Single Double Excitation Research Articles

Relative Energies and Geometries of the cis- and trans-HO3 Radicals from the Parametric 2-Electron Density Matrix Method

The parametric 2-electron reduced density matrix (2-RDM) method employing the M functional [Mazziotti, D. A. Phys. Rev. Lett. 2008, 101, 253002], also known as the 2-RDM(M) method, improves on the accuracy of coupled electron-pair theories including coupled cluster with single-double excitations at the computational cost of configuration interaction with single-double excitations. The cis- and trans-HO(3) isomers along with their isomerization transition state were examined using the recent extension of 2-RDM(M) to nonsinglet open-shell states [Schwerdtfeger, C. A.; Mazziotti, D. A. J. Chem. Phys. 2012, 137, 034107] and several coupled cluster methods. We report the calculated energies, geometries, natural-orbital occupation numbers, and reaction barriers for the HO(3) isomers. We find that the 2-RDM(M) method predicts that the trans isomer of HO(3) is lower in energy than the cis isomer by 1.71 kcal/mol in the correlation-consistent polarized valence quadruple-ζ (cc-pVQZ) basis set and 1.84 kcal/mol in the augmented correlation-consistent polarized valence quadruple-ζ (aug-cc-pVQZ) basis set. Results include the harmonic zero-point vibrational energies calculated in the correlation-consistent polarized valence double-ζ basis set. On the basis of the results of a geometry optimization in the augmented correlation consistent polarized valence triple-ζ basis set, the parametric 2-RDM(M) method predicts a central oxygen-oxygen bond of 1.6187 Å. We compare these energies and geometries to those predicted by three single-reference coupled cluster methods and experimental results and find that the inclusion of multireference correlation is important to describe properly the relative energies of the cis- and trans-HO(3) isomers and improve agreement with experimental geometries.

Isoelectronic analogue of oxywater: a parametric two-electron reduced-density-matrix study of ammonia oxide

A parametrization of the two-electron reduced density matrix (2-RDM) provides energies that improve on the accuracy of coupled electron-pair theories including coupled cluster with single-double excitations at the computational cost of configuration interaction with single-double excitations [Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. This parametric 2-RDM method was recently employed to study the isomerization of oxywater to hydrogen peroxide where it predicted a lower energy barrier from oxywater (2.1 kcal mol−1) than coupled cluster methods (4.2 kcal mol−1). In this paper we study an isoelectronic analogue, the isomerization of ammonia oxide to hydroxylamine. In the extrapolated basis-set limit, using the augmented correlation-consistent polarized valance quadruple-zeta (aug-cc-pVQZ) basis set, the parametric 2-RDM method predicts a 27.5 kcal mol−1 barrier from ammonia oxide to hydroxylamine. We report reaction energies, barriers, geometries, and natural-orbital occupation numbers for the ammonia-oxide reaction and compare them to those from the oxywater reaction. We find that the parametric 2-RDM method agrees with dynamic correlation wavefunction methods when the multi-reference character of the system is small as in the ammonia-oxide isomerization computed here but that it captures additional multi-reference correlation, usually requiring a multi-reference method, when such correlation increases as in the oxywater isomerization.

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

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.

Polarizabilities of theMg+andSi3+ions

A polarization analysis of the fine-structure intervals for the $n=17$ Rydberg states of Mg and the $n=29$ states of ${\mathrm{Si}}^{2+}$ is performed. The coefficients of all terms in the polarization expansion up to ${r}^{\ensuremath{-}8}$ were computed using a semiempirical single electron analysis combined with the relativistic all-order single-double method (MBPT-SD) which includes all single-double excitations from the Dirac-Fock wave functions to all orders of perturbation theory. The revised analysis yields dipole polarizabilities of ${\ensuremath{\alpha}}_{1}=35.04(3)\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ for ${\mathrm{Mg}}^{+}$ and ${\ensuremath{\alpha}}_{1}=7.433(25)\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ for ${\mathrm{Si}}^{3+}$, values only marginally larger than those obtained in a previous analysis [E. L. Snow and S. R. Lundeen, Phys. Rev. A 75, 062512 (2007); E. L. Snow and S. R. Lundeen, Phys. Rev. A77, 052501 (2008)]. The polarizabilities are used to make estimates of the multiplet strength for the resonant transition for both ions. The revised analysis did see significant changes in the slopes of the polarization plots. The dipole polarizabilities from the MBPT-SD calculation, namely $35.05(12)\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ and $7.419(16)\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$, are within 0.3% of the revised experimental values.

