Lionel Salem

Attractive Forces between Long Saturated Chains at Short Distances

The assumption of locally additive forces is used to describe the London—van der Waals dispersion attraction between long saturated chains. For two linear chains of length L, opposed and parallel, each built out of N identical units of length λ(Nλ=L), the total dispersion energy is given by W=A4λ2D4ρ(3tan−1ρ+ρ1+ρ2),  ρ=LD, where D is the mutual distance of the two chains; A is the coefficient of the dispersion interaction between two basic units. At distances D much smaller than the molecular length L, the energy becomes proportional to L (or N) and inversely proportional to the fifth power of the intermolecular distance.The coefficient A is calculated for the interaction between two CH2 units in hydrocarbon chains and the result is used to estimate the sublimation energy at 0°K of paraffin crystals. Sound agreement with experiment is obtained. Finally, the particularities of the attractive forces between long saturated chains are examined in more detail and their great sensitivity to distance is shown by...

Theoretical Interpretation of Force Constants

The quantum‐mechanical definition of the force constant k of a diatomic molecule is given. The three main approaches to the calculation of force constants—the perturbation approach, the virial theorem approach, and the strict Hellmann—Feynman approach—are discussed. Several new expressions for k are derived. In particular the Hellmann—Feynman theorem leads to a general expression for k in terms of the charge density ρ and of the change δρ/δR with internuclear distance R. It is also possible to relate the force constant to the quadrupole coupling constant (eqQ) of either nucleus by the formula k=ZA[qA+43πρ(A)− ∫  (∂ρ/∂XA) (cosθA/rA2) dτ]. The experimentally observed relation k≅qH for diatomic hydrides is then interpreted in terms of the properties of the charge density of these molecules.

Reliability of the Hellmann—Feynman Theorem for Approximate Charge Densities

A spherical atom in a uniform external field and the long‐range interaction of two molecules are examples which illustrate the unreliability of the Hellmann—Feynman theorem when applied to systems described by approximate wave functions or charge densities. However, in the first case a wave function correct to first order in the perturbing field and in the second case a wave function correct to second order in the mutual interaction will yield the correct force.For spherical atoms in an external field, the contribution of the continuum states to the electronic screening of the field is very large, 54% for hydrogen and about 72% for helium. From this case also one can evolve general considerations concerning the use of effective nuclear charges in electrostatic force calculations.In the general case it is shown that for a system submitted to a given perturbation the wave function correct to order n, or the corresponding charge density, yields the force correct to order n and to order n only. This result le...

Energy of Interaction between Two Molecules

An expression for the energy of interaction between two molecules has been obtained by solving the secular equation using a double‐iteration procedure based on the exact wavefunctions of the isolated molecules. This expression exhibits the intermolecular interaction energy explicitly and its leading terms agree with those recently obtained by Murrell et al. and Salem within the limits specified by these authors.

Energies of Excited Electronic States as Calculated with the Zero Differential Overlap Approximation

It is shown that electronic excitation energies, calculated using the zero differential overlap approximation, can always be expressed in terms of the difference between two‐electron Coulombic integrals. These differences can then be used as empirical parameters for the calculation of excitation energies.

Numerical Calculations by the Hellmann—Feynman Procedure

Simple calculations of atomic forces and of force constants in homonuclear diatomics confirm the unreliability of the Hellmann—Feynman procedure for calculating molecular forces unless very accurate one‐electron densities are used.Electronic forces are extremely sensitive to polarization and to small density changes near atomic centers, so that in general they cannot be used alone to determine accurately a totally a priori one‐electron density. They may, however, be useful in testing the features of the density obtained from a variational wavefunction.

Organic Transition States

The theoretical basis of Organic Chemistry lies in the understanding of organic reaction mechanisms. The reaction mechanism is generally a cursory description of the pathway followed by the different atoms in the molecule (or molecules) during the reaction. One important feature of the pathway is the actual geometry of the col, or potential barrier: the so-called transition state. Transition states are not amenable to direct experimental observation; only indirect gross information is available via experimental activation energies, entropies of activation, etc. Computation therefore seems an extremely appropriate tool for elucidating the structure of transition states. Of course the lack of available experimental data will be a drawback for any direct comparison; computation of the potential surface, to which we will restrict ourselves, would have to be followed by computation of dynamical trajectories before any meaningful comparison of rates, for instance, could be made. However the calculated transition state, and its energy relative to other competing points, can give information on the likely products to be obtained in the reaction.

Conformation of vinylic methyl groups

A molecular orbital based model is constructed to show the observed tendency for eclipsing of vinylic methyl groups.

Competition between concerted and non-concerted modes in a π-diradical

In diradicals with degenerate molecular orbitals of opposite symmetry there is no preferred motion for re-closure, nonconcerted modes being equally probable as the two concerted modes.

Ring puckering and methylene rocking in cyclobutane

Calculations of the ring puckering potential in cyclobutane show no double minimum potential unless methylene rocking is introduced.