Marius Stroe

Magda Fifirig
email: magda.fifirig@g.unibuc.ro.

Dissociation of vibrationally excited D + 2 by electrons

Keywords: dissociative excitation, dissociative recombination, hydrogen molecular ion , multichannel quantum defect theory dissociative excitation, dissociative recombination, hydrogen molecular ion, multichannel quantum defect theory

Dissociation of vibrationally excited D2+ by electrons

Magda Fifirig, Marius

Molecular hydrogen is a major constituent of divertor plasma in tokamak reactors [START_REF] Fantz | ASDEX Upgrade Team[END_REF][2][3]. Since the performance of the core fusion plasma is influenced by the reactive collisions between plasma constituents in its outer region [4], the study of such collisions is of great importance. In the boundary regions of the magnetically confined fusion plasmas, the molecular deuterium D 2 is subject to a destruction chain consisting of the electron impact ionization into the deuterium molecular ion

D 2 + e -→ D + 2 + 2e -, (1)
followed by the dissociative excitation (DE) of the D + 2 molecular ion

D + 2 + e -→ D + D + + e -. (2)
The deuterium molecule is also implicated in the D + conversion into D + 2 by the change exchange process

D + + D 2 → D + D + 2 , (3)
followed by the D + 2 dissociative recombination (DR)

D + 2 + e -→ D + D * . (4)
Since the molecular ions formed by these collision processes are left in vibrationally excited states [5], it is expected that the vibrational levels and their population play an important role in the electron impact processes in such cold hydrogen plasma. The estimation of the particle balance [4,6] of deuterium in divertor plasma needs the rates coefficients for electron collisions with D 2 and D + 2 for various vibrational states. Experimental investigation of the electron impact dissociation of the hydrogen molecular ions is based on crossed and merged beam techniques. There are two types of merged beam equipments: single-pass merged beam apparatus and ion storage ring device. The main advantage with the storage ring experiments is that the infrared active molecular ions relax toward the vibrational ground state through emission of radiation during their storage [7][8][9]. In the case of homonuclear molecular ions a vibrational cooling can be achieved through vibrational de-excitation induced by collisions with near-zero relative energy electrons [10,11]. Most experiments were dedicated to the dissociative recombination (the principal destruction process of molecular ions in collision with slow electrons) for H + 2 and its isotopomer HD + [8,[10][11][12][13][14][15][16][17][START_REF] Krohn | Dissociative Recombination of Molecular Ions with Electrons[END_REF][START_REF] Al-Khalili | [END_REF][20][21]. Only few experimental works were focused on the D + 2 dissociative recombination [11,[16][17][START_REF] Krohn | Dissociative Recombination of Molecular Ions with Electrons[END_REF]20,22]. The experiment [16] carried out at the storage ring TARN II has emphasized that the relative population of the D + 2 ions in the vibrational ground state reached 0.9 at a storage time of 10.5 s and that the populations of the vibrational levels 2 -4 were less than 0.01 at any storage time. The vibrational level populations of the stored beams were estimated from the kinetic energy release spectrum in the dissociative recombination process at a relative energy of 0 eV using a two-dimensional imaging technique. The experiment [17] dissociative excitation and ionization in the energy range 5 -3000 eV. The vibrational population of the primary ion beam was analysed by dissociative charge exchange on a potassium target. A Franck-Condon vibrational population distribution of the D + 2 ions was found.

Most theoretical studies dedicated to the electron collision with the hydrogen molecular ion have investigated the H + 2 and HD + dissociative recombination [23][24][25][26][27][28][29][30][31][32]. In literature there are few numerical computations devoted to D + 2 dissociation by electron impact [24,31]. The first results of the DE cross sections of H + 2 , HD + and D + 2 were reported by Takagi [31] for various initial vibrational states of these molecular ions.

The cross sections and rate coefficients for the D 2 electron impact dissociation

D 2 (X 1 Σ + g ) + e -→ D * 2 (b 3 Σ + u ) + e -→ D + D + e -, (5)
at electron energies ranging from threshold to 12 eV were evaluated by Trevisan and Tennyson [33]. Note the review on the electron-scattering cross sections for elastic and inelastic processes at different electron energies for HD and D 2 molecules [34]. This paper continues a previous work [35] investigating the slow electron collision with the D + 2 molecular ion in its electronic ground state and in a low vibrational level (0 -2). Here we are focused on the D + 2 dissociation for a Franck-Condon distribution of the initial vibrational levels given by electron impact ionization of D 2 . Section 2 gives the outline of the theoretical procedure used in this work. Section 3 presents the numerical results for the DE and DR cross sections for vibrationally hot D + 2 molecular ions. The contribution of each initial vibrational level to the total DR and DE cross sections were also evaluated. The numerical results for the D + 2 dissociative recombination cross section (for the vibrational ground state) have been compared with the experimental ones [17] carried out at the Heidelberg Test Storage Ring (TSR). In the case of dissociative excitation process a comparison with the experimental results reported by Abdellahi El Ghazaly et al [20] has also been performed. Brief conclusions are given at the end.

Theoretical approach

This work investigates the dissociation of D + 2 molecular ions in the electronic ground state X 2 Σ + g in collisions with electrons. At a colliding electron energy below the dissociation threshold, the bound rovibrational levels in the Rydberg states built on the electronic ground state are involved in the electron capture leading to the neutral excited molecular system D * * 2 which dissociates. Above the dissociation threshold these rovibrational levels are not energetically accessible. Thus the influence of the rotational structure diminishes at the incoming electron energy above the dissociation threshold. Since we are focused on the energy range above the dissociation threshold, the rotational couplings are neglected here. The non-rotational approach [36,37] used in the present computations is briefly summarised here. It consists of inclusion of the vibration continua of the two lowest electronic states 1sσ g and 2pσ u as explicit ionization channels [38]. The ionization channels associated with the vibrational continua of the two electronic states correspond to states obtained by discretization of these continua.

The computations start with the evaluation of the reaction matrix K close to the reaction zone [39] characterized by short-range interactions. First, its rows and columns correspond to the arrangement of the ionization channels according to their affiliation to the ionic cores. Since the ionization channel thresholds are the successive vibrational levels or discretized levels which are ranked with respect to their energy, a permutation of the K matrix rows and columns is performed. The rows and columns of the new K matrix correspond to the natural arrangement of the ionization channels according to their energy [36].

The connexion between the interaction zone and the asymptotic one describing the motion of the external electron, is performed by a frame transformation [39] (characterized by two matrices expressed in terms of the eigenvalues and the corresponding eigenvector of the reaction matrix K) leading to the scattering matrix S [40] expressing the cross sections for dissociative recombination and excitation of molecular cations in collision with electrons.

