Michele Casula

Correlated geminal wave function for molecules: An efficient resonating valence bond approach

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 Li(2) to benzene by obtaining total energies, bond lengths and binding energies comparable with much more demanding multiconfiguration schemes.

Geminal wave functions with Jastrow correlation: A first application to atoms

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 at...

Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods

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 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 ( approximately 2 kcal/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)].

Beyond the locality approximation in the standard diffusion Monte Carlo method

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.

Resonating valence bond wave function with molecular orbitals: application to first-row molecules.

We introduce a method for accurate quantum chemical calculations based on a simple variational wave function, defined by a single geminal that couples all the electrons into singlet pairs, combined with a real space correlation factor. The method uses a constrained variational optimization, based on an expansion of the geminal in terms of molecular orbitals. It is shown that the most relevant nondynamical correlations are correctly reproduced once an appropriate number n of molecular orbitals is considered. The value of n is determined by requiring that, in the atomization limit, the atoms are described by Hartree-Fock Slater determinants with Jastrow correlations. The energetics, as well as other physical and chemical properties, are then given by an efficient variational approach based on standard quantum Monte Carlo techniques. We test this method on a set of homonuclear (Be(2), B(2), C(2), N(2), O(2), and F(2)) and heteronuclear (LiF and CN) dimers for which strong nondynamical correlations and/or weak van der Waals interactions are present.

Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited

We propose improved versions of the standard diffusion Monte Carlo (DMC) and the lattice regularized diffusion Monte Carlo (LRDMC) algorithms. For the DMC method, we refine a scheme recently devised to treat nonlocal pseudopotential in a variational way. We show that such scheme-when applied to large enough systems-maintains its effectiveness only at correspondingly small enough time-steps, and we present two simple upgrades of the method which guarantee the variational property in a size-consistent manner. For the LRDMC method, which is size-consistent and variational by construction, we enhance the computational efficiency by introducing: (i) an improved definition of the effective lattice Hamiltonian which remains size-consistent and entails a small lattice-space error with a known leading term and (ii) a new randomization method for the positions of the lattice knots which requires a single lattice-space.

Satellites and large doping and temperature dependence of electronic properties in hole-doped BaFe2As2

An approach to first-principles simulations that incorporates dynamically screened Coulomb interactions between iron d electrons enables the low-energy electronic structure and angle-resolved photoemission spectroscopy spectra of iron-based superconductors to be modelled with unprecedented accuracy.

Intercalant and Intermolecular Phonon Assisted Superconductivity in K-Doped Picene

K(3) picene is a superconducting molecular crystal with a critical temperature of T(c) = 7 or 18 K, depending on the preparation conditions. Using density functional theory we show that electron-phonon interaction accounts for T(c) 3-8 K. The average electron-phonon coupling, calculated by including the phonon energy scale in the electron-phonon scattering, is λ = 0.73 and ω(log) = 18.0 meV. Intercalant and intermolecular phonon modes contribute substantially (40%) to λ as also shown by the isotope exponents of potassium (0.19) and carbon (0.31). The relevance of these modes makes superconductivity in K-doped picene peculiar and different from that of fullerenes.

Density functional theory beyond the linear regime: Validating an adiabatic local density approximation

We present a local density approximation (LDA) for one-dimensional (1D) systems interacting via the soft-Coulomb interaction based on quantum Monte Carlo calculations. Results for the ground-state energies and ionization potentials of finite 1D systems show excellent agreement with exact calculations obtained by exploiting the mapping of an N-electron system in d dimensions onto a single electron in Nxd dimensions, properly symmetrized by the Young diagrams. We conclude that 1D LDA is of the same quality as its three-dimensional (3D) counterpart, and we infer conclusions about 3D LDA. The linear and nonlinear time-dependent responses of 1D model systems using LDA, exact exchange, and the exact solution are investigated and show very good agreement in both cases, except for the well-known problem of missing double excitations. Consequently, the 3D LDA is expected to be of good quality beyond the linear response. In addition, the 1D LDA should prove useful in modeling the interaction of atoms with strong laser fields, where this specific 1D model is often used.

Hexatic and mesoscopic phases in a 2D quantum coulomb system.

We study the Wigner crystal melting in a two-dimensional quantum system of distinguishable particles interacting via the 1/r Coulomb potential. We use quantum Monte Carlo methods to calculate its phase diagram, locate the Wigner crystal region, and analyze its instabilities towards the liquid phase. We discuss the role of quantum effects in the critical behavior of the system, and compare our numerical results with the classical theory of melting, and the microemulsion theory of frustrated Coulomb systems. We find a Pomeranchuk effect much larger then in solid helium. In addition, we find that the exponent for the algebraic decay of the hexatic phase differs significantly from the Kosterilitz-Thouless theory of melting. We search for the existence of mesoscopic phases and find evidence of metastable bubbles but no mesoscopic phase that is stable in equilibrium.