Coupled Electron Pair Approach Research Articles

A Hierarchy of Methods for the Energetically Accurate Modeling of Isomerism in Monosaccharides.

The performance of different wave-function-based and density functional theory (DFT) methods was evaluated with respect to the prediction of relative energies for gas-phase monosaccharide isomers. A test set of 58 structures was employed, representing all forms of isomerism encountered in d-aldohexoses. The set was built from eight hexopyranose epimers by deriving subsets of isomers that include hydroxymethyl rotamers, anomers, ring conformers, furanose, and open-chain forms. Each subset of isomers spans a different energy range and involves various stereoelectronic effects. Reference energy values were obtained with coupled-cluster calculations extrapolated to the complete basis set limit, CCSD(T)/CBS. The tested CBS-extrapolated ab initio methods include various types of Møller-Plesset (MP) perturbation theory and the localized paired natural orbital coupled electron pair approach (LPNO-CEPA). Extensive benchmarking of DFT methods was carried out with 31 functionals. The results allow us to establish a hierarchy of methods that forms a reference guide for further computational studies. Among wave-function-based methods, LPNO-CEPA proved indistinguishable from CCSD(T), offering a promising alternative for a reference method that can be applied to larger systems. MP2 and SCS-MP2 follow closely, surpassing SOS-MP2 and MP3. The mPW2PLYP-D double hybrid and the Minnesota M06-2X hybrid meta-GGA are the best performing density functionals and are directly competitive with wave-function-based ab initio methods. Among the remaining functionals, B3PW91, TPSSh, mPW1PW91, and PBE0 yield the best results on average, while PBE is the best general-purpose GGA functional, surpassing meta-GGAs and several hybrids such as B3LYP. The choice of method strongly depends on the type of isomerism that needs to be considered, since many DFT methods perform well for purely conformational isomerism, but most of them fail to describe ring versus open-chain isomerism, where LYP-based GGA functionals perform particularly poorly.

Vibronic Coupling Effects in Resonant Auger Spectra of H2O

We present a theoretical investigation of the resonant Auger effect in gas-phase water. As in our earlier work, the simulation of nuclear dynamics is treated in a one-step picture, because excitation and decay events cannot be disentangled. Extending this framework, we now account for the vibronic coupling in the cationic final states arising from degeneracies in their potential energy surfaces (PESs). A diabatization of the cationic states permits a correct treatment of non Born-Oppenheimer dynamics leading to a significantly better agreement with experimental results. Moreover, we arrive at a more balanced understanding of the various spectral features that can be attributed to nuclear motion in the core-excited state or to vibronic coupling effects. The nuclear equations of motion have been solved using the multiconfiguration time-dependent Hartree (MCTDH) method. The cationic PESs were recalculated using the coupled electron pair approach (CEPA) whereas previously a multireference configuration interaction method had been employed.

Method of Local Increments for the Calculation of Adsorption Energies of Atoms and Small Molecules on Solid Surfaces. 2. CO/MgO(001)

The method of local increments is used in connection with an embedded cluster approach and wave function based quantum chemical ab initio methods to describe the adsorption of a single CO molecule on the MgO(001) surface. The first step in this approach is a conventional Hartree-Fock calculation. The occupied orbitals are then localized by means of the Foster-Boys localization procedure, and the full system is decomposed into several "subunits" that consist of the orbitals localized at the CO molecule and at the Mg and O atoms of the MgO cluster. The correlation energy is expanded into a series of local n-body increments that are evaluated separately and independently. In this way, big savings in computer time can be achieved because (a) the treatment of a large system is replaced with a series of much faster calculations for small subsystems and (b) the big basis sets necessary for describing dispersion effects are only needed for the atoms in the respective subsystem while all other atoms can be treated by medium size Hartree-Fock type basis sets. The coupled electron pair approach, CEPA, an approximate coupled cluster method, is used to calculate the correlation energies of the various subsystems. For the vertical adsorption of CO on top a Mg atom of the MgO(001) surface with the C atom toward Mg, the individual one- and two-body increments are calculated as functions of the CO-MgO separation and a full potential energy curve is constructed from them. A very shallow minimum with an adsorption energy of 0.016 eV at a Mg-C distance of 3.04 Å is found at the Hartree-Fock level, while inclusion of correlation (dispersion) effects shortens the Mg-C distance to 2.59 Å and yields a much larger adsorption energy of 0.124 eV. This is in very good agreement with the best experimental value of 0.14 eV. The basis set superposition error, BSSE, was fully corrected for by the counterpoise method and the bonding mechanism was analyzed at the Hartree-Fock level by means of the constrained space orbital variation, CSOV, analysis.

