5,810 research outputs found

    Accurate ab initio spin densities

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    We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys. 2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insights into chemically interesting features of the molecule under study such as the distribution of α\alpha- and ÎČ\beta-electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput. 2011, 7, 2740].Comment: 37 pages, 13 figure

    Self-Consistent Electron-Nucleus Cusp Correction for Molecular Orbitals

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    We describe a method for imposing the correct electron-nucleus (e-n) cusp in molecular orbitals expanded as a linear combination of (cuspless) Gaussian basis functions. Enforcing the e-n cusp in trial wave functions is an important asset in quantum Monte Carlo calculations as it significantly reduces the variance of the local energy during the Monte Carlo sampling. In the method presented here, the Gaussian basis set is augmented with a small number of Slater basis functions. Note that, unlike other e-n cusp correction schemes, the presence of the Slater function is not limited to the vicinity of the nuclei. Both the coefficients of these cuspless Gaussian and cusp-correcting Slater basis functions may be self-consistently optimized by diagonalization of an orbital-dependent effective Fock operator. Illustrative examples are reported for atoms (\ce{H}, \ce{He} and \ce{Ne}) as well as for a small molecular system (\ce{BeH2}). For the simple case of the \ce{He} atom, we observe that, with respect to the cuspless version, the variance is reduced by one order of magnitude by applying our cusp-corrected scheme.Comment: 23 pages, 5 figure

    Quantum Monte Carlo with very large multideterminant wavefunctions

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    An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman-Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin-specific determinants: for typical configuration interaction-type wavefunctions the number of unique spin-specific determinants NdetσN_{\rm det}^\sigma (σ=↑,↓\sigma=\uparrow,\downarrow) with a non-negligible weight in the expansion is of order O(Ndet){\cal O}(\sqrt{N_{\rm det}}). We show that a careful implementation of the calculation of the NdetN_{\rm det}-dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin-specific determinants,   Ndet↑+Ndet↓\; N_{\rm det}^\uparrow + N_{\rm det}^\downarrow, over a wide range of total number of determinants (here, NdetN_{\rm det} up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all-electron Fixed-Node Diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750 000 determinants with a computational increase of ∌\sim 400 compared to a single-determinant calculation are shown to be feasible.Comment: 9 pages, 3 figure

    Orbital Dependent Exchange-Only Methods for Periodic Systems

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    Various orbital-dependent exchange-only potentials are studied which exhibit correct long-range asymptotic behaviour. We present the first application of these potentials for polymers and by one of these potentials for molecules. Kohn-Sham type calculations have been carried out for polyethylene in order to make valuable comparison of these potentials with each other as well as with Hartree-Fock and exchange-only LDA methods. The Kohn-Sham band gap obtained with the optimized effective potetial method is corrected with the exchange contribution to the derivative discontinuity of the exchange-correlation potential. The corrected band gap obtained with the Slater's exchange potential is 9.7 eV close to the experiment.Comment: 11 pages, 2 figures. Phys. Rev. B60, 1999, in pres

    Excited electronic states from a variational approach based on symmetry-projected Hartree--Fock configurations

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    Recent work from our research group has demonstrated that symmetry-projected Hartree--Fock (HF) methods provide a compact representation of molecular ground state wavefunctions based on a superposition of non-orthogonal Slater determinants. The symmetry-projected ansatz can account for static correlations in a computationally efficient way. Here we present a variational extension of this methodology applicable to excited states of the same symmetry as the ground state. Benchmark calculations on the C2_2 dimer with a modest basis set, which allows comparison with full configuration interaction results, indicate that this extension provides a high quality description of the low-lying spectrum for the entire dissociation profile. We apply the same methodology to obtain the full low-lying vertical excitation spectrum of formaldehyde, in good agreement with available theoretical and experimental data, as well as to a challenging model C2vC_{2v} insertion pathway for BeH2_2. The variational excited state methodology developed in this work has two remarkable traits: it is fully black-box and will be applicable to fairly large systems thanks to its mean-field computational cost

    Optimized Jastrow-Slater wave functions for ground and excited states: Application to the lowest states of ethene

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    A quantum Monte Carlo method is presented for determining multi-determinantal Jastrow-Slater wave functions for which the energy is stationary with respect to the simultaneous optimization of orbitals and configuration interaction coefficients. The approach is within the framework of the so-called energy fluctuation potential method which minimizes the energy in an iterative fashion based on Monte Carlo sampling and a fitting of the local energy fluctuations. The optimization of the orbitals is combined with the optimization of the configuration interaction coefficients through the use of additional single excitations to a set of external orbitals. A new set of orbitals is then obtained from the natural orbitals of this enlarged configuration interaction expansion. For excited states, the approach is extended to treat the average of several states within the same irreducible representation of the pointgroup of the molecule. The relationship of our optimization method with the stochastic reconfiguration technique by Sorella et al. is examined. Finally, the performance of our approach is illustrated with the lowest states of ethene, in particular with the difficult case of the singlet 1B_1u state.Comment: 12 pages, 2 figure

    Multi-component symmetry-projected approach for molecular ground state correlations

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    The symmetry-projected Hartree--Fock ansatz for the electronic structure problem can efficiently account for static correlation in molecules, yet it is often unable to describe dynamic correlation in a balanced manner. Here, we consider a multi-component, systematically-improvable approach, that accounts for all ground state correlations. Our approach is based on linear combinations of symmetry-projected configurations built out of a set of non-orthogonal, variationally optimized determinants. The resulting wavefunction preserves the symmetries of the original Hamiltonian even though it is written as a superposition of deformed (broken-symmetry) determinants. We show how short expansions of this kind can provide a very accurate description of the electronic structure of simple chemical systems such as the nitrogen and the water molecules, along the entire dissociation profile. In addition, we apply this multi-component symmetry-projected approach to provide an accurate interconversion profile among the peroxo and bis(Ό\mu-oxo) forms of [Cu2_2O2_2]2+^{2+}, comparable to other state-of-the-art quantum chemical methods
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