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An ab initio study on BeX3− superhalogen anions (X = F, Cl, Br)
7 June 2002
Chemical Physics Letters 358 (2002) 426–434 www.elsevier.com/locate/cplett
An ab initio study on BeX 3 superhalogen anions (X ¼ F, Cl, Br) Iwona Anusiewicz, Piotr Skurski
*
Department of Chemistry, University of Gda nsk, ul. Sobieskiego 18, 80952 Gda nsk, Poland Department of Chemistry, University of Utah, Salt Lake City, UT 84112, USA Received 4 April 2002
Abstract The vertical electron detachment energies (VDE) of 10 BeX 3 (X ¼ F, Cl, Br) anions were calculated at the outer valence Green function (OVGF) level with the 6-311++G(3df) basis sets. The largest vertical electron binding energy was found for BeF 3 system (7.63 eV). All negatively charged species possess the vertical electron detachment energies that are larger than 5.5 eV and thus may be termed superhalogen anions. The strong dependence of the VDE of the BeX 3 species on the ligand–central atom (Be–X) distance and on the partial atomic charge localized on Be was observed and discussed, as well as the other factors that may influence the electronic stability of such anions. In addition, the usefulness of the various theoretical treatments for estimating the VDEs of superhalogen anions was tested and analyzed. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction It is well known that halogen atoms possess the highest electron affinities (EA) among the elements (fluorine 3.40 eV, chlorine 3.62 eV) [1]. However, the EA of a polyatomic system may exceed the 3.62 eV limit due to collective effects. Such species are of a great importance in chemistry since they can be used for the oxidation of counterpart systems with relatively high ionization potentials (such as O2 , Xe) and allow the synthesis of unusual chemical compounds (e.g., involving nobel gases
*
Corresponding author. E-mail address: [email protected] (P. Skurski).
atoms). In addition, molecules possessing high electron affinities are widely used in the production of organic superconductors [2,3]. Although such species have been attracting chemists’ attention since early 60s, it was only in 1981 when Gutsev and Boldyrev proposed to term them superhalogens and introduced a simple formula for one class of these compounds, MXkþ1 , where M is a main group or transition metal atom, X is a halogen atom, and k is the maximal formal valence of the atom M [4]. It was a milestone work since Gutsev and Boldyrev not only provided theoretically estimated electron binding energies of superhalogenbased anions but they also pointed out a few main reasons as being responsible for the increase of the vertical electron detachment energy (VDE) in MX kþ1 relative to X , such as: (i) delocalization of
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the extra electron over k þ 1 halogen atoms instead of one, (ii) nonbonding character of the highest occupied molecular orbital (HOMO), (iii) coordination of X anion to the electropositive ion Mkþ (electrostatic effect), and (iv) stabilizing electron relaxation and correlation effects [4]. Since early 80s, many other theoretical efforts have been undertaken to estimate the VDEs of various anions having superhalogens as their neutral parents (see [5–8] and references cited therein). In 1999 a dramatic progress has been made in the investigating superhalogen systems due to the joined theoretical and experimental effort that resulted in an excellent report comprising of the first experimental photoelectron spectra of superhalogens (measured by Wang’s group) together with their theoretical interpretations provided by Boldyrev and Simons [9]. In particular, the photoelectron spectra of MX 2 (where M ¼ Li, Na, and X ¼ Cl, Br, I) anions have been obtained and assigned on the basis of ab initio outer valence Green function (OVGF) calculations. An excellent agreement between experimentally and theoretically estimated values of VDEs has been achieved and all the anions have proven to be superhalogen-based species since their electron binding energies were found to be greater than 3.62 eV (see [9] for details). It should be noted that although there are many theoretical results for superhalogens anions available, most of them were obtained in 80s when the computational resources limited the level of calculations. In particular, early discrete-variational Xa -method calculations led to underestimated values of the VDEs of many superhalogen anions, although it should be stated that the main goal of these investigations was to prove that such species are indeed exhibiting extremely large electron binding energies rather than to provide precise vertical detachment energies [4,5]. We faced this problem (inaccuracy of VDEs or lack thereof) recently while studying a completely different class of molecular anions (i.e., dipole-bound anions supported by the neutral systems involving dative bonds). In a course of our studies we encountered BeX 3 anions (where X ¼ F, Cl, Br) that were involved in complexes with certain cations (e.g., H3 Oþ ) as their counterparts [10]. In fact, one would wonder if attaching of an extra electron to
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(H3 Oþ =BeX 3 ) species leads to the anion of Rydberg or dipole-bound nature. In order to understand this phenomenon better, we performed a literature search for relatively accurate VDEs of BeX 3 superhalogen anions. Unfortunately, the results we found were either old (and thus not accurate) or incomplete (i.e., not containing ‘mixed’ species, such as BeFCl 2 or BeFClBr , for example). This lack of data has motivated us to take a closer look at the various superhalogen anions of this type and to calculate possibly accurate values of their vertical electron detachment energies. In this contribution, we present our ab initio results for 10 negatively charged species exhibiting ‘superhalogen nature’ and having beryllium as the metal component (BeX 3 ). We also show that the theoretical treatment we used performs very well if applied to other previously described superhalogen anions whose accurate experimental VDEs are available.
2. Methods Since our main goal was to calculate the vertical electron detachment energies for the BeX 3 anions we limited our geometry optimization calculations to the closed-shell anionic species for which we also obtained harmonic vibrational frequencies at their minimum energy structures. For this purpose we applied second-order Møller–Plesset (MP2) perturbational method with the 6-311++G(d) basis sets [11,12]. Providing reliable vertical electron detachment energies of the BeX 3 anions requires using more accurate treatment thus we decided to perform both direct and indirect calculations of the electron binding energies. A direct scheme was based on applying the outer valence Green function (OVGF) method [13,14] while the latter (indirect) approach consisted in subtracting the anion energies from those of the neutral (both calculated at the same level of theory). In an indirect approach we used MPn perturbational methods up to the fourth order (n ¼ 2, 3, 4) and the coupledcluster method with single, double, and noniterative inclusion of triple excitations (CCSD(T)) [15]. The core electrons were kept frozen in treating the electron correlation.
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As far as the basis sets are concerned, we applied both the 6-311++G(d) and 6-311++G(3df) basis sets [11] while estimating vertical electron detachment energies at various levels since analogous basis sets have recently been used by others for LiX 2 and NaX2 (X ¼ F, Cl, Br, I) superhalogen anions and provided an excellent agreement between such calculated and experimentally measured VDEs [9]. All calculations were performed with the GA U S S I A N 98 program [16] on Intel Pentium IV computers and an SGI Origin2000 numerical server. The three-dimensional plots of molecular orbitals were generated with the MO L D E N program [17].
