Bonding and Phosphorescence Trends in 1-D, 2-D, and 3-D

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Bonding and Phosphorescence Trends in 1-D, 2-D and 3-D Oligomers and Extended Excimers of Group 12 Metals: Validation of Cooperativity in Both Metallophilic and Excimeric Bonding John Joseph Determan, Pankaj Sinha, Angela K Wilson, and Mohammad A. Omary J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 07 Nov 2014 Downloaded from http://pubs.acs.org on November 7, 2014

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The Journal of Physical Chemistry

Bonding and Phosphorescence Trends in 1-D, 2-D and 3-D Oligomers and Extended Excimers of Group 12 Metals: Validation of Cooperativity in Both Metallophilic and Excimeric Bonding John J. Determan,a,b Pankaj Sinha, a,b Angela K. Wilsonb*and Mohmammad A. Omarya*. University of North Texas, a) Department of Chemistry and Center for Advanced Research and Technology (CART), and b) Department of Chemistry and Center for Advanced Scientific Computing and Modelling (CASCaM), 1155 Union Circle #305070, Denton, TX 76203-5017, United States.

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ABSTRACT Spectroscopic and bonding trends of group 12 clusters of various size (M2-8) have been studied to access proper models for solid-state materials that exhibit ground-state metallophilic bonding and excited-state excimeric bonding. Both of these bonding types are found to exhibit increased bond strength as the cluster size increases, hence modulating the bond distance and spectroscopic constants and manifesting cooperativity in the 1Σ ground state and lowest-lying 3Σ and 3Π open-shell excited states. The cooperative bonding effects are shown to be caused by delocalization of the electron density as the size of the clusters increases. Spinforbidden excitation and emission energies correspond to electron delocalization of the clusters, hence exhibit red shift with cluster size increase. The electron delocalization, and consequently the bonding and photophysical parameters, are studied as a function of cluster size and shape upon 1-D, 2-D, or 3-D growth of the cluster atoms. Near convergence in the cooperative trends are attained upon octuplet clustering with faster convergence attained for the 3-D or 2-D versus the 1D cluster expansion.

KEYWORDS: group 12 clusters, metallophilic bonding, metal-metal bonds, extended excimers, phosphorescence, cooperativity


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INTRODUCTION In previous studies of small M1-M4 neutral mercury clusters and Cd and Zn atoms and dimers, we have investigated both bonding and photophysical properties.1-2 In doing so, dimerization or small-cluster oligomerization has been found to systematically affect bond lengths and energies as well as spin-forbidden excitation and phosphorescence energies. Those studies have targeted sufficiently-small models, which has allowed the assessment of various method/basis set combinations toward quantitative and qualitative accuracy versus experiment of bonding and photophysical trends upon changing cluster size or identity of the metal atom. For example, CCSD(T)/aug-cc-pVTZ-PP provides bond lengths and spectroscopic constants for atoms, dimers and trimers that well-reproduce experimental parameters for the equilibrated electronic ground state, whereas the two lowest-lying triplet excited states were sufficiently described via hybrid density functionals in combination with triple-zeta quality correlation consistent basis sets (e.g., B3PW91/aug-cc-pVTZ-PP).3 However, computations of larger clusters beyond trimers at similar levels of accuracy have not been feasible. The bonding and photophysical properties computed for smaller oligomers such as dimers and trimers are not expected to reproduce the experimental values for complexes that exhibit extended oligomerization of metal atoms. Indeed, earlier work by Elbjeirami et al.4 demonstrated that MP2-computed excimer phosphorescent emission energies of *[Au(CO)Cl]2 were in good agreement with experiment for the more dilute solutions that exhibited luminescence in a frozen matrix. However, as the concentration of the solution increased and ultimately reached the Au(CO)Cl solid state material to increase oligomerization beyond dimers, the corresponding phosphorescence energies were not well-described by dimer models. As the solution becomes more concentrated and the molecules in solution aggregate, the emission wavelength red shifts


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and approaches the solid-state behavior.4 It is, therefore, necessary to model the evolution of the spectroscopic constants and related bonding structures as a function of aggregation. A simple approach to this may be to model the trends in the bonding and photophysical parameters as the metal core of the organometallic clusters increases in size. However, this may not be feasible for large aggregates of ligand-containing complexes. For example, our aforementioned study on Au(CO)Cl has failed to model sufficiently large clusters that adequately describe the concentrated solution or solid state behavior and sufficed with solving the problem experimentally via the frozen solution measurements versus concentration, by which experimental conditions were controlled to produce the excimer emission and dimer excitation energies that agreed with the computationally-viable MP2 treatment. The phosphorescence energies are sensitive to the change in geometry, bond strength, and cluster size.1 Several previous studies have modelled the electronic structures of the ground state of group 12 clusters as a function of size without addressing excited-state bonding or photophysics as done herein.5-10 In small closed shelled mercury clusters, the atomic interactions are of van der Waals strength and length, resulting in an insulating behavior.11-12 As the number of atoms in the cluster increases, the bond strength also increases and covalent bonds are formed. In large mercury clusters (>100 atoms), metal-metal interactions are seen.13-14 The strength and type of interaction (e.g., van der Waals, covalent) of similar metal clusters have been assessed in previous studies for clusters ranging from 4-50 atoms. Evidence found in these studies suggest that the transformation of bond strength from van der Waals interactions to covalent bonding occurs due to a broadening of the atomic bandwidths, causing an increased overlap of the s and p orbitals, which strengthens the bond.15-17


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The exact group 12 metal cluster size where the bonding type change occurs may be difficult to define, as atomic interactions are often found to be comprised of more than one type of interaction. Bond strengths in metal-metal clusters have also been observed to be cooperative in nature, thus the actual bond strength and defined bonding type does not change instantaneously but occurs gradually with cluster size increases.18 The interactions of atoms in group 12 metal clusters may explain properties such as magnetism, luminescence, atomic and electronic structure, and stability of electronically charged clusters during redox processes. To better understand these properties, a proper model of the interactions of atoms in metal clusters is needed. While traditional DFT, such as BLYP or B3LYP can properly model the covalent and metallic bonding of the medium to large size metal clusters, studies have shown the difficulty these DFT functionals can have in describing longrange dispersion forces, such as those that are present in small group 12 clusters.19-25 Previous studies have shown that simple GGA or hybrid density functional methods do not properly treat long-range correlation and thus do not properly describe the metallophilic bonding and/or cooperativity effects.1-2 Recently, dispersion corrected functionals have been developed to correct for the inability of GGA and hybrid DFT methods to properly model metallophilic bonding and/or cooperativity. These methods have been evaluated in the current study to assess the ability of dispersion correction to model metallophilic bonding. The current study also uses mPW2PLYP/aug-cc-pVTZ-PP to model these systems. This approach allows for a systematic description of cooperativity (the increase of bond and cohesion energies with increased cluster size) in group 12 clusters and potentially renders this as a backdrop for future expansion to include other transition metal cluster systems, including ligand-containing clusters. The mPW2PLYP/aug-cc-pVTZ-PP results are also compared with those based upon the MP2/aug-cc-


