#
Dyson orbitals for ionization from the ground and electronically
excited states in EOM-CCSD formalism

To model angular distributions of photoelectrons, we implemented the
calculation of Dyson orbitals using EOM-EE/IP/EA-CCSD.

For the Hartree-Fock wave functions and within Koopmans' approximation of
the ionized states, the Dyson orbitals are just the canonical HF orbitals. For
general correlated wave functions, Dyson orbitals represent the overlap
between an N electron molecular wavefunction and the N-1/N+1 electron
wavefunction of the corresponding cation/anion:

The probability of an electron being ejected in a certain direction
(photoelectron angular distribution) is given by the ionization dipole moment:

Ψ^{el} is the wavefunction of the outgoing electron, and
its angular momentum can be described by spherical harmonics
Y_{l,m}(θ, φ):

Dyson orbitals can be thought of as the wavefunction of the leaving
electron (before ionization), analogous to the Koopmans' picture, which
is quite transparent from the equations above. Thus,
for the ground-state ionization, the Dyson orbital is usually well approximated by
the molecular orbital (MO) of the ionized electron. For example,
the calculated Dyson orbital for ionization of water in its ground state
has 99.7% 3a_{1} MO contribution.

**Occupied (top) and selected virtual (bottom) HF molecular
orbitals of water**

For the ionization from electronically excited states, the shape of
the Dyson orbital is less intuitive. For the ionization of water
1B_{2} excited state (1b_{2} to 4a_{1} electron
excitation) to the ground state (1A_{1}) of the cation
(3a_{1} MO ionized), the Dyson orbital consists in a combination
of virtual and occupied b_{2} orbitals:
85.5% 3b_{2} + 0.3% 2b_{2}
+ 11.3% 1b_{2}.

**Dyson orbital for the transition between the ground state
H**_{2}O (1A_{1}) to ground state
H_{2}O^{+} (1A_{1})

**Dyson orbital for the transition between the excited state
H**_{2}O (1B_{2}) and ground state
H_{2}O^{+} (1A_{1})

We have used this approach to aid in the interpretation of the experimental
results for the photodissociation of the (NO)_{2} species. Shown below are the
calculated photoelectron angular distributions for four different excited states and
the corresponding Dyson orbitals. Comparison with experimental data suggests that the
B_{2} state is the one leading to the dissociation of the dimer, although the
shapes of the calculated photoelectron angular distributions vary drastically with
the kinetic energy of the electron.

**Dyson orbitals and calculated photoelectron angular distributions for
several excited states in the NO dimer**

## Related Publications

**168. **T.-C. Jagau and A.I. Krylov

*Characterizing metastable states beyond energies and lifetimes: Dyson orbitals and transition dipole moments
*

J. Chem. Phys. **144**, 054113
(2016)
Abstract
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**163. **S. Gozem, A.O. Gunina, T. Ichino, D.L. Osborn, J.F. Stanton, and A.I. Krylov

*Photoelectron wave function in photoionization: Plane wave or Coulomb wave?
*

J. Phys. Chem. Lett. **6**, 4532 – 4540
(2015)
Abstract
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**85. **C.M. Oana and A.I. Krylov

*
Cross sections and photoelectron angular distributions
in photodetachment from negative ions using
equation-of-motion coupled-cluster Dyson orbitals
*

J. Chem. Phys. **131**, 124114
(2009)
Abstract
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**59. **C.M. Oana and A.I. Krylov

*Dyson orbitals for ionization from the ground and electronically
excited states within equation-of-motion coupled-cluster formalism:
Theory, implementation, and examples*

J. Chem. Phys. **127**, 234106
(2007)
Abstract
PDF (873 kB)