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

Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations

The past several years have seen renewed interest in the use of symmetry-projected Hartree-Fock for the description of strong correlations. Unfortunately, these symmetry-projected mean-field methods do not adequately account for dynamic correlation. Presumably, this shortcoming could be addressed if one could combine symmetry-projected Hartree-Fock with a many-body method such as coupled cluster theory, but this is by no means straightforward because the two techniques are formulated in very different ways. However, we have recently shown that the singlet $S^2$-projected unrestricted Hartree-Fock wave function can in fact be written in a coupled cluster-like wave function: that is, the spin-projected unrestricted Hartree-Fock wave function can be written as a polynomial of a double-excitation operator acting on some closed-shell reference determinant. Here, we extend this result and show that the spin-projected generalized Hartree-Fock wave function (which has both $S^2$ and $S_z$ projection) is likewise a polynomial of low-order excitation operators acting on a closed-shell determinant, and provide a closed-form expression for the resulting polynomial coefficients. We include a few preliminary applications of the combination of this spin-projected Hartree-Fock and coupled cluster theory to the Hubbard Hamiltonian, and comment on generalizations of the methodology. Results here are not for production level, but a similarity transformed theory that combines the two offers the promise of being accurate for both weak and strong correlation, and particularly may offer significant improvements in the intermediate correlation regime where neither projected Hartree-Fock nor coupled cluster is particularly accurate.Comment: accepted by Phys. Rev.

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

On the difference between variational and unitary coupled cluster theories

There have been assertions in the literature that the variational and unitary forms of coupled cluster theory lead to the same energy functional. Numerical evidence from previous authors was inconsistent with this claim, yet the small energy differences found between the two methods and the relatively large number of variational parameters precluded an unequivocal conclusion. Using the Lipkin Hamiltonian, we here present conclusive numerical evidence that the two theories yield different energies. The ambiguities arising from the size of the cluster parameter space are absent in the Lipkin model, particularly when truncating to double excitations. We show that in the symmetry adapted basis under strong correlation the differences between the variational and unitary models are large, whereas they yield quite similar energies in the weakly correlated regime previously explored. We also provide a qualitative argument rationalizing why these two models cannot be the same. Additionally, we study a generalized non-unitary and non-hermitian variant that contains excitation, de-excitation and mixed operators with different amplitudes and show that it works best when compared to the traditional, variational, unitary, and extended forms of coupled cluster doubles theories

A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model

We introduce a mean-field and perturbative approach, based on clusters, to describe the ground state of fermionic strongly-correlated systems. In cluster mean-field, the ground state wavefunction is written as a simple tensor product over optimized cluster states. The optimization of the single-particle basis where the cluster mean-field is expressed is crucial in order to obtain high-quality results. The mean-field nature of the ansatz allows us to formulate a perturbative approach to account for inter-cluster correlations; other traditional many-body strategies can be easily devised in terms of the cluster states. We present benchmark calculations on the half-filled 1D and (square) 2D Hubbard model, as well as the lightly-doped regime in 2D, using cluster mean-field and second-order perturbation theory. Our results indicate that, with sufficiently large clusters or to second-order in perturbation theory, a cluster-based approach can provide an accurate description of the Hubbard model in the considered regimes. Several avenues to improve upon the results presented in this work are discussed.Comment: 22 pages, 21 figure

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

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