Electronic Structure of the Acetonitrile and Acetonitrile Dimer Anions: A

Dec 22, 2007 - Acetonitrile molecules are known for their intriguing ability to accommodate an excess electron in either a diffuse dipole-bound orbita...
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J. Phys. Chem. B 2008, 112, 520-528

Electronic Structure of the Acetonitrile and Acetonitrile Dimer Anions: A Topological Investigation† Qadir K. Timerghazin‡ and Gilles H. Peslherbe* Centre for Research in Molecular Modeling and Department of Chemistry & Biochemistry, Concordia UniVersity, Montre´ al, Que´ bec H4B 1R6, Canada ReceiVed: September 17, 2007; In Final Form: October 24, 2007

Acetonitrile molecules are known for their intriguing ability to accommodate an excess electron in either a diffuse dipole-bound orbital, away from the valence electrons, or in its valence orbitals, depending on the environment. In this work, we report a computational investigation of the monomer and dimer acetonitrile anions, with the main goal of gaining further insight into the unusual electronic structure of these species. To this end, the topology of the electron density distribution has been examined in detail with the quantum theory of atoms in molecules (AIM). The excess electron is found to affect the topology of the electron density very differently for two dipole-bound-electron isomers of the acetonitrile dimer anion: for the headto-tail isomer, the electron density simply decays away from the atomic nuclei, and the presence of the excess electron only manifests itself in the Laplacian of the electron density as a very diffuse region of “dipolebound” charge concentration; in contrast, for the “solvated-electron” head-to-head isomer, a maximum of electron density without a corresponding atomic nucleus is observed, which topologically corresponds to a pseudo-atom of electron density. The acetonitrile dimer appears to be the smallest solvent cluster anion to exhibit such a non-nuclear attractor due to the presence of a solvated electron. Although the “solvatedelectron” isomer is thermodynamically less stable than the head-to-tail isomer at 0 K, its floppy nature leads to a higher vibrational entropy that makes it the most stable acetonitrile dimer, anionic or neutral, above 150 K. As for the acetonitrile dimer anion with a valence-bound electron, its structure is characterized by acetonitrile molecules connected to each other at the cyanide carbon atoms; the AIM analysis reveals that, although this C-C bond is relatively weak, with an estimated bond order of 0.6, it possesses genuine covalent character and is not a “pseudo-bond” as previously speculated. We also report the first multireference electronic structure calculations of the valence-bound-electron acetonitrile monomer and dimer anions, the highest-level calculations of these species to date. The acetonitrile radical anion is unstable in the gas phase and is topologically characterized by a radical-like nonbonded charge concentration located at the cyanide carbon atom. Based on the results of the AIM analysis, the previously proposed resonance description of the valence-bound-electron acetonitrile anion is refined, and a new resonance description of the dimer anion is proposed. Overall, this work demonstrates the rich topological variety of the excess electron interacting with acetonitrile molecules, which manifests itself as charge concentrations, pseudo-atoms, and covalent bonds.

Introduction The interaction of a free electron with a neutral molecule is one of the most fundamental processes in chemistry. Most often, an additional (excess) electron can be accommodated in an empty or half-filled valence orbital of the accepting molecule. Alternatively, if the molecule possesses a sufficiently large multipole moment, the excess electron can be trapped in the electric field exerted by the molecule, producing a multipolebound anion.1-3 Dipole-bound anions appear to be the most abundant, although a number of quadrupole-bound anions have also been reported.2,4 An interesting situation arises when the electron-accepting molecule has a dipole moment large enough to trap an electron and, at the same time, a low-lying empty valence orbital which can accommodate the excess electron. Mutual interconversion between the anions with dipole-bound excess electrons (DBE) and valence-bound excess electrons †

Part of the “James T. (Casey) Hynes Festschrift”. * To whom correspondence should be addressed. ‡ Present address: Department of Chemistry, University of Alberta, 11227 Saskatchewan Drive, Edmonton, Alberta, Canada T6G 2G2.

(VBE) has attracted considerable attention.5,6 As a matter of fact, the trapping of low-energy electrons leading to DBE anions with subsequent interconversion to VBE anions may be an important step in the radiation damage of DNA and RNA molecules.6,7 The charge distribution of the DBE and VBE anions is significantly different, and the equilibrium between the two forms may thus be altered by the medium, as is observed in the case of acetonitrile anions. The DBE acetonitrile anion8-12 CH3CN- is produced by Rydberg electron transfer8,13 or by relaxation of charge-transferto-solvent (CTTS) excited states of the binary iodide-acetonitrile complex I-(CH3CN).10 The DBE acetonitrile dimer anion (CH3CN)2- was also synthesized by photoexcitation and CTTS relaxation of the ternary iodide-acetonitrile cluster I-(CH3CN)2, and the resulting dimer anion was postulated to have a linear head-to-tail structure NCCH3‚‚‚NCCH3-.10 The lowest unfilled valence π*(C-N) orbitals of acetonitrile are relatively high in energy (ca. 2.8 eV higher than the highest occupied molecular orbital),14 and the VBE acetonitrile radical-anion CH3CN•exists only as a metastable species in the gas phase.11,14 Note

10.1021/jp0774948 CCC: $40.75 © 2008 American Chemical Society Published on Web 12/22/2007

