0 (n = 1-3) Clusters from

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

The Electronic Structures of CoGen-/0 (n = 1-3) Clusters from Multiconfigurational CASSCF/CASPT2 and RASSCF/RASPT2 Calculations Van Tan Tran, and Quoc Tri Tran J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b04846 • Publication Date (Web): 12 Jul 2018 Downloaded from http://pubs.acs.org on July 16, 2018

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The Journal of Physical Chemistry

The Electronic Structures of CoGen−/0 (n = 1-3) Clusters from Multiconfigurational CASSCF/CASPT2 and RASSCF/RASPT2 Calculations Van Tan Tran1*, Quoc Tri Tran1 (1) Theoretical and Physical Chemistry Division, Dong Thap University, 783-Pham Huu Lau, Ward 6, Cao Lanh City, Dong Thap, Vietnam.

ABSTRACT Density functional theory and multiconfigurational CASPT2 and RASPT2 methods are employed to investigate the low-lying states of CoGen−/0 (n = 1-3) clusters. With the RASPT2 approach, the active space is extended to 14 orbitals for CoGe−/0, 17 orbitals for CoGe2−/0, and 20 orbitals for CoGe3−/0. These active spaces include the 3d, 4s, and 4d of Co and 4p of Ge. The 4d of Co is incorporated into these active spaces in order to account for the important doubleshell effect of Co. The structural parameters, vibrational frequencies, and relative energies of the low-lying states of CoGen−/0 (n = 1-3) are reported. The ground states of CoGen− (n = 1-3) are computed to be the 3Φ of linear CoGe−, the 3B1 of cyclic CoGe2−, and the 3B1 of cyclic CoGe3− isomer. The ground states of the neutral clusters are calculated to be the 2Δ of linear CoGe, the 4

B1 of cyclic CoGe2, and the 4A″ of tetrahedral CoGe3 isomer. The calculated adiabatic and

vertical detachment energies of the anionic ground states are in agreement with the experimental values as observed in the 266 nm anion photoelectron spectra.

* Corresponding authors. E-mail: [email protected] 1 ACS Paragon Plus Environment

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1. INTRODUCTION Cobalt-doped germanium clusters have attracted great attention of scientists because of their potential applications in electronic and magnetic materials.1-8 Investigation on the geometrical and electronic structures of cobalt-doped germanium clusters was performed with several experimental and theoretical methods.7,9-14 Regarding the CoGen−/0 (n = 1-3) clusters, the structural, electronic, and magnetic properties of the neutral clusters were studied with density functional theory, but the spin states of these clusters were not reported.9,10 Also, the photoelectron spectra of CoGe2− and CoGe3− clusters were measured with a photon energy of 266 nm.7 The anion spectra showed four bands at 1.96, 2.71, 3.33, and 3.60 eV for CoGe2− and four bands at 2.12, 2.66, 3.37, and 3.98 eV for CoGe3− cluster. The adiabatic detachment energies of CoGe2− and CoGe3− were measured to be 1.56 and 1.85 eV. The computational results as obtained with the B3PW91 functional15-17 show that the ground states of CoGe2−/0 were the triplet and quartet states of a cyclic isomer, while that of CoGe3−/0 were the triplet and quartet states of a rhombic isomer.7 The adiabatic detachment energies of CoGe2− and CoGe3− were computed to be 1.85 and 2.21 eV. These computational adiabatic detachment energies agreed with the experimental values of 1.56 and 1.85 eV. To best of our knowledge, there is no investigation on the low-lying states of CoGe− by any experimental and computational methods. Although the B3PW91 functional was employed to investigate the CoGe2−/0 and CoGe3−/0 clusters,7 all the relevant electronic states of these clusters were not reported. That is the reason why only the first bands in the anion spectra are interpreted. In order to give assignments for the higher energy bands, the excited states of these clusters should be investigated. This can be done by using time-dependent density functional theory. However, this method is rarely applied to study the excited states of transition metal-containing compounds because of the heavy spin contamination problem.18 Also, the relative energies of the low-lying states of transition metal-containing clusters as computed with density functional theory strongly depend on the employed functionals.19,20 A more popular approach to investigate the ground and excited states is multiconfigurational CASSCF/CASPT2 method. In the literature, we can see that the CASSCF/CASPT2 method is applied to study a large amount of transition metal-containing 2 ACS Paragon Plus Environment

