We report a systematic study of the weak chemical bond between two benzene molecules. We first show that it is possible to obtain a very good description of the ${\mathrm{C}}_2$ dimer and the benzene molecule by using pseudopotentials for the chemically inert $1s$ electrons and a resonating valence bond wave function as a variational ansatz, expanded on a relatively small Gaussian basis set. We employ an improved version of the stochastic reconfiguration technique to optimize the many-body wave function, which is the starting point for highly accurate simulations based on the lattice regularized diffusion Monte Carlo method. This projection technique provides a rigorous variational upper bound for the total energy, even in the presence of pseudopotentials, and substantially improves the accuracy of the trial wave function, which already yields a large fraction of the dynamical and nondynamical electron correlation. We show that the energy dispersion of two benzene molecules in the parallel displaced geometry is significantly deeper than the face-to-face configuration. However, contrary to previous studies based on post-Hartree-Fock methods, the binding energy remains weak $(\simeq 2\mathrm{kcal}∕\mathrm{mol})$ also in this geometry, and its value is in agreement with the most accurate and recent experimental findings [H. Krause et al., Chem. Phys. Lett. 184, 411 (1991)].

QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.

We present a way to include nonlocal potentials in the standard diffusion Monte Carlo method without using the locality approximation. We define a stochastic projection based on a fixed node effective Hamiltonian, whose lowest energy is an upper bound of the true ground-state energy, even in the presence of nonlocal operators in the Hamiltonian. The variational property of the resulting algorithm provides a stable diffusion process, even in the case of divergent nonlocal potentials, like the hard-core pseudopotentials. It turns out that the modification required to improve the standard diffusion Monte Carlo algorithm is simple.

We show that a simple correlated wave function, obtained by applying a Jastrow correlation term to an antisymmetrized geminal power, based upon singlet pairs between electrons, is particularly suited for describing the electronic structure of molecules, yielding a large amount of the correlation energy. The remarkable feature of this approach is that, in principle, several resonating valence bonds can be dealt simultaneously with a single determinant, at a computational cost growing with the number of electrons similar to more conventional methods, such as Hartree-Fock or density functional theory. Moreover we describe an extension of the stochastic reconfiguration method, which was recently introduced for the energy minimization of simple atomic wave functions. Within this extension the atomic positions can be considered as further variational parameters, which can be optimized together with the remaining ones. The method is applied to several molecules from ${\mathrm{Li}}_2$ to benzene by obtaining total energies, bond lengths and binding energies comparable with much more demanding multiconfiguration schemes.

We introduce a simple generalization of the well-known geminal wave function already applied in quantum chemistry to atoms and small molecules. The main feature of the proposed wave function is the presence of the antisymmetric geminal part together with a Jastrow factor. Both the geminal and the Jastrow play a crucial role in determining the remarkable accuracy of the many-body state: the former permits the correct treatment of the nondynamic correlation effects; the latter allows the wave function to fulfill the cusp conditions and makes the geminal expansion rapidly converge to the lowest possible variational energies. This ansatz is expected to provide a substantial part of the correlation energy for general complex atomic and molecular systems. The antisymmetric geminal term can be written as a single determinant even in the polarized cases. In general, therefore, the computational effort to sample this correlated wave function is not very demanding, the scaling of the algorithm with the number of atoms being comparable with the simplest Hartree–Fock calculation. We applied this Jastrow-geminal approach to atoms up to $\text{Z=14,}$ always getting good variational energies, by particularly improving those with a strong multiconfigurational nature. Our wave function is very useful for Monte Carlo techniques, such as fixed node. Indeed, the nodal surface obtained within this approach can be substantially improved through the geminal expansion.