3.5 Results and Discussion
79
energy gap decreases further as θ NNN continues to decrease, reaching a minimum
energy separation of 1.5 eV at 115
◦ .
The energy of T 1 also decreases with θ N N N . An energetic minimum is observed
at ca. θ N N N = 130
◦ , where
T 1 E(θ N N N = 180
◦
) −
T 1 E(θ N N N = 130
◦
) ≈ 1.7 eV.
At this angle, the energy separation between S 0 and T 1 reduces from 4.2 eV to only
0.7 eV. This energy is less than the energy associated with the second overtone of
δ R A . As θ N N N is compressed further, a conical intersection (CI) is reached, with an
S 0 /T 1 crossing at θ N N N ≈ 120
◦ . The T 1 state remains more energetically favourable
than S 0 over a small range of θ N N N in this region, Fig. 3.5b. Thus, the bending mode
of N
−
3 appears to offer a mechanism for the athermal electronic excitation of the
molecule.
Discussion of the PES associated with δR S is done with respect to the symmetric
N-N bond lengths, Fig. 3.5c. Across the eigenvector of this mode, the T 1 state remains
lowest in energy amongst the excited states. In contrast to the bending mode, however,
extending the eigenvectors of this mode does not lead to a CI, even up to a bond
stretch of 2.0 Å and an associated U ≈ 11 eV. Similarly, discussion of the PES
of δR A requires definition of a distortion parameter α. This dimensionless value
represents the degree to which the eigenvector is perturbed, with R 1 = R eqm + α/10
and R 2 = R eqm − α/10 in Fig. 3.5d. Due to contraction of R 2 as the eigenvector is
imposed on equilibrium geometries, the energy is found to rise considerably faster
than for the symmetric mode. Again, no CI is observed below U ≈ 30 eV along
this eigenvector.
It follows from the above that a CI is only attainable through the bending motion
of N
−
3 . However, the geometry of a real molecule results from the time-dependent
superposition of all vibrational normal modes. The combination of δθ NNN with δR S
and δR A are therefore of interest. At relatively low energies, the excitation energies
between the S o and excited states decreases substantially further in δR S as compared
to δR A , Fig. 3.5. Hence, only the combination of δθ NNN + δR S is considered here.
At θ NNN = 150
◦ (U ≈ 0.7 eV according to Fig. 3.5b), the PES of δR S is found to
deviate from that observed in the linear molecule, Fig. 3.6a in comparison to Fig. 3.5c.
Most notably, with only a small distortion of θ NNN , the T 1 /S 0 CI becomes accessible
via δR S , with the CI observed at R S ≈ 1.65 Å. However, this pathway is clearly not
most energetically favourable. The total U (i.e. U(δθ NNN ) = U(δR S ) associated
with this CI is over twice that required to achieve the CI by bending alone. As θ NNN is
decrease to 130
o (U ≈ 2 eV according to Fig. 3.5b), it is instead possible to access
the CI along the δR S eigenvector (at R S ≈ 1.5 Å) with a total U ≈ 4 eV, Fig. 3.6b.
The total energy required to achieve the CI by this pathway is therefore comparable
to that required to access it by bending alone, but requires a smaller distortion of the
molecule within the confinements of a crystal lattice.
The T 1 state is accessible by extending the normal modes of the N
−
3 molecule.
For the linear geometry in this state, the N
−
3 dissociation barrier was found to be
ca. 1 eV. When θ NNN is bent to 150
◦ , the S 0 dissociation energy decreases from
4.5 to 3.6 eV, with the dissociation barrier on the T 1 PES decreasing to 0.67 eV,
Fig. 3.7a. As compared to the linear geometry, however, the energetic drive to dissociation at this angle decreases considerably, and is only −0.2 eV at this angle. At
79
energy gap decreases further as θ NNN continues to decrease, reaching a minimum
energy separation of 1.5 eV at 115
◦ .
The energy of T 1 also decreases with θ N N N . An energetic minimum is observed
at ca. θ N N N = 130
◦ , where
T 1 E(θ N N N = 180
◦
) −
T 1 E(θ N N N = 130
◦
) ≈ 1.7 eV.
At this angle, the energy separation between S 0 and T 1 reduces from 4.2 eV to only
0.7 eV. This energy is less than the energy associated with the second overtone of
δ R A . As θ N N N is compressed further, a conical intersection (CI) is reached, with an
S 0 /T 1 crossing at θ N N N ≈ 120
◦ . The T 1 state remains more energetically favourable
than S 0 over a small range of θ N N N in this region, Fig. 3.5b. Thus, the bending mode
of N
−
3 appears to offer a mechanism for the athermal electronic excitation of the
molecule.
Discussion of the PES associated with δR S is done with respect to the symmetric
N-N bond lengths, Fig. 3.5c. Across the eigenvector of this mode, the T 1 state remains
lowest in energy amongst the excited states. In contrast to the bending mode, however,
extending the eigenvectors of this mode does not lead to a CI, even up to a bond
stretch of 2.0 Å and an associated U ≈ 11 eV. Similarly, discussion of the PES
of δR A requires definition of a distortion parameter α. This dimensionless value
represents the degree to which the eigenvector is perturbed, with R 1 = R eqm + α/10
and R 2 = R eqm − α/10 in Fig. 3.5d. Due to contraction of R 2 as the eigenvector is
imposed on equilibrium geometries, the energy is found to rise considerably faster
than for the symmetric mode. Again, no CI is observed below U ≈ 30 eV along
this eigenvector.
It follows from the above that a CI is only attainable through the bending motion
of N
−
3 . However, the geometry of a real molecule results from the time-dependent
superposition of all vibrational normal modes. The combination of δθ NNN with δR S
and δR A are therefore of interest. At relatively low energies, the excitation energies
between the S o and excited states decreases substantially further in δR S as compared
to δR A , Fig. 3.5. Hence, only the combination of δθ NNN + δR S is considered here.
At θ NNN = 150
◦ (U ≈ 0.7 eV according to Fig. 3.5b), the PES of δR S is found to
deviate from that observed in the linear molecule, Fig. 3.6a in comparison to Fig. 3.5c.
Most notably, with only a small distortion of θ NNN , the T 1 /S 0 CI becomes accessible
via δR S , with the CI observed at R S ≈ 1.65 Å. However, this pathway is clearly not
most energetically favourable. The total U (i.e. U(δθ NNN ) = U(δR S ) associated
with this CI is over twice that required to achieve the CI by bending alone. As θ NNN is
decrease to 130
o (U ≈ 2 eV according to Fig. 3.5b), it is instead possible to access
the CI along the δR S eigenvector (at R S ≈ 1.5 Å) with a total U ≈ 4 eV, Fig. 3.6b.
The total energy required to achieve the CI by this pathway is therefore comparable
to that required to access it by bending alone, but requires a smaller distortion of the
molecule within the confinements of a crystal lattice.
The T 1 state is accessible by extending the normal modes of the N
−
3 molecule.
For the linear geometry in this state, the N
−
3 dissociation barrier was found to be
ca. 1 eV. When θ NNN is bent to 150
◦ , the S 0 dissociation energy decreases from
4.5 to 3.6 eV, with the dissociation barrier on the T 1 PES decreasing to 0.67 eV,
Fig. 3.7a. As compared to the linear geometry, however, the energetic drive to dissociation at this angle decreases considerably, and is only −0.2 eV at this angle. At