Biomedical Engineering Reference
In-Depth Information
More recent calculations that employed the R-matrix method for the HCN and
the CNH molecules [
15
] found a
2
˘ TNI resonance for the former species and
for the latter, while only the HCN molecule exhibited around 8 eV a much smaller
resonance of
2
˙ symmetry.
A very complete study on the DEA process for HCN/HNC molecules has
also been carried out recently [
16
]. The dissociation mechanisms were analysed
for both molecules and for their deuterated variants DCN/DNC: a curve crossing
between
2
˙ and
2
˘ complex potential energy surfaces of the metastable anions was
computationally located, leading to a barrier for the bent structure and a suggested
tunnelling mechanism for DEA processes leading to CN
formation from HCN.
The methodology that we shall describe in the next Section allows one to
follow precisely this behaviour of shape resonances, i.e. their energy changes and
width shifts as the molecular geometries are modified along specific bonds. It will
therefore be a test of our modelling to follow the behaviour of the postulated
resonances of
and
symmetry for HCN as they evolve into metastable
fragments and localize their resonant wavefunctions into specific molecular regions
as stretching and bending deformations are taking place. In other words, we wish
to test out model quantum scattering calculations on the features of the established
TNIs of HCN
and follow them upon bond-deforming vibrational excitations of
the molecular fragments. We shall show that the present quantum modelling is
able to relate the changing lifetimes of such metastable states to the appearance
of CN
fragments and/or to the detachment of fragments. Our calculations are
therefore expected to shed more light on the features of the resonant processes at
low scattering energies and to link our findings with existing experiments and earlier
calculations.
The next section
4.2
describes our computational method while section
4.3
reports our calculations, comparing them with the existing data. Our conclusions
are finally given in section
4.4
.
4.2
The quantum scattering model
4.2.1
Single-center expansion and static exchange (SE) forces
Both the target one-electron bound orbitals (MOs) and the impinging electron
wavefunction are expanded as linear combinations of symmetry-adapted spherical
harmonics [
17
], where the indexes label the relevant Irreducible Representation
(IR) by p and its component by , while l labels the angular momenta and its
component h.
X
1
r
˚
p
i
u
i;p
lh
.r/X
p
.r;#;/
D
lh
.#; /
(4.1)
lh
