Symmetry adapted versus symmetry broken wavefunctions: the 1s core level ions of O+2

It is shown that, for O₂, in a MC SCF determination of the core ionization potentials employing the full Molecular point group, very few (N-1)-particle configurations are required in order to account for the symmetry breaking in the corresponding Hartree-Fock calculations.     

Fast calculation of excited-state potentials for rare-gas diatomic molecules: Ne2 and Ar2

A fast method for obtaining excited-state potentials of rare-gas diatomic molecules is described. Two types of excited orbitals are used: molecular orbitals calculated in the field of a singly charged molecular ion, and atomic orbitals (properly symmetrized) obtained in a similar atomic system. The RPA equations are solved within the manifold of excitations from the highest occupied orbital in each symmetry to the lowest excited orbital of either type in each symmetry. A simple model for estimating the dynamic correlation correction to excitation (and ionization) energies is given. Applications to excited states of Ne₂(^1,3Σ⁺_{g, u}, ^1,3Π_{g, u}) and Ar₂(^1,3Σ⁺_{g, u}) are described. Two-electron integral transformations involve only three orbitals of each symmetry, and the RPA matrices are four-dimensional. The computational effort required for all excited-state potentials adds less than one-tenths (in terms of computer time) to the effort involved in the preliminary ground state Hartree—Fock calculations. The resulting potentials compare favorably with more elaborate CI calculations and give good agreement with spectroscopic and scattering data. Potential curves for the molecular ions are also given.     

Influence of the Delocalization Error and Applicability of Optimal Functional Tuning in Density Functional Calculations of Nonlinear Optical Properties of Organic Donor–Acceptor Chromophores

Nonempirically tuned hybrid density functionals with range‐separated exchange are applied to calculations of the first hyperpolarizability (β_∥) and charge‐transfer (CT) excitations of linear “push–pull” donor–acceptor‐substituted organic molecules with extended π‐conjugated bridges. An unphysical delocalization with increasing chain length in density functional calculations can be reduced significantly by enforcing an asymptotically correct exchange‐correlation potential adjusted to give frontier orbital energies representing ionization potentials. The delocalization error for a number of donor–acceptor systems is quantified by calculations with fractional electron numbers and from orbital localizations. Optimally tuned hybrid variants of the PBE functional incorporating range‐separated exchange can produce similar magnitudes for β_∥ as Møller–Plesset second‐order perturbation (MP2) correlated calculations. Improvements are also found for CT excitation energies, with results similar to an approximate coupled‐cluster model (CC2).     

An AB initio molecular orbital study of the NF2 and N2F4 molecules,and ESR hyperfine coupling constants in NF2

In this publication, we present the results of gaussian type orbital calculations of ESR hyperfine coupling constants in NF₂. We also present electron density maps for the molecule, and the results of a calculation of ΔH⁰₂₉₈ for the reaction N₂F₄ → 2NF₂.     

Density functional theory calculation of 2p spectra of SiH4, PH3, H2S,HCl, and Ar

The method developed recently for prediction of 1s electron spectra is now extended to the 2p spectra of SiH₄, PH₃, H₂S, HCl, and Ar. The method for X‐ray absorption spectra involves the use of ΔE for the excitation and ionization energies, and application of time‐dependent density functional theory using the exchange‐correlation potential known as statistical average of orbital potentials for the intensities. Additional assumptions and approximations are also made. The best exchange‐correlation functional E_xc for the earlier calculation of ΔE in 1s spectra of C to Ne (namely Perdew–Wang 1986 exchange, combined with Perdew–Wang 1991 correlation) is no longer used in this work on 2p spectra of Si to Ar. Instead, recently tested E_xc good for 2p core‐electron binding energies (known as OPTX) for exchange and LYP for correlation, plus scalar zeroth‐order regular approximation is adopted here for the ΔE calculations. Our calculated X‐ray absorption spectra are generally in good agreement with experiment. Although the predictions for the higher excitations suffer from basis set difficulties, our procedure should be helpful in the interpretation of absorption spectra of 2p electrons of Si to Ar. In addition, we report calculated results for other kinds of electron spectra for SiH₄, PH₃, H₂S, HCl, and Ar, including valence electron ionizations and excitations as well as X‐ray emission. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Theoretical study of the vertical electron affinity and ionization potentials of C3

The electron affinity and first three ionization potentials of C₃ are calculated using the multiconfigurational SCF and configuration interaction methods and by Möller-Plesset perturbation theory. Whereas Koopmans' theorem and SCF calculations indicate that the first cation state is ²Π_u, upon inclusion of correlation effects both the ²Σ_u and ²Σ_g cation states are found to lie lower in energy. CI calculations indicate that the ground state (²Π_g) anion is stable by 1.74 eV. Allowing for the error in the calculated electron affinity of the carbon atom, C₃^? is estimated to be stable by 2.0 eV, in excellent agreement with the 2.05 eV value determined from recent photodetachment measurements. No excited anion states are found to be bound at the equilibrium geometry of the neutral molecule.     

