Pressure-induced diamond to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>-tin transition in bulk silicon: A quantum Monte Carlo study

Purwanto, Wirawan; Krakauer, Henry; Zhang, Shiwei

doi:10.1103/physrevb.80.214116

Cited by 63 publications

(109 citation statements)

References 46 publications

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“…Our VMC technique is in agreement with the value of the transition pressure recently reported by the AFQMC technique 20 . A clear increase of the transition pressure by about 1GPa is obtained when the accuracy of the cal-method raw (GPa) corrected (GPa) (T = 300 K) LDA culation is improved by the LRDMC scheme.…”

Section: Discussionsupporting

confidence: 80%

“…The discrepancy was attributed to the fixed-node (FN) approximation 19 , since the other source of errors (time step error, pseudopotential locality error, size effects) were considered negligible. More recently, Purwanto et al 20 obtained a transition pressure of 12.6 using the auxiliary-field QMC (AFQMC) method with the phaseless approximation to cure the sign problem, whose bias has been shown to be very small 21 . The very recent DMC calculation in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Ab initiocalculations for theβ-tin diamond transition in silicon: Comparing theories with experiments

et al. 2011

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We investigate the pressure-induced metal-insulator transition from diamond to β-tin in bulk Silicon, using quantum Monte Carlo (QMC) and density functional theory (DFT) approaches. We show that it is possible to efficiently describe many-body effects, using a variational wave function with an optimized Jastrow factor and a Slater determinant. Variational results are obtained with a small computational cost and are further improved by performing diffusion Monte Carlo calculations and an explicit optimization of molecular orbitals in the determinant. Finite temperature corrections and zero point motion effects are included by calculating phonon dispersions in both phases at the DFT level. Our results indicate that the theoretical QMC (DFT) transition pressure is significantly larger (smaller) than the accepted experimental value. We discuss the limitation of DFT approaches due to the choice of the exchange and correlation functionals and the difficulty to determine consistent pseudopotentials within the QMC framework, a limitation that may significantly affect the accuracy of the technique.

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Section: Discussionsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Ab initiocalculations for theβ-tin diamond transition in silicon: Comparing theories with experiments

et al. 2011

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“…[22][23][24][25] It has modest polynomial scaling with system size M [O M 3 or O M 4 ] rather than the exponen-tial scaling of CI calculations, or the high-order polynomial scaling of typical quantum chemistry many-body methods. The FP AFQMC, 26,27 which leaves the fermion sign/phase problem uncontrolled, 25 is exact but has exponential scaling due to rapidly increasing stochastic noise with projection imaginary-time. The AFQMC phaseless approximation (ph-AFQMC) 22 was introduced to control this, resulting in a practical method which restores the low computational scaling.…”

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confidence: 99%

An auxiliary-field quantum Monte Carlo study of the chromium dimer

Purwanto

Zhang

Krakauer

2015

The Journal of Chemical Physics

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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 nearexact 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. The chromium dimer is a strongly correlated molecule which poses a formidable challenge to even the most accurate many-body methods. It features a formal sextuple bond, with a weak binding energy (∼ 1.5 eV), a short equilibrium bond length (∼ 1.7Å), and an unusual "shoulder" structure in its potential energy curve (PEC). [1][2][3] The ground state of Cr 2 is highly multiconfigurational, and proper theoretical description requires an accurate treatment of the strong 3d electron correlations (both static and dynamic). The nature of the PEC in Cr 2 is representative of the competing tendencies separated by small energy differences seen in many strongly correlated materials. Because of the fundamental and technological significance of such materials, improving our abilities for accurate calculations in strongly correlated systems is one of the most pressing needs in condensed matter physics and quantum chemistry.Standard quantum chemistry methods, such as density functional theory (DFT), Hartree-Fock (HF), and post-HF methods such as single-reference second-order Møller-Plesset perturbation theory (MP2) and single-reference coupled cluster with singles, doubles, and perturbative triples [CCSD(T)], all fail to describe the correct binding of Cr 2 . Representative standard quantum chemistry results are shown in Fig. 1. As often is the case, the DFT results vary greatly, depending on the choice of exchange-correlation functional. There have also been numerous attempts to calculate the PEC of Cr 2 using sophisticated multireference quantum chemistry methods, 4-9 including the complete active space second-order perturbation theory (CASPT2) 10-12 and, more recently, CASPT2 based on a large density matrix renormalization group (DMRG) reference wave function (DMRG-CASPT2). 13 These calculations obtain qualitatively correct binding, but the results are sensitive to choice of active space and/or basis set. Standard quantum Monte Carlo (QMC) approaches 14,15 have also been severely challenged. A recent fixed-node diffusion Monte Carlo (DMC) study, which examined the use of a variety of single-and multi-determinant trial wave functions, did not obtain satisfactory binding (i...

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“…In AFQMC, first conceived by G. Sugiyama and S. E. Koonin [20], later perfected and extended by S. Zhang [21,22,25] and F.Assaad [23] and successfully applied to the investigation of molecular systems [26][27][28], the association between (4) and a stochastic process in D(N ) is made possible by a discretization:…”

Section: The Phaseless Afqmcmentioning

confidence: 99%

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

Motta

Galli

Moroni

et al. 2014

The Journal of Chemical Physics

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The phaseless Auxiliary Field Quantum Monte Carlo method provides a well established approximation scheme for accurate calculations of ground state energies of many-fermions systems. Here we apply the method to the calculation of imaginary time correlation functions. We give a detailed description of the technique and we test the quality of the results for static and dynamic properties against exact values for small systems.

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Pressure-induced diamond toβ-tin transition in bulk silicon: A quantum Monte Carlo study

Cited by 63 publications

References 46 publications

Ab initiocalculations for theβ-tin diamond transition in silicon: Comparing theories with experiments

Ab initiocalculations for theβ-tin diamond transition in silicon: Comparing theories with experiments

An auxiliary-field quantum Monte Carlo study of the chromium dimer

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

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