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.     

Quantum chemical study of the electronic structure of NiCH2 + in its ground state and low-lying electronic excited states

The electronic structure of NiCH(2) (+), representative of transition metal carbene ions, is investigated by means of several methods of quantum chemistry. The relative stabilities of the four low-lying doublet electronic states ((2)A(1), (2)A(2), (2)B(1), and (2)B(2)) are determined at the coupled cluster singles and doubles level (CCSD) and triples level [CCSD(T) and CCSDT-3] with both a Hartree-Fock and density functional theory (Kohn-Sham) reference. The equation-of-motion coupled cluster for treatment of excited states in singles and doubles approximation (EOM-CCSD) is used to characterize the transition energies from the (2)A(1) electronic ground state to the low-lying doublet excited states. The (2)A(2) and (2)B(1) states are nearly degenerate, found to be separated by 940 cm(-1) at the EOM-CCSD level, in agreement with the CASSCF energy ordering. The (2)B(2) state is calculated to be higher in energy by more than 1.0 eV. The spin purity of the low-lying doublet and quadruplet states described by CCSD calculations based on the unrestricted open-shell Hartree-Fock reference is discussed.     

Explicit correlation and basis set superposition error: the structure and energy of carbon dioxide dimer

We have investigated the slipped parallel and t-shaped structures of carbon dioxide dimer [(CO(2))(2)] using both conventional and explicitly correlated coupled cluster methods, inclusive and exclusive of counterpoise (CP) correction. We have determined the geometry of both structures with conventional coupled cluster singles doubles and perturbative triples theory [CCSD(T)] and explicitly correlated cluster singles doubles and perturbative triples theory [CCSD(T)-F12b] at the complete basis set (CBS) limits using custom optimization routines. Consistent with previous investigations, we find that the slipped parallel structure corresponds to the global minimum and is 1.09 kJ mol(-1) lower in energy. For a given cardinal number, the optimized geometries and interaction energies of (CO(2))(2) obtained with the explicitly correlated CCSD(T)-F12b method are closer to the CBS limit than the corresponding conventional CCSD(T) results. Furthermore, the magnitude of basis set superposition error (BSSE) in the CCSD(T)-F12b optimized geometries and interaction energies is appreciably smaller than the magnitude of BSSE in the conventional CCSD(T) results. We decompose the CCSD(T) and CCSD(T)-F12b interaction energies into the constituent HF or HF CABS, CCSD or CCSD-F12b, and (T) contributions. We find that the complementary auxiliary basis set (CABS) singles correction and the F12b approximation significantly reduce the magnitude of BSSE at the HF and CCSD levels of theory, respectively. For a given cardinal number, we find that non-CP corrected, unscaled triples CCSD(T)-F12b/VXZ-F12 interaction energies are in overall best agreement with the CBS limit.     

Bond dissociation energies in second-row compounds

Heats of formation at 0 and 298 K are predicted for PF3, PF5, PF3O, SF2, SF4, SF6, SF2O, SF2O2, and SF4O as well as a number of radicals derived from these stable compounds on the basis of coupled cluster theory [CCSD(T)] calculations extrapolated to the complete basis set limit. In order to achieve near chemical accuracy (+/-1 kcal/mol), additional corrections were added to the complete basis set binding energies based on frozen core coupled cluster theory energies: a correction for core-valence effects, a correction for scalar relativistic effects, a correction for first-order atomic spin-orbit effects, and vibrational zero-point energies. The calculated values substantially reduce the error limits for these species. A detailed comparison of adiabatic and diabatic bond dissociation energies (BDEs) is made and used to explain trends in the BDEs. Because the adiabatic BDEs of polyatomic molecules represent not only the energy required for breaking a specific bond but also contain any reorganization energies of the bonds in the resulting products, these BDEs can be quite different for each step in the stepwise loss of ligands in binary compounds. For example, the adiabatic BDE for the removal of one fluorine ligand from the very stable closed-shell SF6 molecule to give the unstable SF5 radical is 2.8 times the BDE needed for the removal of one fluorine ligand from the unstable SF5 radical to give the stable closed-shell SF4 molecule. Similarly, the BDE for the removal of one fluorine ligand from the stable closed-shell PF3O molecule to give the unstable PF2O radical is higher than the BDE needed to remove the oxygen atom to give the stable closed-shell PF3 molecule. The same principles govern the BDEs of the phosphorus fluorides and the sulfur oxofluorides. In polyatomic molecules, care must be exercised not to equate BDEs with the bond strengths of given bonds. The measurement of the bond strength or stiffness of a given bond represented by its force constant involves only a small displacement of the atoms near equilibrium and, therefore, does not involve any reorganization energies, i.e., it may be more appropriate to correlate with the diabatic product states.     

