ROHF Theory Made Simple

Restricted open-shell Hartree-Fock (ROHF) theory is formulated as a projected self-consistent unrestricted HF (UHF) model by mathematically constraining spin density eigenvalues. The resulting constrained UHF (CUHF) wave function is identical to that obtained from Roothaan's effective Fock operator. Our $\alpha$ and $\beta$ CUHF Fock operators are parameter-free and have canonical orbitals and orbital energies that are physically meaningful as in UHF, except for eliminating spin contamination. The present approach removes ambiguities in ROHF orbital energies and the non-uniqueness of methods that build upon them. We present benchmarks to demonstrate CUHF physical correctness and good agreement with experimental results

On the equivalence of LIST and DIIS methods for convergence acceleration

Self-consistent field extrapolation methods play a pivotal role in quantum chemistry and electronic structure theory. We here demonstrate the mathematical equivalence between the recently proposed family of LIST methods [J. Chem. Phys. 134, 241103 (2011); J. Chem. Theory Comput. 7, 3045 (2011)] with Pulay's DIIS [Chem. Phys. Lett. 73, 393 (1980)]. Our results also explain the differences in performance among the various LIST methods

Edge Effects in Finite Elongated Graphene Nanoribbons

We analyze the relevance of finite-size effects to the electronic structure of long graphene nanoribbons using a divide and conquer density functional approach. We find that for hydrogen terminated graphene nanoribbons most of the physical features appearing in the density of states of an infinite graphene nanoribbon are recovered at a length of 40 nm. Nevertheless, even for the longest systems considered (72 nm long) pronounced edge effects appear in the vicinity of the Fermi energy. The weight of these edge states scales inversely with the length of the ribbon and they are expected to become negligible only at ribbons lengths of the order of micrometers. Our results indicate that careful consideration of finite-size and edge effects should be applied when designing new nanoelectronic devices based on graphene nanoribbons. These conclusions are expected to hold for other one-dimensional systems such as carbon nanotubes, conducting polymers, and DNA molecules.Comment: 4 pages, 4 figure

Computational Nanotechnology Program

The objectives are: (1) development of methodological and computational tool for the quantum chemistry study of carbon nanostructures and (2) development of the fundamental understanding of the bonding, reactivity, and electronic structure of carbon nanostructures. Our calculations have continued to play a central role in understanding the outcome of the carbon nanotube macroscopic production experiment. The calculations on buckyonions offer the resolution of a long controversy between experiment and theory. Our new tight binding method offers increased speed for realistic simulations of large carbon nanostructures

Composite Boson Mapping for Lattice Boson Systems

We present a canonical mapping transforming physical boson operators into quadratic products of cluster composite bosons that preserves matrix elements of operators when a physical constraint is enforced. We map the 2D lattice Bose-Hubbard Hamiltonian into $2\times 2$ composite bosons and solve it at mean field. The resulting Mott insulator-superfluid phase diagram reproduces well Quantum Monte Carlo results. The Higgs boson behavior along the particle-hole symmetry line is unraveled and in remarkable agreement with experiment. Results for the properties of the ground and excited states are competitive with other state-of-the-art approaches, but at a fraction of their computational cost. The composite boson mapping here introduced can be readily applied to frustrated many-body systems where most methodologies face significant hurdles.Comment: 8 pages, 4 figure