Density functional calculation of the structure and electronic properties of Cu_nO_n (n=1-8) clusters

Abstract

Ab initio simulations and calculations were used to study the structures and stabilities of copper oxide clusters, Cu_nO_n (n=1-8). The lowest energy structures of neutral and charged copper oxide clusters were determined using primarily the B3LYP/LANL2DZ model chemistry. For n ≥ 4, the clusters are nonplanar. Selected electronic properties including atomization energies, ionization energies, electron affinities, and Bader charges were calculated and examined as a function of n.

Introduction

There is a growing recognition that catalytic metal oxide nanoclusters can play a key role in various environmental processes,^1,2 and it has been suggested that metal oxide clusters contribute to health hazards associated with airborne fine particles.^3–6 Polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/F) can be formed in almost any thermal system if there are sources of carbon, chlorine, and transition metals to catalyze chlorination and condensation reactions.⁷ Copper and iron oxide nanostructured particles have been shown to be particularly effective catalysts for the formation of PCDD/F and other pollutants at relatively low temperatures as gases exit a combustor.⁸ Environmentally persistent free radicals (EPFRs) form over copper and iron oxide-containing nanoparticles, and these EPFRs have been shown to be intermediates in the formation of PCDD/F and be a possible cause of the observed health impacts of airborne fine particles.^9–13 It is thought the EPFRs are formed by an electron transfer from a physisorbed molecular species to the metal atom in a metal oxide cluster. For this reason, studies that determine the geometric structures and charge distributions in neutral and anionic metal oxide clusters are needed.

There are relatively few experimental and theoretical studies of how copper and iron oxide clusters catalyze or mediate the formation of pollutants in combustion systems or the environment. Estimates of the relevant cluster sizes range from a micrometer down to just a few metal atoms; Therefore, this work studies the structures and energetics of small copper oxide clusters as a first step towards understanding the interactions between metal oxides and free radicals.

Experimental^14–24 and computational^21,25–39 studies exist for some small copper oxide clusters. Three isomers have been suggested as possible structures for CuO₂:²⁰ bent CuOO (bent, C_s), linear OCuO, and C_2v OCuO. Evidence has been found for both bent CuOO^18,27,36,37 and linear OCuO.^20,23,32 Vibrational frequencies have been calculated²³ for CuO₃, ${\text{OCuO}}_2^{-}$, and Cu(O₃)⁻ clusters. Recently, the structures of CuO₄, CuO₅,³⁸ and neutral and negatively charged CuO₆ clusters⁴⁰ were determined using plane-wave density functional theory. In addition, Cu₂O_n (n=1-4) clusters have been studied using anion photoelectron spectroscopy and density functional calculations.^21,39 In this paper, we investigate the electronic and geometric structures of neutral and charged copper oxide clusters (CuO)_n n=1-8.

Methods

We evaluated several basis sets as candidates for our studies: 6-31G**,^41–436-31++G**,^41,44–48 6-311G**,^47,49–51 6-311++G**,^46,47 LANL2DZ,^52–54 and DGDZVP.^55,56 Density functional theory using the B3LYP functional was used for the majority of the calculations; the M06 and BHandHLYP functionals were used as a check on the reliability of the B3LYP functional. All calculations were restricted so that the spin states were pure and did not contain any spin contamination.

The study of atomic and molecular clusters can be hindered by the existence of multiple isomers for a given size cluster. Without an a priori knowledge of the global energy minima, the use of computer simulation methods, such as simulated annealing, often allow the determination of global minima. For this reason, we performed ab initio simulated annealing Monte Carlo (MC) simulations to locate stable geometric structures for the smaller (n_Cu ≤ 4) clusters. Standard single particle MC moves were used and instead of a classical force field Gaussian 03⁵⁷ was used to calculate the energy using the B3LYP/6-31G** model chemistry. This 6-31G** basis was chosen as a good compromise between basis set accuracy and computational effort. A MC “pass” corresponded to an attempt to move each atom in the three cartesian directions by up to 0.2 A in each direction. The Metropolis algorithm⁵⁸ was used to accept or reject proposed moves. The temperature was linearly decreased from 2000 K to 300 K for up to 500 MC passes. As in standard MC simulations, the total number of passes was dependent on the size of the cluster and the number of passes required before the energy of the cluster equilibrated. For each cluster size, several different initial geometries were used in order to locate with confidence the global minimum. For example, three different starting geometries were used to simulate the Cu₄O₄ cluster, all generated by adding a Cu-O unit to the minimum energy neutral Cu₃O₃ cluster (two added equatorially and one added axially). All three geometries converged to the same final Cu₄O₄ geometry.

