Dyson orbitals for ionization from the ground and electronically excited states in EOM-CCSD formalism
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:  Ψel is the wavefunction of the outgoing electron, and its angular momentum can be described by spherical harmonics Yl,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% 3a1 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 1B2 excited state (1b2 to 4a1 electron excitation) to the ground state (1A1) of the cation (3a1 MO ionized), the Dyson orbital consists in a combination of virtual and occupied b2 orbitals: 85.5% 3b2 + 0.3% 2b2 + 11.3% 1b2. 
Dyson orbital for the transition between the ground state H2O (1A1) to ground state H2O+ (1A1) 
Dyson orbital for the transition between the excited state H2O (1B2) and ground state H2O+ (1A1) 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 B2 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 |
