Exploiting the spatial locality of electron correlation within the parametric two-electron reduced-density-matrix method

Abstract

The parametric variational two-electron reduced-density-matrix (2-RDM) method is applied to computing electronic correlation energies of medium-to-large molecular systems by exploiting the spatial locality of electron correlation within the framework of the cluster-in-molecule (CIM) approximation [S. Li et al., J. Comput. Chem. 23, 238 (2002); J. Chem. Phys. 125, 074109 (2006)]. The 2-RDMs of individual molecular fragments within a molecule are determined, and selected portions of these 2-RDMs are recombined to yield an accurate approximation to the correlation energy of the entire molecule. In addition to extending CIM to the parametric 2-RDM method, we (i) suggest a more systematic selection of atomic-orbital domains than that presented in previous CIM studies and (ii) generalize the CIM method for open-shell quantum systems. The resulting method is tested with a series of polyacetylene molecules, water clusters, and diazobenzene derivatives in minimal and nonminimal basis sets. Calculations show that the computational cost of the method scales linearly with system size. We also compute hydrogen-abstraction energies for a series of hydroxyurea derivatives. Abstraction of hydrogen from hydroxyurea is thought to be a key step in its treatment of sickle cell anemia; the design of hydroxyurea derivatives that oxidize more rapidly is one approach to devising more effective treatments.

Testing the parametric two-electron reduced-density-matrix method with improved functionals: Application to the conversion of hydrogen peroxide to oxywater

“…[3][4][5][6] In an effort to determine an N-representable 2-RDM directly, two classes of approaches have been developed. Recently, we have developed a parametric formulation of the variational 2-RDM method [17][18][19][20][21][22][23][24][25] in which the N-representability conditions are approximately enforced not by constraints but by parametrization of the 2-RDM. 10,11 The other approach, known as the variational 2-RDM method, a) Electronic mail: damazz@uchicago.edu.…”

“…minimizes the ground-state energy as a functional of the 2-RDM, constrained by subsets of N-representability conditions. DePrince and Mazziotti [18][19][20][21][22][23] extended Kollmar's work by (i) incorporating single excitations explicitly into the 2-RDM parametrization, 18 (ii) casting the energy minimization as an unconstrained optimization without slack variables for the constraints, 19 (iii) treating non-equilibrium geometries including transition states (TS) and bond dissociation, 20,23 and (iv) extending the method to perform open-shell 21 and linear-scaling 22 calculations. Recently, we have developed a parametric formulation of the variational 2-RDM method [17][18][19][20][21][22][23][24][25] in which the N-representability conditions are approximately enforced not by constraints but by parametrization of the 2-RDM.…”

Parametric two-electron reduced-density-matrix method with application to diradical rectangular H4

“…The parametric 2-RDM method can be used to obtain 2 D directly without the N -particle wavefunction [18,19,33,[43][44][45][46][47][48]. We parameterize the 2-RDM as a functional of itself.…”

Density-fitted singles and doubles coupled cluster on graphics processing units

“…[4] [20][21][22][23], one can reduce the scaling of any coupled cluster method to a linear dependence on system size. Fragment-based local correlation methods such as natural linear-scaling coupled cluster [24,25], cluster-in-molecule methods [26][27][28][29][30], and divide-expand-consolidate methods [31][32][33] are promising routes to large coupled cluster computations in general, as well as to efficient GPU implementations of CC methods. These fragment-based methods divide a single problem into a collection of small computations.…”