Temporary Anion States of Ethene Interacting with Single Molecules of

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Temporary Anion States of Ethene Interacting with Single Molecules of Methane, Ethane, and Water Thomas Sommerfeld, Joshua B. Melugin, and Masahiro Ehara J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b12669 • Publication Date (Web): 16 Feb 2018 Downloaded from http://pubs.acs.org on February 18, 2018

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The Journal of Physical Chemistry

Temporary Anion States of Ethene Interacting with Single Molecules of Methane, Ethane, and Water Thomas Sommerfeld,∗,† Joshua B. Melugin,† and Masahiro Ehara∗,‡ †Department of Chemistry and Physics, Southeastern Louisiana University, SLU 10878, Hammond, LA 70402, USA ‡Institute for Molecular Science, Research Center for Computational Science, Myodai-ji, Okazaki 444-8585, Japan E-mail: [email protected]; [email protected] February 15, 2018 Abstract When an excess electron is added into the π* orbital of ethene, the resulting anion decays by electron autodetachment—that is, it represents an electronic state referred to as a temporary anion or resonance state. Here the influence of a cluster environment on the energy and lifetime of this state is investigated. The clusters considered are ethene· · ·CH4 , ethene· · ·C2 H6 , and ethene· · ·H2 O. Most of these clusters are systematically constructed so that the solvent interacts with the π system in a specific way, and are thus by construction not minima with respect to all intermolecular degrees of freedom. However, for water, in addition a minimal energy structure is examined. Systematic variation of the solvent and solvation geometry allows us to identify trends regarding effects due to polarizability, excluded volume, and polarity of the solvent molecules. The resonance parameters of ethene and all temporary cluster anions

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are computed with the symmetry-adapted cluster-configuration interaction electronic structure method in combination with a complex absorbing potential. This method is well established for small to intermediate sized molecules. In addition to studying the solvation effects themselves, the question of how many basis functions are needed on the closed-shell solvating unit is examined.

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Introduction

If an excess electron is added into an unoccupied π* orbital of a typical organic molecule, the resulting anion states are—as a rule—not bound, but rather so-called temporary anions with finite lifetimes. For examples, the temporary anion created by adding an electron into the π* orbital of ethene shows a lifetime of 1 to 2 fs. 1–4 Exceptions are the lowest π* orbitals of molecules with strongly electron-withdrawing groups. For example, for 1,4-benzoquinone, the lowest π* anion is bound while the higher π* anion states are temporary in nature. Temporary anions and other electronic states that can decay by autodetachment are in general called resonances and are characterized by their energy, the so-called resonance position, Er , and by their width, Γ, which essentially represents a first-order decay constant. 5–8 In other words, a temporary anion is associated with a typical decay time τ = h ¯ /Γ—referred to as its lifetime—that is inversely proportional to its width. Examples for resonances other than temporary anions are small dianions in the gas phase, core-ionized atoms and molecules decaying via the Auger process, the analogous Auger-like decay of inner-valence ionized clusters, doubly excited states with energies in excess of the ionization energy of the neutral, and molecules subject to field ionization (for some specific examples see 9–12 ). Many temporary anions have been characterized in the gas phase, on the one hand, by electron transmission spectroscopy 13 or electron scattering techniques. 14 On the other hand, a wealth of data on electron-induced dissociation (EID)—also referred to as dissociative attachment or electron capture dissociation—is available. 15 Since this bond-breaking process is thought to be strongly enhanced by temporary anions, a resonance in the EID cross section suggests the existence of a temporary anion. In electron scattering, temporary anions in a microsolvation environment present a far greater challenge than their respective monomers, since a cluster beam will typically show a broad size distribution. Thus, while the products resulting from EID can be readily observed, it is—as a rule—unclear from which neutral cluster they originate. 15–17 A different window to resonances opens if the molecular anion in question possesses a bound ground state, say, 1,4-benzoquinone. Then the temporary anion 3