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pVTZ-PP (or the MP2/LANL2DZ approach that we had initially used in this study). In addition, 2-dimensional mercury clusters have been modeled with several DFT methods (M06-2X, B98, B97-D) used in combination with aug-cc-pVTZ-PP. To date, excited state complexes have not been studied to the same extent as ground state structures for group 12 clusters. Cooperativity of the triplet state excited structures may be more difficult to interpret based on bond length or formal bond order. While the formal bond order of the ground state is zero regardless of the number of atoms in the cluster, the bond order in the triplet excited states varies with cluster size, as only one electron is promoted from the antibonding HOMO to the bonding LUMO of the cluster. This individual bonding electron is shared among the entire excited state cluster and thus the bond order will vary with the size of the cluster. For example, the formal bond order in lowest-triplet excited-state clusters is 1 for the dimer, 1/2 for the trimer, 1/3 for the tetramer, etc. As such, bond lengths may become longer (as the overall bonding order decreases) even though the overall cooperativity is increasing. Previous studies have shown cooperativity in the excited states of smaller mercury cluster can be evaluated using energies per individual bonds of excited states. Regardless of the bond order, the energy per bond was found to increase with cluster size increase, hence manifesting cooperativity.1 In the low-lying triplet excited states or paramagnetic excited states involving the excitation of more than one electron (denoted as high-spin excitations in the current study) may also be important in the study of the spectroscopy of metal clusters. Extended excimers that have higher spin states than triplet (e.g., quintet) have been studied for small Hg clusters previously1 and will be expanded upon herein for even larger clusters of all group 12 metals in order to investigate possible photoinduced magnetic coupling.


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The current study models the structural and electronic spectral changes of M2-8, where M = Zn, Cd, or Hg, as the cluster size is increased. Linear, 2- and 3-dimensional structures were examined to study changes in cooperativity and photophysical spectral constants as interactions of neighboring atoms are increased. Linear clusters of increasing size serve as a model of change in bonding strength and transition energies as observed in the aggregation of closed-shell complexes such as (RNC)AuCl.4, 26

COMPUTATIONAL METHODS All computations in this study were carried out using the Gaussian program suite.27 Computations were performed for Znn, Cdn, and Hgn (where n=2-8 atoms) species with linear (D2h, the highest Abelian group available using Gaussian program) symmetry. 3-dimensional structures of several representative systems were determined to gain insight into how structure affects bonding properties and spectroscopy constants. These representative clusters were chosen to be the lowest energy structures for the ground state cluster (similar to what has been done in previous studies such as in ref 21). Upon excitation to their lowest phosphorescent states, the clusters were allowed to freely distort. No attempt to force symmetry was made. It is necessary to choose a method that models electron correlation interactions in order to accurately describe the dispersion forces present in the ground state of these systems. The mPW2PLYP double hybrid method was employed in this study.28 Double hybrid density functionals include a fraction of Gorling-Levy second-order perturbative correlation. Adding perturbative correlation to density functional methods causes double hybrid approaches to have computational costs akin to those of MP2 methods, thus losing some of the appeal of using


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density functional methods. However, unlike GGA and traditional hybrid density functional approaches, these double hybrid methods are able to model non-local dynamic electron correlation that is responsible for the metallophilic interactions of the group 12 metal clusters modelled in this study. Double hybrids also have the advantage of reproducing CCSD(T) level binding and dissociation energies at MP2 levels of cost.29 Mercury clusters were also modeled using conventional MP2 method30-31 and the M06-2X,32 B98,33-34 and B97-D35 density functionals. Excimeric clusters were modeled with restricted open-shell Møller-Plesset second order perturbation theory (ROMP2). The importance of using ROMP2 rather than employing unrestricted MP2 has been demonstrated by Wilson and co-workers.36 This approach aided in avoiding spin contamination of excited state clusters, allowing proper modeling of the 3Σ, 3Π, and other higher-spin states. For density functionals, spin contamination was also found to be minimal, and thus unrestricted computations were employed. The augmented correlation consistent triple-zeta level (aug-cc-pVTZ-PP) basis set was used in this work. This basis set treats the 3s, 3p, 4s, and 3d electrons explicitly for zinc, 4s, 4p 5s and 4d electrons explicitly for cadmium and the 5s, 5p, 6s, and 5d electrons explicitly for mercury. The core is treated with an ECP developed by the Stuttgart group, replacing the core electrons with a scalar relativistic pseudopotential. The importance of scalar relativistic effects has been accounted for in these basis sets as described in the literature.37 Basis set superposition error due to the use of a small basis set can be addressed using a counterpoise correction, as follows:38 ∆ECP (R) = EAB – EA{AB} – EB{AB}, (1) where R represents distance between A and B, EAB represents the energy of the complex and EA{AB} represents the energy of fragment A in the presence of the basis sets for both the A and B


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fragments. Previous computations showed BSSE corrections for group 12 dimers computed with the aug-cc-pVTZ-PP basis set to be minimal. BSSE effects were thus not considered in this study. Frequency calculations were run on optimized structures to ensure the clusters were local minima. While forcing the geometries of the clusters to be linear may lead to structures that are not necessarily the global minima, the linear models may well represent the aggregation of closed-shell atoms in polymers and complexes. The 3-dimensional structures were optimized to be minima unless otherwise indicated. Electronic constants are computed as vertical transitions of optimized structures. This means the excitation energy is taken from the triplet minus the singlet energy at the optimized 1Σ structure. The emission energy is the triplet energy minus the singlet energy at the 3Σ or 3Π optimized structures. The dissociation energies, De, of the ground state oligomers are computed as the difference in energies of the oligomer minus the energy of the complex fully dissociated into ground state monomers. For the triplet excited state the bond energies for an extended excimer Mn (where n is the number of metal atoms) were computed as the energy of the cluster minus the energy of one monomer in a triplet excited state plus n-1 ground state monomers. The dissociation of high-spin extended excimers were computed relative to the energy of fully dissociated triplet excited monomers.