Laser-induced fluorescence measurement of the nascent rotational distribution of N+2 (X2Σ+g) formed by electron impact on N2

The internal state distribution of ground state N⁺₂ ions formed from N₂ by electron impact ionization is measured under collision-free conditions using laser-induced fluorescence. Analysis of the B–X (0, 0) band shows the rotational distribution to be characterized by a temperature which increases slightly with decreasing electron energy (60–100 eV). Cascade contributions are unimportant.     

The hel photoelectron spectrum of S2O

The Hel photoelectron spectrum of the transient species S₂O has been measured and the experimentally determined ionization potentials are compared with the results of CNDO/2 molecular orbital calculations using Koopmans' theorem. The assignments are compared with those previously given for the series of related molecules NSF, NSCI, and SO₂ by means of a correlation diagram.     

On the accuracy of density functionals and their basis set dependence: An extensive study on the main group homonuclear diatomic molecules Li2 to Br2

The equilibrium bond distances, harmonic frequencies, and bond dissociation energies of the 21 homonuclear diatomics Li₂—F₂, Na₂—Cl₂, and K₂—Br₂ have been determined using approximate density functional theory (DFT) employing various widely used functionals and basis sets ranging from single zeta to triple zeta plus polarization quality. The results are in general much less sensitive to the size of the basis set as in conventional ab initio molecular orbital (MO) theory, while the choice of the functional is of much more significance. For one basis set (6-311G*), the performance of the DFT-based calculations has been compared and found to be superior to Hartree-Fock (HF) Møller Plesset second order perturbation theory (MP2), or configuration interaction with single and double excitations (CISD) calculations. Particularly, no pathological cases, such as the group 2 dimers (Be₂, Mg₂, Ca₂), are observed. © 1995 by John Wiley & Sons, Inc.     

Frozen local hole approximation

The frozen local hole approximation (FLHA) is an adiabatic approximation which is aimed to simplify the correlation calculations of valence and conduction bands of solids and polymers or, more generally, of the ionization potentials and electron affinities of any large system. Within this approximation correlated local hole states (CLHSs) are explicitly generated by correlating local Hartree-Fock (HF) hole states, i.e., (N-1)-particle determinants in which the electron has been removed from a local occupied orbital. The hole orbital and its occupancy are kept frozen during these correlation calculations, implying a rather stringent configuration selection. Effective Hamilton matrix elements are then evaluated with the above CLHSs; diagonalization finally yields the desired correlation corrections for the cationic hole states. We compare and analyze the results of the FLHA with the results of a full multireference configuration interaction with single and double excitations calculation for two prototype model systems, (H2)n ladders and H-(Be)n-H chains. Excellent numerical agreement between the two approaches is found. Comparing the FLHA with a full correlation treatment in the framework of quasidegenerate variational perturbation theory reveals that the leading contributions in the two approaches are identical. In the same way it could be shown that a much less demanding self-consistent field (SCF) calculation around a frozen local hole fully recovers, up to first order, all the leading single excitation contributions. Thus, both the FLHA and the above SCF approximation are well justified and provide a very promising and efficient alternative to fully correlated wave-function-based treatments of the valence and conduction bands in extended systems.     

The orbital relaxation energy for single and double ionizations from valence shells of CH4, NH3, H2O and HF

The orbital relaxation energy is defined for single and double ionizations of valence electrons, and is calculated for CH₄, NH₃, H₂O and HF molecules with the ab initio SCF method. It is shown that the orbital relaxation energy for the ionization from a bonding orbital is about half of that for a non-bonding orbital, and the orbital relaxation energy for the double ionization is about double of that for the single ionization. This result gives a theoretical foundation for the empirical method of interpret Auger electron spectra by using experimental single ionization potentials.     

Possible cyclic triatomic molecules including N2O and O3

Proposed metastable cyclic conformations of N₂O⁺ and O₃, have been examined by INDO and ab initio calculations. INDO is found to exaggerate the stability of possible cyclic species. In ab initio calculations a multi-dimensional energy surface must be explored. With a [5, 3] basis SCF calculations yield a trivariate local minimum for cyclic O₃. However, for N₂O, N₂O⁺ and O²⁺₃, starting from cyclic “bonded” structures, paths involving asymmetric deformations run downhill in energy to a diatomic molecule and a separated atom. A paradox concerning the removal of an electron from an antibonding orbital in a cyclic molecule is resolved.     

