Quantum Drude oscillators coupled with Coulomb potential as an efficient model for bonded and non-covalent interactions in atomic dimers.

The quantum Drude oscillator (QDO) model has been widely used as an efficient surrogate to describe the electric response properties of matter as well as long-range interactions in molecules and materials. Most commonly, QDOs are coupled within the dipole approximation so that the Hamiltonian can be exactly diagonalized, which forms the basis for the many-body dispersion method [Phys. Rev. Lett. 108, 236402 (2012)]. The dipole coupling is efficient and allows us to study non-covalent many-body effects in systems with thousands of atoms. However, there are two limitations: (i) the need to regularize the interaction at short distances with empirical damping functions and (ii) the lack of multipolar effects in the coupling potential. In this work, we convincingly address both limitations of the dipole-coupled QDO model by presenting a numerically exact solution of the Coulomb-coupled QDO model by means of quantum Monte Carlo methods. We calculate the potential-energy surfaces of homogeneous QDO dimers, analyzing their properties as a function of the three tunable parameters: frequency, reduced mass, and charge. We study the coupled-QDO model behavior at short distances and show how to parameterize this model to enable an effective description of chemical bonds, such as the covalent bond in the H2 molecule.

Molecules in Environments: Toward Systematic Quantum Embedding of Electrons and Drude Oscillators.

We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.

The three-center two-positron bond.

Computational studies have shown that one or more positrons can stabilize two repelling atomic anions through the formation of two-center positronic bonds. In the present work, we study the energetic stability of a system containing two positrons and three hydride anions, namely 2e+[H3 3-]. To this aim, we performed a preliminary scan of the potential energy surface of the system with both electrons and positrons in a spin singlet state, with a multi-component MP2 method, that was further refined with variational and diffusion Monte Carlo calculations, and confirmed an equilibrium geometry with D 3h symmetry. The local stability of 2e+[H3 3-] is demonstrated by analyzing the vertical detachment and adiabatic energy dissociation channels. Bonding properties of the positronic compound, such as the equilibrium interatomic distances, force constants, dissociation energies, and bonding densities are compared with those of the purely electronic H3 + and Li3 + systems. Through this analysis, we find compelling similarities between the 2e+[H3 3-] compound and the trilithium cation. Our results strongly point out the formation of a non-electronic three-center two-positron bond, analogous to the well-known three-center two-electron counterparts, which is fundamentally distinct from the two-center two-positron bond [D. Bressanini, J. Chem. Phys., 2021, 155, 054306], thus extending the concept of positron bonded molecules.

Correlated Wave Functions for Electron-Positron Interactions in Atoms and Molecules.

The positron, as the antiparticle of the electron, can form metastable states with atoms and molecules before its annihilation with an electron. Such metastable matter-positron complexes are stabilized by a variety of mechanisms, which can have both covalent and noncovalent character. Specifically, electron-positron binding often involves strong many-body correlation effects, posing a substantial challenge for quantum-chemical methods based on atomic orbitals. Here we propose an accurate, efficient, and transferable variational ansatz based on a combination of electron-positron geminal orbitals and a Jastrow factor that explicitly includes the electron-positron correlations in the field of the nuclei, which are optimized at the level of variational Monte Carlo (VMC). We apply this approach in combination with diffusion Monte Carlo (DMC) to calculate binding energies for a positron e+ and a positronium Ps (the pseudoatomic electron-positron pair), bound to a set of atomic systems (H-, Li+, Li, Li-, Be+, Be, B-, C-, O- and F-). For PsB, PsC, PsO, and PsF, our VMC and DMC total energies are lower than that from previous calculations; hence, we redefine the state of the art for these systems. To assess our approach for molecules, we study the potential-energy surfaces (PES) of two hydrogen anions H- mediated by a positron (e+H22-), for which we calculate accurate spectroscopic properties by using a dense interpolation of the PES. We demonstrate the reliability and transferability of our correlated wave functions for electron-positron interactions with respect to state-of-the-art calculations reported in the literature.

TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo.

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.

Angle-resolved photoemission spectroscopy from first-principles quantum Monte Carlo.