In terms of the S matrix elements, the DR cross section (in atomic units) of the molecular cation initially in the vibrational level v, has the expression

σ DR,v (ǫ) = π 4ǫ sym,d,l ρ sym | S sym d←lv (ǫ) | 2 , (6)
where ρ sym is the multiplicity ratio between the electronic state of the neutral molecular system and the electronic state of the molecular cation. The quantity ǫ in the above equation stands for the colliding electron energy. The summation in ( 6) is achieved over all dissociative states (of the same symmetry) labeled by d, partial waves labeled by l and symmetries of the neutral molecular system contributing to the process. The DE cross section σ DE,v is the sum of two terms of type

π 4ǫ sym,l ρ sym | S sym v ′ ←lv (ǫ) | 2 , (7)
with v < v ′ . The first term corresponds to the vibrational excitation in the ground state vibrational continuum (indirect DE mechanism) with index v ′ running over all discretized levels of the ground state vibrational continuum. The other term corresponds to the vibrational excitation in the excited state vibrational continuum (direct DE mechanism) with index v ′ running over all discretized levels of the excited core vibrational continuum. By summing over all contributions of the available vibrational states of the ground electronic state, we obtain the total DE cross given by

σ DE = v σ DE,v p v , (8)
where p v is the normalized population ( v p v = 1) of the vibrational level v. Similarly, the total DR cross section can be determined. The relative contribution q v of the initial vibrational state v to the DE cross section has the expression

q v = σ DE,v p v σ DE . (9)
The relative contribution of the initial vibrational state v to the DR cross section is similarly defined. A comparison between theoretical results and experimental counterparts must take into account experimental conditions. The storage ring experiments on electron impact dissociation processes yield averaged cross sections over the electron velocity distribution. In order to simulate the experimental conditions of such experiments the theoretical cross section must be convoluted over an anisotropic Maxwell-Boltzmann electron velocity distribution [START_REF] Larsson | Dissociative Recombination of Molecular Ions[END_REF] characterized by different longitudinal T and transverse T ⊥ electron temperatures. If detuning energy exceeds the thermal velocity spread of the electron beam, the convoluted cross section σ is obtained from the rate coefficient α after dividing it by the detuning velocity v d . Starting from [START_REF] Takagi | [END_REF] the rate coefficient α at the energy ǫ can be expressed as

α(ǫ) = 2/m k(T ⊥ -T ) exp ǫ k(T ⊥ -T ) ∞ 0 dǫ ′ σ(ǫ ′ ) I(ǫ ′ , ǫ) , ( 10
)
where k is the Boltzmann constant and m is the electron mass. The function I(ǫ ′ , ǫ) is given by

I(ǫ ′ , ǫ) = ǫ ′ kT ⊥ 2 exp ǫ ′ kT ⊥ {erf [x(ǫ ′ ) -y(ǫ)] + erf [x(ǫ ′ ) + y(ǫ)] } , (11)
where

x(ǫ ′ ) = ǫ ′ kT T ⊥ -T T ⊥ , y(ǫ) = ǫ kT T ⊥ T ⊥ -T . ( 12
)

Numerical results

Present numerical results for the DR and DE cross sections of the vibrationally excited D + 2 were obtained using the above outlined theoretical procedure for the collision energy range 1 -12 eV. The energies are measured from the ground vibrational level of the D + 2 molecular cation. The computations require input molecular data, such as potential energy curves of the ion and the relevant doubly excited states of the neutral molecule, as well as the dependence of the quantum defects and electronic couplings on internuclear distance. Potential energy curves of hydrogen molecular ion and seven dissociative curves ( 1 Σ + g , 1,3 Σ + u , 1,3 Π + g and 1,3 Π + u ) of neutral hydrogen molecule, the quantum defects characterising the Rydberg states built on the 1sσ g ground state and the electronic couplings between Rydberg states and dissociative states are the same as in a previous work [38]. The quantum defects at the 2 Σ u threshold and the couplings between different ionization channels associated to the two ionic cores are extracted from the numerical results reported by Tennyson [43].

Figure 1 shows our results for the D + 2 DR and DE cross sections for a mixture of vibrational states whose populations obey a Franck-Condon distribution (defined by the overlap factors between the vibrational ground state of D 2 and different vibrational levels of D + 2 [44,45]) along with the experimental DE cross section (assuming the same distribution of the initial vibrational level populations) reported by Abdellahi El Ghazaly et al [20]. As we can see, below 3 eV the dissociative recombination process is the most important destruction process of the D + 2 ions while above this electron energy the dissociative excitation is dominant due to the electronic excitation to the first excited state 2pσ u (more likely in this electron energy domain). Note a small protuberance of the DR curve around 4 eV and a broad shape of the DE curve. The small protuberance of the DR curve is due to the cumulative contributions of the dissociative Rydberg states with 2pσ u core. In the case of the dissociative excitation process a relatively good agreement (within a factor 2) has been found. Taking into account the high sensitivity of the DE cross section to the initial vibrational state of D + 2 (see the next figure), the calculation limitations (our computations involve a second order Born expansion of the K matrix) and the fact that small deviations from the initial distribution of the vibrational populations in the molecular beam can occur (through vibrational transitions) the agreement is satisfactory.

In order to explain the broad shape of DE curve in the investigated electron energy range we shall analyse the dependence of DE cross section on the initial vibrational state. Figure 2 presents the DE cross section for all twenty-six vibrational levels of the initial electronic state 1sσ g . Two structures of the DE curves are emphasized. The second structure starting at an energy value close to the excitation energy E ex (the energy difference between the energy of the repulsive state and the energy of the initial vibrational level at the outer classical turning point) corresponds to the autoionization into an antibonding state (D + 2 ) * belonging to the 2pσ u ionic core

D + 2 + e -(ǫ) → (D + 2 ) * + e -(ǫ ′ ) → D + D + + e -(ǫ ′ ) , (13)
where ǫ ′ is the energy of the scattered electron. Below the excitation energy the D + 2 ions dissociate to the same atomic fragments D and D + through the reaction channel

D + 2 + e -(ǫ) → D * * 2 → (D + 2 ) * + e -(ǫ ′ ) → D + D + + e -(ǫ ′ ) , (14)
involving the electron capture into a doubly-excited dissociative state D * * 2 followed by the autoionization into an antibonding state (D + 2 ) * belonging to the vibrational continuum of the electronic ground state 1sσ g . This reaction channel is connected to the first structure of the DE curve. It starts to work at an energy E diss equal to the energy difference between the dissociation threshold of the ground state and the energy of the initial vibrational level. Figure 2 shows that the magnitude of the DE cross section and its dependence on the electron energy are strongly influenced by the vibrational level v. The high sensitivity of the two DE thresholds (E diss and E ex ) on the vibrational level of the initial electronic state of D + 2 is illustrated in Table 1. Note that the first structure is broad for v = 0 and 1. With increasing vibrational quantum number v the first structure narrows quickly. It practically dissapears for v = 11.

