Stability and Spectroscopic Properties of Singly and Doubly Charged

Article pubs.acs.org/JPCA

Stability and Spectroscopic Properties of Singly and Doubly Charged Anions Swayamprabha Behera* and Purusottam Jena Physics Department, Virginia Commonwealth University, Richmond, Virginia 23284-2000, United States S Supporting Information *

ABSTRACT: Using density functional theory and hybrid B3LYP exchange-correlation energy functional we have studied the structure, stability, and spectroscopic properties of singly and doubly charged anions composed of simple metal atoms (Na, Mg, Al) decorated with halogens such as Cl and pseudohalogens such as CN. Since pseudohalogens mimic the chemistry of halogen atoms, our objective is to see if pseudohalogens can also form superhalogens much as halogens do and if the critical size for a doubly charged anion depends upon the ligand. The electron affinities of MCln (M = Na, Mg, Al) exceed the value of Cl for n ≥ (k + 1), where k is the normal valence of the metal atom. However, for M(CN)n complexes this is only true when n = k + 1. In addition, while the electron affinities and vertical detachment energies of MCln complexes are close to each other, they are markedly different when Cl is replaced by pseudohalogen, CN. The origin of these anomalous results is found to be due to the large binding energy of cyanogen, (NCCN) molecule. Because of the tendency of CN molecules to dimerize, the ground state geometries of the neutral and anionic M(CN)n complexes are very different when their number exceed the normal valence of the metal atom. While our calculations support the conclusion of Skurski and co-workers that pseudohalogens can form the building blocks of superhalogens, we show that there is a limitation on the number of CN moieties where this is true. Equally important, we find large differences between the ground state geometries of the neutral and anionic M(CN)n complexes for n ≥ (k + 2) which could play an important role in interpreting future experimental data on M(CN)n complexes. This is because the electron affinity defined as the energy difference between the ground states of the anion and neutral can be very different from the adiabatic detachment energy defined as the energy difference between the ground state of the anion and its structurally similar neutral isomer.

I. INTRODUCTION Studies of negative ions constitute an important area in chemistry due to their commercial role in forming salts, purifying agents, and biocatalysts.1,2 One of the most important quantities of interest is the stability of singly and multiply charged anions. In the former case, most atoms and a large number of molecules form stable and singly charged negative ions. However, their electron affinity, which is defined as the energy gain when an electron is attached to a neutral species, varies from atom to atom and from molecule to molecule. For example, Cl has the highest electron affinity, namely 3.61 eV, of any element in the periodic table. These values can be exceeded in molecules or clusters, particularly when they contain a metal atom at the core surrounded by multiple halogen atoms. Gutsev and Boldyrev named such molecules as superhalogens3,4 and prescribed their composition as MX(k+1)/m where M is a metal atom with maximal valence of k and X is an electronegative atom with normal valence, m. These include sp metal atoms (alkali, alkaline earth, and Al)5−8 or transition metal atoms9 at the core and halogen as well as O atoms on the outer shell. Molecules or clusters with large electron affinities can interact © 2012 American Chemical Society

with the core electrons of metal atoms and form new compounds that may not exist when halogen atoms are used. Multiply charged anions, on the other hand, mostly exist in solutions, on surfaces, or as building blocks of condensed matter systems where they are stabilized by charges on counterions. Since the stability and electronic properties of multiply charged anions in the above systems are influenced by the medium they exist in, their fundamental understanding without the influence of the environment can only be achieved when studies are performed in the gas phase. The most important question then concerns the critical size of a multiply charged anion. In these systems the Coulomb repulsion between the added charges has to be balanced by the binding energy of the constituent atoms that hold them together. An unstable multiply charged anion in the gas phase can either eject an electron or fragment into binary species to stabilize itself. Received: October 20, 2011 Revised: May 18, 2012 Published: May 21, 2012 5604

dx.doi.org/10.1021/jp210095q | J. Phys. Chem. A 2012, 116, 5604−5617

The Journal of Physical Chemistry A

Article

Figure 1. Optimized geometries of neutral (left), anionic (middle) and dianionic (right) NaCln clusters at B3LYP/6-311++G(3df) level of theory: Na (purple balls) and Cl (green balls).

II. COMPUTATIONAL METHODS Calculations have been carried out using density functional theory (DFT) with B3LYP hybrid functional for exchange and correlation (XC) potential.26,27 This level of theory has been successful in predicting the electron affinities of a large number of systems correctly.5,25 However, we should point out that earlier studies by Weimer et al.28 and Jensen29 have shown that B3LYP leads to wrong asymptotes regarding electron-molecule interactions. Furthermore, it has also been pointed out that B3LYP has difficulties in distinguishing between different spin multiplicities.30 Calculations with a functional corrected for selfinteraction for anions and dianions are, therefore, desirable to validate the accuracy of DFT-B3LYP level of theory. Consequently, we have repeated some of our calculations at the MP2 (second order Moller−Plesset perturbation) and CCSD(T) (coupled-cluster method with singles and doubles and noniterative inclusion of triples) levels of theory using the geometries obtained at the DFT-B3LYP level. These single point calculations are often used in the literature as the geometries are not very sensitive to the choice of exchangecorrelation potential. In addition, we have also compared our results with prior theoretical,5,23 and experimental,22,25 results where available. In all our calculations we have used the Gaussian 03 package31 and 6-311++G(3df) basis set which is known to provide excellent agreement between calculated and experimental results.22,25 For each cluster several initial geometries were taken where ligands were allowed to bind either individually or in groups. Optimizations were carried out without any symmetry constraint. These were followed by frequency calculations to confirm that the structures represent genuine minima in the potential energy surface. We have also calculated the total energies as a function of spin multiplicities using both DFT-B3LYP and CCSD(T) levels