The final geometry from each MC simulation was optimized using standard ab initio methods with the GAMESS⁵⁹ quantum chemistry package using the B3LYP/LANL2DZ model chemistry, d-functions were represented with 6 cartesian functions, the default for GAMESS. The smaller clusters were then used as starting points to look for the global minimum geometries for larger clusters where the Monte Carlo procedure was not computationally feasible. For the larger clusters, standard ab initio optimizations were performed using several starting geometries for each cluster size. This procedure was chosen as the option when computational resources did not allow for MC simulations since, consistent with the MC procedure, it did use different initial geometries. In effect, we followed the standard protocol for studying clusters using ab initio methods. An alternative would be to use smaller basis sets that would allow larger clusters to be simulated; however, concerns about the accuracy of the smaller basis sets led us to avoid this option.

For the GAMESS optimizations, we used the B3LYP (Becke's 3-parameter exchange functional with Lee-Yang-Parr correlation energy functional) ^60–62 version of DFT in combination with a variety of basis sets. Although there are well known deficiencies with the B3LYP functional (particularly for excited states⁶³), there are plenty of studies of transition metal clusters (neutral and charged) for which the B3LYP/LANL2DZ basis set has been used successfully.^64–68 For TiO₂ and TiO, Qu and Kroes⁶⁴ found (in comparison to experiment) vibrational frequencies accurate to about 60 wavenumbers, ionization energies accurate to 0.2 eV, and electron affinities accurate to 0.2 eV. For neutral and charged gold atoms, Okumura, Kitagawa, Haruta, and Yamaguchi found⁶⁶ ionization energies and electron affinities accurate to 0.2 eV. For the neutral clusters, singlet and triplet states were optimized for n even and doublet and quartet states were optimized for n odd. For the neutral clusters with triplet/quartet lowest energy structures, single point calculations of quintet/sextet states at the geometries of the triplet/quartet were used as a check of the lowest energy spin state. The spin states examined for the anion and cation were dependent on the spin state of the neutral. For the anions, the two spin states examined corresponded to the addition of an electron to an unfilled orbital and to the addition of an electron to a half-filled orbital (where applicable). For the cations, two spin states were also examined and corresponded to the removal of an electron from a half-filled orbital (were applicable) and a doubly filled orbital. For the neutral clusters, all isomers and spin states were optimized using the M06/LANL2DZ and BHandHLYP/LANL2DZ model chemistries. The lowest energy geometries and spin states were the same for all model chemistries.

Bader charge densities were calculated using the Firefly QC software package⁶⁹ to generate cube files, which where then used by the Texas Bader software package⁷⁰ to calculate the charge densities. No geometric symmetry was enforced in the calculations in order to allow for symmetry-breaking to lower the total energy. In selected cases, a higher symmetry was used, but in these cases the resulting optimized structure was found to be higher in energy than the structure with no symmetry and to be a transition state (based on vibrational frequencies).

Results and Discussion

We evaluated several basis sets as candidates for our studies: 6-31G**,^41–43 6-31++G**,^41,44–48 6-311G**,^47,49–51 6-311++G**,^46,47 LANL2DZ,^52–54 and DGDZVP.^55,56 Monte Carlo calculations followed by GAMESS optimization found the lowest energy clusters for Cu₂O_n (n = 1 – 4) shown in Figure 1. For Cu₂O₃ and Cu₂O₄, different isomers were found depending on basis set (Cu₂O₃-a: 6-31G**; Cu₂O₃-b: 6-31++G**, 6-311G**, 6-311++G**, LANL2DZ and DGDZVP; Cu₂O₄-a: 6-31++G**, 6-311++G**, LANL2DZ and DGDZVP; Cu₂O₄-b: 6-31G** and 6-311G**). A comparison of calculated (adiabatic) and measured electron affinities²¹ is shown in Table 1. For comparison, the table also presents results using a customized basis set with diffuse orbitals (WWD).²¹ The 6-31++G**, 6-311++G**, DGDZVP, and the WWD basis sets use diffuse orbitals, which are expected to be more accurate for anions. The best agreement with experimental electron affinities was found with the LANL2DZ basis set, despite its lack of diffuse orbitals. Based on the agreement with experimental electron affinities and the success of this model chemistry in previous studies,^64–68 the LANL2DZ basis set was used in the remainder of this work.

Figure 1.

Lowest energy clusters for Cu₂O_n, n = 1 – 4. Different basis sets give different lowest energy isomers for n = 3 and 4 (Cu₂O₃-a: 6-31G**; Cu₂O₃-b: 6-31++G**, 6-311G**, 6-311++G**, LANL2DZ and DGDZVP; Cu₂O₄-a: 6-31++G**, 6-311++G**, LANL2DZ and DGDZVP; Cu₂O₄-b: 6-31G** and 6-311G**).