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RESULTS AND DISCUSSION Ground-State Bonding. The increase of cooperativity in the ground state clusters is demonstrated by the shortening of bonds as the cluster size of the molecules is increased, as is shown in Tables 1a-3a. The group 12 dimers in the ground state have bond lengths consistent with metallophilic interactions in which weak dispersion forces are significant. As the cluster size increases, the bond lengths decrease. The bond lengths in the zinc octamer are on average 0.141 Å shorter than in the corresponding dimer. The center bond length of the cadmium octamer is found to be shorter by more than 0.130 Å than in the corresponding dimer. Changes in bond length are less extreme as the clusters increase in size, as shown in Table 1a. For example, there is a difference of 0.065 Å between the dimer and trimer bond lengths, whereas the difference in average bond length between the zinc heptamer and octamer is only 0.032 Å. The changes in bond lengths are greatest in the inner most (3-4 atoms) bonds of the metal clusters. The exterior bonds (outside the 3-4 innermost atoms of the cluster) of the tetramer through octamer are shown to remain fairly close in length. Periodic trends of the ground state cluster bond lengths are similar to those seen in experiment for other transition metal groups such as the coinage metals. That is, 3d clusters have the shortest bond lengths, while 4d clusters have the longest bond lengths rather than the 5d clusters.18, 39-41 The shortest ground state bond lengths occur for the 3d metal clusters, as the metals in this row have the smallest radii. The 5d metals have the second shortest bond lengths due to relativistic contractions of atomic radii, causing the bond lengths of ground state mercury clusters to be shorter than the bond lengths computed for ground state cadmium clusters. The relativistically enhanced electron correlation (metallophilic interactions) of the mercury clusters is larger in


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magnitude than the electron correlation of the zinc and cadmium clusters. Another likely contributing factor is the lanthanide contraction phenomenon that can cause the atomic radii of 5d elements to become shorter than the radii of the 4d elements, especially for late transition metals, as Schmidbaur et al. and Omary et al. have shown previously.42-43

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Σ Excited-State Bonding. The formal M-M bond order decreases as the number of bonds in the

excited state increase, because only one electron is excited over all atoms in the metal cluster. Variation of bond order (i.e. 1/2 for the excited dimer, 1/3 for an excited trimer, 1/4 for an excited tetramer, etc.) makes assessing cooperativity of excited states based solely on the length of bonds difficult. As the clusters increase in size (shown in Tables 1b-3b), the lengths of the exterior bonds of the cluster become longer instead of shorter. The exterior excited state bonds in the 3Σ extended excimers are similar in bond length to those of the 1Σ ground state clusters, indicating the excited electron may be more localized on interior atoms of the triplet 3Σ cluster. Localization of the excited state electron density on the most interior atoms of the 3Σ metal clusters can be seen in Figures 1-3 as the cluster increases. The higher electron density corresponds to shorter interior bonds of the excited state cluster. The bond length of the 3Σ cadmium excimer is shorter than that of the corresponding mercury excimer, opposite of what is found in the corresponding 1Σ ground state dimers. As a metal cluster is photoexcited, the bonding interactions are strengthened and the nature of the bonds transition from weak metallophilic to covalent with the latter delocalized on multiple cluster atoms. The bond distortions in the cadmium clusters upon photoexcitation are greater


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than those in the corresponding mercury clusters. The reversal of bond length trend (between the 4d and 5d metal cluster) vs the corresponding ground-state trend herein is similar to what was seen for group 11 complexes investigated in previous experiments. For example, Raman studies revealed that photoexcitiation to the phosphorescent excited state attained greater distortion in Ag-Ag excimeric bonding than in Au-Au excimeric bonding of analogous silver and gold complexes.41 Π Excited-State Bonding. The exterior bonds of the group 12 clusters in the 3Π excited state

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also exhibit greater elongation as the cluster size increases (Tables 1c-3c). The electron delocalization (delocalization qualitatively assessed from SOMO diagrams in Figures 1-3, 10 and 11, using the default isodensity value of 0.0004) of the group 12 clusters in their 3Π excited state is less extensive than in their 3Σ excited state. The electron density of these 3Π excimeric clusters is only delocalized over the innermost 3-4 atoms of the cluster. Similar to what is seen for the corresponding 3Σ extended excimers, the exterior bonds of the 3Π extended excimers are also in the range of metallophilic bond lengths (Tables 1-3). High-Spin Excited-State Bonding. In the clusters that are in high-spin (HS) excited states, beyond triplet spin multiplicity, each atom may have an excited electron in the ferromagnetic coupling limit. Unpaired electrons on the s and/or p orbitals can cause covalent metal-metal bonds between each pair of atoms throughout the entire cluster in that situation, whereas in intermediate situations between triplet and the ferromagnetic coupling limit, the delocalization of excimeric bonding can extend further toward the exterior atoms. As shown in Tables 1d-3d, each of the individual bond lengths in the HS excited state clusters is similar to the corresponding bond length of the photoexcited dimer with no bonds in the metallophilic range, unlike the


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situation encountered in the triplet excimeric clusters. Cooperativity does not seem to have a large effect on the length of the bonds in these HS excited states, as the resulting bond lengths remain similar, overall, within the excimeric range regardless of cluster size. This is not surprising, as the overall bond order per bond is constant in such situations. Lack of increased cooperativity in bonding is due to reduced delocalization of electrons over the s to the p orbitals. In these high spin excimeric clusters, the s and p orbitals each have one electron in the orbital. Therefore, electron correlation involving the interaction of the s and p orbital will not increase electron delocalization of the cluster. Ground-State Cohesive Energy. Cohesive energy (the energy required to break the cluster into isolated atoms) can be used to qualify the change in bonding strength as the cluster size increases. The extent of this change can be observed in Tables 1a-3a and Figure 4. The bonding interactions of zinc clusters are the least affected by the cluster size. The dimer has a relatively weak dissociation energy of only 135 cm-1. Upon increasing the cluster size of ground-state zinc clusters, the cohesive energy increases by approximately 12 cm-1/bond on going from dimer to trimer, 5 cm-1/bond on going from trimer to tetramer, 3 cm-1/bond on going from tetramer to pentamer, and only 1 cm-1/bond on going from heptamer to octamer. The cohesive energies have a similar trend to that observed for bond lengths, in direct correspondence to electron delocalization. As the electron delocalization converges to a constant level, the bond lengths and cohesive energies are also seen to converge to essentially constant values. The cohesive energy in the mercury ground-state clusters undergoes the greatest change (337 cm-1/bond to 356 cm-1/bond on going from dimer to trimer models, for example). As the cluster size increases, the change in cooperativity is not as great, which is evident in the difference in cohesive energies of the trimer versus teteramer models compared to those of the


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dimer versus trimer models (approximately 9 cm-1/bond). The overall change from the dimer to octamer is greater for mercury clusters than for zinc clusters, as mercury clusters do not converge to a constant energy as quickly as the zinc clusters do. The relative change in cohesive energy is greatest for the cadmium clusters. The cohesive energy increases from 217 cm-1/bond for a cadmium dimer to 236 cm-1/bond for a cadmium trimer cluster. The change in the cohesive of the cadmium cluster as a function of size is slower to converge to a constant value when compared to the cohesive energies of zinc and mercury clusters. This suggests greater electron delocalization in cadmium clusters. 3