Double excitation effect in non-adiabatic time-dependent density functional theory with an analytic construction of the exchange–correlation kernel in the common energy denominator approximation

Time-dependent density functional (response) theory (TDDF(R)T) is applied almost exclusively in its adiabatic approximation (ATDDFT), which is restricted to predominantly single electronic excitations and neglects additional roots of the TDDFT eigenvalue problem stemming from the interaction between single and double excitations. We incorporate the effect of the latter interaction into a non-adiabatic frequency-dependent and spatially non-local Hartree-exchange-correlation (Hxc) kernel fCEDAHxc (r1, r2, omega), the explicit analytical expression of which is derived for interacting single and double excitations well separated from the other excitations, within the common energy denominator approximation (CEDA) for the Kohn-Sham (KS) and interacting density response functions, chis and chi, respectively. The kernel fCEDAHxc (r1, r2, omega) obtained from the direct analytical inverse of chiCEDAs and chiCEDA is a sum of the delta-function and non-local orbital-dependent spatial terms with frequency-dependent factors, with which fCEDAHxc acquires a modulated quadratic dependence on omega. The effective incorporation in fCEDAHxc of the complete manifold of excited states (through the delta function term) represents an extension of the kernel reported by Maitra, Zhang, Cave, and Burke [J. Chem. Phys., 2004, 120, 5932]. In the TDDFT eigenvalue equations considered in the diagonal approximation, fCEDAHxc generates two excitation energies omegaq and omegaq+1, which both correspond to the same single KS excitation omegasq, thus producing the effect of the single-double excitation interaction.

Endo-Effect-Driven Regioselectivity in the Cyclopalladation of (S)-2-tert-Butyl-4-phenyl-2-oxazoline

Direct cyclopalladation of (S)-2-tert-butyl-4-phenyl-2-oxazoline using palladium acetate in acetic acid or acetonitrile provided a mixture of two isomeric compounds, the endo μ-AcO dimeric complex with a C(sp3)−Pd bond and the corresponding exo derivative with a C(sp2)−Pd bond, with the former being the major product. The μ-AcO dimeric complexes were converted to the corresponding μ-Cl analogues 3 and 4 by treatment with LiCl in acetone; the latter compounds were transformed to the corresponding PPh3 adducts 5 and 6. The NMR data suggested the puckered structure of the endo palladacycle in complexes 3 and 5, the twisted λ(S) conformation of the oxazoline ring in 3, 4, and 6, and the δ(S) conformation of the heterocycle in complex 5. The X-ray crystal structure of 5 confirmed the δ(S) conformation of the oxazoline ring in the solid state and the twisted conformation of the palladacycle and revealed a P-propeller chiral configuration of the PPh3 ligand. A series of ab initio quantum chemical calculations were performed on two model compounds generated by replacing the PPh3 ligands with NH3 in complexes 5 and 6. The structures and energies of the two model exo and endo isomers were calculated at the RHF, BLYP, and MP2 levels of theory with a 6-31G* basis for the light atoms and LANL2DZ ECP for the palladium and were found to be comparable. Single point coupled cluster calculations, with single double excitations (CCSD), corroborated the results.

Complete fourth-order relativistic many-body calculations for atoms

We report, to our knowledge, the first relativistic calculation for many-electron atoms complete through the fourth order of many-body perturbation theory. Owing to an overwhelmingly large number of underlying diagrams, the calculations are aided by our suite of symbolic algebra tools. We augment all-order single-double excitation method with 1648 omitted fourth-order diagrams and compute amplitudes of principal transitions in Na. The resulting ab initio relativistic electric dipole amplitudes are in an excellent agreement with $0.05%$-accurate experimental values. Analysis of previously unmanageable classes of diagrams provides a useful guide to a design of even more accurate, yet practical, many-body methods.

Fourth-order perturbative extension of the single-double excitation coupled-cluster method

Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wavefunction. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulae are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e. contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed.

Metal and Ancillary Ligand Structural Effects on Ethylene Insertion Processes at Cationic Group 4 Centers. A Systematic, Comparative Quantum Chemical Investigation at Various ab Initio Levels

Ethylene insertion into the metal−methyl bonds of group 4 (Ti, Zr) (C5H5)2MCH3+ and H2Si(C5H4)(tBuN)MCH3+ catalyst cations has been investigated at the ab initio level, employing DZV- and DZP-quality basis sets together with Moller−Plesset perturbative and coupled-cluster single-double excitation wave function expansions. All reactions are found to proceed from reactants to products via intermediate π-complexes and subsequent Cossee−Arlman four-center transition state structures. Enthalpic barriers for the insertion step strongly depend on the nature of the ancillary ligand and metal, with ΔH⧧ increasing in the order (C5H5)2TiCH3+ < (C5H5)2ZrCH3+ ≈ H2Si(C5H4)(tBuN)TiCH3+ < H2Si(C5H4)(tBuN)ZrCH3+. Furthermore, metallocene H2Si< bridging has the effect of increasing the electrophilicity toward ethylene. The observed ethylene activation/insertion structural and energetic trends may be rationalized using qualitative electronic structure arguments, ancillary ligand steric hindrance, and metal ionic radius. Ele...