A spin adapted configuration interaction scheme is proposed for the evaluation of ionization potentials in α high spin open shell reference functions. There are three different ways to remove an electron from such a reference, including the removal of an alpha or a beta electron from doubly occupied or an alpha electron from singly occupied molecular orbitals. Ionization operators are constructed for each of these cases, and the resulting second quantized expressions are implemented using an automated code generator environment. To achieve greater computational efficiency, the virtual space is reduced using an averaged pair natural orbital machinery developed earlier and applied with great success in the calculation of X-ray absorption spectra [D. Manganas et al., J. Chem. Phys. A 122, 1215 (2018)]. Various approximate integral evaluation schemes including the resolution of identity and seminumerical techniques are also invoked to further enhance the computational efficiency. Although the resulting method is not particularly accurate in terms of predicting absolute energy values, with a simple shift in the ionization potentials, it is still possible to use it for the qualitative characterization of the basic features of X-ray photoionization spectra. While satellite intensities cannot be computed with the current method, the inclusion of vibrational effects using a path integral technique allows for the computation of vibrational transitions corresponding to main peaks.

1.
A.
Dreuw
and
M.
Head-Gordon
, “
Single-reference ab initio methods for the calculation of excited states of large molecules
,”
Chem. Rev.
105
,
4009
4037
(
2005
).
2.
K.
Sneskov
and
O.
Christiansen
, “
Excited state coupled cluster methods
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
,
566
584
(
2012
).
3.
D.
Cremer
, “
Møller–Plesset perturbation theory: From small molecule methods to methods for thousands of atoms
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
1
,
509
530
(
2011
).
4.
M.
Head-Gordon
,
R. J.
Rico
,
M.
Oumi
, and
T. J.
Lee
, “
A doubles correction to electronic excited states from configuration interaction in the space of single substitutions
,”
Chem. Phys. Lett.
219
,
21
29
(
1994
).
5.
M.
Head-Gordon
,
D.
Maurice
, and
M.
Oumi
, “
A perturbative correction to restricted open shell configuration interaction with single substitutions for excited states of radicals
,”
Chem. Phys. Lett.
246
,
114
121
(
1995
).
6.
C. D.
Sherrill
and
H. F.
Schaefer
,
The Configuration Interaction Method: Advances in Highly Correlated Approaches
(
Academic Press
,
1999
), pp.
143
269
.
7.
R. J.
Buenker
and
S. D.
Peyerimhoff
, “
Individualized configuration selection in Cl calculations with subsequent energy extrapolation
,”
Theor. Chem. Acc.
35
,
33
58
(
1974
).
8.
J.
Miralles
,
J.-P.
Daudey
, and
R.
Caballol
, “
Variational calculation of small energy differences. the singlet-triplet gap in Cu2Cl62-
,”
Chem. Phys. Lett.
198
,
555
562
(
1992
).
9.
J.
Miralles
,
O.
Castell
,
R.
Caballol
, and
J.-P.
Malrieu
, “
Specific Cl calculation of energy differences: Transition energies and bond energies
,”
Chem. Phys.
172
,
33
43
(
1993
).
10.
F.
Neese
, “
A spectroscopy oriented configuration interaction procedure
,”
J. Chem. Phys.
119
,
9428
9443
(
2003
).
11.
F.
Neese
,
T.
Petrenko
,
D.
Ganyushin
, and
G.
Olbrich
, “
Advanced aspects of ab initio theoretical optical spectroscopy of transition metal complexes: Multiplets, spin-orbit coupling and resonance Raman intensities
,”
Coord. Chem. Rev.
251
,
288
327
(
2007
).
12.
J.
Čížek
, “
On the use of the cluster expansion and the technique of diagrams in calculations of correlation effects in atoms and molecules
,” in
Advances in Chemical Physics
(
John Wiley & Sons, Inc.
,
1969
), pp.
35
89
.
13.
J.
Pople
,
J.
Binkley
, and
R.
Seeger
, “
Theoretical models incorporating electron correlation
,”
Int. J. Quantum Chem.
S10
,
1
19
(
1976
).
14.