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compounds.20-25 However, the application of CASSCF/CASPT2 is limited because of the active space. Most of the computational systems can handle CASSCF/CASPT2 calculations with an active space of 14 orbitals, but the active space with 14 orbitals is not enough to get reliable relative energies for the low-lying states of CoGe2−/0 and CoGe3−/0. The CASPT2 calculations for these clusters require active spaces of 17 and 20 orbitals that include the 3d, 4s, 4d of Co and 4p of Ge. The 4d of Co is included in the active space with the purpose to account for the 3d double-shell effect which is important in systems with a high 3d occupation number.26 In order to extend the active space, the RASSCF/RASPT2 method should be used.21,26-30 In the RASSCF/RASPT2 calculations, the active space is divided into RAS1, RAS2, and RAS3 subspaces. In RAS1 subspace, the orbitals are doubly occupied and a maximum number of holes are allowed. In RAS3 subspace, the orbitals are empty and a limited number of electrons are allowed. In RAS2 subspace, electrons are distributed over the orbitals as in the case of complete active space. With a large number of active space orbitals, the RASSCF/RASPT2 is expected to give true relative energy order for the low-lying states of CoGe2−/0 and CoGe3−/0 clusters. In this work, we apply density functional theory, CASSCF/CASPT2, and RASSCF/RASPT2 methods to investigate the low-lying states of CoGen−/0 (n = 1-3) clusters. The geometrical structures, vibrational frequencies, and relative energies of the relevant states of CoGen−/0 (n = 1-3) are reported. The ground states of these clusters are determined. The adiabatic and vertical detachment energies of the anionic clusters are calculated. The computational results are used to interpret all features in the available anion photoelectron spectra.

2. COMPUTATIONAL METHODS The low-lying states of CoGen−/0 (n = 1-3) were investigated with density functional theory and multiconfigurational CASSCF/CASPT2 and RASSCF/RASPT2 methods. By considering all the possible structures as reported in the previous works,7,9,10 we found several important isomers of CoGen−/0 (n = 1-3) as presented in Figure 1. The BP86 functional31,32 were utilized because this functional proves to be efficient to calculate the relative energies of several transitional metal-doped germanium clusters.20 The def2-TZVPP basis sets33 were used for both Co and Ge. Density functional theory was applied to optimize the structures and calculate the 3 ACS Paragon Plus Environment


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vibrational frequencies of CoGe2−/0 and CoGe3−/0 clusters. All the density functional theory calculations were carried out with NWCHEM 6.5.34 The multiconfigurational CASSCF/CASPT2 and RASSCF/RASPT2 were performed with MOLCAS@UU 8.0.35 The aug-cc-pwCVTZ-DK and aug-cc-pVTZ-DK basis sets were employed for Co and Ge.36,37 The scalar relativistic effects were included by using second-order Douglas-Kroll Hamiltonian.38-40 In the perturbation steps, the 3s, 3p of Co and 3d of Ge were correlated, an imaginary shift of 0.1 was applied, and the default IPEA shift of 0.25 was used. The CASSCF/CASPT2 calculations were employed to build the potential energy profiles for the low-lying states of CoGe−/0. On the basis of the potential energy profiles, the Co-Ge bond distances, vibrational frequencies, and relative energies of the relevant electronic states were determined. The adiabatic detachment energy of the anion was evaluated. The wave functions for CASPT2 were obtained from the CASSCF calculations. The active space for CASSCF calculations could be composed of the valence 3d, 4s of Co and 4p of Ge. In order to include the double shell effect, the 4d orbitals of Co were included in the active space. As a result, the active spaces for CoGe−/0 clusters have 12 or 11 electrons distributed in 14 orbitals that could be denoted by [12(11),14]. With the purpose to reduce the computational cost for multiconfigurational calculations with large active spaces, we applied the RASSCF/RASPT2 method. For CoGe−/0, RAS1 subspace had no orbital, RAS2 included the 3d, 4s of Co and 4p of Ge, and RAS3 contained the 4d orbitals of Co. And a maximum of two electrons was allowed to excite into RAS3. This active space was labeled as [12(11),SD;9,5)]. For CoGe2−/0 and CoGe3−/0, in addition to the 4d orbitals of Co, several unoccupied 4p orbitals of Ge were added to RAS3. This approach results in a active space of [14(13),SD;9,8] for CoGe2−/0 and of [16(15),SD;10,10] for CoGe3−/0. In the RASPT2 calculations, the structures of the low-lying states of CoGe2−/0 and CoGe3−/0 were allowed to relax. The energetic accuracy of the RASPT2 method was calibrated on the basis of the CASPT2 results for CoGe−/0 clusters.