Σ Excited-State Cohesive Energy. Tables 1b-3b and Figure 5 show the changes in bonding

strength vs cluster size in the 3Σ excimeric state. The cohesive energy of the excited state corresponds to the delocalization of electron density of the cluster. The electron density is delocalized over all atoms in Zn2-5 clusters. The bond energy steadily increases as the electron density becomes more delocalized in larger clusters. The electron density is delocalized over all atoms of the trimer, thus the cohesive energy is increase substantially from the bonding energy of the dimer, -27.2 x 103 cm-1/bond verses -21.7 x 103 cm-1/bond, respectively. The increase in binding energy per bond is also substantial from the trimer to the tetramer, a difference of 2.3 x 103 cm-1/bond. The extent of electron delocalization represented in Figure 3, as well as the energy per bond, shown in Figure 5, both decrease in magnitude with the addition of each atom to the cluster size. The increase of the electron delocalization ceases after the zinc hexamer, which is evident by the cohesive energy converging to a constant value. In the mercury clusters, there is a decrease in electron delocalization as the cluster size is increased.


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The decrease in the electron delocalization is not as significant as for zinc but is shown to decrease in clusters larger than the pentamer. The highest energy sigma SOMO of the mercury octamer is shown in Figure 3, and the majority of the electron density is localized on the innermost 3-4 atoms of the cluster with size only a small amount of electron density on the outermost atoms (atoms outside the 3-4 strongly bonded interior atoms of the cluster). Therefore, the change in cohesive energies is not significant in mercury clusters that are larger than the tetramer. 3

Π Excited-State Cohesive Energy. Tables 1c-3c and Figure 6 show the changes in bonding

strength vs cluster size in the 3Π excimeric state. Similar to the group 12 clusters in the 3Σ state, the cohesive energy of the group 12 clusters in the 3Π state corresponds to the electron delocalization. The cohesive energy of tetramer clusters is seen to be much larger than the dissociation energy of the dimer due to the delocalization of electron density over the entire cluster. Examples of this increase are seen in all three group 12 clusters (Znn, Cdn, and Hgn). The cohesive energies of the dimer, trimer, and tetramer zinc clusters are -22.4 x 103, -27.4 x 103 and29.8 x 103 cm-1, respectively. Though the cohesive energy increases in clusters larger than the pentamer, as is graphed in Figure 6, the rate does not increase as fast as the cohesive energy of the clusters smaller than the pentamer. The electron density of the larger clusters is not fully delocalized as is evident in the cohesion energies of the pentamer, hexamer and heptamer, which are -30.8 x 103, -31.41x 103 and-31.79 x 103 cm-1, respectively. High-Spin Excited-State Cohesive Energy. The cohesive energies of the zinc, cadmium and mercury clusters in high-spin excited states are larger than the cohesive energies of the excited state dimers. The increase in the cohesive energy may indicate that the ferromagnetism of these


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clusters provides a stabilizing factor. As the clusters increase in size, the cohesion energy remains somewhat constant. As was indicated in the high-spin excited state bonding section, lack of changes is likely due to a lack of cooperativity, corresponding to no change in the electron delocalization. Without cooperative effects, the bonds are not strengthened and thus the cohesive energies remain relatively constant regardless of cluster size. Σ-3Σ Excitation Energies. The 1Σ−3Σ excitation energy is evaluated, as shown in Figure 7,

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corresponding to the vertical transition at the ground state geometry. The transition is formally Laporte-allowed for dimer models. When electron delocalization in the 3Σ state becomes essentially constant, the red shift in the 1Σ−3Σ excitation energy vs increased cluster size also stabilizes. For example, the zinc dimer, trimer and tetramer excitation energies are 31.5 x 103, 30.0 x 103 and 29.1 x 103 cm-1. The cadmium excitation can also be seen to decrease as the cadmium cluster size increases. Examples of this are shown in the dimer, trimer and tetramer clusters, which have respective excitation energies of 28.6 x 103, 26.6 x 103 and 25.2x 103 cm-1.. Another important result is seen by comparing the 1Σ−3Σ excitation energies of the dimer and octamer clusters, which have a 103 cm-1 magnitude difference in all three cluster types. The zinc dimer has an excitation energy of 31.5 x 103 cm-1, which red shifts to 28.0 x 103 cm-1 for the octamer. A greater red shift is seen for analogous mercury clusters, for which the dimer excitation energy is 40.7 x 103 cm-1 versus 31.7 x 103 cm-1 for the octamer. Changes in excitation energy as metal complexes aggregate have also been noted previously in the literature by several investigators, particularly in coinage metal organometallic complexes. As the concentration of organometallic complex solutions is increased, aggregation of monomers to dimers or larger oligomers causes excitation peaks to red shift due to weak metallophilic interactions of the metal centers.44-49


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Σ−1Σ Phosphorescence Energies. The 3Σ−1Σ phosphorescence (Figure 8) is also directly

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related to the delocalization of electron density of group 12 clusters. The transition is formally Laporte-allowed for dimer models. The increased delocalization of Zn clusters shown in Figure 1 above extrapolates to progressively red shifted 3Σ−1Σ emission energy (Figure 8). The largest red shift rate occurs upon going from the dimer toward the tetramer with 3Σ−1Σ phosphorescence of 21.2 x 103, 14.8 x 103 and 14.8 x 103 cm-1 for the zinc dimer, trimer and tetramer, respectively. The 3Σ−1Σ emission energies of the zinc hexamer, heptamer and octamer clusters are 6.9 x 103, 5.6 x 103, and 4.6 x 103 cm-1, respectively. As the electron density becomes more delocalized, the 3Σ−1Σ emission exhibits corresponding red shifts. The effect the electron delocalization has on the 3Σ−1Σ emission energy is also evident when correlating the mercury sigma SOMO, shown in Figure 3, with the mercury 3Σ−1Σ emission energy plot of Figure 8. Similar to the case of cadmium, as the electron density is delocalized over the 3Σ excited mercury cluster, the 3Σ−1Σ emission energy exhibits greater red shifts. Π−1Σ Phosphorescence Energies. We evaluate the 3Π−1Σ phosphorescence (Figure 9)

3

although the transition is formally Laporte-forbidden (3Πg−1Σg+) for dimer models, as the transition becomes allowed (3Πu−1Σg+) for linear trimer models, for example. Indeed, modelling the 3Π−1Σ transition energies in our previous study of small Hg clusters has facilitated the assignment of the known experimental spectra of Hg vapor.1 The M-M bonding in the 3Π excited state is localized on only the inner-most atoms of the zinc, cadmium and mercury clusters (Figures 1-3). The 3Π excited state electron density in group 12 cluster species is largely localized on only the three central atoms of the pentamer and heptamer clusters and only the four inner most atoms of the hexamer and octamer clusters. The density is seen to oscillate between


