Dennis J. Caldwell

MCD behavior of benzene and its derivatives

A general method for correlating data from CD and MCD spectra is formulated. The origin dependence of the MCD terms is resolved by minimization of appropriate terms in the Lagrangian density expression. Approximate summation techniques are developed for magnetic and natural optical activity. The salient features of the MCD spectra of benzene derivatives are analyzed. The observed opposite signed magnetic rotational strengths of (o,p)‐ and m‐directors is accounted for by a variation calculation which includes electron donor and acceptor wavefunctions based on occupied and unoccupied substituent orbitals. The uniqueness of the alternating signed benzene spectrum as compared with most hexasubstituted derivatives of D6h symmetry is rationalized on the basis of the vibrational modes of E2g symmetry for carbon‐carbon bond stretching and bending. The importance of comparable vibronic and electronic effects is emphasized in the anomalous behavior of the B2u and B1u bands for low symmetry derivatives.

Vibronic Theory of Circular Dichroism

The effect of molecular vibrations on optically active absorption bands is treated by assuming a total wavefunction of the form ψ(Q) χn(Q − Q), where ψ(Q) is the electronic wavefunction with the normal coordinates as parameters and χn(Q − Q) is a harmonic oscillator function in the nuclear coordinates. The electric and magnetic dipole moments of a transition G → A are determined as functions of Q, μGA(Q), MAG(Q). The rotational strength for the 0–n vibrational mode, 〈χ0(QG) | μGA(Q) | χn(QA)〉· 〈χn(QA) |  MAG(Q) | χ0(QG)〉, is evaluated by expanding μGA(Q) and MAG(Q) as a power series in Q about the conformation of zero rotation. Formulas are obtained which indicate the possibility of several sign changes within a nondegenerate absorption band. The theory shows that these sign changes are possible not only for multiply excited vibrational modes but for those of a single symmetry as well.

Localized Orbitals in Spectroscopy

Publisher Summary The concept of localized orbitals is one of the most important links between quantum molecular physics and interpretive physical chemistry. Most spectroscopic data can be explained by models that resort wholly or in part to localization. A distinction should be made, however, between the transferability of localized orbitals and Hartree–Fock (HF) matrix elements. The first case is far more restrictive and implies zero bond order between non-nearest neighbors or atoms that are not in a simple conjugated or aromatic system. Because many spectroscopic and thermodynamic properties have a close dependence on such bond order parameters, it is certain that the complex connectivity of a molecule is also reflected in this manner. Hence, the most flexible interpretive methods require a consideration of more general interatomic parameters. The HF matrix elements have the feature of providing a quantitative transferability scheme for zeroth-order localized orbitals. For simple ground-state properties, such as the dipole moment, the one-electron density matrix offers a viable alternative to localized self-consistent field (SCF) orbitals in situations where a more exact treatment than the HF calculation is required.

Magnetic Circular Dichroism and Diamagnetic Molecules

Publisher Summary This chapter discusses magnetic circular dichroism and diamagnetic molecules. Unlike ordinary absorption and natural optical activity, the Faraday effect cannot be evaluated by one or two matrix elements, because the magnetic field provides a static perturbation that mixes all other states with the one being studied. In many instances excited states are classed into groups where it is equally tractable to construct a wave function for one as for another. In this case it may often happen that the greater part of the magnetic circular dichroism (MCD) will come from the mixing of these states. In other cases it will be generally possible to employ an approximate summation or variation technique, particularly at this stage of development where a qualitative understanding of the observed behavior is still to be gained. Among the general factors that appear to play an interesting role in MCD research are vibronic, degeneracy, and spin phenomena. Closely coupled to this behavior is the strength of the transition with the categories, strong, weak, and forbidden often providing qualitatively distinct types. In circular dichroism (CD) spectra weakly allowed transitions give large effects when they are magnetically allowed; however, there are still no well-established reasons for spin-forbidden transitions to play any more important role than they do in ordinary absorption.

An explicit series for the semiempirical analysis of NMR coupling constants

Abstract An iterative series for calculating NMR coupling constants is developed. The development is based on the unrestricted Hartree-Fock treatment of coupling constants and serves as an alternative to finite perturbation theory. The series is broken down into several terms which can be summed separately using the multinomial expansion. The first and third terms have explicit dependence on local properties while the second depends on the symmetry and dispersion of the molecular orbitals. These formulas may be used to relate the changes in the coupling constant in a homologous series of molecules to properties such as bond order, ionization energies, etc. They may also be used in direct conjunction with a semiempirical program to calculate a molecules coupling constants.