There have been several reports on doubly charged negative ions of fairly large organic molecules.10 For example, the longlived stable organic dianion is the dimer of benzo[cd] pyrene-6one, a large organic ketone.10 It was the first long-lived doubly charged negative ion to be observed in the gas phase. Several theoretical11−19 and experimental19−21 investigations have been carried out in search of small stable dianions. The smallest known long-lived dianions thus far are found to be the alkali trihalide AX32− (A = Li, Na, K and X = F or Cl) clusters whose existence had been predicted theoretically18 and studied experimentally.20 The dianionic alkaline earth tetrahalides EX42− (E = Be, Mg, Ca and X = F or Cl) have also been predicted theoretically13 and later verified experimentally.21 In this paper we address both these problems by focusing on superhalogens consisting of different electronegative ligands. In the first part we use Cl as a ligand and present a systematic study of the structure, stability, and spectroscopic properties of neutral, singly and doubly charged negative ions of MCln (M = Na, Mg, Al) clusters for n ≤ k + 2, where k is the valence of the metal atom. We compare these results with previous calculations and experiments on MClk+1 clusters5,22−25 to validate our method and provide a base for comparison when Cl is replaced by other ligands such as pseudohalogens (CN or NC). The study of pseudohalogens as building blocks of superhalogens has two objectives. First, we want to see if there are any limitations in using pseudohalogens, CN to build superhalogens? Second, can the critical size of a multiply charged anion be affected by using pseudohalogens as ligands? In section II, we provide a brief description of the computational procedure and discuss results in section III. Section IV provides a summary of our conclusions. 5605



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Table 1. Preferred Fragmentation Channels and Energies of NaCln Clusters (Neutral, Monoanion, and Dianion) neutral channel

monoanion ΔE (eV)

dianion ΔE (eV)

channel −

−

channel

ΔE (eV)

NaCl → Na + Cl

4.06

NaCl → NaCl + e

NaCl 2 → NaCl + Cl

1.31

NaCl 2− → NaCl + Cl−

2.2

NaCl 2 2 − → NaCl 2− + e−

−1.99

0.54

NaCl3−

1.26

NaCl32 − →NaCl 2− + Cl−

−1.88 +0.55

NaCl3 → NaCl + Cl 2

0.86

−

→ NaCl 2 + Cl

→

of theory to obtain the preferred spin configuration of the neutral and anionic species. The preferred spin multiplicities of even and odd electron clusters were found to be singlet and doublet, respectively in both DFT-B3LYP and CCSD(T) method. In Tables S1−S6 of the Supporting Information, we provide the energy differences between two low-lying spin configurations for all the systems studied. The electron affinities, EA (energy difference between the neutral and the corresponding anion at their respective ground state geometries), the vertical detachment energy, VDE (energy difference between the ground state of the anion and its corresponding neutral at the anionic geometry), and adiabatic detachment energy, ADE (energy difference between the ground state of the anion and the structurally similar neutral isomer) were calculated. We note that EA and ADE are the same only when the ground state geometries of the anion and neutral are similar. However, when these geometries are very different, photoelectron electron spectroscopy measurements would yield values consistent with ADE. For a detail discussion, we refer the reader to a recent article by Samanta et al.38 For comparison we have also used a direct method (outer valence green function (OVGF) method)32,33 to calculate the VDE. The EA and ADE values are different in cases where the ground state geometry of the anion is very different from that of its neutral. Since the electron detachment from the anion in a photoelectron spectroscopy experiment is a vertical process, experiment in that case would measure the ADE.

+e

−

For calculating the corresponding fragmentation energies of the anion and dianion, one has to further consider which fragment carries the extra charge(s) or if the electron is autoejected? For this, we define, ΔE1anion(n) = −[E(NaCl n−) − E(NaCl n − m−) − E(Cl m)], m≤2

(2)

ΔE2 anion(n) = −[E(NaCl n−) − E(NaCl n − m) − E(Cl m−)] ,

m≤2

(3)

ΔE3anion(n) = −[E(NaCl n−) − E(NaCl n) − e−]

(4)

ΔE1dianion(n) = −[E(NaCl n 2 −) − E(NaCl n − m 2 −) − E(Cl m)],

m≤2

(5)

ΔE2 dianion(n) = −[E(NaCl n 2 −) − E(NaCl n − m−) − E(Cl m−)],

m≤2

(6)

ΔE3dianion(n) = −[E(NaCl n 2 −) − E(NaCl n−) − e−], m≤2

(7)

The preferred channel for fragmentation and the corresponding energy are given in Table 1. Positive ΔE means that the parent cluster is more stable than the products while negative ΔE means the products are more stable than the parent. We see that among neutral NaCln clusters, NaCl is the most stable cluster as can be expected from ionic bonding arguments. While NaCl2 fragments into NaCl + Cl, NaCl3 prefers to fragment by ejecting a Cl2 molecule. Among the monoanion series, NaCl2− is the most stable cluster. The fragmentation of monoanionic species yields different products. NaCl− prefers to eject an electron while NaCl2− dissociates into NaCl + Cl−. During fragmentation of NaCl3−, the negative charge resides on the NaCl2− species, a consequence of its high stability. NaCl22− is unstable against ejection of an electron. As has been discussed earlier,12,18,19 in NaCl32− one could envision that the repulsion between the two electrons may be counter balanced by the energy gain in closing the 3p shell of the third Cl atom, and hence NaCl32− may be stable. However, results in Table 1 show that NaCl32− is unstable against ejection of a Cl− ion. Since the geometries of NaCl22− and NaCl32− have no imaginary frequencies, it implies that these structures correspond to local minima in the potential energy surface and hence are metastable. The results again are consistent with previous studies.12,18,19 We now discuss the electron affinities (EAs) and vertical detachment energies (VDEs). The EAs of neutrals and VDEs of anions are calculated using DFT as well as MP2 and CCSD(T) methods. The results are given in Table 2. The experimental

