ORIGINAL PAPER

Ab initio study of the structures and electronic states of small neutral and ionic DABCO – Arn clusters Kevin Mathivon & Roberto Linguerri & Majdi Hochlaf

Received: 4 October 2013 / Accepted: 3 January 2014 / Published online: 20 February 2014 # Springer-Verlag Berlin Heidelberg 2014

Abstract In the present theoretical work, we investigated the stationary points (minima and transition states) on the ground state potential energy surfaces of neutral and ionic 1,4diazabicyclo[2.2.2]octane (DABCO) – Arn0,+1 (n=1–4) clusters. As established in our systematic work on DABCO – Ar cluster (Mathivon et al., J Chem Phys 139:164306, 2013), the (R)MP2/aug-cc-pVDZ level is accurate enough for validating the prediction of stable forms. For n = 1 and 2, further computations at the MP2/aug-cc-pVTZ level confirm these assumptions. We show that some of the already known isomers of these heteroclusters derived using lower levels of theory are not realistic. More interestingly, our work reveals that DABCO is subject to slight deformations when binding to a small number of Ar atoms. Moreover, we computed the potential energy surfaces of the lowest singlet electronic states of DABCO – Arn (n=1–3) and of DABCO+ – Arn (n=1–3), and the transition moments for the Sp (p=1–3) ← S0 neutral transitions. These electronic states are found to be Rydberg in nature. The shape of their potentials is mainly repulsive with slight stabilization in the S2 potentials. Finally, the effects of microsolvation of DABCO in Ar clusters in ground and electronic excited states are discussed. The photophysical and photochemical dynamics of these electronic states may be complex.

Keywords Ab initio calculations . Electronic states . Potential energy surfaces . van der Waals interactions Electronic supplementary material The online version of this article (doi:10.1007/s00894-014-2135-6) contains supplementary material, which is available to authorized users. K. Mathivon : R. Linguerri : M. Hochlaf (*) Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France e-mail: [email protected]

Introduction The present theoretical investigations treat the 1,4diazabicyclo[2.2.2]octane (an azabicyclooctane) – Arn (n small) clusters (denoted hereafter as DABCO – Arn) as a case study for microsolvation of molecules in ground or electronically excited states in non-polar solvents (e.g., rare gas clusters or cold matrices). In the literature, there are mainly two theoretical works dealing with spectroscopy and structures of ground state DABCO – Arn: (i) Back in 1993, Shang et al. [1] determined the ground state minimum geometry of such clusters using a Lennard-Jones (6–12) potential to model the atom-molecule van der Waals (vdW) interaction. These authors identified the binding sites for DABCO – Arn (n=1,2,3) (cf. Fig. 9 of ref. [1]). They found structures where Ar is in front of the (CH2)2 branches and/or on top of the N atoms. As discussed in ref. [2], the latter structure is unphysical because of the non-bonding nature of the Ar orbitals and the nitrogen lone pair. More surprisingly, the binding energies associated with these Ar locations are the largest. The origin of such inconsistencies resides on the parameters used to model the vdW interactions which were calibrated for DABCO – Ar and may not be suited for DABCO – Arn (n≥2) [1, 3]. For these reasons, accurate ab initio computations are needed to correctly describe structural and energetic properties of DABCO – Arn (n≥2) clusters; (ii) in 2004, Belcher et al. [4] performed RMP2/cc-pVDZ calculations on these heteroclusters. For DABCO – Ar2, the isomer with argon atoms in equivalent halfway equatorial (face) locations between two adjacent (CH2)2 bridges is found to be the most stable, hence invalidating Shang et al. findings. For DABCO – Ar3 complex, a C2v structure in which all three Ar atoms bind to the same side of the DABCO framework is computed as the most stable, instead of the D3h structure where the three argons are in equatorial position.

