degree of control can be achieved in a collinear beam geometry by controlling the
phases of the various beams. A linear combination of measurements with different
phases can then yield the desired signal with ϕ 4 ¼ Æϕ 3 Æ ϕ 2 Æ ϕ 1 corresponding to
the equivalent spatial-phase selection in the non-collinear arrangement [37,
38]. This technique is known as phase cycling [39] and is always employed in
multidimensional NMR because the wavevectors are close to zero in radio frequencies [40]. In the infrared, visible, and X-ray regimes, both phase matching and
phase cycling protocols for pathway selection are possible depending on experimental convenience.
So far, we have been concerned with processes in which the system is initially in
the ground state. In the X-ray regime, techniques employed can then study resonances of core excitations in relation to this ground state as well as the evolution of
valence excitations along the ground state potential surface. This procedure may be
generalized to account for a more general initial density matrix as may be obtained
from previous excitation or pumping of the system. A complete account of these
more general techniques involves explicit incorporation of the pumping process and
results in higher-order correlation functions [18, 30]. Although more complicated,
these techniques open up the possibility of studying excited state resonances
(as well their correlations) and tracking the motion of valence excitations in the
presence of core holes.
The present formalism may be further utilized in electronic spectroscopies such as
time-resolved photoelectron and Auger electron spectroscopy (TRPES and AES,
respectively). These techniques provide an alternative toolbox that complements and
supplements the optical techniques discussed here. In particular, TRPES has simplified selection rules compared to optical detection schemes (any orbital may be ionized
and the transition dipole to the continuum states does not depend much on the precise
continuum state and may be approximated as flat in certain regions). The probabilities
for excitation to various continuum states still depend sensitively on the final molecular electronic state and one can therefore use knowledge of the continuum as a probe
[41, 42]. On the other hand, AES has entirely different selection rules, being based on a
Coulomb matrix element (rather than a transition dipole) and has been used to track the
radiationless decay of photoexcited molecules [43]. Despite these differences, a very
similar formalism can be applied, the only differences being in the operators in the
correlation functions. This then allows the use of the array of simulation procedures
discussed for electronic spectroscopies and, in particular, gives a straightforward way
to incorporate bath dynamics and dissipation effects without explicitly including
corresponding degrees of freedom at the Hamiltonian level [44].
3 Quantum Chemistry Methods
Signal expressions in Sect. 2 require the calculation of core excited states and
transition dipole moments. Here we review the quantum chemistry methods that
can be used in their simulation and present a few examples.
292
Y. Zhang et al.
phases of the various beams. A linear combination of measurements with different
phases can then yield the desired signal with ϕ 4 ¼ Æϕ 3 Æ ϕ 2 Æ ϕ 1 corresponding to
the equivalent spatial-phase selection in the non-collinear arrangement [37,
38]. This technique is known as phase cycling [39] and is always employed in
multidimensional NMR because the wavevectors are close to zero in radio frequencies [40]. In the infrared, visible, and X-ray regimes, both phase matching and
phase cycling protocols for pathway selection are possible depending on experimental convenience.
So far, we have been concerned with processes in which the system is initially in
the ground state. In the X-ray regime, techniques employed can then study resonances of core excitations in relation to this ground state as well as the evolution of
valence excitations along the ground state potential surface. This procedure may be
generalized to account for a more general initial density matrix as may be obtained
from previous excitation or pumping of the system. A complete account of these
more general techniques involves explicit incorporation of the pumping process and
results in higher-order correlation functions [18, 30]. Although more complicated,
these techniques open up the possibility of studying excited state resonances
(as well their correlations) and tracking the motion of valence excitations in the
presence of core holes.
The present formalism may be further utilized in electronic spectroscopies such as
time-resolved photoelectron and Auger electron spectroscopy (TRPES and AES,
respectively). These techniques provide an alternative toolbox that complements and
supplements the optical techniques discussed here. In particular, TRPES has simplified selection rules compared to optical detection schemes (any orbital may be ionized
and the transition dipole to the continuum states does not depend much on the precise
continuum state and may be approximated as flat in certain regions). The probabilities
for excitation to various continuum states still depend sensitively on the final molecular electronic state and one can therefore use knowledge of the continuum as a probe
[41, 42]. On the other hand, AES has entirely different selection rules, being based on a
Coulomb matrix element (rather than a transition dipole) and has been used to track the
radiationless decay of photoexcited molecules [43]. Despite these differences, a very
similar formalism can be applied, the only differences being in the operators in the
correlation functions. This then allows the use of the array of simulation procedures
discussed for electronic spectroscopies and, in particular, gives a straightforward way
to incorporate bath dynamics and dissipation effects without explicitly including
corresponding degrees of freedom at the Hamiltonian level [44].
3 Quantum Chemistry Methods
Signal expressions in Sect. 2 require the calculation of core excited states and
transition dipole moments. Here we review the quantum chemistry methods that
can be used in their simulation and present a few examples.
292
Y. Zhang et al.