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3. RESULTS AND DISCUSSION 3.A. CoGe−/0 The potential energy profiles of the low-lying states of CoGe−/0 are presented in parts a and b of Figure 2. On the basis of the potential energy profiles, the bond distances, harmonic vibrational frequencies, and relative energies of the low-lying states are determined and collected in Table 1. For CoGe−, the 3Φ is predicted to be the ground states. At the CASPT2 level, the bond distance and vibrational frequency of this triplet are computed to be 2.177 Å and 298 cm−1. The CASSCF molecular orbitals and electron occupation numbers of the 3Φ as displayed in Figure 3 show that the wave function of this triplet has very strong multireference character. The leading configuration of this triplet states is calculated to be 13σ214σ26π47π12δ3 with a reference weight of 25%. In this configuration, the 13σ is predominantly 4s orbital of Co, the 14σ is bonding orbital of 3dz2 of Co and 4pz of Ge, the 2δ are mainly 3dxy and 3dx2-y2 of Co, and the 6π and 7π are respectively bonding and anti-bonding orbitals of 3dxz and 3dyz of Co and 4px and 4py of Ge. The computational results also show that the 1Σ+ is almost degenerate with the triplet ground state. This singlet is formed from the triplet by moving one electron from the 7π to the 2δ orbital. At the CASPT2 level, the singlet is computed to be 0.04 eV above the triplet. Also, the 3Δ, 5Φ, and 5Δ are 0.34, 0.39, and 0.47 eV above the triplet ground state. For the CoGe cluster, the 2Δ is predicted to be the ground state with a bond distance of 2.141 Å and a vibrational frequency of 340 cm−1. This doublet state can be obtained from the 3

Φ of CoGe− by the removal of one electron from the 7π orbital. As can be seen from Figure 3,

7π is an anti-bonding orbital and the detachment of one electron from an anti-bonding orbital would result in a decrease of bond distance. Indeed, in the transition from the triplet to the doublet ground state, the Co-Ge distance is reduced from 2.177 to 2.141 Å. The adiabatic detachment energy of the transition from 3Φ to 2Δ as computed at the CASPT2 level is 0.74 eV. The 4Φ, 4Σ−, and 2Φ are less stable than the doublet ground state by 0.75, 0.77, and 0.90 eV. The RASPT2 calculations give almost the same relative energies for the low-lying states of CoGe− and CoGe. As can be seen from Table 1, the RASPT2 relative energies are slightly higher than the CASPT2. The largest deviation is seen in the case of the excited 5Φ state in which the RASPT2 relative energy differs from the CASPT2 by 0.12 eV. Also, the adiabatic 5 ACS Paragon Plus Environment


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detachment energy of the CoGe− is computed to be 0.80 eV by the RASPT2 method. It can be seen that the RASPT2 adiabatic detachment energy is just 0.06 eV larger than the CASPT2. In general, we can conclude that the RASPT2 method is efficient to calculate the energies of the low-lying states of CoGe− and CoGe.

3.B. CoGe2−/0 The most stable isomer of CoGe2−/0 clusters has a cyclic structure in C2v symmetry as can be seen in Figure 1. The linear isomer of CoGe2−/0 is not investigated in this work because this isomer is known to be less stable than the cyclic one by more than 1 eV.7 The calculated relative energies of the low-lying states of CoGe2−/0 are presented in Table 2. The results show that the BP86 energies are slightly larger than the RASPT2 in most of the states. At the RASPT2 level, the geometry optimization and the single-point energy calculations based on the BP86 optimized geometries give almost the same relative energies. For all the calculated states, the differences between the relative energies computed at the RASPT2 and BP86//RASPT2 levels are about 0.04 eV. It means that the BP86 optimized geometries are sufficient to calculate the relative energies at the RASPT2 level. The ground state of CoGe2− is determined to be the 3B1 with Co-Ge and Ge-Ge bond distances of 2.251 and 2.431 Å as computed with BP86 functional. The vibrational frequencies of the 3B1 are 190, 253, and 315 cm−1. The RASSCF molecular orbitals and electron occupation numbers of the 3B1 as displayed in Figure 4 propose a leading configuration of 17a1218a1219a1220a117b128b1114b225a22. In this configuration, the 19a1, 20a1, 8b1, 14b2, and 5a2 are predominantly 3d of Co, while the 17a1, 18a1, and 7b1 are mainly 4p orbitals of Ge2 ligands. The 3A1 and 3A2 are formed from the 3B1 by moving one electron from the 19a1 and from the 5a2 to the 8b1 orbital. At the RASPT2 level, the 3A1 and 3A2 are computed to be just 0.06 and 0.15 eV above the ground state. For the CoGe2 cluster, the 14B1 is computed to be the ground state with Co-Ge and Ge-Ge distances of 2.269 and 2.431 Å as calculated with the BP86 functional. Also, the vibrational frequencies of the 14B1 are calculated to be 202, 214, and 317 cm−1. The 4B2, 12B1, 12A1, and 2B2 are less stable than the neutral ground state by 0.03, 0.22, 0.34, and 0.49 eV.


