Significance of non-linear terms in the relativistic coupled-cluster theory in the determination of molecular properties

The relativistic coupled-cluster (RCC) theory has been applied recently to a number of heavy molecules to determine their properties very accurately. Since it demands large computational resources, the method is often approximated to singles and doubles excitations (RCCSD method). The effective electric fields (${\cal E}_{eff}$) and molecular permanent electric dipole moments (PDMs) of SrF, BaF and mercury monohalides (HgX with X = F, Cl, Br, and I) molecules are of immense interest for probing fundamental physics. In our earlier calculations of ${\cal E}_{eff}$ and PDMs for the above molecules, we had neglected the non-linear terms in the property evaluation expression of the RCCSD method. In this work, we demonstrate the roles of these terms in determining above quantities and their computational time scalability with number of processors of a computer. We also compare our results with previous calculations that employed variants of RCC theory as well as other many-body methods, and available experimental values

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

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

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