Angle-resolved photoemission spectroscopy allows one to visualize in momentum space the probability weight maps of electrons subtracted from molecules deposited on a substrate. The interpretation of these maps usually relies on the plane wave approximation through the Fourier transform of single particle orbitals obtained from density functional theory. Here we propose a first-principle many-body approach based on quantum Monte Carlo (QMC) to directly calculate the quasi-particle wave functions (also known as Dyson orbitals) of molecules in momentum space. The comparison between these correlated QMC images and their single particle counterpart highlights features that arise from many-body effects. We test the QMC approach on the linear C2H2, CO2, and N2 molecules, for which only small amplitude remodulations are visible. Then, we consider the case of the pentacene molecule, focusing on the relationship between the momentum space features and the real space quasi-particle orbital. Eventually, we verify the correlation effects present in the metal CuCl 4 2 - planar complex.

Carbon nanotubes as excitonic insulators.

Fifty years ago Walter Kohn speculated that a zero-gap semiconductor might be unstable against the spontaneous generation of excitons-electron-hole pairs bound together by Coulomb attraction. The reconstructed ground state would then open a gap breaking the symmetry of the underlying lattice, a genuine consequence of electronic correlations. Here we show that this excitonic insulator is realized in zero-gap carbon nanotubes by performing first-principles calculations through many-body perturbation theory as well as quantum Monte Carlo. The excitonic order modulates the charge between the two carbon sublattices opening an experimentally observable gap, which scales as the inverse of the tube radius and weakly depends on the axial magnetic field. Our findings call into question the Luttinger liquid paradigm for nanotubes and provide tests to experimentally discriminate between excitonic and Mott insulators.

Role of Electron Correlation along the Water Splitting Reaction.

Electron correlation plays a crucial role in the energetics of reactions catalyzed by transition metal complexes, such as water splitting. In the present work we exploit the performance of various methods to describe the thermodynamics of a simple but representative model of water splitting reaction, based on a single cobalt ion as catalyst. Density Functional Theory (DFT) calculations show a significant dependence on the adopted functional, and not negligible differences with respect to CCSD(T) findings are found along the reaction cycle. We performed quantum Monte Carlo calculations using an unrestricted single Slater determinant wave function multiplied by a Jastrow factor using both DFT and fully optimized orbitals. Variational and Lattice Regularized Diffusion Monte Carlo results are in overall agreement with the CCSD(T) free-energy profile, even though differences in the description of the thermodynamics of the reaction cycle are found. NEVPT2 calculations reveal that the role of the static correlation of the different reaction steps is not large, and it is limited to only a few intermediate structures. Finally, the free-energy difference of the overall water splitting reaction computed at the quantum Monte Carlo level shows an excellent match with the experimental value of 4.92 eV, underlining the capability of these techniques to properly describe the dynamical correlation of such reactions.

Geometries of low spin states of multi-centre transition metal complexes through extended broken symmetry variational Monte Carlo.

The correct description of the ground state electronic and geometrical properties of multi-centre transition metal complexes necessitates of a high-level description of both dynamical and static correlation effects. In di-metallic complexes, the ground state low spin properties can be computed starting from single-determinants High-Spin (HS) and Broken Symmetry (BS) states by reconstructing an approximated low spin potential energy surface through the extended broken symmetry approach, based on the Heisenberg Hamiltonian. In the present work, we first apply this approach within the variational Monte Carlo method to tackle the geometry optimization of a Fe2S2(SH)42- model complex. To describe the HS and BS wavefunctions, we use a fully optimized unrestricted single determinant with a correlated Jastrow factor able to recover a large amount of dynamical correlation. We compared our results with those obtained by density functional theory and other multiconfigurational approaches, discussing the role of the nodal surface on the structural parameters.

Correlation Effects in Scanning Tunneling Microscopy Images of Molecules Revealed by Quantum Monte Carlo.

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.

Neutral, Anionic, and Cationic Manganese Dimers through Density Functional Theory.