Table 1. Electron affinity comparing basis sets with experimental data.

	Electron Affinities (eV)
	Cu2O	Cu2O2	Cu2O3	Cu2O4
6-31G**	0.94	1.41	2.35	3.26
6-31++G**	1.27	2.33	2.65	3.34
6-311G**	0.14	0.89	1.67	2.75
6-311++G**	1.24	1.76	3.09	3.35
LANL2DZ	1.15	2.41	3.25	3.54
DGDZVP	1.15	2.24	3.08	3.31
WWD.21	1.10	2.12	3.03	2.94
EXP21	1.10	2.46	3.54	3.50

The optimized structures of neutral and charged (CuO)_n clusters with n=1-8 clusters are shown in Figure 2, Figure 3, and Figure 4. With the exception of Cu₂O₂, the displayed geometries were between 0.6 and 2.0 eV more stable than any other isomer studied in this work. The Bader charges and spin densities are shown for the neutral clusters in Figure 2. The spin states, spin densities, and the copper- and oxygen-centered charges are displayed for the neutral clusters in Table 2. Detailed Bader charges are given in Table 3. The bondlengths are given in Table 6 and Table 7. The calculated bond lengths for CuO⁻ and CuO are 1.74Å and 1.81Å and compare well with the measured values of 1.67Å and 1.72Å.²⁴

Figure 2.

Optimized structures of neutral (CuO)_n clusters with n=1-8 using the B3LYP/LANL2DZ model chemistry. Bader charges and spin densities for the copper atoms are shown in parentheses. Copper/oxygen atoms are colored white/black.

Figure 3.

Optimized structures of cationic (CuO)_n clusters with n=1-8 using the B3LYP/LANL2DZ model chemistry. Copper/oxygen atoms are colored white/black.

Figure 4.

Optimized structures of anionic (CuO)_n clusters with n=1-8 using the B3LYP/LANL2DZ model chemistry. Copper/oxygen atoms are colored white/black.

Table 2. Average Bader Charges and spin densities for the neutral (CuO)_n clusters on the copper and oxygen atoms in a cluster as a function of n using the B3LYP/LANL2DZ model chemistry.

n	Spin Multiplicity	Charge Cu	Charge O	Spin Density Cu	Spin Density O
1	2	+0.57	-0.57	0.10	0.90
2	0	+0.87	-0.89	0	0
3	4	+0.94	-0.93	0.79	2.21
4	3	+0.71	-0.71	0.51	1.49
5	4	+0.78	-0.78	0.98	2.02
6	3	+0.74	-0.74	0.82	1.18
7	4	+0.68	-0.68	0.50	2.50
8	3	+0.69	-0.69	0.50	1.50

Table 3. Bader charges on the copper and oxygen atoms in (CuO)_n (n=1-8) clusters using the B3LYP/LANL2DZ model chemistry. The numbers in parentheses indicate the atom labels from Figure 2.

