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.     

An ICSCF investigation of Walsh's rules

The ICSCF method is applied to the calculation of orbital energies as a function of bond angle for several AH₂ molecules. The resulting orbital energy diagrams are quite similar in appearance to the canonical SCF results even though the sum of the ICSCF energies is the SCF energy. The method is also applied to Li₂O, CO₂, HCN and a few AH₃ molecules with similar results. The sum of the ICSCF valence orbital energies generally correlates better with the equilibrium bond angle than does the similar sum of canonical orbital energies.     

Systematic regularities of molecular SCF energies

New formulae for the approximate computation of total molecular energies are developed based on ab initio calculations of n-alkanes. Their application to various kinds of molecules reveals that good expectation values for total molecular energies can be obtained by considering only the one-electron terms h _i and the nuclear repulsion energy. It is further shown that very good agreement with SCF total energies is obtained by a relationship which connects the total energy with the sum of inner-shell (core) orbital energies. The results turn out to be better than those obtained using Ruedenberg's approximation, which takes both inner-shell and valence-shell orbital energies into account.     

An ab initio CI investigation of structure and bonding in LiC2H2 complexes

The structures and energies of various LiC₂H₂ complexes have been investigated by means of ab initio molecular orbital calculations. Analytic SCF gradients were employed with a double-ζ basis set to locate and characterize stationary points on the energy surface. Single-point CI calculations using a double-ζ + diffuse and polarization basis set have been carried out at the DZ + P SCF stationary points. With the highest-level theory, the Li—vinylidene complex and the cis bridged adduct are found to be the most favorable arrangements, the former complex being slightly more stable by about 2 kcal mol⁻¹. These molecules are bound respectively by about 5 and 3 kcal mole⁻¹ relative to infinitely separated lithium plus acetylene. Harmonic vibrational frequencies are also reported and confirm the existence of the cis LiC₂H₂ species recently observed in a solid argon matrix.     

Theoretical study on the hydrogen migration reactions in ground state vinyl fluoride: Basis set and correlation energy effects

We performed ab initio molecular orbital (MO) calculations using Hartree—Fock SCF, and second- and fourth-order Møller—Plesset perturbation theory for hydrogen migration reactions on the singlet vinyl fluoride potential energy surface. We used different basis sets and polarization functions to obtain the stationary point geometries and activation barriers. Basis set and the polarization function extension have small effects, while the correlation energy evaluation leads to new conclusions for one of the studied reactions: the product singlet CHCH₂F is not a true local minimum on the potential energy surface.     

Electron momentum spectroscopy of sulphurhexafluoride

The SF₆ molecule has been studied using high-resolution electron momentum spectroscopy [EMS], at a total energy of 1200 eV and using non-coplanar symmetric kinematics. Binding-energy spectra ranging up to 62 eV were measured at out of plane azimuthal angles from 0° to 28°, and in the outer-valence region from 0° to 34°, corresponding to target electron momenta from about 0.1–2.8 au. The binding-energy spectra and electron momentum distributions obtained for the valence orbitals are compared with the results of Green function calculations for the ionization energies and their corresponding pole strengths and the spherically averaged momentum distributions obtained from the SCF wavefunction on which the Green function calculations are based. The SCF basis includes d components on both S and F atoms. In the outer-valence region, where the one-particle picture holds for the ionization process, there is very good agreement between the theoretical energies and pole strengths and the measured ones, but the orbital momentum distributions are given poorly by the SCF wavefunctions. The measured momentum distributions are significantly higher at low momentum (< 1 au), particularly for the 1t_2u and 3e_g orbitals. In the inner-valence region a substantial splitting of the lines occurs, which is only predicted in a qualitative way. The SCF momentum distribution for the 2e_g orbital is in poor agreement with the data, whereas that of the 3t_1u orbital is in very good agreement with the measurements.     

An AB initio SCF MO CI study of the n → π* transition of methylenimine

The electron correlation energies of both the ground and n → π* excited states of methylenimine (CH₂NH) are investigated by means of ab initio SCF MO CI calculations. Then n → π* singlet and triplet state energies of methylenimine are obtained through 3461-dimensional CI including the singly, doubly and triply excited configurations. the excitation energy from the ground state to the ¹(n → π*) state nearly coincides with that obtained in the framework of the singly excited configuration interaction (SECI) procedure. This result suggests that there is good cancellation of the correlation energy between the ground and the excited singlet sates, proving the usefulness of the SECI method for the excitation energies.     

