Chemical shift bond derivatives for molecules containing first-row atoms

The primary and secondary first and second derivatives of the NMR isotropic chemical shift with respect to bond length modification have been calculated in the gauge invariant atomic orbital (GIAO) perturbed Hartree–Fock approach for some 177 first-row nuclei in 63 molecules using the mixed basis heavy:6–311G(d)/hydrogen:4–31. The shift derivative with respect to multiple bond length changes correlates linearly with the shift itself while changes involving single bonds behave differently. Agreement between experimental derivatives and those calculated theoretically is good but the calculations show that second derivatives as well as both types of secondary effects cannot always be neglected. The correlation between the shift derivative and the isotropic shift indicates an exponential variation of the chemical shift with bond length near the vicinity of the equilibrium structure for multiple bonds.     

Valency. II. Applications to molecules with first-row atoms

A quantum chemical definition of valency proposed in Part I is used to calculate the valency of carbon, nitrogen, oxygen, lithium, beryllium and boron in a number of compounds with the SINDO1 method. It is demonstrated that consistency of the basis set is necessary for comparable results. The general features of valency and bonding in these molecules are discussed. The π-electron concept of free valence is generalised to sigma systems and atoms in molecules are classified as subvalent, normal or hypervalent. The relation between valency and natural hybrid occupancy is illustrated. The symmetry properties of natural hybrid orbitals are discussed by means of group theory. A preliminary attempt is made to relate covalency and covalent reactivity. Bond indices and the σ, π character of bonds are obtained by a suitable partitioning and projection of valency into bonding and antibonding contributions. Alexander von Humboldt Fellow 1982–83.     

Core-valence correlation effects for molecules containing first-row atoms. Accurate results using effective core polarization potentials

The accuracy of employing effective core polarization potentials (CPPs) to account for the effects of core-valence correlation on the spectroscopic constants and dissociation energies of the molecules B₂, C₂, N₂, O₂, F₂, CO, CN, CH, HF, and C₂H₂ has been investigated by comparison to accurate all-electron benchmark calculations. The results obtained from the calculations employing CPPs were surprisingly accurate in every case studied, reducing the errors in the calculated valence D _e values from a maximum of nearly 2.5 kcal/mol to just 0.3 kcal/mol. The effects of enlarging the basis set and using higher-order valence electron correlation treatments were found to have only a small influence on the core-valence correlation effect predicted by the CPPs. Thus, to accurately recover the effects of intershell correlation, effective core polarization potentials such as the ones used in the present work provide an attractive alternative to carrying out computationally demanding calculations where the core electrons are explicitly included in the correlation treatment. Received: 11 May 1998 / Accepted: 27 July 1998 / Published online: 28 October 1998     

Contracted well-tempered Gaussian basis sets in SCF calculations on the ground and excited electronic states of neutral and ionized diatomic molecules containing first-row atoms

Summary Calculations were done on ground and excited states of C₂, C ₂ ⁺ , C ₂ ^– , N₂, N ₂ ⁺ , O₂, O ₂ ⁺ , O ₂ ^– , CO, CO⁺, CO²⁺, and CO^– using contracted well-tempered basis sets. The (14s 10p) basis sets were augmented with threed, one or twof, and oneg functions. Total energies, orbital energies, and spectroscopic constants were compared with the best available computational data.     

Extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms. I. Methodological developments

An extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms is presented. In addition to the use of pseudo-potentials in the calculations, the consequences of this extension on the different components of the energy partition which is the basic idea of the method, is analysed. Particular emphasis is placed on the specific role played by the 3d orbitals in each of the energy components. First, at the zeroth order, the energy is found to be very sensitive to the optimization of the 3d polarization functions. Secondly, the internal correlation energy, calculated by CI, requires the optimization of distinct 3d correlation orbitals to describe adequately the strong near-degeneracy effects that occur within the valence space. Finally it is shown that the 3d orbitals contribute partially to the non-internal correlation energy and that, the atoms-in-molecule structures corresponding typically to all-external contributions are negligible. The concept of error energy is introduced in place of the non-internal correlation energy: it includes the relativistic contributions within the semi-empirical tables. Such tables are presented for second row atoms and for the chlorine atom. From these tables, predicted values for some atomic term energies, experimentally undetermined, are derived. The methodological tests are limited here to the chlorine atom which is chosen for further applications in the next paper of this series. The conclusions concerning the applicability of the method to third row atoms are however quite general.Boursier I.R.S.I.A     

