The first magnetic 2D material discovered, monolayer (ML) CrI3, is particularly fascinating due to its ground state ferromagnetism. However, because ML materials are difficult to probe experimentally, much remains unresolved about ML CrI3’s structural, electronic, and magnetic properties. Here, we leverage Density Functional Theory (DFT) and high-accuracy Diffusion Monte Carlo (DMC) simulations to predict lattice parameters, magnetic moments, and spin–phonon and spin–lattice coupling of ML CrI3. We exploit a recently developed surrogate Hessian DMC line search technique to determine CrI3’s ML geometry with DMC accuracy, yielding lattice parameters in good agreement with recently published STM measurements—an accomplishment given the ∼10% variability in previous DFT-derived estimates depending upon the functional. Strikingly, we find that previous DFT predictions of ML CrI3’s magnetic spin moments are correct on average across a unit cell but miss critical local spatial fluctuations in the spin density revealed by more accurate DMC. DMC predicts that magnetic moments in ML CrI3 are 3.62 μB per chromium and −0.145 μB per iodine, both larger than previous DFT predictions. The large disparate moments together with the large spin–orbit coupling of CrI3’s I-p orbital suggest a ligand superexchange-dominated magnetic anisotropy in ML CrI3, corroborating recent observations of magnons in its 2D limit. We also find that ML CrI3 exhibits a substantial spin–phonon coupling of ∼3.32 cm−1. Our work, thus, establishes many of ML CrI3’s key properties, while also continuing to demonstrate the pivotal role that DMC can assume in the study of magnetic and other 2D materials.
Quantum Monte Carlo (QMC) forces have been studied extensively in recent decades because of their importance with spectroscopic observables and geometry optimization. Here, we benchmark the accuracy and computational cost of QMC forces. The zero-variance zero-bias (ZVZB) force estimator is used in standard variational and diffusion Monte Carlo simulations with mean-field based trial wavefunctions and atomic pseudopotentials. Statistical force uncertainties are obtained with a recently developed regression technique for heavy tailed QMC data [P. Lopez Rios and G. J. Conduit, Phys. Rev. E 99, 063312 (2019)]. By considering selected atoms and dimers with elements ranging from H to Zn (1 ≤ Zeff ≤ 20), we assess the accuracy and the computational cost of ZVZB forces as the effective pseudopotential valence charge, Zeff, increases. We find that the costs of QMC energies and forces approximately follow simple power laws in Zeff. The force uncertainty grows more rapidly, leading to a best case cost scaling relationship of approximately Zeff6.5(3) for diffusion Monte Carlo. We find that the accessible system size at fixed computational cost scales as Zeff−2, insensitive to model assumptions or the use of the “space warp” variance-reduction technique. Our results predict the practical cost of obtaining forces for a range of materials, such as transition metal oxides where QMC forces have yet to be applied, and underscore the importance of further developing force variance-reduction techniques, particularly for atoms with high Zeff.
In this work, we propose new field-free estimators for static field-gradient polarizabilities in finite temperature PIMC simulation. Namely, dipole-quadrupole polarizability A, dipole-dipolequadrupole polarizability B and quadrupole-quadrupole polarizability C are computed for several up to two-electron systems: H, H − , He, Li + , Be 2+ , Ps2, PsH, H + 2 , H2, H + 3 and HeH + . We provide complementary data for ground state electronic properties within the adiabatic approximation, and demonstrate good agreement with available values in the literature. More importantly, we present fully non-adiabatic results from 50 K to 1600 K, which allow us to analyze and discuss strong thermal coupling and rovibrational effects in total field-gradient polarizabilities. These phenomena are most relevant but clearly overlooked, e.g., in the construction of modern polarizable force field models. However, our main purpose is demonstrating the accuracy and simplicity of our approach in a problem that is generally challenging.
We
demonstrate computation of total dynamic multipole polarizabilities
using path-integral Monte Carlo method (PIMC). The PIMC approach enables
accurate thermal and nonadiabatic mixing of electronic, rotational,
and vibrational degrees of freedom. Therefore, we can study the thermal
effects, or lack thereof, in the full multipole spectra of the chosen
one- and two-electron systems: H, Ps, He, Ps2, H2, and HD+. We first compute multipole–multipole
correlation functions up to octupole order in imaginary time. The
real-domain spectral function is then obtained by analytical continuation
with the maximum entropy method. In general, sharpness of the active
spectra is limited, but the obtained off-resonant polarizabilities
are in good agreement with the existing literature. Several weak and
strong thermal effects are observed. Furthermore, the polarizabilities
of Ps2 and some higher multipole and higher frequency data
have not been published before. In addition, we compute isotropic
dispersion coefficients C
6, C
8, and C
10 between pairs of
species using the simplified Casimir–Polder formulas.
We present an efficient energy-based method for structural optimization with stochastic electronic structure theories, such as diffusion quantum Monte Carlo (DMC). This method is based on robust line-search energy minimization in reduced parameter space, exploiting approximate but accurate Hessian information from a surrogate theory, such as density functional theory. The surrogate theory is also used to characterize the potential energy surface, allowing for simple but reliable ways to maximize statistical efficiency while retaining controllable accuracy. We demonstrate the method by finding the minimum DMC energy structures of the selected flake-like aromatic molecules, such as benzene, coronene, and ovalene, represented by 2, 6, and 19 structural parameters, respectively. In each case, the energy minimum is found within two parallel line-search iterations. The method is near-optimal for a line-search technique and suitable for a broad range of applications. It is easily generalized to any electronic structure method where forces and stresses are still under active development and implementation, such as diffusion Monte Carlo, auxiliary-field Monte Carlo, and stochastic configuration interaction, as well as deterministic approaches such as the random-phase approximation. Accurate and efficient means of geometry optimization could shed light on a broad class of materials and molecules, showing high sensitivity of induced properties to structural variables.
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