III. RESULTS AND DISCUSSION In section A, we briefly discuss the structure, stability, and electronic properties of neutral, singly charged and doubly charged anions of NaCln (n ≤ 3), MgCln (n ≤ 4) and AlCln (n ≤ 5) clusters as these have been thoroughly studied by previous authors.5,23,24 Our purpose is to validate our theoretical method and see in section B how these results are affected when Cl atoms are replaced with pseudohalogen moieties CN and NC. A. Metal-Chloride anions and dianions. (i). NaCln (n ≤ 3). In Figure 1 we provide the ground state optimized geometries of neutral, singly charged and doubly charged anions of NaCln (n ≤ 3) clusters. The bond lengths and natural bond orbital (NBO) charges are also given in the figure. These results are in good agreement with previous work5,22 and validate the accuracy of our current theoretical method. The stability of neutral, monoanionic, and dianionic clusters of NaCln (n ≤ 3) is determined by calculating the least energy needed to fragment the cluster among all possible channels. We define these fragmentation energies as: ΔEneutral(n) = −[E(NaCl n) − E(NaCl n − m) − E(Cl m)], m≤2

NaCl3−

(1) 5606



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Table 2. Electron Affinities (EA in eV) of NaCln, Adiabatic Detachment Energy (ADE in eV), and Vertical Detachment Energies (VDE in eV) of NaCln− Calculated Using Various Levels of Theory NaCl

NaCl2

NaCl3

method

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

B3LYP MP2 CCSD(T) OVGF expt

0.86 (0.86) 0.68 0.69

0.91 0.71 0.72 0.73

4.58 (4.97) 4.78 4.68

4.98 5.85 5.74 5.89 5.8622

4.21 (4.59) 3.92 3.98

5.64 6.16 5.78 5.87

Figure 2. Optimized geometries of neutral (left), anionic (middle) and dianionic (right) MgCln clusters calculated at B3LYP/6-311++G(3df) level of theory: Mg (yellow balls) and Cl (green balls).

value is only available for the VDE of NaCl2. With the exception of the VDE’s of NaCl2 and NaCl3 we see that the results based on DFT agree with those based on quantum chemical methods within 0.2 eV which currently is the accuracy of DFT-based methods. While the EA and VDE values of NaCl cluster are close to each other, they are very different in NaCl2 and NaCl3 clusters due to the large difference between their corresponding geometries. Our results for NaCl2 cluster agree quite well with previous theoretical5 and experimental values.22

Note that the EA value of NaCl2 is significantly higher than that of Cl, thus making it a superhalogen. Although NaCl3 remains as a superhalogen, its EA is less than that of NaCl2 due to its filled shell. One of the ways to understand the stability of NaCln clusters and origin of the superhalogen behavior of NaCl2 and NaCl3 clusters is to analyze the charge distribution both in neutral and anionic states. This was done by calculating the charge on Na and Cl atoms as a function of n based on the natural bond 5607



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Table 3. Preferred Fragmentation Channels and Energies of MgCln Clusters (Neutral, Monoanion, and Dianion) neutral

monoanion ΔE (eV)

channel

−

dianion ΔE (eV)

channel −

channel

ΔE (eV)

MgCl → Mg + Cl

3.21

MgCl → Mg + Cl

1.13

MgCl2 → MgCl + Cl

4.66

MgCl2− → MgCl2 + e−

1.15

MgCl2 2 − → MgCl2− + e−

−2.76

MgCl3 → MgCl2 + Cl

1.09

MgCl3− → MgCl2 + Cl−

2.84

MgCl32 − → MgCl3− + e−

−2.97

MgCl4 → MgCl2 + Cl 2

0.28

MgCl4− → MgCl3− + Cl

0.99

MgCl4 2 − →MgCl3− + Cl−

−1.61

−

→ MgCl4 + e

−

+1.07

Table 4. Electron Affinities (EA in eV) of MgCln, Adiabatic Detachment Energy (ADE in eV) and Vertical Detachment Energies (VDE in eV) of MgCln− Calculated Using Various Levels of Theory MgCl

MgCl2

MgCl3

MgCl4

method

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

B3LYP MP2 CCSD(T) OVGF expt

1.61 (1.61) 1.30 1.53

1.74 1.45 1.68 1.65

1.15 (1.15) 1.0 1.52

1.87 1.69 1.72 1.79

5.43 (5.43) 5.75 5.65

5.74 6.62 6.53 6.89 6.6025

4.85 (4.85) 4.61 4.65

6.40 6.95 6.58 6.77

Cl atoms bind quasi-molecularly with a bond length of 2.05 Å which is very close to the bond length of a Cl2 molecule (2.01 Å), resulting in an adduct like structure . Since the Mg atom can only afford to lose two electrons, the extra electron is distributed among all the Cl atoms and the bond between the quasi-molecularly bound Cl atoms breaks while the bonds between Mg and corresponding Cl atoms stretch to 2.47 Å. As the monoanionic cluster needs one more electron to close the 3p shell of all the four Cl atoms, the resulting MgCl42− has a perfect tetrahedral geometry and gains more stability as its energy is lowered by 1.07 eV compared to its anion. The stability of neutral, anionic and dianionic clusters of MgCln are determined by calculating the fragmentation energies as defined in eqs 1−7. In Table 3, we give the preferred channel and the corresponding fragmentation energy. Note that energy needed to fragment MgCl2 is the highest among the neutral clusters and hence it is the most stable species. MgCl4 dissociates into MgCl2 and a Cl2 molecule while MgCl3 ejects only a Cl atom. MgCl3− is the most stable cluster among the MgCln− cluster series. While MgCl2− prefers to eject an electron, the other anions either eject a Cl− ion for n = 1 and n = 325 or a Cl atom for n = 4. The later is due to the fact that the MgCl3 is a superhalogen which will be discussed later. MgCln2− (n = 2, 3) clusters are thermodynamically unstable against ejection of an electron or Cl−, but for n = 2−4, they belong to local minima in the potential energy surface. Hence, these are metastable. This is consistent with the previous studies of BeF42− and MgF42− where these species were shown to be metastable.13,21 The EAs of the neutrals and VDEs of the anions calculated using different levels of theory are given in Table 4. Prior experimental25 and theoretical23 values are available only for MgCl3 cluster. Note that with the exception of the VDE of MgCl3, results based on MP2 and CCSD(T) methods agree within 0.3 eV of the results predicted by DFT-B3LYP method. Significant differences exist between EA and VDE values for MgCl2, MgCl3, and MgCl4. In particular, the difference between EA and VDE is especially large, nearly 2 eV, for MgCl4. These