On a definition of bond energies based on localized molecular orbitals

A theoretical model is presented for defining bond energies based on localized molecular Orbitals. These bond energies are obtained by rearranging the total SCF energy including the nuclear repulsion term to a sum over orbital and orbital interaction terms and then to total orbital terms, which can be interpreted as the energies of localized orbitals in a molecule. A scaling procedure is used to obtain a direct connection with experimental bond dissociation energies. Two scale parameters are employed, the C-C and the C-H bond dissociation energy in C₂H₆ for A-B and C-H type bonds, respectively. The implications of this scaling procedure are discussed. Numerical applications to a number of organic molecules containing no conjugated bonds gives in general a very satisfactory agreement between experimental and theoretical bond energies.     

Association of metal cations with alkanes: Na(CH4)+ versus Cu(CH4)+ as molecular models

Summary Ab initio molecular orbital calculations give small stabilization energies for the various Na(CH₄)⁺ adducts (less than 4 kcal mol^–1), but predict a stronger binding for the copper compounds (about 13 kcal mol^–1). The different behaviour of Na⁺ and Cu⁺, already present at the SCF level, is reinforced by electron correlation. This can be attributed to an important contribution of the dispersion energy to the binding energy of the copper ion: about 40% of the total, including basis set superposition corrections.Dedicated to Mrs A. Pullman     

Convergence studies in configuration interaction calculations

A series of CI calculations for the ground state of BH₃ in which various levels of excitation from the ground state are included are compared with each other and with the full-CI (196 configurations) result. The comparisons cover calculations in terms of two different molecular orbital bases—the canonical SCF basis and a simple, arbitrarily chosen, symmetry orbital basis. As expected, single and, to a lesser extent, triple excitations are of little importance in the SCF case but cannot be ignored for the arbitrary basis. However, as soon as all excitations ≦4 are included, there is practically no difference in the results for the two bases, both giving energies quite close to the full-CI value. In fact, the energies for the two bases are in close agreement also in the (0 + 1 + 2 + 3)-excitation calculation and in qualitative agreement in the (0 + 1 + 2) case. Two methods are tested for the selection of the important higher-excitation configurations, and it is found that results very close to full CI can be obtained with substantially fewer functions. Particularly promising is the application of the “unlinked cluster” approach, based on the ideas developed by Sinano?lu and others, to the prediction of the coefficients of evenly excited configurations from those of the doubly-excited functions in a limited-CI calculation.     

An efficient self-consistent field method for large systems of weakly interacting components

An efficient method for removing the self-consistent field (SCF) diagonalization bottleneck is proposed for systems of weakly interacting components. The method is based on the equations of the locally projected SCF for molecular interactions (SCF MI) which utilize absolutely localized nonorthogonal molecular orbitals expanded in local subsets of the atomic basis set. A generalization of direct inversion in the iterative subspace for nonorthogonal molecular orbitals is formulated to increase the rate of convergence of the SCF MI equations. Single Roothaan step perturbative corrections are developed to improve the accuracy of the SCF MI energies. The resulting energies closely reproduce the conventional SCF energy. Extensive test calculations are performed on water clusters up to several hundred molecules. Compared to conventional SCF, speedups of the order of (N/O)2 have been achieved for the diagonalization step, where N is the size of the atomic orbital basis, and O is the number of occupied molecular orbitals.     

Perturbation expansion theory corrected from basis set superposition error. I. Locally projected excited orbitals and single excitations

The locally projected self-consistent field molecular orbital method for molecular interaction (LP SCF MI) is reformulated for multifragment systems. For the perturbation expansion, two types of the local excited orbitals are defined; one is fully local in the basis set on a fragment, and the other has to be partially delocalized to the basis sets on the other fragments. The perturbation expansion calculations only within single excitations (LP SE MP2) are tested for water dimer, hydrogen fluoride dimer, and colinear symmetric ArM+ Ar (M = Na and K). The calculated binding energies of LP SE MP2 are all close to the corresponding counterpoise corrected SCF binding energy. By adding the single excitations, the deficiency in LP SCF MI is thus removed. The results suggest that the exclusion of the charge-transfer effects in LP SCF MI might indeed be the cause of the underestimation for the binding energy.     

