Canonical transformation theory for multireference problems

We propose a theory to describe dynamic correlations in bonding situations where there is also significant nondynamic character. We call this the canonical transformation (CT) theory. When combined with a suitable description of nondynamic correlation, such as given by a complete-active-space self-consistent Field (CASSCF) or density matrix renormalization group wave function, it provides a theory to describe bonding situations across the entire potential energy surface with quantitative accuracy for both dynamic and nondynamic correlation. The canonical transformation theory uses a unitary exponential ansatz, is size consistent, and has a computational cost of the same order as a single-reference coupled cluster theory with the same level of excitations. Calculations using the CASSCF based CT method with single and double operators for the potential energy curves for water and nitrogen molecules, the BeH_2 insertion reaction, and hydrogen fluoride and boron hydride bond breaking, consistently yield quantitative accuracies typical of equilibrium region coupled cluster theory, but across all geometries, and better than obtained with multireference perturbation theory

Canonical transformation theory from extended normal ordering

The canonical transformation theory of Yanai and Chan [J. Chem. Phys. 124, 194106 (2006)] provides a rigorously size-extensive description of dynamical correlation in multireference problems. Here we describe a new formulation of the theory based on the extended normal ordering procedure of Mukherjee and Kutzelnigg [J. Chem. Phys. 107, 432 (1997)]. On studies of the water, nitrogen, and iron oxide potential energy curves, the linearized canonical transformation singles and doubles theory is competitive in accuracy with some of the best multireference methods, such as the multireference averaged coupled pair functional, while computational timings (in the case of the iron oxide molecule) are two to three orders of magnitude faster and comparable to those of the complete active space second-order perturbation theory. The results presented here are greatly improved both in accuracy and in cost over our earlier study as the result of a new numerical algorithm for solving the amplitude equations

Application of PLD-Fabricated Thick-Film Permanent Magnets

Isotropic Nd-Fe-B thick-film magnets have been prepared using a pulsed laser deposition (PLD) method with the control of laser energy density (LED) followed by post-annealing. The characteristics of the method are a high deposition rate up to several tens of microns per hour together with a reliability of magnetic properties due to the good transfer of composition from an Nd-Fe-B target to a film. Several micro-machines comprising the isotropic Nd-Fe-B films such as a miniaturized DC motor and a swimming machine in liquid were demonstrated. Furthermore, the deposition of isotropic Nd (or Pr)-Fe-B thick-film magnets on a Si or glass substrate was carried out to apply the films to various micro-electro-mechanical-systems (MEMS). We also introduced the preparation of isotropic Sm-Co, Fe-Pt, and nano-composite Nd-Fe-B+α-Fe film magnets synthesized using the PLD

Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and \beta-carotene

In previous work we have shown that the Density Matrix Renormalization Group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional Complete Active Space algorithms. Here, we implement orbital optimisation with the Density Matrix Renormalization Group to further allow the self-consistent improvement of the active orbitals, as is done in the Complete Active Space Self-Consistent Field (CASSCF) method. We use our resulting DMRGCASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as \beta-carotene, correlating with near-exact accuracy the optimised complete \pi-valence space with up to 24 active electrons and orbitals, and analyse our results in the light of the recent discovery from Resonance Raman experiments of new optically dark states in the spectrum.Comment: 16 pages, 8 figure

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

Canonical transformation theory for multireference problems

We propose a theory to describe dynamic correlations in bonding situations where there is also significant nondynamic character. We call this the canonical transformation (CT) theory. When combined with a suitable description of nondynamic correlation, such as given by a complete-active-space self-consistent Field (CASSCF) or density matrix renormalization group wave function, it provides a theory to describe bonding situations across the entire potential energy surface with quantitative accuracy for both dynamic and nondynamic correlation. The canonical transformation theory uses a unitary exponential ansatz, is size consistent, and has a computational cost of the same order as a single-reference coupled cluster theory with the same level of excitations. Calculations using the CASSCF based CT method with single and double operators for the potential energy curves for water and nitrogen molecules, the BeH_2 insertion reaction, and hydrogen fluoride and boron hydride bond breaking, consistently yield quantitative accuracies typical of equilibrium region coupled cluster theory, but across all geometries, and better than obtained with multireference perturbation theory

Comment on "Canonical transcorrelated theory with projected Slater-type geminals" [J. Chem. Phys. 136, 084107 (2012)]

This Comment identifies errors in the formalism/implementation reported in Ref. 1 and discusses some aspects of that work that were not fully specified in the original publication. This Comment also provides reference numerical results for a simple system to ease future implementation of the approach by other researchers.Comment: 3 page