orbital (NBO) analysis. As seen from Figure 1 the charge on Na atom in neutral NaCln clusters is same for n ≤ 3 irrespective of how the Cl atoms are bound to it and the transferred charge is distributed among the Cl atoms. When an extra electron is added, it goes to the Na atom in NaCl, but in NaCl2 and NaCl3 the electron is distributed over all the Cl atoms. Consequently, the electron affinity increases sharply. In NaCl2 dianion, both the electrons reside on the Cl atoms while Na remains electrically neutral. The electrostatic repulsion makes NaCl2 dianion unstable. The case is totally different for NaCl3. Here the charge on Na atom is nearly +1 and each of the Cl atoms shares the extra electrons. The electrostatic interaction between Na+ and Cl− atoms improves the stability for the NaCl3 dianion. (ii). MgCln (n ≤ 4). The ground state optimized geometries of neutral, monoanionic, and dianionic clusters of MgCln (n ≤ 4) are displayed in Figure 2. The bond lengths and charges obtained from the NBO analysis are also listed. The geometry of the MgCl2 monoanion is a bent structure while that of the neutral is a linear chain. The charge on Mg in neutral MgCl2 is +1.65e and the transferred charges are equally shared by both the Cl atoms. On addition of an extra electron to the neutral, the resulting anion assumes a bent shape as the extra electron preferentially goes to the Mg site. When one more electron is added to the MgCl2− cluster, the resulting dianion becomes unstable against autoejection of an electron. Note that the energy difference between the monoanionic and dianionic MgCl2 is 2.76 eV. In MgCl3 cluster, there is also a significant geometrical change between the monoanion and the neutral. In MgCl3− the third electron required to fill the 3p shells of the three Cl atoms is supplied by the added electron, giving it a perfect trigonal planar geometry. Upon addition of one more electron the resulting dianion is again unstable as most of the charges are taken by the Mg atom and the large Coulomb repulsion dominates its binding energy. Note that the energy difference between the monoanionic and dianionic MgCl3 is nearly 3 eV. In MgCl4 cluster, the situation is very similar to that for NaCl3. Because of its electron deficient nature, the two 5608



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Figure 3. Optimized geometries of neutral (left), anionic (middle) and dianionic (right) AlCln clusters calculated at B3LYP/6-311++G(3df) level of theory: Al (pink balls) and Cl (green balls).

are consistent with the geometries shown in Figure 2. From our data, we note that the values of EAs and VDEs are small for MgCln (n = 1, 2) clusters, but increase substantially for MgCl3 and MgCl4 indicating the onset of superhalogen behavior. In order to understand the nature of bonding, we calculated the charge on Mg atom as a function of n for neutral, monoanion and dianion species using NBO analysis. The results are given in Figure 2. We found that in all the neutral clusters the bonding is primarily ionic in nature. When an

electron is added to the neutral cluster, the charge prefers to reside on Mg atom for n ≤ 2 but for n > 2 it prefers to reside on the Cl atoms which cause the EA to rise sharply. Note that in neutral MgCl4, the charge transfer is no longer possible and subsequently two Cl atoms bind quasi-molecularly. When one more electron is added to the MgCln− cluster for 1< n ≤ 3, most of the charges are transferred to Mg atom. The energy differences between the monoanionic and dianionic clusters are very high, around 3 eV. In MgCl42− dianion the extra charge is 5609



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Table 5. Preferred Fragmentation Channels and Energies of AlCln Clusters (Neutral, Monoanion, and Dianion) neutral

monoanion ΔE (eV)

channel

dianion ΔE (eV)

channel −

−

AlCl → Al + Cl

5.10

AlCl → AlCl + e

AlCl 2 → AlCl + Cl

2.94

AlCl 2− → AlCl + Cl−

1.62

4.80

AlCl3−

1.44

0.88

−

0.18

AlCl3 → AlCl 2 + Cl AlCl4 → AlCl3 + Cl AlCl5 → AlCl4 + Cl

→ AlCl3 + e

ΔE (eV)

channel

0.19

−

−3.83

AlCl 2 2 − → AlCl 2− + e−

AlCl3

2−

→

AlCl3−

+e

−

−2.75

−

−3.93

−

AlCl4 → AlCl3 + Cl

3.08

AlCl4

AlCl5−

→ AlCl4 + Cl

0.15

AlCl52 − →AlCl4− + Cl−

−

2−

−

→ AlCl4 + e

→

AlCl5−

+e

−2.95

−

+0.21

Table 6. Electron Affinities (EA in eV) of AlCln, Adiabatic Detachment Energy (ADE in eV) and Vertical Detachment Energies (VDE in eV) of AlCln− Calculated Using Various Levels of Theory AlCl