A comprehensive parametrization and computational program for the analysis of MCD and absorption data

A tractable method is presented for separating vibronic and static effects, which does not require extensive vibrational analysis of each molecule. The parameters so obtained can be expressed in terms of explicit matrix elements for a computation using only equilibrium position geometry and orbitals. The behavior of these vibronic quantities can provide an extremely sensitive means for studying the effects of substitution on the transition density matrix. This paper has been designed with sufficient flexibility in both the phenomenological and computational formalism to indicate how results of one procedure suggest appropriate modifications in the other. Benzene and its derivatives provide a fitting example for summarizing the procedure.

Local density functional calculations on metathesis reaction precursors

Calculations were carried out to assess the role of Local Density Functional (LDF) programs in following the course of metathesis reactions in large molecular systems. This study was designed to provide preliminary information on: (1) the nature of weakly bound ligands in cocatalyst structures, (2) the influence of phenyl ring substitution on catalytic activity, (3) the role of AlCl3 as a cocatalyst, and (4) the influence of macroenvironment on the basic electronic structure of the reactive site. For this purpose, calculations were carried out on an MoCl4O/tetrahydrofuran (THF) complex, ring substituted derivatives of MoCl5O-phenyl, the basic metallacyclobutane ring prototype, Mo(CH2)3CH3ClO/AlCl3, and a large fluorinated molybdenum complex.

An explicit model for the NMR coupling constant of the hydrogen molecule and the breakdown of INDO-FPT

Abstract We have previously obtained explicit equations, which are based on the ideas of finite perturbation theory (FPT), for calculating NMR proton-proton coupling constant. Using this model and the INDO formalism, a simple closed-form expression for the coupling constant of the hydrogen molecule is developed. This expression has several unique features: it shows that the convergence criteria for the iterative calculation is ¦ x ¦ x = HH /ΔϵX and it allows the H 2 coupling constant to be expressed directly in terms of the semiempirical parameters, showing specifically how each parameter affects the coupling constant. In this way the formalism of semiempirical SCF Theory lends itself to the construction of a model for coupling constants which is not purely numerical in nature. An INDO-FPT calculation is developed for the hydrogen molecule. As long as parameters are chosen for which ¦ x ¦ x ¦ > 1, the UHF calculation breaks down, the extremum corresponding to symmetrical molecular orbitals no longer being the minimum.

Modelling magnetic circular dichroism with application to imidazoles

Abstract The magnetic circular dichroism of imidazole and its derivatives are calculated using the π-electron approximation, where the resonance integral is computed by using the formula plus higher order terms. The magnetic circular dichroism (MCD) spectra for the molecules are also presented. As a complementary procedure to the π-electron calculation, Michls perimeter model [1] for predicting the signs of the MCD is employed.

Inductive and deductive science

An important unfinished problem is the theory of transition from deflagration to detonation DDT. The understanding of this problem is critical for the safe handling of explosives. Some of the successes of deflagration and detonation theory are outlined. For detonation to occur in a cylindrical explosive, for example, one must remember that as a shock wave moves into cold explosive the shock loses energy and is dying out. Behind a developed wave front there is a succession of increasingly exothermic reaction surfaces rising to a maximum at the Chapman-Jouguet surface where rarefaction begins. A sufficiently sharp blow or an intense beam of laser light falling on unreacted explosive generates this type of structure which travels through the material as a self supporting shock wave. How to avoid forming such structures which will grow into travelling self supporting waves has many aspects. Here we consider: 1. Starvation kinetics which arise from a change of reaction mechanism due to the sudden introduction of unburned material into a hot environment. As the gradient from unburned to burned material rises a situation develops where the fastest way to get energy into the bond that breaks is not directly from translation to this bond but through a reservoir which readily communicates energy. This shifts the developing bottle neck of energizing the molecule (starvation kinetics) to a new pathway with interesting consequences; 2. Turbulence promotes initiation of detonation by sharpening the concentration and temperature gradients between unburned and burned materials; 3. The dependence of shock wave velocity, due to momentum loss out the side is related to the diameter of the explosive; and 4. The curvature of the wave front is related to drag of telescoping cylinders on the central axis of the cylindrical explosive.