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Figure 1. Structures (with relevant geometrical parameters) of (CH3CN)2- and corresponding singly occupied molecular orbitals.

that, for the anions of a molecule X, we use X- and X•- for the DBE and VBE forms, respectively, as the dot symbol implies an unpaired valence electron in contrast to the diffuse dipolebound electron. Experimental studies of γ- or X-ray irradiated solid15,16 and liquid17,18 acetonitrile suggest that, in a polar medium, the CH3CN molecules bind an excess electron into valence orbitals. Two distinct species can be produced in solid acetonitrile, depending on the crystal structure: the (CH3CN)2•dimer is formed in R-acetonitrile, whereas the monomeric radical anion CH3CN•- is formed in β-acetonitrile.15,16,19 Since CH3CN•readily reacts with a neutral CH3CN molecule to form (CH3CN)2•-, it can only be observed in solid β-acetonitrile, whose crystal structure precludes dimerization.15,16 In liquid acetonitrile,17,18 an excess electron may exist as either a VBE in (CH3CN)2•- like in solid acetonitrile or a classical solvated electron in dynamic equilibrium. The latter is a separate entity in a solvent cavity, which is stabilized by the aggregate field of the solvent and can be considered as a condensed-phase analog of the DBE. Photoelectron spectroscopy studies20 of negatively charged acetonitrile clusters (CH3CN)n- have shown that the DBE and VBE forms coexist for clusters with n ) 11-100, but for clusters with n g 13, the VBE form prevails.20 Densityfunctional theory (DFT) calculations suggest that, for n ) 4-6, the VBE form becomes thermodynamically stable,21 in semiquantitative agreement with the aforementioned experimental results.20 Interestingly, the experimentally observed addition of a hydrogen atom to an acetonitrile molecule inside water cluster anions has been proposed to involve transfer of the excess electron to the acetonitrile molecule and subsequent reaction of CH3CN•- with a water molecule.22 The available data on the peculiar electronic structure of the VBE acetonitrile anions is relatively scarce. According to electron paramagnetic resonance (EPR) studies,15 (CH3CN)2•has a symmetric structure with the spin density mostly localized on the nitrogen atoms (ca. 75%) and the cyanide carbon atoms (ca. 25%). The spin density in CH3CN•- is also concentrated mainly on the nitrogen atom (ca. 55%). It was proposed that the two acetonitrile moieties in (CH3CN)2•- are oriented in an antiparallel fashion with the excess electron residing in a delocalized molecular orbital formed by the combination of two π*(C-N) orbitals.15 Whereas the acetonitrile moieties in (CH3CN)2•- were considered to remain linear, the C-C-N angle was estimated to be 130° for CH3CN•-. However, DFT calculations17,18 suggest a bent geometry for the CH3CN moieties in both (CH3CN)2•- and CH3CN•-, with a C-C-N angle of ca. 130°. The distance between the two cyanide carbon atoms in (CH3CN)2•- is fairly short (1.6-1.8 Å), suggesting a “pseudobond”17 between the carbon atoms. In this article, we report a quantum-chemical investigation and a topological analysis of the electron density distribution with the quantum theory of atoms in molecules (AIM)23,24 of

the DBE and VBE acetonitrile anions (CH3CN)n- (n ) 1, 2) to gain further insight into their electronic structure. The outline of this article is as follows. The computational methodology is first described in section 2. The structure, stability, and topology of the electron density distribution of the DBE acetonitrile dimer anions are presented in section 3, whereas section 4 is devoted to the molecular and electronic structure of the VBE acetonitrile monomer and dimer anions in the gas phase and in liquid acetonitrile. Concluding remarks follow in section 5. Computational Methods Unrestricted Hartree-Fock (UHF) calculations for the VBE acetonitrile dimer anion yield a highly spin-contaminated wavefunction with 〈S2〉 > 0.95, which makes the results obtained from post-Hartree-Fock correlation treatments (e.g., perturbation theory) unreliable. In fact, the complicated electronic structure of the VBE acetonitrile anions dictates the use of mutliconfigurational ab initio methods or unrestricted DFT methods, which tend to perform relatively well for open-shell molecules with nearly multiconfigurational character.25 If DBE anions can be reliably described by single-reference postHartree-Fock methods, calculations for these species require an extensive treatment of electron correlation, preferably with coupled-cluster methodologies, whereas DFT methods are generally not suitable for these species.3 Thus, the proper description of the DBE and VBE acetonitrile anions requires different computational methodologies, which is similar to the approach used for the nitromethane anions.26 The geometries of the acetonitrile DBE dimer anions and neutral dimers were optimized with unrestricted second-order Møller-Plesset (UMP2) theory,27 and energies were calculated with the unrestricted coupled cluster with single and double excitations (UCCSD) theory.28 The Dunning-Hay split-valence polarized (SVP) basis set augmented with diffuse functions (SVP+) was used for all atoms,29 except for the methyl group carbons, for which the SVP basis set was augmented with 2s and 2p Rydberg functions29 and additional 2s and 2p functions with exponents obtained in an even-tempered manner from those of the initial Rydberg functions (the smallest exponent is 2.6 × 10-4 au). For brevity, this basis set will be referred to as SVP+R. The augmented double-ζ correlation-consistent basis set of Dunning30 has been used, with additional 3s and 3p diffuse functions on the methyl group carbon atoms (with exponents 5.625 × 10-2, 1.125 × 10-2, and 0.225 × 10-2);31 this basis set will be referred to as aVDZ+R. Thermodynamic properties were calculated under the rigid-rotor/harmonic-oscillator approximation using UMP2/SVP harmonic frequencies. Calculations of the VBE acetonitrile anions have employed the complete active space self-consistent field32 (CASSCF) method. (9,8) and (7,7) active spaces were used for (CH3CN)•and (CH3CN)2•-, respectively; the shapes and occupancies of