Figure 3 displays the D + 2 DR cross section for all twenty-six vibrational levels. It emphasizes the strong sensitivity of the DR cross section on the initial vibrational state labeled by v, specially for the lowest vibrational quantum numbers (see panel (a)) or the highest vibrational quantum number (see panel (d)). Note that the magnitude of the DR curves is practically unchanged for the vibrational quantum number ranging the interval 11 -18. At an electron energy below the dissociation threshold the DR curves exhibit a resonant structure due to the temporary electron capture into a bound Rydberg state D * 2 (which are energetically accessible in this electron energy domain) followed by the dissociation via the doubly excited state D * * 2 into two neutral atomic fragments D and

D * D + 2 + e -(ǫ) → D * 2 , D * * 2 → D + D * . ( 15
)
The bound rovibrational levels in the Rydberg states D * 2 are involved in the DR mechanism (schematically described by Equation ( 15)) leading to a large number of low energy resonances. Such rotational resonances in the HD + recombination were experimentally emphasized [46]. In this electron energy domain the magnitude of the DR curve for v = 0 is larger than that for v = 0. We expect such behaviour because the Frank-Condon factor for v = 0 is larger than that for v = 0. With increasing vibrational quantum number the dissociation threshold E diss decreases, see Table 1. This explains why the resonant structure practically disappears for v = 11. Above the dissociation threshold, the bound Rydberg states with 1sσ g core are not accessible. So the DR process acts on a direct mechanism consisting of the electron capture in the doubly excited state D * * 2 followed by dissociation into the same two neutral atomic fragments D and

D * D + 2 + e -(ǫ) → D * * 2 → D + D * . (16)
Since the bound rovibrational levels in the Rydberg states are not energetically accessible in this electron energy range, we do not expect significant rotational effects above the dissociation threshold. The HD + DR computations performed by Schneider et al [29] have shown that rotational couplings have small contributions at electron energies above 3 eV. Figure 4 shows the comparison of the experimental D + 2 DR rate coefficient (for v = 0) reported by Krohn [17] with that calculated using Equation (10). In our computation the transverse and longitudinal electron velocities are those characterizing the storage ring experiment [17] namely, kT = 0.1 meV and kT ⊥ = 12 meV. Below 2.69 eV (the dissociation threshold for v = 0) the DR curve reveals a resonant structure due to the temporary electron capture in a bound Rydberg state, see Equation (15). Above the dissociation threshold the DR curve exhibits a broad structure at about 10 eV resulting from the cumulative contributions of the dissociative Rydberg states with the excited core 2pσ u . Note the satisfactory agreement with the experiment.

Assuming a Franck-Condon distribution of the populations of the initial vibrational levels, we present the contributions of these vibrational states to the DR cross section in Figure 5. Lines are drawn to guide the eye through the values. As we can see at 2 eV, the significant contribution to the DR cross section is given by vibrational levels between 4 and 12. Increasing electron energy the contributions of high vibrational levels to the DR cross section decrease. At relatively high electron energy (ǫ ≥ 8 eV) only the low vibrational states play an important role in the D + 2 DR. The q v contributions of the initial vibrational levels to the DE cross section are illustrated in Figure 6. The inset indicates the populations of the initial vibrational levels for the D + 2 Franck-Condon distribution. As in the previous figure the lines are drawn to guide the eye through the values. According to panel (a) at 2 eV many high vibrational states (7 < v < 18) have important contributions to the total D + 2 DE cross section. This result can be explain using Figure 2. The DE cross sections for the high vibrational states are much larger than those for the low vibrational states. With increasing electron energy, the magnitude of the DE cross section for the low vibrational levels begins significant. Therefore we expect a different behaviour for higher electron energies. As we can see in panel (b), the shape of the q v curve mimics the vibrational population. Taking into account that the magnitude of DE cross sections σ DE,v for almost vibrational states has the same order of magnitude in the energy range 8 -12 eV (see Figure 2) the shape of the q v curve can be anticipated. We then conclude that only the low initial vibrational states have significant contributions to the D + 2 DE cross section at relatively high electron energy (ǫ ≥ 8 eV).

Finally

Summary

We have reported new computations for the dissociative recombination and excitation cross sections for a mixture of the D + 2 vibrational states characterized by a Franck-Condon distribution. The energy range 1 -12 eV has been considered. The analysis of the dependence of the dissociative recombination and excitation cross sections on the electron energy reveals that at an electron energy above 3 eV the D + 2 dissociation proceeds via the dissociative excitation process. This work also shows that at relatively high electron energy (ǫ ≥ 8 eV) only the low initial vibrational states have significant contributions to the D + 2 dissociation (see Figures 5 and6).

F

Figure 1 .

 1 Figure 1. DR and DE cross sections of the vibrationally excited D +2 assuming a Franck-Condon distribution of the initial vibrational levels. Black solid line: our results for DE, brown/grey solid line: our results for DR and circles: experimental DE results reported by Abdellahi El Ghazaly et al[20].

Figure 2 .

 2 Figure 2. DE cross section (σ DE,v ) of the D + 2 molecular ion initially in the electronic ground state and the vibrational state v.

Figure 3 .

 3 Figure 3. Same as Figure 2 but for the DR cross section (σ DR,v ).

Figure 4 .

 4 Figure 4. Comparison of the D +2 DR rate coefficient for v = 0 (black solid line) with experimental DR rate coefficient reported by Krohn[17] (black circles).

Figure 5 .

 5 Figure 5. Relative contribution of each initial vibrational state v to the total DR cross section for a Franck-Condon distribution of the vibrational levels.

Figure 6 . 12 Page 12 of 15 URL

 61215 Figure 6. Same as Figure 5 but for dissociative excitation. The inset shows the D + 2 populations for a Franck-Condon distribution of the vibrational levels.

  carried out at the storage ring TSR has revealed an almost complete cooling into the vibrational ground state of the D + 2 molecular ions. It was found that the population of the vibrational ground state increased from initially less than 10 % to about 75 % in 4 s, while the population of the first excited vibrational state increased in the first 20 s to almost 35 %. So, after a storage time of 25 s only the lowest four vibrational states of D + 2 were populated. The experiment performed by Abdellahi El Ghazaly et al[20] using the crossed-beam technique has reported the absolute total cross sections for H + 2 and D + 2

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  , we compare the DR and DE cross sections for vibrationally excited D + 2 (Figures1-3) with those for vibrationally hot H + 2 (Figures 7 and 8 from our previous paper[37]). The DR and DE cross sections for D + 2 are somewhat smaller, which can be explained by the fact that the vibrational levels (0 ≤ v ≤ 18) of D + 2 are deeper in the potential well than those for H + 2 , leading to smaller Franck-Condon factors. It should be noted that the DR and DE cross sections for the two isotopomers have similar dependence on the vibrational quantum number. Above the dissociation threshold, the DR curve reveals a structure due to the cumulative contributions of the dissociative Rydberg states with 2pσ u core. With increasing vibrational quantum number, this structure shifts towards 0 eV as the threshold E diss . For low vibrational levels, the DE curve displays two structures, each of them corresponding to a DE mechanism. Since the direct DE threshold E ex tends to the indirect DE threshold E diss , the first DE structure narrows and practically disappears for v = 7 in the case of H + 2 and for v = 11 in the case of D + 2 .