states can be “interrogated” through laser spectroscopy, and a particular solvated anion can be mass selected prior to the excitation. 18 In contrast to ground electronic states, the theoretical description of resonances represents a far greater challenge as it combines an electron-continuum with an electron-correlation problem. Loosely speaking, currently one may pick two out of the following three: continuum, correlation, and size. Resonances of relatively large molecular systems can be studied by ignoring the continuum aspect and confining the excess electron to the valence region, 7,19 but the variational collapse on states with high pseudo-continuum character is always a danger. The second alternative is to choose straightforward and therefore inexpensive electronic structure methods to describe the excess electron system. Examples are configuration interaction (CI) wavefunctions built from all one-particle configurations or from all oneparticle and all two-particle-one-hole configurations. These two CI wavefunctions for the anion are referred to as static-exchange and static-exchange-plus-polarization in the scattering literature, however, both are practically uncorrelated—even though that may at first seem counterintuitive. Static-exchange is strictly equivalent to Koopmans’s Theorem for a bound anion, the difference for temporary anions is that the right linear combination of 1p configurations is not a unit vector, but has to be found by a scattering or CAP calculation. Static-exchange-plus-polarization is constructed to recover the orbital relaxation missing in static-exchange, and the goal is a wavefunction equivalent to unrestricted Hartree Fock for a bound anion. Yet, if all 2p1h configurations are included, static-exchange-plus-polarization is unbalanced, and in practical calculations only a subset of the 2p1h space is used (see Ref. 20 or 14 ). However, due to the low cost of these CI spaces, fairly large molecules and clusters can be studied, and recently scattering calculations employing these computational levels have been applied to water clusters of formaldehyde, phenol, pydridine, and thymine. 21–24 Last, applications can focus on small to moderately sized molecules. Then suitably modified quantum chemistry methods can predict the energy and lifetime of temporary anions using coupled cluster quality or similarly reliable approaches (for recent examples see 2,25–27 ).

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Here we compute the energy and lifetime with complex absorbing potentials and treat correlation at a coupled-cluster-like level, 28 but pay the price of confining ourselves to fairly small clusters. What is gained is that variation of the solvent and of the solvent position enables us to establish reliable trends. The π* resonance of ethene is taken as a reference system and change of the resonance parameters Er and Γ upon attachment of a single solvent molecule X to ethene is studied. The solvent molecules X considered are methane, CH4 , ethane, C2 H6 , and water. Most ethene· · ·X clusters investigated are model systems in the sense that the orientation of the solvent molecule relative to ethene is fixed, while the rest of the geometrical parameters are optimized. For ethene· · ·H2 O, in addition, a minimal energy structure is considered. Yet, the difference in interaction energy between the two neutral molecules in the minimum energy structure and in the model structures is in the same order of magnitude as kT at room temperature, suggesting that the neutral target should be thought of as possessing a highly flexible if not fluctional structure (see below). After describing our computational methods in the next section, section 3 discusses the studied model clusters, results for the noncovalent interaction energy of the two cluster constituents, and the shifts in the resonance energy of ethene in the environment of the cluster. Moreover, we investigate the basis set convergence with respect to the basis set placed on the closed-shell solvent molecule. Section 4 concludes.

2

Computational Methods

First, the geometries of ethene and all ethene· · ·X model clusters (X = CH4 , C2 H6 , or H2 O) were optimized using Møller-Plesset perturbation theory (MP2) and Dunning’s augmented correlation-consistent triple-ζ (aug-cc-pVTZ) basis set 29 as implemented in the PSI4 package. 30 The model clusters were constructed by confining each cluster to have C2v symmetry. In other words, the X molecules are confined to one of the three symmetry axes of the ethene molecule, the rotation of the X molecules with respect to ethene are implicitly confined by

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symmetry, and the same is true for the internal rotation of ethane. We note that this symmetry confinement impacts a few selected torsions only; all distances and angles as well as all totally symmetric torsions are optimized. Moreover, for ethene· · ·H2 O, we optimized one structure, where the water molecule points (donates) just one hydrogen bond to the ethene π system. This structure is almost—but not quite—Cs symmetrical. To compute the resonance, Cs symmetry was imposed resulting in an energy increase of 3 · 10−6 Hartree. The particular ethene· · ·X clusters considered are discussed in the next section. The high-symmetry model clusters were selected for the following two reasons: First, considering systems with high symmetry aids in the assignment of the resonance states. Second, the potential energy surface of a loosely bound molecule cluster such as the ethene· · ·X dimers can be expected to show several very shallow minima of similar depth, which will be connected by low barriers. Thus, at any but the lowest temperatures the cluster will sample a considerable region of its potential energy surface. A minimum energy structure as such is fairly meaningless, and a more systematic approach is needed. After establishing the structures to be investigated, the neutral ethene· · ·X clusters were further examined by characterizing the noncovalent interaction energy (NIE) with the help of symmetry-adapted perturbation theory (SAPT). 31 Specifically the NIE was computed using the so-called SAPT2+3dMP2 variant 32 as implemented in the PSI4 package 30 together with the aug-cc-pVTZ basis set. Then the π* temporary anion states of ethene and all clusters were investigated by computing the complex resonance energy Er − iΓ/2 with the symmetry-adapted clusterconfiguration interaction (SAC-CI) electronic structure method 33,34 in conjunction with a complex absorbing potential (CAP). 28,35–37 The SAC-CI approach by itself is a high-level method for computing electron attachment energies. In a sense, SAC-CI and equation-of-motion coupled-cluster methods for electron attachment 38–41 start out from the same set of equations, and the two approaches are consequently closely related to each other. The SAC-CI method is by construction size-consistent