Elastic scattering and rotational excitation of nitrogen molecules by sodium atoms

A quantal study of the rotational excitation of nitrogen molecules by sodium atoms is carried out. We present the two-dimensional potential energy surface of the NaN(2) complex, with the N(2) molecule treated as a rigid rotor. The interaction potential is computed using the spin unrestricted coupled-cluster method with single, double, and perturbative triple excitations (UCCSD(T)). The long-range part of the potential is constructed from the dynamic electric dipole polarizabilities of Na and N(2). The total, differential, and momentum transfer cross sections for rotationally elastic and inelastic transitions are calculated using the close-coupling approach for energies between 5 cm(-1) and 1500 cm(-1). The collisional and momentum transfer rate coefficients are calculated for temperatures between 100 K and 300 K, corresponding to the conditions under which Na-N(2) collisions occur in the mesosphere.     

Ground states of molecules. 56. MNDO calculations for molecules containing sulfur

MNDO has been extended to sulfur, but without inclusion of 3d AO s. Calculations are reported for heats of formation, geometries, dipole moments, and ionization energies of a variety of sulfur-containing molecules. The average discrepancy between calculated and observed heats of formation is larger than for compounds of other elements, a difference probably due, at least partly, to the lower accuracy of the thermochemical data for sulfur compounds. The calculated dipole moments agree well with experiment as do the calculated ionization energies, except for those corresponding to ionization from sulfur “lone-pair” orbitals which are too high by ca. 1 eV, probably as a result of the neglect in NDDO of interactions between inner and valence shell orbitals. As in the case of other third-period elements, the calculated heats of formation of compounds of sulfur in its higher valence states (S^IV, S^VI) were too positive by large amounts, due presumably to the neglect of 3d AO s.     

Ground states of molecules. 53.MNDO calculations for molecules containing chlorine

MNDO calculations of heats of formation, dipole moments, ionization potentials, and structures are reported for a wide range of compounds containing chlorine in its characteristic valence state (Cl^I) and one or more of the elements H, B, Be, C, N, O, and F. The calculated errors in the heats of formation and the dipole moments are not significantly greater than those previously reported for compounds containing no chlorine. First vertical ionization potentials were on average 0.95 eV too high. The ordering of higher cationic states was found to be correct, even for species such as Cl₂O, Cl₂, and HOCl, where ab initio–Koopmans' theorem calculations predict the incorrect ordering. The calculated energies and geometries of compounds such as CIF₃ are qualitatively incorrect, probably because of the lack of 3d atomic orbitals in the orbital basis set.     

Determining the geometry of hydrogen bonds in solids with picometer accuracy by quantum-chemical calculations and NMR spectroscopy.

The structure of multiply hydrogen-bonded systems is determined with picometer accuracy by a combined solid-state NMR and quantum-chemical approach. On the experimental side, advanced 1H-15N dipolar recoupling NMR techniques are capable of providing proton-nitrogen distances of up to about 250 pm with an accuracy level of +/-1 pm for short distances (i.e., around 100 pm) and +/-5 pm for longer ones (i.e., 180 to 250 pm). The experiments were performed under fast magic-angle spinning, which ensures sufficient dipolar decoupling and spectral resolution of the 1H resonance lines. On the quantum-chemical side, the structures of the hydrogen-bonded systems were computationally optimised, yielding complete sets of nitrogen-proton and proton-proton distances, which are essential for correctly interpreting the experimental NMR data. In this way, nitrogen-proton distances were determined with picometer accuracy, so that vibrational averaging effects on dipole-dipole couplings need to be considered. The obtained structures were finally confirmed by the complete agreement of computed and experimental 'H and '5N chemical shifts. This demonstrates that solid-state NMR and quantum-chemical methods ideally complement each other and, in a combined manner, represent a powerful approach for reliable, high-precision structure determination whenever scattering techniques are inapplicable.     