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The electron detachment energies of CoGe2− as computed at the RASPT2 level are shown in Table 2. These calculated detachment energies are used to interpret the anion photoelectron spectrum. The photoelectron spectrum of CoGe2− has four bands at 1.96, 2.71, 3.33, and 3.60 eV.7 From the spectrum, the adiabatic detachment energies are measured to be 1.56 eV. The first broad band at 1.96 eV in the spectrum is composed of the transitions from triplet anionic ground state to the 14B1, 4B2, 12B1, 12A1, and 2B2. In these transitions, one electron is respectively detached from the 19a1, 5a2, 20a1, 8b1, and 5a2 orbitals. The vertical detachment energies of these transitions are 1.55, 1.59, 1.76, 1.91, and 2.06 eV as computed at the RASPT2 level. Because the vertical detachment energies of these transitions are very similar, they overlap together to form the broad band at 1.96 eV. The adiabatic detachment energy of the transition to the 14B1 is calculated to be 1.52 eV that is in agreement with the experimental value of 1.56 eV. The second band at 2.71 eV is the results of the transitions to the 32B1 and 4A1 with vertical detachment energies of 2.46 and 2.61 eV. The third band at 3.33 eV is attributed to the transitions to 24B1, 22A1, and 42B1 with vertical detachment energies of 3.30, 3.31, and 3.39 eV. The fourth band at 3.60 eV is assigned to the transitions to the 52B1, 34B1, and 62B1. The vertical detachment energies of these transitions are computed to be 3.43, 3.52, and 3.70 eV. In general, all features in the photoelectron of CoGe2− are explained. 3.C. CoGe3−/0 The CoGe3−/0 clusters can have three isomers that are labeled as A-CoGe3−/0, B-CoGe3−/0, and C-CoGe3−/0 as displayed in Figure 1. The A-CoGe3−/0 isomers have a cyclic structure in C2v symmetry. The B-CoGe3−/0 isomers possess a tetrahedral structure in C3v or Cs symmetry. For computational convenience, all the calculations for the B-CoGe3−/0 are performed in Cs point group. The C-CoGe3−/0 isomers have a rhombic structure in C2v. The calculated relative energies of the relevant states of CoGe3−/0 are collected in Table 3. The results show that the RASPT2 relative energies are slightly smaller than the BP86 functional. The relative energies of the lowlying states of CoGe3−/0 as computed at the BP86//RASPT2 and RASPT2 levels are almost same. For the anionic cluster, the 3B1 of A-CoGe3− isomer is predicted to be the ground state, while the 3

A1 and 1A1 are above by 0.02 and 0.25 eV. The BP86 functional calculations for the 3B1 of A7 ACS Paragon Plus Environment


