Modeling Photoelectron Spectra of CuO, Cu2O, and CuO2 Anions with

Article pubs.acs.org/JPCA

Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX

Modeling Photoelectron Spectra of CuO, Cu2O, and CuO2 Anions with Equation-of-Motion Coupled-Cluster Methods: An Adventure in Fock Space Natalie Orms and Anna I. Krylov* Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, United States S Supporting Information *

ABSTRACT: The experimental photoelectron spectra of di- and triatomic copper oxide anions have been reported previously. We present an analysis of the experimental spectra of the CuO−, Cu2O−, and CuO−2 anions using equation-of-motion coupled-cluster (EOM-CC) methods. The open-shell electronic structure of each molecule demands a unique combination of EOM-CC methods to achieve an accurate and balanced representation of the multiconfigurational anionic- and neutral-state manifolds. Analysis of the Dyson orbitals associated with photodetachment from CuO− reveals the strong non-Koopmans character of the CuO states. For the lowest detachment energy, a good agreement between theoretical and experimental values is obtained with CCSD(T) (coupled-cluster with single and double excitations and perturbative account of triple excitations). The (T) correction is particularly important for Cu2O−. Use of a relativistic pseudopotential and matching basis set improves the quality of results in most cases. EOM-DIPCCSD analysis of the low-lying states of CuO−2 reveals multiple singlet and triplet anionic states near the triplet ground state, adding an extra layer of complexity to the interpretation of the experimental CuO−2 photoelectron spectrum. on density functional theory (DFT)18−36with BLYP,22,24,32,35 BPW91,22,32 B3LYP,22,26−28,32−36 and PBE25 functionals. Timedependent DFT has been used to compute excited states.24 Previous treatments that utilize wave function methods include multiconfigurational self-consistent field methods,18,30 perturbation theory,23,27 configuration interaction,18−21,23,29 and coupledcluster23,27,34 methods. In this contribution, we report a systematic study of low-lying electron-detached and excited states of the CuO−, Cu2O−, and CuO−2 anions using a uniform single-reference approach capable of treating dynamical and nondynamical correlation, equation-ofmotion coupled-cluster method with single and double excitations (EOM-CCSD). We describe the excitation and electron detachment transitions that give rise to the low-energy photoelectron spectra of these species. On the basis of the analysis of the underlying wave functions, we show that extreme open-shell character of these species calls for a careful choice of methodology. In EOMCCSD, the target states are described using the following ansatz:

1. INTRODUCTION Photoelectron spectroscopy (PES) allows one to characterize multiple electronic states of the excited or photodetached species in a single experimental setup.1−4 Photodetachment from anions, which can be mass-selected, is often used to characterize transient open-shell neutral states.5−7 A particularly attractive feature of PES is that, owing to different selection rules, it can characterize energy differences between electronic states from different spin manifolds. In the present work, we apply state-ofthe-art quantum chemistry methods based on the equationof-motion coupled-cluster (EOM-CC) approach8−10 to model photoelectron spectra in di- and triatomic copper oxide anions. Copper oxides serve as a component of semiconductors,11 a pigment in glazes for ceramics,12 and have even been assembled in nanoparticles for antimicrobial applications.13 Complexes of copper with oxygen are also involved in catalytic oxidation and oxygen transport in biomolecules14 and in catalysis.15 The structure and low-lying electronic states of transition metal oxide clusters are important in the study of corrosion processes and the reaction of oxygen with metal surfaces. In addition to their relevance to applications, these simple molecules are also popular because of their fundamental importancethey illustrate basic bonding concepts in transition metal compounds. Several experimental studies investigated neutral and anionic copper oxide clusters by using PES.4,16,17 Different aspects of their electronic structure have been also interrogated theoretically. The bulk of previous theoretical studies have been limited to methods based © XXXX American Chemical Society

̂

̂

Ψ = (R̂ 0 + R1̂ + R̂ 2)eT1+ T2 Φ0

(1)

T̂ 1+T̂ 2

where e Φ0 is the reference CCSD wave function, and operator R̂ is a general excitation operator. By a deliberate combination Received: October 26, 2017 Revised: December 14, 2017 Published: December 18, 2017 A

DOI: 10.1021/acs.jpca.7b10620 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

section.38,39 Detached states that can be generated by removing one electron from the reference have norms of Dyson orbitals close to 1 and result in principal peaks in PES, whereas the states 2 that have large ∥RIP 2 ∥ have small norms of Dyson orbitals and show up as satellite shakeup excitations. Our analysis of the excited and ionized states in neutral and anionic copper oxides can serve as a basis for calibrating other electronic structure methods and as a tutorial into practical application of EOM-CC methods. To include the effect of higher excitations, for selected states we also performed CCSD(T) calculations. One of the aims of our analysis is to outline the domain of applicability of more approximate methods, such as Kohn−Sham DFT40−42 and its extensions,43 for modeling PES in copper oxide anions and similar systems. For states dominated by a single electronic configuration, these methods are justifiable.44 However, as we show below, the three copper oxide species considered here possess low-lying anionic and neutral states arising from multiple near-degenerate electronic configurations. For highly correlated systems such as these, Koopmanslike behavior is rarely observed, and more sophisticated methodology, like EOM-CCSD, is required for description of photoelectron spectra. The paper is organized as follows: In the next section, we briefly outline the computational details and methodologies applied. Where applicable, we refer the reader to previous work, wherein the relevant methods are explained in detail.8,45−47 We then present our results for the CuxOy anions in the following order: CuO−, Cu2O−, and CuO−2 . We conclude with a brief commentary on the electronic structure of each system, including the extent of open-shell and multiconfigurational character.