17


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Page 18 of 56

three and four central atoms with even and odd number of atoms, thus causing an even/odd oscillation in phosphorescence energies for group 12 clusters. While there is a substantial change in emission energy from the dimer to the tetramer, the amount of electron delocalization does not increase greatly in clusters of a pentamer or larger, thus the emission energy does not vary greatly in these clusters. This is evident in the comparison of the zinc dimer, trimer and tetramer 3Π−1Σ emission energies (17.7 x 103 cm-1, 11.1 x 103 cm-1 and 7.9 x 103 cm-1, respectively) to the zinc pentamer, hexamer, heptamer and octamer emissions energies (6.1 x 103 cm-1, 5.0 x 103 cm-1, 4.4 x 103 cm-1 and 4.0 x 103 cm-1, respectively). High-Spin Phosphorescence Energies. Phosphorescence energies of the high-spin (HS) excimeric clusters exhibit an apparent increase with increasing cluster size. The HS zinc octameric extended excimer, for example, is predicted to phosphoresce at 60.39 x 103 cm-1 versus only 21.2x 103 cm-1 for the analogous triplet excimer. Such cases are modelled for the emissions of larger clusters instead of simply modelling a dimer emission to represent highpressure gas phase or condensed matter (whether for the same group 12 species or other ligandcontaining excimeric systems that have similar M-M bonded excitons). At first sight, phosphorescence from such HS states gives rise to intractable emissions in the deep UV region where interference from air or solvents becomes relevant. However, the “raw” computed values entail one-photon excitation routes whereas a larger linear chain of metal atoms may also exhibit multi-photon excitations that engender non-linear optical (NLO) properties and associated applications thereof. For the even-numbered models illustrated herein, analysis of the phosphorescence energies in Tables 1d-3d gives rise to multi-photon energies that are actually red-shifted from those corresponding to the corresponding dimer models. For example, the


18

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tetrameric, hexameric, and octameric zinc clusters give rise to 13.35 x 103 cm-1, 13.73 x 103 cm-1, and 13.48 x 103 cm-1 if one considers 2-, 3-, and 4-photon excitation routes, respectively, according to MP2/LANL2DZ computations. These values give rise to red shifts by more than 1000 cm-1 versus the dimer’s 3Π-1Σ phosphorescence energy (and even greater red shift, by more than 4000 cm-1, versus the dimer’s 3Σ-1Σ phosphorescence energy). This phenomenon also would have significant consequences upon “on-off” magnetic applications in which ferromagnetic coupling would be turned on and, indeed, thermodynamically favored upon irradiation of such clusters that exhibit similar bonding and photophysical properties. The results herein, therefore, represent a promising backdrop for theoretical and experimental investigations to facilitate the excited-state assignment and study the NLO and magnetic switching properties and applications of gas- and condensed-phase transition metal species that exhibit this behavior. Mercury Ground State Bonding, Dissociation and Excitation Energy Methods Comparison. The mPW2PLYP double hybrid is found to reasonably agree with experimental and CCSD(T)/cc-pVTZ-PP computational bond lengths in pertinent dimer models. The mPW2PLYP/aug-cc-pVTZ combination results in a dimer bond length of 3.703 Å in comparison to values of 3.976 Å for the CCSD(T)/cc-pVTZ computations and 3.63 Å found experimentally for Hg2.59 The dissociation energy (337 cm-1) also rather closely resembles the experimental value (350 cm-1). The excitation energy computed via mPW2PLYP/aug-cc-pVTZ (40.7 x 103 cm-1) is also in good agreement with the experimental value (37.6 x 103 cm-1) and excellent agreement with the CCSD(T)/cc-pVTZ-PP value (39.3 x 103 cm-1). Values computed with MP2/aug-cc-pVTZ-PP are found to underestimate the bond length (3.320 Å), overestimate the dissociation energy (1177 cm-1) and to overestimate the excitation


19


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Page 20 of 56

energy (42.4 x 103 cm-1) in comparison to both experimental and CCSD(T)/cc-pVTZ-PP computed values. Similarly to the mPW2PLYP, MP2 computed bond lengths decrease as the cluster size is increase (e.g., Hg dimer bond length 3.320 Å vs average octamer bond length 3.179 Å). The De/bond also significantly increases with cluster size (dimer 1177 cm-1 versus octamer 1485 cm-1) and the excitation energy is shown to substantially decrease (dimer 42.4 x 103 cm-1 versus octamer 35.8 x103 cm-1). The deviation from experimental or rigorous theoretical results for MP2 is even greater upon using a smaller basis (LANL2DZ) in dimer models, although the qualitative trends of cooperative metallophilic and excimeric bonding as well as the consequent spectral red shifts upon proceeding to the larger clusters are similar to those attained via mPW2PLYP/aug-cc-pVTZ, as shown in the Supporting Information for all MP2/LANL2DZ computations we had undertaken initially to establish such trends. While the M06-2X finds bond lengths and dissociation energies that compare fairly well with experimental values for Hg2, the excitation energy (35.7 x 103 cm-1) is slightly underestimated in comparison to the experimental value. The M06-2X functional also does not show a significant change in De/bond (445 cm-1 for the Hg dimer versus 453 cm-1 for the octamer) and the bond lengths actually increase instead of decreasing as would be expected for cooperative bonding. This is due to the failure of traditional hybrid density functional methods to include long range correlation effects. The B98 GGA results in bond lengths that are too long in comparison to CCSD(T) and experimental dimer values and slightly underestimates the dissociation energy. This functional is able to show limited amounts of cooperativity as the average bond length of the mercury octamer (3.843 Å) is slightly shorter than the dimer bond length (3.876 Å) and the De/bond is slightly increased by 9 cm-1 (the mPW2PLYP finds a change in the De/bond of 42 cm-1).