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CoGe3− show that the Co-Ge distances are 2.221 and 2.861 Å, while Ge-Ge distances are 2.439 and 3.668 Å. At the same computational level, the vibrational frequencies of the triplet anionic ground states are computed to be 95, 111, 218, 231, 280, and 321 cm−1. The RASSCF molecular orbitals and electron occupation numbers of the 3B1 of A-CoGe3− as displayed in Figure 5 show a leading configuration of 25a1226a1227a1228a1110b1211b1117b2218b226a22. In this configuration, the 26a1, 27a1, 28a1, 11b1, 18b2, and 6a2 are predominantly 3d, 4s orbitals of Co, while the 25a1, 10b1, and 17b2 are mainly 4p orbitals of Ge3 ligand. The 3A″, 3A′, and 1A′ of B-CoGe3− and the 3B2 of C-CoGe3− are less stable than the anionic ground state by 0.12, 0.43, 0.64, and 0.25 eV. It should be noted that our BP86 and RASPT2 calculations give a different anionic ground state as compared to the previous B3PW91 calculations.7 In the previous B3PW91 functional calculations,7 the triplet of C-CoGe3− is predicted to be the ground state, the triplet of B-CoGe3− and the quintet of A-CoGe3− are above by 0.45 and 0.60 eV, while the triplet of A-CoGe3− is not reported. The RASPT2 results for the neutral cluster as presented in Table 3 show that the 12B1 of A-CoGe3 and the 4A″ of B-CoGe3 are almost degenerate together. The former state is less stable than the latter one by only 0.03 eV. The 2A″ of B-CoGe3 are 0.24 eV higher than the 12B1. The 4

B2, 4A2, and 4B1 of C-CoGe3 are above the 12B1 by 0.44, 0.55, and 0.59 eV. This finding is new

because, in the previous B3PW91 functional calculations, the quartet of C-CoGe3 is evaluated to be the ground state, the quartet of B-CoGe3 and sextet of A-CoGe3 are 0.10 and 1.03 eV less stable, while the doublet of A-CoGe3 is not studied. Because the anionic ground state is determined to be the 3B1 of A-CoGe3−, all the observed features in the anion photoelectron spectrum should be interpreted based on the electron detachments from this ground state. The anion photoelectron spectrum has four bands with vertical detachment energies of 2.12, 2.66, 3.37, and 3.98 eV.7 The adiabatic detachment energy of the first band is proposed to be 1.85 eV. The adiabatic and vertical detachment energies of CoGe3− as computed at the RASPT2 level are collected in Table 3. The first band at 2.12 eV is attributed to the transitions from the 3B1 to the 12B1 and 14B1 with vertical detachment energies of 1.84 and 2.26 eV. In these two transitions, one electron is removed from 28a1 and 27a1 orbital. The adiabatic detachment energy of the transition to 12B1 8 ACS Paragon Plus Environment

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is computed to be 1.69 eV that is consistent to the experimental value of 1.84 eV. The second band at 2.66 eV is assigned to the transitions to the 4B2, 22A1, and 24B1 with vertical detachment energies of 2.54, 2.69, and 2.73 eV. The third band at 3.37 eV is the results of the transitions to the 24A2, 34A2, and 24A1 with vertical detachment energies of 3.07, 3.10, and 3.36 eV. The last band at 3.98 eV is ascribed to the transitions to the 34B1 and 62B1 with vertical detachment energies of 3.66 and 3.88 eV. In general, all features in the photoelectron spectrum of CoGe3− are explained by the electron detachments from the 3B1 of A-CoGe3−.

4. CONCLUSIONS The low-lying states of CoGen−/0 (n = 1-3) were investigated with the density functional theory and the multiconfigurational CASSCF/CASPT2 and RASSCF/RASPT2 methods. The lowlying states of CoGe− and CoGe have strong multireference wave functions. The ground states of CoGe− and CoGe are predicted to be the 3Φ and 2Δ. The bond distances of CoGe− and CoGe is evaluated to be 2.177 and 2.141 Å by the CASPT2 method. The adiabatic detachment energies of CoGe− is calculated to be 0.74 and 0.80 eV by the CASPT2 and RASPT2 methods. For CoGe2−/0 clusters, the ground states are proposed to be 3B1 and 14B1. The adiabatic detachment energy of the anionic cluster is computed to be 1.52 eV that is in good agreement with the experimental value of 1.56 eV. The first broad band in the photoelectron spectrum of CoGe2− consists of the transitions to the 14B1, 4B2, 12B1, 12A1, and 2B2. The second band at 2.71 eV is explained by the transitions to 32B1 and 4A1, the third band at 3.33 eV is assigned to the transitions to 24B1, 22A1, and 42B1, and the fourth band at 3.60 eV is attributed to the transitions to the 52B1, 34B1, and 62B1. For CoGe3−/0 clusters, the anionic ground state is determined to be the 3B1 of cyclic isomer. The 4A″ of tetrahedral isomer is the neutral ground state, while the 12B1 of cyclic isomer is less stable by only 0.03 eV. The photoelectron spectrum of CoGe3− is interpreted on the basis of the electron detachment from the 3B1. The first band at 2.12 eV in the photoelectron spectrum of CoGe3− is assigned to the transitions to the 12B1 and 14B1. The adiabatic detachment energy of the anionic cluster is computed to be 1.69 eV by the RASPT2 methods. The second band at 2.66 eV is the results of the transitions to the 4B2, 22A1, and 24B1. The third band at 3.37 eV is attributed to the transitions to the 24A2, 34A2, and 24A1. The last 9 ACS Paragon Plus Environment