3. Results 3.1. Testing the theoretical treatment for previously described superhalogen anions In order to determine the usefulness and accuracy of our theoretical treatment for calculating the vertical electron detachment energies of superhalogen anions we decided to perform some test calculations of the VDEs of previously studied anions exhibiting similar nature. For this purpose, we chose LiCl 2 and NaCl2 anions, whose experimentally measured VDEs have been recently published [9]. Our results are collected in Table 1 where the experimental values are also presented for comparison. The analysis of the vertical elec-
tron detachment energies calculated at various levels of theory with two different basis sets indicates that the VDEs obtained by using the CCSD(T) and OVGF methods are in good agreement with the experimental results when the 6-311++G(3df) basis set is used. The 6-311++G(d) basis set leads to somewhat underestimated VDEs (by ca. 0.3 eV, see Table 1). It is also clear that the best estimates come from applying the OVGF method and such calculated vertical electron detachment energies of the LiCl 2 (5.98 eV) and NaCl (5.89 eV) differ from the measured VDEs 2 by 0.06 and 0.03 eV, respectively. These deviations are within the experimental uncertainties range reported by Wang et al. [9], and thus we feel confident that our OVGF/6-311++G(3df) treatment should be sufficient for calculating vertical electron detachment energies of other superhalogen anions. 3.2. The MP2 equilibrium geometries and vibrational frequencies The MP2 minimum energy structures of the superhalogen anions BeX 3 (X ¼ F, Cl, Br) are characterized in Table 2 where the corresponding harmonic vibrational frequencies are also collected. Since for each negatively charged system studied in this work all the Hessian matrix eigenvalues were found positive we are confident these structures correspond to the minima on the MP2 ground-state anion potential energy surface.
Table 1 The vertical electron detachment energies (in eV) of LiCl 2 and NaCl2 calculated at various levels of theory with two different basis sets: 6-311++G(d) and 6-311++G(3df) VDE (eV) LiCl 2
VDE (eV) NaCl 2
6-311++G(d)
6-311++G(3df)
6-311++G(d)
6-311++G(3df)
MP2 MP3 MP4 CCSD CCSD(T) OVGF
5.568 5.559 5.763 5.586 5.527 5.666
5.858 5.856 5.866 5.879 5.837 5.979
5.455 5.459 5.440 5.485 5.423 5.564
5.753 5.766 5.765 5.792 5.744 5.892
EXP.
5:92 0:04
The experimental results are taken from [9].
5:86 0:06
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Table 2 The MP2 geometrical parameters, harmonic vibrational frequencies, and the best estimates of the vertical electron detachment energies (VDE) for all the anions studied in this work Species
Symmetry point group
VDE (eV) OVGF/ 6-311++G(3df)
Geometry
Vibr. freq. (cm1 )
BeF 3
D3h
7.630a
R(Be–F) ¼ 1.492 \(FBeF) ¼ 120.00
m1:2 ¼ 315 ðe0 Þ m3 ¼ 541 ða002 Þ m4 ¼ 580 ða01 Þ m5:6 ¼ 1037 ðe0 Þ
BeF2 Cl
C2v
6.239
R(Be–F) ¼ 1.474 R(Be–Cl) ¼ 1.963 \(FBeF) ¼ 123.06 \(FBeCl) ¼ 118.47
m1 m2 m3 m4 m5 m6
¼ 228 ðb2 Þ ¼ 279 ða1 Þ ¼ 474 ða1 Þ ¼ 477 ðb1 Þ ¼ 876 ða1 Þ ¼ 1093 ðb2 Þ
BeCl2 F
C2v
6.166
R(Be–F) ¼ 1.460 R(Be–Cl) ¼ 1.939 \(FBeCl) ¼ 120.45 \(ClBeCl) ¼ 119.10
m1 m2 m3 m4 m5 m6
¼ 183 ða1 Þ ¼ 243 ðb2 Þ ¼ 398 ða1 Þ ¼ 416 ðb1 Þ ¼ 744 ðb2 Þ ¼ 1030 ða1 Þ
BeCl 3
D3h
6.171
R(Be–Cl) ¼ 1.922 \(ClBeCl) ¼ 120.00
m1:2 ¼ 176 ðe0 Þ m3 ¼ 342 ða01 Þ m4 ¼ 365 ða002 Þ m5:6 ¼ 770 ðe0 Þ
BeF2 Br
C2v
5.585
R(Be–F) ¼ 1.467 R(Be–Br) ¼ 2.158 \(FBeF) ¼ 124.60 \(FBeBr) ¼ 117.70
m1 m2 m3 m4 m5 m6
¼ 199 ðb2 Þ ¼ 230 ða1 Þ ¼ 424 ða1 Þ ¼ 455 ðb1 Þ ¼ 840 ða1 Þ ¼ 1119 ðb2 Þ
BeFClBr
Cs
5.715
R(Be–F) ¼ 1.455 R(Be–Cl) ¼ 1.929 R(Be–Br) ¼ 2.131 \(FBeCl) ¼ 121.92 \(FBeBr) ¼ 119.32 \(ClBeBr) ¼ 118.76
m1 m2 m3 m4 m5 m6
¼ 152 ða0 Þ ¼ 216 ða0 Þ ¼ 350 ða0 Þ ¼ 397 ða00 Þ ¼ 694 ða0 Þ ¼ 1038 ða0 Þ
BeCl2 Br
C2v
5.803
R(Be–Cl) ¼ 1.913 R(Be–Br) ¼ 2.109 \(ClBeCl) ¼ 121.00 \(ClBeBr) ¼ 119.50
m1 m2 m3 m4 m5 m6
¼ 148 ¼ 155 ¼ 297 ¼ 347 ¼ 694 ¼ 788
BeBr2 F
C2v
5.602
R(Be–F) ¼ 1.451 R(Be–Br) ¼ 2.118 \(FBeBr) ¼ 120.59 \(BrBeBr) ¼ 118.82
m1 m2 m3 m4 m5 m6
¼ 118 ða1 Þ ¼ 203 ðb2 Þ ¼ 303 ða1 Þ ¼ 378 ðb1 Þ ¼ 636 ðb2 Þ ¼ 1038 ða1 Þ
BeBr2 Cl
C2v
5.692
R(Be–Cl) ¼ 1.906 R(Be–Br) ¼ 2.100
m1 ¼ 118 ða1 Þ m2 ¼ 139 ðb2 Þ
ðb2 Þ ða1 Þ ða1 Þ ðb1 Þ ða1 Þ ðb2 Þ
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Table 2 (continued) Species
BeBr 3
a
Symmetry point group
D3h
VDE (eV) OVGF/ 6-311++G(3df)
5.647
Geometry
Vibr. freq. (cm1 )
\(BrBeCl) ¼ 120.37 \(BrBeBr) ¼ 119.26
m3 m4 m5 m4
R(Be–Br) ¼ 2.092 \(BrBeBr) ¼ 120.00
m1:2 ¼ 108 ðe0 Þ m3 ¼ 206 ða01 Þ m4 ¼ 312 ða00 Þ m5:6 ¼ 666 ðe0 Þ
¼ 253 ¼ 330 ¼ 653 ¼ 758
ða1 Þ ðb1 Þ ðb2 Þ ða1 Þ
, valence angles (\) in degrees, vertical electron detachment energies in eV. Bond lengths (R) in A CCSD(T)/6-311++G(3df) result (see Section 3.3).
