Article pubs.acs.org/Organometallics
Bonding Analysis of TM(cAAC)2 (TM = Cu, Ag, and Au) and the Importance of Reference State Clark R. Landis,*,† Russell P. Hughes,‡ and Frank Weinhold† †
Department of Chemistry, University of WisconsinMadison, 1101 University Avenue, Madison, Wisconsin 53706, United States Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
‡
S Supporting Information *
ABSTRACT: A recent analysis of the bonding in transition metal (TM) complexes with cyclic aminoalkyl carbene (cAAC) ligands, TM(cAAC)2 (TM = Cu, Ag, and Au), purports to show that metal−ligand bonding involves the TM in the excited 2P state and that TM(pπ) → (cAAC)2 backdonation is not properly recognized in NBO analysis because of biases against participation of np functions in transition metal bonding. The questions of TM np orbital involvement in bonding and the possible biases in the NBO occupancy-weighted symmetric orthogonalization procedure have been examined by performing NBO analyses in two ways: (1) single Lewis structure (loc) analysis with TM np orbitals treated as valence (NBOs) or nonvalence (NBOx) and (2) direct comparison of a two-configuration resonance model (res/NBOs) treatment with a single configuration model using the expanded valency (loc/NBOx) treatment. The principal bonding picture that emerges from NBO analysis features a TM cation with two “non-innocent” cAAC ligands that are each reduced by 0.5 electrons. The unpaired spin delocalizes over a π network spanning the two ligands, whether or not a TM cation is present. In the localized NBO framework, the unpaired spin primarily occupies a 1e π-type “long-bond” between the carbonic carbon centers, with secondary resonance delocalization over the TM npπ and the two Npπ orbitals. This description is consistent with all experimental data. Energy decomposition analysis−natural orbitals for chemical valence (EDA-NOCV) analysis of the Cu complex with different reference states reveals that the inferred nature of the bonding depends wholly on the choice of reference state. We show that the earlier selection of a neutral, excited 2P Cu reference state virtually dictates the bonding description to feature an unphysical degree of TM(pπ) → (cAAC)2 backdonation.
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involve the TM in the excited 2P state,” “cAAC ligands in TM(cAAC)2 are stronger π-acceptors than σ donors!,” “The TM(pπ) → (cAAC)2 backdonation··· is not recognized by the calculation of the bonding orbitals by the NBO method because it is biased against mixing of n(p) functions for the TMs,” and “The NBO picture of the C-TM-C bonding situation does not correctly represent the nature of the metal-ligand interaction in [TM(cAAC)2].”1 Because isolable, formally zerovalent molecular complexes of Cu, Ag, and Au are rare new additions to the literature, they arouse interest regarding the nature of their electronic structures. Are the metal centers best viewed as zerovalent in the ground 4s13d104p0 or excited 4s03d104p1 configurations or as cationic 4s03d104p0 metal centers? Such distinctions are not physical observables and, hence, are not provable. Nevertheless, these distinctions ultimately form the basis of conceptual models that can be used to understand and integrate empirical and computational data. Herein, we briefly appraise the role of
INTRODUCTION In recent publications, Jerabek, Roesky, Bertrand, Frenking (JRBF) and coauthors1−3 demonstrate that cyclic aminoalkylcarbenes (cAACs) are capable of stabilizing coinage metals in the formal oxidation state zero, leading to crystallographically characterized structures for Cu and Au. The neutral coinage transition metals complexes [TM(cAAC)2] (TM = Cu, Ag, and Au), which are generated by reduction of the [TM(cAAC)2]+ cations for TM = Cu,Au, exhibit interesting experimental and computational metrics, linear coordination geometries, EPR gvalues, and hyperfine couplings, indicating that the unpaired spin density is largely located on the carbene carbon atoms and that C-TM bond lengths that are slightly longer for the [TM(cAAC)2]+ cations than for the neutral complexes. A recent analysis of the bonding in these complexes using energy decomposition analysis−natural orbitals for chemical valence (EDA-NOCV)4−8 and natural bond orbital (NBO) methods9−15 prompted several claims from the authors that appear contrary to the empirical data and to previously published examinations of bonding at transition metals. Representative statements include “Metal-ligand interactions in [TM(cAAC)2] © XXXX American Chemical Society
Received: May 20, 2015
A
DOI: 10.1021/acs.organomet.5b00429 Organometallics XXXX, XXX, XXX−XXX
Article
Organometallics the TM p-orbitals in bonding, the NBO perspective on bonding in these transition metal complexes, and the consequences of the reference state used for bonding analysis. We begin with a short analysis of the bonding in cationic complexes [TM(cAAC)2]+ using a simplified cAAC ligand (Figure 1). The
TM ns orbital to give a 14e TM count. How should this bonding be described: two weak donor−acceptor interactions (model A), a single 2c/2e bond TM-C bond (either one of the two equivalent structures in model B), 3c/4e “hyperbonding” (model C, resonance among two structures), or as two sphybridized 2c/2e bonds (model D)? At the heart of JRBF’s claim that the NBO method is “biased against mixing of n(p) functions for the TMs”1 (a possibility first raised by Morokuma and Maseras19) lies distinction between the competing models A−D shown below.20 Model A describes a coordinate Cu/ cAAC bonding interaction at the polar limit (less than 10% covalency) that comprises a Cu+ ion with five lone pairs shown as a stack of dots and two neutral carbenes, model B features two resonance configurations (I and II) each having one polar covalent Cu−C bond, model C admits resonance between the two localized configurations of model B, and model D has two polar covalent Cu−C bonds.