of an appropriate reference state and a particular form of the EOM operator,8 the EOM-CC family of methods allows one to access different types of states probed in these experiments. Here, we utilize the following EOM-CCSD methods: EE (excitation energies), SF (spin-flip), IP (ionization potentials), EA (electron attachment), and DIP (double IP). Figure 1 illustrates types of

Figure 1. Different EOM models are defined by choosing the reference (Φ0) and the form of the operator R̂ . EOM-EE allows access to electronically excited states of closed-shell molecules, EOM-IP and EOM-EA can describe doublet target states, and EOM-SF and EOMDIP describe multiconfigurational wave function of diradical/triradical character.

2. COMPUTATIONAL METHODS The Q-Chem electronic structure package was used for all electronic structure calculations.48,49 We optimized the structures of the ground states of CuO− (closed-shell singlet), Cu2O− (doublet with one unpaired electron), and CuO−2 (triplet) using the ωB97X-D method50 and all-electron cc-pVTZ basis; relevant Cartesian geometries are provided in the Supporting Information. We report only vertical electronic energy separations, computed at the equilibrium structures of the anionic ground states. Zeropoint energies are not included. Because the available experimental spectra16 are broad and not vibrationally resolved, vertical detachment energies (DE) are sufficient for an adequate comparison. EOM−EE/IP/DIP/SF/EA−CCSD and CCSD(T) calculations were performed using an all-electron cc-pVTZ basis, or the Stuttgart−Cologne ECP10MDF pseudopotential51 paired with a matching correlation-consistent basis for Cu (indicated in results tables). ECP10MDF has been shown to perform well in the EOM-CCSD analysis of small copper compounds.52 User-defined basis sets for Cu were obtained from ref 53. For selected states, additional calculations were performed with aug-cc-pVTZ and aug-cc-pVQZ. In calculations employing open-shell reference states (doublets, triplets, quartets), unrestricted Hartree−Fock solutions were used. For linear molecules (CuO− and CuO−2 ), we report symmetry labels corresponding to the largest Abelian subgroup. Tables S1 and S2 in the SI show the mapping between C2v and C∞v, and D2h and D∞h groups,54 which can be used to obtain proper spectroscopic term labels. We note that Q-Chem does not follow the standard Mulliken convention55 for molecular orientation; consequently, some symmetry labels (in particular, for C2v

target-state manifolds accessed via these methods. Operator R̂ 1 describes the singly excited part of the target wave function; that is, in EOM-EE it generates all hole-particle (hp) configurations from the reference determinant Φ0, whereas in EOM-IP it generates all singly ionized Koopmans-like determinants (hole configurations, h). R̂ 0 is only present in EOM-EE. The relative magnitude of R̂ 1 and R̂ 2, which reflects the correlation effects, can be quantified by their norms: R1EE R1IP

2 2

= ∑ia (ria)2 = ∑i (ri)2 ...

(2)

The states that are predominantly singly excited with respect to 2 the reference have ∥REE 1 ∥ ≈ 1. In addition to the magnitude of R1, it is also instructive to look at the leading amplitude, to distinguish whether the target state is dominated by one or several configurations. The latter situation is described as nondynamical correlation. The role of R2 is to describe dynamical correlation. 2 The states with ∥REE 1 ∥ ≈ 1 can be described by configuration interaction singles (CIS) or TDDFT ansatz. Likewise, singly ionized states for which there is one leading ri amplitude 2 and ∥RIP 1 ∥ ≈ 1 can, in principle be described by Koopmans 2 approximation. The overall singly ionized character (∥RIP 1 ∥ ) is 37 related to the norm of the Dyson orbital, which determines the magnitude of the photoionization/photodetachment cross B


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For each system, the specific choice of an EOM-CCSD method (or a combination of several EOM-CC approaches) depends on an open-shell pattern exhibited by the respective ground-state anions and target states accessible via one-electron detachment processes. We will describe the approaches used for CuO−, Cu2O−, and CuO−2 on a case-by-case basis in the following section. In selected cases, we also computed Dyson orbitals:37 ϕd(1) =

N

∫ ΨN(1, 2, ..., N )ΨN−1(2, 3, ..., N )d2 ... dN (3)

Dyson orbitals are related to photoionization/photodetachment cross sections:38,39 their norms quantify the extent of differential electron correlation in the initial (N-electron) and final (N−1 electron) states. For example, for Hartree−Fock (or Kohn−Sham) wave functions and within Koopmans approximation, the Dyson orbitals are just canonical SCF orbitals, and their norms equal one. We note that even when the ionized states have predominantly Koopmans character; that is, when the respective correlated wave functions have one leading ionized determinant, the quantitative accuracy of Koopmans theorem can be rather poor. For example, it is not uncommon that the order of ionized states changes relative to that predicted by the Koopmans theorem, when correlation is included.

