X-ray Emission Spectra of Some Carbon-containing Molecules

Abstract

Ab initio molecular orbital calculations for the energy and intensity of X-ray transitions associated with the carbon monoxide, hydrogen cyanide and carbon dioxide molecules have been calculated at the Hartree-Fock level. It is demonstrated that in general the absolute transition probabilities are sensitive to the inclusion of electronic relaxation effects and interatomic transition moment contributions. It is concluded that calculations for molecular X-r!ly emission henomena should be undertaken at least at the multicentre relaxed Hartree-Fock level to achieve a realistic basis for comparison with experiment. Total carbon-K X-ray rates do not show a strong variation with changes in the molecular environment. The total rates are of a similar magnitude to those reported for the atom. The calculated carbon-K fluorescence yield is also similar in both the carbon atom and the CO2 molecule.

An ab initio treatment of the X-ray emission spectra of the HCl molecule

“…For relaxed orbital calculations, where the states are not necessarily orthogonal, the transition moment M , is dependent on the choice of origin of the coordinate system, and so we have chosen the coordinate system at the centre of mass consistent with the work of Yoshimine et a1 (1973). The theory involved in the present calculations has been discussed in more detail elsewhere (Phillips and Larkins 1986).…”

“…It should also be noted, despite the success of the frozen orbital and one-centre models in this case, that caution must be used when applying such techniques, because it is expected that the frozen orbital and especially the one-centre approximations will fail when applied to more complicated molecules than HC1 with substantial electron delocalisation (Phillips and Larkins 1986).…”

“…Appropriate observation of spin and spatial symmetry allows equation ( 2 ) to be expressed as (Phillips and Larkins 1986) where K is the number of spin and spatial symmetry blocks, D, is the determinant of molecular orbital overlap integrals of block I, the 4 are one-electron molecular spin orbitals and Dk(ij) is the cofactor of block k formed by eliminating the ith row and jth column from D k . For relaxed orbital calculations, where the states are not necessarily orthogonal, the transition moment M , is dependent on the choice of origin of the coordinate system, and so we have chosen the coordinate system at the centre of mass consistent with the work of Yoshimine et a1 (1973).…”

“…The results of relativistic Hartree-Fock relaxed (ASCF) average energy calculations for atomic chlorine (Dyall 1987) and the relaxed orbital relativistic Hartree-Fock transition rate calculations of Scofield (1974b) are also presented. The molecular rate calculations are presented from both the length and velocity forms of the dipole operator (equation (4) (Phillips and Larkins 1986) in those cases where the transition probabilities were small. The relative rates (column 5 ) are presented only for the length form since there is close agreement with the relative rates using the velocity form.…”

“…Theoretical interpretations of XES have been based upon semiempirical or ab initio approaches (Manne 1970, Agren and Nordgren 1981, Agren and Arneberg 1983, Agren et a1 1984, Phillips and Larkins 1986. Previous research by our group, cited above, has shown that multicentre (interatomic) terms and electronic relaxation effects can make a major contribution to absolute transition probabilities involving valence electrons.…”