Dimol Emission of Oxygen Made Possible by Repulsive Interaction

Letter pubs.acs.org/JPCL

Dimol Emission of Oxygen Made Possible by Repulsive Interaction Attila Tajti,*,† György Lendvay,*,‡ and Péter G. Szalay† †

ELTE Eötvös Loránd University, Laboratory of Theoretical Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary Institute of Materials and Environmental Chemistry, Research Centre for Natural Sciences of the Hungarian Academy of Sciences, Magyar tudósok körútja 2., 1117 Budapest, Hungary

‡

S Supporting Information *

ABSTRACT: For the energy emitted in a textbook example of chemiluminescence, the peculiar red light produced by singlet molecular oxygen is about twice that of the spinforbidden O2(a1Δg) → O2(X3∑−g ) transition. Theoretical studies suggest that the O2(a1Δg)−O2(a1Δg) van der Waals interaction is weak, and at room temperature no long-lived complex is formed. Our high-level ab initio calculations show that in the bound domain of the dimer, the oscillator strength is very small, but increases at smaller intermolecular separations, where, however, the interaction is repulsive. We propose that the emission is induced by collisions: it takes place “on-the-fly”, when the collision energy allows the system to access the repulsive part of the potential energy surface where the oscillator strength is relatively large. The contribution of different orientations of the two O2 molecules to the emission has been evaluated with a simple semiclassical model. The position of the emission peak is in accord with the experiment, and the estimated rate coefficient of collision-induced emission averaged over orientation is in reasonable agreement with the measurements.

T

which also require the determination of the concentration of the transient O2(a1Δg)were reported recently by Zagidullin et al.11,12 The theoretical investigations performed so far mostly concerned the potential energy surfaces of the electronic states13−19 that determine the geometry and binding energy of the dimer complex. These studies showed that the O2−O2 intermolecular potential is predominantly repulsive,19 and shows only a shallow van der Waals minimum at large intermolecular separation with very small binding energy.17 The reverse process to the dimol emission, absorption by two triplet O2 molecules is perhaps known in more detail.26−29 Already in 1973, Long and Ewing28 suggested that besides the broad absorption band observable at all temperatures, at 90 K “discrete features” also appear, which have been assigned to transitions from and to bound van der Waals pairs. Recently, Vigasin29 attempted to quantify the process and suggested a mechanism where at high temperatures (near room T) the absorption takes place during collisions (collision-induced absorption, CIA), while at low temperatures, the bound states of the complex are assumed to be responsible for absorption. In any event, the community seems to agree that both the complex and the collision induced mechanism can play a role in the absorption, depending on the temperature. In case of the emission, however, the mechanism does not seem to be proven yet. Kasha in his classic paper5 speaks about a vaguely defined “simultaneous transition” of a pair of molecules, and many authors believe that the emission comes from dimers even at room temperature.10 Billington9 argues

he red light emitted by singlet molecular oxygen is a standard textbook example of chemiluminescence,1,2 and has a long history of experimental1−12 and theoretical2,13−25 investigations. The energy of the strongest band of the emitted light is approximately twice as large as that of the vertical O2(a1Δg) → O2(X3∑−g ) transition, which is spin-forbidden. The intensity of the emission depends quadratically on the concentration of singlet excited oxygen, and the process therefore has been assigned to a simultaneous (“dimol”) transition of two singlet oxygen molecules into the singlet ground state of the complex, followed by its dissociation into two triplet oxygen molecules:2,4,5,11,12 O2 (a1Δg , ν = 0) + O2 (a1Δg , ν = 0) → 1(O2 (X3Σ−g , ν = 0) + O2 (X3Σ−g , ν = 0)) + hν

(633nm)

The process involves states corresponding to the 1πg2 configuration of the O2 molecule: the (X3∑−g ) ground state and the (a1Δg) excited state. The states of the (O2)2 complex arise from the combination of these molecular states. Certain excited state combinations (see Section 1 of the Supporting Information) are degenerate at infinite separation; the degeneracy breaks up when the two molecules start to interact. Depending on the orientation, some components can have a nonzero transition moment to the ground state. Since the emission starts from short-lived excited species and requires the intermolecular interaction of two systems in which the corresponding transitions are forbidden individually, the signal is very weak and relatively hard to study experimentally.1,2 The spectral characteristics, the band position and shape, along with their temperature dependence, were recorded long time ago,6,8,9 while the corresponding rate constants © XXXX American Chemical Society