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The Ar – Ar interaction potential depth (99.2 cm−1 [5, 6]) is of the same order of magnitude as the Ar – DABCO potential (∼ 300 cm−1 [2]), so there is a competition between Ar – Ar (leading to C2v cluster structures) and Ar – DABCO bonding (resulting in D3h structures). As detailed in our systematic studies on DABCO – Rg (Rg=rare gas) [2], MP2 is accurate enough to account for these subtle effects and represents a good compromise between accuracy and computational cost. Experimentally, Bernstein and co-workers [1, 3], Parker and co-workers [7] and Cockett and co-workers [4] investigated the DABCO – Arn (small n) by means of two color (1+ 1) mass resolved excitation spectroscopy (MRES), (1+1) resonance enhanced multi-photon ionization (REMPI) and a combination of (1+1′) resonance enhanced multiphoton ionization (REMPI) and zero electron kinetic energy (ZEKE) spectroscopy techniques, respectively. These works give an insight into the lowest electronic states of these heteroclusters. Mostly, they show that the electronic excited states of these species are Rydberg in nature as it is well established for the bare molecule [8–14], where the S1 state corresponds to the promotion of the outermost DABCO valence electron into the 3s molecular orbital (MO). The analysis of these spectra reveals that the measured spectral shifts for the DABCO – Ar, DABCO – Ar2, and DABCO – Ar3 complex band origins are 106, 208, and 302 cm−1, respectively, where the band origin in each case is the redmost band, regardless of intensity. These spectral shifts reflect the binding energies of the corresponding species. The additivity of these shifts/binding energies strongly suggests that each argon atom binds in an energetically equivalent site relative to the DABCO solute. A priori, the C2v structure previously proposed for DABCO – Ar3 does not account for these observations since the three Ar atoms are not equivalent. In addition, Shang et al. [3] proposed empirically the shape of the S1 state of azabicyclooctanes, which is viewed to be less deep than the ground state potential because of the repulsion of the Ar atomic orbital and the diffuse 3s MO of DABCO. In summary, a large amount of information is available on the ground states of the neutral and ionic DABCO – Arn (n small) complexes, and on the electronic excited states of the neutral species. The experimental data are of high quality and Table 1 Number of configuration state functions (CSFs) in CASSCF/aug-cc-pVDZ and of contracted and uncontracted CSFs in MRCI for the A1 symmetry of the C2v point group when computing the DABCO – Arn0,+1 (n=1–3) electronic states

DABCO – Ar DABCO – Ar2 DABCO – Ar3 DABCO – Ar+ DABCO – Ar2+ DABCO – Ar3+

the resulting spectra are highly resolved. Nevertheless, the DABCO – Arn clusters structures were derived using either empirical formalism or low level theoretical treatments and discrepancies were found between these structures and those deduced experimentally. More generally, modern theoretical chemistry methods account correctly for the diffuse nature of the wavefunction of these vdW clusters and for electron correlation. This is mandatory for the accurate description of bonding and solvation in these species. In ref. [2], we proved that theoretical methodologies based on simple additive models are not suited for describing the DABCO – Ar long range intermonomer interaction so that one may expect the occurrence of different stable structures for DABCO – Arn clusters if larger computations are performed. Here, we use the (R)MP2/aug-cc-pVDZ approach to compute neutral and ionic DABCO – Arn (n≥ 2) structures. Through benchmarking computations with different basis sets and post Hartree-Fock ab initio methods and after comparison with the available experimental results [2], we showed that this level of theory is accurate enough to provide reliable structural and spectroscopic parameters for DABCO – Rg vdW systems. In addition, we treat the electronic excited states of DABCO – Arn (n=1–3) using configuration interaction approaches. Our data are used later for the reassignment of the experimental spectra and for discussing the solvation effects of DABCO embedded into Ar clusters or into cold Ar matrices.

Computational details The aug-cc-pVDZ and the aug-cc-pVTZ basis sets were used for the description of H, C, N, and Ar atoms [15–17]. The stationary points on the ground potential energy surface of the neutral and ionic DABCO – Arn (n=1–4) clusters were characterized using the GAUSSIAN09 [18] program suite, in the C1 molecular point group. These computations were done at the Møller Plesset (R)MP2 level [19–21] using the standard options as implemented in GAUSSIAN09 program. We deduced hence the geometrical parameters and the harmonic frequencies.

