Calculated Resonance Energies Research Articles

Least-squares technique for resonances

A modified version of the least-squares variational technique is proposed to calculate resonance energies and widths with the help of the coordinate-rotation method. A numerical example is given for a model potential.

Calculation of Resonance Energies of Some Alternant Hydrocarbons

Calculation of Resonance Energies of Some Alternant Hydrocarbons

Conjugated circuits and resonance energies of benzenoid hydrocarbons

A concept of conjugated circuits contained in Kekulé forms of benzenoid hydrocarbons is considered. Circuits of size (4 n + 2) in which CC single and double bonds formally alternate are enumerated and serve as the basis for the characterization of a given system. Resonance energies of benzenoid systems are given by contributions of conjugated circuits of different size. The scheme permits the expression of resonance energies of different molecules in terms of selected reference compounds, such as linear acenes. The approach is illustrated on a dozen benzenoid hydrocarbons and the calculated resonance energies are on average within 0.05 eV of the values obtained by SCF MO calculations.

Calculation of Resonance Energies of Some Alternant Hydrocarbons

Calculation of Resonance Energies of Some Alternant Hydrocarbons

The Resonance Energies of Polyacenes and Related Compounds

Abstract The resonance energies of polyacenes were determined on the basis of the additive principle of π-bond energies in nonaromatic compounds. The additive components in the total π-energies for these compounds were reasonably estimated from the infinitely large polyacene. The calculated resonance energies appear to be much improved as compared with those calculated by Hess and Schaad.

Thermochemical parameters for benzenoid hydrocarbons

The heats of atomization of aromatic hydrocarbons are correlated with an incremental 5-term scheme that includes CH and CC bond energy terms, resonance energies, and two steric parameters. Regression analysis of the experimental data with respect to the proposed parameters gives reasonable values for each term. A simple method for calculating resonance energies is illustrated that agrees with the results of SCFLCAOMO calculations.

A compound atom state in neon. Bound-state calculation of resonance energy

The first resonance energy in elastic electron scattering from neon is estimated from a single-configuration Hartree-Fock calculation of the resonance state. Radial wave functions and other related parameters for the Ne- ion in the configuration (2p)5 (3s)22P are tabulated.

On the aromaticity of heterocycles containing the amine nitrogen or the ether oxygen

A new method of predicting aromaticity [B. A. Hess, Jr. and L. J. Schaad, J. Am. Chem. Soc. 93, 305 (1971)] is extended to conjugated heterocyclic systems containing the amine nitrogen or the ether oxygen. Coulomb and resonance integrals for these atoms were determined using experimental heats of atomization. Empirical π bond energies for the carbon-heteroatom bonds were determined from heteroatom containing acyclic molecules. These were in turn used to calculate the HMO π resonance energies of a wide variety of heterocyclic compounds. An excellent correlation between calculated resonance energy and experimental aromaticity was found.

Single-particle formulation of electron-atom scatterings with strong correlation effects

The continuum shell model with configuration interactions is reformulated in terms of the commuting single-particle projection operators. Diagonalization of the energy submatrix for the target state configurations constructed from the single-particle basis provides improved threshold energies and allows a simple form of open-channel projection operators. The continuum electron is treated by solving a set of coupled integro-differential equations with complete exchange symmetry. The correlation effect is included as an effective distortion potential which is to be estimated variationally using either the single-particle or the Hylleraas form of wave functions. The nonorthogonality of the exchange channel wave functions, the calculation of resonance energies and their widths, and approximate bounds on scattering parameters are discussed. Two- and three-electron scattering systems are considered in some detail.

Stabilization Method of Calculating Resonance Energies: Model Problem

Resonance energies of elastic scattering from one dimensional model potential containing barrier, using stabilization method

Generalized Variational Bounds for Multichannel Scatterings

The variational bounds on scattering parameters are reformulated without the explicit use of multichannel projection operators, thus avoiding completely the difficulty of nonorthogonality in rearrangement and exchange collisions. Resonance-energy calculations can be carried out using the operator which is effectively projected on the closed channels.

Quasimolecular states in the interaction between 12C and 12C nuclei

The resonances observed in the reactions of 12C on 12C at the energies just about the Coulomb barrier are investigated by assuming the molecule-like compound state formed by the two carbon nuclei, one in the ground state and another in the first excited state. These compound states are assumed to be coupled to the incident channel only and a resonance formula for the amplitude of the elastic scattering is derived. The interaction potential between two carbon nuclei is that obtained by introducing the effects of deformation and a repulsive core into spherical optical potential. The depth of the potential is taken to be rather shallow (≈ −20 MeV). The numerical calculations show that the energies of the compound state are approximately reproduced with the rotational deformation parameter of β ≈ −0.2. The calculated resonance energies are slightly shifted from the level energies of the compound states, and the reasonable carbon widths are obtained.