Received: May 19, 2017 Accepted: July 5, 2017 Published: July 5, 2017 3356

DOI: 10.1021/acs.jpclett.7b01256 J. Phys. Chem. Lett. 2017, 8, 3356−3361

Letter

The Journal of Physical Chemistry Letters

Figure 1. MR-CISD+QP total energies (E axis, solid lines) and Einstein A coefficients of the (a1Δg + a1Δg)i → (X3∑−g + X3∑−g ) transitions (A axis, dotted lines) as a function of the distance between the centers of mass R, in various orientations. The arrows mark the average location of the van der Waals minimum. Data for the collinear arrangement are not shown, because the Einstein coefficients are identically zero.

routinely used in the literature,13−19 with the O−O intramolecular bond distance fixed at the experimental value of 1.2179 Å30 (see Figure S1, Supporting Information, for an illustration). In Figure 1, the asymptotically corrected ab initio potential curves and Einstein A coefficients are shown for the various orientations. Regardless of the arrangement and the electronic state, the potential energy curves at first glance look repulsive, with no obvious minimum. Closer investigation, however, shows that shallow van der Waals minima do exist in all orientations, and at a given orientation they are located at essentially the same R for all four (a1Δg + a1Δg) states (see marks in the figures). The characteristics of these minima are shown in Table S1 of the Supporting Information. The potential wells are at large intermolecular distances, where each manifold is essentially degenerate. The well depths are between 10 and 228 cm−1 depending on the orientation and the state, with the rectangular and crossed systems exhibiting the most stable complexes. The minima are, nevertheless, still very shallow, and the system (at least at room temperature and above) is not likely to be trapped in the van der Waals well in any state of the (a1Δg + a1Δg) manifold. The Einstein A coefficients (dotted lines in Figure 1, numerical values in Table S1), characterizing the probability of the (a1Δg + a1Δg)i → (X3Σ−g + X3Σ−g ) spontaneous emission at the van der Waals minimum are very small (below 5 s−1), practically negligible at distances where the energy is below the asymptotic limit. (Note that typical forbidden transitions are characterized by A-values below 102 s−1.) The probability of emission steeply increases with the reduction of the intermolecular distance in the region where the repulsive intermolecular interaction becomes significant. This is accompanied, in complete agreement with the expectations, by the breakup of the 4-fold degeneracy of the excited-state energies.

that dimers would not exist above 100 K, and proposes the emission to be collision induced (CIE). However, if the emitting state is not stable, it is not trivial to explain the welldefined band structure of the spectrum. This paradox has inspired us to investigate the theoretical background of the dimer emission in the high temperature regime, taking into account that the properties of the potential energy surfaces alone are not sufficient to explain the mechanism of emission. In this paper, we present the results of high-level ab initio calculations on the singlet (a1Δg + a1Δg) states of the oxygen dimer. In addition to accurate ab initio potential energy surfaces, we also calculated transition moments, which were not known before. We use the ab initio data to estimate the rate coefficient of photon production in a semiclassical model of collision-induced emission. The investigation was carried out, following the approach of Liu et al.19 and Bussery-Honvault et al.13−18 at various orientations representative for the O2−O2 intermolecular interaction, with fixed O−O bond length. Varying the intermolecular separation, the potential energy curves corresponding to five individual electronic states (four in the singlet and one in the triplet manifold) and transition probabilities were calculated using a Multi-Reference Configuration Interaction Singles and Doubles31 method with a posteriori Pople correction for size-consistency32 (MR-CISD+QP). This method provides more accurate energies than any of the previous calculations. (For a detailed description of the employed ab initio model, see Section 2 of the Supporting Information.) First we analyze the energy and Einstein coefficient profiles for the rectangular (D2h), the “crossed” (D2d), the cistrapezoidal (denoted as C2v) with the ∠(OOO) angle fixed at 120.0°, the T-shaped, and the collinear (D∞h) arrangements 3357


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Figure 2. Simulated emission intensities (I, solid lines and filled symbols, right axis) and emission wavelengths (λ, dotted lines and open symbols, left axis) at T = 300 K, as a function of the distance between the centers of mass R, in various orientations.

pathway, taking into account the time spent at each intermolecular distance R, Boltzmann averaging over the collision energy. (The time spent in equal sections of R is determined by the instantaneous relative velocity, which comes from the initial kinetic energy E less the potential energy at R, V(R), including the centrifugal potential E·b2·R−2 arising when the collision is not head-on.) This model is formally the same as that used in radiative association of atoms,33−37 the difference being that here we are interested in the rate of emission, not in the rate of formation of a stable ground state. The rate of emission from state i is then given by ki[O2(a1Δg)]2 with