Figure 2. Structures of the three copper oxide anions included in the study: closed-shell singlet CuO− (top left), doublet Cu2O− (top right), and triplet CuO−2 (bottom). All structures were optimized at the ωB97X-D/cc-pVTZ level of theory.

3. RESULTS AND DISCUSSION Figure 2 shows the structures of the three copper oxide anions studied. Although they are superficially similar, these species feature distinct electronic structure patterns, calling for different electronic structure approaches. CuO−, which has the singlet ground state, is the simplest of the three oxides. In this system, most of the target neutral states have clear Koopmans character. The ground states of Cu2O− and CuO−2 are a doublet and triplet, respectively, which results in more complicated target-state patterns. In all three oxides, the attached electron is rather strongly bound, with the detachment energies exceeding 1 eV. 3.1. CuO−. The Hartree−Fock molecular orbitals (MOs) of closed-shell singlet CuO− are depicted in Figure 3. As a singlet closed-shell anion, CuO− is the easiest to model: the majority of transitions that appear in the experimental PES of CuO− can be computed via EOM-IP-CCSD from the closed-shell singlet reference. Most of the target states have well-defined Koopmans character, as evidenced by the norms of the respective Dyson orbitals and the values of the leading EOM-IP amplitudes. We note that CuO− features low-lying excited states; these states can be computed by a straightforward application of EOM-EECCSD. Importantly, the lowest triplet state lies only 0.5 eV (vertically) above the singlet. The triplet and other excited states can be populated at the experimental conditions,16 giving rise to additional transitions. For most target states, we computed the energies of these hot bands by combining EOM-EE excitation energies (of the closed-shell anion) with EOM-IP detachment energies of the singlet anion (for example, energy of the A band can be computed by subtracting EOM-EE-CCSD energy of the lowest triplet state from the EOM-IP-CCSD detachment energy of the X band). In order to compute the energy corresponding to an open-shell quartet state (4B1/B2), which cannot be accessed by detachment from the singlet, we performed EOM-SF calculations from the quartet reference.56 This scheme allows us to accurately estimate the energy gap between the quartet and open-shell doublet states, so that the energy of this state can be computed relative to other detached states.

Figure 3. Canonical Hartree−Fock molecular orbitals of singlet CuO−.

symmetry) differ from the standard notation. Core electrons (1s on oxygen and 1s, 2s, 2p, 3s, and 3p on copper) were frozen in the all-electron EOM/CC calculations. C


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Table 3. Lowest Vertical Detachment Energy (X1A1 →2 B1/B2 Transition), in eV, Computed As Energy Difference Using CCSD and CCSD(T) Methods with All-Electron Basis Setsa

Table 1. Six Lowest EOM-IP-CCSD/ECP10MDF/aug-ccpVTZ-PPa Detachment Energies Obtained from the ClosedShell Singlet CuO− Referenceb orbitalc 3b1/3b2 7a1 5a1 1a2 6a1 2b1/2b2

state 2

2

B1/ B2 2 A1 2 A1 2 A2 2 A1 2 B1/2B2

DE (eV)

∥R1∥2

leading ri

Dyson normd

basis

CCSD

CCSD(T)

1.889 2.556 4.829 4.829 5.114 5.571

0.901 0.928 0.907 0.907 0.868 0.898

0.942 0.959 0.953 0.953 0.922 0.941

0.930 0.956 0.941 0.941 0.911 0.934

cc-pVTZ aug-cc-pVTZ aug-cc-pVQZ

0.893 1.155 1.180

1.420 1.678 1.723

a

Experimental value: 1.78 eV (ref 16).

a

Augmented by even-tempered diffuse 6s, 6p, 3d functions. bECP applied to Cu only. All-electron aug-cc-pVTZ basis used for oxygen. c See Figure 3 for the symmetries and shapes of Hartree−Fock orbitals. dNorm of the right Dyson orbital associated with the EOM-IP transition.

Figure 5. Six lowest singlet (left) and triplet (right) EOM-EE-CCSD/ cc-pVTZ excited states obtained from the closed-shell singlet CuO− reference. Photodetachment threshold indicated by the dotted gray line (the states above the dashed line correspond to autodetaching resonances).

