Theoretical Bond Lengths Research Articles

Momentum distributions for two-electron systems: the Coulomb shift and correlation coefficients for the HeH+molecular ion

With the objective of gaining further insight into the effects of correlation on the electronic momentum distribution in small molecules, the authors have calculated the Coulomb shift Delta f(p12) for HeH+ in its ground state. For comparison, the Coulomb hole in position space Delta f(r12) has been reported at the theoretical bond length RTh approximately=1.4. By introducing the distribution function Delta g(p12, p1, theta 1) the authors have been able to examine the effects of correlation with respect to the magnitude and orientation of the momentum p1 for the 'test' electron 1; theta 1 is measured relative to the internuclear axis. Various 'radial' and 'angular' correlation coefficients were determined by evaluating several one- and two-particle expectation quantities, and they also obtained results for the spherically averaged Compton profile. The variations of the radial and angular components of correlation are examined as a function of the internuclear separation R. A brief discussion is also presented concerning the effects of correlation and bond formation on the molecular momentum density rho (p) at RTh approximately=1.4. The authors' results have revealed, once again, that momentum space is especially advantageous for an analysis of electron correlation into its radial and angular contributions.

Representations of molecular force fields. V. On the equilibrium structure of methane

The correction from mean (rg) to equilibrium (re) bond lengths in methane is reinvestigated in response to suggestions that the original Kuchitsu–Bartell (KB) corrections were excessive by as much as 0.006 Å. It is found that the KB model anharmonic force field with its original parameterization does overcorrect, relative to the new Pulay ab initio force field, but only by 10% of the original (rg−re) corrections, or 0.0022 Å for CH4 and 0.0015 Å for CD4. The KB model with the more recent MUB-2 nonbonded parameterization gives results in close accord with the ab initio results, supporting the utility of the augmented anharmonic Urey–Bradley representation of force fields. Reported discrepancies between experimental and theoretical methane bond lengths cannot be due solely to the form of or original parameterization of the KB model field.

The electronic structure of NO2. II. The ? 2B2← ? 2A1 and ? 2B1←? 2A1 absorption systems

The results of an accurate ab initio study of the electronic structure of NO2 have been applied to an analysis of the two important visible and near infrared absorption systems of this molecule. The long wavelength absorption (λ≳6000 Å) arises from an ? 2B2←? 2A1 transition. A theoretical absorption spectrum that is generated from the C2V ab initio potential surfaces of these two states qualitatively reproduces most of the features of an experimental low resolution absorption spectrum between 9000 and 6000 Å. The (0–0) band of the transition is predicted to be several times less intense than nearby hot bands even at temperatures as low as 300 K. The computed ? 2B2 spectroscopic parameters are Te=1.18 eV, Re=1.26 Å, ϑe=102°, ω1=1461 cm−1, ω2=739 cm−1, and μ=0.46 D. There is a marked difference between experimentally determined ? 2B2 rotational constants and those deduced from the ab initio equilibrium geometry; this datum adds to the rapidly increasing evidence for strong vibronic coupling of the ? 2B2 state with high vibrational levels of the ground electronic state. The theoretical spectroscopic parameters of the experimentally better understood ? 2B1 excited state are Te=1.66 eV, Re=1.20 Å, ϑe=180°, ω1=1192 cm−1, 2 ω2=960 cm−1, ω3=2040 cm−1, and μ=0.0 D. The adiabatic excitation energy, bond angle, and bending frequency are in good agreement with experiment. However, the theoretical equilibrium bond length is significantly shorter than the value deduced from the experimental spectroscopic data and possible reasons for this discrepancy are discussed.

Calculations of geometries of organic molecules using the CNDO/2 method—I : Empirical correlations between observed and calculated bond lengths in simple acyclics, strained cycloalkenes and some polycyclic molecules

It is shown that calculations of CC and CH bond lengths in hydrocarbons using the CNDO/2 semi-empirical MO method exhibit systematic deviations from the observed values. An empirical correlation relating the observed and calculated bond lengths with the number of substituents attached to the bond may be devised. This correlation is capable of providing theoretical bond lengths within 0·008 Å of the experimental for a wide range of simple acyclic molecules. Furthermore, calculations of molecular geometries for some strained cycloalkenes and also some larger molecules, e.g., naphthalene, biphenylene and azulene, are similarly found to be in good agreement with experiment.