The transition probabilities show a large variation with the orientation and also change with the electronic state components. In the collinear (D∞h) arrangement, the transition probability from each (a1Δg + a1Δg) singlet state is zero due to symmetry. In the D2h (rectangular) orientation, only one state appears to be radiatively active. In the D2d (crossed) orientation, there are two active states with similar intensity, while in the lowest-symmetry C2v and T-shaped arrangements, there are three active states with different intensities. The shape of the potential curves is very similar to that characterizing the interaction of two ground-state O2 molecules, thus one can assume that the mechanism of dimol emission is similar to that of absorption. At room temperature, the population of the stationary states of the very weakly bound excited dimol can be expected to be too low to produce observable emission. On the other hand, the collision energy of two a1Δg O2 molecules is significant and allows the system to penetrate, although for a relatively short time only, the repulsive region where the emission probability is significant. The dimol emits “on the fly” when the two molecules are temporarily close enough together. In more detail, when the two a1Δg O2 molecules approach each other, they can come as close to each other as their kinetic energy can overcome the repulsive interaction. On the way in, the molecules slow down in the region where the Einstein coefficient is non-negligible, and have an appreciable chance to emit light, going down to the ground-state potential surface of the complex. (If emission does not happen on the way in, there is still chance on the way out when, being repelled, the two molecules separate again). To quantitatively evaluate the rate coefficient of the collision-induced emission, one has to integrate the emission probability along the approach-departure

⎛ 1 ⎞3/2 ki = 8 π ⎜ ⎟ σi ⎝ kBT ⎠

∫R

∞ min

∫0

∞

dE

bAi (R ) 1−

Vi (R ) E

−

b2 R2

∫0

bmax (E)

db

E1/2e−E /(kBT ) dR (1)

where [O2(a1Δg)] is the concentration of singlet oxygen, Ai(R) is the probability of light emission as determined by the Einstein coefficient, Vi(R) is the intermolecular potential energy function, b is the impact parameter, bmax(E) is the maximum impact parameter where E exceeds the maximum of Vi(R) + E·b2·R−2, and Rmin is the classical inner turning point at collision energy, E. kB and T are the Boltzmann constant and the temperature, respectively, while σi is the statistical weight factor of state i. By recording the energy of the emitted photon corresponding to every R interval during the numerical integration, and collecting the contributions of different intervals to the same wavelength, the line shape of the emission 3358


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Figure 3. Simulated emission spectra at T = 300 K, at various orientations.

Table 1. Predicted Emission Rate Constants k (in 10−23 cm3 s−1) at T = 300 K for all (a1Δg + a1Δg)i States at Various Orientations

spectrum can also be determined. To the best of our knowledge, this is the first application of the semiclassical model to actually calculate an emission spectrum. Figure 2 shows how the intensity is gathered during collisions (for details, see Section 4 of the Supporting Information and refs 36 and 37). At all orientations, the vast majority of the intensity is produced, in agreement with the qualitative picture described above, in the approximately 1.5 a0 long region on the short-distance side of the van der Waals minimum, where the emission wavelength remains in a narrow range. The rectangular and trapezoidal collisions turn out to be the most effective, while the weakest peaks are produced in the D2d orientation. This latter case differs from the rest in both the tendency of the emission wavelength and the shape of the intensity curves, which is caused by the special interaction of the π orbitals of the two perpendicular molecules. The wavelength spectra are shown in Figure 3. The location of the emission peaks well reproduces the experimental value, which is 634 nm in the gas phase at 190 K, with fwhm of about 25 nm12. The line shape is found to vary with the alignment. The D2h peak is wide and highly asymmetric, while other arrangements give sharper, yet still asymmetric peaks. Nevertheless, a well-defined, clear peak is produced in all cases, even though the transition is not bound-to-bound. The numerical values of the emission rate constants simulated using eq 1 are summarized and compared to the experiment of Zagidullin et al.11,12 in Table 1. In agreement with the simulated intensities, the predicted rate constants also show a large variation with the orientation, giving, in certain cases, zero value due to symmetry. The calculation of the emission parameters has been repeated at many orientations between the limiting cases shown above, which allowed us to estimate the overall rate constant averaged over orientations via interpolation (detailed in Section 5 of the Supporting Information). The average of the four ki’s obtained this way

D2h (rectangular) D2d (crossed) C2v (trapezoidal) T-shaped D∞h (collinear) averageda experiment a

i=1

i=2

i=3

i=4

0.00 0.00 0.00 0.22 0.00

0.00 0.12 34.05 0.00 0.00

0.00 0.10 4.62 6.91 0.00

48.70 0.00 1.51 5.48 0.00

2.00 6.72 ± 0.15b

See the Supporting Information for details. bValue from ref 11.