We found all the BeX 3 (X ¼ F, Cl, Br) anions to be planar and possess D3h (BeF 3 , BeCl3 , BeBr3 ), C2v (BeF2 Cl , BeCl2 F , BeF2 Br , BeCl2 Br , BeBr2 F , BeBr2 Cl ), and Cs (BeFClBr ) symmetry. This finding is consistent with the earlier cal culations performed by others for BeF 3 and BeCl3 in which planar D3h -symmetry geometries were assumed [4,18]. The beryllium–fluorine bond length for the optimized anions are within the 1.451–1.492 A range and we found the largest Be–F separation for the BeF 3 species (see Table 2). Data collected in Table 2 demonstrate that the Be–X distance gradually decreases when X atoms in BeX 3 are subsequently substituted with the less electronegative Y atoms, whereas the reverse is observed when Y is more electronegative than X. To illustrate, the shortening of the Be–F bond length by accompanies subsequent substica. 0.02–0.03 A tution of fluorine atoms with chlorine ones in BeF 3 . Similarly, the 0.03–0.07 A elongation of the Be–Br distance is observed when bromine atoms in BeBr 3 are subsequently replaced with fluorine atoms (see Table 2). Even though the reported geometry differences seem relatively small, it should be noted that they could play an important role in superhalogen species because the halogen–central atom distance significantly influences the vertical electron detachment energy of such anions, as was previously concluded by Gutsev and Boldyrev [4]. Moreover, it was found on the basis of the simple electrostatic model consisting of F anion and the positive charge þq separated by the 3.0 a.u. distance, that
the electron binding energy of F increases by approximately 1 eV when q increases by 0.1 a.u. [4] Since the superhalogen anion, such as BeX 3 , may be considered as the neutral BeX2 system with the X attached, one may expect the strong dependence of the partial atomic positive charge localized on the central atom (Be) on the VDE of such an anion. The significance of these effects for BeX 3 (X ¼ F, Cl, Br) anions is discussed in the following section. 3.3. Vertical electron detachment energies The vertical electron detachment energies of BeX 3 (X ¼ F, Cl, Br) anions calculated at the OVGF/6-311++G(3df) level are collected in Tables 2 and 3 while those obtained at the CCSD(T) level with the 6-311G(3df) basis sets are shown in Table 3. As it was concluded in Section 3.1 we consider the VDEs calculated at the OVGF level with the 6-311++G(3df) basis sets as the most reliable since they are in a very good agreement with the experimentally measured values (see Table 1). Therefore, let us begin with the discussion of such obtained vertical electron detachment energies of the superhalogen anions studied in this work. First, we want to stress that all the calculated VDEs greatly exceed the electron affinity of the chlorine atom (3.62 eV) and thus the studied BeX 3 species should be classified as the superhalogen anions. The largest VDE among systems considered was found for the BeF 3 , however, this happens to be the only case where our OVGF and
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Table 3 The vertical electron detachment energies (in eV) of all superhalogen anions studied in this work calculated at the CCSD(T) and OVGF level with two different basis sets: 6-311++G(d) and 6-311++G(3df) CCSD(T)
BeF 3 BeF2 Cl BeCl2 F BeCl 3 BeF2 Br BeFClBr BeCl2 Br BeBr2 F BeBr2 Cl BeBr 3
OVGF
6-311++G(d)
6-311++G(3df)
6-311++G(d)
6-311++G(3df)
7.406 5.801 5.721 5.693 5.260 5.361 5.416 5.274 5.327 5.292
7.630 6.081 6.029 6.027 5.486 5.614 5.691 5.513 5.590 5.549
8.256 5.952 5.855 5.839 5.367 5.474 5.542 5.374 5.444 5.406
8.472 6.239 6.166 6.171 5.585 5.715 5.803 5.602 5.692 5.647
CCSD(T) results differ significantly from each other. In particular, the OVGF value of VDE (8.472 eV) seems overestimated while compared to our CCSD(T) result (7.630 eV) and the result obtained by Weikert et al. [19] (7.86 eV) who used the third-order algebraic diagrammatic construction (ADC(3)) Green’s function approach. Therefore, in the case of BeF 3 we prefer to rely on our CCSD(T) value rather than that derived from the OVGF calculation. The vertical electron detachment energies of the remaining anions are always larger than 5.5 eV (see Table 2). The correlation between the VDEs (collected in Table 2) and the chemical constitution, geometrical parameters, or partial atomic charges [20] is not straightforward, however, a few tendencies could be noticed: (i) In the BeF 3 –BeCl3 –BeBr3 series the VDE decreases with an increase of the atomic number of the halogen atoms (i.e., the lowest VDE corresponds to BeBr 3 ). It is consistent with the partial atomic charge on beryllium (qBe ) becoming less positive (qBe ¼ 1:182, 0.696, and 0.552 a.u. for BeF 3 , BeCl3 , and BeBr3 , respectively). (ii) The analysis of the results calculated for the BeF 3 , BeF2 Cl , and BeF2 Br indicates that replacing the fluorine atom in BeF 3 with Cl or Br also leads to lower VDE (by 1.4 and 2.0 eV, respectively, see Table 2) which is accompanied again by the decrease of the qBe (qBe ¼ 1:034 a.u. for BeF2 Cl and 0.992 a.u. for BeF2 Br ). (iii) If one compares the results for BeCl 3 with these obtained when one or two chlorine atoms
are replaced with the F or Br atoms, it seems that similar tendencies are preserved (i.e., the decrease of the VDE accompanies the decrease of the qBe ). For example, qBe ¼ 0:664 a.u. for BeCl2 Br and 0.696 a.u. for BeCl 3 while the VDE of the latter exceeds that of the former by 0.37 eV (see Table 2). (iv) The shortening of the Be–F bond length observed when the fluorine atoms in BeF 3 are being subsequently substituted with chlorine (BeF2 Cl , BeCl2 F ) or bromine (BeF2 Br , BeBr2 F ) is consistent with the decrease of the VDE (see Table 2). These conclusions are in agreement with the general predictions formulated previously for the superhalogen anions [4,5]. In particular, the observation that smaller ‘size’ of the halogen ligands usually leads to larger vertical electron detachment energies is confirmed by our results. Moreover, it seems clear that the partial atomic charge localized on the central atom (Be in our case) as well as the ligand–central atom separations are strongly related to the VDE of the resulting anion. In order to support our discussion we present the three-dimensional pictures of the highest occupied molecular orbital (HOMO) for three cho sen anions: BeF and BeFClBr (see 3 , BeCl2 F Fig. 1). It is shown that in each case the HOMO is composed purely of ligand atomic orbitals (AO) while the contributions from the central atom (beryllium) are absent. As a consequence, the HOMO is a nonbonding molecular orbital (MO)
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Fig. 1. The highest occupied molecular orbital (HOMO) of the BeF 3 (top), BeCl2 F (middle), and BeFClBr (bottom) superhalogen anions (plotted with 0.03 bohr3=2 contour spacing).