522 J. Phys. Chem. B, Vol. 112, No. 2, 2008 the active space orbitals are provided as Supporting Information. Dynamic electron correlation was included with second-order multireference perturbation theory33 (CASPT2) using the CASSCF reference wavefunction just described. CASSCF and CASPT2 calculations employed the Dunning-Hay polarized split valence basis set augmented with diffuse functions (SVP+).29 DFT calculations were also performed with the hybrid Perdew-Burke-Ernzerhof functional (PBE0)34 and the augmented polarization-consistent basis set aug-pc-1.35 Geometries of the VBE acetonitrile anions were optimized with CASSCF, CASPT2, and PBE0. UMP2 and UCCSD calculations were performed with the Gaussian 03 program package,36 and the gas-phase CASSCF and CASPT2 calculations were performed with the MOLPRO suite of ab initio programs,37 whereas all PBE0 calculations were performed with the Gaussian 98 package.38 Solvent effects were included using the conductor-like polarizable continuum model (CPCM) of Barone and Cossi,39 as implemented in Gaussian 98 (for PBE0 calculations) and in Gaussian 0336 (for CASSCF calculations). The topology of the electron density distribution was analyzed with the AIMPAC program package,40 using electron densities obtained from CCSD, CASSCF, and PBE0 calculations. Dipole-Bound Electron Acetonitrile Dimer Anions Since the DBE acetonitrile monomer anion, CH3CN-, has been extensively studied,1,10,13,31,41 we focus on the structure and stability of the acetonitrile dimer anions. Two isomers are known for the neutral acetonitrile dimer (CH3CN)2, a cyclic structure with antiparallel orientation of the dipoles and a collinear, head-to-tail structure42,43

The cyclic dimer, the lowest-energy isomer with a binding energy 5-6 kcal/mol,43 has a zero net dipole moment and thus cannot bind an electron in a dipole-bound fashion. Indeed, Rydberg electron-transfer experiments failed to produce (CH3CN)2- by attaching an electron to a neutral dimer.44 The higher-energy collinear isomer, with a binding energy of ca. 3 kcal/mol,43 has a substantial dipole moment of ca. 8.5 D,43 and electron attachment to it may lead the head-to-tail isomer of (CH3CN)2- (Figure 1a). The excess electron distribution of this isomer is very similar to that of CH3CN-,12,31 but the excess electron vertical detachment energy is much larger (102 meV, as calculated with UCCSD/aVDZ+R//UMP2/SVP+R vs 1012 meV10,13,31) because of the much larger dipole that binds the excess electron. In the second (CH3CN)2- isomer (Figure 1b), the excess electron is “sandwiched” between two acetonitrile molecules facing each other. This head-to-head isomer can only exist due to the presence of the excess electron, which is screening the repulsive interaction between the acetonitrile dipoles. Removal of the excess electron leads to highly repulsive NCCH3‚‚‚H3CCN interactions resulting in prompt dissociation. The excess electron vertical detachment energy for this isomer (155 meV, as calculated with UCCSD/aVDZ+R//UMP2/SVP+R) is sig-

Timerghazin and Peslherbe

Figure 2. Temperature dependence of the dimer formation Gibbs free energies of the neutral acetonitrile dimers and DBE dimer anions. The reference free energy is that of the free acetonitrile molecules.

nificantly larger than for the collinear head-to-tail isomer, in agreement with recent computational results by Takayanagi.12 Similar cluster anions with the excess electron trapped between molecular dipoles have been predicted;45-48 these structures are referred to as having an “internally suspended electron”,45 a “solvated electron”,47 or an “e--bond”.48 For instance, Gutowski et al. have provided experimental and computational evidence that the hydrogen fluoride trimer anions (HF)3- may exist in two forms at finite temperature in the gas phase: a chain DBE isomer FH‚‚‚FH‚‚‚FH- and a “solvated electron” structure HF(e-)HF‚‚‚HF, where the excess electron is trapped between a hydrogen fluoride molecule and a hydrogen fluoride dimer.47 As for water cluster anions, the competition between the surface and internal solvation of the excess electron remains a matter of dispute.49 The relative stability of the neutral and anionic acetonitrile dimers was investigated in the gas phase by inspecting the temperature dependence of the dimer formation Gibbs free energy of the (CH3CN)2- and (CH3CN)2 isomers (Figure 2). At 0 K, all neutral and anion dimers are stable with respect to dissociation; the most stable form of the acetonitrile dimer is the collinear head-to-tail (CH3CN)2-, whereas the head-to-head (CH3CN)2- is the least stable of all neutral and anionic acetonitrile dimers. As temperature increases, the thermodynamic stability of both neutral dimers and of the collinear headto-tail anion rapidly decreases, whereas changes in the stability of the head-to-head (CH3CN)2- are negligible. This is mainly due to the vibrational contribution to the entropy, which is significantly larger for the dimers with relatively stiff, direct acetonitrile-acetonitrile intermolecular interactions, compared to that for the head-to-head (CH3CN)2-, where the CH3CN moieties are bound via the excess electron, resulting in a very floppy structure. In fact, the head-to-head (CH3CN)2- is the only acetonitrile dimer which is stable at temperatures above 250 K. A similar temperature dependence of the relative stability of the classical DBE and “solvated electron” isomers of (HF)3has been reported.47 Although the free energy profiles shown in Figure 2 are obtained under the rigid-rotor/harmonic oscillator approximation and do not account for anharmonisity of the potential energy surface, they still provide insight into the thermal stability of the acetonitrile dimer anions and suggest that, at finite temperatures, the “solvated-electron” (CH3CN)2isomer may coexist with the collinear head-to-tail isomer and even become predominant and that it could be experimentally observed.