is also shown in Table 1. The comparison with experiment shows that the simulation predicts the overall rate constant reasonably close to the experimental value. Note that, due to the simplifications employed in the model, no perfect agreement with experiment is expected. This level of sophistication, however, provides a reliable insight into the process, and explains the emission mechanism, which was the goal of the present investigation. Our high-level ab initio calculations confirm the expectation that the emission probability increases at smaller O2−O2 separations where the interaction is mostly repulsive. The suggested CIE model indicates that the emission is made possible by the collision energy of the two O2 molecules making the emissive region energetically accessible. In the hightemperature domain, no complex is formed, but those pairs of O2 molecules that climb the repulsive wall on the potential energy surface of the excited state of the combined system emit instantaneously and land in the ground state of the complex consisting of two triplet O2 molecules. Although the transition probabilities are low, the emission is relatively strong because the colliding singlet O2 molecules slow down due to the 3359


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(5) Khan, A.; Kasha, M. Chemiluminescence Arising from Simultaneous Transitions in Pairs of Singlet Oxygen Molecules. J. Am. Chem. Soc. 1970, 92, 3293−3300. (6) Akimoto, H.; Pitts, J. N. Emission Spectra of O2 (1Δg) Trapped in Solid Oxygen at 4.2 K. J. Chem. Phys. 1970, 53, 1312. (7) Gijzeman, O. L. J. Temperature Dependence of Induced Electronic Transitions in Compressed Gaseous Oxygen. J. Chem. Phys. 1970, 52, 3718. (8) Boodaghians, R.; Borrell, P. M.; Borrell, P.; Grant, K. R. Intensities of Hot Bands in the Dimol Emissions of Singlet Molecular Oxygen. O2 (1Δg). J. Chem. Soc., Faraday Trans. 2 1982, 78, 1195− 1209. (9) Billington, A. P.; Borrell, P.; Rich, N. H. Low-temperature Spectroscopic Measurements of the ‘Dimol’ Transitions of Singlet Molecular Oxygen [O2 (a 1Δg)]. J. Chem. Soc., Faraday Trans. 2 1988, 84, 727−735. (10) Adelhelm, M.; Aristov, N.; Habekost, A. The Properties of Oxygen Investigated with Easily Accessible Instrumentation. J. Chem. Educ. 2010, 87, 40−44. (11) Zagidullin, M. V. The Rate Constants of Singlet Oxygen Collision-Induced Emission at 634 and 703 nm Wavelengths. Russ. J. Phys. Chem. B 2011, 5, 3−7. (12) Zagidullin, M. V.; Svistun, M. I.; Khvatov, N. A.; Insapov, A. S. Collision-Induced Emission of Singlet Oxygen in the Visible Spectral Region at Temperatures of 90−315 K. Opt. Spectrosc. 2014, 116, 542− 547. (13) Bussery, B.; Wormer, P. E. S. A van der Waals Intermolecular Potential for (O2)2. J. Chem. Phys. 1993, 99, 1230−1239. (14) Bussery, B. An Intermolecular Potential for (O2)2 involving O2(1Δg). Chem. Phys. 1994, 184, 29−38. (15) Bussery-Honvault, B.; Veyret, V. Comparative Studies of the Lowest Singlet States of (O2)2 Including ab Initio Calculations of the Four Excited States Dissociating into O2 (1Δg)+ O2 (1Δg). J. Chem. Phys. 1998, 108, 3243. (16) Bussery-Honvault, B.; Veyret, V. Quantum Mechanical Study of the Vibrational−Rotational Structure of [O2(3Σg−)]2 Part I. Phys. Chem. Chem. Phys. 1999, 1, 3387−3393. (17) Veyret, V.; Bussery-Honvault, B.; Ya. Umanskii, S. Quantum Mechanical Study of the Vibrational−Rotational Structure of [O2(3Σg−)]2 Part II. Phys. Chem. Chem. Phys. 1999, 1, 3395−3402. (18) Biennier, L.; Romanini, D.; Kachanov, A.; Campargue, A.; Bussery-Honvault, B.; Bacis, R. Structure and Rovibrational Analysis of the [O2(1Δg)]2←[O2(3Σg−)]2 Transition of the O2 Dimer. J. Chem. Phys. 2000, 112, 6309. (19) Liu, J.; Morokuma, K. Ab initio Potential Energy Surfaces of O2(X 3Σg−, a 1Δg, b1Σg+) + O2(X 3Σg−, a 1Δg, b1Σg+): Mechanism of Quenching of O2(a 1Δg). J. Chem. Phys. 2005, 123, 204319. (20) Hernández-Lamoneda, R.; Bartolomei, M.; Hernández, M. I.; Campos-Martínez, J.; Dayou, F. Intermolecular Potential of the O2-O2 Dimer. An Ab Initio Study and Comparison with Experiment. J. Phys. Chem. A 2005, 109, 11587−11595. (21) Dayou, F.; Hernández, M. I.; Campos-Martínez, J.; HernándezLamoneda, R. Spin-orbit Coupling in O2(ν) + O2 Collisions: I. Electronic Structure Calculations on Dimer States Involving the X 3 − Σg , a 1Δg, and b1Σg+ States of O2. J. Chem. Phys. 2005, 123, 074311. (22) Bartolomei, M.; Hernández, M. I.; Campos-Martínez, J.; Carmona-Novillo, E.; Hernández-Lamoneda, R. The Intermolecular Potentials of the O2−O2 Dimer: a Detailed Ab Initio Study of the Energy Splittings for the Three Lowest Multiplet States. Phys. Chem. Chem. Phys. 2008, 10, 5374−5380. (23) Pérez-Ríos, J.; Bartolomei, M.; Campos-Martínez, J.; Hernández, M. I.; Hernández-Lamoneda, R. Quantum-Mechanical Study of the Collision Dynamics of O2(3Σg−) + O2(3Σg−) on a New ab Initio Potential Energy Surface. J. Phys. Chem. A 2009, 113, 14952−14960. (24) Dayou, F.; Hernández, M. I.; Campos-Martínez, J.; HernándezLamoneda, R. Nonadiabatic Couplings in the Collisional Removal of O2(b 1Σg+) by O2. J. Chem. Phys. 2010, 132, 044313. (25) Carmona-Novillo, E.; Bartolomei, M.; Hernández, M. I.; Campos-Martínez, J.; Hernández-Lamoneda, R. Ab initio Rovibra-

