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

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu2O2]^(2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu2O2]^(2+)

Extended implementation of canonical transformation theory: parallelization and a new level-shifted condition

The canonical transformation (CT) theory has been developed as a multireference electronic structure method to compute high-level dynamic correlation on top of a large active space reference treated with the ab initio density matrix renormalization group method. This article describes a parallelized algorithm and implementation of the CT theory to handle large computational demands of the CT calculation, which has the same scaling as the coupled cluster singles and doubles theory. To stabilize the iterative solution of the CT method, a modification to the CT amplitude equation is introduced with the inclusion of a level shift parameter. The level-shifted condition has been found to effectively remove a type of intruder state that arises in the linear equations of CT and to address the discontinuity problems in the potential energy curves observed in the previous CT studies

Grid photocoagulation combined with intravitreal bevacizumab for recurrent macular edema associated with retinal vein occlusion

Purpose: To report the efficacy of grid photocoagulation combined with intravitreal bevacizumab (IVB) for macular edema recurring after previous IVBs associated with retinal vein occlusion (RVO).　　Methods: This retrospective study consisted of 19 eyes with branch retinal vein occlusion (BRVO) and nine eyes with central retinal vein occlusion (CRVO), which were treated with grid photocoagulation combined with IVB for recurrent macular edema after previous IVBs. The mean duration of total follow-up was 29.3 ± 5.8 months.　　Results: After this combination therapy, foveal thickness was reduced, significant with slight improvement in visual acuity (VA). At 1 month after treatment, although 25 of the 28 eyes showed complete resolution of the cystoid space, the macular edema recurred to some extent in 19 eyes. Compared with initial values, final foveal thickness was reduced significantly in both BRVO and CRVO groups (P < 0.001), but improvement in VA was significant only for eyes with BRVO (P = 0.012). The total number of IVB was 2.8 ± 0.7 for eyes with either BRVO or CRVO.　　Conclusion: Grid photocoagulation combined with IVB has a substantial effect on reducing recurrent macular edema associated with RVO, but the effect on visual acuity is limited

Ligand-Protected Gold Clusters

Small gold clusters with diameters less than or equal to 2 nm (below approximately 200 atoms) possess geometric and electronic structures different from bulk gold. When these gold clusters are protected by ligands, these clusters can be treated as chemical compounds. This review focuses on gold clusters protected by chalcogenate (thiolate, selenolate, or tellurolate) ligands and describes the methods by which these clusters are synthesized as well as their geometric/electronic structures and physical and chemical properties. Recent findings regarding ligand exchange reactions, which may be used to impart functionality to these compounds, are also described

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu2O2]^(2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu2O2]^(2+)

Extended implementation of canonical transformation theory: parallelization and a new level-shifted condition

The canonical transformation (CT) theory has been developed as a multireference electronic structure method to compute high-level dynamic correlation on top of a large active space reference treated with the ab initio density matrix renormalization group method. This article describes a parallelized algorithm and implementation of the CT theory to handle large computational demands of the CT calculation, which has the same scaling as the coupled cluster singles and doubles theory. To stabilize the iterative solution of the CT method, a modification to the CT amplitude equation is introduced with the inclusion of a level shift parameter. The level-shifted condition has been found to effectively remove a type of intruder state that arises in the linear equations of CT and to address the discontinuity problems in the potential energy curves observed in the previous CT studies