The manganese dimer is the only first row transition metal dimer that presents an antiferromagnetic 1Σg + ground state bonded by a van der Waals interaction. The various density functional theory (DFT) investigations devoted to the study of the ground state of this molecule and of its anionic and cationic states, are usually based on the generalized gradient approximation, giving results which contradict the experimental observations. In this work, we describe the overall spectroscopic properties of the neutral, cationic and anionic manganese dimers with DFT, focusing on understanding the effects of the percentage of Hartree-Fock exchange and of the different exchange-correlation functionals, on the relative stability of the various potential energy curves. For each of the three species we classify the ferromagnetic and antiferromagnetic states, studying the vertical detachment energies, the ionization energies and the electron affinities. In this way, we locate a hybrid exchange-correlation functional able to give for all the three species, results comparable with the experimental measurements and with previous accurate multiconfigurational calculations, defining a more accurate density functional theory approach to study larger charged or neutral manganese clusters.

Investigating Disjoint Non-Kekulé Diradicals with Quantum Monte Carlo: The Tetramethyleneethane Molecule through the Jastrow Antisymmetrized Geminal Power Wave Function.

Disjoint non-Kekulé molecules are diradicals that present two independent radical centers and can violate Hund's rule, according to which the ground state should have triplet spin symmetry. The prototype of this class of systems is the tetramethyleneethane (TME) molecule for which indeed ion photoelectron spectroscopy (IPS) experiments revealed the singlet (1)A state to be more stable than the triplet (3)Bu. In this work we investigate the potential energy curves of the two spin states of TME and of the two anionic states of TME(-) ((2)A and (2)B1) as a function of the torsion of the central dihedral angle, with quantum Monte Carlo methods and a Jastrow Antisymmetrized Geminal Power wave function. Through ab initio geometrical optimizations we study the possible structural interconversions between the states, finding results which are in full agreement with the IPS experimental data.

π-Conjugation in trans-1,3-butadiene: static and dynamical electronic correlations described through quantum Monte Carlo.

We investigate the effects of the static and dynamical electronic correlations on the level of conjugation of the trans-1,3-butadiene molecule through Quantum Monte Carlo methods applied to an Antisymmetrized Geminal Power (AGP) wave function, with a Jastrow factor similar to the Gutzwiller ansatz. The degree of conjugation is measured through the convergence of the structural properties of 1,3-butadiene and in particular of the Bond Length Alternation (BLA), that is the difference between the lengths of the single and double carbon bonds. After verifying the different roles of the Fermionic AGP part of our wave function and of the Jastrow factor in recovering electronic correlation, we study the effects of a constrained Active Space AGP (AGPAS), similar to that used in the Complete Active Space (CAS) representation. Through this AGPAS, we are able to identify the effect of the limited active space on the degree of conjugation, showing that in the limit of infinite active space the structural properties converge exactly to those of the atomic AGP, giving a BLA for 1,3-butadiene around 0.1244(5) Å.

Ground State Geometries of Polyacetylene Chains from Many-Particle Quantum Mechanics.

Due to the crucial role played by electron correlation, the accurate determination of ground state geometries of π-conjugated molecules is still a challenge for many quantum chemistry methods. Because of the high parallelism of the algorithms and their explicit treatment of electron correlation effects, Quantum Monte Carlo calculations can offer an accurate and reliable description of the electronic states and of the geometries of such systems, competing with traditional quantum chemistry approaches. Here, we report the structural properties of polyacetylene chains H-(C2H2)(N)-H up to N = 12 acetylene units, by means of Variational Monte Carlo (VMC) calculations based on the multi-determinant Jastrow Antisymmetrized Geminal Power (JAGP) wave function. This compact ansatz can provide for such systems an accurate description of the dynamical electronic correlation as recently detailed for the 1,3-butadiene molecule [J. Chem. Theory Comput. 2015 11 (2), 508-517]. The calculated Bond Length Alternation (BLA), namely the difference between the single and double carbon bonds, extrapolates, for N → ∞, to a value of 0.0910(7) Å, compatible with the experimental data. An accurate analysis was able to distinguish between the influence of the multi-determinantal AGP expansion and of the Jastrow factor on the geometrical properties of the fragments. Our size-extensive and self-interaction-free results provide new and accurate ab initio references for the structures of the ground state of polyenes.

Kohn-Sham orbitals and potentials from quantum Monte Carlo molecular densities.

