400 nm. We may notice a very small spin-orbit splitting of the triplets. The
structural deformations when going from the electronic ground state to the relaxed
low-lying excited states are quite small. After nuclear relaxation into the potential
wells of the excited states, the Re–X shortening does not exceed 0.097 Å in the
singlet states and 0.043 Å in the triplet states. This deformation is accompanied by
an elongation of the Re–C ax bonds (<3%) together with a minor shortening of the
Re–N bonds in all excited states.
According to the calculations, the luminescence should start from the b
1 A
0 state
calculated at 505 nm (or 496 nm with SOC) and 522 nm (or 505 nm with SOC) for
the chloride 11 and bromide 12 complexes, respectively. These values lead to
theoretical Stokes shifts of 5,640 (5,200) cm
À1 and 5,880 (5,640) cm
À1 , respectively, in agreement with the experimental data (~6,000 cm
À1 ). Accordingly, the
two complexes behave similarly and the small calculated red shift is also observed
on the experimental luminescence spectra when going from Cl to Br [120].
The emission wavelengths reported in Table 6 correlate nicely with the three
domains of luminescence detected by ultra-fast resolved spectroscopy [120],
namely in the ranges 500–550, 550–600, and 600–620 nm for the three molecules.
It is noteworthy that both b
3
A
00 and b
1 A
0 states participate in the early short-lived
emission whereas both a
1 A
00 and a
3 A
0 contribute to the intermediate band. The only
purely phosphorescent process is the long-lived emission generated by a
3 A
00 in the
chloride and bromide complexes and by both a
3 A
0 and a
3 A
00 in the iodide complex,
these states keeping a nearly pure triplet character.
5 Ultra-Fast Intersystem Crossings
This chapter is devoted to the simulation of ultra-fast ISC processes in first-,
second- and third-row transition metal complexes by means of various approaches,
namely the time-dependent formalism within the Condon approximation, the
non-adiabatic surface-hopping semi-classical method, and the quantum wavepacket
dynamics propagation.
5.1 Excited States Dynamics in Spin Crossover Fe (bpy) 3 ]
2+
Complex
A recent promising approach, applied to the spin crossover complex [Fe (bpy) 3 ]
2+
[90] has been developed by C. M. Marian et al. [101, 102]. This method is based on
time-dependent calculations of ISC rates in the multi-mode harmonic oscillator and
Condon approximations and beyond, where the electronic spin-orbit matrix elements depend linearly on the nuclear coordinates within a spin-vibronic coupling
scheme. The ISC rate can be decomposed into three contributions, namely direct,
mixed direct vibronic, and vibronic.
Absorption Spectroscopy, Emissive Properties, and Ultrafast Intersystem. . .
401
structural deformations when going from the electronic ground state to the relaxed
low-lying excited states are quite small. After nuclear relaxation into the potential
wells of the excited states, the Re–X shortening does not exceed 0.097 Å in the
singlet states and 0.043 Å in the triplet states. This deformation is accompanied by
an elongation of the Re–C ax bonds (<3%) together with a minor shortening of the
Re–N bonds in all excited states.
According to the calculations, the luminescence should start from the b
1 A
0 state
calculated at 505 nm (or 496 nm with SOC) and 522 nm (or 505 nm with SOC) for
the chloride 11 and bromide 12 complexes, respectively. These values lead to
theoretical Stokes shifts of 5,640 (5,200) cm
À1 and 5,880 (5,640) cm
À1 , respectively, in agreement with the experimental data (~6,000 cm
À1 ). Accordingly, the
two complexes behave similarly and the small calculated red shift is also observed
on the experimental luminescence spectra when going from Cl to Br [120].
The emission wavelengths reported in Table 6 correlate nicely with the three
domains of luminescence detected by ultra-fast resolved spectroscopy [120],
namely in the ranges 500–550, 550–600, and 600–620 nm for the three molecules.
It is noteworthy that both b
3
A
00 and b
1 A
0 states participate in the early short-lived
emission whereas both a
1 A
00 and a
3 A
0 contribute to the intermediate band. The only
purely phosphorescent process is the long-lived emission generated by a
3 A
00 in the
chloride and bromide complexes and by both a
3 A
0 and a
3 A
00 in the iodide complex,
these states keeping a nearly pure triplet character.
5 Ultra-Fast Intersystem Crossings
This chapter is devoted to the simulation of ultra-fast ISC processes in first-,
second- and third-row transition metal complexes by means of various approaches,
namely the time-dependent formalism within the Condon approximation, the
non-adiabatic surface-hopping semi-classical method, and the quantum wavepacket
dynamics propagation.
5.1 Excited States Dynamics in Spin Crossover Fe (bpy) 3 ]
2+
Complex
A recent promising approach, applied to the spin crossover complex [Fe (bpy) 3 ]
2+
[90] has been developed by C. M. Marian et al. [101, 102]. This method is based on
time-dependent calculations of ISC rates in the multi-mode harmonic oscillator and
Condon approximations and beyond, where the electronic spin-orbit matrix elements depend linearly on the nuclear coordinates within a spin-vibronic coupling
scheme. The ISC rate can be decomposed into three contributions, namely direct,
mixed direct vibronic, and vibronic.
Absorption Spectroscopy, Emissive Properties, and Ultrafast Intersystem. . .
401