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Scanning tunneling microscopy (STM) and spectroscopy probe the local density of states of single molecules electrically insulated from the substrate. The experimental images, although usually interpreted in terms of single-particle molecular orbitals, are associated with quasiparticle wave functions dressed by the whole electron-electron interaction. Here we propose an ab initio approach based on quantum Monte Carlo to calculate the quasiparticle wave functions of molecules. Through the comparison between Monte Carlo wave functions and their uncorrelated Hartree-Fock counterparts we visualize the electronic correlation embedded in the simulated STM images, highlighting the many-body features that might be observed.

Resolving the interplay between magnetic interactions and structural properties in strongly correlated materials through a quantitatively accurate approach has been a major challenge in condensed-matter physics. Here we apply highly accurate first-principles quantum Monte Carlo (QMC) techniques to obtain structural and magnetic properties of the iron selenide (FeSe) superconductor under pressure. Where comparable, the computed properties are very close to the experimental values. Of potential ordered magnetic configurations, collinear spin configurations are the most energetically favorable over the explored pressure range. They become nearly degenerate in energy with bicollinear spin orderings at around 7 GPa, when the experimental critical temperature Tc is the highest. On the other hand, ferromagnetic, checkerboard, and staggered dimer configurations become relatively higher in energy as the pressure increases. The behavior under pressure is explained by an analysis of the local charge compressibility and the orbital occupation as described by the QMC many-body wave function, which reveals how spin, charge, and orbital degrees of freedom are strongly coupled in this compound. This remarkable pressure evolution suggests that stripelike magnetic fluctuations may be responsible for the enhanced Tc in FeSe and that higher Tc is associated with nearness to a crossover between collinear and bicollinear ordering.

Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard for providing high-quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation relies on modifications of the Green's function to avoid singularities near the nodal surface of the trial wave function. Here we show that these modifications affect the DMC energies in a way that is not size consistent, resulting in large time-step errors. Building on the modifications of Umrigar et al. and DePasquale et al. we propose a simple Green's function modification that restores size consistency to large values of the time step, which substantially reduces time-step errors. This algorithm also yields remarkable speedups of up to two orders of magnitude in the calculation of molecule-molecule binding energies and crystal cohesive energies, thus extending the horizons of what is possible with DMC.

We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t 1 and t 2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of and the on-site Coulomb repulsion U, for two values of the Hund's coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.

We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half-filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction U, we can identify a hidden critical point UMott, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of U), where magnetism induces a potential energy gain, and a Mott insulator (at large values of U), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of UMott has crucial consequences when doping the system: We observe a tendency for phase separation into hole-rich and hole-poor regions only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above UMott, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above UMott shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.

The metal-insulator transition has been a subject of intense research since Mott first proposed that the metallic behavior of interacting electrons could turn to an insulating one as electron correlations increase. Here, we consider electrons with massless Dirac-like dispersion in two spatial dimensions, described by the Hubbard models on two geometrically different lattices, and perform numerically exact calculations on unprecedentedly large systems that, combined with a careful finite-size scaling analysis, allow us to explore the quantum critical behavior in the vicinity of the interaction-driven metal-insulator transition. Thereby, we find that the transition is continuous, and we determine the quantum criticality for the corresponding universality class, which is described in the continuous limit by the Gross-Neveu model, a model extensively studied in quantum field theory. Furthermore, we discuss a fluctuation-driven scenario for the metal-insulator transition in the interacting Dirac electrons: The metal-insulator transition is triggered only by the vanishing of the quasiparticle weight, not by the Dirac Fermi velocity, which instead remains finite near the transition. This important feature cannot be captured by a simple mean-field or Gutzwiller-type approximate picture but is rather consistent with the low-energy behavior of the Gross-Neveu model.

We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen.

Gutzwiller-projected fermionic states can be efficiently implemented within quantum Monte Carlo calculations to define extremely accurate variational wave functions for Heisenberg models on frustrated two-dimensional lattices, not only for the ground state but also for low-energy excitations. The application of few Lanczos steps on top of these states further improves their accuracy, allowing calculations on large clusters. In addition, by computing both the energy and its variance, it is possible to obtain reliable estimations of exact results. Here, we report the cases of the frustrated Heisenberg models on square and Kagome lattices.