and 1h1p in EOM-EE) in the EOM-CCSD wave functions. The deviation of ∥R12∥ from one quantifies the weight of 2h1p/2h2p configurations, which describe dynamic correlation of the target states. The absolute value of the leading R1 amplitude shows how well this state can be described by Koopmans approximation; for example, several amplitudes with comparable values signify mixing of several Koopmans configurations in the target states, which can be described in terms of nondynamical correlation. The most experimentally relevant quantity is the norm of the Dyson orbitals, which determines the magnitude of the photodetachment cross sections: for example, transitions which cannot be described by one-electron ejection, the norms of Dyson orbitals give rise to small norms and, consequently, low cross sections. ∥R1∥2 and leading amplitudes (leading ri) of the EOM-IP-CCSD transitions indicate that the states arising from photodetachment of CuO− have one-electron character and are dominated by a single electronic configuration. Yet, there is notable dissimilarity between the correlated Dyson orbitals and the canonical Hartree−Fock MOs associated with the leading amplitudes of the lowest three EOM-IP-CCSD/cc-pVTZ transitions (Figure 4). Moreover, the lowest EOM-IP-CCSD detached state obtained from the closedshell CuO− reference does not arise from detachment of an electron occupying the HOMO, and instead arises from detachment from the HOMO−1/HOMO−2. These results highlight the quantitative limitations of Koopmans’ approximation in describing the detached states of CuO−. Norms of the Dyson orbitals (Table 1 and Tables S3/S4 in SI) are all greater than 0.9 and approximately equal, indicating that the corresponding experimental peaks should have similar intensities. With the exception of the quartet state, most transitions have dominant Koopmans character and, therefore, can be modeled by Kohn−Sham DFT and GW (Green-function-based extension of DFT43) type of approaches. The EOM-IP-CCSD/aug-cc-pVTZ

Figure 4. Six lowest EOM-IP-CCSD/cc-pVTZ electron-detached states obtained from the closed-shell singlet CuO− reference. Molecular orbitals associated with dominant amplitudes in each EOM-IP transition are depicted in red and blue. Dyson orbitals associated with each EOMIP transition are rendered in magenta and yellow. Correlated detachment energies are shown (EOM-IP-CCSD values).

Table 2. Six Lowest Excitation Energies (from the ClosedShell Singlet Reference) of CuO− Computed at the EOM-EECCSD/ECP10MDF/aug-cc-pVTZ-PPa Level of Theoryb transitionc 7a1 → 24a1 3b1/3b2 → 4b1/4b2 3b1/3b2 → 24a1 3b1/3b2 → 9a1

state 3

A1 A1, 1A2 3 A1, 3A2 1 B1, 1B2 3 B1, 3B2 1 B1, 1B2 3 B1, 3B2

1

Eex (eV)

∥R1∥2

leading rai

0.925 1.901 1.902 0.861 0.442 1.894 1.894

0.956 0.901 0.901 0.907 0.919 0.901 0.901

0.358 0.393 0.310 0.334 0.325 0.411 0.375

a Augmented by even-tempered diffuse 6s, 6p, 3d functions. bECP applied to Cu only. All-electron aug-cc-pVTZ basis used for oxygen. c See Figure 3 for the symmetries and shapes of Hartree−Fock orbitals.

Table 1 and Figure 4 summarize the results of the EOM-IP calculations (the results with other basis sets are collected in Tables S3 and S4 in SI). Table 2 and Figure 5 summarize the results of excited-state calculations (in Tables S5−S7 in the SI, we also provide EOM-EE-CCSD excitation energies computed with smaller basis sets and CIS/cc-pVTZ excitation energies for comparison). Finally, Figure 6 compares the computed energy differences with the experimentally derived values.16 To quantify the effect of electron correlation, we analyze the amplitudes of the EOM-CCSD wave functions. The norm of R1 gives the weight of one-electron configurations (1h in EOM-IP D


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Figure 6. Comparison of spectral transitions calculated at the EOM-IP-CCSD/cc-pVTZ level of theory (left), spectral transitions calculated at the EOM-IPCCSD/cc-pVTZ-PP level of theory (middle), and experimental spectral transitions (right) for CuO−. EOM-IP-CCSD/aug-cc-pVTZ-PP transition energies are reported in the middle panel in parentheses. Energies are in eV. Calculations were performed from the closed-shell singlet reference, with the exception of the 4B1/4B2 → 2B1/2B2 transition (left), which was calculated by EOM-SF-CCSD/cc-pVTZ from the quartet reference. Experimental data is reproduced from ref 16. See Table S1 in SI for mapping C2v point group symmetry labels to those of C∞v.

Table 4. Six Lowest EOM-EE-CCSD/ECP10MDF/aug-ccpVTZ-PPa Excitation Energies of Closed-Shell Singlet Cu2Ob orbitalc 4b2 → 10a1

state 1

B2 B2 1 B1 3 B1 1 A2 3 A2 1 A1 3 A1 1 B1 3 B2 1 A1 3 A1 3

7b1 → 10a1 4b2 → 8b1 2a2 → 10a1 7b1 → 8b1 6b1 → 10a1 9a1 → 10a1

Eex (eV)

∥R1∥2

leading rai

1.620 1.180 1.676 1.228 2.085 1.670 2.189 1.672 2.329 1.823 2.375 1.581

0.920 0.928 0.925 0.937 0.926 0.932 0.928 0.936 0.930 0.940 0.930 0.947

0.451 0.432 0.450 0.432 0.296 0.280 0.276 0.252 0.333 0.350 0.323 0.337

a No diffuse f or g functions. bECP applied to copper only. All-electron basis used for oxygen. cSee Figure 7 for the symmetries and shapes of Hartree−Fock orbitals.