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Table 1 :

 1 Thresholds of the two DE mechanisms for the first fifteen vibrational levels of the D + 2 molecular ion.

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Acknowledgments

The financial support of the UEFISCSU (Romania) through the grant ID 967 under the Contract 143 is warmly acknowledged.


Iwona Świerszcz

Iwona Anusiewicz
email: iwonaa@chem.univ.gda.pl

Low Ionization Potentials of Na 4 OCN Superalkali Molecules

Keywords: superalkalies, hypervalent, cations

The structure and properties of hypermetalated Na 4 OCN molecules and their corresponding Na 4 OCN + daughter cations were investigated using ab initio methods at the CCSD(T)/6-311+G(3df)//MP2/6-311+G(d) level of theory. Eight neutral Na 4 OCN geometrically stable isomers were found to possess similar electronic energies. The vertical ionization potentials (IP) of the Na 4 OCN isomeric systems (determined at the OVGF/6-311+G(3df) level) were calculated to span the 4.117-4.640 eV range which allowed to classify the Na 4 OCN species as superalkali molecules (the predicted ionization potentials are smaller than the IP of the Na atom, 5.14 eV). The global minimum on the Na 4 OCN ground-state neutral potential energy surface was found to correspond to the kite-shaped structure whose vertical IP was estimated to be 4.478 eV.

Introduction

The term "superalkalies" was introduced in 1982 by Gutsev and Boldyrev [1] to describe molecular systems whose first ionization potential (IP) is smaller than that of the alkali metals (IP (in eV): Li, 5.39; Na, 5.14; K, 4.34; Rb, 4.17; Cs, 3.89) [START_REF] Lias | Gas-Phase Ion and Neutral Thermochemistry[END_REF]. For example, the Li 3 O molecule was reported to possess the superalkali nature with the IP of 3.54±0.3 eV [3][4][5] which is lower than the ionization potential of Cs atom (3.89 eV). The superalkalies belong to a group of hypervalent or hypermetalated molecules. This term describes ML k+n species (where L is an alkali metal atom, k is the maximum formal valence of the central atom M, and n≥1) [1,[START_REF] Schleyer | New Horizons of Quantum Chemistry[END_REF][START_REF] Schleyer | [END_REF][8][9] containing two or more metal atoms in stoichiometries that exceed normal valence expectations. The strong bonding interactions among the alkali metal "ligands" (L) which help to offset the octet-ruleviolating structure and antibonding L-M interactions are believed to be the major contributions to both the structure and stability of these species [1,[START_REF] Schleyer | New Horizons of Quantum Chemistry[END_REF][START_REF] Schleyer | [END_REF][8][9][10][11][12][13][14][15][16]. Since the first evidence of the Li 3 O molecule in 1978 [11], a number of lithium and other alkali metal containing compounds with unusual stoichiometries (e.g., Li 4 O, Li 5 O, Li 2 Cl, Li 2 F, Li 6 C, Na 3 O, Na 4 O) have been studied theoretically and experimentally [1,[3][4][5][START_REF] Schleyer | New Horizons of Quantum Chemistry[END_REF][START_REF] Schleyer | [END_REF][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The most prominent examples of superalkalies are small (i.e., triatomic) alkali metal clusters and hyperalkali molecules ML k+n with n=1 which are characterized by the lowest IPs (i.e., Li 3 4.11 eV vs. Li 4 4.74 eV [23] or Na 3 O 3.13 eV vs. Na 4 O 3.60 eV [22]).

Superalkalies are of a great importance in chemistry since they can be used as components of new nontraditional salts in which the anions are molecular systems exhibiting low electron affinity. The first salts of this type, i.e., Li 3 O + NO -and Li 3 O + NO 2 -, were synthesized in the 70's by Jensen and the presence of the Li 3 O + cation has been confirmed by the X-ray diffraction [24][25][26].

In this contribution we present our theoretical investigation of the electronic and geometric structure of the Na 4 OCN system exhibiting "superalkali nature". In particular, we focused our studies on the various structures of Na 4 OCN and its corresponding cation Na 4 OCN + .

Our goal was to investigate if such species are geometrically and thermodynamically stable and whether they possess small IP values. We believe that the vertical ionization potentials we provide in this work might be found useful for experimental chemists, especially those designing new materials in which strong reducers are involved.

Methods

We present the equilibrium geometrical structures of the Na 4 OCN and Na 4 OCN + species for which we also calculated harmonic vibrational frequencies (available upon request). For this purpose we applied the second-order Møller-Plesset (MP2) perturbational method with the 6-311+G(d) basis set [27,28]. The coupled-cluster method with single, double and non-iterative triple excitations (CCSD(T)) [29] was used to calculate the final energies of the species at their geometries obtained with the MP2 method. In order to provide reliable vertical ionization potentials (VIP) of superalkali species studied we performed direct calculations of the electron binding energies at the neutral (Na 4 OCN) and cationic (Na 4 OCN + ) equilibrium geometries which resulted in estimating the VIP n and VIP c , respectively. However, we limit our discussion to the ionization potentials obtained for the neutral equilibrium geometries (i.e., VIP n ) as they seem more important for experimentalists, whereas the VIP c values are only provided for comparison.

A direct scheme applied to calculate the ionization potentials was the outer valence Green function (OVGF) method (B approximation) [30][31][32][33][34][35][36][37][38]. Since the OVGF approximation remains valid only for outer valence ionizations for which the pole strengths (PSs) are greater than 0.80-0.85 [39] we verified that the smallest PS found for the states studied in this work is 0.80. As far as the basis sets are concerned, we applied the 6-311+G(3df) basis [27,28] for calculating the VIP values and the final CCSD(T) energies of the species. The partial atomic charges were fitted to the electrostatic potential according to the Merz-Singh-Kollman scheme [40].

All calculations were performed with the Gaussian03 program [41] while the plots showing the molecular structures were generated with the ChemCraft program [42].

Results

As it was explained in the preceding sections, the most favorable stoichiometry for the superalkali species matches the ML k+1 formula (where L is an alkali metal atom and k stands for the maximum formal valence of the central atom M). Due to the anticipated potential energy surface (PES) complexity, the superalkali molecules with more complex center M (i.e., built of more than one atom, such as OH [START_REF] Tanaka | [END_REF]44] or CN [45,46]) are of particular interest since the existence of several minima of comparable stability might be expected. The electrostatic attraction between the cationic metallic network L (k+1)+ and anionic M -(regardless of the complexity of center M) contributes to the stability of the system. Therefore, we decided to verify these assumptions for hypermataleded molecules composed of ambidentate centers M, such as OCN. The cyanate group (OCN), which we chose as a representative polyatomic center M, is an important halogenoid characterized by relatively large electron affinity (EA(OCN)=3.609±0.05 eV [47]) comparable to that of the chlorine atom (EA(Cl)=3.61 eV [48]). The term halogenoid (or pseudohalogen) was introduced in 1925 [49] for strongly bound, linear or planar univalent radicals X · (such as CN, OCN, N 3 , SCN) which form X -anions and HX acids.