Clusters		qCu(atom number)			qO(atom number)
CuO	CuO	0.57(1)			-0.57(2)
	CuO+	0.99(1)			0.01(2)
	CuO−	-0.02(1)			-0.99(2)
Cu2O2	Cu2O2	0.89(1)	0.89(2)		-0.89(3)	-0.89(4)
	${\text{Cu}}_2{\text{O}}_2^{+}$	0.91(1)	0.91(2)		-0.40(3)	-0.44(4)
	${\text{Cu}}_2{\text{O}}_2^{-}$	0.58(1)	0.58(2)		-1.09(3)	-1.09(4)
Cu3O3	Cu3O3	0.86(1)	0.98(2)	0.97(3)	-0.58(4)	-0.91(5)	-1.31(6)
	${\text{Cu}}_3{\text{O}}_3^{+}$	1.13(1)	1.11(2)	1.12(3)	-0.79(4)	-0.78(5)	-0.80(6)
	${\text{Cu}}_3{\text{O}}_3^{-}$	0.71(1)	0.71(2)	0.70(3)	-1.04(4)	-1.04(5)	-1.03(6)
Cu4O4	Cu4O4	0.77(1)	0.67(2)		-1.05(5)	-1.05(6)
		0.66(3)	0.77(4)		-0.41(7)	-0.34(8)
	${\text{Cu}}_4{\text{O}}_4^{+}$	1.13(1)	0.65(2)		-0.96(5)	-0.98(6)
		0.64(3)	1.19(4)		-0.34(7)	-0.33(8)
	${\text{Cu}}_4{\text{O}}_4^{-}$	0.68(1)	0.64(2)		-1.06(5)	-0.76(6)
		0.68(3)	0.64(4)		-1.06(7)	-0.76(8)
Cu5O5	Cu5O5	0.87(1)	0.85(2)	0.69(3)	-0.96(6)	-1.10(7)	-0.35(8)
		0.69(4)	0.79(5)		-0.39(9)	-1.11(10)
	${\text{Cu}}_5{\text{O}}_5^{+}$	1.00(1)	1.05(2)	0.76(3)	-0.30(6)	-1.18(7)	-0.31(8)
		0.75(4)	0.79(5)		-0.36(9)	-1.20(10)
	${\text{Cu}}_5{\text{O}}_5^{-}$	0.66(1)	0.67(2)	0.62(3)	-0.93(6)	-1.17(7)	-0.42(8)
		0.62(4)	0.55(5)		-0.43(9)	-1.17(10)
Cu6O6	Cu6O6	0.69(1)	0.69(2)	0.68(3)	-0.57(7)	-0.58(8)	-1.08(9)
		0.69(4)	0.68(5)	1.01(6)	-0.60(10)	-0.56(11)	-1.06(12)
	${\text{Cu}}_6{\text{O}}_6^{+}$	0.75(1)	0.76(2)	0.76(3)	-0.48(7)	-0.44(8)	-1.08(9)
		0.75(4)	1.01(5)	0.95(6)	-0.42(10)	-0.48(11)	-1.07(12)
	${\text{Cu}}_6{\text{O}}_6^{-}$	0.57(1)	0.57(2)	0.56(3)	-0.64(7)	-0.66(8)	-1.12(9)
		0.57(4)	0.52(5)	1.01(6)	-0.62(10)	-0.64(11)	-1.13(12)
Cu7O7	Cu7O7	0.69(1)	0.69(2)	0.69(3)	-0.37(8)	-0.37(9)	-1.21(10)
		0.68(4)	0.49(5)		-0.91(11)	-0.37(12)
		0.77(6)	0.77(7)		-0.34(13)	-1.19(14)
	${\text{Cu}}_7{\text{O}}_7^{-}$	0.64(1)	0.63(2)	0.62(3)	-0.86(8)	-0.86(9)	-1.16(10)
		0.63(4)	0.36(5)		-0.19(11)	-0.86(12)
		1.11(6)	0.98(7)		-0.86(13)	-1.14(14)
Cu8O8	Cu8O8	0.66(1)	0.66(2)	0.64(3)	-0.59(9)	-0.62(10)	-1.20(11)
		0.64(4)	1.04(5)	0.50(6)	-0.34(12)	-0.38(13)	-1.20(14)
		0.69(7)	0.69(8)		-0.59(15)	-0.61(16)
	${\text{Cu}}_8{\text{O}}_8^{+}$	0.70(1)	0.71(2)	0.70(3)	-0.58(9)	-0.64(10)	-1.19(11)
		0.69(4)	0.85(5)	0.48(6)	-0.05(12)	-0.06(13)	-1.09(14)
		0.92(7)	0.91(8)		-0.64(15)	-0.59(16)
	${\text{Cu}}_8{\text{O}}_8^{-}$	0.64(1)	0.68(2)	0.61(3)	-0.60(9)	-0.43(10)	-1.21(11)
		0.65(4)	0.90(5)	0.51(6)	-0.86(12)	-0.86(13)	-1.19(14)
		0.63(7)	0.62(8)	24	-0.63(15)	-0.46(16)

Table 6. Bond lengths (Å) of Cu-O in (CuO)_n (n=1-8) clusters using the B3LYP/LANL2DZ model chemistry.