20

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Addition of dispersion corrections (B97-D) is found to decrease the for Hg2 bond length to 3.718 Å (a length that corresponds more closely to CCSD(T) and experimental values). However, the dissociation energy (1644 cm-1) becomes overestimated on similar orders to MP2. Bond lengths are also seen to decrease very little, suggesting that cooperativity depends on more than dispersion interactions. Inclusion of long range correlation (as is the case in MP2 and mPW2PLYP) is shown to be needed to properly estimate cooperativity in mercury clusters. Ground-State Bonding in 2-/3-Dimensional Structures. The linear clusters are not always the lowest-energy structures. Metal-metal interactions increase in many luminescent compounds as a result of linear aggregation in the solid state or concentrated solutions.4, 48-51 It is, however, also important to understand how 2-dimensional52-53 and 3-dimensional54-57 metal-metal interactions will affect the preferred geometric structure and spectroscopic constants, as other classes of mononuclear and multinuclear phosphorescent complexes entail such interactions in an intermolecular and/or intramolecular manner.52-57 The bond lengths of the dimer and trimer models are typical for dispersion interactions that are prevalent in metallophilic bonding. The diagrams in Figure 10 show that a bent trimer model exhibits shorter bonds than those in the linear trimer structure. Comparison of this structure to the linear trimer clearly shows electron delocalization is directly related to the number of bonding interactions each atom experiences. The tetramer cluster can exist in either the 2-dimensional planar rhombus or the 3-dimensional trigonal pyramidal configuration. While the rhombus is a transition state and thus not a minimum, it is instructive to represent this structure in Table 4 for comparison vs the 3-dimensional trigonal pyramidal structure. The imaginary frequency for the zinc rhombus is an out of plane bending mode with a magnitude of 8.9 cm-1. If the bonds primarily entailed p- orbital overlap, the rhombus would be favored.


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However, all ground-state structure atoms have a majority of electron density in the s orbital with only a slight amount of p orbital delocalization. The 3-dimensional structure is, consequently, favored as it encompasses 3 bonds per atom instead of only 2 bonds per atom, akin to the situation in the rhombus. The greater electron delocalization leads to shorter, stronger bonds in 3dimensional group 12 clusters when compared to the linear configurations. Bond lengths of zinc clusters greatly decrease from the trimer to the tetramer. The bonding in the C2v trimer is 3.284 Å, while the 3-dimensional trigonal pyramidal tetramer has bond lengths of 2.782 Å. This result compares well with ground state computations of previous studies.15 The difference in bond lengths suggests a change from van der Waals-type metallophilic interactions to covalent-type metallic bonds. While the bond lengths in cadmium and mercury tetramers also contract, the magnitude of the contraction is not as great as in the case of zinc. As was the case in the linear clusters, cooperativity effects are also noted in the 3-dimensional states. In these three cluster types, average bonds become shorter and stronger. Bond lengths of the zinc pentamer are more than an angstrom shorter versus the zinc dimer’s bond length. The cadmium clusters also exhibit significant changes in bond length as the cluster size increases from the dimer to the pentamer model. While the change in bond length is not as drastic in mercury clusters, the bonds still contract by 0.267 Å from the dimer to the pentamer clusters. Excited-State Distortions in 3-Dimensional Clusters. Upon photoexcitation of the cluster from the ground state (S0) to the lowest-lying phosphorescent excited state (T1), the bonding strength increases from a formally non-bonded closed-shell cluster to a partially covalent (integer or subinteger) bonded system. Several structural consequences result from this change in electronic bonding scheme. As is the case with the linear arrangement, the bonds of the excited state species contract as the bonding becomes stronger and more covalent in nature versus the ground


22

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state cluster. A second consequence is that the excited state bonding will exhibit increased porbital characteristics. In the 3-dimensional ground state, atoms primarily interact through s orbital overlap and thus the stabilization of these orbitals was primarily from an increased number of interactions, causing the structures to shift to 3-dimensional structures. In the case of the excited state, the bonding interaction contains more p orbital character and thus bonding is not only stabilized by the number of bonds but also by structural arrangements that favor porbital overlap. This change in bonding interactions can be noted in the tetramer cluster of all three cluster types. In the ground state of all of the clusters, the 3-dimensional tetramer was the most stable structure. In the excited state however, the tetramer structures become planar as to increase the amount of p-orbital overlap, allowing for delocalization through the p as well as s orbitals. Clusters of pentamer or larger in the excited state also show a preference for point groups that favor p-orbital overlap over number of bonds per atom.

This preference may be best noted in

the excited state (T1) cadmium hexamer distortion to a D4h symmetry. The D4h distortion is favored by both the excitation of cadmium hexamer clusters with C2v and Oh ground states. Emission Energies of 3-Dimensional Clusters. Emission energies of the 3-dimensional clusters exhibit a similar trend to that for the linear clusters. As the electron density is delocalized over the cluster, the emission energies decrease in magnitude, as shown in Figure 11 and Table 5. As the 3-dimensional clusters in the excited state have an increased amount of electron delocalization within the cluster when compared with the ground state, the emission energy also decreases at a substantially faster rate than is the case for the linear clusters. The structural changes in the group 12 metal clusters have a huge impact on emission energies. Zinc clusters, which have the greatest change in bonding strengths upon photoexcitation, also have the greatest


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Page 24 of 56

change in emission energies. For example, for the pentamer cluster, the linear structure has a phosphorescence energy of 8.7 x 103 cm-1 (Table 1b), which is nearly halved to reach 5.4 x 103 cm-1 in the 3-dimensional structure (Table 5). This effect is not as dramatic in cadmium clusters, which exhibit a difference of only 2.2 x 103 cm-1 between the linear and 3-dimensional structures for the pentamer models (Table 2c versus Table 5). The difference in the magnitude of these changes stems from the difference in the electron density of the clusters (Figure 11 vs Figures 13).

CONCLUSIONS The effect of size and structure of group 12 clusters has been demonstrated to have important impacts on bond strengths and spectral data in the ground state (1Σ) and the low-lying triplet excited states (3Σ and 3Π). The weakly-bound ground state clusters have been shown to have metallophilic interactions that are enhanced by electron delocalization. Excited-state linear structures have electron delocalization over the inner most atoms, leading to bond strengths on the order of typical covalent bonding interactions. Exterior bonds in the triplet excited states of the large clusters are weaker, manifesting metallophilic interactions, with strengths and lengths similar to ground-state complexes. Electron density is fully delocalized over all atoms in highspin excited clusters, suggesting ferromagnetic coupling that could be significant for NLO properties such as multi-photon excitation as well as magnetic switching applications in such systems. Addition of atoms to the high-spin excited clusters does not increase the strength of the bonds, thus the bonds lengths remain constant and covalent in strength. Cohesive energies and excitation and emission energies are directly related to electron delocalization. The 3-


24

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dimensional structures lead to greater delocalization of electron density and thus the cohesive energy and excitation and emission energies converge to a constant value much more rapid than with the linear structures. In all structures, cooperativity increases bonding strengths and directly impacts excitation and phosphorescence energies.


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FIGURES

Figure 1. Zinc cluster 3Σ, 3Π and high spin SOMO diagrams.


26

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Figure 2. Cadmium cluster 3Σ, 3Π and high spin SOMO diagrams.


27


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Page 28 of 56

Figure 3. Mercury cluster 3Σ, 3Π and high spin SOMO diagrams.


28

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Figure 4. De/bond in 1Σ ground states vs cluster size.


29


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Page 30 of 56

Figure 5. Energy per bond in 3Σ excited states vs cluster size.