CASSCF

MRCI

Number of CSFs

Number of uncontracted CSFs

Number of contracted CSFs

107,751 107,751 42,746 107,436 107,436 84,992

9,499,364 8,531,188 6,373,570 6,801,544 6,604,508 19,662,992

1,967,975 1,264,245 2,093,067 1,035,100 971,513 1,872,284

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For mapping the electronic states of DABCO – Arn (n=1– 3), we used the MOLPRO program suite [22]. The onedimensional cuts of the potential energy surfaces (PESs) of these states are computed using the complete active space selfconsistent field (CASSCF) approach [23, 24] followed by the internally contracted multi-reference configuration interaction (MRCI) method [25, 26]. These computations were done in the C2v point group. In CASSCF, the electronic states were Fig. 1 Optimized structures of neutral and ionized DABCO – Arn complexes (n=1–4). We give the front and top views. For DABCO – Ar0/+, we quoted the structures from ref. [2]

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averaged together with equal weights using the MOLPRO state averaging procedure. Several tests were done in order to identify an optimum active space for an accurate description of the lowest singlet electronic states (S0 up to S4). For C2v symmetry, the good compromise (computational cost vs. accuracy) corresponds to the inclusion of all molecular orbitals (MOs) from HOMO-2 to LUMO+2 per C2v irreducible representation. The lowest MOs are kept frozen. The CASSCF

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vectors are constructed using all configuration state functions (CSFs) obtained from excitations of all active electrons in

these orbitals. For illustration, we list in Table 1 the number of considered CSFs of A1 symmetry in C2v point group. Later

Table 2 Main geometrical parameters (distances in Å and angles in degrees), total (E, in hartree) and relative energies (Er, in cm−1) of the neutral and cationic DABCO - Arn complexes (n=2–4) obtained at the

(R)MP2/aug-cc-pVDZ level of theory. Ri corresponds to the distance between the center of mass of DABCO and the ith Ar atom. See Fig. 1 for the definition of the structures

Distances

Angles

E

Er

DABCO – Ar2 N-C FORM I TS

1.478 2.600 1.562 1.103 4.775 4.562

C-N- N-C- N-C-H (a) C C 108.2 110.3 107.5

FORM II TS

1.478 2.601 1.562 1.103 4.335 4.638

108.2 110.4 107.4

108.2

FORM III MIN

1.477 2.600 1.564 1.103 5.920 5.550

108.4 110.5 107.7

107.7

FORM III (deformed) MIN FORM IV TS

1.478 2.601 1.563 1.103 4.757 4.321

108.3 110.4 107.5

108.1

1.478 2.601 1.564 1.103 4.272 4.272

108.4 110.5 107.7

107.7

FORM IV (deformed) MIN FORM V MIN

1.478 2.601 1.563 1.103 4.296 4.296

108.3 110.5 107.5

108.0

1.478 2.600 1.563 1.103 4.761 4.761

108.2 110.3 107.5

108.2

1.442 2.478 1.636 1.098 4.683 4.197 1.442 2.478 1.636 1.098 4.197 4.197 1.441 2.477 1.637 1.098 4.685 4.685

111.8 107.0 110.2 111.8 107.0 110.2 111.9 107.0 110.3

DABCO+ – Ar2 FORM III MIN FORM IV MIN FORM V TS DABCO – Ar3

N-C FORM I MIN FORM II TS FORM III TS FORM III (deformed) MIN DABCO+ – Ar3 FORM I MIN FORM II MIN FORM III MIN DABCO – Ar4

FORM I MIN FORM II TS FORM III TS FORM IV TS DABCO+ – Ar4 FORM I MIN FORM II MIN FORM III TS FORM IV TS a

N-N

C-C

N-N

C-C

H-C

H-C

R1

R1

R2

R2

R3

−1398.235754 −1398.685262a −1398.232458 −1398.682514a −1398.235677 −1398.685269a −1398.236084 −1398.685708a −1398.236099 −1398.685713a −1398.235319 −1398.684878a

75.7 73.5a 798.9 521.5a 92.6 72.3a 3.2 1.0a 0.0 0.0a 171.2 136.1a

110.2 110.2 110.3

−1397.986952 −1397.987794 −1397.986134

184.8 0.0 364.4

N-C-H (b) 107.7 107.7 107.7

−1925.194255 −1925.192847 −1925.194500

57.1 366.2 3.4

1.478 2.602 1.564 1.103 4.289 4.289 4.289 1.477 2.598 1.564 1.103 4.748 4.748 4.748 1.478 2.600 1.564 1.103 4.268 4.268 4.709 1.478 2.601 1.563 1.103 4.303 4.303 4.710

108.4 110.5 107.5

108.0

−1925.1945160 0.0

1.442 2.478 1.635 1.098 4.197 4.197 4.197 1.442 2.477 1.636 1.098 4.685 4.685 4.685 1.442 2.478 1.636 1.098 4.191 4.191 4.654