Locally correlated equation-of-motion coupled cluster theory for the excited states of large molecules

We report an extension of the local correlation concept to electronically excited states via the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method. We apply the same orbital domain structure used successfully for ground-state CCSD by Werner and co-workers and find that the resulting localized excitation energies are in error generally by less than 0.2 eV relative to their canonical EOM-CCSD counterparts, provided the basis set is flexible and includes Rydberg-like functions. In addition, we account for weak-pair contributions efficiently using a correction to local-EOM-CCSD transition energies based on the perturbative (D) correction used with configuration interaction singles (CIS).     

Theoretical prediction of new dipole-bound singlet states for anions of interstellar interest

Anions that exhibit dipole-bound singlet states have been proposed as a potential class of molecules that may be identified in the interstellar medium. Using high-level coupled cluster theory, we have computed the dipole moments, electron binding energies, and excited states of 14 neutral radicals and their corresponding closed-shell anions. We have calibrated our methods against experimental data for CH(2)CN(-) and CH(2)CHO(-) and demonstrated that coupled cluster theory can closely reproduce experimental dipole moments, electron binding energies, and excitation energies. Using these same methods, we predict the existence of dipole-bound excited states for six of the 14 previously unknown anions, including CH(2)SiN(-), SiH(2)CN(-), CH(2)SiHO(-), SiN(-), CCOH(-), and HCCO(-). In addition, we predict the existence of a valence-bound excited state of CH(2)SiN(-) with an excitation wavelength near 589 nm.     

Approximate variational coupled cluster theory

We show that it is possible to construct an accurate approximation to the variational coupled cluster method, limited to double substitutions, from the minimization of a functional that is rigorously extensive, exact for isolated two-electron subsystems and invariant to transformations of the underlying orbital basis. This approximate variational coupled cluster theory is a modification and enhancement of our earlier linked pair functional theory. It is first motivated by the constraint that the inverse square root of the matrix that transforms the cluster amplitudes must exist. Low-order corrections are then included to enhance the accuracy of the approximation of variational coupled cluster, while ensuring that the computational complexity of the method never exceeds that of the standard traditional coupled cluster method. The effects of single excitations are included by energy minimization with respect to the orbitals defining the reference wavefunction. The resulting quantum chemical method is demonstrated to be a robust approach to the calculation of molecular electronic structure and performs well when static correlation effects are strong.     

Heats of formation of xenon fluorides and the fluxionality of XeF(6) from high level electronic structure calculations

Atomization energies at 0 K and heats of formation at 0 and 298 K are predicted for XeF(+), XeF(-), XeF(2), XeF(4), XeF(5)(-), and XeF(6) from coupled cluster theory (CCSD(T)) calculations with new correlation-consistent basis sets for Xe. To achieve near chemical accuracy (+/-1 kcal/mol), up to four corrections were added to the complete basis set binding energies based on frozen core coupled cluster theory energies: a correction for core-valence effects, a correction for scalar relativistic effects, a correction for first-order atomic spin-orbit effects, and in some cases, a second-order spin-orbit correction. Vibrational zero-point energies were computed at the coupled cluster level of theory. The structure of XeF(6) is difficult to obtain with the C(3)(v)() and O(h)() structures having essentially the same energy. The O(h)() structure is only 0.19 kcal/mol below the C(3)(v)() one at the CCSD(T)/CBS level using an approximate geometry for the C(3)(v)() structure. With an optimized C(3)(v)() geometry, the C(3)(v)() structure would probably become slightly lower in energy than the O(h)() one. The calculated heats of formation for the neutral XeF(n)() fluorides are less negative than the experimental values from the equilibrium measurements by 2.0, 7.7, and 12.2 kcal/mol for n = 2, 4, and 6, respectively. For the experimental values, derived from the photoionization measurements, this discrepancy becomes even larger, suggesting a need for a redetermination of the experimental values. Evidence is presented for the fluxionality of XeF(6) caused by the presence of a sterically active, free valence electron pair on Xe.     

Calculating stacking interactions in nucleic acid base-pair steps using spin-component scaling and local second order Møller-Plesset perturbation theory

Stacking interaction energies for ten B-DNA base-pair steps are computed with density fitted local second-order M?ller-Plesset perturbation theory (DF-LMP2), and with the spin-component scaled (SCS) and spin-component scaled for nucleobases (SCSN) variants of DF-LMP2. Comparison with existing CBS(T) reference data indicates larger than expected energy differences for both SCS variants. After an analysis of the errors involved, an alternative method of producing reference data is proposed where DF-LMP2/aug-cc-pVTZ and DF-LMP2/aug-cc-pVQZ energies for the whole complex are extrapolated to produce interaction energies that do not require many-body correction and show reduced error in estimation of the basis set limit. A literature correction term from coupled cluster theory with perturbative triples is then added to the DF-LMP2 estimated basis set limit. These new reference data are consistently around 1 kcal mol(-1) less than previous literature data. DF-SCSN-LMP2/aug-cc-pVTZ is found to reproduce the new reference interaction energies with a root mean square error (RMSE) of 0.71 kcal mol(-1), while SCS consistently underestimates the binding energy.     