R. J.
Bartlett
, “
Many-body perturbation theory and coupled cluster theory for electron correlation in molecules
,”
Annu. Rev. Phys. Chem.
32
,
359
401
(
1981
).
15.
I.
Shavitt
and
R. J.
Bartlett
,
Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory
, Cambridge Molecular Science (
Cambridge University Press
,
2009
).
16.
K.
Andersson
,
P. A.
Malmqvist
,
B. O.
Roos
,
A. J.
Sadlej
, and
K.
Wolinski
, “
Second-order perturbation theory with a casscf reference function
,”
J. Phys. Chem.
94
,
5483
5488
(
1990
).
17.
K.
Andersson
,
P.-Å.
Malmqvist
, and
B. O.
Roos
, “
Second-order perturbation theory with a complete active space self-consistent field reference function
,”
J. Chem. Phys.
96
,
1218
1226
(
1992
).
18.
K.
Andersson
and
B. O.
Roos
,
Modern Electronic Structure Theory
(
1995
), pp.
55
109
.
19.
P. G.
Szalay
,
T.
Müller
,
G.
Gidofalvi
,
H.
Lischka
, and
R.
Shepard
, “
Multiconfiguration self-consistent field and multireference configuration interaction methods and applications
,”
Chem. Rev.
112
,
108
181
(
2012
).
20.
H.
Lischka
,
D.
Nachtigallová
,
A. J.
Aquino
,
P. G.
Szalay
,
F.
Plasser
,
F. B.
Machado
, and
M.
Barbatti
, “
Multireference approaches for excited states of molecules
,”
Chem. Rev.
118
,
7293
(
2018
).
21.
R. J.
Bartlett
, “
To multireference or not to multireference: That is the question?
,”
Int. J. Mol. Sci.
3
,
579
603
(
2002
).
22.
D. I.
Lyakh
,
M.
Musiał
,
V. F.
Lotrich
, and
R. J.
Bartlett
, “
Multireference nature of chemistry: The coupled-cluster view
,”
Chem. Rev.
112
,
182
243
(
2011
).
23.
A.
Köhn
,
M.
Hanauer
,
L. A.
Mueck
,
T.-C.
Jagau
, and
J.
Gauss
, “
State-specific multireference coupled-cluster theory
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
3
,
176
197
(
2013
).
24.
R.
Maitra
,
D.
Sinha
, and
D.
Mukherjee
, “
Unitary group adapted state-specific multi-reference coupled cluster theory: Formulation and pilot numerical applications
,”
J. Chem. Phys.
137
,
024105
(
2012
).
25.
F. A.
Evangelista
, “
Perspective: Multireference coupled cluster theories of dynamical electron correlation
,”
J. Chem. Phys.
149
,
030901
(
2018
).
26.
H.
Nakatsuji
and
K.
Hirao
, “
Cluster expansion of the wavefunction. symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory
,”
J. Chem. Phys.
68
,
2053
2065
(
1978
).
27.
H.
Nakatsuji
, “
Description of two-and many-electron processes by the SAC-CI method
,”
Chem. Phys. Lett.
177
,
331
337
(
1991
).
28.
Y.
Ohtsuka
,
P.
Piecuch
,
J. R.
Gour
,
M.
Ehara
, and
H.
Nakatsuji
, “
Active-space symmetry-adapted-cluster configuration-interaction and equation-of-motion coupled-cluster methods for high accuracy calculations of potential energy surfaces of radicals
,”
J. Chem. Phys.
126
,
164111
(
2007
).
29.
K.
Emrich
, “
An extension of the coupled cluster formalism to excited states (I)
,”
Nucl. Phys. A
351
,
379
396
(
1981
).
30.
K.
Emrich
, “
An extension of the coupled cluster formalism to excited states: (II). Approximations and tests
,”
Nucl. Phys. A
351
,
397
438
(
1981
).
31.
J.
Geertsen
,
M.
Rittby
, and
R. J.
Bartlett
, “
The equation-of-motion coupled-cluster method: Excitation energies of Be and CO
,”
Chem. Phys. Lett.
164
,
57
62
(
1989
).
32.