111.8 107.0 110.2 111.9 107.0 110.2 111.8 107.0 110.2

110.2 110.2 110.2

−1924.947262 −1924.944761 −1924.947147

0.0 549.0 25.3

N-CC 110.5 110.5 110.5 110.3

N-C-H (a) 107.7 107.7 107.7 108.1

N-C-H (b) 107.7 107.7 107.7 107.5

−2452.152687 −2452.151819 −2452.1515185 −2452.150228

0.0 190.4 256.5 539.6

107.0 107.0 107.1 107.1

110.2 110.2 110.1 110.2

110.2 110.2 110.1 110.2

−2451.906605 −2451.905003 −2451.905341 −2451.902866

0.0 351.6 277.3 820.5

N-N

C-C

H-C

R1

R2

R3

R4

1.478 1.477 1.477 1.477

2.600 2.598 2.599 2.597

1.564 1.564 1.564 1.563

1.102 1.103 1.103 1.103

4.266 4.238 4.260 4.749

4.266 4.751 4.260 4.749

4.266 4.751 4.260 4.749

4.709 4.751 4.794 4.794

C-NC 108.4 108.4 108.4 108.3

1.442 1.442 1.441 1.441

2.478 2.477 2.477 2.476

1.535 1.536 1.635 1.636

1.098 1.098 1.098 1.098

4.190 4.165 4.203 4.681

4.190 4.684 4.203 4.681

4.190 4.684 4.203 4.681

4.653 4.684 4.608 4.609

111.8 111.8 111.8 111.8

Computed at the MP2/aug-cc-pVTZ level

N-C-H (a) 107.7 107.7 107.7

−1398.235255 185.2 −1398.684871a 137.2a

C-NC 108.4 108.5 108.4

N-C

N-CC 110.6 110.5 110.5

N-C-H (b) 108.2

J Mol Model (2014) 20:2135 Table 3 Counterpoise corrected binding energies (BE) of some DABCO0,+1 – Arn (n=2,3) clusters. We also give the contributions of the fragments to the basis set superposition error (BSSE). All values are in cm−1

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BSSE from DABCO

BSSE from Arn

Total BSSE

BE

DABCO – Ar2 FORM I DABCO – Ar2 FORM II DABCO – Ar2 FORM III DABCO – Ar2 FORM III (deformed) DABCO – Ar2 FORM IV

177 186 53 192 213

432 484 137 471 525

608 670 191 663 738

393 434 252 443 498

DABCO – Ar2 FORM IV (deformed) DABCO – Ar2 FORM V DABCO+ – Ar2 FORM III DABCO+ – Ar2 FORM IV DABCO – Ar2+ FORM V DABCO – Ar3 FORM I DABCO – Ar3 FORM II DABCO – Ar3 FORM III DABCO – Ar3 FORM III (deformed) DABCO+ – Ar3 FORM I DABCO+ – Ar3 FORM II DABCO+ – Ar3 FORM III

204 186 211 218 203 318 286 315 301 328 302 324

522 426 525 592 463 781 648 793 791 894 700 876

725 612 736 810 666 1,099 934 1,108 1,092 1,222 1,002 1,200

489 407 909 1,017 799 763 622 666 651 1,517 1,193 1,369

on, we used the CASSCF wavefunctions to deduce the transition moments for the Sp (p=1–3) ← S0 transitions. In MRCI, only the configurations of the CASSCF wavefunction with coefficient modulus larger than 0.05 were included in the reference vector. Table 1 gives the number of contracted and uncontracted configurations when computing the DABCO – Arn states (for the A1 symmetry). We also computed the D0 ground state potential of DABCO – Arn+ (1 – 3) following the same methodology.

