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

Abstract

Parametrization of the two-electron reduced density matrix (2-RDM) has recently enabled the direct calculation of electronic energies and 2-RDMs at the computational cost of configuration interaction with single and double excitations. While the original Kollmar energy functional yields energies slightly better than those from coupled cluster with single-double excitations, a general family of energy functionals has recently been developed whose energies approach those from coupled cluster with triple excitations [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. In this paper we test the parametric 2-RDM method with one of these improved functionals through its application to the conversion of hydrogen peroxide to oxywater. Previous work has predicted the barrier from oxywater to hydrogen peroxide with zero-point energy correction to be 3.3-to-3.9 kcal/mol from coupled cluster with perturbative triple excitations [CCSD(T)] and -2.3 kcal/mol from complete active-space second-order perturbation theory (CASPT2) in augmented polarized triple-zeta basis sets. Using a larger basis set than previously employed for this reaction-an augmented polarized quadruple-zeta basis set (aug-cc-pVQZ)-with extrapolation to the complete basis-set limit, we examined the barrier with two parametric 2-RDM methods and three coupled cluster methods. In the basis-set limit the M parametric 2-RDM method predicts an activation energy of 2.1 kcal/mol while the CCSD(T) barrier becomes 4.2 kcal/mol. The dissociation energy of hydrogen peroxide to hydroxyl radicals is also compared to the activation energy for oxywater formation. We report energies, optimal geometries, dipole moments, and natural occupation numbers. Computed 2-RDMs nearly satisfy necessary N-representability conditions.

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

“…Ref. [20]. The 2-RDM(M) method provides a tool for the accurate, efficient calculation of electronic energies even for molecular systems with significant diradical correlation.…”

“…The wavefunction calculations employed the GAMESS electronic structure package [60] while the parametric 2-RDM calculations employed the implementation from Ref. [20].…”

“…These constraints, given the name N -representability conditions by Coleman in 1963 [4], are needed to ensure that the 2-RDM represents a realistic N -electron system [5][6][7][8]. While progress in computing the 2-RDM was long stymied by the search for suitable N -representability conditions-the N -representability problem, three general approaches for the direct calculation of the 2-RDM have been recently developed: (i) the minimization of the energy with the 2-RDM constrained explicitly by N -representability conditions [9][10][11][12], which leads to a problem in semidefinite programming [13][14][15][16][17], (ii) the minimization of the energy with the 2-RDM parameterized (or constrained implicitly) by N -representability conditions [3,[18][19][20][21][22], and (iii) the calculation of the 2-RDM from the solution of the contracted Schrödinger equation (or its anti-Hermitian part) with cumulant reconstruction of the higher RDMs [23-26, 29? ?…”

“…The parametric 2-RDM(M) method has an accuracy approaching that of coupled cluster with single, double, and triple excitations, particularly in the presence of some multireference correlation, at a computational cost that is less than coupled cluster with single-double excitations. It has been applied to several molecular systems [3,[18][19][20][21][22] including the computation of (i) the small barrier separating oxywater from hydrogen peroxide [20], (ii) the relative energies of the cis-cis and cis-trans isomers of carbonic acid, (iii) the rotational barrier separating cis and trans diazene [21], and (iv) the relative energies of the cis and trans isomers of the HOOO radical [34].…”

Accurate prediction of diradical chemistry from a single-reference density-matrix method: Model application to the bicyclobutane to gauche-1,3-butadiene isomerization

“…Examples of this class include the completely renormalized coupled cluster (CR-CC) method 23,24 and the parametric 2-RDM method. [25][26][27][28][29][30][31][32][33] Finally, other techniques for describing certain aspects of strong correlation without the CASSCF approximation include: natural-orbital functional theories [34][35][36][37][38][39] such as the natural-orbital functional theory of Piris [34][35][36] which uses a 2-RDM parametrization based on the natural orbitals and their occupation numbers and the variational quasi-particle theory 40 of Scuseria et al…”