level of theory where the ECP10MDF pseudopotential is used for Cu yields EOM-IP-CCSD transitions from the CuO− reference that are in closest agreement with experimentally obtained values, relative to other choices of basis sets. The EOM-EE-CCSD/cc-pVTZ level of theory best reproduces the energy gaps between the closed-shell singlet CuO− ground state and the two lowest-lying triplet states. The energy of the second-lowest EOM-IP-CCSD detached state is more sensitive to choice of basis set than the lowest detached state. The detachment energy corresponding to the X1A1 →2 B1/B2 transition (X-band) can also be computed as a difference between total CCSD or CCSD(T) energies of the two states. The results of these calculations are summarized in Table 3. As one can see, such ΔE CCSD calculation with cc-pVTZ basis agrees well with EOM-IP-CCSD. As expected, including triples correction and extending the basis set improves the agreement with the experimental value. Our best estimate of the lowest detachment energy (from the ground state of the anion) is 1.723 eV (CCSD(T)/ aug-cc-pVQZ) is within 0.05 eV from the experimental value. 3.2. Cu2O−. Figure 7 shows the Hartree−Fock MOs of closed-shell singlet Cu2O; the ground-state structure of the anion is shown in Figure 2. Because the ground state of Cu2O− is a doublet, the majority of photodetached states that appear in the experimental PES of Cu2O− can be computed relative to each

Figure 7. Molecular orbitals of doublet Cu2O−. MO surfaces correspond to the closed-shell neutral reference (Cu2O). The red box around the 14a1 LUMO indicates the orbital that becomes occupied in the ground state of the doublet anion species. E


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other via EOM-EE-CCSD from the closed-shell singlet (N−1)electron reference. Table 4 and Figure 8 show the results (see also Tables S8 and S9 in SI). The lowest photodetachment energyi.e., the energy gap between the closed-shell singlet reference and the lowest energy (doublet) anioncan be computed by a number of approaches, which are compared in Table 5. Our best results are summarized and compared with experiment in Figure 9. ∥R1∥2 of the EOM-EE-CCSD states show that these transitions have one-electron character (Table 4 and S8/S9). The lowest EOM-EE-CCSD excited state obtained from the closedshell Cu2O reference does not arise from a HOMO → LUMO excitation, and instead arises from a HOMO−2 → LUMO excitation. This result indicate that Koopmans’ approximation based on Hartree−Fock MOs is insufficient for modeling the PES in this system featuring strong correlation.

Figure 8. Six lowest singlet (left) and triplet (right) EOM-EE-CCSD/ cc-pVTZ excited states obtained from the closed-shell singlet Cu2O reference.

Table 5. Lowest Vertical Detachment Energy, in eV, of Cu2O− Calculated by Different Approachesa method

basis −

reference state

DE

−

CCSD[Cu2O] − CCSD[Cu2O ]

cc-pVTZ

doublet Cu2O and closed-shell singlet Cu2O

0.584

CCSD(T)[Cu2O] − CCSD(T)[Cu2O−]

cc-pVTZ

doublet Cu2O− and closed-shell singlet Cu2O

0.751

CCSD[Cu2O] − CCSD[Cu2O−]

aug-cc-pVTZ


0.774


aug-cc-pVTZ


0.953

CCSD[Cu2O] − CCSD[Cu2O−]

aug-cc-pVQZ


0.790


aug-cc-pVQZ


0.975


ECP10MDF/cc-pVTZ-PP(Cu) + cc-pVTZ(O)


0.811


ECP10MDF/aug-cc-pVTZ-PPb(Cu) + aug-cc-pVTZ(O)


0.996

EOM-EA-CCSDc

cc-pVTZ

closed-shell singlet Cu2O

0.353

EOM-EA-CCSDc

ECP10MDF/aug-cc-pVTZ-PPb(Cu) + aug-cc-pVTZ(O)

closed-shell singlet Cu2O

0.578

EOM-IP- CCSDd

cc-pVTZ

doublet Cu2O−

0.574

cc-pVTZ

closed-shell singlet Cu2O2−

0.579

EOM-DIP-CCSD[Cu2O2−]e

Experimental value: 1.10 eV (ref 17). Partial aug-cc-pVTZ-PP basis: diffuse f and g functions were omitted. c∥R1∥2 = 0.96, leading r1 = 0.95−0.97. d ∥R1∥2 = 0.97, leading r1 = 0.96. e∥R1∥2 = 0.95−0.96, leading r1 = 0.94−0.95. a

b

Figure 9. Comparison of spectral transitions calculated at the EOM-EE-CCSD/cc-pVTZ level of theory (left), spectral transitions calculated at the EOM-EE-CCSD/cc-pVTZ-PP level of theory (middle), and experimental spectral transitions (right) for Cu2O−. EOM-EE-CCSD/aug-cc-pVTZ-PP transition energies are reported in the middle panel in parentheses. Experimental data is from ref 17. All transitions were computed with the EOM-EECCSD method from the closed-shell (N−1)-electron Cu2O reference, with the exception of the lowest electron-detachment energies, which were computed as differences in CCSD(T) total energies between the doublet anion and lowest neutral state. The all-electron cc-pVTZ basis (left) and the ECP10MDF/(aug)-cc-pVTZ-PP basis (middle) for copper were used in the ΔE[CCSD(T)] calculations. F


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− Figure 10. Molecular orbitals of the singlet CuO3− 2 closed-shell reference state (bottom) and associated low-lying states of CuO2 (top). The relative reference. We consider the energy separations of the states that are provided in blue were obtained using EOM-DIP-CCSD and the closed-shell CuO3− 2 ordering of CuO−2 states obtained from this method to be most reliable, but other relative energy separations using different EOM methods/references are also provided in the diagram when possible.