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band at 3.98 eV is ascribed to the transitions to 34B1 and 62B1. All the calculated vertical detachment energies correspond well with the experimental values as observed in the anion photoelectron spectra.

ACKNOWLEDGMENT This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 104.06-2016.16.

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Page 14 of 22

Table 1. The calculated bond distances, vibrational frequencies, and relative energies of the low-lying states of −/0 CoGe clusters. (b)

(a)

(a)

−1

RE (eV) (c) CASPT2 CASPT2//RASPT2

state leading configuration Co-Ge (Å) freq. (cm ) − CoGe (C2v, C∞v) 3 3 2 2 4 1 3 B1 ( Φ) 13σ 14σ 6π 7π 2δ (25%) 2.177 298 0.00 0.00 1 1 + 2 2 4 0 4 A1 ( Σ ) 13σ 14σ 6π 7π 2δ (16%) 2.171 295 0.04 0.12 3 3 2 2 3 1 4 A1 ( Δ) 13σ 14σ 6π 7π 2δ (12%) 2.273 261 0.34 0.43 5 5 2 2 3 2 3 B1 ( Φ) 13σ 14σ 6π 7π 2δ (51%) 2.287 265 0.39 0.51 5 5 1 2 4 2 3 A2 ( Δ) 13σ 14σ 6π 7π 2δ (78%) 2.223 276 0.47 0.53 CoGe (C2v, C∞v) 2 2 2 2 4 0 3 A2 ( Δ) 13σ 14σ 6π 7π 2δ (49%) 2.141 340 0.00 (0.74) 0.00 (0.80) 4 4 1 2 4 1 3 B1 ( Φ) 13σ 14σ 6π 7π 2δ (62%) 2.198 318 0.75 0.76 4 4 − 2 2 3 1 3 A1 ( Σ ) 13σ 14σ 6π 7π 2δ (36%) 2.272 281 0.77 0.79 2 2 1 2 4 1 3 B1 ( Φ) 13σ 14σ 6π 7π 2δ (33%) 2.229 318 0.90 0.95 (a) The bond distances and vibrational frequencies are reported at the CASPT2 level. (b) The numbers in 3 2 −/0 parentheses are adiabatic detachment energies of the transition from the Φ to the Δ within CoGe clusters. (c) The RASPT2 single-point energies are computed based on the geometries optimized at the CASPT2 level.


Page 15 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


−/0

Table 2. The calculated structural parameters, vibrational frequencies, and relative energies of the low-lying states of CoGe2 of the anionic cluster. (a)

bond distance (Å) Co-Ge, Ge-Ge

clusters and vertical detachment energies (VDEs) (b)

(a)

−1

relative energy (eV) BP86 BP86//RASPT2 RASPT2

(c)

VDE (eV) RASPT2 expt.