Structures of DABCO0,+1 – Arn (n=1–4) The stationary points on the ground state PESs of DABCO – Ar and DABCO – Ar+ are detailed in ref. [2]. They are Fig. 2 CASSCF/MRCI/aug-ccpVDZ one-dimensional cuts of the lowest singlet electronic excited states of DABCO – Ar along the R coordinate. We give also the ionic D0 potential. The reference energy is the ground state potential energy minimum. See text for more details

collected in Fig. 1. Briefly, neutral DABCO – Ar and DABCO – Ar+ possess two minimal structures (MIN, denoted as position 1 and position 3) and one transition state (TS, denoted as position 2). The minima correspond to Ar binding DABCO in the σh plane of the isolated DABCO molecule whereas TS is when Ar is located along the DABCO C3 axis. For neutral and cationic DABCO – Arn (n=2–4) clusters, the (R)MP2/aug-cc-pVDZ optimized structures are presented in Table 2 and Fig. 1. We give as Supplementary material the full set of harmonic frequencies [27]. Generally, it appears that the optimized geometries for the DABCO unit are very close for all systems and depend slightly on the number of Ar atoms. For DABCO – Ar2 clusters, we located four MINs and three TSs. Further computations at the MP2/aug-cc-pVTZ level were done. The results are included in Table 2. They

DABCO–Ar POSITION 1

DABCO–Ar POSITION 3

2135, Page 6 of 10 Fig. 3 CASSCF/MRCI/aug-ccpVDZ one-dimensional cuts of the lowest singlet electronic excited states of DABCO-Ar2 along the R coordinate. We also give the ionic D0 potential. The reference energy is the ground state potential energy minimum. See text for more details

J Mol Model (2014) 20:2135 DABCO–Ar2 FORM III

confirm the results obtained using MP2/aug-cc-pVDZ. Indeed, the most stable form (FORM IV (deformed)) corresponds to both argons binding in the σh plane of a slightly distorted DABCO. This agrees with the additivity of binding energies vs. the increase of number of argons as suggested previously. In TS (FORM IV, 3.2 cm−1 higher in energy) DABCO recovers the D3h symmetry. In FORM III, FORM III (deformed) and FORM V, which are also equilibrium structures, both argons are in the σh plane and at least one of the Ar atoms lies in front of a (CH2)2 branch. In FORM I and FORM II (TSs), one of the argon atoms binds in the DABCO equatorial plane, whereas the second Ar lies along the CC bond line of a (CH2)2 branch. For DABCO+ – Ar2, only FORM III and FORM IV correspond to a MIN with the latter being the most stable. FORM V turns out to be a TS. For all ionic structures, the bare molecule belongs to the D3h group. The existence of three structures for DABCO – Ar2 was already suggested by Shang et al. [1] after analysis of their two

Fig. 4 CASSCF/MRCI/aug-ccpVDZ one-dimensional cuts of the lowest singlet electronic excited states of DABCO-Ar3 along the R coordinate. We also give the ionic D0 potential. The reference energy is the ground state potential energy minimum. See text for more details

DABCO–Ar2 FORM IV

color, 1+1, mass resolved excitation spectra. The LennardJones (6–12) potential modelizations by Shang et al. [1] lead to three isomers, where the most stable has an Ar - N vdW bond. This is not supported by our calculations since this position of Ar corresponds to a TS regardless of the number of argons around DABCO (cf. ref. [2] and Table 2). According to their model, FORM III is the least stable calculated geometry. In 2004, Belcher et al. [4] performed MP2/cc-pVDZ computations that support FORM IV as the most stable. In contrast, we find that FORM IV is a TS, which connects to FORM IV (deformed). Both Shang et al. [1] and Belcher et al. [4] used their theoretical results to assign their experimental spectra, that need hence to be reassigned in light of our more reliable theoretical results. DABCO – Ar2 experimental spectra exhibit an extended vibrational progression with divergent energy level spacings. The most intense band appears ∼6 cm−1 to the blue of the nominal band origin. The proposed assignment to a vdW