with respect to the ligand–central atom interaction. This finding is consistent with the prediction formulated by Gutsev and Boldyrev [4] who suggested that the species for which the HOMO has such character should possess relatively high VDE values. The calculations of the vertical electron binding energies, although doable for BeX 3 (X ¼ F, Cl, Br) anions, can be found very expensive and time consuming for larger systems when performed at the OVGF and especially at the CCSD(T) level with large basis sets. Therefore, we decided to check if any lower-level theoretical treatment could be found sufficient for approximate estimating the VDEs for superhalogen anions. Since it was not our goal to undertake any systematic studies in this matter, we limit our discussion to the results obtained at the MPn (n ¼ 2, 3, 4), CCSD, CCSD(T), and OVGF level with the 6-311++G(d) and 6-311++G(3df) basis sets. The vertical electron detachment energies calculated at these levels for two anions, BeCl 3 and BeBr3 , are collected in Table 4. In addition, we support our discussion with the results obtained for the LiCl 2 and NaCl 2 while testing the accuracy of the applied treatment (see Table 1 and Section 3.1). According to our conclusions (see the preceding paragraphs in this section) the most reliable VDEs of the superhalogen anions are those calculated at the OVGF/6-311++G(3df) level and therefore we use these values as the reference while analyzing the vertical electron detachment energies obtained at different levels. At the first glance it seems clear that the VDEs of the BeCl 3 and BeBr3 anions are underestimated
Table 4 The vertical electron detachment energies (in eV) of BeCl 3 and BeBr3 calculated at various levels of theory with two different basis sets: 6-311++G(d) and 6-311++G(3df) VDE (eV) BeCl 3
VDE (eV) BeBr 3
MP2 MP3 MP4 CCSD CCSD(T) OVGF
6-311++G(d)
6-311++G(3df)
6-311++G(d)
6-311++G(3df)
5.343 5.349 5.299 5.415 5.292 5.406
5.552 5.568 5.554 5.656 5.549 5.647
5.728 5.764 5.693 5.832 5.693 5.839
6.021 6.066 6.028 6.117 6.027 6.171
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at each level of theory used (with respect to the OVGF values). The only exception is the CCSD result for the BeBr 3 that is slightly overestimated. In particular, the use of the CCSD(T) method leads to the VDEs that are lower by 0.144 and 0.098 eV for BeCl 3 and BeBr3 , respectively (see Table 4), when compared with the OVGF values. Similar agreement among the VDEs calculated at the CCSD, CCSD(T), and OVGF levels can be noted for the LiCl 2 and NaCl2 species. In particular, the CCSD(T) results, although underestimated (by ca. 0.15 eV), are in good agreement with both OVGF and experimental results (see Table 1). This indicates that one may expect the CCSD(T) treatment to provide the VDE with a decent accuracy for an unknown superhalogen anion. Moreover, it can be anticipated that such a value could be slightly underestimated. The analysis of the VDEs calculated at the MP2, MP3, and MP4 levels shows that the convergence of the MP series is satisfactory for BeCl 3, BeBr , LiCl and NaCl anions (see Tables 1 and 2 2 3 4). Moreover, it should be noted that relatively inexpensive MP2 treatment leads to quite reliable estimates of the VDEs. The vertical electron detachment energies calculated at the MP2 level with the 6-311++G(3df) basis sets are always underestimated and the difference between the MP2 and OVGF results is always lower than 0.15 eV (for the anions studied in this work). This finding would allow for an easy and fast estimate of the electronic stability of a superhalogen anion when neither experimental nor theoretical results are available. We therefore conclude that the OVGF method should be considered as the most reliable for predicting VDEs of superhalogen anions. For any crude or preliminary estimates, however, we recommend applying the MP2 method which should result with an underestimated vertical electron detachment energies.
4. Summary The vertical electron detachment energies of the superhalogen anions BeX 3 (X ¼ F, Cl, Br) were calculated at the OVGF/6-311++G(3df) and CCSD(T)/6-311++G(3df) level. All the negatively
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charged species studied in this work were derived from their neutral parent radicals and have proven to exhibit a ‘superhalogen’ nature which means their electron binding energies were found to significantly exceed the electron affinity of chlorine (3.62 eV). It was concluded the OVGF/ 6-311++G(3df) treatment produces reliable estimates of the previously studied superhalogen anions and the following vertical detachment energies of 10 BeX 3 (X ¼ F, Cl, Br) species considered in this work were found to be: 7.630 eV (BeF 3 ), 6.239 eV (BeF2 Cl ), 6.166 eV (BeCl2 F ), 6.171 eV (BeCl 3 ), 5.585 eV (BeF2 Br ), 5.715 eV (BeFClBr ), 5.803 eV (BeCl2 Br ), 5.602 eV (BeBr2 F ), 5.692 eV (BeBr2 Cl ), and 5.647 eV (BeBr 3 ).
Acknowledgements We would like to thank Prof. J. Rak for his valuable comments. This work was supported by the Polish State Committee for Scientific Research (KBN) Grant No. DS/8371-4-0137-2 and the NSF Grants 9618904 and 9982420. The computer time provided by the Academic Computer Center in Gdask (TASK) and the Center for High Performance Computing at the University of Utah is also gratefully acknowledged.