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and balanced, and the electron attachment energies are obtained directly, that is, after the correlated electronic ground state of the neutral molecule has been computed, several attachment states ((N + 1)-electron states) are computed directly by finding eigenpairs of a configuration-interaction-like Hamiltonian for the (N + 1)-electron system. In the present context SAC-CI has two key advantages: First, it naturally yields many states, which is a basic requirement for identifying a resonance in a discretized continuum. Second, it is balanced, that is, in a curve crossing situation between the neutral and the anion, the resonance position and width will go to zero at the same place. In the standard implementation the anion states are described as a combination of all one-particle and two-particle-one-hole configurations of a similarity transformed Hamiltonian, where the transformation implies that three-particle-two-hole configurations as well as coupling to yet higher excitations are implicitly taken into account. Here the investigated molecules are small, so we do not use any of the further approximations traditionally available in SAC-CI (variational SAC-CI, configuration selection through perturbation criteria), however, as usual higher-order contributions of the single substitution operators such as, S1 S1 S1 , are neglected. 42 Moreover, use is made of the direct algorithm where sigma-vectors are directly calculated including all the product (non-linear) terms. 42 The SAC-CI calculations were done with the GAUSSIAN09 suite of programs, Revision B.01. 43 The CAP—SAC-CI combination (CAP/SAC-CI) has been extensively studied in the literature. 26,28,44–46 Specifically, the potential used as a CAP is a cut-off harmonic potential in the ‘distance-to-the-molecule’ coordinate: 44,45 In the vicinity of the nuclei the CAP is zero, but from a cut-off radius of 4 Bohr it grows quadratically with the distance-to-the-molecule, which is defined as an average heavily biased toward the distance to the nearest atom, 44,45 making the isocontours of the CAP a smoothed Voronoi surface that closely follows the molecular shape similar to a van der Waals surface. For the CAP calculations the correlation-consistent triple-ζ (cc-pVTZ) valence basis set 29 was augmented with a (2s5p2d) set of diffuse functions on C and O (even-scaled exponents

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starting from the smallest exponents of the respective angular momentum in the original basis set, even scaling factor of 2.0 for s and d functions, and 1.5 for p functions) and a (1s1p) set on H (even scaling factor of 2).

3

Results

In this section we first describe the structures of the 13 ethene· · ·X model clusters investigated, then the NIEs and resonance parameters of these clusters are discussed, and finally the basis set convergence regarding the diffuse functions placed on the solvent X molecule is considered. The studied ethene· · ·X model clusters, where X = CH4 , C2 H6 , or H2 O, are schematically shown in Figs. 1, 2, and 3, and Fig. 4 shows the optimized structure of ethene· · ·H2 O. Note that only a small subset of all possible C2v symmetrical conformations has been considered. For example, for ethene· · ·methane, for each model cluster (1), (2), and (3) (Fig. 1) one could consider another structure in which the methane molecule is rotated by 90◦ with respect to the ethene molecule. However, no significant new insight is expected from these small changes. For ethene· · ·ethane, the three structures studied, (4), (5), and (6), (Fig. 2) are all derived from (2), that is, ethane was placed below (or above) the plane of the ethene molecule (Fig. 2) so as to maximize its effect on the ethene π system. These ethene· · ·ethane clusters were specifically selected to investigate so-called crowding or “excluded-volume” effects: 47 Loosely speaking, solvent molecules exclude a certain volume from potential occupation by excess electrons, because the orbital of an excess electron must be orthogonal to all occupied orbitals of the neutral and must therefore oscillate wherever there are occupied valence orbitals. Alternatively, one can view this effect as orbital mixing between a filled orbital from the solvent molecule and the ethene unoccupied π* orbital that pushes the energies of the two orbitals apart.