Of the model chemistries used to calculate the energy separation between the doublet anion and the lowest photodetached state (presented in Table 5), our best results were obtained when the

onset of electron detachment was calculated by CCSD(T) with ECP10MDF/aug-cc-pVTZ-PP/aug-cc-pVTZ. The CCSD(T) results with all-electron aug-cc-pVQZ are very close. The inclusion G


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Table 6. Twelve Lowest States of CuO−2 Computed by EOM-DIP-CCSD/cc-pVTZ from the Closed-Shell Singlet CuO3− 2 Reference state

configuration

Eex (eV)

∥R2∥2

leading rij

B1g 1 B1g 1 Ag 1 Au 3 Au 3 B1u 1 B2g/1B3g 3 B2g/3B3g 1 B2u/1B3u 3 B2u/3B3u 3 B1u 1 Ag

triplet open-shell singlet closed-shell singlet open-shell singlet triplet triplet open-shell singlet triplet open-shell singlet triplet triplet closed-shell singlet

0.000 0.106 0.163 0.165 0.193 0.211 0.421 0.370 1.246 1.082 1.546 1.686

0.838 0.841 0.843 0.845 0.845 0.845 0.845 0.842 0.850 0.852 0.851 0.877

0.543 0.521 0.509 0.458 0.458 0.458 0.608 0.613 0.483 0.493 0.631 0.800

orbitalsa 2b2g + 2b3g 2b2g/2b3g (3b2u + 2b2g), (3b3u + 2b3g) (3b3u + 2b2g), (3b2u + 2b3g) (8ag + 2b2g)/(8ag + 2b3g) (8ag + 3b2u)/(8ag + 3b3u) 8ag + 5b1u 8ag a

3

See Figure 10 for the symmetries and shapes of Hartree−Fock orbitals.

of perturbative triples recovers ∼0.2 eV, and the inclusion of diffuse functions in the basis recovers ∼0.2 eV, relative to CCSD/ cc-pVTZ. Our best estimate for this lowest energy transition (X-band) is within 0.1 eV from the experimental peak position. Figure 9 compares the computed and experimental transitions. Here, we combined the results of the EOM-EE-CCSD and CCSD(T) calculations to obtain higher electron detached states by using CCSD(T) energy for the lowest doublet-singlet gap and EOM-EE-CCSD energy differences between singlets and triplets. We find that the use of the ECP10MDF pseudopotential generally improves the quality of results. The inclusion of diffuse functions in the basis set improves the quality of lower energy transitions while a nonaugmented set better reproduces the energy of high-lying photodetached states. 3.3. CuO2−. Of the three molecules studied here, CuO−2 presents the most challenging electronic structure pattern. Its groundstate equilibrium geometry is shown in Figure 2. Although earlier studies argued in favor of bent molecular structure, the most recent experimental study4 of photodetachment from CuO−2 has presented conclusive evidence for the linear structure being predominant in the gas phase. The difficulties in choosing an appropriate reference for describing relevant electronic states of the neutral CuO2 and CuO−2 become apparent upon examining frontier MOs and possible electronic configurations. Let us begin with the anion. Formally, it has an even number of electrons, so one might attempt to employ a closed-shell singlet reference and to describe low-lying open-shell singlets and triplets by EOM-EE-CCSD, as we did in CuO−. This strategy is perfectly legitimate provided that all pairs of formally degenerate orbitals (π orbitals) are either fully occupied or empty and that all relevant low-lying states can be described as single-electron excitations from such reference. Unfortunately, the degeneracy pattern of the frontier orbitals in CuO−2 precludes us from using this approach and the only way to correctly describe the manifold of low-lying states is to use the reference with 2 additional electrons and employ EOM-DIP-CCSD. Figure 10 shows frontier Hartree−Fock MOs of the closed-shell singlet CuO3− 2 state and the energies and electronic configurations of the low-lying states of CuO−2 . The results of EOM-DIP-CCSD/cc-pVTZ calculation are collected in Table 6. As one can see, the lowest electronic state of CuO−2 is triplet (3B1g or 3Σ−g ), in agreement with theoretical result by Zhu and co-workers.31 Within 0.2 eV, there are 4 singlet states, 1 B1g (1Σ−g ), a doubly degenerate closed-shell like singlet (1Δg), and nearly degenerate singlet and triplet pair (1,3Au, corresponding to 1,3Σ−g ). All these states (and possibly higher lying ones too) can