Electronic spectrum and structure of 11,11,12,12-tetracyano-1,4-naphthaquinodimethane

The lower π-electronic states of 11,11,12,12-tetracyano-1,4-naphthaquinodimethane (TCNNQ) were calculated by the usual SCF-CI and the VESCF-CI methods within a Pariser-Parr-Pople scheme. The absorption spectrum of TCNNQ was measured in cyclohexane and methanol. The observed lower excitation energies were 3·14, 4·32, 4·5, 5·6 and 5·96 eV. The lower three excitation energies calculated by both methods are in good agreement with the observed values. It was shown that the effect of doubly excited configurations is far from being negligible. As for charge distribution, the VESCF method was found to give more reasonable results than the usual SCF method. Theoretical bond lengths obtained from bond orders suggest partial breakdown of the quinoid structure, which may be associated with the fact that the electron affinity of TCNNQ is relatively small compared with those of the 2,6-analogue and TCNQ.

The Crystal and Molecular Structure of Carbazole

Abstract The crystal structure of carbazole has been refined with three-dimensional X-ray data. Single crystals obtained from the melt are orthorhombic with four molecules in a unit cell of the dimensions a=7.772, b=19.182 and c=5.725 Å; space group is Pnma. Positional and thermal parameters were obtained by the least-squares method. The final discrepancy index R is 10.9% excluding zero intensity data. The e.s.d.’s in bond lengths not involving hydrogen atoms are 0.006–0.010 Å, and the corresponding errors in bond angles are about 0.5°. The molecule is planar within the deviation of 0.03 Å. A crystallographic mirror plane normal to the b-axis passes through the nitrogen atom and is perpendicular to the molecular plane. Comparison of the observed and theoretical bond lengths is made with discussion thereof. Some physical properties related to the crystal structure are also discussed by comparing its structure with that of fluorene. With the help of thermodynamical data, it has been argued that the hydrogen bond of N–H···N between molecules is not formed not only in the crystalline state but also in the liquid state.

A one-centre calculation for HeH+using orbitals with angularly dependent effective nuclear charges

Wave functions possessing effective nuclear charges which are explicitly angularly dependent have been used as a simple minimal basis set for a one-centre study of HeH+. Correlation effects were introduced by using spatially different orbitals for electrons of opposite spin. Although the basis functions themselves are of considerable interest, the values obtained for the molecular energy and the theoretical bond length were somewhat disappointing.

One-Center Study of the Rare-Gas Hydride Ions NeH+ and ArH+

The ground states of the rare-gas hydride ions NeH+ and ArH+ have been studied by means of the united-atom (UA) treatment. Values are reported for the energy, theoretical bond length, force constant, and the diamagnetic part of the molar magnetic susceptibility. However, the present work is primarily intended as a test of the UA approach and, as such, it was useful to compare the results with those obtained by the same treatment for HF and HCl. Also, it proved to be most instructive to analyze the forces which act on the protons within each molecular ion. As anticipated, the UA treatment of NeH+ and ArH+ met with meager success. Nevertheless, the analysis provided considerable understanding as to why a similar study, applied to neon- and argonlike molecules, yields fairly reasonable values for the above molecular properties when compared with experiment.

Bond lengths in diphenyloctatetraene

AbstractThe crystal structure of all trans‐diphenyloctatetraene has been refined. The C‐C bond lenghts from previous work were confirmed. The experimental bond lenghts are compared with the values calculated by the Hückel method both with constant and variable β, and with those calculated by the approximate SCMO method for three sets of parameters. The discrepancies between the best theoretical bond lengths and the experimental values need not be significant.

The HMO treatment of the ONO 2, NNO 2 and CNO 2 groups

Parameters have been chosen for the coulomb and resonance integrals for the HMO treatment of the ONO 2, NNO 2 and CNO 2 groups, which correctly predict values of the dipole moments of nitric esters, nitramines and aromatic C-nitro compounds. In most cases good agreement is also obtained between the theoretical and experimental bond lengths.