Equation-of-motion coupled-cluster study on exciton states of polyethylene with periodic boundary condition

Equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) method has been applied to exciton states of polyethylene using ab initio crystal Hartree-Fock method with one-dimensional periodic boundary condition. Full transformation of two-electron integrals from atomic-orbital basis to crystal-orbital basis has been performed for EOM-CCSD calculations. In order to make transformed integrals to have correct properties of translational symmetry, a lattice summation scheme has been proposed. The EOM-CCSD excitation energies have been obtained for the lowest singlet and triplet exciton states of polyethylene. The excitation energies converge with system size much faster than oligomer calculations using n-alkanes. Quasiparticle energy-level calculations by second-order many-body perturbation theory and by solving the inverse Dyson equation have also been performed to obtain exciton binding energies. Basis set dependencies on excitation energy, quasiparticle band gap, and exciton binding energy have been investigated. At the 6-31+G level, the excitation energy of the lowest singlet-exciton state and its binding energy are calculated to be 8.1 and 3.2 eV, respectively. The calculated excitation energy is well comparable with the corresponding experimental value, 7.6 eV.     

Variational treatment on the energy of the He‐sequence ground state with weakest bound electron potential model theory

The concept of spin–orbital of the weakest bound electron is described used to construct the antisymmetric wave function of atomic or ionic systems within weakest bound electron potential model theory (WBEPM theory). The total energies of He‐sequence (Z = 2–9) in the ground states is calculated with a variational method. The effect of fixed orbital approximation is discussed quantitatively. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Explicitly correlated treatment of H2NSi and H2SiN radicals: electronic structure calculations and rovibrational spectra

Various ab initio methods are used to compute the six dimensional potential energy surfaces (6D-PESs) of the ground states of the H(2)NSi and H(2)SiN radicals. They include standard coupled cluster (RCCSD(T)) techniques and the newly developed explicitly correlated RCCSD(T)-F12 methods. For H(2)NSi, the explicitly correlated techniques are viewed to provide data as accurate as the standard coupled cluster techniques, whereas small differences are noticed for H(2)SiN. These PESs are found to be very flat along the out-of-plane and some in-plane bending coordinates. Then, the analytic representations of these PESs are used to solve the nuclear motions by standard perturbation theory and variational calculations. For both isomers, a set of accurate spectroscopic parameters and the vibrational spectrum up to 4000 cm(-1) are predicted. In particular, the analysis of our results shows the occurrence of anharmonic resonances for H(2)SiN even at low energies.     

Third-order corrections to random-phase approximation correlation energies

Several random-phase approximation (RPA) correlation methods were compared in third order of perturbation theory. While all of the considered approaches are exact in second order of perturbation theory, it is found that their corresponding third-order correlation energy contributions strongly differ from the exact third-order correlation energy contribution due to missing interactions of the particle-particle-hole-hole type. Thus a simple correction method is derived which makes the different RPA methods also exact to third-order of perturbation theory. By studying the reaction energies of 16 chemical reactions for 21 small organic molecules and intermolecular interaction energies of 23 intermolecular complexes comprising weakly bound and hydrogen-bridged systems, it is found that the third-order correlation energy correction considerably improves the accuracy of RPA methods if compared to coupled-cluster singles doubles with perturbative triples as a reference.     

Quantum-chemical investigation of the structures and electronic spectra of the nucleic acid bases at the coupled cluster CC2 level

We study the ground-state structures and singlet- and triplet-excited states of the nucleic acid bases by applying the coupled cluster model CC2 in combination with a resolution-of-the-identity approximation for electron interaction integrals. Both basis set effects and the influence of dynamic electron correlation on the molecular structures are elucidated; the latter by comparing CC2 with Hartree-Fock and M?ller-Plesset perturbation theory to second order. Furthermore, we investigate basis set and electron correlation effects on the vertical excitation energies and compare our highest-level results with experiment and other theoretical approaches. It is shown that small basis sets are insufficient for obtaining accurate results for excited states of these molecules and that the CC2 approach to dynamic electron correlation is a reliable and efficient tool for electronic structure calculations on medium-sized molecules.     

Beyond vinyl: electronic structure of unsaturated propen-1-yl, propen-2-yl, 1-buten-2-yl, and trans-2-buten-2-yl hydrocarbon radicals

Vertical excitation energies and oscillator strengths for several valence and Rydberg electronic states of vinyl, propen-1-yl, propen-2-yl, 1-buten-2-yl, and trans-2-buten-2-yl radicals are calculated using the equation-of-motion coupled cluster methods with single and double substitutions (EOM-CCSD). The ground and the lowest excited state (n <-- pi) equilibrium geometries are calculated using the CCSD(T) and EOM-SF-CCSD methods, respectively, and adiabatic excitation energies for the n <-- pi state are reported. Systematic changes in the geometries, excitation energies, and Rydberg state quantum defects within this group of radicals are discussed.     