Correlation effects on cis—trans energy differences in open-shell systems: The hoco radical as an example

Ab initio SCF and Cl calculations have shown that the most important factor in determining the relative energies of conformational isomers in free radicals is the movement of electron density into the singly occupied orbital. This is most favorable when an electron pair is situated trans to the radical site (trans correlation effect). In the HOCO radical we find that the trans isomer is more stable than the cis by 3.3 kcal/mol while SCF calculations yield virtually no energy difference between the two isomers.     

SCF and localized orbitals in ethylene: MBPT/CC results and comparison with one-million configuration Cl

Many-body perturbation theory (MBPT) and coupled-cluster (CC) calculations are performed on the ethylene molecule employing canonical SCF and simple bond-orbital localized orbitals (LO). Full fourth-order MBPT [i.e. SDTQ MBPT(4)], CC doubles (CCD) and CC singles and doubles (CCSD) energies are compared with the over one-million configuration ‘bench-mark” Cl calculation of Saxe et al. Though the SCF and LO reference determinant energies differ by 0.29706 hartree, the CCSD energy difference is only 1.7 mhartrees (mh). Our most extensive SCF orbital calculation, CCSD plus fourth-order triples, is found to be lower in energy than the CI result by 5.3 mh.     

Temperature-dependent reaction kinetics of NH (a1Δ)

The gas-phase reactions of NH(a¹Δ) with H₂ and selected saturated and unsaturated hydrocarbons have been studied over the 250-600 K temperature range. Olefin reactions proceed at near the gas kinetic collision rate and show no temperature dependence. H₂ and saturated hydrocarbons show temperature-dependent reactions rates, with activation energies of = 0.8-2 kcai/mole. No evidence of electronic quenching of NH(a¹Δ) to the ground state was observed with any of the hydrocarbons studied. First-order reactions rates, Arrhenius A factors and activation energies for the reactions are reported. We discuss a mechanistic interpretation of the kinetics in view of earlier kinetic and reaction-product studies and ab initio SCF Cl calculations.     

An analysis of the through-bond interaction using the localized molecular orbitals with ab initio calculations—II : Lone-pair orbital energies in bicyclo compounds: 7-azabicyclo[2.2.1]heptane and 2-azabicyclo[2.2.2]octane,and their n-methyl derivatives

Ab intio SCF MO calculations using STO-3G basis set were performed on 7-azabicyclo[2.2.1]heptane, N-methyl-7-azabicyclo[2.2.1]heptane, 2-azabicyclo[2.2.2)octane, N-methyl-2-azabicyclo[2.2.2)octane, and their model molecules. The orbital energies obtained by these calculations were compared with the experimental ionization potentials The canonical MOs obtained for the model molecules were then transformed into the localized Mos. With the use of the localized MOs thus obtained, the lone-pair orbital energies were pursued in the light of the through-space and/or the through-bond interactions between thw specified localized MOs. As a result of this analysis, it was found that the effects of the inner shell orbitals, 1s electrons of the N atom, and of the neighbouring N-C bonds of the skeleton (through-bond interaction) play a dominant role in the interaction with the lone-pair orbitals. It was also found that the effect of the N-Me group on the lone-pair orbital energy is considerably important.     