state leading configuration freq. (cm ) − CoGe2 (C2v) 3 2 2 2 1 0 2 1 2 0 2 0 B1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (88%) 2.251, 2.431 190, 253, 315 0.00 0.00 0.00 3 2 2 1 1 0 2 2 2 0 2 0 A1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (88%) 2.290, 2.407 200, 209, 309 0.21 0.03 0.06 3 2 2 2 1 0 2 2 2 0 1 0 A2 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (88%) 2.340, 2.371 170, 217, 294 0.42 0.11 0.15 CoGe2 (C2v) 4 2 2 1 1 0 2 1 2 0 2 0 1 B1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (80%) 2.269, 2.431 202, 214, 317 0.00 (1.82) 0.00 (1.50) 0.00 (1.52) 1.55 1.96 4 2 2 2 1 0 2 1 2 0 1 0 B2 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (82%) 2.314, 2.387 180, 223, 310 0.18 0.06 0.03 1.59 1.96 2 2 2 2 0 0 2 1 2 0 2 0 1 B1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (61%) 2.226, 2.402 189, 247, 322 0.17 0.24 0.22 1.76 1.96 2 2 2 2 1 0 2 0 2 0 2 0 1 A1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (68%) 2.229, 2.520 227, 289, 347 0.19 0.34 0.34 1.91 1.96 2 2 2 2 1 0 2 1 2 0 1 0 B2 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (61%) 0.49 2.06 1.96 2 2 2 2 2 0 2 0 2 0 1 0 A2 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (60%) 2.369, 2.480 218, 236, 302 0.97 0.72 0.72 2 2 2 1 1 0 2 1 2 0 2 0 2 B1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (45%) 2.29 2 2 2 1 1 0 2 1 2 0 2 0 3 B1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (33%) 2.46 2.71 4 2 2 2 1 0 1 1 2 0 2 0 A1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (89%) 2.61 2.71 4 2 1 2 1 0 2 1 2 0 2 0 2 B1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (51%) 3.30 3.33 2 2 2 2 1 0 1 1 2 0 2 0 2 A1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (18%) 3.31 3.33 2 2 1 2 1 0 2 1 2 0 2 0 4 B1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (19%) 3.39 3.33 2 1 2 2 1 0 2 1 2 0 2 0 5 B1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (16%) 3.43 3.60 4 1 2 2 1 0 2 1 2 0 2 0 3 B1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (17%) 3.52 3.60 2 1 2 2 1 0 2 1 2 0 2 0 6 B1 17a1 18a1 19a1 20a1 21a1 7b1 8b1 14b2 15b2 5a2 6a2 (18%) 3.70 3.60 (a) The structural parameters and vibrational frequencies are computed with the BP86 functional. (b) The numbers in parentheses are adiabatic detachment energies (ADEs) of 3 4 −/0 3 the transition from the B1 to the 1 B1 within CoGe2 clusters. (c) The vertical detachment energies are calculated for the transitions from the B1 anionic ground state to the relevant states of the neutral cluster.


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 16 of 22

−/0

Table 3. The calculated structural parameters, vibrational frequencies, and relative energies of the low-lying states of CoGe3 (VDEs) of the anionic cluster.

state A-CoGe3− (C2v) 3 B1 3 A1 1 A1 B-CoGe3−(Cs) 3 A″ 3 A′ 1 A′ (1A1, C3v) C-CoGe3−(C2v) 3 B2 A-CoGe3 (C2v) 2 1 B1

bond distance(a) (Å) Co-Ge Ge-Ge (R1, R2) (R4, R5)

leading configuration

clusters and the vertical detachment energies

freq.(a) (cm−1)

BP86

RE(b) (eV) BP86// RASPT2

VDE (eV) RASPT2

25a1226a1227a1228a1110b1211b1117b2218b226a22 (76%) 25a1226a1227a1128a1110b1211b1217b2218b226a22 (85%) 25a1226a1227a1228a1010b1211b1217b2218b226a22 (63%)

2.221, 2.861 2.241, 2.975 2.226, 2.657

2.439, 3.668 2.439, 3.604 2.403, 3.782

95, 111, 218, 231, 280, 321 92, 97, 218, 234, 274, 301 86, 118, 229, 230, 280, 324

0.00 0.18 0.24

0.00 0.04 0.26

0.00 0.02 0.25

34a′235a′236a′237a′238a′239a′122a″223a″224a″1 (80%) 34a′235a′236a′237a′238a′139a′122a″223a″224a″2 (79%) 34a′235a′236a′237a′238a′239a′222a″223a″224a″0 (69%)

2.307, 2.307 2.307, 2.307 2.234, 2.353

2.655, 2.655 2.644, 2.737 2.459, 2.774

114, 115, 168, 220, 220, 309 160, 162, 188, 259, 261, 326 144, 151, 210, 220, 277, 323

0.28 0.58 0.97

0.15 0.53 0.67

0.12 0.43 0.64

25a1226a1227a1228a1110b1211b1217b2218b216a22 (82%)

2.356, 3.891

2.426, 2.780

93, 112, 132, 203, 246, 268

0.49

0.27

0.25

25a1226a1227a1228a1010b1211b1117b2218b226a22

(71%)

2.251, 2.554

2.381, 3.859

90, 143, 231, 250, 285, 318

12A1

25a1226a1227a1128a1010b1211b1217b2218b226a22 (70%)