30

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Figure 6. Energy per bond in 3Π excited states vs cluster size.


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Page 32 of 56

Figure 7. 1Σ-3Σ excitation energy vs cluster size.


32

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Figure 8. 3Σ-1Σ phosphorescence energy vs cluster size.


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Page 34 of 56

Figure 9. 3Π-1Σ phosphorescence energy vs cluster size.


34

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Figure 10. 3-dimensional structures of (a) zinc (b) cadmium and (c) mercury ground state.


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Page 36 of 56

Figure 11. 3-dimensional structures of (a) zinc (b) cadmium and (c) mercury triplet (T1) excited state.


36

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Table 1. Bonding and spectroscopic constants of zinc clusters in multiple electronic states: (a)) 1Σ ground state, (b)) lowest 3Σ excited state, (c) ( ) lowest 3Π excited state, and (d) high-spin paramagnetic excited state. (a) # Atoms

re (Å)

De

De/Bond

Excitation

(cm-1)*

(cm-1)

(103 cm-1)

2 Expt.58

4.19

279

279

32.5

2 CCSD(T)/CBS Limit/(PP)2-3

3.840

221

221

31.9

2 CCSD(T)/CBS Limit (DK)2

3.827

224

224

32.0

2

3.891

135

135

31.5

3

3.826, 3.826

294

147

30.0

4

3.811, 3.752, 3.811

457

152

29.1

5

3.811, 3.752, 3.752, 3.811

621

155

28.8

6

3.811, 3.752, 3.700, 3.752, 3.811

785

157

28.2

7

3.812, 3.739, 3.725, 3.725, 3.739, 3.812

949

158

28.4

8

3.812, 3.739, 3.725, 3.700, 3.725, 3.739, 3.812

1113

159

28.0

De

E/Bond

Emission

(cm-1)

(cm-1)

(103 cm-1)

(b) # Atoms

re (Å)

2 CCSD(T)/CBS Limit/(PP)2

2.504

9593

9593

20.6


2.472

9820

9820

20.5

2

2.531

9964

-21.65

21.2

3

2.561, 2.561

15067

-27.24

14.8

*

1 cm-1 = 1.239 81 × 10-4 eV = 2.85911 × 10-3 kcal/mol


37


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Page 38 of 56

4

2.613, 2.527, 2.613

18046

-29.51

11.2

5

2.670, 2.536, 2.536, 2.670

20038

-30.67

8.7

6

2.726, 2.560, 2.524, 2.560, 2.726

21463

-31.35

6.9

7

2.783, 2.588, 2.531, 2.531, 2.588, 2.783

22532

-31.79

5.6

8

2.844, 2.619, 2.544, 2.525, 2.544, 2.544, 2.619, 2.844

23367

-32.09

4.6

(c) # Atoms

re

De

E/Bond

Emission

(Å)

(cm-1)

(cm-1)

(103 cm-1)

2 CCSD(T)/CBS Limit/(PP)2

2.339

11619

-

-


2.341

11912

-

-

2

2.354

11479

-22.41

17.7

3

2.424,2.424

16439

-27.40

11.1

4

2.567, 2.383, 2.567

19070

-29.77

7.9

5

2.655, 2.420, 2.420, 2.655

20673

-30.80

6,1

6

2.783, 2.488, 2.393, 2.488, 2.783

21776

-31.41

5.0

7

2.907, 2.576, 2.418, 2,418, 2.576, 2.907

22497

-31.79

4.4

8

3.030, 2.677, 2.472, 2.401, 2.472, 2.677, 3.030

23042

-32.05

4.0

(d) # Atoms

re

De

E/Bond

Emission

(2S+1)

(Å)

(cm-1)

(103 cm-1)

(103 cm-1)

4 (5)

2.357, 2.418, 2.357

60651

-23.50

29.8

6 (7)

2.467, 2.491, 2.332, 2.491, 2.467

111879

-24.20

44.6

8 (9)

2.387, 2.420, 2.324, 2.492, 2.324, 2.420, 2.387

157534

-23.86

60.3


38

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Table 2. Bonding and spectroscopic constants of cadmium clusters in multiple electronic states: (a)) 1Σ ground state, (b)) lowest 3Σ excited state, (c) ( ) lowest 3Π excited state, and (d) high-spin paramagnetic excited state. (a) # Atoms

re

De

De/Bond

Excitation

(Å)

(cm-1)

(cm-1)

(103 cm-1)

2 Expt.58

4.07

330.5

330.5

30.7

2 CCSD(T)/CBS Limit (PP)2-3

3.889

327

327

29.0

2

3.922

217

217

28.6

3

3.853, 3.853

473

236

26.6

4

3.838, 3.764, 3.838

737

246

25.2

5

3.838, 3.764, 3.764, 3.838

1005

251

24.6

6

3.836, 3.748, 3.730, 3.748, 3.836

1273

255

23.9

7

3.863, 3.748, 3.730, 3.730, 3.748, 3.836

1542

257

23.7

8

3.836, 3.748, 3.730, 3.730, 3.730, 3.748, 3.836

1810

259

23.5


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Page 40 of 56

(b) # Atoms

re (Å)

2 Expt.58

De

E/Bond

Emission

(cm-1)

(cm-1)

(103 cm-1)

-

-

21.1

8727

8727

20.8

-

2 CCSD(T)/CBS Limit (PP)2

2.810

2

2.841

8945

-20.35

21.3

3

2.869, 2.869

13392

-25.63

16.0

4

2.928, 2.830, 2.928

16130

-27.85

12.3

5

2.996, 2.846, 2.846, 2.928

17824

-28.97

10.9

6

3.072, 2.878, 2.832, 2.878, 3.072

19076

-29.64

9.6

7

3.157, 2.920, 2.842, 2.842, 2.920, 3.157

20010

-30.08

8.69

8

3.260, 2.973, 2.864, 2.835, 2.864, 2.973, 3.260

20738

-30.38

8.0

De

E/Bond

Emission

(cm-1)

(cm-1)

(103 cm-1)

-

-

(c) # Atoms

re (Å)

2 CCSD(T)/CBS Limit (PP)2

2.650

9957

2

2.663

9986

-20.87

18.6

3

2.732, 2.732

14289

-25.93

13.1

4

2.847, 2.690, 2.847

16679

-27.99

10.3

5

2.972, 2.727, 2.727, 2.972

18137

-29.03

8.8

6

3.123, 2.803, 2.698, 2.803, 3.123

19055

-29.64

8.0

7

3.262, 2.907, 2.725, 2.725, 2.907, 3.262

19745

-30.04

7.5

8

3.396, 3.029, 2.789, 2.705, 2.789, 3.029, 3.396

20293

-30.32

7.2

(d)


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# Atoms

De

E/Bond

Emission

(Å)

(cm-1)

(cm-1)