An efficient scheme is introduced for a fast and smooth convergence to the thermodynamic limit of electronic properties obtained with finite-size calculations on correlated Hamiltonians. This is obtained by modifying the energy levels of the free electron part of the Hamiltonian in a way consistent with the corresponding one-particle density of states in the thermodynamic limit. After this modification, free electron ground state energies, exact in the thermodynamic limit, are obtained with finite-size calculations and for all the particular fillings that satisfy the so called "closed-shell condition." For those fillings the auxiliary field quantum Monte Carlo technique is particularly efficient and, by combining it with the present method, we provide strong numerical evidence that phase separation occurs in the low doping region and moderate Uâ‰4t regime of this model.

We study the ionization energy, electron affinity, and the π → π- (1La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the 1La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral 1La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.

Although liquid water is ubiquitous in chemical reactions at roots of life and climate on the earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article, we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in good agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous density functional theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab initio simulations of complex chemical systems.

We perform molecular dynamics simulations driven by accurate quantum Monte Carlo forces on dense liquid hydrogen. There is a recent report of a complete atomization transition between a mixed molecular-atomic liquid and a completely dissociated fluid in an almost unaccessible pressure range [Nat. Commun. 5, 3487 (2014)]. Here, instead, we identify a different transition between the fully molecular liquid and the mixed-atomic fluid at ∼400GPa, i.e., in a much more interesting pressure range. We provide numerical evidence supporting the metallic behavior of this intermediate phase. Therefore, we predict that the metallization at finite temperature occurs in this partially dissociated molecular fluid, well before the complete atomization of the liquid. At high temperature this first-order transition becomes a crossover, in very good agreement with the experimental observation. Several systematic tests supporting the quality of our large scale calculations are also reported.

The cerium α-γ phase transition is characterized by means of a many-body Jastrow-correlated wave function, which minimizes the variational energy of the first-principles scalar-relativistic Hamiltonian, and includes correlation effects in a nonperturbative way. Our variational ansatz accurately reproduces the structural properties of the two phases, and proves that even at temperature T=0K the system undergoes a first-order transition, with ab initio parameters which are seamlessly connected to the ones measured by experiment at finite T. We show that the transition is related to a complex rearrangement of the electronic structure, with a key role played by the p-f hybridization. The underlying mechanism unveiled by this work can hold in many Ce-bearing compounds, and more generally in other f-electron systems.

We present a systematic study of a recently developed ab initio simulation scheme based on molecular dynamics and quantum Monte Carlo. In this approach, a damped Langevin molecular dynamics is employed by using a statistical evaluation of the forces acting on each atom by means of quantum Monte Carlo. This allows the use of an highly correlated wave function parametrized by several variational parameters and describing quite accurately the Born-Oppenheimer energy surface, as long as these parameters are determined at the minimum energy condition. However, in a statistical method both the minimization method and the evaluation of the atomic forces are affected by the statistical noise. In this work, we study systematically the accuracy and reliability of this scheme by targeting the vibrational frequencies of simple molecules such as the water monomer, hydrogen sulfide, sulfur dioxide, ammonia, and phosphine. We show that all sources of systematic errors can be controlled and reliable frequencies can be obtained with a reasonable computational effort. This work provides convincing evidence that this molecular dynamics scheme can be safely applied also to realistic systems containing several atoms.

We report an extensive theoretical study of the protonated water dimer H5O2+ (Zundel ion) by means of the highly correlated variational Monte Carlo and lattice regularized Monte Carlo approaches. This system represents the simplest model for proton transfer (PT), and a correct description of its properties is essential in order to understand the PT mechanism in more complex aqueous systems. Our Jastrow correlated AGP wave function ensures an accurate treatment of electron correlation. By exploiting the advantage of contracting the primitive basis set over atomic hybrid orbitals, we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision, a crucial ingredient in order to simulate larger systems. For both energetics and geometrical properties, our QMC results are found to be in excellent agreement with state-of-the-art coupled cluster CCSD(T) techniques. A comparison with density functional theory in the PBE approximation points to the crucial role of electron correlation for a correct description of the PT in the dimer. We prove that the QMC framework used in this work is able to resolve the tiny energy differences (∼0.3 kcal/mol) and structural variations involved in proton transfer reactions. Our approach combines these features and a favorable N 4 scaling with the number of particles which paves the way to the simulation of more realistic PT models. A test calculation on a larger protonated water cluster is carried out. The QMC approach used here represents a promising candidate to provide the first high-level ab initio description of PT in water. © 2014 American Chemical Society.

