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Bound electron contribution to the Doppler-shift of gamma-ray spectra in thepositron-electron annihilation process of molecular methane has been studied ingas phase. Two accurate ab initio quantum mechanical schemes, i.e. thedelocalized molecular orbital (MO) and the localized natural bond orbital (NBO)schemes, are applied to study the multi-centred methane molecule. The presentab initio calculations of methane indicate that the C-H bonds are polarizedwith the partial negative charge of -0.36 a.u. on the carbon atom and thepartial positive charge of +0.09 a.u. on each of the hydrogen atoms. Thepositively charged hydrogen atoms produce repulsive Coulomb potentials to apositron. Both the MO and NBO schemes further reveal that the 2a1 electrons ofmethane, that is, the 2a1 electron component of the C-H bonds rather than thewhole C-H bonds of methane, predominates the positron-electron annihilationgamma-ray spectra of the molecule. Electrons of a molecule which are dominantthe positron-electron annihilation processes are called positrophilic electronsin the present study. It is further shown that the negative electrostaticpotential (ESP) of methane facilitates with the density of the positrophilic2a1 electrons of methane. Other valence electrons (e.g. 1t2) in the C-H bondsplay a minor spectator role in the annihilation process of methane.

Gamma-ray spectra of methane in the positron-electron annihilation process