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Chemical Physics Letters 358 (2002) 426–434 www.elsevier.com/locate/cplett
An ab initio study on BeX 3 superhalogen anions (X ¼ F, Cl, Br) Iwona Anusiewicz, Piotr Skurski
*
Department of Chemistry, University of Gda nsk, ul. Sobieskiego 18, 80952 Gda nsk, Poland Department of Chemistry, University of Utah, Salt Lake City, UT 84112, USA Received 4 April 2002
Abstract The vertical electron detachment energies (VDE) of 10 BeX 3 (X ¼ F, Cl, Br) anions were calculated at the outer valence Green function (OVGF) level with the 6-311++G(3df) basis sets. The largest vertical electron binding energy was found for BeF 3 system (7.63 eV). All negatively charged species possess the vertical electron detachment energies that are larger than 5.5 eV and thus may be termed superhalogen anions. The strong dependence of the VDE of the BeX 3 species on the ligand–central atom (Be–X) distance and on the partial atomic charge localized on Be was observed and discussed, as well as the other factors that may influence the electronic stability of such anions. In addition, the usefulness of the various theoretical treatments for estimating the VDEs of superhalogen anions was tested and analyzed. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction It is well known that halogen atoms possess the highest electron affinities (EA) among the elements (fluorine 3.40 eV, chlorine 3.62 eV) [1]. However, the EA of a polyatomic system may exceed the 3.62 eV limit due to collective effects. Such species are of a great importance in chemistry since they can be used for the oxidation of counterpart systems with relatively high ionization potentials (such as O2 , Xe) and allow the synthesis of unusual chemical compounds (e.g., involving nobel gases
*
Corresponding author. E-mail address: [email protected] (P. Skurski).
atoms). In addition, molecules possessing high electron affinities are widely used in the production of organic superconductors [2,3]. Although such species have been attracting chemists’ attention since early 60s, it was only in 1981 when Gutsev and Boldyrev proposed to term them superhalogens and introduced a simple formula for one class of these compounds, MXkþ1 , where M is a main group or transition metal atom, X is a halogen atom, and k is the maximal formal valence of the atom M [4]. It was a milestone work since Gutsev and Boldyrev not only provided theoretically estimated electron binding energies of superhalogenbased anions but they also pointed out a few main reasons as being responsible for the increase of the vertical electron detachment energy (VDE) in MX kþ1 relative to X , such as: (i) delocalization of
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the extra electron over k þ 1 halogen atoms instead of one, (ii) nonbonding character of the highest occupied molecular orbital (HOMO), (iii) coordination of X anion to the electropositive ion Mkþ (electrostatic effect), and (iv) stabilizing electron relaxation and correlation effects [4]. Since early 80s, many other theoretical efforts have been undertaken to estimate the VDEs of various anions having superhalogens as their neutral parents (see [5–8] and references cited therein). In 1999 a dramatic progress has been made in the investigating superhalogen systems due to the joined theoretical and experimental effort that resulted in an excellent report comprising of the first experimental photoelectron spectra of superhalogens (measured by Wang’s group) together with their theoretical interpretations provided by Boldyrev and Simons [9]. In particular, the photoelectron spectra of MX 2 (where M ¼ Li, Na, and X ¼ Cl, Br, I) anions have been obtained and assigned on the basis of ab initio outer valence Green function (OVGF) calculations. An excellent agreement between experimentally and theoretically estimated values of VDEs has been achieved and all the anions have proven to be superhalogen-based species since their electron binding energies were found to be greater than 3.62 eV (see [9] for details). It should be noted that although there are many theoretical results for superhalogens anions available, most of them were obtained in 80s when the computational resources limited the level of calculations. In particular, early discrete-variational Xa -method calculations led to underestimated values of the VDEs of many superhalogen anions, although it should be stated that the main goal of these investigations was to prove that such species are indeed exhibiting extremely large electron binding energies rather than to provide precise vertical detachment energies [4,5]. We faced this problem (inaccuracy of VDEs or lack thereof) recently while studying a completely different class of molecular anions (i.e., dipole-bound anions supported by the neutral systems involving dative bonds). In a course of our studies we encountered BeX 3 anions (where X ¼ F, Cl, Br) that were involved in complexes with certain cations (e.g., H3 Oþ ) as their counterparts [10]. In fact, one would wonder if attaching of an extra electron to
427
(H3 Oþ =BeX 3 ) species leads to the anion of Rydberg or dipole-bound nature. In order to understand this phenomenon better, we performed a literature search for relatively accurate VDEs of BeX 3 superhalogen anions. Unfortunately, the results we found were either old (and thus not accurate) or incomplete (i.e., not containing ‘mixed’ species, such as BeFCl 2 or BeFClBr , for example). This lack of data has motivated us to take a closer look at the various superhalogen anions of this type and to calculate possibly accurate values of their vertical electron detachment energies. In this contribution, we present our ab initio results for 10 negatively charged species exhibiting ‘superhalogen nature’ and having beryllium as the metal component (BeX 3 ). We also show that the theoretical treatment we used performs very well if applied to other previously described superhalogen anions whose accurate experimental VDEs are available.
2. Methods Since our main goal was to calculate the vertical electron detachment energies for the BeX 3 anions we limited our geometry optimization calculations to the closed-shell anionic species for which we also obtained harmonic vibrational frequencies at their minimum energy structures. For this purpose we applied second-order Møller–Plesset (MP2) perturbational method with the 6-311++G(d) basis sets [11,12]. Providing reliable vertical electron detachment energies of the BeX 3 anions requires using more accurate treatment thus we decided to perform both direct and indirect calculations of the electron binding energies. A direct scheme was based on applying the outer valence Green function (OVGF) method [13,14] while the latter (indirect) approach consisted in subtracting the anion energies from those of the neutral (both calculated at the same level of theory). In an indirect approach we used MPn perturbational methods up to the fourth order (n ¼ 2, 3, 4) and the coupledcluster method with single, double, and noniterative inclusion of triple excitations (CCSD(T)) [15]. The core electrons were kept frozen in treating the electron correlation.
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As far as the basis sets are concerned, we applied both the 6-311++G(d) and 6-311++G(3df) basis sets [11] while estimating vertical electron detachment energies at various levels since analogous basis sets have recently been used by others for LiX 2 and NaX2 (X ¼ F, Cl, Br, I) superhalogen anions and provided an excellent agreement between such calculated and experimentally measured VDEs [9]. All calculations were performed with the GA U S S I A N 98 program [16] on Intel Pentium IV computers and an SGI Origin2000 numerical server. The three-dimensional plots of molecular orbitals were generated with the MO L D E N program [17].