repulsive interaction and spend a relatively long time in the emissive region. The ab initio calculations also explain why the emission occurs in a narrow wavelength range around 633 nm. The potential energy surfaces of the ground and excited states are found to be parallel in the region accessible at thermal energies. Therefore, the excitation energy hardly depends on the intermolecular distance and orientation of the colliding molecules, so that the emission wavelength is more or less constant at a larger interval of intermolecular distance. As a result, the spectrum shows a relatively sharp line, the transition energy being close to twice of the excitation energy of the single molecule. Performing simulations based on this dynamical model, we found that the calculated spectra resemble the experimental one with respect to position and line shape, while the emission rate constant is also in good agreement with the measured value. From this we conclude that at around room temperature it is not the attractive interaction of the two singlet oxygen molecules that makes the emission leading to the triplet ground state possible; instead, the dimol emits light when the interaction is in fact repulsive. The proposed model might provide an explanation to other chemiluminescence events involving singlet oxygen.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b01256. Overview of electronic states, electronic structure methods, characteristics of the van der Waals minima, parameters of the CIE simulation, method used for simulating wavelength spectra and for rate constant averaging (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*(A.T.) Phone: +36 1 372 2931; E-mail: [email protected]. *(G.L.) Phone: +36 1 382 6508; E-mail: lendvay.gyorgy@ttk. mta.hu. ORCID

Attila Tajti: 0000-0002-7974-6141 György Lendvay: 0000-0002-2150-0376 Péter G. Szalay: 0000-0003-1885-3557 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge support by OTKA (Grant Nos. F72423 and K108966) and by the Government of Hungary (Grant No. VEKOP-2.3.2-16-2017-00013, G.L.).

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REFERENCES

(1) Schweitzer, C.; Schmidt, R. Physical Mechanisms of Generation and Deactivation of Singlet Oxygen. Chem. Rev. 2003, 103, 1685− 1757. (2) Adam, W.; Kazakov, D.; Kazakov, V. Singlet-Oxygen Chemiluminescence in Peroxide Reactions. Chem. Rev. 2005, 105, 3371− 3387. (3) Khan, A.; Kasha, M. Physical Theory of Chemiluminescence in Systems Evolving Molecular Oxygen. J. Am. Chem. Soc. 1966, 88, 1574−1576. (4) Krishna, V. G. Simultaneous and Induced Electronic Transitions in Oxygen. J. Chem. Phys. 1969, 50, 792. 3360


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Dimol Emission of Oxygen Made Possible by Repulsive Interaction

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