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Register a new userAn inhomogeneous and anisotropic Jastrow function for non-uniform many-electron systems
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Quantum Monte Carlo simulations of interacting electrons in solids often use Slater-Jastrow trial wave functions. The Jastrow function takes into account correlations between pairs of electrons. In simulations of solids, it is common to use a Jastrow function which is both homogeneous and isotropic. The use of a homogeneous and isotropic Jastrow factor is questionable in applications to systems with strong density inhomogeneities, such as surfaces and multilayers. By generalizing the original derivation of the RPA Jastrow factor for the homogeneous electron gas [Gaskell] to inhomogeneous systems we derive an scheme for generating inhomogeneous and anisotropic Jastrow factors for use in nonuniform systems, from the non-interacting static structure factor and density of the system. We discuss aspects of our scheme and illustrate it with a first application to an inhomogeneous electron gas.
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Quantum Monte Carlo simulations of interacting electrons in solids often use Slater-Jastrow trial wave functions with Jastrow factors containing one- and two-body terms. In uniform systems the long-range behavior of the two-body term may be deduced from the random-phase approximation (RPA) of Bohm and Pines. Here we generalize the RPA to nonuniform systems. This gives the long-range behavior of the inhomogeneous two-body correlation term and provides an accurate analytic expression for the one-body term. It also explains why Slater-Jastrow trial wave functions incorporating determinants of Hartree-Fock or density-functional orbitals are close to optimal even in the presence of an RPA Jastrow factor. After adjusting the inhomogeneous RPA Jastrow factor to incorporate the known short-range behavior, we test it using variational Monte Carlo calculations. We find that the most important aspect of the two-body term is the short-range behavior due to electron-electron scattering, although the long-range behavior described by the RPA should become more important at high densities.
We propose a Jastrow factor for electron-electron correlations that interpolates between the radial symmetry of the Coulomb interaction at short inter-particle distance and the space-group symmetry of the simulation cell at large separation. The proposed Jastrow factor captures comparable levels of the correlation energy to current formalisms, is 40% quicker to evaluate, and offers benefits in ease of use, as we demonstrate in quantum Monte Carlo simulations.
The accuracy and efficiency of ab-initio quantum Monte Carlo (QMC) algorithms benefits greatly from compact variational trial wave functions that accurately reproduce ground state properties of a system. We investigate the possibility of using multi-Slater-Jastrow trial wave functions with non-orthogonal determinants by optimizing identical single particle orbitals independently in separate determinants. As a test case, we compute variational and fixed-node diffusion Monte Carlo (FN-DMC) energies of a C$_2$ molecule. For a given multi-determinant expansion, we find that this non-orthogonal orbital optimization results in a consistent improvement in the variational energy and the FN-DMC energy on the order of a few tenths of an eV. Our calculations indicate that trial wave functions with non-orthogonal determinants can improve computed energies in a QMC calculation when compared to their orthogonal counterparts.
We investigate wrinkling patterns in a tri-layer torus consisting of an expanding thin outer layer, an intermediate soft layer and an inner core with a tunable shear modulus, inspired by pattern formation in developmental biologies, such as follicle pattern formation during the development of chicken embryos. We show from large-scale finite element simulations that hexagonal wrinkling patterns form for stiff cores whereas stripe wrinkling patterns develop for soft cores. Hexagons and stripes co-exist to form hybrid patterns for cores with intermediate stiffness. The governing mechanism for the pattern transition is that the stiffness of the inner core controls the degree to which the major radius of the torus expands this has a greater effect on deformation in the long direction as compared to the short direction of the torus. This anisotropic deformation alters stress states in the outer layer which change from biaxial (preferred hexagons) to uniaxial (preferred stripes) compression as the core stiffness is reduced. As the outer layer continues to expand, stripe and hexagon patterns will evolve into Zigzag and segmented labyrinth, respectively. Stripe wrinkles are observed to initiate at the inner surface of the torus while hexagon wrinkles start from the outer surface as a result of curvature-dependent stresses in the torus. We further discuss the effects of elasticities and geometries of the torus on the wrinkling patterns.
LaB6 has been used as a commercial electron emitter for decades. Despite the large number of studies on the work function of LaB6, there is no comprehensive understanding of work function trends in the hexaboride materials family. In this study, we use Density Functional Theory (DFT) calculations to calculated trends of rare earth hexaboride work function and rationalize these trends based on the electronegativity of the metal element. We predict that alloying LaB6 with Ba can further lower the work function by ~0.2 eV. Interestingly, we find that alloyed (La, Ba)B6 can have lower work functions than either LaB6 or BaB6, benefitting from an enhanced surface dipole due to metal element size mismatch. In addition to hexaborides we also investigate work function trends of similar materials families, namely tetraborides and transition metal nitrides, which, like hexaborides, are electrically conductive and refractory and thus may also be promising materials for electron emission applications. We find that tetraborides consistently have higher work functions than their hexaboride analogues as the tetraborides having less ionic bonding and smaller positive surface dipoles. Finally, we find that HfN has a low work function of about 2.2 eV, making HfN a potentially promising new electron emitter material.
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