Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance (EPR) $g$-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute $g$-tensors for the \ce{TiF3} and \ce{CuCl4^2-} complexes, a [2Fe-2S] model of the active center of ferredoxins, and a \ce{Mn4CaO5} model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining $g$-tensors in multireference calculations with a large number of open shells.Comment: 19 page

Tensor factorizations of local second-order M{\o}ller Plesset theory

Efficient electronic structure methods can be built around efficient tensor representations of the wavefunction. Here we describe a general view of tensor factorization for the compact representation of electronic wavefunctions. We use these ideas to construct low-complexity representations of the doubles amplitudes in local second order M{\o}ller-Plesset perturbation theory. We introduce two approximations - the direct orbital specific virtual approximation and the full orbital specific virtual approximation. In these approximations, each occupied orbital is associated with a small set of correlating virtual orbitals. Conceptually, the representation lies between the projected atomic orbital representation in Pulay-Saeb{\o} local correlation theories and pair natural orbital correlation theories. We have tested the orbital specific virtual approximations on a variety of systems and properties including total energies, reaction energies, and potential energy curves. Compared to the Pulay-Saeb{\o} ansatz, we find that these approximations exhibit favourable accuracy and computational times, while yielding smooth potential energy curves

C_8H_8: a density functional theory study of molecular geometries introducing the localised bond density

In this paper we use density functional theory with all the common exchange-correlation functionals to investigate the structures of three isomers of C_8H_8 found in F. A. Cotton's text, barrelene, cyclooctatetraene, tetramethylenecyclobutane and also ethane and ethene. All calculations were performed with TZ2P basis sets and large quadrature. The results are compared with experiment and those obtained with Hartree–Fock theory. Delocalisation in the three molecules is discussed. A localised bond density in introduced to explain the transferability of the trends in the predictions of the functionals between different molecules. Three-parameter adiabatic connection functionals are examined and their usefulness in geometry prediction questioned. Finally a physical picture of the correlation as modelled by density functional theory is presented and used to explain trends in the overestimation or underestimation of bond lengths

Perfect Reflection of Chiral Fermions in Gated Graphene Nanoribbons

We describe the results of a theoretical study of transport through gated metallic graphene nanoribbons using a non-equilibrium Green function method. Although analogies with quantum field theory predict perfect transmission of chiral fermions through gated regions in one dimension, we find \emph{perfect reflection} of chiral fermions in armchair ribbons for specific configurations of the gate. This effect should be measurable in narrow graphene constrictions gated by a charged carbon nanotube.Comment: 9 pages, 3 figures. Submitted to Nano Letter

A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions

A novel approach to strongly contracted N-electron valence perturbation theory (SC-NEVPT2) as a means of describing dynamic electron correlation for quantum chemical density matrix renormalization group (DMRG) calculations is presented. In this approach the strongly contracted perturber functions are projected onto a renormalized Hilbert space. Compared to a straightforward implementation of SC-NEVPT2 with DMRG wavefunctions, the computational scaling and storage requirements are reduced. This favorable scaling opens up the possibility of calculations with larger active spaces. A specially designed renormalization scheme ensures that both the electronic ground state and the perturber functions are well represented in the renormalized Hilbert space. Test calculations on the N_2 and [Cu_2O_2(en)_2]^(2+) demonstrate some key properties of the method and indicate its capabilities

Exploring the magnetic properties of the largest single molecule magnets

The giant {Mn₇₀} and {Mn₈₄} wheels are the largest nuclearity single-molecule magnets synthesized to date, and understanding their magnetic properties poses a challenge to theory. Starting from first-principles calculations, we explore the magnetic properties and excitations in these wheels using effective spin Hamiltonians. We find that the unusual geometry of the superexchange pathways leads to weakly coupled {Mn₇} subunits carrying an effective S = 2 spin. The spectrum exhibits a hierarchy of energy scales and massive degeneracies, with the lowest-energy excitations arising from Heisenberg-ring-like excitations of the {Mn₇} subunits around the wheel. We further describe how weak longer-range couplings can select the precise spin ground-state of the Mn wheels out of the nearly degenerate ground-state band

Correlation potentials and functionals in Hartree-Fock-Kohn-Sham theory

We compute molecular Hartree-Fock-Kohn-Sham correlation potentials from ab initiocoupled-cluster densities via a modified Zhao, Morrison and Parr [Phys. Rev. A, 50, (1994) 2138] scheme involving exact exchange. We examine the potential for several small systems, and observe complex structure. By fitting a functional expansion to our potentials we obtain a closed-shell functional which is an improvement over other pure correlationfunctionals in Hartree-Fock-Kohn-Sham calculations. The leading term in our functional is dependent on the number of electrons. Our results lead us to question the utility of correlation defined within the Hartree-Fock-Kohn-Sham scheme, and to consider alternative partitionings of the exchange-correlation energy

Five years of density matrix embedding theory

Density matrix embedding theory (DMET) describes finite fragments in the presence of a surrounding environment. In contrast to most embedding methods, DMET explicitly allows for quantum entanglement between both. In this chapter, we discuss both the ground-state and response theory formulations of DMET, and review several applications. In addition, a proof is given that the local density of states can be obtained by working with a Fock space of bath orbitals

C_8H_8: a density functional theory study of molecular geometries introducing the localised bond density

In this paper we use density functional theory with all the common exchange-correlation functionals to investigate the structures of three isomers of C_8H_8 found in F. A. Cotton's text, barrelene, cyclooctatetraene, tetramethylenecyclobutane and also ethane and ethene. All calculations were performed with TZ2P basis sets and large quadrature. The results are compared with experiment and those obtained with Hartree–Fock theory. Delocalisation in the three molecules is discussed. A localised bond density in introduced to explain the transferability of the trends in the predictions of the functionals between different molecules. Three-parameter adiabatic connection functionals are examined and their usefulness in geometry prediction questioned. Finally a physical picture of the correlation as modelled by density functional theory is presented and used to explain trends in the overestimation or underestimation of bond lengths

A practical guide to density matrix embedding theory in quantum chemistry

Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample S$_{\text{N}}$2 reaction. The source code for the calculations in this work can be obtained from \url{https://github.com/sebwouters/qc-dmet}.Comment: 41 pages, 10 figure