AlCl2

AlCl3

AlCl4

AlCl5

method

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

B3LYP MP2 CCSD(T) OVGF

0.19 (0.19) −0.01 0.07

0.30 0.13 0.20 0.21

2.36 (2.36) 2.09 2.26

2.91 2.74 2.89 2.91

1.44 (1.44) 1.22 1.26

2.67 2.57 2.58 2.73

5.88 (5.88) 6.20 6.08

6.17 7.16 6.90 7.04

4.71 (4.71) 4.37 4.45

6.50 6.81 6.44 6.95

belong to minima in the potential energy surface, and are metastable. The EAs of the neutrals and the VDEs of the anions calculated using different levels of theory are given in Table 6. No experimental values are available for these clusters. Note that the results obtained using DFT-B3LYP again agrees well with those obtained from quantum chemical approaches, within the exception of the VDE of AlCl4. Because of closed shell the EA is small for AlCl. The electron affinity of AlCl2 increases sharply, but decreases for AlCl3. This odd−even effect is again the result of shell closure. AlCl4 with an electron affinity of 5.88 eV is a superhalogen. Our results agree well with the theoretical value of the VDE of AlCl4− cluster calculated by Skurski and coworkers8 using the OVGF method. The EA of AlCl5 is higher than that of Cl but smaller than that of AlCl4, due to even number of electrons. The charges on neutral, monoanionic and dianionic clusters are displayed in Figure.3. Unlike in the case of NaCln clusters, the charge on Al atom never reaches its maximal valence, namely +3 irrespective of how many Cl atoms are attached to it. However, it increases from +0.69 in neutral AlCl to +1.46 in AlCl3. This reflects significant covalent character of the bond. In AlCl4− the extra charge is distributed among all the four Cl atoms and AlCl4 becomes a superhalogen. The charges on the Cl atoms range from 0.47e to 0.81e except in the case of AlCl4 and AlCl5 where the quasi-molecular Cl atoms carry very little extra charge. B. Metal−Cyanide MXn (M = Na, Mg, Al and X = CN or NC) Clusters. In the above we discussed conventional superhalogens that consist of metal atoms surrounded by halogen atoms. There exists a class of molecules called pseudohalogens whose chemistry mimics that of halogen atoms. A typical example of a pseudohalogen is CN. In this section, we explore if CN moieties can also be used to form superhalogens and if so is there any limitation? While previous studies on cyanogen (NCCN), isocyanogen (CNCN), diisocyanogen (CNNC), and interaction of CN with metal atoms such as Al, Pt, and Au are available in the literature34−40

delocalized among all the four Cl atoms rather than residing on the Mg atom. This makes it more stable against Coulomb repulsion than in MgCln2− (n = 2, 3) due to its high binding energy. It can be noted from Figure 2 that the charges on the Mg atom in the neutral, anion and the dianion are nearly the same at n = 4. (iii). AlCln (n ≤ 5). The ground state optimized geometries of neutrals, singly and doubly charged AlCln (n ≤ 5) clusters are given in Figure 3. Also listed are various bond lengths and NBO charges. Unlike the clusters discussed before, the geometries of the neutral and the monoanionic AlCln clusters are similar for n ≤ 3, but the differences are larger for n ≥ 4. In the neutral AlCl4 cluster, two of the Cl atoms bind to the Al atom with bond lengths of 2.24 Å while the other two have a shorter bond length of 2.09 Å. AlCl4−, on the other hand, has a perfect tetrahedral geometry, as the extra electron can fill the 3p shell of the fourth Cl atom, resulting in a closed shell structure. In the neutral AlCl5 cluster, two Cl atoms are bound in a quasimolecular form having a bond length of 2.02 Å resulting in an adduct-like structure AlCl3·Cl2 which is very similar to those seen in NaCl3 and MgCl4 clusters. In AlCl5−, the extra electron is not enough to fill the 3p shells of all the Cl atoms. Consequently, the quasi-molecular bond between the two Cl atoms in neutral AlCl5 cluster is stretched to 2.71 Å. The geometries of dianions are similar to their corresponding monoanionic clusters except for n = 5. AlCl52− forms a closed shell cluster and all the Cl atoms are bound chemically to the Al atom. It is the only species among all the dianions of AlCln clusters that is stable against auto ejection of an electron. The preferred fragmentation channel and corresponding dissociation energy of the neutral, monoanion and dianion of AlCln clusters are given in Table 5. We note that AlCl and AlCl3 clusters are among the most stable neutral clusters. In the monoanions, AlCl4− is the most stable species. All dianions studied here are unstable against either autoejection of an electron or Cl− ion. However, the frequencies associated with the dianion geometries are all real and hence the structures 5610



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Figure 4. Optimized geometries of neutral (top), anionic (middle) and dianionic (bottom) Na(X)n (X = CN or NC) clusters calculated at B3LYP/ 6-311++G(3df) level of theory: Na (purple balls), N (blue balls), and C (gray balls).

(i). NaXn (X = CN or NC, n ≤ 3). In obtaining the geometries of Na(X)n complexes we have considered the possibility that Na can bind by attaching to the C or the N atom and for n ≥ 2 the CN molecules can either bind individually or in dimerized form. In the case of Au(X)n (for n ≥ 3) Samanta et al. also considered structures where CN molecules form trimers and then bind to Au; but these structures were found to be much higher in energy. We therefore, did not consider this possibility while computing the structure of Na(X)3. In Figure 4, we provide the ground state optimized geometries of neutral, singly and doubly charged anion of NaXn (n ≤ 3) clusters corresponding to the preferred spin multiplicities. The bond lengths and NBO charges are also listed in the figure. While the minimum energy geometries correspond to clusters when N atom is bound to the metal atom, in most of the cases the cyanide and isocyanide groups were found to be energetically nearly degenerate. The geometries of NC pseudohalogens interacting with Na are different from that of NaCln clusters. For neutral NaNC, the structure is an irregular triangle. In neutral Na(NC)2, two of the CN moieties dimerize forming NCCN (cyanogen) complex which then binds to Na, but not in a linear chain configuration. Neutral Na(NC)3 assumes a linear structure where the Na atom is bound to an NC and NCCN unit on opposite sides. Monoanionic NaNC− structure becomes a linear chain. Na(NC)2− assumes a very different geometry than its neutral counterpart and Na binds to two separate NC moieties in a nearly linear chain configuration. The geometry of Na(NC)3− deviates slightly from that of its neutral counterpart in the sense that the NCCN moiety is now bent which is analogous to the geometry of isolated NCCN−. We will show later that this is due to the nature of charge distribution. In dianions addition of extra electron removes the electron deficiency which then leads to very different geometries. For example, Na(NC)32− has a C3v structure with Na binding to N of three separate NC units. The geometries of both the dianions computed using both B3LYP and CCSD(T) level of theory are nearly degenerate whether C or N is bound to the Na atom (Table S7).