DABCO–Ar3 FORM I

DABCO–Ar3 FORM III

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fundamental would then suggest a significant geometry change along this intermolecular coordinate in accordance with the Franck–Condon principle. Nevertheless, the lowest vibrational mode of DABCO – Ar2 FORM IV (deformed) complex lies at ∼19 cm−1 [27]. As discussed for DABCO – Ar [2], anharmonic effects would not reduce this harmonic frequency by 50 % for such a heavy atom system. Instead, we believe that this first band is due to splitting of the ground vibrational level due to tunneling as in DABCO – Ar [2]. The upper bands correspond to excitation of the vdW modes as suggested in [1, 4]. For DABCO – Ar3, two MINs and two TSs are found. For all forms, the three argons are located in the σh plane. The most stable isomer has three argon binding DABCO from the same side and a deformed DABCO. It is followed by a TS (FORM III). At 57 cm−1 higher in energy, we found FORM I (of D3h symmetry) where the three argons are in between the (CH2)2 branches. Both minima are connected to a second TS (FORM II) where the argons are in front of the (CH2)2 branches. FORM I is the most stable because of the stabilization induced by forming Ar – Ar bonding. Nevertheless, the difference in energy between the two minimal energy structures is relatively small. For DABCO – Ar3+ ion, FORM I, FORM II, and FORM III correspond to minima in the ground doublet potential. Our results invalidate the structures of Shang et al. [1] (most likely because of the unsuited parameters used for Ar) and possibly close the debate on the open question of Cockett and coworkers [4]. Experimentally, the one photon two color (1+1) MRES, ZEKE, and REMPI spectra of DABCO – Ar3 consist of relatively long vibrational progressions. The first excited band (at 10 cm−1) was assigned erroneously to the low vdW bending, which is computed ∼22 cm−1 [27]. This band corresponds again to tunneling splitting as discussed for DABCO – Ar and DABCO – Ar2.

MO

HOMO

LUMO (3s)

For DABCO – Ar4 cluster, a unique stable form is located (FORM I), where all argons are in the σh plane: three of them are equivalent and the fourth one is relatively far away from the DABCO center of mass (Table 2). Better saying, the first set of argons is located on the first shell of solvation whereas the second set (fourth Ar) is located on the second shell. We also compute three TSs. For these TSs, the fourth argon added to DABCO – Ar3 corresponds to positions providing mostly TS structures for DABCO – Arn (n=1,2,3), i.e., either on top of a nitrogen atom or in front of a (CH2)2 branch. For DABCO – Ar4+ ion, FORM I turns out to be the most stable. In addition, FORM II is also a minimum. Two TSs (FORM III and FORM IV) are calculated. We list in Table 3 the counterpoise corrected binding energies (BE) and the contributions of the fragments to the basis set superposition error (BSSE) of DABCO0,+1 – Arn (n=2,3) clusters. For DABCO – Ar, we showed in ref. [2] that binding one argon to DABCO results in ∼300 cm−1 stabilization. For the most stable forms, this table reveals that there is additivity of BEs when the number of Ar increases. Indeed, for neutral DABCO – Ar2 FORM IV (deformed), we compute a BE∼ 490 cm−1 (i.e., ∼ 250 cm−1 per Ar). This agrees well with the additivity of BEs and of the spectral shifts observed experimentally. Finally, the analysis of Table 3 data shows that the contribution of BSSE (either from DABCO or from Arn) to BE is quite large and cannot be omitted to derive accurate potentials for such species. This is not surprising because of the van der Waals/ charge transfer nature of bonding in these complexes. Generally, our systematic work on the DABCO – Arn (n≤ 4) shows that DABCO undergoes changes by binding one, two and three argons in the first solvation shell and that the fourth rare gas atom is positioned on the second solvation shell. For DABCO – Arn (n≥5) complexes, the added argons

LUMO (3pz)

LUMO (3px)

LUMO (3py)

DABCO

DABCO-Ar3 FORM I

Fig. 5 MOs of DABCO and of DABCO – Ar3 Form III isomer obtained at the HF/aug-cc-pVDZ level. We give also the structure of the molecular species considered here. The C3 and y axes coincide with the N-N axis and the argon atoms are located in the xz plane

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Fig. 6 CASSCF/aug-cc-pVDZ one-dimensional evolution of the transition dipole moments between the S0 and Sp (p=1–3) states of DABCO – Arn (n=1–3) along the R coordinate. See text for more details

DABCO – Ar Position 1

DABCO – Ar Position 3

DABCO – Ar2 FORM III

DABCO – Ar2 FORM IV

DABCO – Ar3 FORM I

DABCO –Ar3 FORM III

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will perturb slightly the bare molecule. Therefore, DABCO – Arn (n≤2–3) heteroclusters represent models of DABCO adsorbed on the surface of Ar matrices or large Ar clusters. Whereas DABCO – Arn (n=3, 4) are a model of DABCO embedded into large Ar clusters or into cold matrices.