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Figure 1: Model ethene· · ·CH4 clusters. H

H

H

H

H

H H H

H

H H

H H H H

H H

H

H H

H H

(1)

H

(2)

H (3)

Figure 2: Model ethene· · ·C2 H6 clusters. H H

H

H H

H

H

H

H (4)

H H

H H

H H

H

H

H

H

H H

H H H

H H

(5)

H (6)

In contrast to methane and ethane, water possesses a substantial dipole moment. Thus, in addition to the placement of the water molecule with respect to the ethene molecule, the relative orientation of the water dipole is crucial. For example, for those orientations, where the water molecule is localized below (or above) the plane of the ethene molecule, we could find bound C2v clusters only if the water hydrogen atoms point toward the ethene π system (model clusters (9) and (10) in Fig. 3). In other words, if clusters analogous to (9) and (10) are constructed, however, with the water oxygen pointing toward the ethene π system, the MP2/aug-cc-pVTZ potential energy surface becomes repulsive and a MP2 geometry optimization yields “dissociated” neutrals. The NIE of all model clusters as well as the resonance positions and widths of the π* temporary anions of ethene and the ethene· · ·X clusters are collected in Tab. 1. The computed fixed-nuclei resonance position for isolated ethene is about 0.2 eV too high in comparison

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Figure 3: Model ethene· · ·H2 O clusters. H

H

H

H

H

H

H

H

H H

O

O

H H

(7)

H H

H H

H H

H

(9)

(8)

H H

H O

H

H

H

H

H

H

H

H

H H

H H

O

O

O

H H

(10)

(11)

(12)

with experiment, 1 however, that is expected for the most part owing to vibrational effects. 28 Both position and width agree favorably with earlier theoretical work. 2–4 Small differences are due to different geometries, different basis sets, different electronic structure methods, and different methods to address the continuum nature of the wavefunction. From a neutral· · ·neutral noncovalent interaction point of view, methane is expected to show the weakest attraction, because it is non-polar and has a polarizability that is only about 50% larger than that of water. The NIEs of our model clusters (1), (2) and (3) (Fig. 1) lie accordingly between 1.4 and 3.6 kJ/mol (less than 1.5 kT at room temperature). The resonance energies of the temporary anions, on the other hand, will not only be affected by the polarizability of methane, but also by its excluded-volume effect. Still, methane is a small molecule and its distance from ethene is fairly large, so that its net effect on the π* resonance is limited (Tab. 1). In comparison to free ethene, the resonance position is very slightly lowered and the width for (1) and (2) is slightly narrower while it is unchanged for (3). However, in view of the typical precision of CAP calculations with Gaussian basis sets, 2,28,37,44 the differences are too small to draw quantitative conclusions. An attached 10


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Figure 4: Ethene· · ·H2 O cluster (13).

methane unit has clearly very little influence on the π* temporary anion of ethene, and the small influence is stabilizing regarding both, a lower resonance position by up to 0.1 eV and a narrower width by up to 0.05 eV. In comparison to methane, ethane’s molecular volume is almost twice as large, and the same is true for its polarizability. Accordingly, the NIEs computed for (4), (5), and (6) are also roughly twice as large as the NIE of (2) (Tab. 1), but they represent, of course, still very weak interactions (≈ 3 kJ/mol). A similar trend—at least qualitatively—is observed for the resonance energies associated with the three ethene· · ·ethane clusters. The individual Er and Γ values are shifted with respect to their reference values for isolated ethene, and the shifts for (4), (5), and (6) are very roughly twice as large as the shift for (2) (factors in the range between 1.5 and 3). Yet, whereas the shifts for (2) and (6) are stabilizing in the sense of lower resonance positions and narrower widths, the shifts for (4) and (5) destabilize the resonance relative to isolated ethene. Moreover, the energetic order, with (4) being the least stable, followed by (5), and then by (6), suggests that the temporary anion parameters are qualitatively determined by the excluded-volume effect. In (6) the carbon-carbon bonds of ethene and ethane are arranged orthogonal to each other, and consequently the ethane molecule interferes least with the π* orbital of ethene. The slightly stabilizing net interaction 11