J. F.
Stanton
and
R. J.
Bartlett
, “
The equation of motion coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties
,”
J. Chem. Phys.
98
,
7029
7039
(
1993
).
33.
H.
Sekino
and
R. J.
Bartlett
, “
A linear response, coupled-cluster theory for excitation energy
,”
Int. J. Quantum Chem.
26
,
255
265
(
1984
).
34.
H.
Koch
and
P.
Jørgensen
, “
Coupled cluster response functions
,”
J. Chem. Phys.
93
,
3333
3344
(
1990
).
35.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
, “
The second-order approximate coupled cluster singles and doubles model CC2
,”
Chem. Phys. Lett.
243
,
409
418
(
1995
).
36.
S.
Chattopadhyay
,
U. S.
Mahapatra
, and
D.
Mukherjee
, “
Development of a linear response theory based on a state-specific multireference coupled cluster formalism
,”
J. Chem. Phys.
112
,
7939
7952
(
2000
).
37.
C.
Hättig
and
F.
Weigend
, “
CC2 excitation energy calculations on large molecules using the resolution of the identity approximation
,”
J. Chem. Phys.
113
,
5154
5161
(
2000
).
38.
C.
Hättig
,
A.
Köhn
, and
K.
Hald
, “
First-order properties for triplet excited states in the approximated coupled cluster model CC2 using an explicitly spin coupled basis
,”
J. Chem. Phys.
116
,
5401
5410
(
2002
).
39.
P. K.
Samanta
,
D.
Mukherjee
,
M.
Hanauer
, and
A.
Köhn
, “
Excited states with internally contracted multireference coupled-cluster linear response theory
,”
J. Chem. Phys.
140
,
134108
(
2014
).
40.
L. S.
Cederbaum
,
W.
Domcke
, and
J.
Schirmer
, “
Many-body theory of core holes
,”
Phys. Rev. A
22
,
206
(
1980
).
41.
J.
Schirmer
, “
Beyond the random-phase approximation: A new approximation scheme for the polarization propagator
,”
Phys. Rev. A
26
,
2395
(
1982
).
42.
A.
Dreuw
and
M.
Wormit
, “
The algebraic diagrammatic construction scheme for the polarization propagator for the calculation of excited states
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
5
,
82
95
(
2015
).
43.
T.
Korona
and
H.-J.
Werner
, “
Local treatment of electron excitations in the EOM-CCSD method
,”
J. Chem. Phys.
118
,
3006
3019
(
2003
).
44.
A. K.
Dutta
,
F.
Neese
, and
R.
Izsák
, “
Towards a pair natural orbital coupled cluster method for excited states
,”
J. Chem. Phys.
145
,
034102
(
2016
).
45.
E.
Runge
and
E. K.
Gross
, “
Density-functional theory for time-dependent systems
,”
Phys. Rev. Lett.
52
,
997
(
1984
).
46.
F.
Neese
, “
Prediction of molecular properties and molecular spectroscopy with density functional theory: From fundamental theory to exchange-coupling
,”
Coord. Chem. Rev.
253
,
526
563
(
2009
).
47.
S.
Grimme
, “
Density functional calculations with configuration interaction for the excited states of molecules
,”
Chem. Phys. Lett.
259
,
128
137
(
1996
).
48.
S.
Grimme
and
M.
Waletzke
, “
A combination of Kohn–Sham density functional theory and multi-reference configuration interaction methods
,”
J. Chem. Phys.
111
,
5645
5655
(
1999
).
49.
P.
Borowski
,
K.
Jordan
,
J.
Nichols
, and
P.
Nachtigall
, “
Investigation of a hybrid TCSCF-DFT procedure
,”
Theor. Chem. Acc.
99
,
135
140
(
1998
).
50.
J.
Gräfenstein
,
E.
Kraka
, and
D.
Cremer
, “
Density functional theory for open-shell singlet biradicals
,”
Chem. Phys. Lett.
288
,
593
602
(
1998
).
51.
M.
Filatov
and
S.
Shaik
, “
Spin-restricted density functional approach to the open-shell problem
,”
Chem. Phys. Lett.
288
,
689
697
(
1998
).
52.
M.
Roemelt
and
F.