Electronic excited states of DABCO - Arn (n=1,2,3) Figures 2, 3, and 4 display the CASSCF/MRCI/aug-cc-pVDZ one-dimensional cuts of the PESs of the lowest singlet electronic states (S1, S2, S3, and S4) of some DABCO – Arn (n= 1–3) structures. These curves are obtained by lengthening symmetrically the R coordinate, which corresponds to the distance between the center of mass of DABCO and the Ar atoms. We also give the potential of the corresponding ionic forms (D0). The vertical position of these curves is off by less than 0.2 eV when compared to experimental results. They should be shifted accordingly if one needs to use them to assign highly resolved experimental spectra. The vertical thin lines highlight the middle of the Franck-Condon region accessed from the corresponding ground state potentials. These figures show that the parts of the potentials of S1 of DABCO – Ar3 FORM I present a shallow potential well in the Franck–Condon region accessed after vertical excitation from the corresponding ground state, whereas the S1 potential of DABCO – Ar3 FORM III is repulsive. For DABCO – Ar1,2,3 complexes, we compute S2 potentials with a slight stabilization (shallow potential well). The S3 and S4 states are repulsive. For the ionic potentials, a relatively deep potential well is calculated. The lowest excited states S1, S2, S3, and S4 of DABCO wavefunctions are dominantly described by the promotion of one electron from the HOMO into the LUMO (3s), LUMO (3px), LUMO (3py), and LUMO (3pz) MOs as displayed in Fig. 5. As stated in the literature [8–14], these states are mainly Rydberg in nature. The situation remains similar when clustering the argon atoms to DABCO. For illustration, we display in Fig. 5 the DABCO – Ar3 MOs. This figure shows that the interaction of DABCO 3s and 3py MOs with Ar 3s atomic orbital is mainly anti-bonding in nature. It results a priori into repulsive potentials along the DABCO – Ar intermonomer distance. Whereas the interaction between 3px and 3pz MOs and the 3s orbital of Ar may lead to a slight stabilization and hence to a potential well along the R coordinate. This simple picture is in good agreement with the one-dimensional cuts of the lowest electronic states of DABCO – Arn (n=1–3) given in Figs. 2, 3, and 4. Our findings are in line with previous considerations [1, 3, 4]. Figure 6 presents the evolution along R of the CASSCF/ aug-cc-pVDZ transition dipole moments between the ground state of DABCO – Arn (n=1–3) and their corresponding lowest singlet states. As expected, they converge to the

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transition moments of the isolated molecule for large R. For short R, some elements present a non-monotonic evolution, whereas the others are either constant or evolve monotonically. As suggested by Cockett and coworkers [4], a weak oscillator strength to the S1 band origin is computed here for DABCO – Ar. This may explain their failure of recording any appreciable ZEKE signal for this cluster. Moreover, one can clearly see that a crossing exists between the slightly bound S2 potential and the repulsive S3 potential for some clusters and especially when the number of argons surrounding the bare molecule increases. This crossing occurs not far from the Franck-Condon region accessed by electronic excitations from S0. Therefore, the wavepacket dynamics on the S1-S4 potential energy surfaces should be complex. It depends a priori on the environment around DABCO. As mentioned above, these findings can easily be extended to [email protected] (n large) (See [28]).

Conclusions We present an ab initio study of the equilibrium and TS structures of neutral and ionic DABCO – Arn0,+1 (n=1–4) clusters. Our work reveals that some of the structures already known for these systems in the literature are not realistic. In addition, we show that DABCO undergoes slight deformations when surrounded by a small number of argon units and that the first solvation shell is filled by three Ar surrounding DABCO. In addition, we investigated the lowest singlet electronic states of DABCO-Arn (n=1–3). Accordingly, non-polar solvent induced photophysics and photochemistry of the (2p3s) Rydberg state of this diazabicyclooctane may be complex because of the special shapes of the singlet potentials. This is confirmed by the recent experimental investigation of the spectroscopy and the dynamics of the DABCO molecule deposited in an Ar cluster [28]. More generally, our findings may be extended to qualitatively interpret the spectroscopic and dynamical studies of DABCO molecules embedded into large Ar clusters or cold Ar matrices. Using similar methodology, we showed recently that multi charged ions (MCIs) [29] may react with Ar matrices resulting in an increasing number of covalent bonds with the MCI charge. Here we prove that Ar clusters and matrices may perturb the bare molecules so that they cannot be considered as intact (because of the highlighted deformations). μw or farIR spectroscopies of the bare molecules in these environments should help in probing their complex low frequency spectra. Acknowledgments We would like to thank Lionel Poisson (LFP, CNRS/CEA, France) for useful discussions. This research was supported by a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Program under Grant No. PIRSES-GA-2012-31754, the COST Action CM1002 CODECS.