Table 1: Noncovalent interaction energies, resonance positions, and widths. NIEa Erb Γb [ kJ/mol] [eV] [eV] ethene — 2.00 0.50 ethene· · ·CH4 (1) 3.6 1.91 0.45 (2) 1.4 1.95 0.46 (3) 2.1 1.97 0.50 ethene· · ·C2 H6 (4) 2.9 2.16 0.54 (5) 3.5 2.08 0.53 (6) 3.2 1.87 0.39 ethene· · ·H2 O (7) 3.6 1.63 0.33 (8) 5.6 2.23 0.61 (9) 6.0 1.48 0.31 (10) 6.0 1.65 0.28 (11) 1.9 1.48 0.61 (12) 3.5 2.39 0.55 (13) 10.0 1.69 0.79 a SAPT/aug-cc-pVTZ b CAP/SAC-CI/cc-pVTZ+(2s5p2d/1s1p) is most probably due to the polarizability of ethane, that is, an electron correlation effect. In contrast, in (4) and (5) the methyl groups of ethane are much closer to the π* lobes of ethene, and our results suggest that in these two cases the destabilizing excluded-volume effect more than compensates any stabilization gained from the polarizability with the difference between (4) and (5) being due to the different number of hydrogen atoms pointed toward the π system. Third, we turn to water, the chemically hardest but most polar solvent molecule considered. In other words, while methane and ethane are substantially more polarizable than water, water possesses an appreciable dipole moment, and a solvating water molecule may therefore—depending on its orientation—show larger NIEs and have a larger impact on the ethene π* temporary anion state than either methane or ethane. Regarding the interaction of the two neutral molecules, the first thing catching one’s eye (Tab. 1) is that the NIE for ethene· · ·H2 O does indeed strongly depend on the orientation of the water molecule with particular large NIEs (5.6 to 6.0 kJ/mol) for model clusters (8), (9), and (10), while for the other three arrangements the NIE is in the same order of magnitude as for methane or

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ethane. However, there is no simple rule about the orientation of the dipole moment. In the side-on geometry, the high NIE occurs for (8) with the negative end of the dipole pointing toward ethene, whereas in the π-system-on geometry the preferred orientations, (9) and (10), are the ones with the positive end of the dipole pointing toward ethene. Note that inversion of the water molecule of (8) still yields an attractive—if weaker—interaction: (7), whereas inversion of the water molecules of (9) or (10) yields repulsive interactions (see above). The strongest attraction of 10 kJ/mol occurs, of course, in the effectively unconfined Cs structure (13) (Fig.4), but we emphasize that the energy difference to the low-energy model clusters is less than 5 kJ/mol, that is, about 2kT at room temperature, and note that it is likely that an exhaustive investigation of the potential energy surface will produce at least an additional (8)-like minimum energy structure. Both minimal energy structures are expected to be represented by several symmetry equivalent configurations, and the barriers between these minima are expected to be low (at most in the same order as the NIEs). Hence, the cluster will have a dynamic fluctuating structure at any but the lowest temperatures. Regarding the temporary anion states of ethene· · ·H2 O, as expected, those model clusters, where the H atoms of the water molecule points toward ethene ((7), (9), (10), (11) and (13)), are stabilized with respect to isolated ethene, while (8) and (12) are destabilized (Tab. 1). Concentrating for the moment just on the energies, these stabilizations range from 0.3 to 0.5 eV, while the destabilizations are 0.2 and 0.4 eV. The overall dipole alone, however, cannot fully explain the results. For example, geometry-wise (9) and (10) are almost identical, yet (9) shows nevertheless a significantly lower resonance position suggesting that its extra stabilization of the π* state is due to a hydrogen bonding-like interaction. Similarly, both water OH bonds of (11) do not simply point in the general direction of ethene but also directly toward the lobes of the π system, and the resonance position of (11) is as low as that of (9). The same is true for (13) in a reverse sense: Its hydrogen bond is aimed at the center of the ethene π system to maximize the interaction with neutral ethene. The π* orbital lobes, however, point away from the ethene center, and therefore the stabilization of

