Theoretical studies of atmospheric molecules: SCF and correlated energy levels for the NO2, NO 2 + and NO 2 − systems

SCF and MC-SCF/CI calculations were carried out on the low-lying electronic states of NO₂, NO ₂ ⁺ and NO ₂ ^– , using a double-zeta quality basis set of contracted Gaussian functions. The calculations were performed primarily at the equilibrium geometry (R _NO = 2.25 a_o, _ONO=134 °) of theX ² A ₁ state of NO₂. SCF calculations on NO ₂ ⁺ in a linear conformation were also performed. Results are presented and compared with experiment and other calculations.Research supported in part by Air Force Delivery Orders F33615-72-M-5015 and MIPR889474-00117 and Air Force Office of Scientific Research and in part by the United States Energy Research and Development Administration.     

The instability of the planar structure of carbanion ⊖:CH2-CN

Ab initio SCF calculations using uniform quality extended basis set supplemented with polarization functions predict a slightly pyramidal carbanion centre in :CH₂-CN. This finding is in contrast to the usual finding of planar geometry of carbanion centres generated next to other conjugative groups. Although the predicted barrier to pyramidal inversion is very small (0.1 kcal/mole) it is estimated that correlation energy contributions, neglected in any SCF calculations, may be too small to remove the barrier. The present results confirm earlier experimental findings that counter-ion and solvent effects can have a dominant role in determining the geometry of this unusual ion in actual chemical systems.     

Muscarine and water: Ab initio potentials

Ab initio SCF-LCAO-MO (Self Consistent Field-Linear Combination Atomic Orbitals-Molecular Orbital) computations have been carried out on the muscarine ion in different conformations. The rotational barrier around the C3-C2-C1-N dihedral angle has been calculated and the results show that the molecule possesses a fairly rigid structure in this respect. The rotational barrier around the HO2-O2-C4-H4 dihedral angle ( ₂) was also analyzed, and it was found that in vacuum the preferred conformation is the one with ₂=0.SCF calculations have also been carried out on the muscarine-water system at many different separations and/or orientations. The interaction energies were then fitted to pair potential functions, which allowed makeup of isoenergy maps that explicitly show the interaction minima and the repulsive regions. These potential functions are also necessary in order to carry out statistical simulations of the molecule water solution.In order to assess the role of the ring methyl group in muscarinic activity, the interaction of the demethylmuscarine molecule with water was also studied; the results show that the loss of the terminal methyl leads to a distinct loss of hydrophobic character.     

Ab initio study of hydrazoic acid

SCF and CI calculations were carried out on the ground^1A state of HN₃. The equilibrium geometry and vibration frequencies were computed. The results point to a planar structure (groupC _s) but to a non-linear (170 °) N-N-N conformation. The calculated vibration frequencies are in fair agreement with experimental assignments.The dissociation path of the molecule to NH and N₂ products was investigated and compared to the isoelectronic reaction of diazomethane. The dissociation energy of hydrazoic acid is estimated to be about –8 kcal/mole, with a potential barrier to dissociation of about 30 kcal/mole.Boursier IRSIA     

Ab initio study of the He(1S)-Li2(X̃, 1∑) interaction by the SCF and MP2 methods

Ab initio electronic structure calculations have been carried out for the He(¹S)-Li₂ (X?, ¹∑) interaction both by the single-configuration SCF and correlated second-order MP2 methods using an extended basis set. From these calculations, an estimate of the isotropic (V₀) and first two anisotropic (V₂ and V₄) terms of the He-Li₂ potential surface has been obtained. An assessment of the leading induced-dipole-induced-dipole dispersion energy is presented from the MP2 energies. Where possible, a comparison is made with previous unpublished ab initio calculations by Staemmler and Stahl using the CEPA method.     

MCSCF study of polaron- and bipolaron-like defects in smallall-trans conjugated polyenes

Summary A Multiconfigurational Self-Consistent Field study of neutral, singly and doubly ionized C₄H₆, C₆H₈, C₈H₁₀, and C₁₀H₁₂ as model systems for polaron and bipolaron defects in polyacetylene has been carried out. In all computations a double zeta quality basis set was used. The post-Hartree-Fock computations were carried out in the complete active subspace and the fully optimized structures are reported. Comparison with SCF results reveals that the inclusion of electron correlation attenuates the double bond/single bond alternancy in conjugated polyenes as well as the charge waves associated with the cations.Dedicated to Prof. Klaus Ruedenberg     

