Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and they require solving the grand-challenge problem of the many-electron Schrödinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed-matter physics and chemistry while retaining a connection to the paradigmatic Hubbard model. Here, we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantummechanical ground state. Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi-long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition, and an intricate set of intertwined magnetic orders.

TurboRVB is a computational package for ab initio Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC) and diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions (WFs), capable of describing several materials with very high accuracy, even when standard mean-field approaches [e.g., density functional theory (DFT)] fail. The electronic WF is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal power with spin-singlet pairing or as a Pfaffian, including both singlet and triplet correlations. This WF can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) Ansatz, first proposed by Pauling and Anderson in quantum chemistry [L. Pauling, The Nature of the Chemical Bond (Cornell University Press, 1960)] and condensed matter physics [P.W. Anderson, Mat. Res. Bull 8, 153 (1973)], respectively. The RVB Ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. Therefore, its application to large systems is computationally feasible. The WF is expanded in a localized basis set. Several basis set functions are implemented, such as Gaussian, Slater, and mixed types, with no restriction on the choice of their contraction. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization (Jastrow and antisymmetric parts together) is made possible, thanks to state-of-the-art stochastic algorithms for energy minimization. In the optimization procedure, the first guess can be obtained at the mean-field level by a built-in DFT driver. The code has been efficiently parallelized by using a hybrid MPI-OpenMP protocol, which is also an ideal environment for exploiting the computational power of modern Graphics Processing Unit accelerators.

Among different conducting polymers, poly(3,4-ethylenedioxythiophene) (PEDOT) and its doped mixtures are promising candidates for thermoelectric applications due to their intrinsically low thermal conductivity. An accurate estimate of the overall thermoelectric figure of merit requires a sharp thermal conductivity measurement. However, even for pristine PEDOT, the estimated thermal conductivity values show high fluctuations depending on the synthesis procedure employed, suggesting that morphology can be one of the key factors affecting PEDOT thermal conductivity. In this work, we elucidate this issue by demonstrating how morphology ultimately governs thermal transport properties. By means of the approach to equilibrium molecular dynamics method, we estimate thermal conductivity of PEDOT systems with a controlled degree of crystallinity. We show that by going from pure crystalline to nearly amorphous PEDOT samples, a thermal conductivity reduction of more than two orders of magnitude is obtained. Moreover a strong thermal conductivity increase with the PEDOT chain length is observed independently of the degree of crystallinity.

We report a quantum Monte Carlo (QMC) study, on a very simple but nevertheless very instructive model system of four hydrogen atoms, recently proposed in Ref. 1. We find that the Jastrow correlated Antisymmetrized Geminal Power (JAGP) is able to recover most of the correlation energy even when the geometry is symmetric and the hydrogens lie on the edges of a perfect square. Under such conditions the diradical character of the molecule ground state prevents a single determinant ansatz to achieve an acceptable accuracy, whereas the JAGP performs very well for all geometries. Remarkably, this is obtained with a similar computational effort. Moreover we find that the Jastrow Factor is fundamental in promoting the correct resonances among several configurations in the JAGP, that cannot show up in the pure Antisymmetrized Geminal Power (AGP). We also show the extremely fast convergence of this approach in the extension of the basis set. Remarkably only the simultaneous optimization of the Jastrow and the AGP part of our variational ansatz is able to recover an almost perfect nodal surface, yielding therefore state of the art energies, almost converged in the complete basis set limit (CBS), when the so called Diffusion Monte Carlo is applied.In recent years much progress has been made in the definition of variational wave functions (WF) capable to describe rather accurately the electron correlation. To this purpose two strategies have been employed: i) the use of multi-determinant wave functions 2-4 or ii) exploiting the large variational freedom that can be achieved by applying a correlation term, dubbed Jastrow factor (JF), to a generic pairing function 5-7 . Even if the latter approach cannot be systematically improved, it may open the way to deal with large systems, thanks to the moderate scaling with the number of electrons. Indeed, the corresponding correlated WF, can be simulated efficiently within a statistical method, based on quantum Monte Carlo 8 . Thanks to well established advances 9,10 in this field, it is possible nowadays to compute the total energy of a given correlated ansatz and to optimize several variational parameters with a computational effort scaling at most with the fourth power of the number of electrons.A good variational ansatz allows a good description of the ground state by energy optimization. Moreover an even better characterization can be obtain by applying the so called diffusion Monte Carlo (DMC) method with the Fixed Node approximation (FNA) 11,12 . Within this projection method it is possible to obtain the lowest energy state constrained to have the same signs of a chosen trial WF, in the configuration space where electron positions and spins are given. The connected regions of space with the same sign are called nodal pockets and the surface determining this pockets, satisfying WF= 0, the nodal surface. Usually the energy optimization, implemented here, has been shown to be very successful to determine the nodal surface of the WF as we will show also in the present study. In this w...

We propose here a single Pfaffian correlated variational ansatz that dramatically improves the accuracy with respect to the single determinant one, while remaining at a similar computational cost. A much larger correlation energy is indeed determined by the most general two electron pairing function, including both singlet and triplet channels, combined with a many-body Jastrow factor, including all possible spin−spin, spin−density, and density−density terms. The main technical ingredient to exploit this accuracy is the use of the Pfaffian for antisymmetrizing a highly correlated pairing function, thus recovering the Fermi statistics for electrons with an affordable computational cost. Moreover, the application of the diffusion Monte Carlo, within the fixed node approximation, allows us to obtain very accurate binding energies for the first preliminary calculations reported in this study: C 2 , N 2 , and O 2 and the benzene molecule. This is promising and remarkable, considering that they represent extremely difficult molecules even for computationally demanding multideterminant approaches, and opens therefore the way for realistic and accurate electronic simulations with an algorithm scaling at most as the fourth power of the number of electrons.