systematic studies of the stability of dianions of M(X)n (M = Na, Mg, Al; X = CN or NC) complexes and their comparison with corresponding metal−halogen complexes is lacking. We note that recently Skurski and co-workers41 have calculated the VDE of NaX2, MgX3, and AlX4 where X = CN and NC and have shown that they are indeed superhalogens. However, these authors have not carried out a systematic study as a function of number of ligands to see how the superhalogen properties evolve. In addition, no calculations were performed to determine the ground state geometries of their neutral complexes. Hence, no information is available on the electron affinity or the adiabatic detachment energy. We note that study of the interaction of CN with metal atoms poses more challenges than simple halogen atoms do as the metal atom now has the freedom to attach to either C or N atom of CN. In a recent study Samanta et al.39 have shown that the CN molecules have a tendency to dimerize. More importantly, their binding to a metal atom in dimerized form has significant effect on their electron affinity. For example, the anion of Au(X)3 possesses two energetically nearly degenerate isomers with very different spectroscopic signature.39 In one of the isomers of Au(CN)3− all the three CN moieties bind individually with C attached to Au. In the other isomer two of the CN moieties dimerize and bind to Au. While the C atom of individual CN attaches to Au, it is the N atom of the dimerized NCCN that attaches to the Au atom. Au(CN)3 is a superhalogen while NC−Au−NCCN is not. We have carried out a systematic study to probe not only the evolution of superhalogen properties of M(X)n (M = Na, Mg, and Al, X = CN or NC) complexes as a function of the number, n, of ligands, but also studied the relative stability and spectroscopic properties of other isomers lying close to the lowest energy structure. In every cluster we found that the bond length between N and C atoms varies in the range (1.15−1.20 Å). This is very close to the bond length in isolated CN molecule (∼1.17 Å), calculated at the same level of theory. This indicates that the species consisting of −NC or −CN functional group will retain their chemistry. 5611



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Table 7. Preferred Fragmentation Channels and Energies of Na(NC)n Clusters neutral

monoanion ΔE (eV)

channel

dianion ΔE (eV)

channel −

−

ΔE (eV)

channel

NaNC → Na + NC

4.32

Na(NC) → NaNC + e

Na(NC)2 → Na + NCCN

0.43

Na(NC)2− → NaNC + (NC)−

0.94 2.26

Na(NC)2 2 − → Na(NC)2− + e−

−1.94

Na(NC)3 → NaNC + NCCN

0.33

Na(NC)3− → Na(NC)− + NCCN

1.56

Na(NC)32 − →Na(NC)2− + (NC)−

−1.44

→ Na(NC)3− + e− +0.12

Table 8. EA (in eV) of Na(NC)n, ADE (in eV), and VDE (in eV) of Na(NC)n− Calculated Using Various Levels of Theorya NaNC

a

Na(NC)2

Na(NC)3

method

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

B3LYP OVGF

0.94 (1.01)

1.06 0.88

3.89 (5.14)

5.15 5.86

2.16 (2.16)

2.76 2.20

The EA and VDE of NaNC calculated at the MP2 and CCSD(T) level of theory are respectively 0.72 and 0.86 eV; 0.74 and 0.85 eV.

Figure 5. Optimized geometries of neutral (left), anionic (middle) and dianionic (right) Mg(X)n (X = CN or NC) sclusters calculated at B3LYP/6311++G(3df) level of theory: Mg (yellow balls), N (blue balls), and C (gray balls).

energy and Na(NC)2 and Na(NC)3 prefer to dissociate by producing (NC)2 dimer. Among the anionic clusters, Na(NC)2− is the most stable species. Metastability of Na(NC)2

The preferred channel for fragmentation and the corresponding energies are given in Table 7. Among all the neutral clusters, NaNC is the most stable species due to its high fragmentation 5612



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Table 9. Preferred Fragmentation Channels and Energies of Mg(NC)n Clusters neutral channel

monoanion ΔE (eV)

MgNC → Mg + NC

3.39

Mg(NC)2 → Mg + NCCN

1.91

dianion ΔE (eV)

channel −

−

ΔE (eV)

1.10

Mg(NC) → Mg + (NC) −

channel

−

Mg(NC)2 → MgNC + (NC)