Unimolecular rearrangement of α-silylcarbenium ions. An ab initio study

The unimolecular rearrangements of hydrogen, methyl and phenyl groups at the Si atom in α-silylcarbenium ions have been investigated using an ab initio molecular orbital method. MP2/6–31 + G^*//HF/6–31G^* calculations predict that all three groups migrate from the Si to an adjacent C_α with no energy barrier. Thus, the silicenium ion is the only stable species in each potential energy surface. The conformation of the benzylsilicenium ion, (C₆H₅)CH₂−SiH₂⁺, indicates that the phenyl ring is significantly bent toward the silyl cationic center in order to interact with the vacant 3p(Si⁺) orbital. In contrast to MP2 results, Hartree-Fuck calculations (both HF/3–21G^* and HF/6–31G^* levels) predict small energy barriers for 1,2-migrations of H and Me (1.4 kcal mol⁻¹ for H migration, and 1.5 kcal mol⁻¹ for Me migration, respectively, at the HF/6–31G^* level). This difference provides convincing evidence that the incorporation of electron correlation is of particular importance in describing the potential energy surface for the rearrangement of α-silylcarbenium ions to silicenium ions. The results of the calculations have also been applied to the possible rearrangement mechanism of α-chlorosilanes to chlorosilanes, assuming that the experimental conditions are favorable toward the generation of ionic species. Various factors which may govern the migratory aptitudes of various R groups, i.e. (1) activation energies, (2) overall reaction energies and (3) the conformational preference of reactants have been investigated. The calculated activation energy obtained, namely the energy for the generation of the silicenium ion and the C⁻¹ ion from an α-chlorosilane, is consistent with the experimental migratory aptitude in the gas phase observed in mass spectrometers.     

Broken orbital symmetry and the description of valence hole states in the tetrahedral [CrO4]2− anion

The localization of ligand-based valence holes in the tetrahedral complex ion [CrO₄]^2? in a crystalline environment is studied by SCF calculations on the hole states, with progressively less restrictions on the spatial symmetry of the molecular orbitals. The final wavefunctions are obtained by constructing, from the symmetry broken SCF solutions, wavefunctions that exhibit again the proper transformation properties under the operations of T _d . The crystal environment of the [CrO₄]^2? anion is represented by a point charge model. In contrast with the situation for core hole states, the projection afterwards into T _d symmetry is important. The final ionization energies, which are obtained from projected C _3v adapted SCF solutions, are reduced considerably (?3 eV) with respect to the T _d ΔSCF results, but the ordering of the states has not changed essentially. The calculated ionization energies compare favourably with results of XPS experiments on Na₂CrO₄. The evaluation of the energies of projected symmetry broken SCF solutions requires the calculation of hamiltonian matrix elements between determinantal wavefunctions built from mutually non-orthogonal orbital sets. An efficient method for the calculation of such matrix elements is presented.     

Thomas-Fermi-Dirac calculations for molecules

The electrostatic potential derived from a solution to the molecular Thomas-Fermi-Dirac equation for F₂ is combined with the exchange potential and modified to give the correct behavior far from the nuclei. One-electron energy levels in this potential are calculated and are in qualitative agreement with SCF orbital energies. Similar computations are carried through for F and Ar, which correspond to the separated and united atoms for F₂. To compensate for errors in the potential, we subtract from molecular orbital energies the difference of TFD and SCF orbital energies for the separated atoms. Now all the orbital energies are correct to a few electron volts.

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Zusammenfassung Das elektrostatische Potential, das sich für F₂ aus der Thomas-Fermi-Dirac Theorie ergibt, wird mit dem Austauschpotential kombiniert und so modifiziert, daß sich das richtige Verhalten in Kernnähe ergibt. Die berechneten Einelektronenenergien sind in qualitativer Übereinstimmung mit SCF-Werten. Analoge Rechnungen für F und Ar werden ausgeführt und als Grenzfälle für Korrekturen verwendet. Dann ergeben sich alle Orbitalenergien bis auf wenige eV richtig.

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Supported by the National Science Foundation under Grant GP-20718.     

X-ray spectra and core hole energy curves of some diatomic molecules

Soft X-ray emission spectra of the molecules CO, N₂, NO and O₂ are examined for the purpose of deriving information on their core hole energy curves. Molecular force constant and equilibrium bond lengths are determined for the core hole species C*O and N₂*, and a qualitative analysis is made for CO*, N*O, NO* and O₂*. The results show that differences of equilibrium geometries between the core hole states and the ground states are very well reproduced (better than 1 pm) by SCF calculations within the Hartree-Fock formalism. Inclusion of anharmonicity in the Franck-Condon analysis gives a small but significant effect on the best fitted value for the core hole state bond lengths (about 0.5 pm). Oxygen is binding energies determined from the X-ray spectra are shown to agree with ESCA data, in most cases within a few tenths of an eV. Calculated ΔSCF transition energies reproduce the experimental data within a few eV.