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Figure 3. AIM plots for the collinear head-to-tail (a) and head-to-head (b) (CH3CN)2-. Bond paths (purple) and interatomic surfaces (green) are superimposed with the contour plots of the Laplacian of the electron density ∇2F(r) (solid lines for ∇2F(r) < 0, dashed lines for ∇2F(r) > 0). The minimum of ∇2F(r) corresponding to the dipole-bound charge concentration is shown as a purple star.

TABLE 1: AIM Properties of Relevant Critical Points for the DBE Acetonitrile Dimer Anionsa isomer collinear head-to-head

critical point

r

DBCC NNA BCP(C-NNA)

1.57 × 3.20 × 10-4 3.00 × 10-4 10-4

∇2F

G

G/F

H

-1.24 × 10-5 -4.06 × 10-5 5.40 × 10-5

7.05 × 10-7 8.60 × 10-7 1.72 × 10-5

4.50 × 10-3 2.70 × 10-3 5.70 × 10-2

-3.80 × 10-6 -1.10 × 10-5 -3.70 × 10-6

a Electron density (F), Laplacian of the electron density (∇2F), kinetic energy density (G), kinetic energy density per electron (G/F), and total energy density (H). All values (in atomic units) are calculated from CCSD/SVP+R//UMP2/SVP+R electron densities.

TABLE 2: Vertical Detachment Energies (VDEs) and Selected Geometrical Parameters for the VBE Acetonitrile Anionsa (CH3CN)2•solvatedb (CH3CN)2•solvatedb CH3CN•CH3CN

method

VDE

rb

rCN

rCC

R

β

γ

d(N-C-C-N)

d(C-C-C-C)

CASSCF CASPT2 PBE0 CASSCF PBE0 CASSCF PBE0 CASSCF CASPT2 PBE0

-1.24 1.03 1.88 1.17 3.97 0.77 2.19

2.054 1.668 1.668 2.010 1.662

1.215 1.256 1.230 1.217 1.231 1.238 1.213 1.176 1.180 1.156

1.507 1.522 1.511 1.507 1.506 1.529 1.507 1.476 1.472 1.451

134.4 127.8 128.4 134.0 128.5 132.1 133.1 180.0 180.0 180.0

121.5 122.2 121.5 120.3 120.9

104.2 110.0 110.1 105.7 110.7

177.0 171.2 180.0 179.6 167.7

176.5 170.5 180.0 179.1 168.2

a VDE in eV, bond lengths in Å, and angles in degrees. The geometrical parameters are defined in Figure 4. b Solvation effects included using the CPCM continuum solvation model of ref 39.

The quantum theory of AIM was applied to gain a better understanding of the electronic structure and bonding in (CH3CN)2-. The AIM theory is based on the topological analysis of the total electron density F(r) of a molecule, its gradient ∇F(r) and Laplacian ∇2F(r), and related functions such as the energy density H(r) and its components. The theoretical basis and the key applications of AIM theory have been discussed in detail in monographs by Bader23 and Popelier.24 Briefly, the analysis of ∇F(r) and ∇2F(r) allows to find critical points which correspond to maxima, minima, and saddle points of F(r). Local maxima, or attractors, of F(r) usually correspond to atomic nuclei (nuclear critical points). Two nuclear critical points can be connected by a gradient path (bond path) indicative of chemical bonding between the two atoms, which corresponds to the line of maximum F(r) between two nuclei. The point of minimum F(r) along a bond path is a first-order critical point (bond critical point, BCP), whose properties characterize the nature of chemical bonding between two atoms. Zero-flux surfaces perpendicular to the bond paths at the BCP separate the atoms from each other in molecules (interatomic surfaces, IASs). Integration over the atomic volume yields a number of atomic properties (e.g., charge, volume, energy, and its components) which are transferable between molecules to a certain extent. Inspection of ∇2F(r) provides a way to identify regions of charge concentration (∇2F < 0) and depletion (∇2F > 0), distinguishing between covalent and ionic bonds and identifying bonding and/ or lone pairs (local minima of ∇2F). Thus, the AIM theory