Level Shifts of Shell-Model States in the Continuum

A unified theory of nuclear reactions has been given in which shell-model states are rigorously incorporated as states of the compound nucleus. Shell-model states above the particle emission threshold are given a clear interpretation; the calculation of resonance energies and level widths from them is clearly defined. The level shifts resulting from the interactions of these states with the continuum are discussed, and shown to have been mostly included in the usual shell-model calculations. Limits on a residual shift due to damping are derived and evaluated for the giant resonance levels in ${\mathrm{O}}^{16}$.

GROUND STATES OF CONJUGATED MOLECULES. I. SEMIEMPIRICAL SCF MO TREATMENT AND ITS APPLICATION TO AROMATIC HYDROCARBONS.

The π-bonding energies and resonance energies for a series of monocyclic polymethines (CH)n, and several benzenoid and nonbenzenoid hydrocarbons are calculated by the Hückel, Pople, and SPO methods. Special attention is paid to the formulation and definition of such energy terms. For simplicity equal bond lengths are assumed in each case; in the case of the polymethines, the planar configurations of regular polygons are taken. The calculated π-bonding energies of 11 benzenoid hydrocarbons are combined with experimental heats of formation and an assumed carbon—hydrogen bond energy to obtain estimates of the bond energy of a carbon—carbon σ bond in an aromatic ring. The values obtained for the eleven compounds agree very closely, implying that a good estimate of the heat of formation of such hydrocarbons can be obtained by adding the σ-bond energies to the calculated π energy. This approach is used to estimate resonance energies of the aromatic hydrocarbons. The resonance energies of the polymethines are found to alternate strongly, regardless of the choice of methods used; the values are uniformly larger for rings with 4n+2 π electrons than for rings with 4n π electrons. In the Pople and SPO cases, bond alternation is predicted for all the rings with 4n carbon atoms as well as for those with 4n+2 carbon atoms starting at n=4. For certain nonbenzenoid hydrocarbons the calculated resonance energies are only in fair agreement with experimental findings. For most, agreement is satisfactory.

Calculation of Resonance Energies

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTCalculation of Resonance EnergiesJ. L. FranklinCite this: J. Am. Chem. Soc. 1950, 72, 9, 4278–4280Publication Date (Print):September 1, 1950Publication History Published online1 May 2002Published inissue 1 September 1950https://doi.org/10.1021/ja01165a510RIGHTS & PERMISSIONSArticle Views550Altmetric-Citations41LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (425 KB) Get e-Alerts Get e-Alerts

A New Method of Calculating Resonance Energies

A New Method of Calculating Resonance Energies

The calculation of resonance energies from thermal data

The calculation of resonance energies from thermal data

Structure and Diamagnetic Susceptibility of Cyclo-octatetraene

According to Pascal's empirical formulae1, if cyclo-octatetraene has a structure corresponding with a cyclic system of conjugated double and single bonds, which may be puckered, the molecular susceptibility to be expected is — 50·2 × 10−6 c.g.s. On the other hand, if it contains eight ‘aromatic’ carbon atoms with eight pooled electrons, the molecular susceptibility to be expected would be — 73·4 × 10−6 c.g.s. This characteristic increase in diamagnetic susceptibility when a pool of ‘aromatic’ electrons is present2 makes a useful index of aromatic character. In the case of cyclo-octatetraene, recently published data for the heat of formation3 lead to a calculated resonance energy of 25·4 kcal./mole. Although this resonance energy is smaller than in the case of benzene (approximately 39 kcal./mole)5, it is sufficiently high to leave some doubt as to whether cyclo-octatetraene may have its structure stabilized by the formation of an aromatic pool of electrons. Optical evidence4 is not quite decisive on this point. Measurements have now been made on the magnetic susceptibility of cyclo-octatetraene, to test for an aromatic pool of electrons by the enhanced diamagnetism.

The Nature of the Chemical Bond. VII. The Calculation of Resonance Energy in Conjugated Systems

The quantum-mechanical treatment previously applied to benzene, naphthalene, and the hydrocarbon free radicals is used in the calculation of extra resonance energy of conjugation in systems of double bonds, the dihydronaphthalenes and dihydroanthracenes, phenylethylene, stilbene, isostilbene, triphenylethylene, tetraphenylethylene, biphenyl, o, m, and p-diphenylbenzene, and 1,3,5-triphenylbenzene. The calculated values, which are in approximate agreement with empirical values from thermochemical data, are used in the discussion of chemical properties and in the formulation of rules regarding conjugation in overlapping systems.