As we described recently, the Na 2 OCN system, matching the ML k+n formula for n=1, is capable of forming stable molecules of superalkali nature [50]. Moreover, we noticed that the OCN group in addition to its ambidentate nature (exhibited by the ability of forming stable Na 2 OCN and Na 2 NCO isomeric structures) is also able to act as a 'bridge' between two alkali metal atoms. In particular, the lowest energy Na 2 OCN isomer is of C 2v symmetry with both sodium atoms connected to the isocyanate (-NCO), however, C s -symmetry structure (with the OCN in the bridging position between two alkali metal atoms) is only 0.4 kcal/mol higher in energy whereas the structure with both Na atoms linked to the cyanate fragment (-OCN) is 10.9 kcal/mol higher in energy. The vertical ionization potentials (VIP n ) for the Na 2 OCN isomers were found to span the 4.747-5.072 eV range [50].

The ambidentate nature of the OCN moiety and its capability of binding two alkali metal atoms to either O-end or N-end (as confirmed by the existence of both Na 2 OCN and Na 2 NCO systems) [50] have motivated us to verify whether the Na 4 OCN (which matches more general ML k+n formula with n=3) is capable of forming stable molecules exhibiting superalkali nature. We begin our discussion with providing the results obtained for the neutral Na 4 OCN species. An extensive exploration of the ground-state neutral potential energy surface led to 8 stable isomers whose equilibrium structures are depicted in Figure 1 whereas the corresponding geometrical parameters are gathered in Table 1.

The structure corresponding to the global minimum of Na 4 OCN (termed 1 in Figure 1) contains a four-member ring involving three sodium atoms and one nitrogen atom. The remaining Na atom is linked to the O-end of the OCN fragment and the resulting symmetry is C s due to the planarity of the molecule. As a consequence, the structure 1 resembles the most stable structure previously found for Na 3 OCN molecule [51], however, with one additional Na atom linked to the oxygen (Na 4 , see Figure 1). The OCN fragment is almost linear (the OCN valence angle reads 177.8°) while the Na-Na and Na-N bond lengths were found to span the 3.40-3.67 Å and 2.31-2.44 Å range, respectively (see Table 1). The C s -symmetry structure 1 is thermodynamically stable with respect to various channels of isomerization and fragmentation. In particular, if one considers the fragmentation path leading to the sodium atom and Na 3 OCN neutral molecule, the system 1 is thermodynamically stable by 12.1 kcal/mol (at the CCSD(T)/6-311+G(3df)//MP2/6-311+G(d) level). The VIP n value (i.e., the vertical ionization potential calculated for the equilibrium geometry of the neutral system) calculated for isomer 1 of Na 4 OCN with the OVGF method reads 4.478 eV which is lower than the ionization potential of the sodium atom (5.14 eV).

The second low energy structure of Na 4 OCN (local minimum 2) was found to be higher in energy than the isomer 1 by only 0.6 kcal/mol which may suggest the presence of similar amounts of these isomers at room temperature. The structure 2 is planar (C s -symmetry) with the OCN moiety and three sodium atoms engaged in the six-member ring mimicking a pentagon (see Figure 1). The remaining sodium atom (Na 4 ) is bound to the N-end of the OCN group and the corresponding bond length was found to be relatively large (3.35 Å) in comparison to the Na 1 -N distance (2.40 Å). As it was observed for the global minimum 1, the OCN fragment is quasilinear (∠(OCN)=177.9°) and the Na-Na bond lengths are in the 3.36-3.64 Å range (see Table 1).

The vertical ionization potential calculated for the structure 2 (4.112 eV) was found to be even lower (by 0.366 eV) than the VIP n of the isomer 1. The next Na 4 OCN low energy isomer (3) is planar (C s -symmetry) and contains four sodium atoms forming a quasi-rhombic frame connected to the N-end of the OCN moiety via two Na-N bonds, see Figure 1. The OCN fragment is almost perfectly linear in 3 (∠(OCN)=179.7°) whereas the Na-Na bond lengths are in the 3.49-3.69 Å range (see Table 1). The energy of shovel-shaped structure 3 is only 2.0 kcal/mol higher than the energy of the global minimum (1).

The vertical ionization potential calculated for the isomer 3 (4.550 eV) is only slightly higher (by 0.072 eV) than that predicted for the global minimum structure 1.

The fourth (4) and fifth (5) geometrically stable structures of Na 4 OCN were found to be higher in energy by 2.7-2.9 kcal/mol than the global minimum 1. These isomers possess very similar electronic energies (the energy difference is only 0.2 kcal/mol) and differ by the OCN fragment orientation with respect to the Na-Na-Na-Na framework, see Figure 1. Both 4 and 5 structures are planar (C s -symmetry) and cyclic, with the quasi linear OCN moiety (the deviations from linearity do not exceed 0.3°), see Table 1. The VIP n values predicted for the isomers 4 and 5 are similar to the VIP n of isomer 1 and equal to 4.640 and 4.584 eV, respectively.

The sixth geometrically stable structure of Na 4 OCN (labeled 6 in Figure 1 and Table 1) was found to be higher in energy by 3.5 kcal/mol than the most stable isomer 1. This structure can be viewed as the analogous to 2 (see Figure 1) with its similar pentagon-like frame involving three Na atoms and the OCN group, however, the remaining sodium atom (Na 4 ) is linked to the oxygen instead of nitrogen atom. Similarly to the previously described structure 2, the OCN fragment is quasi-linear in structure 6 (∠(OCN)=178.1°) and the Na-Na bond lengths are in the 3.44-3.56 Å range (see Table 1). The vertical ionization potential calculated for 6 (4.273 eV) is higher by 0.15 eV than that predicted for the analogous structure 2 and smaller by 0.21 eV than the VIP n estimated for the global minimum structure 1.