Previously, we approached the issue of p orbitals in bonding at transition metals by examining more than 40 transition metal hydrides using two NBO methods, the standard method (hereafter designated NBOs) in which np orbitals are not considered as valence and the expanded valence method (NBOx) for which the np orbitals belong to the valence class of basis functions.21 The NBOs model emphasizes localized bonds formed by sdn hybridization at the metal, while the NBOx method more readily admits spdn hybridization. In addition, we compared a single Lewis structure model (loc) with a multiple resonance structure (res) model. The figure of merit for distinguishing among competing methods is the RMSD between the model density matrix and that computed by the electronic structure package.22 These studies showed convincingly that (a) for transition metals with electron counts ≤12, the single resonance, sd-hybridized model (loc/NBOs ) described the density as well as do methods with higher degrees of freedom (loc/NBOx or res/NBOs), but (b) for transition metals with electron counts ≥12e, the sd-hybridized plus resonance (res/NBOs) model is superior to a singleresonance, spd-hybridized (loc/NBOx) with greater-than-orequal degrees of freedom. Commonly, some (ca. ≤ 0.1e) population of the TM np orbitals is seen, especially for the third row metals. Thus, the NBO-based emphasis on sdn hybridization and 3c/4e bonding motifs prioritizes the elements needed to provide the best fit to the overall density but does not exclude some np occupation. Overall, this mode of building up a localized bond description illuminates a deep connection between the electronic structures of transition metals with ≥12e counts with the hypervalent molecules of P-block through 3c/4e bonding resonance. Thus, the 12e count for transition metals serves as the threshold separating normal valent (all 2c/2e bonds and lone pairs) from hypervalent molecules, similar to the role of the 8e count in the P-block. We now apply these approaches to the analysis of [TM(cAAC)2]+. Application of the NBOs/loc and NBOx/loc treatments and the NBO search algorithms to [Cu(cAAC)2]+ yields the bonding models B and D, respectively. The topology represented by model A was analyzed by making use of the NBO CHOOSE facility to specify a reference Lewis-like
Figure 1. Line drawings of full and model cAAC ligands and molecular structures of TM(cAAC)2 and [TM(cAAC)2]+ (shown for TM = Cu) used in this study (formal charges are not shown for the Lewis structures).
simplified cAAC differs from the experimental ligand in two ways: the carbon atoms adjacent to the carbene carbon center are not alkylated, and the nitrogen substituent is H rather than the diisopropylphenyl group. However, the computed metrics for the two types of ligand are nearly identical.
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NBO CONCEPTS, THE FREE CAAC LIGAND, AND THE [TM(CAAC)2]+ CATION The free cAAC model ligand illustrates key metrics resulting from NBO analysis (Supporting Information). NBO analysis reveals a single Lewis structure that features a localized sp1.1 lone pair on the “carbene” C and a CN double bond. The analysis provides quantitative metrics, the non-Lewis (NL) density, and the RMSD deviation in density matrices for gauging conformity of the computed (DFT) density with a single Lewis structure. In this case, the NL value indicates that all but 0.4e of the total density is accounted for by a single Lewis structure; deviation from the ideal Lewis limit arises from numerous, small hyperconjugative interactions involving the carbene lone pair and the C−N σ and π antibonds. These delocalizations map directly onto other resonance structures; natural resonance theory (NRT)16−18 analysis weights these structures so as to minimize the RMSD between the DFT density and the model density. For the free cAAC model ligand, the primary resonance structure weighting is greater than 80%. Thus, the cAAC ligand is reasonably well described as a single resonance structure. Addition of two cAAC ligands to a TM+ cation makes bonds primarily by the donation of carbene lone pairs into the vacant B
DOI: 10.1021/acs.organomet.5b00429 Organometallics XXXX, XXX, XXX−XXX
Article
Organometallics Table 1. Standard and Expanded Valency NBO Results for [TM(cAAC)2]+a TM-C bond(s) TM
QTM
Cu NBOs Cu NBOx Ag NBOs Ag NBOx Au NBOs Au NBOx
NEC (TM) 0.71 9.73
+0.551 +0.451 +0.46 +0.39 +0.36 +0.32
s d s0.71p0.11d9.73 s0.79d9.75 s0.79p0.07d9.75 s1.07d9.57 s1.07p0.05d9.57
Hyb(TM)
Pol (%TM)
0.09
sd sp1.09d0.10 (x2) sd0.12 sp1.12d0.10 (x2) sd0.27 sp0.03d0.27
18 15 20 15 27 27
cAAC LP Occ 1.95e 1.88e 1.94e 1.85e 1.95e 1.96e
hyb
occ
NL
sp
1.64e
sp2.88
1.60e
sp2.5 sp2.4
1.53 1.52e
1.14e 0.97e 1.14e 1.00e 1.29e 1.32e
2.5
a
TM natural charge (QM), natural electron configuration (NEC), TM-C bond metrics (TM hybridization, TM polarization, and occupancy), cAAC LP hybridization and occupancy, and non-Lewis density (NL).