Rotational excitation of HOCO+ by helium at low temperature

Context. It has been shown that the HOCO+ ion is present in interstellar space. As a large number of HOCO+ lines can be observed in the millimeter and submillimeter wavelengths, this molecule is a useful tracer for both the temperature and the density structure of the clouds. Modeling of the spectra will require accurate radiative and collisional rates of species of astrophysical interest.Aims. The paper focuses on the calculation of rotational excitation rate coefficients of HOCO+ by He, useful for studies of low-temperature environments.Methods. Cross sections are calculated using the quantum Coupled States approach for a total energy range 0–200 cm-1 . These calculations are based on a new ab initio CEPA (coupled electron pair approach) potential energy surface. It was assumed that the HOCO+ ion was fixed at its theoretical equilibrium geometry.Results. Thermally averaged rate coefficients were calculated from the cross sections, at kinetic temperatures up to 30 K.

Inelastic collision cross sections of CH(X 2Π) with He(1S) on new ab initio surfaces

Full close-coupled (CC) integral inelastic cross sections were determined for collisions between CH(X 2Π)(N′=1) and He. These calculations are based on new ab initio CEPA (coupled electron pair approach) potential energy surfaces computed by Abdallah et al. These theoretical CC cross sections confirm a previous prediction of preferential population of final states levels in which the electronic wave function of the CH molecule is antisymmetric with respect to reflection in the plane of the molecule. These results are compared with the experimental results of Macdonald et al. At all energies the discrepancies were in most cases less than 7% of the ratio of the sum of the cross sections for the four transitions into levels of nominal A″ reflection symmetry divided by the sum of the cross sections for the four transitions into levels of nominal A′ reflection symmetry. Nevertheless, there is substantial disagreement in the magnitudes of the ratios particularly for the transitions with larger inelasticity.

Applications of a variational coupled-electron pair approach to the calculation of intermolecular interaction in the framework of the VB theory: Study of the van der Waals complex He–CH4

A general nonorthogonal coupled electron pair approach for the evaluation of electron correlation contribution is presented in details. The self-consistent field for molecular interactions wave function is used as reference state for a multistructure valence bond (VB) calculation. The central idea of the method is the optimization of the virtual space of the VB wave function by means of a procedure very close to the independent electron pair approach (IEPA) scheme. All the orbitals employed are expanded in the basis set of their fragment so as to exclude the basis set superposition error (BSSE) in a priori fashion. As an example, the application to the study of the van der Waals complex He–CH4 is reported. The equilibrium geometry of the system occurs at a He–C distance of 3.6 Å , with the He atom pointing to the center of one of the faces of the CH4 molecule, with a well depth of 19 cm−1. The potential energy surface of the He–CH4 complex is used to determine the parameters of a potential model which is employed in close-coupling calculations of integral state-to-state cross sections for rotationally inelastic scattering of methane molecules with helium atoms. The predicted values are compared with the available experimental data.

Ab initio calculations of van der Waals interactions in one- and two-dimensional infinite periodic systems

A new CEPA-PNO (coupled electron pair approach with pair natural orbitals) method for the calculation of correlation energies in infinite periodic systems is proposed and applied to one- and two-dimensional He. The method starts from a crystal orbital Hartree-Fock (COHF) wavefunction with the occupied Bloch orbitals transformed into Wannier orbitals. The coupled-cluster equations for the infinite system are simplified by CEPA-type approximations: A CEPA-0 (or linear coupled-cluster) formula is applied for the small intercell contributions to the total correlation energy while CI-SD, ACPF or other CEPA variants are used for the large intracell contributions. The enormous number of single and double excitations into the virtual space is greatly reduced by the use of pair natural orbitals (PNOs), which leads to large savings in the necessary computer time and disk storage. First applications to the van der Waals interaction in the linear chain and the hexagonal plane of He atoms, performed with medium size and large atomic basis sets, show that an accuracy can be reached for the infinite systems which is comparable to the accuracy of the corresponding calculations for small He clusters. Because of the extended use of the translational symmetry of the Wannier orbitals, the calculations for the linear infinite systems are even considerably faster than those for the oligomers He5 and He7.