Another geometrically stable isomer of Na 4 OCN, labeled 7 in Figure 1, was found to be higher in energy by 3.9 kcal/mol than the global minimum 1. The OCN fragment is almost linear in 7 (∠(OCN)=177.9°) and it connects to the sodium atoms through its both termini. In particular, the nitrogen atom is linked to one Na atom (Na 4 ) whereas the oxygen atom forms two bonds (O-Na 1 and O-Na 3 ), see Figure 1. The remaining sodium atom (Na 2 ) is bound to the Na 1 atom and the resulting system is planar (C s -symmetry). The calculated VIP n value for the structure 7 is The least stable isomer we obtained for the Na 4 OCN neutral molecule (labeled 8 in Figure 1 and Table 1) is 8.8 kcal/mol higher in energy than 1 and contains bent Na 3 -Na 1 -Na 4 fragment connected to the both ends of the OCN moiety. The fourth remaining sodium atom (Na 2 ) is bound to the N atom, see Figure 1. Interestingly, the isomer 8 is characterized by the lowest vertical ionization potential (4.117 eV) among all geometrically stable Na 4 OCN isomers described in this contribution.

As discussed in this section, the VIP n values obtained for all eight isomers of Na 4 OCN are relatively low and span the 4.117-4.640 eV range. In particular, the reported VIP n s are not only lower than the ionization potential of the sodium atom (5.14 eV) but also lower than the VIP n values recently found for the Na 2 OCN molecules (4.747-5.072 eV) [50]. Hence, we conclude that the Na 4 OCN isomers should be classified as superalkalies [10] as they are expected to act as electron donors.

The singly occupied molecular orbitals (SOMO) of all 1-8 isomers are depicted in Figure 2. The large number of sodium atoms in Na 4 OCN supports its classification as a hypermetalated molecule, however, the presented SOMO orbitals seem different from those usually described for 'typical' hypermetalated species. In particular, an unpaired electron in the hypermetalated ML k+n system is accommodated in an orbital which is antibonding with respect to the central atom (M) and the surrounding metal atoms (L k+n ) whereas the bonding interaction among all metal atoms L is observed (the latter interaction allows to form a metal network) [45]. Because of this, the hypermetalated molecules are usually described as salts composed of the metallic cation [L k+n ] + and the [M] -anion. For most of the Na 4 OCN isomers, however, the unpaired valence electron density is split into two pairs of alkali metal atoms and hence the Na 4 OCN species cannot be described as a complex of OCN -and Na 4 + radical cation (i.e., similar to other hypermetalated molecules). This seems to imply that the Na 4 OCN might be considered as consisting of metallic Na 2 + and anionic Na 2 OCN -subunits. Moreover, the localization of the metallic Na 2 + subunit (with respect to the OCN fragment) turns out to be important for the ionization process, as described in the following section.

Cationic Species

Since the isomers of the Na 4 OCN molecule exhibit very low ionization potentials (4.117-4.640 eV) it is important to discuss the structure and properties of the corresponding daughter cationic species (generated by the unpaired electron removal). Hence, we performed the geometry optimizations of the cationic species using the neutral 1-8 structures as the initial geometries. Such an approach seems justified because it reproduces the actual geometry relaxation of the system after an electron removal (the electron loss is much faster than the structure relaxation and thus the initial cation structure is expected to be that of its corresponding neutral parent). In addition, we independently searched for other geometrically stable cationic structures (i.e., the cationic structures that are qualitatively different than any of the neutral isomer). The geometrically stable structures that we found for Na 4 OCN + cations are depicted in Figure 3 whereas the corresponding geometrical parameters are collected in Table 2.

The ionization of the most stable isomer 1 leads to the C 2v -symmetry structure 1 + in which three sodium atoms form a four-member ring with the N-end of the OCN moiety while the fourth Na atom is bound to the O-end of the OCN group (see Figure 3). As a result, the 1 + cation contains the linear Na-O-C-N fragment, unlike the neutral parent 1 in which the corresponding Na-O-C-N moiety is significantly bent (see Figure 1). Despite this large difference in the Na-O-C valence angle (from 109° in 1 to 180° in 1 + ), the 1→1 + ionization process causes only small changes in the Na-N, N-C and C-O bond distances (the differences do not exceed 0.12 Å). The charge population analysis indicates that the excess positive charge is not equally distributed among the metal atoms as the terminal sodium atom (Na 1 ) linked to O-end of the OCN group bears the +1.02 a.u. partial charge whereas the charges found for the three remaining sodium atoms are in the 0.10-0.27 a.u. range. Surprisingly, the significant positive partial charge of 1. with the remaining Na atom linked to the nitrogen, see Figure 3. In fact, the geometries of the neutral parent 2 and its 2 + cationic daughter differ only slightly. Namely, the Na 4 -N, Na 1 -Na 3 , and Na 1 -Na 2 bonds shorten by 0.10-0.23 Å whereas the Na 2 -O, Na 1 -N, and Na 2 -Na 3 bonds elongate by 0.05-0.18 Å (see Figures 1 and3 for atom numbering and Tables 1 and2 for detailed values of geometrical parameters). The most significant geometry change upon the 2→2 + ionization was found in the case of the Na 1 -N-Na 4 valence angle which increases from 91° (in 2) to 139° (in 2 + ).

As a result, the two sodium atoms become more distant with respect to each other (the Na 1 -Na 4 separation in the cation reads 4.451 Å), see Figure 3. As far as the charge population analysis is concerned, the ionization of either 2, 3 or 8 causes all sodium atoms to bear larger positive partial charges (up to q(Na 4 )=+0.9 a.u. in 2 + ) while the OCN fragment becomes more negative (from ca.

-0.1, -0.3 and +0.3 a.u. for 2, 3 and 8, respectively, to -0.5 a.u. for 2 + ; see Tables 1 and2).

The ionization of the 4 and 5 neutral isomers (exhibiting similar electronic energies) leads to two different isomeric C 2v -symmetry structures (labeled 4 + and 5 + , respectively) in which the linear OCN fragment is in the bridging position between one sodium atom (bound to either oxygen in 4 + or nitrogen in 5 + ) and the top of the isosceles sodium triangle, see Figure 3. In fact, the only structural difference between 4 + and 5 + cations is related to the orientation of the OCN moiety with respect to the Na-triangle. As a result, both systems become less compact than their corresponding 4 and 5 neutral parents as the seven-member rings open upon the ionization. In addition, the resulting 5 + cation is lower in energy than the 4 + isomer (on the contrary to the neutral parent 4 and 5 species, see the discussion provided in the preceding section) by about 2 kcal/mol. The Na-N and Na-O bonds in 4 + and 5 + are shorter (by 0.05 and 0.14 Å for 4 + and by 0.07 and 0.06 Å for 5 + , respectively) whereas the bond lengths in the OCN moiety remain almost unchanged upon the ionization (the differences are smaller than 0.008 Å; see Figures 1 and3, and Tables 1 and2). The charge population analysis indicates that the excess positive charges in 4 + and 5 + are localized mostly on the terminal sodium atoms Na 1 (carrying the partial charges of ca.