be populated at the experimental conditions, giving rise to different electron-detached states. To describe target states that can be generated by detaching an electron from the lowest state of the anion (3B1g or 3Σ−g ), we use a quartet reference state (4B1g) in which each degenerate π-orbital is singly occupied and describe the three lowest doublet states (of which two form a degenerate Π pair) and Ms = 1/2 component of the quartet state by EOM-SF-CCSD. The frontier MOs and electronic configuration of the 4B1g state and the resulting doublet states are shown in Figure 11. As one see, these calculations predict the ground state of CuO−2 to be a quartet, but the doublet states are very close (within ∼0.3 eV). The two manifolds (EOM-DIP manifold of the anionic states and EOM-SF manifold of the neutral states) can be connected by EOMEA-CCSD or CCSD(T). The EOM-EA-CCSD/cc-pVTZ calculation using a neutral quartet reference (in which each degenerate π-orbital is singly occupied) producing a target 3B1g state. This energy (3.53 eV) corresponds to the high-intensity A-peak in the experimental spectra (using labels by Wu et al.16), which has been later assigned to the lowest detachment from the ground-state (3Σg) of the anion.31 The CCSD(T) values with cc-pVTZ and aug-ccpVTZ bases are 3.473 and 3.846 eV, respectively. As in the other two molecules, the CCSD(T)/aug-cc-pVTZ value is in excellent agreement with the experiment (the difference is ∼0.05 eV). The presence of multiple low-lying states in CuO−2 , each of them giving rise to different target states, makes the assignment of spectral transitions difficult. Figure 12 shows electronic configurations of the lowest states of CuO−2 and low-lying states of the neutral CuO2 and shows which pairs of states are connected by oneelectron transition (i.e., are Koopmans-allowed) and which ones are not. Finally, in Figure 13, we present an energy-level diagram for comparison with experimental transitions.4,17 Our assignment of the low part of the spectrum differs from earlier ones.4,17,31 While we agree with Zhu and co-workers,31 who assigned the high-intensity A-peak to the detachment from the ground-state anion (3Σ−g ) and the low intensity X-peak to the detachment from an electronically excited anion, we point out that the ground state of the neutral is quartet (4Σ−g ). The inspection of MOs and electronic configuration of the ground triplet state of the anion provides qualitative explanation of the quartet state being the ground state of the neutral: the singly occupied orbitals in the triplet are lone pairs on oxygens. Removing the electron from the next doubly occupied orbital creates an unpaired electron on copper. Our calculations also suggest that more than one electronic state of the anion contributes to the electronic hot band (X peak), which is probably responsible for its relatively high intensity. H


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Figure 11. Molecular orbitals of the 4B1g CuO2 reference state (bottom) and its associated excited and electron attached states (top). The relative energy separations and ⟨S2⟩ of states that are shown in purple were obtained using EOM-SF-CCSD from the quartet CuO2 reference. The EOM-EA-CCSD result in orange, which connects the neutral and anionic state manifolds, provides the energy of the lowest photodetachment from CuO−2 (3.53 eV); the respective CCSD(T)/aug-cc-pVTZ value is 3.85 eV. The electronic configuration boxed in red would require both excitation and photodetachment from the ground-state CuO−2 triplet reference. See Table S2 in SI for mapping D2h point group symmetry labels to those of D∞h.

4. CONCLUSIONS In this contribution, we show that variants of the EOM-CCSD family of methods can be combined and applied to describe the photoelectron spectra of CuO−, Cu2O−, and CuO−2 . For the

The experimental value of 3.47 eV (of X-peak) can be compared to our theoretical value of ~3.33 eV. We note that the computed splitting between A and X peak (0.2 eV) is in good agreement with the experimental value17 of 0.3 eV. I


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Figure 12. Electronic configuration of the triplet CuO−2 ground state and closely lying singlet state of the same orbital occupation (left) and of the closedshell 1Ag states (right). From the 3,1B1g configuration, the three lowest-lying Koopmans-allowed detached states (middle) are expected to emerge in the spectrum are indicated by solid green arrows. However, several configurations (middle, dashed red arrows) require excitation as well as removing an electron, making them Koopmans-forbidden from that state. From the 1Ag states, a slightly different set of detached states can be accessed. See Table S2 in SI for mapping D2h point group symmetry labels to those of D∞h.

For all three molecules, the inclusion of perturbative triples correction, CCSD(T), leads to improved agreement between theory and experiment for the photodetachment energy of the ground-state anion. The effect of (T) is particularly large for Cu2O−. Due to the highly correlated nature of the CuO− and Cu2O− systems, careful benchmarking and density-based state analysis57,58 are recommended when lower-level methods, like DFT and its extensions, are applied to model photodetachment. For CuO−2 , we note good agreement with experiment in the low-energy part of the spectrum. However, adequate description of higher-lying photodetached states remains elusive. Our results

former two systems, the calculations agree well with the experimentally derived values. We note improvement in quality of results when the ECP10MDF pseudopotential is applied to Cu, suggesting the relativistic corrections afforded by the use of ECP10MDF (and its associated highly contracted, correlation-consistent basis) might be necessary for accurate description of valence photodetachment. All-electron aug-cc-PVTZ and aug-cc-pVQZ calculations are also in good agreement. Dyson orbitals and analysis of dominant amplitudes in the EOM-CCSD wave functions reveal the nonKoopmans character and multiconfigurational nature of the anionic and neutral states that give rise to the CuO− and Cu2O− PES. J


