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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.

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.

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 1A state to be more stable than the triplet 3Bu. In this work we investigate the potential energy curves of the two spin states of TME and of the two anionic states of TME–(2A and 2B1) 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 initiogeometrical optimizations we study the possible structural interconversions between the states, finding results which are in full agreement with the IPS experimental data.

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 correlationas recently detailed for the 1,3-butadiene molecule [J. Chem. Theory Comput. 201511 (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 initioreferences for the structures of the ground state of polyenes.

We investigate the effects of the staticand dynamical electronic correlationson 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.

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).

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.

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.