provides a solid theoretical footing to interpret molecular electron density distributions in terms of classical chemical concepts. Since perturbation of the electronic structure of CH3CN molecules upon dimerization and/or excess electron dipole binding is marginal,43,47 we concentrate on the features directly related to the excess electron binding. The DBE in the collinear head-to-tail (CH3CN)2- gives rise to a very diffuse region of charge concentration (Figure 3a), far away from the region of valence shell charge concentration (VSCC) representative of covalent bonding in CH3CN. This “dipole-bound” charge concentration (DBCC)50 spreading over the atomic volumes of the hydrogen atoms of the methyl group is similar to the diffuse charge concentrations observed for the Rydberg excited states of ammonia.51 The local minimum of ∇2F(r) for the DBCC is situated at 3.60 Å from the carbon atom of the methyl group (indicated as a purple star and labeled as DBCC in Figure 3a). A low F(r) value and a low negative value of ∇2F(r) are associated with this DBCC critical point (Table 1). The kinetic energy per electron G(r)/F(r) at the critical point is also very low, ca. 5 × 10-3 au, which is typical of loosely bound, diffuse electron distributions,52 and DBEs in particular.3,53 The F(r) distribution for the “solvated electron” head-to-head (CH3CN)2- has a very similar charge concentration region between the acetonitrile molecules (Figure 3b). However, in this case, the excess electron gives rise not only to the region of DBCC and the corresponding local minimum of ∇2F(r) but also

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Figure 4. Structures of (CH3CN)2•- (a) and CH3CN•- (b). Geometrical parameters for these structures are collected in Table 2

to a local maximum of F(r), which is connected to the carbon atoms of the acetonitrile molecules via bond paths and separated from the carbon and hydrogen atoms by IASs. A region of charge concentration with a maximum in F(r), separated from the other atoms in the molecule by IASs, corresponds to a topological atom in the AIM theory. Thus, the excess electron in the head-to-head (CH3CN)2-gives rise to a pseudo-atom of electron density which exists as a separate topological entity, separating the acetonitrile molecules from each other and binding them together via “e- bond”. The maxima, or attractors, of F(r) are typically found at atomic nuclei. Attractors of F(r) without the corresponding nucleus, i.e., non-nuclear attractors (NNA), are fairly uncommon and have only been reported for a few systems, including metal clusters and solids,54 solid lithium fluoride52 with crystal defects (F centers), and aluminosilicates.55 Only very recently have NNAs in solvent cluster anions been reported.50,53,56 However, the formation of the NNAs in other cluster anions [(HF)n- and (H2O)n-] was found to require more than two solvent molecules [n ) 3 for (HF)n- and n ) 4 for (H2O)n-].53,56,57 Thus, (CH3CN)2- appears to be the smallest solvent cluster anion to exhibit an NNA due to the presence of a solvated electron. While Penda´s et al. have shown that NNAs are a natural feature of electron density distributions in molecules and outlined conditions for their formation in diatomic molecules,58 the conditions necessary for the formation of NNAs from a solvated electron in small cluster anions have yet to be understood. The properties of the NNA in head-to-head (CH3CN)2- and the bond critical points connecting it to the carbon atoms are presented in Table 1. The F(r) value at the NNA is almost twice that at the ∇2F(r) critical point for collinear (CH3CN)2-, and ∇2F(r) has a more negative value, consistent with the tighter binding of the excess electron in the “solvated-electron” isomer. Remarkably, the value of the kinetic energy per electron at the NNA is lower than that of the ∇2F(r) critical point for the collinear isomer, even though the excess electron is more confined in the “solvated-electron” structure. The prevalence of stabilizing factors, represented by the potential energy, over destabilizing factors, which can be related to the kinetic energy, is also reflected in the larger negative value of the total energy at the NNA. The BCPs connecting the NNA with acetonitrile molecules are situated outside of the DBCC, therefore ∇2F(r) at the BCP is positive. The value of F(r) is not much lower than that at the NNA, since the distribution of F(r) at the BCP is rather smooth for the pseudo-atom formed by the excess electron, similarly to the F(r) distribution found for pseudoatoms related to crystal defects.52 Integration of F(r) over the pseudo-atom volume gives a charge of -0.53 e; that is, only half of the excess electron is located inside the pseudo-atom (with a volume of ca. 4.6 × 103 Å3). Not surprisingly, the average kinetic energy per electron for the excess electron

Timerghazin and Peslherbe

Figure 5. Spin density plots for (CH3CN)2•- (a) and CH3CN•- (b) calculated with PBE0/aug-pc-1 (0.01 au isosurface)