Neese
, “
Excited states of large open-shell molecules: An efficient, general, and spin-adapted approach based on a restricted open-shell ground state wave function
,”
J. Phys. Chem. A
117
,
3069
3083
(
2013
).
53.
M.
Roemelt
,
D.
Maganas
,
S.
DeBeer
, and
F.
Neese
, “
A combined DFT and restricted open-shell configuration interaction method including spin-orbit coupling: Application to transition metal L-edge X-ray absorption spectroscopy
,”
J. Chem. Phys.
138
,
204101
(
2013
).
54.
F.
Neese
, “
Importance of direct spin-spin coupling and spin-flip excitations for the zero-field splittings of transition metal complexes: A case study
,”
J. Am. Chem. Soc.
128
,
10213
10222
(
2006
).
55.
P. S.
Bagus
,
E. S.
Ilton
, and
C. J.
Nelin
, “
The interpretation of XPS spectra: Insights into materials properties
,”
Surf. Sci. Rep.
68
,
273
304
(
2013
).
56.
M.
Nooijen
and
J. G.
Snijders
, “
Coupled cluster approach to the single-particle green’s function
,”
Int. J. Quantum Chem.
44
,
55
83
(
1992
).
57.
M.
Nooijen
and
J. G.
Snijders
, “
Coupled cluster green’s function method: Working equations and applications
,”
Int. J. Quantum Chem.
48
,
15
48
(
1993
).
58.
M.
Nooijen
and
R. J.
Bartlett
, “
Equation of motion coupled cluster method for electron attachment
,”
J. Chem. Phys.
102
,
3629
3647
(
1995
).
59.
M.
Nooijen
and
J. G.
Snijders
, “
Second order manybody perturbation approximations to the coupled cluster green’s function
,”
J. Chem. Phys.
102
,
1681
1688
(
1995
).
60.
J. F.
Stanton
and
J.
Gauss
, “
Perturbative treatment of the similarity transformed Hamiltonian in equation-of-motion coupled-cluster approximations
,”
J. Chem. Phys.
103
,
1064
1076
(
1995
).
61.
A. K.
Dutta
,
N.
Vaval
, and
S.
Pal
, “
EOMIP-CCSD(2)*: An efficient method for the calculation of ionization potentials
,”
J. Chem. Theory Comput.
11
,
2461
2472
(
2015
).
62.
E.
Epifanovsky
,
D.
Zuev
,
X.
Feng
,
K.
Khistyaev
,
Y.
Shao
, and
A. I.
Krylov
, “
General implementation of the resolution-of-the-identity and cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks
,”
J. Chem. Phys.
139
,
134105
(
2013
).
63.
A. K.
Dutta
,
F.
Neese
, and
R.
Izsák
, “
Speeding up equation of motion coupled cluster theory with the chain of spheres approximation
,”
J. Chem. Phys.
144
,
034102
(
2016
).
64.
A.
Landau
,
K.
Khistyaev
,
S.
Dolgikh
, and
A. I.
Krylov
, “
Frozen natural orbitals for ionized states within equation-of-motion coupled-cluster formalism
,”
J. Chem. Phys.
132
,
014109
(
2010
).
65.
A. K.
Dutta
,
M.
Saitow
,
C.
Riplinger
,
F.
Neese
, and
R.
Izsák
, “
A near-linear scaling equation of motion coupled cluster method for ionized states
,”
J. Chem. Phys.
148
,
244101
(
2018
).
66.
A. A.
Golubeva
,
P. A.
Pieniazek
, and
A. I.
Krylov
, “
A new electronic structure method for doublet states: Configuration interaction in the space of ionized 1h and 2h1p determinants
,”
J. Chem. Phys.
130
,
124113
(
2009
).
67.
A. I.
Krylov
, “
The quantum chemistry of open-shell species
,” in
Reviews in Computational Chemistry
(
John Wiley & Sons, Inc.
,
2017
), pp.
151
224
.
68.
A.
Sadybekov
and
A. I.
Krylov
, “
Coupled-cluster based approach for core-level states in condensed phase: Theory and application to different protonated forms of aqueous glycine
,”
J. Chem. Phys.
147
,
014107
(
2017
).