+0.9 a.u.; see Table 2) forming bonds with the negatively charged oxygen (in 4 + ) or nitrogen (in 5 + ) atoms. Therefore, we conclude that the corresponding 4 and 5 isomers might be viewed as The ionization of the isomer 6 leads to the isomer 6 + cation whose structure is very similar to that of its corresponding neutral parent. In particular, the 6→6 + process causes the shortening of the Na 4 -O, Na 1 -Na 3 , and Na 1 -Na 2 bonds by 0.09-0.23 Å, and the elongation of the Na 2 -N, Na 1 -O and Na 2 -Na 3 bonds by 0.03-0.19 Å (see Figures 1 and3). These changes in the bond lengths are accompanied with the considerable increase of the valence Na 1 -O-Na 4 angle (from 98° to 150°) when the 6 + cation is formed. The performed charge population analysis indicates that the excess positive charge in 6 + is not equally distributed among all sodium atoms, in fact, the terminal Na atom (Na 4 ) bears the largest partial positive charge of ca. +0.9 a.u.

(Na 2 + )( -
The ionization of the neutral structure 7 causes significant geometry reorganization and leads to the C 2v -symmetry structure 7 + which is analogous to 1 + , however, the 7 + and 1 + differ in the relative OCN group orientation, see Figures 1 and3. Importantly, the kite-shaped 7 + cation of which indicates that the Na 4 OCN + is stable towards such decompositions. The 7→7 + ionization process causes only small changes (i.e., not exceeding 0.12 Å) in the Na-O, N-C and C-O bonds whereas the Na-N-C valence angle is strongly affected and increases from 106° in 7 to 180° in 7 + , see Tables 1 and2). Similarly to the 1 + cation, the charge population analysis indicates that the excess positive charge in 7 + is distributed mostly between the carbon atom and the terminal sodium atom (Na 1 ).

C
Further exploration of the Na 4 OCN + cationic potential energy surface led to two additional minimum energy structures labeled 9 + and 10 + , see Figure 3. Since the attachment of an electron to these both cationic species results in thermodynamically unstable neutral structures with respect to decomposition (Na atom loss, by ca. 14-17 kcal/mol), we conclude that the 9 + and 10 + cations do not possess their corresponding neutral parents. -0.7 a.u.; see Table 2.

The least stable isomer 10 + is 13.1 kcal/mol higher in energy than 7 + . Its relatively compact structure is likely caused by the significantly bent configuration of the OCN fragment.

This, in turn, leads to the strong electrostatic repulsion among the positively charged Na atoms (see Figure 3 and Table 2). Since the bent structure of the OCN group seems unusual [52] in compounds containing alkali metal atoms, we propose to view the 10 + as the complex of Na 3 O + and NaCN. This is supported by the fact that the 10 + possesses the longest O-C bond distance (1.365 Å) among all studied Na 4 OCN molecules and Na 4 OCN + cations (see Tables 1 and2).

Summary

On the basis of our ab initio CCSD(T)/6-311+G(3df) and OVGF/6-311+G(3df) calculations for the Na 4 OCN and Na 4 OCN + species (whose structures were determined at the MP2/6-311+G(d) level) we concluded the following:

(1) The neutral Na 4 OCN molecules are geometrically and thermodynamically stable species represented by at least eight isomeric structures.

(2) The co-existence of seven different Na 4 OCN isomers is anticipated at room temperature due to their similar electronic energies (within 4 kcal/mol).

( ( q Na(1) =0.170; q Na(2) =-0.057; r(Na 2 Na 3 )=3.673; r(Na 4 O)=2.343; r(OC)=1.219;

q Na(3) =-0.009; q Na(4) =0.124; r(CN)=1.205; ∠(NNa 1 Na 2 )=114.55; ∠(OCN)=177.80 q O =-0.117; q C =-0.101; ∠(Na 1 Na 2 Na 3 )=55.27; ∠(Na 3 NC)=107.05;

q N =-0.010 q Na(1) =0.065; q Na(2) =0.213; r(Na 1 Na 4 )=3.492; r(Na 3 Na 4 )=3.694; r(OC)=1.197;

q Na(3) =-0.031; q Na(4) =0.082; r(CN)=1.218; ∠(Na 1 NNa 2 )=99.63;

q O =-0.632; q C =0.666; ∠(Na 2 NC)=130.29; ∠(Na 1 Na 4 Na 3 )=60.80;

q N =-0.363 ∠(Na 2 Na 3 Na 4 )=115.01; ∠(NNa 2 Na 3 )=102.27; q Na(1) =0.241; q Na(2) =0.304; r(Na 3 Na 2 )=3.637; r(Na 2 O)=2.240; r(OC)=1.230;

q Na(3) =-0.066; q Na(4) =0.055; r(CN)=1.199; ∠(Na 2 OC)=115.53;

q O =-0.322; q C =0.278; ∠(Na 1 NC)=126.03; ∠(Na 1 Na 4 Na 3 )=61.84;

q N =-0.490 4 (C s ) 4.640 ∠(Na 2 Na 3 Na 4 )=138.72; ∠(OCN)=179.76 r(Na 1 N)=2.255; r(Na 1 Na 4 )=3.646; r(Na 3 Na 4 )=3.667; q Na(1) =0.334; q Na(2) =0.196; r(Na 3 Na 2 )=3.476; r(Na 2 O)=2.237; r(OC)=1.230; q Na(3) =0.073; q Na(4) =-0.068; r(CN)=1.200; ∠(Na 2 OC)=119.92;

q O =-0.333; q C =0.335; ∠(Na 1 NC)=119.84; ∠(Na 1 Na 4 Na 3 )=136.44;

q N =-0.536 q Na(1) =-0.025; q Na(2) =0.315; r(Na 2 Na 3 )=3.442; r(Na 2 N)=2.305; r(OC)=1.241; q Na(3) =-0.028; q Na(4) =-0.104; r(CN)=1.196; ∠(Na 1 ONa 4 )=98.43;

q O =0.356; q C =-0.106; ∠(NNa 2 Na 3 )=131.08 ; ∠(ONa 1 Na 3 )=128.04;

q N =-0.408 ∠(Na 1 OC)=106.88; ∠(OCN)=178.13; q Na(1) =0.108; q Na(2) =-0.015; r(Na 4 N)=2.334; r(OC)=1.242; r(CN)=1.196; q Na(3) =-0.106; q Na(4) =0.203; ∠(Na 1 ONa 3 )=93.07; ∠(Na 3 OC)=108.20;

q O =0.290; q C =-0.214; ∠(Na 4 NC)=106,35; ∠(OCN)=177.87;

q N =-0.265 7 (C s ) 4.350 ∠(ONa 1 Na 2 )=112.48 r(Na 2 N)=2.628; r(Na 3 N)=3.378; r(Na 1 Na 4 )=3.731; q Na(1) =-0.099; q Na(2) =-0.106; r(Na 4 O)=2.449; r(Na 1 Na 3 )=3.309; r(OC)=1.213;

q Na(3) =-0.173; q Na(4) =0.113; r(CN)=1.214; ∠(Na 2 NNa 3 )=115.72;

q O =-0.022; q C =-0.569; ∠(Na 1 Na 3 N)=51.