3. Results 3.1. Testing the theoretical treatment for previously described superhalogen anions In order to determine the usefulness and accuracy of our theoretical treatment for calculating the vertical electron detachment energies of superhalogen anions we decided to perform some test calculations of the VDEs of previously studied anions exhibiting similar nature. For this purpose, we chose LiCl 2 and NaCl2 anions, whose experimentally measured VDEs have been recently published [9]. Our results are collected in Table 1 where the experimental values are also presented for comparison. The analysis of the vertical elec-
tron detachment energies calculated at various levels of theory with two different basis sets indicates that the VDEs obtained by using the CCSD(T) and OVGF methods are in good agreement with the experimental results when the 6-311++G(3df) basis set is used. The 6-311++G(d) basis set leads to somewhat underestimated VDEs (by ca. 0.3 eV, see Table 1). It is also clear that the best estimates come from applying the OVGF method and such calculated vertical electron detachment energies of the LiCl 2 (5.98 eV) and NaCl (5.89 eV) differ from the measured VDEs 2 by 0.06 and 0.03 eV, respectively. These deviations are within the experimental uncertainties range reported by Wang et al. [9], and thus we feel confident that our OVGF/6-311++G(3df) treatment should be sufficient for calculating vertical electron detachment energies of other superhalogen anions. 3.2. The MP2 equilibrium geometries and vibrational frequencies The MP2 minimum energy structures of the superhalogen anions BeX 3 (X ¼ F, Cl, Br) are characterized in Table 2 where the corresponding harmonic vibrational frequencies are also collected. Since for each negatively charged system studied in this work all the Hessian matrix eigenvalues were found positive we are confident these structures correspond to the minima on the MP2 ground-state anion potential energy surface.
Table 1 The vertical electron detachment energies (in eV) of LiCl 2 and NaCl2 calculated at various levels of theory with two different basis sets: 6-311++G(d) and 6-311++G(3df) VDE (eV) LiCl 2
VDE (eV) NaCl 2
6-311++G(d)
6-311++G(3df)
6-311++G(d)
6-311++G(3df)
MP2 MP3 MP4 CCSD CCSD(T) OVGF
5.568 5.559 5.763 5.586 5.527 5.666
5.858 5.856 5.866 5.879 5.837 5.979
5.455 5.459 5.440 5.485 5.423 5.564
5.753 5.766 5.765 5.792 5.744 5.892
EXP.
5:92 0:04
The experimental results are taken from [9].
5:86 0:06
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Table 2 The MP2 geometrical parameters, harmonic vibrational frequencies, and the best estimates of the vertical electron detachment energies (VDE) for all the anions studied in this work Species
Symmetry point group
VDE (eV) OVGF/ 6-311++G(3df)
Geometry
Vibr. freq. (cm1 )
BeF 3
D3h
7.630a
R(Be–F) ¼ 1.492 \(FBeF) ¼ 120.00
m1:2 ¼ 315 ðe0 Þ m3 ¼ 541 ða002 Þ m4 ¼ 580 ða01 Þ m5:6 ¼ 1037 ðe0 Þ
BeF2 Cl
C2v
6.239
R(Be–F) ¼ 1.474 R(Be–Cl) ¼ 1.963 \(FBeF) ¼ 123.06 \(FBeCl) ¼ 118.47
m1 m2 m3 m4 m5 m6
¼ 228 ðb2 Þ ¼ 279 ða1 Þ ¼ 474 ða1 Þ ¼ 477 ðb1 Þ ¼ 876 ða1 Þ ¼ 1093 ðb2 Þ
BeCl2 F
C2v
6.166
R(Be–F) ¼ 1.460 R(Be–Cl) ¼ 1.939 \(FBeCl) ¼ 120.45 \(ClBeCl) ¼ 119.10
m1 m2 m3 m4 m5 m6
¼ 183 ða1 Þ ¼ 243 ðb2 Þ ¼ 398 ða1 Þ ¼ 416 ðb1 Þ ¼ 744 ðb2 Þ ¼ 1030 ða1 Þ
BeCl 3
D3h
6.171
R(Be–Cl) ¼ 1.922 \(ClBeCl) ¼ 120.00
m1:2 ¼ 176 ðe0 Þ m3 ¼ 342 ða01 Þ m4 ¼ 365 ða002 Þ m5:6 ¼ 770 ðe0 Þ
BeF2 Br
C2v
5.585
R(Be–F) ¼ 1.467 R(Be–Br) ¼ 2.158 \(FBeF) ¼ 124.60 \(FBeBr) ¼ 117.70
m1 m2 m3 m4 m5 m6
¼ 199 ðb2 Þ ¼ 230 ða1 Þ ¼ 424 ða1 Þ ¼ 455 ðb1 Þ ¼ 840 ða1 Þ ¼ 1119 ðb2 Þ
BeFClBr
Cs
5.715
R(Be–F) ¼ 1.455 R(Be–Cl) ¼ 1.929 R(Be–Br) ¼ 2.131 \(FBeCl) ¼ 121.92 \(FBeBr) ¼ 119.32 \(ClBeBr) ¼ 118.76
m1 m2 m3 m4 m5 m6
¼ 152 ða0 Þ ¼ 216 ða0 Þ ¼ 350 ða0 Þ ¼ 397 ða00 Þ ¼ 694 ða0 Þ ¼ 1038 ða0 Þ
BeCl2 Br
C2v
5.803
R(Be–Cl) ¼ 1.913 R(Be–Br) ¼ 2.109 \(ClBeCl) ¼ 121.00 \(ClBeBr) ¼ 119.50
m1 m2 m3 m4 m5 m6
¼ 148 ¼ 155 ¼ 297 ¼ 347 ¼ 694 ¼ 788
BeBr2 F
C2v
5.602
R(Be–F) ¼ 1.451 R(Be–Br) ¼ 2.118 \(FBeBr) ¼ 120.59 \(BrBeBr) ¼ 118.82
m1 m2 m3 m4 m5 m6
¼ 118 ða1 Þ ¼ 203 ðb2 Þ ¼ 303 ða1 Þ ¼ 378 ðb1 Þ ¼ 636 ðb2 Þ ¼ 1038 ða1 Þ
BeBr2 Cl
C2v
5.692
R(Be–Cl) ¼ 1.906 R(Be–Br) ¼ 2.100
m1 ¼ 118 ða1 Þ m2 ¼ 139 ðb2 Þ
ðb2 Þ ða1 Þ ða1 Þ ðb1 Þ ða1 Þ ðb2 Þ
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Table 2 (continued) Species
BeBr 3
a
Symmetry point group
D3h
VDE (eV) OVGF/ 6-311++G(3df)
5.647
Geometry
Vibr. freq. (cm1 )
\(BrBeCl) ¼ 120.37 \(BrBeBr) ¼ 119.26
m3 m4 m5 m4
R(Be–Br) ¼ 2.092 \(BrBeBr) ¼ 120.00
m1:2 ¼ 108 ðe0 Þ m3 ¼ 206 ða01 Þ m4 ¼ 312 ða00 Þ m5:6 ¼ 666 ðe0 Þ
¼ 253 ¼ 330 ¼ 653 ¼ 758
ða1 Þ ðb1 Þ ðb2 Þ ða1 Þ
, valence angles (\) in degrees, vertical electron detachment energies in eV. Bond lengths (R) in A CCSD(T)/6-311++G(3df) result (see Section 3.3).