69.
T. J.
Watson
and
R. J.
Bartlett
, “
Infinite order relaxation effects for core ionization energies with a variational coupled cluster ansatz
,”
Chem. Phys. Lett.
555
,
235
238
(
2013
).
70.
S.
Coriani
and
H.
Koch
, “
Communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework
,”
J. Chem. Phys.
143
,
181103
(
2015
).
71.
S.
Coriani
and
H.
Koch
, “
Erratum: ‘communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework’ [J. Chem. Phys. 143, 181103 (2015)]
,”
J. Chem. Phys.
145
,
149901
(
2016
).
72.
J. A.
Nichols
,
D. L.
Yeager
, and
P.
Jo/rgensen
, “
Multiconfigurational electron propagator (MCEP) ionization potentials for general open shell systems
,”
J. Chem. Phys.
80
,
293
314
(
1984
).
73.
D.
Danovich
, “
Green’s function methods for calculating ionization potentials, electron affinities, and excitation energies
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
1
,
377
387
(
2011
).
74.
J. V.
Ortiz
, “
Electron propagator theory: An approach to prediction and interpretation in quantum chemistry
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
3
,
123
142
(
2012
).
75.
M.
Piris
,
J. M.
Matxain
,
X.
Lopez
, and
J. M.
Ugalde
, “
The extended Koopmans’ theorem: Vertical ionization potentials from natural orbital functional theory
,”
J. Chem. Phys.
136
,
174116
(
2012
).
76.
E. N.
Zarkadoula
,
S.
Sharma
,
J. K.
Dewhurst
,
E. K. U.
Gross
, and
N. N.
Lathiotakis
, “
Ionization potentials and electron affinities from reduced-density-matrix functional theory
,”
Phys. Rev. A
85
,
032504
(
2012
).
77.
V.
Carravetta
and
H.
Agren
, “
Computational x-ray spectroscopy
,”
Computational Strategies for Spectroscopy: From Small Molecules to Nano Systems
(
Wiley & Sons
,
2012
), pp.
137
205
.
78.
R.
Arneberg
,
J.
Müller
, and
R.
Manne
, “
Configuration interaction calculations of satellite structure in photoelectron spectra of H2O
,”
Chem. Phys.
64
,
249
258
(
1982
).
79.
W.
von Niessen
,
J.
Schirmer
, and
L.
Cederbaum
, “
Computational methods for the one-particle green’s function
,”
Comput. Physi. Rep.
1
,
57
125
(
1984
).
80.
C.-M.
Liegener
, “
Green’s function calculations on the Auger spectra of CO
,”
Chem. Phys. Lett.
106
,
201
205
(
1984
).
81.
V.
Carravetta
 et al., “
Stieltjes imaging method for molecular Auger transition rates: Application to the Auger spectrum of water
,”
Phys. Rev. A
35
,
1022
(
1987
).
82.
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
).
83.
R.
Pauncz
,
Spin Eigenfunctions: Construction and Use
(
Springer Science & Business Media
,
2012
).
84.
B. T.
Pickup
and
A.
Mukhopadhyay
, “
Spin symmetry adaptation of the one-electron propagator
,”
Chem. Phys. Lett.
79
,
109
114
(
1981
).
85.
P.
Pulay
,
S.
Saebø
, and
W.
Meyer
, “
An efficient reformulation of the closed-shell self-consistent electron pair theory
,”
J. Chem. Phys.
81
,
1901
1905
(
1984
).
86.
E. R.
Davidson
, “
The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
,”
J. Comput. Phys.
17
,
87
94
(
1975
).
87.
M.
Crouzeix
,
B.
Philippe
, and
M.
Sadkane
, “
The Davidson method
,”
SIAM J. Sci. Comput.
15
,
62
76
(
1994
).
88.
M.
Krupička
,
K.
Sivalingam
,
L.
Huntington
,
A. A.
Auer
, and
F.
Neese
, “
A toolchain for the automatic generation of computer codes for correlated wavefunction calculations
,”
J. Comput. Chem.
38
,
1853
(
2017
).
89.
F.
Neese
, “
Software update: The ORCA program system, version 4.0
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
,
e1327
(
2017
).