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the temporary anion state in (13) is substantially less than that of (9) and (11). Having discussed “stabilization” from an energetic point of view, let us now briefly turn to the respective lifetimes. For examples, the two “hydrogen bonded” model clusters (9) and (11) are most stable energy-wise, whereas from a lifetime point of view, only (9) shows a smaller width and consequently longer lifetimes than isolated ethene, while for (11) the opposite is true. Explaining trends in lifetimes remains, however, a challenge, because— with a grain of salt—the width of a resonance is related to the integral of the barrier the excess electron has to tunnel through when leaving the system. Often a simple angular momentum analysis can explain trends in a series of related systems: the lower the angular momentum, l, of the outgoing wave the shorter the lifetime. This analysis works well for − − − explaining, say, the difference between N− 2 and CO or between benzene and toluene and

xylene− isomers. 13 Here, however, isolated ethene is essentially a d-wave, in (9) some p-wave character is mixed in, while in (11) some f-wave character is mixed in. Clearly, the trends of the computed lifetimes (Tab. 1) do not follow this simple angular momentum argument, and we note that as the ethene· · ·water distance is an intermolecular one, the mixing is not too strong in the first place. An alternative explanation for clusters may involve the nature of three-dimensional barriers. In (9) the water molecule would to some extent block an outgoing d-wave and thereby raise the effective barrier for the decay, whereas the water molecule in (11) can be expected to have little impact on the outgoing wave. More systematic investigations of clusters with a larger number of solvent monomers will be needed to answer these questions. To further understand the shifts in the resonance position, we performed the analysis suggested in Ref. , 23 which splits the total shift of the resonance energy into an indirect and a direct contribution (see Fig. 5). The indirect shift measures the shift due to the geometry distortion of the neutral molecule upon solvation, while the direct shift measures the shift due to solvation in a vertical sense, that is, at the geometry ethene has in the cluster. Results for the cluster with the largest NIE, cluster (13), are displayed in Tab. 2. Clearly, for these very

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Figure 5: Schematic Er (Q) surfaces illustrating the analysis of the total solvation effect in terms of a direct and an indirect contribution. The Q-axis is a nuclear coordinate connecting the geometries of free (Q0 ) and solvated ethene (QC ). Note that for π* resonances Er is normally a slowly changing function of the nuclear parameters, and that the Er variations shown here are overemphasized for clarity.

weakly bound systems the direct contribution by far dominates the total, in fact, within the precision of the method the total and the direct shifts are essentially identical, while the indirect shift is essentially zero. We conclude that all shifts reported in Tab. 1 can be considered to be entirely due to the interaction with the solvent molecule, and that geometry distortions of the neutral will start to play a role in systems with stronger intermolecular forces only. Table 2: Indirect, direct, and total shifts of Er and Γ due to formation of cluster (13). ∆Era ∆Γa [eV] [eV] indirect –0.0035 –0.0083 direct –0.3051 0.3009 total –0.3086 0.2926 a CAP/SAC-CI/cc-pVTZ+(2s5p2d/1s1p) Up to this point we used identical basis sets on the ethene unit and on the saturated 15



solvent molecule. However, in view of studying larger systems with more solvent molecules, this type of basis sets is doomed to fail due to near linear dependencies, and here we investigate the methodological question: Can the number of diffuse basis functions on the saturated solvent molecule be reduced? Naively, one may expect that the answer is a resounding “yes,” and that even a valence basis set augmented with one additional set of diffuse functions may be sufficient, because this basis set should describe the solvent molecule well enough—at least as long as the solvent is saturated—and therefore be able to account for the essential effects due to the multipole moment, the polarizability, and the excluded-volume effects. On the other hand, the wavefunction of the outgoing excess electron must be absorbed by the CAP, and the bulkier the molecule cluster becomes, the less clear it is that a diffuse-functions-on-ethene-only strategy can address this situation adequately. To shed light on this issue we took ethene· · ·C2 H6 cluster (6) and eliminated the most diffuse basis functions on the C2 H6 carbon atoms systematically (Tab. 3). Replacing the (2s5p2d) set with a (1s1s1p) set yields qualitatively correct, but unconverged resonance parameters. The (2s2p2d) set performs significantly better: The resonance position is almost converged and the width is acceptable. When a third p-type function is added, the resonance position and width are converged to the precision of the method. Table 3: Ethene· · ·C2 H6 cluster (4) resonance parameters in dependence on the diffuse basis set on ethanea . ethane-Cb

Ebr Γb [eV] [eV] (1s1p1d) 2.25 0.28 (2s2p2d) 2.18 0.45 (2s3p2d) 2.16 0.54 (2s5p2d) 2.16 0.54 a All results for (4) with CAP/SAC-CI. Basis on ethene is cc-pVTZ+(2s5p2d/1s1p). Basis on ethane-H is cc-pVTZ+(1s1p). b Basis on ethane-C is cc-pVTZ + indicated subset of (2s5p2d) with largest exponents.