−2.56

2.41

Mg(NC)2 2 − → Mg(NC)2− + e−

Mg(NC)3 → MgNC + NCCN

0.74

Mg(NC)3− → Mg(NC)2 + (NC)−

−2.72

3.46

Mg(NC)32 − → Mg(NC)3− + e−

Mg(NC)4 → Mg(NC)2 + NCCN

0.70

Mg(NC)4− → Mg(NC)2− + NCCN

−0.70

2.00

Mg(NC)4 2 − →Mg(NC)3− + (NC)− → Mg(NC)4− + e− +0.93

In MgNC cluster, both the geometries of neutral and anion are linear chains and the bonding is partly ionic and partly covalent in nature. Since Mg can afford 2 electrons, the neutral Mg(NC)2 is linear whereas both the anions and dianions are bent because of the Jahn−Teller effect. The geometry of neutral Mg(NC)3 is very different from that of its anionic and dianionic counterpart. In the neutral cluster, due to electron deficiency, NC ligand dimerizes and binds to Mg atom on one side whereas the C atom of the CN moiety binds on the other side. In Mg(NC)3−, the added electron along with the two valence electrons of Mg are enough to fill the shells of the three −NC ligands. Consequently, the geometry of Mg(NC)3− is a perfect trigonal planar. In the corresponding dianion, the extra electron resides on the Mg atom to partially neutralize its positive charge. In neutral Mg(NC)4 cluster, two of the NC units dimerize to form NCCN unit which then binds to the Mg atom along with two separate NC units. While the NCCN unit is linear in neutral Mg(NC)4, it is slightly bent in the Mg(NC)4−. This is because the extra electron preferentially goes to the NCCN unit and hence it mimics the structure of NCCN−. The dimerization of NC before binding to Mg is driven by the large binding energy of NCCN, namely 6.30 eV. In the Mg(NC)4 dianion, there are four electrons and hence all the NC moieties bind individually to the Mg atom. The dianions of Mg(NC)n for n ≥ 2 are thermodynamically unstable against auto ejection of an electron or a NC− unit since the Coulomb repulsion between the extra electrons dominate the binding energies of the clusters. The preferred channel for fragmentation and the corresponding energies are given in Table 9. Among all the neutrals, MgNC is the most stable species against fragmentation. At first, this may seem surprising since Mg is divalent. However, as noted earlier, CN pseudohalogens gain considerable binding energy after dimerization (∼6.30 eV). For the same reason all other neutral clusters prefer to dissociate by ejecting NCCN. Among the anions, Mg(NC)3− is the most stable species. All anions except for n = 4 prefer fragmentation by ejecting a NC−, whereas Mg(NC)4 anion prefers to dissociate into Mg(NC)2− and NCCN. The negative charge resides on Mg(NC)2 due to the small EA of the NCCN ligand. The dianions of Mg(NC)2 and Mg(NC)3 prefer to auto eject an electron and are highly unstable due to their large fragmentation energies. The dianion of Mg(NC)4, on the other hand, is stable against auto ejection of an electron by 0.93 eV. It is metastable against dissociation

and Na(NC)3 dianions was confirmed by frequency analysis; no imaginary frequencies were found. It can be noted that the fragmentation product of the dianions of NaCln and Na(NC)n are similar; when n = 2, the dianions prefer to eject an electron while for n = 3 they prefer to eject a ligand ion. We also note that Na(NC)32− is more stable against fragmentation than NaCl32−. The electron affinities (EA) of neutral and vertical detachment energy (VDE) of anionic Na(NC)n clusters are given in Table 8. The data show that both EA and VDE rise sharply at n = 2 and drop at n = 3. At n = 2, the cluster is a superhalogen. Basically, in superhalogens the extra charge no longer goes to the metal atom. Instead, it is transferred to the electronegative ligand and the charges on the metal atom in both neutral and anion clusters are nearly the same. This is not the case for neutral Na(NC)2. This is due to the small electron affinity of NCCN dimer (∼0.53 eV calculated at the same level of theory). For n = 3 the geometries of both the neutral and the anion are quite similar (as shown in Figure 4). Because of the dimerization of NC there is a drop in the EA at n = 3 and hence it does not behave as a superhalogen. (Its EA could have been high if the NC ligands are not allowed to dimerize. But those clusters do not belong to a genuine minimum as is evidenced by an imaginary frequency). In the case of Na(NC)2 dianion the negative charge is mostly transferred to Na in order to neutralize its positive charge while in the dianion of Na(NC)3, the extra charges are distributed equally among all the ligands resulting in a perfect trigonal planar geometry. Because of this reason, it is more stable than that of its corresponding anion. We also note that the difference between the EA and VDE, namely 1.26 eV, is the largest for the Na(NC)2 cluster. This is because the ground state geometries of neutral and anionic Na(NC)2 clusters are very different. In a photoelectron spectroscopy (PES) experiment it may be difficult to measure the EA since photodetachment is a vertical process. Most likely it is the ADE that will be measured. (ii). MgXn (X = CN or NC, n ≤ 4). The geometries of MgXn are optimized by having either C or N bound to the metal atom Mg. The ground state optimized geometries of neutral, singly charged and doubly charged anion of Mg(X)n (for n ≤ 4) are provided in Figure 5 along with the bond lengths and NBO charges. In all these clusters, the N atom of CN again preferentially binds to the central atom Mg because it is more electronegative than the C atom. 5613



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Table 10. EA (in eV) of Mg(NC)n and VDE (in eV) of Mg(NC)n− Calculated Using Two Levels of Theory MgNC

Mg(NC)2

Mg(NC)3

Mg(NC)4

method

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

B3LYP OVGF

1.76 (1.76)

1.91 1.90

1.64 (1.64)

2.44 2.43

5.29 (6.19)

6.21 7.15

2.93 (2.93)