In this work we show the possibility to extract Kohn-Sham orbitals, orbital energies, and exchange correlation potentials from accurate Quantum Monte Carlo (QMC) densities for atoms (He, Be, Ne) and molecules (H2, Be2, H2O, and C2H4). The Variational Monte Carlo (VMC) densities based on accurate Jastrow Antisymmetrised Geminal Power wave functions are calculated through different estimators. Using these reference densities, we extract the Kohn-Sham quantities with the method developed by Zhao, Morrison, and Parr (ZMP) [Phys. Rev. A 50, 2138 (1994)]. We compare these extracted quantities with those obtained form CISD densities and with other data reported in the literature, finding a good agreement between VMC and other high-level quantum chemistry methods. Our results demonstrate the applicability of the ZMP procedure to QMC molecular densities, that can be used for the testing and development of improved functionals and for the implementation of embedding schemes based on QMC and Density Functional Theory.

Reaction pathways by quantum Monte Carlo: insight on the torsion barrier of 1,3-butadiene, and the conrotatory ring opening of cyclobutene.

Quantum Monte Carlo (QMC) methods are used to investigate the intramolecular reaction pathways of 1,3-butadiene. The ground state geometries of the three conformers s-trans, s-cis, and gauche, as well as the cyclobutene structure are fully optimised at the variational Monte Carlo (VMC) level, obtaining an excellent agreement with the experimental results and other quantum chemistry high level calculations. Transition state geometries are also estimated at the VMC level for the s-trans to gauche torsion barrier of 1,3-butadiene and for the conrotatory ring opening of cyclobutene to the gauche-1,3-butadiene conformer. The energies of the conformers and the reaction barriers are calculated at both variational and diffusional Monte Carlo levels providing a precise picture of the potential energy surface of 1,3-butadiene and supporting one of the two model profiles recently obtained by Raman spectroscopy [Boopalachandran et al., J. Phys. Chem. A 115, 8920 (2011)]. Considering the good scaling of QMC techniques with the system's size, our results also demonstrate how variational Monte Carlo calculations can be applied in the future to properly investigate the reaction pathways of large and correlated molecular systems.

Molecular Electrical Properties from Quantum Monte Carlo Calculations: Application to Ethyne.

We used Quantum Monte Carlo (QMC) methods to study the polarizability and the quadrupole moment of the ethyne molecule using the Jastrow-Antisymmetrised Geminal Power (JAGP) wave function, a compact and strongly correlated variational ansatz. The compactness of the functional form and the full optimization of all its variational parameters, including linear and exponential coefficients in atomic orbitals, allow us to observe a fast convergence of the electrical properties with the size of the atomic and Jastrow basis sets. Both variational results on isotropic polarizability and quadrupole moment based on Gaussian type and Slater type basis sets are very close to the Lattice Regularized Diffusion Monte Carlo values and in very good agreement with experimental data and with other quantum chemistry calculations. We also study the electronic density along the C≡C and C-H bonds by introducing a generalization for molecular systems of the small-variance improved estimator of the electronic density proposed by Assaraf et al. (Assaraf, R.; Caffarel, M.; Scemama, A. Phys. Rev. E, 2007, 75, 035701).

Structural Optimization by Quantum Monte Carlo: Investigating the Low-Lying Excited States of Ethylene.

We present full structural optimizations of the ground state and of the low lying triplet state of the ethylene molecule by means of Quantum Monte Carlo methods. Using the efficient structural optimization method based on renormalization techniques and on adjoint differentiation algorithms recently proposed [Sorella, S.; Capriotti, L. J. Chem. Phys.2010, 133, 234111], we present the variational convergence of both wave function parameters and atomic positions. All of the calculations were done using an accurate and compact wave function based on Pauling's resonating valence bond representation: the Jastrow Antisymmetrized Geminal Power (JAGP). All structural and wave function parameters are optimized, including coefficients and exponents of the Gaussian primitives of the AGP and the Jastrow atomic orbitals. Bond lengths and bond angles are calculated with a statistical error of about 0.1% and are in good agreement with the available experimental data. The Variational and Diffusion Monte Carlo calculations estimate vertical and adiabatic excitation energies in the ranges 4.623(10)-4.688(5) eV and 3.001(5)-3.091(5) eV, respectively. The adiabatic gap, which is in line with other correlated quantum chemistry methods, is slightly higher than the value estimated by recent photodissociation experiments. Our results demonstrate how Quantum Monte Carlo calculations have become a promising and computationally affordable tool for the structural optimization of correlated molecular systems.