pseudo-atom is low (G/F ) 8.60 × 10-3 au), which is similar to that of pseudo-atoms corresponding to crystal defects.52 To summarize, the AIM analysis of (CH3CN)2- clusters suggests that the excess electron distributions in the collinear head-to-tail and “solvated electron” head-to-head isomers are qualitatively different. Whereas in the former the electron density simply decays away from the nuclei, in the latter, it gives rise to a (non-nuclear) maximum separating the two solvent molecules.Furthermore,the“solvatedelectron” (CH3CN)2species is the smallest solvent cluster anion to exhibit such a non-nuclear attractor (NNA) of electron density. Incidentally, due to its intrinsic floppiness, it is also the most stable form of acetonitrile dimer (neutral or anionic) at temperatures higher than 150 K. Valence-Bound Electron Acetonitrile Dimer and Monomer Anions We now turn our attention to the VBE acetonitrile anions; Figure 4 displays the structure of the VBE anions, and Table 2 lists selected geometrical parameters and the excess vertical electron binding energies (or ionization potentials) calculated with various model chemistries. The structure of (CH3CN)2•(Figure 4a) is discussed first since it is in many respects better behaved than CH3CN•- and it is a stable species in the gas phase. CASSCF/SVP+ calculations produce a (CH3CN)2•geometry similar to that previously reported on the basis of DFT calculations.17,18,21 (CH3CN)2•- possesses a structure similar to that of the neutral head-to-tail (CH3CN)2, with bent acetonitrile moieties connected at the cyanide carbons. CASSCF predicts a bridging C-C bond somewhat longer than DFT values17,18,21 (rb is 2.05 vs 1.6-1.8 Å for the neutral head-to-tail dimer) and the excess electron vertical detachment energy is negative, suggesting an unstable anionic species. Inclusion of dynamic correlation with CASPT2 leads to a much shorter bridging C-C bond and a positive excess electron vertical detachment energy (Table 2), which highlights the importance of dynamic electron correlation for the description of VBE acetonitrile anions. The PBE0/aug-pc-1 results are in reasonable agreement with those of CASPT2 calculations, although the vertical detachment energy is almost twice as large. Although the molecular spin is not exactly defined in DFT (the wavefunction is not an eigenfunction of the spin operator), it is worth noting that unrestricted PBE0 calculations yield results which are practically unaffected by spin contamination (〈S2〉 ≈ 0.76). Multiconfigurational ab initio calculations (CASSCF and CASPT2) predict the cyanide carbon atoms to be slightly pyramidal, leading to a nonplanar structure with C2 symmetry, whereas DFT calculations suggest a planar C2h structure. Gas-phase (CH3CN)2•- is predicted by CASPT2 and PBE0 to be higher in energy than the neutral collinear head-to-tail (CH3CN)2 isomer by ca. 25 and 17 kcal/mol (or 1.08 and 0.74 eV), respectively (according

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Figure 6. AIM plots for (CH3CN)2•- (a) and CH3CN•- (b). Bond paths (purple) and interatomic surfaces (green) are superimposed with the contour plots of the Laplacian of the electron density ∇2F(r) (solid lines for ∇2F(r) < 0, dashed lines for ∇2F(r) > 0). Insets show ∇2F(r) contour plots for model carbon-centered radicals and carbenes. The nonbonded minima of ∇2F(r) at the carbon atoms are shown as purple stars.

to ZPE-corrected energies). According to the experimental data of Mitsui et al.,20 the preponderance of the valence-bound form of the acetonitrile cluster anion increases with cluster size, which suggests that this energy gap decreases quickly with addition of the solvating acetonitrile molecules. The smallest acetonitrile cluster anion for which the valence-bound form exists in the gas phase is (CH3CN)11-.20 It is reasonable to assume that the valence-bound and neutral/dipole-bound forms are roughly isoenergetic at this cluster size, meaning that the VDE shift between the free and solvated valence-bound dimer anion is around 0.7-1.1 eV. Indeed, shifting the VDEs calculated by CASPT2 and PBE0 (cf. Table 2) by 1.1 and 0.7 eV, respectively, gives values of 2.1 and 2.6 eV, which bracket the experimental VDE for the valence-bound (CH3CN)11- cluster of ca. 2.4 eV.20 However, it should be noted that the VDE calculations in the solvent include equilibrium rather than nonequilibrium solvation of the “vertical neutral”, and therefore are expected to be somewhat overestimated. CASPT2 and PBE0 calculations provide a generally consistent description of the VBE acetonitrile anions, and PBE0 is a reasonable alternative to the computationally expensive CASPT2 approach; PBE0 also allows us to explore bulk solvation effects with continuum solvation models, which are not yet implemented for CASPT2. Solvation in acetonitrile, modeled using the CPCM39 continuum solvation methodology, does not significantly alter the geometry of (CH3CN)2•- calculated with CASSCF and PBE0 (Table 2). The bridging C-C bond length rb decreases, and the cyanide carbon atoms become slightly pyramidal in the case of PBE0. However, solvation has a profound effect on the excess electron binding, as the VDE increases by 2.1-2.4 eV. When solvated, (CH3CN)2•- is lower in energy than the neutral headto-tail acetonitrile dimer by ca. 32 kcal/mol, as predicted by PBE0/aug-pc-1 CPCM calculations. Inclusion of solvation effects allows calculation of the VBE monomer anion CH3CN•-, whose structure resembles that of a single acetonitrile moiety in (CH3CN)2•- (Figure 4b). The monomer anion is bent at the cyanide carbon atom and has a positive vertical detachment energy. CH3CN•- does not exist in the gas phase, unlike (CH3CN)2•-, which is kinetically stable even in the absence of solvation. Gas-phase calculations of CH3CN•- in the equilibrium geometry of the solvated species suggest that the excess electron is not valence- but rather dipolebound: the electron density distribution (not shown) is char-

