Electron correlation in C_(4N+2) carbon rings: aromatic vs. dimerized structures

The electronic structure of C_(4N+2) carbon rings exhibits competing many-body effects of Huckel aromaticity, second-order Jahn-Teller and Peierls instability at large sizes. This leads to possible ground state structures with aromatic, bond angle or bond length alternated geometry. Highly accurate quantum Monte Carlo results indicate the existence of a crossover between C_10 and C_14 from bond angle to bond length alternation. The aromatic isomer is always a transition state. The driving mechanism is the second-order Jahn-Teller effect which keeps the gap open at all sizes.Comment: Submitted for publication: 4 pages, 3 figures. Corrected figure

Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies

A study of fermion nodes for spin-polarized states of a few-electron ions and molecules with $s,p,d$ one-particle orbitals is presented. We find exact nodes for some cases of two electron atomic and molecular states and also the first exact node for the three-electron atomic system in $^4S(p^3)$ state using appropriate coordinate maps and wavefunction symmetries. We analyze the cases of nodes for larger number of electrons in the Hartree-Fock approximation and for some cases we find transformations for projecting the high-dimensional node manifolds into 3D space. The node topologies and other properties are studied using these projections. We also propose a general coordinate transformation as an extension of Feynman-Cohen backflow coordinates to both simplify the nodal description and as a new variational freedom for quantum Monte Carlo trial wavefunctions.Comment: 7 pages, 7 figure

Pfaffian pairing wave functions in electronic structure quantum Monte Carlo

We investigate the accuracy of trial wave function for quantum Monte Carlo based on pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-pfaffian pairing wave functions. We show that a small number of pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.Comment: 4 pages, 2 figures, 2 tables, submitted to PR