The relativistic contribution to the singlet-triplet excitation energy in methylene

The relativistic correction to the s²p²-sp³ energy separation in the carbon atom is shown to be 120 cm^?1 which is too small to resolve the discrepancies between theory and experiment for the ¹A₁-³B₁ energy separation in methylene.     

Relativistic corrections to carbon atom energy levels and their relation to the singlet-triplet splitting in methylene

The relativistic correction to the s ² p ²-sp ³ excitation energy in the carbon atom is shown to be 120 cm^-1 rather than 500 cm^-1 as reported by Desclaux et al. This is too small to explain the 8 kJ mol^-1 discrepancy between theory and experiment for the ¹ A ₁-³ B ₁ energy separation in methylene.

Two pitfalls that can arise when calculating relativistic corrections from approximate wavefunctions are discussed.     

Charge transfer and dispersion interaction stabilization of the D2h isomer of O4

The results of some minimal basis set valence bond calculations, with an antibonding midbond molecular orbital (π_m*) included, are reported for the D_2h isomer of O₄. The in-plane π_m*←π* excitations describe the charge transfer from each monomer, while the π*←π excitations on each monomer partially describe the intermolecular dispersive attractions. It is found that the charge-transfer interactions by themselves are insufficient to stabilize the S=0 spin D_2h dimer of O₄ relative to two O₂ monomers when a correction is included for basis set superposition error. The inclusion of both the charge transfer and dispersion terms yields an estimate of 14 cm⁻¹ for the binding energy (D_e) at an equilibrium separation (R_e) of 3.29 Å. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 129–134, 1998     

Nuclear magnetic double resonance for a spin system subject to scalar relaxation of the second kind

The equation of motion of a reduced spin density operator characterizing the state of a group of spins scalar coupled to a second group of spins which are either relaxing rapidly and/or irradiated with a strong radiofrequency field is derived within the framework of the non-viscous liquid approximation. An analytic expression for the spectral densities entering this equation is derived within the extreme narrowing approximation for the case in which the relaxation rates of the nuclei in the second group of spins are much greater than any scalar couplings between them. The resultant equation is used to discuss the conditions needed in a high resolution nuclear magnetic double resonance experiment to decouple a spin-½ nucleus (A) from a rapidly relaxing quadrupolar nucleus (X) in the fast relaxation limit, defined by |2πJ_AX T _1X | ? 1, in which the A resonance consists of a single broadened line. It is found that, if (ω _A - ω _X )² ? T _1X ^-2 so that the x and y components of the J_AX coupling can be neglected, decoupling, in the sense that all broadening of the A resonance is removed, occurs only when the strength of the B ₂ field be such that γ _X ² B ₂ ² ? T _1X ^-2 and that the conventional decoupling criterion γ _X ² B ₂ ² ? 4π² J_AX ² is not applicable. However, if the x and y components of the A-X scalar coupling cannot be neglected because the condition (ω _A - ω _X )² ? T _1X ^-2 is not satisfied, it is found that the X spin can never be entirely decoupled. It is shown that such double resonance experiments enable both the coupling constants between spin-½ and quadrupolar nuclei and the relaxation times of the latter nuclei to be extracted in situations in which measurement of the half-widths of spin-1/2 transitions can only yield the product J_AX ² T _1X in the absence of irradiation of the quadrupolar nuclei.     

A theoretical study of the cohesion of noble gases on graphite

The interactions of the noble gases with a graphene sheet are investigated theoretically. The short range repulsive interaction between the noble gas and each carbon atom is described using Hartree-Fock atomic densities and a local density functional theory with the exchange functional corrected for the finite range of the interaction by introducing a Rae-type correction depending on the effective number of electrons. The long range interactions are introduced as the sum of the Axilrod-Teller triple-dipole interaction plus the dipole-dipole and dipole-quadrupole dispersive attractions damped according to the theory of Jacobi and Csanak. The energy arising from the interactions between the permanent quadrupoles on the carbon atoms with the dipole they induce on the noble gas is negligible, being nonzero only on account of the atomistic structure of graphene. The mobile and delocalized nature of the graphene pi electrons causes the effective number of electrons to be around 500 rather than that of 12 appropriate for a system of entirely localized interactions with individual carbon atoms. Inclusion of the Axilrod-Teller term is required to obtain reliable predictions for the binding energies and equilibrium geometries. Absorption of a noble gas atom is predicted to occur at the site above the center of a six membered ring although this is preferred over two other sites by only about 5 meV. The methods presented for generating all the potentials can be applied to derive the interactions between any ion and carbon atom in the wall of a single-walled nanotube. Knowledge of these interactions is required to study the alkali halide nanocrystals encapsulated in single-walled carbon nanotubes of current interest.     