	Clusters	Distance
CuO	CuO	d1–2=1.81
	CuO+	d1–2=2.02
	CuO−	d1–2=1.74
Cu2O2	Cu2O2	d1–3=1.86	d1–4=1.86	d2–3=1.86	d2–4=1.86
	${\text{Cu}}_2{\text{O}}_2^{+}$	d1–3=2.01	d1–4=2.01	d2–3=2.01	d2–4=2.01
	${\text{Cu}}_2{\text{O}}_2^{-}$	d1–3=1.92	d1–4=1.92	d2–3=1.92	d2–4=1.92
Cu3O3	Cu3O3	d1–4=1.83	d1–6=2.06	d2–4=1.81	d2–5=1.83	d3–5=1.83	d3–6=2.03
	${\text{Cu}}_3{\text{O}}_3^{+}$	d1–4=1.80	d1–6=1.80	d2–4=1.80	d2–5=1.80	d3–5=1.80	d3–6=1.80
	${\text{Cu}}_3{\text{O}}_3^{-}$	d1–4=1.84	d1–6=1.85	d2–4=1.85	d2–5=1.85	d3–5=1.85	d3–6=1.85
Cu4O4	Cu4O4	d1–5=1.96	d1–6=1.97	d2–6=1.88	d2–7=1.93
		d3–5=1.88	d3–8=1.93	d4–5=1.97	d4–6=1.96
	${\text{Cu}}_4{\text{O}}_4^{+}$	d1–5=1.94	d1–6=1.93	d2–6=1.86	d2–7=2.00
		d3–5=1.86	d3–8=2.00	d4–5=1.95	d4–6=1.97
	${\text{Cu}}_4{\text{O}}_4^{-}$	d1–5=1.85	d1–8=1.80	d2–5=1.85	d2–6=1.80
		d3–6=1.80	d3–7=1.85	d4–7=1.85	d4–8=1.80
Cu5O5	Cu5O5	d1–6=1.83	d1–10=1.87	d2–6=1.83	d2–7=1.88	d3–7=1.88	d3–8=1.92
		d4–9=1.92	d4–10=1.87	d5–7=1.90	d5–10=1.90	d8–9=1.40
	${\text{Cu}}_5{\text{O}}_5^{+}$	d1–6=1.87	d1–10=1.87	d2–6=1.80	d2–7=1.88	d3–7=1.88	d3–8=1.87
		d4–9=1.87	d4–10=1.88	d5–7=1.96	d5–10=1.96	d8–9=1.37
	${\text{Cu}}_5{\text{O}}_5^{-}$	d1–6=1.87	d1–10=1.91	d2–6=1.87	d2–7=1.90	d3–7=1.87	d3–8=1.92
		d4–9=1.92	d4–10=1.87	d5–7=1.96	d5–10=1.96	d8–9=1.41
Cu6O6	Cu6O6	d1–7=1.94	d1–12=1.90	d2–8=1.94	d2–9=1.90	d3–9=1.90	d3–10=1.94
		d4–11=1.94	d4–12=1.90	d5–9=1.88	d5–12=1.89	d6–7=2.02
		d6–8=2.10	d6–10=2.02	d6–11=2.10	d7–8=1.52	d10–11=1.52
	${\text{Cu}}_6{\text{O}}_6^{+}$	d1–7=1.96	d1–12=1.89	d2–8=1.95	d3–9=1.89	d3–9=1.89	d3–10=1.94
		d4–11=1.96	d4–12=1.89	d5–9=1.86	d5–12=1.86	d6–7=2.07
		d6–8=2.24	d6–10=2.28	d6–11=2.06	d7–8=1.46	d10–11=1.46
	${\text{Cu}}_6{\text{O}}_6^{-}$	d1–7=1.96	d1–12=1.92	d2–8=1.96	d2–9=1.94	d3–9=1.94	d3–10=1.96
		d4–11=1.96	d4–12=1.92	d5–9=1.91	d5–12=1.92	d6–7=2.01
		d6–8=2.05	d6–10=2.06	d6–11=2.00	d7–8=1.56	d10–11=1.56

Table 7. Bond lengths (Å) of Cu-O in (CuO)_n (n=1-8) clusters using the B3LYP/LANL2DZ model chemistry.

	Clusters	Distance
Cu7O7	Cu7O7	d1–8=1.94	d1–14=1.92	d2–9=1.94	d2–10=1.92	d3–10=1.92
		d3–12=1.94	d4–13=1.94	d4–14=1.92	d5–10=1.92	d5–14=1.92
		d6–10=1.98	d6–11=1.88	d7–11=1.88	d7–14=1.98	d8–9=1.40
		d12–13=1.40
	${\text{Cu}}_7{\text{O}}_7^{-}$	d1–8=2.19	d1–14=1.89	d2–9=2.18	d2–10=1.90	d3–10=1.90
		d3–12=2.15	d4–13=2.15	d4–14=1.90	d5–10=2.05	d5–14=2.06
		d6–10=2.14	d6–11=1.71	d7–11=1.73	d7–14=2.07	d8–9=1.39
		d12–13=1.40
Cu8O8	Cu8O8	d1–9=1.94	d1–14=1.97	d2–10=1.95	d2–11=1.97	d3–11=1.98
		d3–15=1.93	d4–14=1.96	d4–16=1.93	d5–9=1.99	d5–10=2.06
		d5–15=2.06	d5–16=2.02	d6–11=1.96	d6–14=1.96	d7–11=1.91
		d7–12=1.94	d8–13=1.94	d8–14=1.92	d9–10=1.55	d12–13=1.40
		d15–16=1.55
	${\text{Cu}}_8{\text{O}}_8^{+}$	d1–9=2.08	d1–14=1.93	d2–10=2.07	d2–11=1.94	d3–11=1.94
		d3–15=2.07	d4–14=1.93	d4–16=2.08	d5–10=2.12	d5–15=2.13
		d6–11=1.92	d6–14=1.93	d7–11=1.95	d7–12=1.82	d8–13=1.83
		d8–14=1.95	d9–10=1.42	d12–13=1.38	d15–16=1.42
	${\text{Cu}}_8{\text{O}}_8^{-}$	d1–9=1.92	d1–14=1.95	d2–10=1.84	d2–11=1.97	d3–11=1.95
		d3–15=1.92	d4–14=1.98	d4–16=1.84	d5–9=1.90	d5–15=1.92
		d6–11=1.98	d6–14=1.95	d7–11=1.91	d7–12=2.13	d8–13=2.15
		d8–14=1.93	d9–10=1.58	d12–13=1.39	d15–16=1.58