Self-consistent perturbation theory for conjugated molecules

Self-consistent bond polarizabilities are defined and computed for butadiene, benzene, naphthalene and anthracene. A self-consistent derivation of the bond order-bond length relationship is given and self-consistent formulae for force constants are obtained. Theoretical bond lengths for butadiene, naphthalene and anthracene are calculated in two ways; firstly by using the same values of βrs and γrs for all bonds and secondly by allowing these to vary with bond length. The agreement with experiment is very satisfactory although in some respects the first set of results is to be preferred. Force constants for ethylene and benzene are found which have the correct orders of magnitude although the detailed agreement is not always very good and the interaction force constant between meta bonds in benzene is predicted to have the wrong sign.

Appraisal of Some One-Center Calculations for the Neon- and Argonlike Series of Molecules

The united-atom (UA) method and the self-consistent-field one-center-expansion (OCE) treatment have been applied recently to the study of neonlike and argonlike molecules, namely, HF, H2O, NH3, NH4+, CH4, HCl, H2S, PH3, PH4+, and SiH4. In the present article, the values of physical properties predicted by each method are compared with the corresponding experimental quantities. For each molecule, comparisons with experiment have been made for the molecular energy, theoretical bond lengths, ``breathing'' force constants, and, for NH3 and PH3, the proton affinities. The radial density distribution of electrons, determined by us from the published OCE wavefunctions, has been used to calculate the coherent x-ray scattering factor for the gaseous state of each molecule. The electron densities were also used to determine the purely diamagnetic contribution χr to the total molar magnetic susceptibility. A comparison was made with the corresponding UA results and with the available experimental quantities. From the trend shown by the relationship between the theoretical and ``experimental'' values for χr, it was possible, for a molecule with Td symmetry, to suggest a range of values for the diagonal components (gjj″) of the electronic contribution (g″) to the molecular rotational gyromagnetic tensor (g). Hence, for SiH4, it was suggested that −1.48 < gjj″ < −1.31. No experimental value for this quantity is known by the authors. Although it is seen that the OCE results are, in most instances, superior to the results obtained from the UA approximation, the latter method still provides very useful results with comparatively little computation.

United-Atom Approximation Applied to Argonlike Molecules. II. PH2−, PH3, and PH4+

The united-atom treatment has been applied to the systems PH2−, PH3, and PH4+. For PH3 and PH4+, satisfactory values are obtained for the total molecular energy and ``breathing'' force constants when compared with experiment. The model gives theoretical bond lengths which are in good agreement with the observed values. Coherent x-ray scattering factors are presented for PH3 and PH4+ along with a discussion of the molar diamagnetic susceptibilities. The value of the proton affinity derived here for PH3 is found to be in general agreement with the experimental results. Except for the considerable improvement in the proton-affinity calculation, the results obtained here are in keeping with the conclusions derived from our earlier work concerning the united-atom study of H2S.

United-Atom Approximation Applied to Argonlike Molecules. I. Hydrogen Sulfide

The united-atom approximation was applied to H2S and also to the systems HS— and S——. The wavefunction obtained for H2S was used to calculate the molar diamagnetic susceptibility and the coherent x-ray scattering factor for the gaseous form of the molecule. Values are also reported for the ``breathing'' force constant for H2S and for the theoretical bond length for both H2S and HS—. Within the present approximation a calculation was made of the bond energy for H2S dissociating into HS and S. The proton affinities for HS— and S—— were also determined. Where possible, a comparison was made with experiment. In general, except for the proton affinities and bond-energy calculation, the united-atom model applied to H2S was reasonably successful. A comparison was also made between the present radial density and the density of electrons for H2S provided by the model of ``floating'' hydrogen densities. This comparison helps to substantiate the claim made earlier, namely, that the model of ``floating'' hydrogen densities will provide a very reasonable radial distribution of electrons within molecules of the form XHn.

Bond-Lengths and Force Constants for Methane, Silane and Germane

IN a recent paper by one of us (N. H. M.1), a detailed discussion of the electron distributions and potential fields for molecules of high symmetry was given on the basis of the Thomas–Fermi theory. In this work the nuclei of the outer atoms were smeared out over the surface of a sphere and the electrons then regarded as moving in the resulting spherically symmetrical field. A general discussion of the energy was also given, and the existence of a minimum in the energy curves was demonstrated. However, the theoretical bond-lengths were in poor agreement with the experimental values, and it was suggested that this might be due to the neglect of exchange.