We found all the BeX 3 (X ¼ F, Cl, Br) anions to be planar and possess D3h (BeF 3 , BeCl3 , BeBr3 ), C2v (BeF2 Cl , BeCl2 F , BeF2 Br , BeCl2 Br , BeBr2 F , BeBr2 Cl ), and Cs (BeFClBr ) symmetry. This finding is consistent with the earlier cal culations performed by others for BeF 3 and BeCl3 in which planar D3h -symmetry geometries were assumed [4,18]. The beryllium–fluorine bond length for the optimized anions are within the 1.451–1.492 A range and we found the largest Be–F separation for the BeF 3 species (see Table 2). Data collected in Table 2 demonstrate that the Be–X distance gradually decreases when X atoms in BeX 3 are subsequently substituted with the less electronegative Y atoms, whereas the reverse is observed when Y is more electronegative than X. To illustrate, the shortening of the Be–F bond length by accompanies subsequent substica. 0.02–0.03 A tution of fluorine atoms with chlorine ones in BeF 3 . Similarly, the 0.03–0.07 A elongation of the Be–Br distance is observed when bromine atoms in BeBr 3 are subsequently replaced with fluorine atoms (see Table 2). Even though the reported geometry differences seem relatively small, it should be noted that they could play an important role in superhalogen species because the halogen–central atom distance significantly influences the vertical electron detachment energy of such anions, as was previously concluded by Gutsev and Boldyrev [4]. Moreover, it was found on the basis of the simple electrostatic model consisting of F anion and the positive charge þq separated by the 3.0 a.u. distance, that
the electron binding energy of F increases by approximately 1 eV when q increases by 0.1 a.u. [4] Since the superhalogen anion, such as BeX 3 , may be considered as the neutral BeX2 system with the X attached, one may expect the strong dependence of the partial atomic positive charge localized on the central atom (Be) on the VDE of such an anion. The significance of these effects for BeX 3 (X ¼ F, Cl, Br) anions is discussed in the following section. 3.3. Vertical electron detachment energies The vertical electron detachment energies of BeX 3 (X ¼ F, Cl, Br) anions calculated at the OVGF/6-311++G(3df) level are collected in Tables 2 and 3 while those obtained at the CCSD(T) level with the 6-311G(3df) basis sets are shown in Table 3. As it was concluded in Section 3.1 we consider the VDEs calculated at the OVGF level with the 6-311++G(3df) basis sets as the most reliable since they are in a very good agreement with the experimentally measured values (see Table 1). Therefore, let us begin with the discussion of such obtained vertical electron detachment energies of the superhalogen anions studied in this work. First, we want to stress that all the calculated VDEs greatly exceed the electron affinity of the chlorine atom (3.62 eV) and thus the studied BeX 3 species should be classified as the superhalogen anions. The largest VDE among systems considered was found for the BeF 3 , however, this happens to be the only case where our OVGF and
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Table 3 The vertical electron detachment energies (in eV) of all superhalogen anions studied in this work calculated at the CCSD(T) and OVGF level with two different basis sets: 6-311++G(d) and 6-311++G(3df) CCSD(T)
BeF 3 BeF2 Cl BeCl2 F BeCl 3 BeF2 Br BeFClBr BeCl2 Br BeBr2 F BeBr2 Cl BeBr 3
OVGF
6-311++G(d)
6-311++G(3df)
6-311++G(d)
6-311++G(3df)
7.406 5.801 5.721 5.693 5.260 5.361 5.416 5.274 5.327 5.292
7.630 6.081 6.029 6.027 5.486 5.614 5.691 5.513 5.590 5.549
8.256 5.952 5.855 5.839 5.367 5.474 5.542 5.374 5.444 5.406
8.472 6.239 6.166 6.171 5.585 5.715 5.803 5.602 5.692 5.647
CCSD(T) results differ significantly from each other. In particular, the OVGF value of VDE (8.472 eV) seems overestimated while compared to our CCSD(T) result (7.630 eV) and the result obtained by Weikert et al. [19] (7.86 eV) who used the third-order algebraic diagrammatic construction (ADC(3)) Green’s function approach. Therefore, in the case of BeF 3 we prefer to rely on our CCSD(T) value rather than that derived from the OVGF calculation. The vertical electron detachment energies of the remaining anions are always larger than 5.5 eV (see Table 2). The correlation between the VDEs (collected in Table 2) and the chemical constitution, geometrical parameters, or partial atomic charges [20] is not straightforward, however, a few tendencies could be noticed: (i) In the BeF 3 –BeCl3 –BeBr3 series the VDE decreases with an increase of the atomic number of the halogen atoms (i.e., the lowest VDE corresponds to BeBr 3 ). It is consistent with the partial atomic charge on beryllium (qBe ) becoming less positive (qBe ¼ 1:182, 0.696, and 0.552 a.u. for BeF 3 , BeCl3 , and BeBr3 , respectively). (ii) The analysis of the results calculated for the BeF 3 , BeF2 Cl , and BeF2 Br indicates that replacing the fluorine atom in BeF 3 with Cl or Br also leads to lower VDE (by 1.4 and 2.0 eV, respectively, see Table 2) which is accompanied again by the decrease of the qBe (qBe ¼ 1:034 a.u. for BeF2 Cl and 0.992 a.u. for BeF2 Br ). (iii) If one compares the results for BeCl 3 with these obtained when one or two chlorine atoms
are replaced with the F or Br atoms, it seems that similar tendencies are preserved (i.e., the decrease of the VDE accompanies the decrease of the qBe ). For example, qBe ¼ 0:664 a.u. for BeCl2 Br and 0.696 a.u. for BeCl 3 while the VDE of the latter exceeds that of the former by 0.37 eV (see Table 2). (iv) The shortening of the Be–F bond length observed when the fluorine atoms in BeF 3 are being subsequently substituted with chlorine (BeF2 Cl , BeCl2 F ) or bromine (BeF2 Br , BeBr2 F ) is consistent with the decrease of the VDE (see Table 2). These conclusions are in agreement with the general predictions formulated previously for the superhalogen anions [4,5]. In particular, the observation that smaller ‘size’ of the halogen ligands usually leads to larger vertical electron detachment energies is confirmed by our results. Moreover, it seems clear that the partial atomic charge localized on the central atom (Be in our case) as well as the ligand–central atom separations are strongly related to the VDE of the resulting anion. In order to support our discussion we present the three-dimensional pictures of the highest occupied molecular orbital (HOMO) for three cho sen anions: BeF and BeFClBr (see 3 , BeCl2 F Fig. 1). It is shown that in each case the HOMO is composed purely of ligand atomic orbitals (AO) while the contributions from the central atom (beryllium) are absent. As a consequence, the HOMO is a nonbonding molecular orbital (MO)
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Fig. 1. The highest occupied molecular orbital (HOMO) of the BeF 3 (top), BeCl2 F (middle), and BeFClBr (bottom) superhalogen anions (plotted with 0.03 bohr3=2 contour spacing).