The structure of the lowest energy Cu₂O₂ cluster is a rhombus. The spin states of optimized structures are singlet, doublet, and doublet for the neutral, cation and anion clusters, respectively. Wang et al.²¹ and Dai et al.³⁹ have suggested minimum energy structures for Cu₂O₂ based on ab initio calculations and/or experimental measurements. Wang et al. suggest the structure is a rhombus while Dai et al. suggest the structure is linear or near linear. Our optimized linear Cu₂O₂ cluster structure is about 0.02eV higher in total energy than our rhombus structure. While this is a small energy difference, the three density functionals (B3LYP, M06, and BHandHLYP) used in this study all agreed that rhombus is the lowest energy structure. The rhombic structure of Wang et al. has a Cu-O bond length of 1.78Å and a Cu-O-Cu bond angle of 80°. Our calculations give a Cu-O bond length of ≈ 1.86Å and a Cu-O-Cu bond angle of ≈ 82°. The present work supports the rhombic structure as the lowest energy structure for Cu₂O₂.

Our calculations find Cu₃O₃ clusters to be nearly planar. The spin states of optimized structures are quartet, singlet, and triplet for the neutral, cation and anion clusters, respectively. The average Cu-O-Cu bond angles are 119.9° (cation), 98.1° (neutral), and 94.2° (anion). The calculated Cu-O bond lengths are 1.80Å (cation), 1.90Å (neutral) and 1.85Å (anion). The Cu₄O₄ cluster is the first nonplanar structure found for Cu_nO_n and consists of 2 copper atoms above and below the plane of a Cu₂O₄ unit. Notably, there is an O-O bond in this structure. The addition of the O-O unit helps form a nonplanar 7-membered ring, as well as increasing the O-Cu-O bond angles to ≈ 161°, closer to the 180° angle found in the bulk. A similar structure is found for the cation cluster, while the anion cluster is planar. The spin states of the optimized structures are triplet (neutral) and quartet (cation and anion.) The Cu-O bond lengths are 1.94Å (cation), 1.94Å (neutral), and 1.83Å (anion).

The Cu₅O₅ clusters consist of fused 6-membered (Cu₃O₃) and 7-membered (Cu₃O₄) rings sharing a O-Cu-O edge. The angle between the rings is ≈113°. In these clusters, there is one O-O bond. The spin states of the optimized structures are quartet(neutral) and triplet(cation and anion). Cu₆O₆ clusters have cage structures. The spin states of the optimized structures are triplet(neutral), quartet(cation) and doublet(anion). Cu₇O₇ clusters exhibit another type of fused structure, with three rings sharing a common edge. Similar to the Cu₅O₅ clusters the rings are 6- and 7-membered. There are two O-O bonds in these structures. We were unable to optimize the ${}^3\text{C}{\text{u}}_7{\text{O}}_7^{+}$ due to severe spin-contamination issues. The spin states of optimized structures are quartet(neutral) and triplet(anion). Cu₈O₈ is formed by adding a Cu₂O₂ group to the edge of the Cu₆O₆ cluster. The spin states of the optimized clusters are triplet (neutral), quartet (cation and anion.)

Table 5 displays the spin state, the adiabatic ionization energies, the electron affinities, and the atomization energies per CuO group. The bond lengths are given in Table 6 and Table 7. The atomization energies per atom have been calculated from

Table 5. Spin states, ionization energies (IE), electron affinities (EA), and binding energies (E_b) for Cu_nO_n, n = 1 – 8. Energies are in electron volts and are calculated using the B3LYP/LANL2DZ model chemistry.

