFQMC, increasing its reach to larger and more complicated systems. We discuss the use of non-local pseudopotentials in the separable Kleinman-Bylander form, and the implementation in pw-AFQMC of the multiple-projector optimized norm-conserving pseudopotential ONCVPSP of Hamann. The accuracy of the method is first demonstrated by equation-of-state calculations of the ionic insulator NaCl and more strongly correlated metal Cu. The method is then applied to calibrate the accuracy of density functional theory (DFT) predictions of the phase stability of recently discovered high temperature and pressure superconducting sulfur hydride systems. We find that DFT results are in good agreement with pw-AFQMC, due to near cancellation of electron-electron correlation effects between different structures.

cond-mat.mtrl-sci↗

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↗

arXiv2015

Electron-phonon coupling and exchange-correlation effects in superconducting ${\rm H_3S}$ under high pressure

We investigate the ${\rm H_3S}$ phase of sulphur hydride under high pressure $\simeq$ 200 GPa by means of {\it ab-initio} calculations within the framework of the density-functional theory (DFT) with the PBE0 hybrid exchange-correlation ($E_{\rm xc}$) approximation. The choice of $E_{\rm xc}$ has the largest effect on the calculated electron-phonon coupling (EPC) matrix elements; the high pressure equation of state and phonon frequencies are only slightly modified. Mode-dependent EPC correction factors are determined from PBE0 using a frozen-phonon supercell approach, while standard density-functional perturbation theory is used to determine the EPC with PBE generalized-gradient approximation $E_{\rm xc}$. Our principle finding is that the calculated PBE0 $T_c$ is enhanced by 25\% compared to PBE. This is similar in magnitude, but in opposite direction, to the proposed suppression of $T_c$ by anharmonic effects [Errea {\em et al., Phys. Rev. Lett.} {\bf 114}, 157004 (2015)]. Our calculations demonstrate the importance of considering exchange-correlation approximations for calculations of superconducting properties for this class of materials.

cond-mat.supr-con↗

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

Excited state calculations in solids by auxiliary-field quantum Monte Carlo

We present an approach for ab initio many-body calculations of excited states in solids. Using auxiliary-field quantum Monte Carlo, we introduce an orthogonalization constraint to prevent collapse of the stochastic Slater determinants in the imaginary-time propagation. Trial wave functions from density-functional calculations are used for the constraints. Detailed band structures calculated for standard semiconductors are in good agreement with GW and experimental results. For the challenging ZnO wurtzite structure, we obtain a fundamental band gap of 3.26(16) eV, consistent with experiments.

cond-mat.mtrl-sci↗

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↗

arXiv2011

Finite-size correction in many-body electronic structure calculations of magnetic systems

We extend the post-processing finite-size (FS) correction method, developed by Kwee, Zhang, and Krakauer [Phys. Rev. Lett. 100, 126404 (2008)], to spin polarized systems. The method estimates the FS effects in many-body electronic structure calculations of extended systems by a modified density functional theory (DFT) calculation, without having to repeat expensive many-body simulations. We construct a unified FS DFT exchange-correlation functional for spin unpolarized and fully spin polarized systems, under the local density approximation. The results are then interpolated to arbitrary spin polarizations. Generalization to other functional forms in DFT are discussed. The application of this FS correction method to several typical magnetic systems with varying supercell sizes demonstrates that it consistently removes most of the FS errors, leading to rapid convergence of the many-body results to the infinite size limit.

cond-mat.str-el↗

arXiv2011

First-principles calculations of $^{17}$O NMR chemical shielding in Pb(Zr$_{1/2}$Ti$_{1/2}$)O$_3$ and Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$: linear dependence on transition-metal/oxygen bond lengths

First-principles density functional theory (DFT) oxygen chemical shift tensors were calculated for A(B,B$^{\prime}$)O$_3$ perovskite alloys Pb(Zr$_{1/2}$Ti$_{1/2}$)O$_3$ (PZT) and Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$ (PMN). Quantum chemistry methods for embedded clusters and the GIPAW method [C.\ J.\ Pickard and F.\ Mauri, {\it Phys. Rev. B} {\bf 63} 245101 (2001)] for periodic boundary conditions were used. Results from both methods are in good agreement for PZT and prototypical perovskites. PMN results were obtained using only GIPAW. Both isotropic $δ_\mathrm{iso}$ and axial $δ_\mathrm{ax}$ chemical shifts were found to vary approximately linearly as a function of the nearest-distance transition-metal/oxygen bond length,$r_\mathrm{s}$. Using these results, we argue against Ti clustering in PZT, as conjectured from recent $^{17}$O NMR magic-angle-spinning measurements. Our findings indicate that $^{17}$O NMR measurements, coupled with first-principles calculations, can be an important probe of local structure in complex perovskite solid solutions.

cond-mat.mtrl-sci↗

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↗

arXiv2009

High sensitivity of 17O NMR to p-d hybridization in transition metal perovskites: first principles calculations of large anisotropic chemical shielding

A first principles embedded cluster approach is used to calculate O chemical shielding tensors, sigma, in prototypical transition metal oxide ABO_3 perovskite crystals. Our principal findings are 1) a large anisotropy of sigma between deshielded sigma_x ~ sigma_y and shielded sigma_z components (z along the Ti-O bond); 2) a nearly linear variation, across all the systems studied, of the isotropic sigma_iso and uniaxial sigma_ax components, as a function of the B-O-B bond asymmetry. We show that the anisotropy and linear variation arise from large paramagnetic contributions to sigma_x and sigma_y due to virtual transitions between O(2p) and unoccupied B(nd) states. The calculated isotropic delta_iso and uniaxial delta_ax chemical shifts are in good agreement with recent BaTiO_3 and SrTiO_3 single crystal 17O NMR measurements. In PbTiO_3 and PbZrO_3, calculated delta_iso are also in good agreement with NMR powder spectrum measurements. In PbZrO_3, delta_iso calculations of the five chemically distinct sites indicate a correction of the experimental assignments. The strong dependence of sigma on covalent O(2p)-B(nd) interactions seen in our calculations indicates that 17O NMR spectroscopy, coupled with first principles calculations, can be an especially useful tool to study the local structure in complex perovskite alloys.

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↗