The ground state of MoCr(O2CH)4 at theab initio SCF and CI levels. A symmetry adapted RHF energy functional with an artificial double minimum

Ab initio restricted Hartree-Fock (RHF) calculations carried out on the ground state of MoCr(O₂CH)₄ lead to two distinct energy minima according to the initial guess made for the set of trial vectors. It is shown that these two symmetry-adapted wavefunctions can be correlated with a twofold degenerate broken-symmetry solution previously characterized for the related system of higher symmetry Cr₂(O₂CH)₄. Complete CI expansions have been carried out from either RHF polarized wavefunction using as a basis the set of eight frontier MO's with high metal character. These expansions yield poorly resymmetrized wavefunctions. A similar CI expansion has finally been carried out from a wavefunction resymmetrized at the SCF level and corresponding to a saddle point of the RHF energy hypersurface. The total energy associated with this latter expansion is the lowest obtained in the present work. The natural orbital analysis corresponds to ()^1.86()^3.58()^1.54()^0.46()^0.42 (^*)^0.14 and shows that this resymmetrized CI expansion is in many respects similar to the correlated wavefunctions obtained for the homobinuclear parent systems.     

Relative stability of the2 A 1g and2 E g states of the C2H 6 + ion

Anab initio study of the relative stability for the states² A _1g and² E _g of C₂H ₆ ⁺ has been carried out. The results of the Open Shell Restricted Hartree-Fock calculations lead to assign the² A _{1 g} as the ground state of the molecule in agreement with previous SCF calculations.The correlation energy associated to both states has been calculated within the correlation hole model and the results, contrary to those obtained from Configuration Interaction calculations, do not alter qualitatively the conclusions from SCF.     

MO-Berechnungen an Heterocyclen, 24. Mitt.: Eine Interpretation der UPS der 2,2′-und 4,4′-Bipyridyle und deren N-Monoxide

The He I photoelectron spectra (UPS) of the 2,2- and 4,4-bipyridyls and their mono-N-oxides habe been reported and interpreted on the basis of modified CNDO-type calculations. The calculations show that the sequence of the eigenvalues _i is nearly independent from the dihedral angle around the central bond and that the different pattern of the _i must be related to the different positions of the N-atoms. For the N-oxides an assignment is given up to 12eV using the calculated results. Furthermore, the conformations of these compounds has been discussed.

23. Mitt.:Remane, H., Kluge, G., Scholz, M., Z. phys. Chem. (Leipzig), im Druck.     

An SCF study of 10-vertex and 12-vertex boranes and heteroboranes

For symmetry-constrained boranes B₁₀H, B₁₂H, and their valence isoelectronic analogues containing a single hetero atom, completely optimized geometries were obtained using Hartree–Fock SCF calculations with the 3-21G and 6-31G* basis sets. For the anionic and dianionic species, the geometry optimization was also carried out using the 6-31 + G* basis set. Harmonic vibrational frequencies were obtained at HF/3-21G level. The results compare well with experiment where available.     

On the dimerization process of nitroso compounds

Summary Many organic C-nitroso compounds R-NO form stable dimers with a covalent NN bond. To gain insight into the dimerization reaction 2 R-NO (R-NO)₂ a theoretical study of the dimerization to atrans-form was performed using HNO as a model compound. Complete geometry optimizations were carried out at the HF, MP2 and QCISD levels using a 6–31G* basis. In the stationary points energies were calculated at the MP4(SDTQ) and QCISD(T) levels. For the equilibrium structure of the monomer and dimers stable RHF solutions were found, whereas for the TS UHF and UMPn calculations were applied. Extensive spin contamination was found in the UHF wavefunction, and projections up tos+4 were invoked. Relative energies were corrected for differences in ZPE. Calculations were made (a) for the least-motion path (C _2h symmetry) and (b) for a path with complete relaxation of all internal coordinates. Along the latter path a TS having virtuallyC _i symmetry was found. Along path (a) an activation energy of around 150 kcal/mol was predicted, in conformity with a symmetry forbidden reaction. On the relaxed path (b) the barrier to dimerization was estimated to be 10.7 kcal/mol at the MP4(SDTQ)//MP2 level, and 10.9 kcal/mol at the QCISD(T)//QCISD level. Unscaled ZPE corrections, calculated at the SCF level, changed these values to 12.7 and 12.9 kcal/mol, respectively. The reaction energy for the dimerization process is predicted to be – 17.2 kcal/mol at the MP4(SDTQ)//MP2 level corrected for ZPE. Calculations at the G1 level gave a corresponding value of – 16.4 kcal/mol. The equilibrium constant for the association to thetrans dimer is estimated to beK _p =259 atm, indicating that the dimer should be an observable species in the gas phase.     