with respect to the ligand–central atom interaction. This finding is consistent with the prediction formulated by Gutsev and Boldyrev [4] who suggested that the species for which the HOMO has such character should possess relatively high VDE values. The calculations of the vertical electron binding energies, although doable for BeX 3 (X ¼ F, Cl, Br) anions, can be found very expensive and time consuming for larger systems when performed at the OVGF and especially at the CCSD(T) level with large basis sets. Therefore, we decided to check if any lower-level theoretical treatment could be found sufficient for approximate estimating the VDEs for superhalogen anions. Since it was not our goal to undertake any systematic studies in this matter, we limit our discussion to the results obtained at the MPn (n ¼ 2, 3, 4), CCSD, CCSD(T), and OVGF level with the 6-311++G(d) and 6-311++G(3df) basis sets. The vertical electron detachment energies calculated at these levels for two anions, BeCl 3 and BeBr3 , are collected in Table 4. In addition, we support our discussion with the results obtained for the LiCl 2 and NaCl 2 while testing the accuracy of the applied treatment (see Table 1 and Section 3.1). According to our conclusions (see the preceding paragraphs in this section) the most reliable VDEs of the superhalogen anions are those calculated at the OVGF/6-311++G(3df) level and therefore we use these values as the reference while analyzing the vertical electron detachment energies obtained at different levels. At the first glance it seems clear that the VDEs of the BeCl 3 and BeBr3 anions are underestimated
Table 4 The vertical electron detachment energies (in eV) of BeCl 3 and BeBr3 calculated at various levels of theory with two different basis sets: 6-311++G(d) and 6-311++G(3df) VDE (eV) BeCl 3
VDE (eV) BeBr 3
MP2 MP3 MP4 CCSD CCSD(T) OVGF
6-311++G(d)
6-311++G(3df)
6-311++G(d)
6-311++G(3df)
5.343 5.349 5.299 5.415 5.292 5.406
5.552 5.568 5.554 5.656 5.549 5.647
5.728 5.764 5.693 5.832 5.693 5.839
6.021 6.066 6.028 6.117 6.027 6.171
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at each level of theory used (with respect to the OVGF values). The only exception is the CCSD result for the BeBr 3 that is slightly overestimated. In particular, the use of the CCSD(T) method leads to the VDEs that are lower by 0.144 and 0.098 eV for BeCl 3 and BeBr3 , respectively (see Table 4), when compared with the OVGF values. Similar agreement among the VDEs calculated at the CCSD, CCSD(T), and OVGF levels can be noted for the LiCl 2 and NaCl2 species. In particular, the CCSD(T) results, although underestimated (by ca. 0.15 eV), are in good agreement with both OVGF and experimental results (see Table 1). This indicates that one may expect the CCSD(T) treatment to provide the VDE with a decent accuracy for an unknown superhalogen anion. Moreover, it can be anticipated that such a value could be slightly underestimated. The analysis of the VDEs calculated at the MP2, MP3, and MP4 levels shows that the convergence of the MP series is satisfactory for BeCl 3, BeBr , LiCl and NaCl anions (see Tables 1 and 2 2 3 4). Moreover, it should be noted that relatively inexpensive MP2 treatment leads to quite reliable estimates of the VDEs. The vertical electron detachment energies calculated at the MP2 level with the 6-311++G(3df) basis sets are always underestimated and the difference between the MP2 and OVGF results is always lower than 0.15 eV (for the anions studied in this work). This finding would allow for an easy and fast estimate of the electronic stability of a superhalogen anion when neither experimental nor theoretical results are available. We therefore conclude that the OVGF method should be considered as the most reliable for predicting VDEs of superhalogen anions. For any crude or preliminary estimates, however, we recommend applying the MP2 method which should result with an underestimated vertical electron detachment energies.
4. Summary The vertical electron detachment energies of the superhalogen anions BeX 3 (X ¼ F, Cl, Br) were calculated at the OVGF/6-311++G(3df) and CCSD(T)/6-311++G(3df) level. All the negatively
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charged species studied in this work were derived from their neutral parent radicals and have proven to exhibit a ‘superhalogen’ nature which means their electron binding energies were found to significantly exceed the electron affinity of chlorine (3.62 eV). It was concluded the OVGF/ 6-311++G(3df) treatment produces reliable estimates of the previously studied superhalogen anions and the following vertical detachment energies of 10 BeX 3 (X ¼ F, Cl, Br) species considered in this work were found to be: 7.630 eV (BeF 3 ), 6.239 eV (BeF2 Cl ), 6.166 eV (BeCl2 F ), 6.171 eV (BeCl 3 ), 5.585 eV (BeF2 Br ), 5.715 eV (BeFClBr ), 5.803 eV (BeCl2 Br ), 5.602 eV (BeBr2 F ), 5.692 eV (BeBr2 Cl ), and 5.647 eV (BeBr 3 ).
Acknowledgements We would like to thank Prof. J. Rak for his valuable comments. This work was supported by the Polish State Committee for Scientific Research (KBN) Grant No. DS/8371-4-0137-2 and the NSF Grants 9618904 and 9982420. The computer time provided by the Academic Computer Center in Gdask (TASK) and the Center for High Performance Computing at the University of Utah is also gratefully acknowledged.
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