90.
F.
Neese
,
F.
Wennmohs
,
A.
Hansen
, and
U.
Becker
,
Chem. Phys.
356
,
98
(
2009
).
91.
R.
Izsák
and
F.
Neese
,
J. Chem. Phys.
135
,
144105
(
2011
).
92.
P.
Pinski
,
C.
Riplinger
,
E. F.
Valeev
, and
F.
Neese
, “
Sparse maps: A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals
,”
J. Chem. Phys.
143
,
034108
(
2015
).
93.
C.
Riplinger
,
P.
Pinski
,
U.
Becker
,
E. F.
Valeev
, and
F.
Neese
, “
Sparse maps: A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory
,”
J. Chem. Phys.
144
,
024109
(
2016
).
94.
M.
Saitow
,
U.
Becker
,
C.
Riplinger
,
E. F.
Valeev
, and
F.
Neese
, “
A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory
,”
J. Chem. Phys.
146
,
164105
(
2017
).
95.
M.
Schwilk
,
D.
Usvyat
, and
H.-J.
Werner
, “
Communication: Improved pair approximations in local coupled-cluster methods
,”
J. Chem. Phys.
142
,
121102
(
2015
).
96.
H.-J.
Werner
, “
Communication: Multipole approximations of distant pair energies in local correlation methods with pair natural orbitals
,”
J. Chem. Phys.
145
,
201101
(
2016
).
97.
M.
Schwilk
,
Q.
Ma
,
C.
Köppl
, and
H.-J.
Werner
, “
Scalable electron correlation methods. 3. efficient and accurate parallel local coupled cluster with pair natural orbitals (PNO-LCCSD)
,”
J. Chem. Theory Comput.
13
,
3650
3675
(
2017
).
98.
B.
Helmich
and
C.
Hättig
, “
Local pair natural orbitals for excited states
,”
J. Chem. Phys.
135
,
214106
(
2011
).
99.
M. S.
Frank
and
C.
Hättig
, “
A pair natural orbital based implementation of CCSD excitation energies within the framework of linear response theory
,”
J. Chem. Phys.
148
,
134102
(
2018
).
100.
M. C.
Clement
,
J.
Zhang
,
C. A.
Lewis
,
C.
Yang
, and
E. F.
Valeev
, “
Optimized pair natural orbitals for the coupled cluster methods
,” preprint arXiv:1803.09135 (
2018
).
101.
C.
Peng
,
M. C.
Clement
, and
E. F.
Valeev
, “
Exploration of reduced scaling formulation of equation of motion coupled-cluster singles and doubles based on state-averaged pair natural orbitals
,” preprint arXiv:1802.06738 (
2018
).
102.
J.
Yang
,
Y.
Kurashige
,
F. R.
Manby
, and
G. K. L.
Chan
, “
Tensor factorizations of local second-order Møller-Plesset theory
,”
J. Chem. Phys.
134
,
044123
(
2011
).
103.
D.
Manganas
,
S.
DeBeer
, and
F.
Neese
, “
Pair natural orbital restricted open-shell configuration interaction (PNO-ROCIS) approach for calculating x-ray absorption spectra of large chemical systems
,”
J. Phys. Chem. A
122
,
1215
(
2018
).
104.
Y.
Niu
,
Q.
Peng
,
C.
Deng
,
X.
Gao
, and
Z.
Shuai
, “
Theory of excited state decays and optical spectra: Application to polyatomic molecules
,”
J. Phys. Chem. A
114
,
7817
7831
(
2010
).
105.
G. C. S. A.
Ratner
,
Quantum Mechanics in Chemistry
(
Dover Publications
,
1819
).
106.
F.
Duschisnky
,
Acta Physicochim. U. R. S. S.
7
,
551
(
1937
).
107.
F.
Jensen
,
Introduction to Computational Chemistry
, 3rd ed. (
Wiley
,
Chichester, UK; Hoboken, NJ
,
2017
).
108.
B.
de Souza
,
F.
Neese
, and
R.
Izsák
, “
On the theoretical prediction of fluorescence rates from first principles using the path integral approach
,”
J. Chem. Phys.
148
,
034104
(
2018
).