Topological analysis of the charge density response of a Ni4 cluster to a probe H2 molecule

Local density self-consistent field (SCF) discrete variationalX calculations are performed on a Ni₄ tetrahedron interacting with a probe H₂ molecule in special geometries. Optimized basis functions generated from the spherically averaged SCF potential are used. Topological charge-density analyses and binding energy calculations are used to study a portion of the energy surface for the approach of the H₂ molecule toward the Ni₄ tetrahedron. The effect of the H₂ molecule on Ni-Ni, Ni-H bonds and changes in the H-H covalent bond are investigated with the help of the field and various data at its critical points. The qualitative relationship between these data and the calculated binding energies is exploited.     

An investigation of the relative stabilities of the isomers of CF2N2: Comparison of ab initio and MNDO calculations

Ab initio SCF calculations at the HF/3-21G level and semi-empirical MNDO calculations have been used to locate the stationary points on the CF₂N₂ energy surface. Perfluorodiazomethane is predicted to be most stable isomer, but perfluorodiazirine is predicted to lie only ca 41 kJ higher in energy at the SCF level. There are significant differences between the ab initio and MNDO results for the ordering of some of the isomers. Frequency calculations give results in good agreement with the limited experimental data on these molecules.     

Ab initio MRD–CI calculations on cubane (neutral,carbocation, carboanion) and dissociation of nitrocubanes based on localized orbitals

Ab initio MRD –CI calculations based on localized orbitals were carried out for cubane (neutral, carbocation, carboanion) both in our customary MODPOT basis set and in an all-electron 4–31G basis set. The calculated MRD –CI charge distributions on C1 (the skeletal atom from which the H^? or H⁺ was removed) (ab initio MODPOT neutral 4.221, carbocation 3.796, carboanion 4.282; all-electron 4–31G neutral 6.171, carbocation 5.717, carboanion 6.078) indicate that the + or - charge does not remain localized on C1 but redistributes itself. This has significant implications for preparative reactions of energetically substituted cubanes. The MRD –CI population analyses differ somewhat from the SCF population analyses, especially in the calculated total overlap populations. To investigate this effect on electrostatic molecular potential contour (EMPC ) maps generated from SCF or MRD –CI wave functions, we wrote additional routines to calculate EMPC maps from MRD –CI wave functions. The EMPC maps generated from SCF or MRD –CI wave functions are different if the molecule needs an MRD –CI multideterminant wave function to describe it adequately. The EMPC map is a one-electron property. One-electron properties are derived from the 1-matrix. The 1-matrix is different for SCF or MRD –CI wave functions. Thus, all the one-electron properties (EMPC maps, population analyses, bond deviation indices, etc.) are different when calculated from SCF or MRD –CI wave functions if MRD –CI wave functions are necessary to describe a system properly. We calculate these one-electron properties from the 1-matrix from the final natural orbitals. Our preliminary calculations for the dissociation pathway indicate it takes more energy to dissociate a bond in 1-nitrocubane than in octanitrocubane. Even in their ground electronic states at equilibrium geometry, both 1-nitrocubane and octanitrocubane require MRD –CI wave functions to describe them properly. The c² of the single determinant SCF wave function is only 0.8401 for 1-nitrocubane and 0.8300 for octanitrocubane. There are contributions from skeletal excitations as there are for cubane itself as well as excitations involving the nitrogroup. As the bond in nitrocubane is dissociated to 8.00 bohrs, the c² of the SCF contribution drops to only 0.4606 (1-nitrocubane) and 0.4445 (octanitrocubane). At this C₁? N₁ intermolecular distance, the largest excitations are in the C₁? N₁ bond: (C₁? N₁)² → (C₁? N₁*)², (C₁? N₁) → (C₁? N₁*). We also calculated the first electronically excited state for the dissociation pathway for selected points for both 1-nitrocubane and octanitrocubane.     