Geometry optimization calculations in molecules containing second row atoms with various polarization function basis sets

Ab initio MO geometry optimization studies on a number of molecules containing second-row atoms using various polarization basis sets are presented. In particular the use of gaussian bond functions is shown to be a good substitute for the more conventional (and expensive) atom-centered d functions. Molecules examined to a double zeta plus polarization basis set level are HCP, P₂, SO, SO₂, H₂S, SF₂, CIF, HCl and Cl₂.     

On the fixed-nuclei approximation as applied to rotational excitation of molecules by atoms

The applicability of the fixed-nuclei approximation to the rotational excitation of a diatomic molecule by an atom is investigated. The approximation is shown to predict accurate quantum cross sections for the model system H₂ + N₂ at thermal collision energies. A quasi-classical Monte-Carlo study of the same problem is also performed, and the success of the fixed-nuclei approximation is interpreted by investigating in detail a number of coplanar classical trajectories.     

A correlation of excited state rotational constants for diatomic molecules

The concepts of “orbital stress” and “transition stress” are defined and applied to N₂, N⁺₂, CO, and CO⁺. The bond lengths and rotational constants of excited electronic states are related to the transition stress, and the response of the electrons and nuclei to the transition stress is shown to be a molecular property, essentially independent of the electronic configuration or state.     

The effect of electronegative atoms on the structures of hydrocarbons. ab initio calculations on molecules containing fluorine or (carbonyl) oxygen

A series of ab initio calculations have been carried out, using the 4-21G basis set. Ethane and propane were first studied to obtain reference points. The effect of adding an electronegative atom (fluorine, or carbonyl oxygen) onto the framework was then studied as a function of the torsional angle about the single bond. Some pronounced trends in structural changes were observed, and these can in part be correlated with hyperconjugative effects. For example, fluoroethane has bond lengths which are shorter than those in ethane itself, by 0.024 Åin the C C bond, and 0.003 Åin the α C H bonds. These changes are essentially torsionally independent. On the other hand, in propionaldehyde, the C C bond length of the methyl group and the C H bond lengths of the hydrogens attached to the alpha carbon vary as a function of the torsion angle. If the methyl C C bond in the carbonyl plane is taken as a reference, the bond stretches .016 Åwhen the torsion angle is increased to 90°, an α C H bond similarly stretches up to .007 Å. Many of these geometric changes are large, well beyond the experimental errors in modern measurements.     

Diamagnetic shielding constants of first-row atoms: Studies with a piecewise exponentially decaying electron density function

The piecewise exponentially decaying electron density model of Wang and Parr is used to calculate the diagmagnetic shielding constants of first-row atoms. Numerical results are presented for all first-row atoms and comparisons are made with the results obtained from the one-zone (i.e., single exponential) model. Results obtained from the two-zone (i.e., piecewise exponential) model are in better agreement with the Hartree–Fock results.     

The use of interparticle coordinates in electronic energy calculations for atoms and molecules

The use of interparticle coordinates in atomic and molecular calculations is reviewed and emphasized. For states where the wave function is dependent only upon interparticle coordinates the Hamiltonian is a relatively simple expression. If the wave function is a linear combination of products of functions of single interparticle coordinates of the exponential power form the formulas for local energy are particularly simple.

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Zusammenfassung Es wird über Teilchenabständc als Koordinaten in Atom- und Molekülproblemen referiert und auf ihren Wert hingewiesen. In Fällen, wo die Wellenfunktion nur von Teilchenabständen abhängt, wird der Hamilton-Operator verhältnismäßig einfach. Ist die Wellenfunktion eine Linearkombination von Produkten von Potenz-Exponential-Funktionen einzelner Teilchenabstände, so werden die Ausdrücke für die lokale Energie besonders einfach.

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Résumé L'auteur fait une revue et souligne l'importance de l'emploi des distances relatives des particules comme coordonnées pour les calculs atomiques et moléculaires. Pour des états dont les fonctions d'onde ne dépendent que de ces distances le l'Hamiltonien devient relativement simple. Si la fonction d'onde s'écrit comme une combinaison linéaire de produits de fonctions exponentielles (à puissances) ne dépendant que d'une seule coordonnée interparticulaire, les formules pour l'énergie locale se simplifient particulièrement.