	Spin State	IE	EA	Eb
CuO	doublet	9.28	1.35	1.22
CuO+	triplet
CuO−	singlet
Cu2O2	singlet	8.24	2.35	1.85
${\text{Cu}}_2{\text{O}}_2^{+}$	doublet
${\text{Cu}}_2{\text{O}}_2^{-}$	doublet
Cu3O3	quartet	9.16	3.65	2.19
${\text{Cu}}_3{\text{O}}_3^{+}$	singlet
${\text{Cu}}_3{\text{O}}_3^{-}$	triplet
Cu4O4	triplet	8.23	4.10	2.35
${\text{Cu}}_4{\text{O}}_4^{+}$	quartet
${\text{Cu}}_4{\text{O}}_4^{-}$	quartet
Cu5O5	quartet	8.78	3.64	2.48
${\text{Cu}}_5{\text{O}}_5^{+}$	triplet
${\text{Cu}}_5{\text{O}}_5^{-}$	triplet
Cu6O6	triplet	8.02	3.61	2.47
${\text{Cu}}_6{\text{O}}_6^{+}$	quartet
${\text{Cu}}_6{\text{O}}_6^{-}$	doublet
Cu7O7	quartet		2.00	2.53
${\text{Cu}}_7{\text{O}}_7^{-}$	triplet
Cu8O8	triplet	8.26	3.13	2.53
${\text{Cu}}_8{\text{O}}_8^{+}$	quartet
${\text{Cu}}_8{\text{O}}_8^{-}$	doublet

$$E_a=[nE(Cu)+nE(O)-E(C{u}_n{O}_n)]/2n$$ (1)

Figure 5 displays the atomization energy per atom, E_a, as a function of the number of copper atoms in the cluster. This energy rises rapidly from n = 1 to n = 5 and appears to be converging at about 2.5 eV. The second difference in energies is defined by

Figure 5.

Atomization energies of neutral (CuO)_n clusters with n=1-8 using the B3LYP/LANL2DZ model chemistry.

$${\mathrm{\Delta }}^{2}E(n)=[E(n+1)-E(n)]-[E(n)-E(n-1)]$$ (2)

and is often used to identify so-called “magic clusters”, clusters that are particularly stable. The second difference is plotted in Figure 6. For the neutral clusters, there is an odd-even alternation in the values of Δ²E(n) with Cu₅O₅ and Cu₇O₇ (and possibly Cu₃O₃) appearing to be particularly stable. The trends for the anionic clusters is similar to the trends for neutral clusters with the exception of n = 7, where the neutral cluster is relatively quite stable while the anionic cluster is relatively less stable (and not a magic cluster). There is a change in coordination of one of the copper atoms in the n = 8 cluster from 4-coordinate to 2-coordinate in oxygen upon formation of the anion (copper atom five in Figure 5). This change in geometry may account for the different behavior in the value of Δ²E(n) for the n = 7 neutral and anion. The cationic clusters have the opposite behavior in that magic neutral and anionic clusters have correspondingly unstable cationic clusters for n = 2 – 5.

Figure 6.

Second differences of the energy of copper oxide clusters with n=1-8 using the B3LYP/LANL2DZ model chemistry.

Of particular interest in this work are the charge and spin density differences between neutral and anionic clusters as these differences may lead to reactivity differences between different clusters and EPFR precursors. The average values for these quantities on the copper and oxygen atoms in the neutral clusters are displayed in Table 2 and the values for all atoms in all the clusters are displayed in Table 3. These quantities may correlate with the reactivity of these clusters towards EPFRs. As should be expected, the unpaired electrons reside primarily on the oxygen atoms. For n ≥ 3, there is a clear alternation in the oxygen spin density indicating that extra unpaired electron for the quartet state (n even) clusters resides mainly on the oxygen atoms. With the exception of n = 5 and n = 6, the most and least stable clusters according to the second difference in energies, there is roughly 0.5e of unpaired electron density on the copper atoms. The magic n = 5 cluster has an extra 0.5e on the copper atoms, as compared to the other odd numbered clusters with n ≥ 3. This shift of about one half of an electron is also seen for n = 6. The charge densities seem to be converging to values consist with the transfer of approximately 0.7 electrons from the copper atoms to the oxygen atoms. Reactions of these clusters with persistent free radicals are expected to be facilitated by the transfer of electron density from the free radical to the metal oxide cluster. Therefore, we calculated the difference in charge density between the anion and neutral clusters for each copper atom as a measure of the likelihood that a particular atom may be a reaction site for a free radical. These differences are displayed in Table 4. For n ≥ 4, there are substantial differences in the change in the charge between copper atoms in a cluster. For n = 4, n = 5, and 7 the copper atoms in the most highly strained (smallest) ring in the neutral accept the largest portion of the negative charge. For n = 5, the central copper atom (atom 5 in Figure 2) does not accept any of the negative charge even though it is a member of the most strained ring. For n = 6, all copper atoms except the 4-coordinated atom (atom 6 in Figure 2) accept roughly an equal amount of charge. In the n = 8 cluster, there is a change in geometry from neutral to anion, resulting in the conversion of a 4-coordinate copper atom to a 2-coordinate oxygen atom (atom 5 in Figure 2). It is this copper atom that accepts the majority of the added charge.

