Variational Excitations in Real Solids: Optical Gaps and Insights into Many-Body Perturbation Theory

We present an approach to studying optical band gaps in real solids in which quantum Monte Carlo methods allow for the application of a rigorous variational principle to both ground and excited state wave functions. In tests that include small, medium, and large band gap materials, optical gaps are predicted with a mean-absolute-deviation of 3.5% against experiment, less than half the equivalent errors for typical many-body perturbation theories. The approach is designed to be insensitive to the choice of density functional, a property we exploit in order to provide insight into how far different functionals are from satisfying the assumptions of many body perturbation theory. We explore this question most deeply in the challenging case of ZnO, where we show that although many commonly used functionals have shortcomings, there does exist a one particle basis in which perturbation theory's zeroth order picture is sound. Insights of this nature should be useful in guiding the future application and improvement of these widely used techniques.Comment: 8 pages, 5 figures, 2 table

Chemical accuracy from quantum Monte Carlo for the Benzene Dimer

We report an accurate study of interactions between Benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory (DFT) using different van der Waals (vdW) functionals. In our QMC calculations, we use accurate correlated trial wave functions including three-body Jastrow factors, and backflow transformations. We consider two benzene molecules in the parallel displaced (PD) geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the CCSD(T)/CBS limit is -2.65(2) kcal/mol [E. Miliordos et al, J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.Comment: Accepted for publication in the Journal of Chemical Physics, Vol. 143, Issue 11, 201

Excitations in photoactive molecules from quantum Monte Carlo

Despite significant advances in electronic structure methods for the treatment of excited states, attaining an accurate description of the photoinduced processes in photoactive biomolecules is proving very difficult. For the prototypical photosensitive molecules, formaldimine, formaldehyde and a minimal protonated Schiff base model of the retinal chromophore, we investigate the performance of various approaches generally considered promising for the computation of excited potential energy surfaces. We show that quantum Monte Carlo can accurately estimate the excitation energies of the studied systems if one constructs carefully the trial wave function, including in most cases the reoptimization of its determinantal part within quantum Monte Carlo. While time-dependent density functional theory and quantum Monte Carlo are generally in reasonable agreement, they yield a qualitatively different description of the isomerization of the Schiff base model. Finally, we find that the restricted open shell Kohn-Sham method is at variance with quantum Monte Carlo in estimating the lowest-singlet excited state potential energy surface for low-symmetry molecular structures.Comment: 10 pages, 6 figure

Effect of intra-ply voids on the homogenized behavior of a ply in multidirectional laminates

This work focuses on the effect of intra-ply voids on the homogenized nonlinear behavior of a ply in multidirectional composites. Voids were modeled explicitly on the fiber scale and linked to the ply-scale by the recently developed two-scale framework which couples Classical Laminate Theory on the macro-scale with Finite Element analysis on the micro-scale. Laminates [+/- 45](2s) and [+/- 67.5](2s) were used as validation cases. The computed homogenized behavior of plies with and without voids for each laminate were compared against existing experimental data on manufactured plates. The nonlinearity of the homogenized stress-strain curves of all models is in a good agreement with experiments up to 1% of applied deformation for a laminate [+/- 45](2s) and up to 0.4% for a laminate [+/- 67.5](2s). The effect of voids was assessed only virtually and it is shown that 4% of void content decreases the ply strength by 30%, transversal Young's and shear moduli by around 10% and 8% respectively, whereas longitudinal stiffness is only slightly affected by the presence of voids. This work is the first step towards automatization of the virtual identification of the complete set of damage-plasticity parameters for the LMT-Cachan damage model accounting for the presence of intra-ply voids

Complementary First and Second Derivative Methods for Ansatz Optimization in Variational Monte Carlo

We present a comparison between a number of recently introduced low-memory wave function optimization methods for variational Monte Carlo in which we find that first and second derivative methods possess strongly complementary relative advantages. While we find that low-memory variants of the linear method are vastly more efficient at bringing wave functions with disparate types of nonlinear parameters to the vicinity of the energy minimum, accelerated descent approaches are then able to locate the precise minimum with less bias and lower statistical uncertainty. By constructing a simple hybrid approach that combines these methodologies, we show that all of these advantages can be had at once when simultaneously optimizing large determinant expansions, molecular orbital shapes, traditional Jastrow correlation factors, and more nonlinear many-electron Jastrow factors

Variational Monte Carlo studies of attractive Hubbard model I

Normal states of the attractive Hubbard model, especially in two dimension, are studied in the light of a transition from a Fermi liquid to an insulating or gapped state. A series of variational Monte Carlo calculations with better statistics is carried out to estimate accurately expectation values by several many-body wave functions. Although a relatively clear crossover is observed even in the plain Gutzwiller wave function, the states in both regimes are metallic. Meanwhile, a substantial metal-insulator transition takes place at |U|\sim W (band width) in an improved wave function in which intersite correlation is introduced by taking account of virtual states in the second-order perturbation in the infinite-|U| limit. The critical value is favorably compared with recent results of the dynamical-mean-field approximation. In contrast, a conventional Jastrow-type wave functions scarcely improve the normal state. In addition, the issue of Brinkman-Rice metal-insulator transition is reconsidered with much larger systems.Comment: 32 pages (Latex with PTPTeX.sty), with 61 figures. To appear in Prog. Theor. Phys. 108 (2002) vol.

Variational Monte Carlo Studies of Pairing Symmetry for the t-J Model on a Triangular Lattice

As a model of a novel superconductor Na_xCoO_2\cdotyH_2O, a single-band t-J model on a triangular lattice is studied, using a variational Monte Carlo method. We calculate the energies of various superconducting (SC) states, changing the doping rate \delta and sign of t for small J/|t|. Symmetries of s, d, and d+id (p+ip and f) waves are taken up as candidates for singlet (triplet) pairing. In addition, the possibility of Nagaoka ferromagnetism and inhomogeneous phases is considered. It is revealed that, among the SC states, the d+id wave always has the lowest energy, which result supports previous mean-field studies. There is no possibility of triplet pairing, although the f-wave state becomes stable against a normal state in a special case (\delta=0.5 and t<0). For t<0, the complete ferromagnetic state is dominant in a wide range of \delta and J/|t|, which covers the realistic parameter region of superconductivity.Comment: 10 pages, 13 figure