structure with no TM-C bonds and five lone pairs at the metal cation. The two-structure resonating model C, which represents a 3c/4e hyperbond, was explored by NRT analysis with high thresholds to limit consideration of any resonance structures other than I and II. Thus, the standard NBOs valence definition was used for models A−C, whereas the higher number of TMC bonds of model D required the expanded valence (NBOx) definition. Some of the metrics resulting from default NBO searches according to model B (loc/NBOs) and model D (loc/ NBOx) treatments are shown in Table 1. Table 2 gives the overall RMSD figure of merit for all four models. Note that model A always has the highest RMSD and will not be discussed further.
or 3c/4e hyperbond, description over an spd-hybridized expanded valency description.
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DESCRIPTION OF NEUTRAL [TM(CAAC)2] If an electron is added to [TM(cAAC)2]+, where does it go? The low-lying, potential acceptor orbitals are the TM np orbitals and the CN π* orbitals; addition of an electron to the former corresponds to reduction of the TM, whereas addition to the latter is a ligand-based reduction. Empirical and computational data clearly indicate that the electron primarily occupies the ligand π* orbitals.2,3 Perhaps most telling are the empirical EPR spectral data (g-values and hyperfine coupling constants) for the Cu and Au complexes. As stated by JRBF and other authors in the original publication of these data, “the isotropic g factors close to the free electron value of 2.0023 confirm marginal contributions from the transition element to the SOMO, suggesting a three-center carbene/copper/carbene description with predominately carbene radical character.”2 Analysis of the computed electronic structure demonstrates little spin density at the Cu (2% by Mulliken analysis and 7% by natural population analysis) in complete accord with the experimental data. Because the π* orbitals are polarized to the carbene carbon atoms, placing an electron in these orbitals will yield high spin density at the C. To create a Lewis-like description of the TM(cAAC)2 radical, we begin by adding one α-spin electron to the CN π*orbitals of the [TM(cAAC)2]+ complex and applying the “different Lewis structures for different spins” (DLDS) paradigm15 that naturally accompanies unrestricted wave functions (Figure 2). The β-spin electronic structure is unaffected by addition of an additional α-spin; the Lewis structure for the β-spins retains the hypervalent bonding pattern of the 14e cationic complexes. Addition of approximately 1/2 e to each of the CN π* orbitals in the α-spin set yields three electrons spread over the two C and two N p-π orbitals (recall that a bond spin−orbital accommodates a maximum of one electron). Because N has higher electronegativity than C, the π* orbital has a larger coefficient at the C than N. The best single resonance structure (loc) description of this 3e/4 orbital interaction features one electron shared between the two C atoms and the remaining two localized on each of the N atoms. This creates the equivalent of a one electron C−C π long-bond, although it is clear that this bond is not driven by a large overlap between the distant C orbitals. For the moment, we neglect the role of Cu, but note that the C−C pπ long-bond is retained in NBO analysis of the electronic structure of the anion resulting from deletion of the Cu+ cation, without structural relaxation, from the neutral complex. Indeed, as shown in the left panel of Figure 3, the delocalized Kohn−Sham HOMO (α-spin) of the (cAAC)2− radical anion obtained by deletion of Cu+ from the optimized
Table 2. Density Matrix RMSD Values for Different Treatments of [TM(cAAC)2]+ TM
model A
model B
model C
model D
Cu Ag Au
0.039 0.042 0.055
0.025 0.027 0.033
0.0045 0.0045 0.0047
0.016 0.027 0.033
Let us compare the standard (loc/NBOs, model B) and expanded valence analyses (loc/NBO x , model D) as summarized in Table 1. What happens when the valence space is expanded to include the np orbitals? Not much, as indicated by the small increase of p-character in the TM natural electron configuration (NEC) by ca. 0.08e and a small drop in the non-Lewis density (
