Populations of Carbonic Acid Isomers at 210 K from a Fast Two-Electron Reduced-Density Matrix Theory

Abstract

Parametrization of the 2-electron reduced density matrix (2-RDM) rather than the many-electron wave function yields a new family of electronic-structure methods that are faster and more accurate than traditional coupled electron-pair methods including coupled cluster with single and double excitations. Deriving the parametrization from N-representability conditions generates a 2-RDM that captures significant correlation from triple and higher-order excitations at the cost of double excitations. We apply the parametric 2-RDM method to confirm recent experiments determining the relative thermodynamic populations of the cis-cis and cis-trans isomers of carbonic acid. In 2010 Bernard et al. showed by infrared spectroscopy that the populations of cis-cis and cis-trans isomers have a 10:1 ratio at 210 K. By use of the parametric 2-RDM method, we predict a 8:1 ratio at 210 K. Comparable ab initio methods overestimate the stability of the cis-cis isomer with 24:1 and 21:1 ratios. These 2-RDM-based methods promise to have significant applications throughout chemistry.

Stable solid and aqueous H2CO3 from CO2 and H2O at high pressure and high temperature

“…Yet, the exact crystal structure of β -H 2 CO 3 is still unknown. The FT-IR and Raman spectra of solid H 2 CO 3 below 220 K at low pressure are now well established and several theoretical studies have reported on the structure and stability of H 2 CO 3 with respect to decomposition to CO 2 and H 2 O as well as on the relative stability of its isomers and on their vibrational characteristics 7 8 13 14 15 . Its molecular decomposition rate has been investigated both experimentally 16 and theoretically and it was found to be accelerated over 10 12 times at ambient conditions by as few as three water molecules to reach macroscopically observed decomposition rates 1 17 .…”

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

“…We calculated the energies of bicyclobutane, gauche-1,3-butadiene, and two transition states using the K and M p2-RDM methods [25][26][27][28][29][30][31][32][33] as well as six wave function methods: Hartree-Fock, configuration interaction with single and double excitations (CISD), coupled cluster with single and double excitations (CCSD), 22,23,58 coupled cluster with a correction for triple excitations [CCSD(T)], 23 completely renormalized coupled cluster [CR-CC(T)], 23,24 and coupled cluster with single, double, and full triple excitations (CCSDT). 59,60 Additionally, characterization was performed with CASSCF (10 electrons, 10 active orbitals) and second-order multireference perturbation theory (MRPT2).…”

“…Parametric 2-RDM methods can be used to obtain 2 D directly without the N-particle wave function. [25][26][27][28][29][30][31][32][33] In parametric 2-RDM methods, the 2-RDM is parametrized as a functional of its lowest order components. The 2-RDM can be expressed as the sum of two Hermitian matrices,…”

“…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…”

“…47 In this paper we re-examine the conversion of bicyclobutane to gauche-1,3-butadiene through the parametric 2-RDM (p2-RDM) method. [25][26][27][28][29][30][31][32][33] Even though the p2-RDM method is based on a single-reference wave function from the HartreeFock calculation, it has been shown in previous calculations to capture some nontrivial multireference electron correlation such as that found in bond dissociation and diradical transition states. Applications, for example, have been made to determining the energy barrier of the diradical rotational transition state connecting the cis and trans isomers of diazene 29 and predicting the energies of olympicene's diradical isomers relative to hydrogen dissociation.…”