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References 1. Shang QY, Moreno PO, Li S, Bernstein ER (1993) J Chem Phys 98: 1876 2. Mathivon K, Linguerri R, Hochlaf M (2013) J Chem Phys 139: 164306 3. Shang QY, Moreno PO, Dian C, Bernstein ER (1993) J Chem Phys 98:6769 4. Belcher DE, Watkins MJ, Tonge N, Cockett MCR (2004) J Chem Phys 120:7894 5. Tao F-M, Pan YK (1994) Mol Phys 81:507 6. Patkowski K, Murdachaew G, Fou C-M, Szalewicz K (2005) Mol Phys 103:2031 7. van den Hock G, Consalvo D, Parker DH (1993) J Reuss Z Phys D 27:73 8. Boogaarts MGH, Holleman I, Jongma RT, Parker DH, Meijer G (1996) J Chem Phys 104:4357 9. Parker DH, Avouris P (1979) J Chem Phys 71:1241 10. Fujii M, Ebata T, Mikami N, Ito M (1984) J Phys Chem 88:4265 11. Consalvo D, Drabbels M, Berden G, Leo Meerts W, Parker DH (1993) J Reuss Chem Phys 174:267 12. Fujii M, Ebata T, Mikami N, Ito M (1983) Chem Phys Lett 101:578 13. Poisson L, Maksimenska R, Soep B, Mestdagh J-M, Parker DH, Nsangou M, Hochlaf M (2010) J Phys Chem A 114:3313 14. Boguslavskiy AE, Schuurman MS, Townsend D, Stolow A (2011) Faraday Discuss 150:419 15. Dunning TH (1989) J Chem Phys 90:1007 16. Kendall RA, Dunning TH, Harrison RJ (1992) J Chem Phys 96:6796 17. Woon DE, Dunning TH (1993) J Chem Phys 98:1358 18. Gaussian 09, Revision A.02, Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery Jr.

19. 20. 21. 22.

23. 24. 25. 26. 27.

28.

29.

JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam, NJ, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian, Inc., Wallingford, CT Møller C, Plesset MS (1934) Phys Rev 46:618 Curtiss LA, Redfern PC, Raghavachari K, Rassolov V (1999) J A Pople J Chem Phys 110:4703 Knowles PJ, Andrews JS, Amos RD, Handy NC (1991) J A Pople Chem Phys Lett 186:130 Werner H-J, Knowles PJ, Knizia G, Manby FR, Schütz M, Celani P, Korona T, Lindh R, Mitrushenkov A, Rauhut G, Shamasundar KR, Adler TB, Amos RD, Bernhardsson A, Berning A, Cooper DL, Deegan MJO, Dobbyn AJ, Eckert F, Goll E, Hampel C, Hesselmann A, Hetzer G, Hrenar T, Jansen G, Köppl C, Liu Y, Lloyd AW, Mata RA, May AJ, McNicholas SJ, Meyer W, Mura ME, Nicklaß A, O’Neill DP, Palmieri P, Pflüger K, Pitzer R, Reiher M, Shiozaki T, Stoll H, Stone AJ, Tarroni R, Thorsteinsson T, Wang M, Wolf A (2012) MOLPRO version 2012.1. https:// www.molpro.net/ Knowles PJ, Werner H-J (1985) Chem Phys Lett 115:259 Werner H-J, Knowles PJ (1985) J Chem Phys 82:5053 Werner H-J, Knowles PJ (1988) J Chem Phys 89:5803 Knowles PJ, Werner H-J (1988) Chem Phys Lett 145:514 This supplementary material contains the full set of the optimized structures and harmonic frequencies of DABCO0,+1 - Arn (n≤4). See online version of this article for further details Awali S, Poisson L, Soep B, Gaveau M-A, Briant M, Pothier Ch, Mestdagh J-M, Ben El Hadj Rhouma M, Hochlaf M, Mazet V, Faisan S (2014) Phys Chem Chem Phys 16:516. doi:10.1039/C3CP53172D Linguerri R, Komiha N, Hochlaf M (2012) Phys Chem Chem Phys 14:4236