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Register a new userThe Role of High-Order Electron Correlation Effects in a Model System for Non-valence Correlation-bound Anions
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The diffusion Monte Carlo (DMC), auxiliary field quantum Monte Carlo (AFQMC), and equation-of-motion coupled cluster (EOM-CC) methods are used to calculate the electron binding energy (EBE) of the non-valence anion state of a model (H$_2$O)$_4$ cluster. Two geometries are considered, one at which the anion is unbound and the other at which it is bound in the Hartree-Fock (HF) approximation. It is demonstrated that DMC calculations can recover from the use of a HF trial wave function that has collapsed onto a discretized continuum solution, although larger electron binding energies are obtained when using a trial wave function for the anion that provides a more realistic description of the charge distribution, and, hence, of the nodal surface. For the geometry at which the cluster has a non-valence correlation-bound anion, both the inclusion of triples in the EOM-CC method and the inclusion of supplemental diffuse d functions in the basis set are important. DMC calculations with suitable trial wave functions give EBE values in good agreement with our best estimate EOM-CC result. AFQMC using a trial wave function for the anion with a realistic electron density gives a value of the EBE nearly identical to the EOM-CC result when using the same basis set. For the geometry at which the anion is bound in the HF approximation, the inclusion of triple excitations in the EOM-CC calculations is much less important. The best estimate EOM-CC EBE value is in good agreement with the results of DMC calculations with appropriate trial wave functions.
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Different computational methods are employed to evaluate elastic (rotationally summed) integral and differential cross sections for low energy (below about 10 eV) positron scattering off gas-phase C$_2$H$_2$ molecules. The computations are carried out at the static and static-plus-polarization levels for describing the interaction forces and the correlation-polarization contributions are found to be an essential component for the correct description of low-energy cross section behavior. The local model potentials derived from density functional theory (DFT) and from the distributed positron model (DPM) are found to produce very high-quality agreement with existing measurements. On the other hand, the less satisfactory agreement between the R-matrix (RM) results and measured data shows the effects of the slow convergence rate of configuration-interaction (CI) expansion methods with respect to the size of the CI-expansion. To contrast the positron scattering findings, results for electron-C$_2$H$_2$ integral and differential cross sections, calculated with both a DFT model potential and the R-matrix method, are compared and analysed around the shape resonance energy region and found to produce better internal agreement.
A method and codes for two-step correlation calculation of heavy-atom molecules have been developed, employing the generalized relativistic effective core potential and relativistic coupled cluster (RCC) methods at the first step, followed by nonvariational one-center restoration of proper four-component spinors in the heavy cores. Electron correlation is included for the first time in an ab initio calculation of the interaction of the permanent P,T-odd proton electric dipole moment with the internal electromagnetic field in a molecule. The calculation is performed for the ground state of TlF at the experimental equilibrium, R_e=2.0844 A, and at R=2.1 A, with spin-orbit and correlation effects included by RCC. Calculated results with single cluster amplitudes only are in good agreement (3% and 1%) with recent Dirac-Hartree-Fock (DHF) values of the magnetic parameter M; the larger differences occurring between present and DHF volume parameter (X) values, as well as between the two DHF calculations, are explained. Inclusion of electron correlation by GRECP/RCC with single and double excitations has a major effect on the P,T-odd parameters, decreasing M by 17% and X by 22%.
Multi-configurational approaches yield universal wave function parameterizations that can qualitatively well describe electronic structures along reaction pathways. For quantitative results, multi-reference perturbation theory is required to capture dynamic electron correlation from the otherwise neglected virtual orbitals. Still, the overall accuracy suffers from the finite size and choice of the active orbital space and peculiarities of the perturbation theory. Fortunately, the electronic wave functions at equilibrium structures of reactants and products can often be well described by single-reference methods and hence are accessible to accurate coupled cluster calculations. Here, we calculate the heterolytic double dissociation energy of four 3d-metallocenes with the complete active space self-consistent field method and compare to highly accurate coupled cluster data. Our coupled cluster data are well within the experimental error bars. This accuracy can also be approached by complete active space calculations with an orbital selection based on information entropy measures. The entropy based active space selection is discussed in detail. We find a very subtle balance between static and dynamic electron correlation effects that emphasizes the need for algorithmic active space selection and that differs significantly from restricted active space results for identical active spaces reported in the literature.
Neutral molecules with sufficiently large dipole moments can bind electrons in diffuse nonvalence orbitals with most of their charge density far from the nuclei, forming so-called dipole-bound anions. Because long-range correlation effects play an important role in the binding of an excess electron and overall binding energies are often only of the order of 10-100s of wave numbers, predictively modeling dipole-bound anions remains a challenge. Here, we demonstrate that quantum Monte Carlo methods can accurately characterize molecular dipole-bound anions with near threshold dipole moments. We also show that correlated sampling Auxiliary Field Quantum Monte Carlo is particularly well-suited for resolving the fine energy differences between the neutral and anionic species. These results shed light on the fundamental limitations of quantum Monte Carlo methods and pave the way toward using them for the study of weakly-bound species that are too large to model using traditional electron structure methods.
A single-term density functional model for nondynamic and strong correlation is presented, based on single-determinant Kohn-Sham density functional theory. It is derived from modeling the adiabatic connection and contains only two nonlinear empirical parameters. Preliminary tests show that the model recovers majority of nondynamic correlation during a molecular dissociation and at the same time performs reasonably for atomization energies. It demonstrates the feasibility of developing DFT functionals for nondynamic and strong correlation within the single-determinant KS scheme.
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