Ab initio relativistic lattice energy calculations for fluorides of the 7p series of superheavy elements

Lattice energies of the ionic fluorides of Ag, Pb, E113 and E116 are calculated by an ab initio relativistic method. Previous predictions of the exothermicity of the ionic fluorides of E113 and E116 are confirmed. For AgF and PbF₂ small discrepancies between theory and experiment are explained by semi-empirical calculations of the dispersion energy.     

Fundamental global model for the structures and energetics of nanocrystalline ionic solids

This paper presents a general theory elucidating the relationships between the structures and cohesive energetics of alkali halide nanocrystals consisting of small sections of bulk rocksalt structures with m(1) and m(2) rows but infinite along the z axis. The theory introduces the electrostatic interactions between the ions treated as point charges and the short-range repulsions between the closest ion neighbors with the latter terms written in the Born form Ar(-)(n). Minimum energy structures are defined by the distances a(e) and b(e) separating the closest ions perpendicular and parallel to the z direction. The ratio a(e)/b(e), defining the crystal shape, is independent of the strength A of the short-range repulsion, greater than the bulk value of unity, and increases with decrease of the crystal cross section or n. This ratio tends toward unity in the hard sphere limit of infinite n. Both b(e)/R(6:6)(e) and a(e)/R(6:6)(e), with the bulk separation R(6:6)(e), are less than one, increase with increase of the crystal cross section or n, and are independent of A if this is independent of structure. The structural dependence of A increases its value with a decreasing crystal cross section rendering closer to unity the ratios a(e)/b(e), b(e)/R(6:6)(e), and a(e)/R(6:6)(e). Energy gains on relaxing the crystal toward equilibrium from its bulk separations decrease with increase of the crystal cross section or n, being about 60 kJ/mol for a one-dimensional chain with n = 6 but 0.5 kJ/mol for m(1) = m(2) = 4 with n = 12. The energy gained on relaxing to a structure with a(e)/b(e) constrained at unity is about 10 times greater than the further energy gains consequent on removing this constraint. The present theory neglecting the interaction between ions and the encapsulating nanotube explains the experimentally measured b(e)/R(6:6)(e) ratios. The observation that the a(e)/R(6:6)(e) values are greater than one shows that ion-wall interactions are important in determining the values of a(e).     

The determination of moisture in solids: A Selected Review

The scientific literature published since Pande's comprehensive monograph Handbook of Moisture Determination and Control (1974) was surveyed (to mid-1984) for new or improved techniques of determining moisture in solids. Particular attention is given to methods that might distinguish between bound and free moisture in organic solids. The classification of moisture is discussed, as well as pitfalls in sampling, in sample handling, and in the comparison of different methods. Six methods that show promise of being able to distinguish between bound and free moisture were identified: dynamic dielectric thermal analysis, coherent microwave measurements, infrared spectrometry, near-infrared reflectance spectrometry, thermal methods and nuclear magnetic resonance spectrometry.     

Theory of nuclear magnetic resonance line shapes for spin systems containing several quadrupolar nuclei

The general method of calculating the high resolution nuclear magnetic resonance band shape of a group of spin -½ nuclei scalar coupled to more than one quadrupolar nucleus is described, the ²A³X³Y case considered in detail, and computed spectra presented. The detailed treatment is carried out with the assumption that molecular reorientation is sufficiently rapid for the extreme narrowing approximation to be applicable. The relationship between the relaxation matrix method of conducting such band-shape calculations and that based upon analogy with chemical exchange is investigated and it is concluded that the latter approach is inadequate. The band shapes resulting in the limit of rapid quadrupole relaxation are discussed and it is shown that these can be understood using a theory [6] of scalar relaxation of the second kind.