Formatted

Formatted

4 . 8 isomer 1 ,

 481 350 eV. Even though the isomer 7 is less stable and possesses slightly larger VIP n than the we consider it particularly important as its ionization leads to the most stable positively charged species Na 4 OCN + (see the discussion provided in the following section).

Formatted

3 a 1 )the neutral isomer 2 .and 8 +

 3128 .u. is predicted for the carbon atom in the 1 + cation. The localization of such a significant positive partial charge on the Na 1 atom is likely responsible for the shortage of the Na-O bond (by 0.21 Å) upon an ionization (i.e., with respect to the Na-O bond predicted for the neutral isomer whereas the bonds formed by the carbon atom (i.e., C-O and C-N) are only slightly affected (the differences in the bond lengths do not exceed 0.007 Å).Detachment of an electron from isomers 2, 3, and 8 leads to the same C s -symmetry structure of the cation which we decided to term 2 + (rather than 3 + or 8 + ) due to its structural Hence, the cationic isomers that would have been labeled 3 + are absent (the ionization of any of 2, 3, or 8 leads to the same cation (2 + )). The 2 + cation contains a quasi-pentagon frame (built of three sodium atoms and nearly linear OCN fragment)

)( 4 )

 4 The vertical ionization potentials (VIP n ) of Na 4 OCN systems are in the range of 4.117-4.640 eV (lower than the IP of Na (5.14 eV)) which justifies their classification as superalkalies. The VIP n predicted for the Na 4 OCN systems (4.117-4.640 eV) are substantially lower than those estimated earlier for the Na 2 OCN species (4.747-5.072 eV).

  1 N)=2.256; r(Na 1 Na 4 )=3.532; r(Na 3 Na 4 )=3.597;

  2 Na 3 Na 4 )=61.21; ∠(OCN)=179.94 r(Na 1 O)=2.365; r(Na 4 O)=2.302; r(Na 1 Na 3 )=3.563;

  1 Na 3 Na 2 )=66.22; ∠(Na 2 NC)=109.64; 1 O)=2.253; r(Na 3 O)=2.412; r(Na 1 Na 2 )=3.338;

Figure 1 .

 1 Figure 1. The MP2/6-311+G(d) equilibrium structures of the Na 4 OCN isomers.

Figure 2 .

 2 Figure 2. Singly occupied molecular orbitals (SOMO) of the Na 4 OCN isomers.

Figure 3 .

 3 Figure 3. The MP2/6-311+G(d) equilibrium structures of the Na 4 OCN + cationic isomers.

  2v symmetry is the global minimum on the ground state cationic Na 4 OCN + potential energy surface. In order to verify the Na 4 OCN + (represented by the structure 7 + ) susceptibility to fragmentation we considered the Na 4 OCN + →Na 3 OCN+Na + and Na 4 OCN + →Na 2 OCN + +Na 2 processes and found them energetically unfavorable (by 43.0 and 21.7 kcal/mol, respectively)

  The C 2v -symmetry isomer 9 + is higher in energy by 7.7 kcal/mol than the lowest energy cationic structure 7 + . The 9 + structure is characterized by rather large Na-O and Na-N distances (2.60 and 2.46 Å, respectively) with respect to other sodium-oxygen and sodium-nitrogen distances found for most Na 4 OCN + isomers studied in this work. The charge population analysis indicates that the excess positive charge in is delocalized over all atoms excluding the carbon atom which carries the partial charge of ca.

	9 +
	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y
	12

Table 1 .

 1 ) The ionization of the Na 4 OCN species may lead to at least 7-8 various isomeric Na 4 OCN + structures characterized by the similar electronic energies. (6) The lowest-energy isomer of Na 4 OCN possesses a kite-shaped C s -symmetry structure, the vertical ionization potential of which is 4.478 eV. This work was supported by the Polish State Committee for Scientific Research (KBN) Grant No.DS/8371-4-0137-1. The computer time provided by the Academic Computer Center in Gdańsk (TASK) is also gratefully acknowledged. The MP2 geometrical parameters (bond lengths in Å, angles in degrees) and partial atomic charges (in a.u.) fitted to the electrostatic potential according to the Merz-Singh-Kollman scheme for the Na 4 OCN isomers. See Figure1for atom numbering. Vertical ionization potentials (VIP n ) in eV.

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Table 2. The MP2 geometrical parameters (bond lengths in Å, angles in degrees) and partial atomic charges (in a.u.) fitted to the electrostatic potential according to the Merz-Singh-Kollman scheme for the Na 4 OCN + cationic species. See Figure 3 q Na(3) =0.177; q Na(4) =0.869; r(CN)=1.210; ∠(Na 1 NNa 4 )=139.49;

q O =0.001; q C =-0.265; ∠(Na 1 NC)=93.55; ∠(Na 1 Na 3 Na 2 )=61.83;

q N =-0.240 ∠(NNa 1 Na 3 )=164.07; ∠(ONa 2 Na 3 )=122.53;

q Na(1) =0.924; q Na(2) =0.033; r(OC)=1.232; r(CN)=1.191; ∠(Na 3 Na 2 Na 3 )=53.65; q Na(3) =0.269; q O =-0.477;

∠(Na 3 Na 2 N)=153.18 q C =-0.037; q N =0.019 r(Na 1 N)=2.182; r(Na 2 O)=2.181; r(Na 2 Na 3 )=3.662; q Na(1) =0.930; q Na(2) =-0.036; r(OC)=1.222; r(CN)=1.195; ∠(Na 3 Na 2 Na 3 )=54.52; q Na(3) =0.293; q O =0.191;

∠(Na 3 Na 2 O)=152.74 q C =0.098; q N =-0.767 r(Na 2 N)=2.336; r(Na 1 O)=2.544; r(Na 2 Na 3 )=3.628; q Na(1) =0.105; q Na(2) = 0.356; r(Na 4 O)=2.210; r(Na 1 Na 3 )=3.421; r(CN)=1.192;

q Na(3) =0.173; q Na(4) =0.879; r(OC)=1.252; ∠(Na 1 ONa 4 )=150.42;

q O =-0.060; q C =-0.254; ∠(Na 4 OC)=118.42; ∠(ONa 1 Na 3 )=143.88;

q N =-0.199 ∠(NNa 2 Na 3 )=126.05; ∠(Na 2 NC)=118.78; q Na(1) =1.045; q Na(2) =0.290; q Na(3) =0.757; q O =-0.609; ∠(Na 2 ONa 2 )=90.26; ∠(Na 3 OC)=87.80; q C =-0.879; q N =-0.772 ∠(OCN)=127.67; ∠(Na 3 ONa 2 Na 2 )=156.28; 10 + (C 1 ) 2.892 ∠(Na 2 ONa 2 C)=-79.17 a CCSD(T)/6-311+G(3df) result (the PS value for the OVGF calculation was too small)