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Figure 13. Comparison of spectral transitions calculated at the EOM-SF/DIP/EA-CCSD/cc-pVTZ level of theory (left) and experimental spectral transitions (right) for CuO−2 . Experimental data is from ref 16, and spectral notation reflects original experimental assignments. Experimental intensities of the spectral transitions are as follows: A > B > X ≈ C. Bold lines in the left panel denote several states clustered around the same energy. See Table S2 in SI for mapping D2h point group symmetry labels to those of D∞h.

indicate that the experimental PES of CuO−2 may arise from multiple neutral states clustered around specific energies, which makes an accurate and balanced description of all of the photodetached states that contribute to the low-energy PES challenging. A variety of EOM-CCSD methodsIP, EE, DIP, SFfrom many neutral and anionic CuO2 references were required to capture this phenomenon. By highlighting extreme open-shell character of CuO2, our study contributes toward fundamental understanding of bonding patterns and electronic structure of transition metal oxides, which are important in many areas of chemistry including catalysis and materials. The analysis of electronic structure patterns in these three small molecules provides a practical tutorial for using EOM-CC methods to describe various open-shell systems.47 Given the high level of theory employed, the reported results can serve as a valuable benchmark for future method development.

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Mabbs (Washington University in St. Louis) and Mr. Pavel Pokhilko (USC) for their feedback regarding the manuscript.

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(1) Kelley, A. M. Condensed-Phase Molecular Spectroscopy and Photophysics, 1st ed.; John Wiley & Sons, Inc.: Hoboken, NJ, 2013. (2) Hufner, S. Photoelectron Spectroscopy: Principles and Applications, 3rd ed.; Springer: Berlin, 2013. (3) Turner, D. W. Molecular photoelectron spectroscopy. Philos. Trans. R. Soc., A 1970, 268, 7−31. (4) Mabbs, R.; Holtgrewe, N.; Dao, D. B.; Lasinski, J. Photodetachment and photodissociation of the linear OCuO molecular anion: energy and time dependence of Cu production. Phys. Chem. Chem. Phys. 2014, 16, 497−504. (5) Wenthold, P. G.; Lineberger, W. C. Negative ion photoelectron spectroscopy studies of organic reactive intermediates. Acc. Chem. Res. 1999, 32, 597−604. (6) Neumark, D. M. Probing chemical dynamics with negative ions. J. Chem. Phys. 2006, 125, 132303−15. (7) Sanov, A.; Mabbs, R. Photoelectron imaging of negative ions. Int. Rev. Phys. Chem. 2008, 27, 53−85. (8) Krylov, A. I. Equation-of-motion coupled-cluster methods for open-shell and electronically excited species: The hitchhiker’s guide to Fock space. Annu. Rev. Phys. Chem. 2008, 59, 433−462. (9) Sneskov, K.; Christiansen, O. Excited state coupled cluster methods. WIREs Comput. Mol. Sci. 2012, 2, 566−584. (10) Bartlett, R. J. Coupled-cluster theory and its equation-of-motion extensions. WIREs Comput. Mol. Sci. 2012, 2, 126−138. (11) Izaki, M. J.; Nagai, M.; Maeda, K.; Mohamad, F. B.; Motomura, K.; Sasano, J.; Shinagawa, T.; Watase, S. Electrodeposition of 1.4-eVbandgap p-copper(II) oxide film with excellent photoactivity. J. Electrochem. Soc. 2011, 158, D578−84. (12) Padovani, S.; Sada, C.; Mazzoldi, P.; Brunetti, B.; Borgia, I.; Sgamellotti, A.; Giulivi, A.; D’Acapito, F.; Battaglin, G. Copper in glazes of renaissance luster pottery: Nanoparticles, ions, and local environment. J. Appl. Phys. 2003, 93, 10058−10063. (13) Ren, G.; Hu, D.; Cheng, E. W. C.; Vargas-Reus, M. A.; Reip, P.; Allaker, R. P. Characterisation of copper oxide nanoparticles for antimicrobial applications. Int. J. Antimicrob. Agents 2009, 33, 587−90. (14) Turecek, F. Copper-biomolecule complexes in the gas phase. The ternary way. Mass Spectrom. Rev. 2007, 26, 563−582.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b10620. Symmetry tables, additional EOM-CCSD results using different basis sets, CIS results for CuO−, relevant Cartesian geometries (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Natalie Orms: 0000-0002-2462-2491 Anna I. Krylov: 0000-0001-6788-5016 Notes

The authors declare the following competing financial interest(s): A.I.K. is a member of the Board of Directors and a part-owner of Q-Chem, Inc.

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ACKNOWLEDGMENTS This work is supported by the Department of Energy through the DE-FG02-05ER15685 grant (to A.I.K.). We thank Prof. Richard K


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Modeling Photoelectron Spectra of CuO, Cu2O, and CuO2 Anions with

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