Delocalized and localized pictures of excited and ionized states

The valence shell repolarization under a core ionization in a diatomic molecule as N₂ is analyzed through localized and delocalized pictures, showing their total equivalence. The interpretation is easier in the localized model, appearing mainly through local single excitation processes; in the delocalized model the repolarization effect is hidden (partly or totally) under double excitation processes involving simultaneous excitations in the valence shell and hole change in the core level, appearing therefore as a “correlation effect”. This effect is analyzed forn Be atoms, showing an ^?1 behaviour of the single excitations effect in the delocalized model, and explains the Hartree-Fock unstability numerically verified on O ₂ ⁺ , but it prevents to give any physical meaning to the “localization of the core hole in a diatomic molecule”.     

Predissociation of the 3pπ D 1Πu+ state in H2, HD,and D2

Predissociation linewidths and lineshapes are reported for selected vibrational levels of the 3_pπ D ¹Π⁺_u state of H₂, HD, and D₂. We also discuss the effect of a perturbation by the 4_pδ B″B? ¹|gs_u⁺ state on the predissociation rate of the D state.     

Relativistic electronic structures of the Ag2 and Au2 molecules

The relativistic electronic structures of the Ag₂ and Au₂ molecules have been calculated using the recently developed self-consistent-field Xα Dirac-scattered-wave programs. Calculations have been carried out for transition energies and ionization potentials for selected molecular orbitals. The results indicate a large degree of s-d hybridization in the ground state of the Au₂ molecule. The calculations are in good agreement with other theoretical work and with existing experimental results.     

Ab initio calculations on the three lowest states of HO+2

Ab initio calculations were performed for the three lowest lying states of HO⁺₂. The ground state was found to be a bend ³A″ state. The first excited ¹A′ state cannot appropriately be described by a single determinant, therefore a MC SCF calculation was employed.     

Structural and electronic properties of compound metal clusters

The equilibrium geometries, relative stabilities, and vertical ionization potentials of compound clusters involving Li _n , Na, Mg, and Al atoms have been calculated using ab initio self-consistent field linear combination of atomic orbitals — molecular orbital (SCF-LCAO-MO) method. The exchange energies are calculated exactly using the unrestricted Hartree-Fock (UHF) method whereas the correlation correction is included within the framework of configuration interaction involving pair excitations of valence electrons. While the later correction has no significant effect on the equilibrium geometries of clusters, it is essential for the understanding of relative stabilities. Clusters with even numbers of electrons are found to be more stable than those with odd numbers of electrons regardless of their charge state and atomic composition. The equilibrium geometries of homo-nuclear clusters can be significantly altered by replacing one of its constituent atoms with a hetero-nuclear atom. The role of electronic structure on the geometries and stabilities of compound clusters is discussed.     

Intermolecular forces for D2, N2, O2, F2 and CO2

The intermolecular potentials for D₂, N₂, O₂, F₂ and CO₂ are determined on the basis of the second virial coeffincients, the polarizabilities parallel and perpendicular to the molecular axes, and the electric quadrupole moment. The repulsive parts of the potentials are taken from the corresponding Kihara core-potentials. Effects of the octopolar induction are taken into consideration in a unique way. The potential depends on relative orientations of the two molecules as well as the distance r between the molecular centers. This dependence is shown in graphs. A measure of the anisotropy of the potential depth is 0.72 for CO₂ 0.36 for D₂, and smaller than 0.27 for N₂ O₂ and F₂. The remarkable anisotropy for CO₂ and D₂ is due to strong electrostatic quadrupole interactions.     

An extended-valence MC SCF procedure: determination of the dissociation energies of C2, N2, O2, and F2

A series of MC SCF calculations have been carried out on C₂, N₂, O₂, and F₂ with the goal of obtaining compact wavefunctions which recover a significant fraction of the electron correlation effects important for bond dissociation. The active orbital space is varied in size, with the largest spaces including the molecular orbitals derived from 2s, 2p, 3s, 3p and 4p atomic orbitals. Several basis sets ranging in size from 5s3p to 5s4p2d1f are investigated to determine the flexibility in the basis set needed with various choices of the active orbital space. The best extended-valence MC SCF (EVMC) dissociation energies are 0.2–0.5 eV less than the experimental values, indicating that further enlargement of the active orbital space is necessary to achieve 0.1 eV accuracy in the computed dissociation energies. The EVMC calculations reveal that, for the calculation of the dissociation energies, inclusion of non-valence orbitals is much more important for O₂ and F₂ than for C₂ and N₂. The EVMC results are compared with the predictions of full fourth-order perturbation theory, coupled cluster theory, and with the best available CI calculations.