An ab initio study of the chemical bond and the 129Xe NMR chemical shifts in M+ −Xe compounds, M = Li, Na, K, Cu, Ag

Quantum chemical ab initio calculations have been performed for the interaction between ground state Xe atoms and the monopositive metal cations Li+, Na+, K+, Cu+, and Ag+. Potential energy curves have been calculated at the SCF and CEPA (coupled electron pair approach) levels. The mechanism of the bonding between Xe and the cation has been analyzed. For the alkali ions Li+, Na+, and K+ the bonds are rather weak (0.367, 0.210, 0.112 eV, respectively) and are caused mainly by inductive forces. In Cu+ −Xe and Ag+−Xe the binding energies are slightly larger (0.632 and 0.380 eV) and contain small contributions of genuine chemical effects and dispersion. 129Xe NMR chemical shifts have been calculated at the SCF level by means of the IGLO method. Only the paramagnetic part of the magnetic shielding constant σ of Xe is affected by the interaction with the cation, the diamagnetic part remains unchanged. For the alkali ions a small downfield shift is obtained which is attributed to the polarization of the Xe wave function by the charge of the cation. For the noble metal cations Cu+ and Ag+ an additional upfield shift is found which is caused by a mixing of the 54p, 4p, 3p orbitals at Xe with the 3d or 4d orbitals at the noble metals in the magnetic response function. This leads to an increased magnetic shielding. Comparison with 129Xe NMR data in X and Y zeolites is made.

Theoretical study of the highly vibrationally excited states of FHF−: Ab initio potential energy surface and hyperspherical formulation

A three-dimensional description of vibrationally highly excited linear molecules is formulated in hyperspherical coordinates, based on a successive adiabatic reduction scheme. The method is applied to the low-lying and highly excited vibrational states of FHF−, a prototype of symmetric bihalide anions, which has attracted spectroscopic interest due to its peculiar vibrational anharmonicity. Ab initio potential energy surfaces (PESs) which cover the ground-state potential well of FHF− and/or its dissociation to the F−+HF channel have been obtained by using the coupled electron pair approach (CEPA) method. An hyperspherical calculation using the ab initio PES of the sixth-order Simons–Parr–Finlan analytical form has correctly reproduced the experimental fundamental frequencies. Specifically, the vibrationally highly excited FHF− above the dissociation threshold is proposed as a candidate for transition state spectroscopy (TSS) of unimolecular dissociation reactions without barrier.

Fit of the potential energy surface for the reaction Ne+H2+→NeH++H using three different functional forms

Three different functional forms are fit to a calculated coupled electron pair approach potential energy surface for the reaction Ne+H2+→NeH++H. Minimum energy pathways and stationary points of the various fits are discussed.

Size consistency corrections for configurational interaction calculations

AbstractA size consistency error formula, correcting for the erratic dependence on the number of particles in a doubly substituted (or otherwise restricted) configurational interaction (CI) treatment, is derived. The formula is expressed in terms of the particle pair eneriges ϵk and the normalization integrals Δk of the corrections to the unperturbed normalized wave function. The theory as well as the results for the 1A1 ground state of H2O and the 2B1 state of H2O+ show close agreement with the coupled electron pair approach (CEPA).

Calculation of vertical ionization potentials of ketene by perturbation corrections to Koopmans' theorem

The vertical ionization potentials of ketene are calculated by perturbation corrections to Koopmans' theorem. The present results are compared with those from the pseudonatural orbital coupled electron pair approach and the experimental values.