Ab initio calculations ofp-Cl2C6H4 molecule and its35Cl NQR parameters

Ab initio calculations ofp-dichlorobenzene molecule were carried out using the Hartree-Fock method in the 6–31 G* valence-split basis set. The molecule was also calculated by the MNDO method in the valence sp-basis set for comparison. The populations of the valent p-orbitals of the C and CI atoms were analyzed. The optimized geometry of the molecule as well as its³⁵Cl NQR frequency and the asymmetry parameter of the electric field gradient at the³⁵CI nuclei calculated using the populations of the less diffuse components of the valent p-orbitals of the Cl atoms are in agreement with the corresponding experimental values for the -modification of 1,4-Cl₂C₆H₄.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 2177–2179, September, 1996.     

Ab initio study,including electron correlation,of the electronic structures,the dipole moments,the static polarizabilities and of the harmonic force fields of H2CO,H2CS and H2SiO

Ab initio calculations including electron correlation (on the PNO-CI and CEPA-PNO levels) are carried out for the isovalence electronic molecules H₂CO, H₂CS and H₂SiO, and for comparison also for H₂O and CO. The CEPA equilibrium distances are accurate to within 0.003 Å, while SCF results show significantly larger errors. The harmonic force constants on CEPA level are satisfactory as well, but for stretching of double or triple bonds inclusion of singly substituted configurations is imperative. Dipole moments were obtained with an error of 0.1 Debye from CEPA calculations with sufficiently large basis sets and inclusion of singly substituted configurations. The dipole polarizabilities are less sensitive to correlation effects but require larger basis sets.The population analysis reveals that the SiO bond in H₂SiO is highly polar and thatd-AO's cannot be regarded as valence AO's in any of the molecules of this study. The binding energy of H₂SiO (with respect to H₂Si(¹ A ₁) + O(³ P)) is predicted as 140 ± 5 kcal/mol. The contributions of different pairs in terms of localized orbitals to the correlation energy of the molecules of this study are analyzed.     

Ab initio SCF investigation of the intramolecular hydrogen bonding in δ-aminopentanoic acid

The potential energy surface of the neutral form of-aminopentanoic acid was investigated by means of ab initio 4-31G SCF calculations. Four symmetry unique local minima are stabilized by an intramolecular O-H NH₂ hydrogen bond. The geometries, energies, and wave numbers of these conformers are reported. The hydrogen bond is discussed with respect to all reactions of these conformers and in comparison with the homologues glycine,-alanine, and-aminobutyric acid and also with the bimolecular adducts between formic acid, acetic acid, and propionic acid, on the one hand, and ammonia, methylamine, and ethylamine, on the other hand.     

Physical properties of many-electron atomic systems evaluated from analytical Hartree-Fock functions

Two types of approximate functions have been tested through the evaluation of various physical properties: for ground states, double-, SCF functions have been used, while for excited states the calculations have been carried out using the expectation values obtained from the Hartree-Fock functions for the corresponding lowest configuration. The agreement with the Hartree-Fock values or the experimental results, respectively, can be considered to be very satisfactory.This work has been supported in part by the National Research Council of Canada.     

Restricted rotation about partial C,N double bonds

The restricted rotation about the partial C,N double bond in 2-chloro-6-NR₂-pyran-4-ones is discussed in the light of NMR spectroscopic data and theoretical calculations.Ab initio calculations at the HF/6-31G^* level were carried out using a continuum model to take solvent effects into account. The delocalization of-electron density [described by natural bond orbital analysis (NBO)] was applied to determine the degree of conjugation in the ground state (GS) and in the transition state (TS) for the restricted rotation of the compounds studied. The reason for the different barriers to rotation of the NR₂ substituents (pyrrolidino > dimethylamino > morpholidino > piperidino) at the 2-chloro-pyran-4-one ring appears to be the different steric hindrance of the NR₂ substituents in the GS for the restricted rotation.     

1-(Nitrosoamino)benzimidazoles Containing Electron-acceptor Substituents at the Amine Nitrogen. Theoretical and Experimental Investigation of Conformational Mobility

The previously unknown 1-(N-nitrosoallylamino)- and 1-(N-nitrosopropargylamino)benzimidazoles have been synthesized and they exist in solution as a mixture of the E- and Z-conformers due to hindered rotation around the N-N(O) bond. The activation energies for the EZ transition in these compounds and for the model N-benzyl analog have been determined by a dynamic ¹H NMR method. With a view to studying the effect of a substituent at the amino nitrogen on the EZ isomerization we have carried out 3-21G and 6-31G** type ab initio calculations of the stable conformers of a series of N-nitrosohydrazines.