Table 4. The Change in Bader charges of copper atoms in (CuO)_n (n=1-8) clusters from neutral to anion using the B3LYP/LANL2DZ model chemistry. The numbers in parenthesis label the different copper atoms.

Clusters	qCu(atom number)
CuO	-0.59(1)
Cu2O2	-0.30(1)	-0.31(2)
Cu3O3	-0.15(1)	-0.27(2)	-0.27(3)
Cu4O4	-0.09(1)	-0.03(2)	0.02(3)	-0.13(4)
Cu5O5	-0.21(1)	-0.18(2)	-0.07(3)
	-0.07(4)	-0.24(5)
Cu6O6	-0.12(1)	-0.12(2)	-0.12(3)
	-0.12(4)	-0.16(5)	0.001(6)
Cu7O7	-0.05(1)	-0.06(2)	-0.07(3)	-0.05(4)
	-0.13(5)	0.34(6)	0.21(7)
Cu8O8	-0.02(1)	0.02(2)	-0.03(3)	0.01(4)
	-0.14(5)	0.01(6)	-0.06(7)	-0.07(8)

The local geometries around Cu and O atoms in bulk CuO are roughly square planar and tetrahedral, respectively. An analysis of the local bond angles shown in Table 8 in the copper oxide clusters gives insight as to the particular stabilities of the odd number clusters (n = 3, 5, and 7). The Cu-O-Cu angles are relatively close to tetrahedral values and correlate reasonably well with the stability suggested by the second energy differences. No correlation was found between O-Cu-O angles (which are quite distorted from the 90 and 180 angles that characterize a square planar geometry) and stability.

Table 8. Average Cu-O-Cu angles in the copper oxide clusters using the B3LYP/LANL2DZ model chemistry.

n	<Cu-O-Cu>
2	82
3	98
4	90
5	103
6	94
7	102

Figure 7 displays the adiabatic ionization energies and electron affinities. The ionization energy of CuO is in good agreement with experiment (calculated 9.28 eV versus experimental 9.41 eV⁷¹). These quantities seem to be converging for n ≥ 3. There is a slight even-odd oscillation in ionization energies, but overall little structure to either quantity except for the electron affinity of Cu₇O₇.

Figure 7.

Calculated adiabatic ionization energies and electron affinities of (CuO)_n clusters with n=1-8 using the B3LYP/LANL2DZ model chemistry.

Conclusions

The electronic and structural properties of small copper oxide clusters have been studied using density functional theory and several basis sets. The LANL2DZ basis set gave the best agreement with existing experimental work and therefore was used to study Cu_nO_n clusters. The M06 and BHandHLYP functionals gave the same structures and spin states as the B3LYP functional for the neutral clusters. It was found that the clusters are planar for up to n = 3 and then become nonplanar. Clusters with an odd number of copper atoms were more stable than clusters containing an even number of copper atoms, possibly due to less strain in the Cu-O-Cu bond angles.

The Bader spin and charge densities show relatively constant spin densities on the copper atoms and alternating (depending on spin state) densities on the oxygen atoms. The magic cluster Cu₅O₅ is the most “copper-centered” radical with the most unpaired electron density on the copper atoms. Stability appears to be correlated with the deviation of the Cu-O-Cu bond angles in a cluster from a tetrahedral geometry; the less distorted structures are the most stable. The odd numbered clusters found in this work have the largest “rings” of copper and oxygen atoms, which allows the Cu-O-Cu angles adopt angles closer to ideal tetrahedral geometries.

Analysis of the differences in charge density between neutral and anionic species show copper atoms in the most strained rings most likely to accept electron density when the neutral is converted to an anion. There are clearly differences between the charge densities on individual copper atoms in a cluster and between the ability (measured by the change in charge density on a given copper atom) of a copper atom to add electron density when the anion is formed. These differences are likely to correlate with the reactivity of different sites on a cluster and should affect the preference for the way in which different clusters react with free radicals and EPFR precursors. We expect that the copper atoms that accept the largest fraction of an electron when forming the anion will be the sites at which free radicals will react.