The relationship between double excitation amplitudes and Z vector components in some post-Hartree-Fock correlation methods

The relationship between Z vector components and excitation amplitudes is analyzed for several post-Hartree-Fock correlation methods limited to double excitation amplitudes. An analytical formula approximating the Z vector for the coupled cluster doubles method is presented and shown to be quite accurate. This approximation is also used to determine the prefactor of the norm of doubly excited states in averaged coupled pair functional-type energy functionals self-consistently leading to better agreement with coupled cluster results.     

Ab initio study of the cyclooctatetraenyl radical

Ab initio calculations have been carried out on the 1,3,5,7- and 1,2,4,7-tetraene configurations of the cyclooctatetraenyl radical at UHF, ROHF, MCSCF, ROCISD, QCISD, and CCSD(T) levels of theory with 6-311G(d,p) and cc-pVDZ basis sets. Although spin contamination is present, the ROCISD calculations support the energies obtained from less intensive, UHF-based coupled cluster calculations over the energies obtained from MCSCF analysis of the pi-electron orbitals. The 1,3,5,7-form is a local minimum at the coupled cluster levels, higher in energy than the resonance-stabilized 1,2,4,7-form by 10-13 kJ/mol, but bounded by a barrier of less than 0.5 kJ/mol. The isomerization surface connecting these two structures is described and results reported from integration of the vibrational Schr?dinger equation on that surface. Excited vibrational states at energies just above the isomerization barrier are dominated by the character of the 1,3,5,7-tetraenyl radical, which suggests that chemistry involving this intermediate at typical combustion temperatures may branch at this juncture.     

Application of a semi-empirical dispersion correction for modeling water clusters

The Grimme-D3 semi-empirical dispersion energy correction has been implemented for the original effective fragment potential for water (EFP1), and for systems that contain water molecules described by both correlated ab initio quantum mechanical (QM) molecules and EFP1. Binding energies obtained with these EFP1-D and QM/EFP1-D methods were tested using 27 benchmark species, including neutral, protonated, deprotonated, and auto-ionized water clusters and nine solute–water binary complexes. The EFP1-D and QM/EFP1-D binding energies are compared with those obtained using fully QM methods: second-order perturbation theory, and coupled cluster theory, CCSD(T), at the complete basis set (CBS) limit. The results show that the EFP1-D and QM/EFP1-D binding energies are in good agreement with CCSD(T)/CBS binding energies with a mean absolute error of 5.9 kcal/mol for water clusters and 0.8 kcal/mol for solute–water binary complexes. © 2018 Wiley Periodicals, Inc.     

Fock space multi-reference coupled cluster study of transition moment and oscillator strength

Summary A method of calculating transition moment and oscillator strength within the framework of the Fock space multi-reference coupled cluster method is described. Diagrammatic technique is used to obtain coupled cluster equations. The general form of equations for the transition moment betweenN-electron ground and excited states is obtained. MBPT analysis of the final equations is done. The excitation energies, dipole transition moments and oscillator strengths for theCH ⁺ molecule are calculated.     

Accurate ab initio predictions of ionization energies of hydrocarbon radicals: CH2, CH3, C2H, C2H3, C2H5, C3H3, and C3H5

The ionization energies for methylene (CH2), methyl (CH3), ethynyl (C2H), vinyl (C2H3), ethyl (C2H5), propargyl (C3H3), and allyl (C3H5) radicals have been calculated by the wave-function-based ab initio CCSD(T)/CBS approach, which involves the approximation to the complete basis set (CBS) limit at the coupled-cluster level with single and double excitations plus a quasiperturbative triple excitation [CCSD(T)]. When it is appropriate, the zero-point vibrational energy correction, the core-valence electronic correction, the scalar relativistic effect correction, the diagonal Born-Oppenheimer correction, and the high-order correlation correction have also been made in these calculations. The comparison between the computed ionization energy (IE) values and the highly precise experimental IE values determined in previous pulsed field ionization-photoelectron (PFI-PE) studies indicates that the CCSD(T)/CBS method is capable of providing accurate IE predictions for these hydrocarbon radicals achieving error limits well within +/-10 meV. The benchmarking of the CCSD(T)/CBS IE predictions by the PFI-PE experimental results also lends strong support for the conclusion that the CCSD(T)/CBS approach with high-level energy corrections can serve as a valuable alternative for reliable IE determination of radicals, particularly for those radicals with very unfavorable Franck-Condon factors for photoionization transitions near their ionization thresholds.