acterized by the presence of a DBCC very similar to that observed for the DBE head-to-tail acetonitrile dimer anion (Figure 3a). Thus, (CH3CN)2•- is the most stable form of the VBE acetonitrile anion, and the valence-bound isomers of the acetonitrile cluster anions (CH3CN)n- observed experimentally20 are likely to be made up of (CH3CN)2•- clustered with neutral acetonitrile molecules [(CH3CN)2•-(CH3CN)n-2]. The R, β, and γ angles at the cyanide carbon atoms (Figure 4 and Table 2) are all close to 120°, consistent with hybridization change from sp to sp2 upon addition of the excess electron. This rehybridization of the cyanide carbons, which is consistent with the elongation of the carbon-nitrogen bond, suggests that one of the carbon-nitrogen π bonds disappears or significantly weakens. Unpaired spin density plots (Figure 5) reveal a strong delocalization of the excess electron over the acetonitrile molecule(s). For both (CH3CN)2•- and CH3CN•-, the majority of the excess electron density is located at the nitrogen atoms and around the cyanide carbon atoms [in between the cyanide carbon atoms for (CH3CN)2•-]. The typical p-orbital shape of the spin density around the nitrogen atoms and, to a lesser extent, around the cyanide carbon atoms suggests that the excess electron resides, at least partially, in the N-C π* orbital. The AIM plots for (CH3CN)2•- and CH3CN•- are shown in Figure 6, whereas the properties of the relevant bond critical points are listed in Table 3, and the integrated properties of the topological atoms are presented in Table 4. AIM plots and the properties of the BCP for the bridging bond between the cyanide carbon atoms in (CH3CN)2•- suggest that this bond, although relatively weak (the estimated bond order is ca. 0.63, Table 3), possesses a clear covalent character and is not a “pseudo bond” as was previously speculated in the literature.16 The charge concentration regions are shared between the carbon atoms (Figure 6a) and the ∇2F(r) value at the BCP is negative (Table 3). The carbon-nitrogen bond partially loses its triple-bond character, as can be seen from the ellipticity value at the BCP ( ) 0.153), which is almost half the ellipticity value for the CdC double bond ( ) 0.345). The ellipticity is related to the anisotropy of the electron density distribution around the BCP in the plane perpendicular to the bond path; a near-zero ellipticity corresponds to an isotropic density distribution typical of single and triple bonds (e.g., the CtN bond in acetonitrile), whereas double bonds have higher ellipticity values at the BCP. Thus, one of the acetonitrile carbon-nitrogen π bonds is weakened

526 J. Phys. Chem. B, Vol. 112, No. 2, 2008

Timerghazin and Peslherbe

TABLE 3: AIM Properties of Selected Bond Critical Points for the VBE Acetonitrile Anions and the Acetonitrile Moleculea (CH3CN)2•(CH3CN)2d solvatede (CH3CN)2•solvatede CH3CN•CH3CN solvatede CH3CN

BCPb

FBCP

∇2FBCP

BCP

Bond orderc

C1-C1 C1-C2 C1-N C1-C1 C1-C2 C1-N C1-C1 C1-C2 C1-N C1-C2 C1-N C1-C2 C1-N C1-C2 C1-N

0.176 0.245 0.422 0.158 0.238 0.424 0.178 0.248 0.421 0.241 0.429 0.265 0.472 0.266 0.472

-0.235 -0.512 -0.657 -0.149 -0.488 -0.551 -0.244 -0.523 -0.665 -0.483 -0.338 -0.621 0.256 -0.629 0.212

0.057

0.63 1.01

0.153 0.022 0.128 0.054

0.56 0.97 0.64 1.04

0.140 0.99 0.020 1.16 0.000 1.17 0.000

a Electron density (F), Laplacian of the electron density (∇2F), ellipticity () of the carbon-nitrogen and the bridging carbon-carbon bonds, and estimated bond orders for carbon-carbon bonds. Calculated based on PBE0/aug-pc-1 electron densities (all values in atomic units). b Atom labels are defined in Figure 4. c Bond orders are estimated using the bond order ) exp[A(FBCP - B)] formula of ref 23, parametrized on the basis of PBE0/aug-pc-1 FBCP values for ethane, ethene, and ethylene (0.2421, 0.3443, and 0.4023 au, respectively). d Neutral dimer in the equilibrium geometry of the anion. e Solvation effects included using the CPCM continuum solvation model.

TABLE 4: Integrated AIM Properties for the Atoms in the VBE Acetonitrile Anions and the Acetonitrile Moleculea •-

(CH3CN)2

(CH3CN)2c solvatedd (CH3CN)2•solvatedd CH3CN•CH3CN solvatedd CH3CN

atomb

N(Ω)

q(Ω)

σ(Ω)

N C1 CH3 N C1 CH3 N C1 CH3 N C1 CH3 N C1 CH3 N C1 CH3

8.300 5.182 9.048 8.021 5.188 8.794 8.338 5.183 8.986 8.493 5.443 9.066 8.258 4.998 8.745 8.316 4.982 8.704

-1.300 +0.818 -0.048 -1.021 +0.812 +0.206 -1.338 +0.817 +0.014 -1.493 +0.557 -0.066 -1.258 +1.002 +0.255 -1.316 +1.018 +0.296