(103 cm-1)

4 (5)

2.667, 2.737, 2.667

55122

-21.72

32.7

6 (7)

2.685, 2.776, 2.662, 2.776, 2.685

99011

-21.79

49.9

8 (9)

2.756, 2.818, 2.661, 2.767, 2.661, 2.818, 2.756

147680

-22.43

63.8

(2S+1)

re


41


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Page 42 of 56

Table 3. Bonding and spectroscopic constants of mercury clusters in multiple electronic states: (a)) 1Σ ground state, (b)) lowest 3Σ excited state, (c) ( ) lowest 3Π excited state, and (d) high-spin paramagnetic excited state. (a) # Atoms

re

De

De/Bond

Excitation

(Å)

(cm-1)

(cm-1)

(103 cm-1)

2 Expt.59

3.63

350

350

37.6

CCSD(T)/ccpVTZ-PP1

3.976

270

270

39.3

2

3.703

337

337

40.7

3

3.674, 3.674

711

356

38.1

4

3.670, 3.630, 3.670

1095

365

35.3

5

3.667, 3.362, 3.632, 3.667

1482

371

34.8

6

3.665, 3.635, 3.625, 3.635, 3.665

1872

374

34.4

7

3.665, 3.630, 3.625, 3.625, 3.630 ,3.665

2262

377

34.2

8

3.665, 3.630, 3.625, 3.620, 3.625, 3.630, 3.665

2652

379

31.7


42

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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


(b) # Atoms

re

De

E/Bond

Emission

(cm-1)

(cm-1)

(103 cm-1)

-

8260

-

29.9

2.754

8032

-

31.4

(Å)

2 Expt.59 2 CCSD(T)/ccpVTZ-PP1

2

2.771

9680

-26.01

31.4

3

2.807, 2.807

14377

-33.02

25.0

4

2.878, 2.776, 2.878

17053

-36.02

21.8

5

2.967, 2.800, 2.800, 2.967

18744

.37.62

20.0

6

3.079, 2.848, 2.789, 2.848, 3.079

19906

-38.60

18.9

7

3.212, 2.915, 2.806, 2.806, 2.915, 3.212

20775

-39.26

18.6

8

3.349, 3.006, 2.844, 2.797, 2.844, 3.006, 3.349

21465

-39.73

19.0

De

E/Bond

Emission

(cm-1)

(cm-1)

(103 cm-1)

9513

-

-

(c) # Atoms

re (Å)

2 CCSD(T)/ccpVTZ-PP1

2.643

2

2.639

10858

-26.60

29.1

3

2.696, 2.696

15936

-33.54

21.2

4

2.803, 2.658, 2.803

18547

-36.39

18.0

5

2.932, 2.694, 2.694, 2.932

20036

-37.99

16.3

6

3.088, 2.771, 2.673, 2.771, 3.088

21000

-38.78

15.5

7

3.252, 2.881, 2.699, 2.699, 2.881, 3.252

21697

-39.39

15.0

8

3.399, 3.024, 2.765, 2.679, 2.765, 3.024, 3.399

22258

-39.83

14.8

(d)


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# Atoms

De

E/Bond

Emission

(Å)

(cm-1)

(cm-1)

(103 cm-1)

4 (5)

2.646, 2.730, 2.646

68067

-27.60

50.5

6 (7)

2.660, 2.768, 2.658, 2.768, 2.660

123489

-27.64

76.3

8 (9)

2.708, 2.806, 2.659, 2.766, 2.659, 2.806, 2.708

183246

-28.20

99.4

(2S+1)

re

Page 44 of 56


44

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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


Table 4. Total and excitation energies in 3-dimensional structures of: (a) zinc, (b) cadmium, and (c) mercury ground (S0) state clusters. Geometry

mPW2PLYP Energy

Excitation Energy

(Hartree)

(103 cm-1)

Ia Linear Zn2

-453.7544259

31.5

IIa Linear Zn3

-680.6320566

30.0

IIIa Trigonal Planar Zn3

-680.6335344

27.1

Iva Planar Zn4

-907.5122841

27.3

Va Tetrahedral Zn4

-907.5248135

23.9

Via Trigonal Bipyramidal Zn5

-1134.4049771

24.0

Ib Linear Cd2

-335.0768476

28.6

IIb Linear Cd3

-502.687501

26.6

IIIb Trigonal Planar Cd3

-502.7753169

26.1

IVb Tetrahedral Cd4

-670.3759998

23.6

Vb Trigonal Bipyramidal Cd5

-837.971121

24.2

Ic Linear Hg2

-306.7781423

40.7

IIc Linear Hg3

-460.1681543

38.1

IIIc Trigonal Planar Hg3

-460.1699157

38.1

IVc Tetrahedral Hg4

-613.5646726

35.9

Vc Trigonal Bipyramidal Hg5

-766.9581853

36.3


45


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Page 46 of 56

Table 5. Total and emission energies in 3-dimensional structures of: (a) zinc, (b) cadmium, and (c) mercury excited (T1) state clusters. Geometry

MP2 Energy

Emission Energy

(Hartree)

(103 cm-1)

Ia Linear Zn2

-453.6542374

17.7

IIa Linear Zn3

-680.5537406

11.1

IIIa Bent Zn3

-680.5547133

10.9

Iva Planar Zn4

-907.4490501

8.2

Va Distorted Trigonal Bipyramidal Zn5

-1134.3470082

5.4

Ib Linear Cd2

-335.0815941

18.6

IIb Linear Cd3

-502.6915859

13.1

IIIb Planar Cd4

-670.3025449

8.4

IVb Distorted Trigonal Bipyramidal Cd5

-837.9070317

8.7

Ic Linear Hg2

-306.6331818

29.1

IIc Linear Hg3

-460.0446259

21.2

IIIc Planar Hg4

-613.4482713

18.6

IVc Distorted Trigonal Bipyramidal Hg5

-766.8464904

19.7


46

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ASSOCIATED CONTENT Supporting Information. Supporting information contains Cartesian coordinates of all computed structures and the associated energies from the output of MP2/LANL2DZ computations. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author * Omary: Fax: 9405654318; Tel: 9405652443 E-mail: [email protected]; Wilson: Fax: 9405654318; Tel: 9405654296 E-mail: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT We acknowledge support for aspects of this work by the Robert A. Welch Foundation (Grant B1542 to M.A.O.) and National Science Foundation (Grants CHE-0911690 to M.A.O. and CHE0809762 and CHE-1213874 to A.K.W.). A.K.W. acknowledges support of computational resources by the National Science Foundation (CHE-0741936), the United States Department of Education, and the Academic Computing Services at the University of North Texas.


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Page 48 of 56

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Table of Content Graphic


56

Bonding and Phosphorescence Trends in 1-D, 2-D, and 3-D

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