2.275, 2.595

2.380, 3.862

90, 134, 225, 243, 277, 306

14B1 4 B2 22A1 24B1 22B1 14A2 14A1 32B1 24A2 34A2 24A1 42B1 52B1 34B1 62B1 B-CoGe3 (Cs) 4 A″

25a1226a1227a1128a1110b1211b1117b2218b226a22 (74%) 25a1226a1227a1228a1110b1211b1117b2218b226a21 (78%) 25a1226a1227a1228a1110b1211b1017b2218b226a22 (59%) 25a1226a1127a1228a1110b1211b1117b2218b226a22 (62%) 25a1226a1227a1128a1110b1211b1117b2218b226a22 (35%) 25a1226a1227a1228a1110b1211b1217b2218b226a21 (58%) 25a1226a1127a1128a1110b1211b1217b2218b226a22 (79%) 25a1226a1227a1128a1110b1211b1117b2218b226a22 (32%) 25a1226a1227a1228a1110b1211b1117b2218b216a22 (25%) 25a1226a1227a1228a1110b1211b1117b2118b226a22 (29%) 25a1226a1227a1228a1110b1111b1117b2218b226a22 (56%) 25a1226a1127a1228a1110b1211b1117b2218b226a22 (29%) 25a1226a1127a1228a1110b1211b1117b2218b226a22 (23%) 25a1126a1227a1228a1110b1211b1117b2218b226a22 (49%) 25a1126a1227a1228a1110b1211b1117b2218b226a22 (14%)

2.242, 2.997

2.474, 3.631

63, 98, 214, 222, 270, 301

0.00 (1.90) 0.20 (2.10) 0.61

0.00 (1.69) 0.10 (1.79) 0.56

0.00 (1.69) 0.10 (1.79) 0.52

34a′235a′236a′237a′238a′139a′122a″223a″224a″1 (76%)

2.299, 2.298

2.640, 2.639

123, 124, 171, 218, 219, 317

2

0.01 (1.62) 0.29

−0.01 (1.53) 0.24

RASPT2

expt.

1.84

2.12

1.94 2.26 2.54 2.69 2.73 2.75 2.77 2.78 2.93 3.07 3.10 3.36 3.50 3.58 3.66 3.88

2.12 2.66 2.66 2.66

3.37 3.37 3.37

3.98 3.98

−0.03 (1.53) 0.24

A″ 34a′235a′236a′237a′238a′239a′022a″223a″224a″1 (69%) 2.296, 2.302 2.566, 2.802 91, 124, 176, 209, 231, 316 C-CoGe3 (C2v) 4 B2 25a1226a1227a1128a1110b1211b1217b2218b216a22 (80%) 2.323, 3.994 2.453, 2.618 83, 151, 168, 214, 261, 271 0.51 (1.91) 0.46 (1.88) 0.44 (1.88) 4 A2 25a1226a1227a1228a1110b1211b1117b2218b216a22 (84%) 2.317, 3.952 2.469, 2.697 64, 129, 134, 223, 252, 255 0.56 0.59 0.55 4 B1 25a1226a1227a1228a1110b1211b1217b2218b216a21 (79%) 2.369, 4.054 2.445, 2.597 77, 144, 163, 197, 250, 271 0.73 0.65 0.59 (a) The structural parameters and vibrational frequencies are computed with the BP86 functional. (b) The numbers in parentheses are adiabatic detachment energies (ADEs) of the transitions from the anionic ground state to the neutral ground state.


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Figure 1. The geometrical structures of CoGen− (n = 1-3) clusters. The Co atom is placed on top of the structures.



Page 18 of 22

(b) CoGe

(a) CoGe− Figure 2. The potential energy profiles of the low-lying states of CoGe− (a) and CoGe (b) as computed with the CASPT2 method.


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Figure 3. Natural molecular orbitals and electron occupation numbers of the 3B1 (3Φ) of CoGe− as obtained from the CASSCF calculations. The Co atom is placed on the left-hand side of the structure.



Page 20 of 22

Figure 4. Natural molecular orbitals and electron occupation numbers of the 3B1 of CoGe2− as obtained from the RASSCF calculations. The Co atom is placed on the left-hand side of the structure.


Page 21 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5. Natural molecular orbitals and electron occupation numbers of the 3B1 of A-CoGe3− as obtained from the RASSCF calculations. The Co atom is placed on the left-hand side of the structure.



Page 22 of 22

TOC Graphic


0 (n = 1-3) Clusters from

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