0.421 0.014 0.068

0.421 0.016 0.065 0.404 0.394 0.203

a Electron populations [N(Ω)], atomic charges [q(Ω)), and spin populations [σ(Ω)]. b The methyl group properties are the sum of the hydrogen and carbon atomic properties. c Neutral dimer in the equilibrium geometry of the anion. d Solvation effects included using the CPCM continuum solvation model.

upon formation of (CH3CN)2•-, in agreement with the bent C-C-N angle discussed above. Interestingly, the properties of the BCPs for (CH3CN)2•practically do not change upon solvation (Table 3). Further, in the neutral structure obtained by removal of the excess electron while retaining the anion geometry, the bridging C-C bond retains covalent character with a bond order similar to that of the anion bridging bond (0.56 vs 0.63). Thus, the excess electron is not solely responsible for the binding of the two acetonitrile moieties in (CH3CN)2•-, but it rather causes changes in the electronic structure and geometry of the acetonitrile molecule that drive the formation of the bridging bond. The AIM atomic charges and unpaired spin populations for (CH3CN)2•- also do not differ much in the gas-phase and in the presence of solvent

TABLE 5: Properties of the Nonbonded Minima of the Laplacian of the Electron Density (Valence-Shell Charge Concentrations, VSCC) at Carbon Atomsa,b CH3CN•CH3CO CH3COH

r, Å

FVSCC

∇2FVSCC

0.488 0.477 0.456

0.222 0.249 0.330

-0.638 -0.924 -1.584

a VBE acetonitrile monomer anion, carbon-centered radical and carbene prototype (Figure 6b). b Distance from the respective nuclei r (in Å), electron density F, and its Laplacian 32F (au). Calculated based on PBE0/aug-pc-1 electron densities, using the CPCM continuum solvation model.

(Table 4). In agreement with experimental EPR measurements,15 the majority of the unpaired spin density (ca. 80%) is concentrated on the nitrogen atoms. In contrast to (CH3CN)2•-, solvated CH3CN•- is characterized by a significantly smaller ellipticity for the carbon-nitrogen bond, relative to that for neutral CH3CN, which suggests that it retains its triple bond character to a greater extent, despite a bent C-C-N structure. The unpaired spin population at the cyanide carbon atom is much larger than that for (CH3CN)2•-, and it is almost equal to that of the nitrogen atom (Table 4). The contour map of ∇2F(r) for CH3CN•- (Figure 6b) reveals a nonbonded charge concentration on the cyanide carbon atom similar to the lone-pair type nonbonded charge concentrations for carboncentered radicals and carbenes (insets in Figure 6). The properties of the corresponding minimum of ∇ 2F(r) (indicated as a purple star and labeled as VSCC for valence-shell charge concentration in Figure 6b) are also very close to those of the critical points in carbon-centered radicals and carbenes (Table 5). The “lone-pair” character of these charge concentrations increases from CH3CN•- to the carbon-centered radical and to the carbene. While the cyanide carbon atom in CH3CN•possesses partial radical character, in (CH3CN)2•- this carbon atom is involved in covalent bonding. Based on the spin densities obtained from EPR experiments,15 it has been proposed that the electronic structure of CH3CN•can be described by a combination of three resonance structures, shown below, and arising from localization of the excess electron at the nitrogen and carbon atoms:

Even though this resonance description is consistent with the unpaired spin density distribution (Figure 5b), the unpaired spin atomic populations (Table 4) and the formation of a VSCC critical point at the cyanide carbon atom (Figure 6b), it cannot account for the build-up of electron density at the methyl group in CH3CN•- when compared to neutral CH3CN (-0.066 vs +0.296 e, respectively). Thus, this suggests that it may be necessary to include a resonance structure with a negatively charged methyl carbon atom to adequately express the electronic structure of CH3CN•-:

Likewise, the electronic structure of (CH3CN)2•- may be described as a combination of the six resonance structures in Scheme 1 (where the dashed line represents a one-electron bond). Greater delocalization of the excess charge and unpaired

Acetonitrile and Acetonitrile Dimer Anions

J. Phys. Chem. B, Vol. 112, No. 2, 2008 527

SCHEME 1

spin density leads to the higher stability of (CH3CN)2•- vs CH3CN•-. Although this resonance description is a very approximate way to qualitatively represent the complex electronic structure of the VBE acetonitrile anions, it agrees well with the quantitative results of the AIM analysis. Concluding Remarks A detailed study of the electronic structure of the acetonitrile and acetonitrile dimer anions, with both dipole-bound and valence bound excess electrons (DBE and VBE, respectively), has been performed using the quantum theory of AIM. One of the main objectives of this analysis is to reveal the topological changes in the electron density distributions induced by the presence of the excess electron. One isomer of the DBE (CH3CN)2- has the acetonitrile molecules oriented in a collinear head-to-tail fashion, with the excess electron trapped in the field of the aggregate dipole away from the cluster. The other isomer has the excess electron trapped in between the acetonitrile molecules oriented in a headto-head fashion and screened from each other by the excess electron cloud (“solvated-electron” isomer). The entropic factors are of crucial importance in determining the thermodynamic stability of the latter isomer. Whereas at low temperatures (