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4

Summary and Conclusions

In order to enhance the understanding of environment’s impact on the energy and lifetime of temporary anions, we have studied the prototypical π* resonance of ethene and a variety of systematically constructed ethene· · ·X (X = methane, ethane, water) clusters. Most clusters have C2v symmetry, which aids in identifying the resonance states, and our computed NIEs show that the global minima are not particularly meaningful in the first place, as the potential energy surfaces of the neutral dimers are so flat that any realistic modeling of the resonance will require some type of sampling approach. Most importantly, however, the systematic study of different absolute positions of the X molecule with respect to the ethene framework and of different orientations of the X molecule in these positions reveal a number of qualitative trends that would remain hidden otherwise. Resonance positions and lifetimes of the ethene temporary anion reference state and all clusters modeling micro solvation were computed with the CAP/SAC-CI method. Electron correlation-wise SAC-CI goes well beyond second-order perturbation theory methods or CI approaches that include one-particle and two-particle-one-hole configurations, because threeparticle-two-hole excitations as well as coupling to even higher excitations are implicitly included through a similarity transformation. The combination of the SAC-CI method with complex absorbing potentials is well established; the computed quantity is the complex resonance energy Er − Γ/2. Out of the three “solvent” units, methane, ethane, and water, water is obviously the only polar molecule considered (dipole of 1.85 D), but it has at the same time the smallest polarizability with methane’s and ethane’s polarizabilities being larger by factors of roughly 1.5 and 3. Moreover, ethane has roughly twice the molecular volume of methane or water and consequently exerts a much larger excluded-volume effect. The following specific trends can be derived from our results. A solvating methane molecule has very little impact on the π* temporary anion of ethene (shifts of up to 0.1 eV in the resonance position and of up to 0.05 eV in the width), while the shifts observed for ethane can be up to twice as large. Moreover, 17



a solvating ethane molecule can both stabilize and destabilize the ethene temporary anion depending on its orientation. Water, on the other hand, can cause significant shifts (up to 0.5 eV in the resonance position and up to 0.2 eV in the width) depending on its orientation, and again both stabilizing and destabilizing orientations have been identified. Further analysis suggests the following more general trends. First, for the unpolar solvents methane and ethane, regardless of the geometrical arrangement, the polarizability of the solvating hydrocarbon molecule stabilizes the resonance slightly. In other words, electron correlation between ethene and methane or ethane leads to a lower resonance position. The excluded-volume effect, on the other hand, has a destabilizing effect, but a strong one only if the solvent molecule “blocks” the ethene π* orbital such as in (4) and (5). Second, for water the dominating effect is due to its polarity, and water will either strongly stabilize or destabilize the π* temporary anion depending on whether it points the positive or negative side of its dipole toward ethene. This is similar to previous findings. 21–24 Yet, a secondary stabilizing effect emerges, if the water OH bonds are pointed directly toward the π* lobes—a hydrogen bond-like stabilization. Note that in the minimum energy structure (13) the OH bond points at the bond center to maximize its interaction with the occupied π orbital of neutral ethene. Thus, its impact on the π* orbital is less than that of model clusters (9) or (11). We conclude that electron attachment to ethene· · ·H2 O will lead to substantial forces in the intermolecular bonds, and that the anion will have a far better defined minimal energy structure than the neutral cluster. Last, the possibility of using smaller basis sets was investigated, where smaller basis sets were constructed by systematically eliminating the most diffuse functions on the solvent molecule. This type of strategy, a large diffuse basis set on the “resonance center” and a smaller set on the solvent units, should work for fairly small clusters, that is, for small solvent molecules and at most one solvent shell. Our calculations show that even for a single solvent molecule, the valence basis set on the solvent needs to be significantly augmented (to a (2s3p2d) set) to archive full convergence. A double augmentation, (2s2p2d), yields

18


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acceptable results, however, augmentation with only a single set of diffuse functions leads to significant deviations, in particular, in the width.

5

Acknowledgments

T.S. acknowledges support by the National Science Foundation under CHE-1565495. M.E. acknowledges the financial support from a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS grants 16H04104 and 16H06511).

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Figure 6: TOC Graphic

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Temporary Anion States of Ethene Interacting with Single Molecules of

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