109.
S.
Sen
,
A.
Shee
, and
D.
Mukherjee
, “
Inclusion of orbital relaxation and correlation through the unitary group adapted open shell coupled cluster theory using non-relativistic and scalar relativistic Hamiltonians to study the core ionization potential of molecules containing light to medium-heavy elements
,”
J. Chem. Phys.
148
,
054107
(
2018
).
110.
R.
Püttner
,
V.
Sekushin
,
H.
Fukuzawa
,
T.
Uhlíková
,
V.
Špirko
,
T.
Asahina
,
N.
Kuze
,
H.
Kato
,
M.
Hoshino
,
H.
Tanaka
 et al., “
Metastable states in NO2+ probed with auger spectroscopy
,”
Phys. Chem. Chem. Phys.
13
,
18436
18446
(
2011
).
111.
S.
Osborne
,
S.
Sundin
,
A.
Ausmees
,
S.
Svensson
,
L.
Saethre
,
O.
Svaeren
,
S.
Sorensen
,
J.
Végh
,
J.
Karvonen
,
S.
Aksela
 et al., “
The vibrationally resolved C 1s core photoelectron spectra of methane and ethane
,”
J. Chem. Phys.
106
,
1661
1668
(
1997
).
112.
I.
Ljubić
, “
Reliability of density functional and perturbation theories for calculating core-ionization spectra of free radicals
,”
J. Chem. Theory Comput.
10
,
2333
2343
(
2014
).
113.
F.
Holzmeier
,
M.
Lang
,
I.
Fischer
,
X.
Tang
,
B.
Cunha de Miranda
,
C.
Romanzin
,
C.
Alcaraz
, and
P.
Hemberger
, “
Threshold photoelectron spectroscopy of unstable n-containing compounds: Resolution of ΔKk subbands in HNCO+ and vibrational resolution in NCO+
,”
J. Chem. Phys.
142
,
184306
(
2015
).
114.
D. W.
Turner
, “
Molecular photoelectron spectroscopy
,”
Philos. Trans. R. Soc., A
268
,
7
31
(
1970
).
115.
Y.
Zhu
,
X.
Wu
,
X.
Tang
,
Z.
Wen
,
F.
Liu
,
X.
Zhou
, and
W.
Zhang
, “
Synchrotron threshold photoelectron photoion coincidence spectroscopy of radicals produced in a pyrolysis source: The methyl radical
,”
Chem. Phys. Lett.
664
,
237
241
(
2016
).
116.
J. D.
Savee
,
J.
Zádor
,
P.
Hemberger
,
B.
Sztáray
,
A.
Bodi
, and
D. L.
Osborn
, “
Threshold photoelectron spectrum of the benzyl radical
,”
Mol. Phys.
113
,
2217
2227
(
2015
).
117.
W.
Jolly
,
K.
Bomben
, and
C.
Eyermann
, “
Core-electron binding energies for gaseous atoms and molecules
,”
Atomic Data Nucl. Data Tables
31
,
433
493
(
1984
).
118.
C.
Li
,
P.
Salén
,
V.
Yatsyna
,
L.
Schio
,
R.
Feifel
,
R.
Squibb
,
M.
Kamińska
,
M.
Larsson
,
R.
Richter
,
M.
Alagia
 et al., “
Experimental and theoretical XPS and NEXAFS studies of N-methylacetamide and N-methyltrifluoroacetamide
,”
Phys. Chem. Chem. Phys.
18
,
2210
2218
(
2016
).
119.
P. J.
Linstrom
and
W. G.
Mallard
, “
The NIST chemistry webbook: A chemical data resource on the internet
,”
J. Chem. Eng. Data
46
,
1059
1063
(
2001
).
120.
F.
Holzmeier
,
I.
Wagner
,
I.
Fischer
,
A.
Bodi
, and
P.
Hemberger
, “
Pyrolysis of 3-methoxypyridine. Detection and characterization of the pyrrolyl radical by threshold photoelectron spectroscopy
,”
J. Phys. Chem. A
120
,
4702
4710
(
2016
).

Supplementary Material

You do not currently have access to this content.