A. Salam

High-level theoretical study of the conformational equilibrium of n-pentane

An accurate calculation of the energy differences between stationary points on the torsional potential energy surface of n-pentane is performed using ab initio Hartree–Fock theory, advanced many-body methods such as MP2, MP3, CCSD, and CCSD(T), as well as density functional theory, together with basis sets of increasing size. This study focuses on the four conformers of this compound, namely, the all staggered trans–trans (TT), trans–gauche (TG), gauche–gauche (G+G+), and gauche–gauche (G+G−) structures, belonging to the C2v, C1, C2, and C1 symmetry point groups, respectively. A focal point analysis up to 635 basis functions is carried out to determine when the series of relative energies of the four conformers approach convergence. It is found that relative to the minimum energy TT conformer, the energy differences of the TG, G+G+, and G+G− conformers obtained from ab initio methods are 0.621, 1.065, and 2.917 kcal mol−1, respectively. Converged energy differences obtained with three density functionals,...

A NEW GENERALIZATION OF THE CASIMIR-POLDER POTENTIAL TO HIGHER ELECTRIC MULTIPOLE POLARIZABILITIES

An elementary method for calculating retarded interaction energies for a pair of molecules with electric multipole polarizabilities of arbitrary order is presented. In the multipolar framework of quantum electrodynamics, the interaction energy is viewed as arising from two‐photon exchange and calculated using fourth order perturbation theory. It is shown how the energy may be expressed in terms of derivatives of the Casimir–Polder formula written in a special form as an integral over imaginary frequency. Explicit formulas are presented for (a) an electric dipole polarizable molecule interacting with an electric quadrupole polarizable molecule, (b) an electric dipole polarizable molecule interacting with an electric octupole polarizable molecule, and (c) an electric quadrupole polarizable molecule interacting with another electric quadrupole polarizable molecule. The results are expressed in terms of reducible and irreducible components of multipole moments. For case (b) it is shown that in addition to the...

Ab initio and density functional theory calculation of the structure and vibrational properties of n-vertex closo-carboranes, n=5, 6 and 7

Abstract An extensive high-level computational study of various possible isomers of five, six and seven vertex closo -carboranes has been carried out using ab initio self-consistent field and density functional (DFT) theories. In total nine different cage structures have been investigated at the Hartree–Fock and B3LYP DFT levels in conjunction with the 6-31G** and 6-31++G** basis sets. Energies, optimized geometries, Mulliken charges, harmonic frequencies and electric dipole and quadrupole moments have been computed and compared with previous calculations and experimental data where applicable. The inclusion of diffuse functions in the basis set is shown not to significantly affect the results obtained for structural parameters and molecular properties. For a fixed cluster size, and for whichever model chemistry is chosen, the energetically most stable isomer is computed to be 1,5-C 2 B 3 H 5 , 1,6-C 2 B 4 H 6 and 2,4-C 2 B 5 H 7 . It is also found that irrespective of cluster vertex number, boron–hydrogen and carbon–hydrogen bond lengths remain relatively constant. The simulated vibrational spectra are analysed in detail and characteristic boron–hydrogen and carbon–hydrogen stretching frequencies and skeletal breathing modes are identified.

Discriminatory dispersion interactions between chiral molecules

Dispersion interactions between a pair of chiral molecules depend on the relative handedness of the molecules. The energy shifts valid for all separations beyond electron overlap have been calculated by two methods: one based on fourth-order perturbation theory and the other on a response theory. Both methods use molecular quantum electrodynamics. The discriminatory energy shifts are shown to depend on the mixed electric-magnetic polarizability tensor. Non-discriminatory energy shifts of the same order dependent on electric quadrupole polarizability or magnetic susceptibility are also presented.

Intermolecular energy shifts between two chiral molecules in excited electronic states

Higher order multipole contributions to the energy shift between two neutral polarizable molecules in excited electronic states are calculated using molecular response theory within the formalism of non-relativistic quantum electrodynamics. The interaction between two electric-magnetic dipole polarizable molecules is discriminatory, being dependent on the chirality of each species. The energy shift between an electric dipole polarizable molecule interacting with either a magnetic dipole or electric quadrupole polarizable molecule is also evaluated. The potentials obtained apply to two randomly oriented molecules and are valid for all intermolecular separation distances outside electron overlap. The interaction energy when one or both of the pair are in ground electronic states is easily deduced from the general result for two excited molecules. The limiting behaviour of the various energy shifts at large and small separation distances is also examined.

A quantum electrodynamical theory of induced circularly polarised luminescence

Abstract A theory of molecule-induced circulary polarised emission for a luminescent chiral-achiral pair employing the multipolar Hamiltonian in both the Schrodinger and Heisenberg formulations of Coulomb gauge quantum electrodynamics is presented. Chirality is induced in an achiral species via intermolecular coupling with a chiral molecule. In the Schrodinger picture time-dependent perturbation theory is used with intermolecular interaction involving virtual photon exchange. In the Heisenberg framework the electric dipole moment of the achiral molecule couples to the time-dependent Maxwell fields of the chiral source. The equivalence of the matrix element obtained for the process using both approaches in demonstrated. The transition rate is then derived for the differential spontaneous emission of left- and right-circularly polarised radiation. Various orientational averages are computed and the dependence of the rate expression on intermolecular separation is investigated.

A quantum electrodynamic theory of two-centre two-photon circular dichroism

Expressions for the rate of two-photon circular dichroism occurring at two identical oriented or completely randomly oriented centres are calculated using perturbation theory and the Fermi golden rule within the framework of non-relativistic quantum electrodynamics. Circular differential absorption in the two-group model arises from the relative dissymmetric juxtaposition of two inherently achiral functional groups. Inter-chromophore coupling is included through the exchange of virtual photons. Absorption of two circularly polarized photons takes place at each centre, and the interference between the two amplitudes depends on the chromophore separation and on the handedness of the incident radiation. In the near zone, the two-centre two-photon circular dichroism rate is found to depend linearly upon the inter-group separation distance.

Retarded intermolecular interactions involving diamagnetic molecules

Second- and third-order time-dependent perturbation theory within the multipolar framework of nonrelativistic quantum electrodynamics is used to calculate the retarded dispersion interaction between two diamagnetic molecules, a diamagnetic molecule and a magnetic-dipole susceptible molecule, and a diamagnetic molecule and an electric-quadrupole polarizable molecule. New expressions for the energy shift valid for all intermolecular separation distances, R, beyond the region of overlap of molecular electronic wave functions and applicable to a pair of randomly oriented molecules in the ground electronic state are given. The R-dependent behavior of the far-zone limit of the interaction energies is also examined