We study the spreading of density-density correlations in Bose-Hubbard models after a quench of the interaction strength, using time-dependent variational Monte Carlo simulations. It gives access to unprecedented long propagation times and to dimensions higher than one. In both one and two dimensions, we find ballistic light-cone spreading of correlations and extract accurate values of the light-cone velocity in the superfluid regime. We show that the spreading of correlations is generally supersonic, with a light-cone propagating faster than sound modes but slower than the maximum group velocity of density excitations, except at the Mott transition, where all the characteristic velocities are equal. Further, we show that in two dimensions the correlation spreading is highly anisotropic and presents nontrivial interference effects. © 2014 American Physical Society.

Diradical molecules are essential species involved in many organic and inorganic chemical reactions. The computational study of their electronic structure is often challenging, because a reliable description of the correlation, and in particular of the static one, requires multireference techniques. The Jastrow correlated antisymmetrized geminal power (JAGP) is a compact and efficient wave function ansatz, based on the valence-bond representation, which can be used within quantum Monte Carlo (QMC) approaches. The AGP part can be rewritten in terms of molecular orbitals, obtaining a multideterminant expansion with zero-seniority number. In the present work we demonstrate the capability of the JAGP ansatz to correctly describe the electronic structure of two diradical prototypes: the orthogonally twisted ethylene, C2H4, and the methylene, CH2, representing respectively a homosymmetric and heterosymmetric system. In the orthogonally twisted ethylene, we find a degeneracy of π and π* molecular orbitals, as correctly predicted by multireference procedures, and our best estimates of the twisting barrier, using respectively the variational Monte Carlo (VMC) and the lattice regularized diffusion Monte Carlo (LRDMC) methods, are 71.9(1) and 70.2(2) kcal/mol, in very good agreement with the high-level MR-CISD+Q value, 69.2 kcal/mol. In the methylene we estimate an adiabatic triplet-singlet (X̃3B1- ã1A1) energy gap of 8.32(7) and 8.64(6) kcal/mol, using respectively VMC and LRDMC, consistently with the experimental-derived finding for Te, 9.363 kcal/mol. On the other hand, we show that the simple ansatz of a Jastrow correlated single determinant (JSD) wave function is unable to provide an accurate description of the electronic structure in these diradical molecules, both at variational level (VMC torsional barrier of C 2H4 of 99.3(2) kcal/mol, triplet-singlet energy gap of CH2 of 13.45(10) kcal/mol) and, more remarkably, in the fixed-nodes projection schemes (LRDMC torsional barrier of 97.5(2) kcal/mol, triplet-singlet energy gap of 13.36(8) kcal/mol) showing that a poor description of the static correlation yields an inaccurate nodal surface. The suitability of JAGP to correctly describe diradicals with a computational cost comparable with that of a JSD calculation, in combination with a favorable scalability of QMC algorithms with the system size, opens new perspectives in the ab initio study of large diradical systems, like the transition states in cycloaddition reactions and the thermal isomerization of biological chromophores. © 2014 American Chemical Society.

The Resonating Valence Bond theory of the chemical bond was introduced soon after the discovery of quantum mechanics and has contributed to explain the role of electron correlation within a particularly simple and intuitive approach where the chemical bond between two nearby atoms is described by one or more singlet electron pairs. In this chapter Pauling’s resonating valence bond theory of the chemical bond is revisited within a new formulation, introduced by P. W. Anderson after the discovery of High-T $$:\text {c}$$ superconductivity. It is shown that this intuitive picture of electron correlation becomes now practical and efficient, since it allows us to faithfully exploit the locality of the electron correlation, and to describe several new phases of matter, such as Mott insulators, High-T $$:\text {c}$$ superconductors, and spin liquid phases.