3.83 3.46

into Mg(NC)3− and (NC)− but is thermodynamically more stable than that of its monoanionic counterpart. The electron affinities (EA) of neutral and vertical detachment energy (VDE) of anionic Mg(NC)n clusters are summarized in Table 10. We found that there is a sudden rise of EA at n = 3 and hence Mg(NC)3 is a superhalogen. The difference between EA and VDE values for n = 3 is quite large which is due to significant changes in the geometries of the neutral and the anion. When an electron is added to the neutral clusters, most of the charges are transferred to Mg until n = 2. Beyond this point it is distributed over the pusedohalogen moieties. Because of this reason, the charges on the Mg atom, in both neutral and anion for n ≥ 3 are found to be similar (as shown in Figure 5). It can also be noted that the charges on Mg in neutral, anionic and dianionic Mg(NC)n clusters for n = 4 are close to each other. There is a precipitous drop in the EA as well as VDE in Mg(NC)4 since in both neutral and anion, two of the NC ligands dimerize. (iii). AlXn (X = CN or NC, n ≤ 5). In Figure 6, we provide the ground state optimized geometries of neutral, singly charged and doubly charged anion of Al(X)n (where n ≤ 5) along with the bond lengths and NBO charges. Once again we had studied the relative binding energies of Al(X)n clusters by allowing both C and N to bind to the Al atom. These structures are different from those of Na(X)n and Mg(X)n clusters. In neutral AlX cluster N binds to Al forming AlNC just as seen in the case of Na and Mg systems, while in the anionic AlX− cluster the preferred structure is AlCN−. However, the energy differences, ΔE between these clusters, whether C or N atom is attached to Al is small (ΔE ∼ 0.3 eV in neutral and 0.03 eV in anion). In Al(X)2 clusters, the geometries of neutral, anion and dianion are bent. In neutral and anionic clusters Al(NC)2 is energetically preferable to Al(CN)2, whereas in dianion, C atom is bound to Al. Neutral Al(X)3 with N bound to Al is the preferred structure. Since three valence electrons of Al are shared by the ligands, neutral Al(NC)3 has a perfectly trigonal geometry. When an extra electron is added, C atom preferentially binds to Al in both the anion and dianion. As the Al atom can at most provide three electrons for bonding, CN prefers to dimerize when the number of ligands exceed the maximal valence of Al. This can be seen from the geometry of neutral Al(NC)4 cluster where Al binds to two NC and one NCCN moiety. When the electron deficiency is fulfilled by adding an electron, the anion assumes tetrahedral symmetry and Al(NC)4− is found to be the most stable species among monoanions. Note that in the dianion, the C atom preferably binds to Al. For n = 5, the neutral and anion have very similar geometries where two of the CN moieties dimerize to form NCCN before binding to Al while in the dianion all the NC moieties bind individually. It is found to be the most stable species among all the dianions. Thus, we conclude that in all neutral clusters N atom preferably binds to Al due to its higher electronegativity compared to C. However, in the dianions, with the exception of Al(NC)52−, C atom binds to Al. The preferred channel for fragmentation and the corresponding energy are given in Table 11. Among all the neutral clusters,

AlNC is the most stable species having high fragmentation energy. All other neutral clusters prefer to dissociate by ejecting NCCN. In the case of anions, Al(NC)4− is the most stable species due its superhalogen behavior which will be explained in the following. While AlCN− and Al(CN)3− auto eject an electron, Al(NC)5− prefers to fragment to Al(NC)3− and NCCN . On the other hand, the dianionic clusters for n ≤ 4 auto eject an electron while Al(NC)52− fragments into Al(NC)4− and (NC)−. This is because Al(NC)4− is the most stable species among the monoanions. The dianion of Al(NC)5 is found to be thermodynamically metastable compared to its anionic counterpart. The EA and VDE of Al(X)n clusters are given in Table 12. Because of the structural similarity between the neutrals and anions for n ≤ 2, EA and VDE values differ little. The extra charges are transferred to the Al atom until its valence is consumed i.e until n = 3. But, as the number of ligands exceeds the valence of Al, the charges no longer reside on the Al atom but are distributed over the CN ligands. Consequently, the EA increases abruptly at n = 4. This is similar to what was seen in AlCln clusters. The charge on Al in neutral Al(NC)4 is (+2.04e) whereas in the anion it is (+1.97e). In Al(NC)5 clusters, due to dimerization of CN in both the neutral and anion, the value of EA drops. However, its dianion has a closed shell structure. Its energy is lower from that of its anion by ∼2.7 eV, thus making it stable.

IV. CONCLUSION A systematic theoretical study of the stability and spectroscopic properties of simple metal atoms (Na, Mg, Al) interacting with Cl as well as X (CN or NC) moieties was carried out using density functional theory and B3LYP functional. For selected systems the accuracy of the B3LYP results was verified by carrying calculations at the MP2 and CCSD(T) level of theory. The objective of the study was to find ways in which electronegative species with electron affinities much higher than that of Cl can be designed and synthesized. Our results led to the following conclusions: (1) In agreement with previous works superhalogen behavior is observed for simple metal atoms (Na, Mg, Al) when the number of Cl atoms exceed the normal valence of Na, Mg, and Al, namely 1, 2, and 3. (2) CN or NC moieties which are known as pseudohalogens can also form the building blocks of a new class of superhalogens. However, unlike halogens, they provide considerable challenge in designing superhalogens. First, CN can bind to a metal atom as cyanide (i.e., CN) or as an isocyanide (i.e., NC). Second, cyanogen (NCCN) has very large binding energy compared to that of Cl2. Consequently, as the number of CN moieties bound to a metal atom increases, the most stable configuration may not be the one where the CN moieties are bound individually, but rather structures where CN moieties dimerize and then bind to the metal atom. In the later case, they may not form superhalogens. This is what our 5614



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Figure 6. Optimized geometries of neutral (left), anionic (middle) and dianionic (right) of Al(X)n (X = CN or NC) clusters at B3LYP/6-311+ +G(3df) level of theory: Al (pink balls), N (blue balls), and C (gray balls).

systematic studies of CN or NC moieties bound to Na, Mg, and Al reveal. For Na, up to two NC moieties can be bound individually and Na(NC)2 is a superhalogen. Beyond this, CN moieties dimerize and the electron

affinity of Na(NC)3 drops below that of Cl. Similar results are seen for Mg and Al when the number of CN moieties bound to these metal atoms is 3 for Mg and 4 for Al. 5615



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Table 11. Preferred Fragmentation Channels and Energies of AlXn (X = CN or NC) Clusters neutral

monoanion ΔE(eV)

channel

dianion ΔE(eV)

channel −

−

AlNC → Al + NC

5.25

AlCN → AlCN + e

Al(NC)2 → Al + NCCN

2.25

Al(NC)2− → AlNC + (NC)−

2.05

2.23

Al(CN)3−

2.65

Al(NC)4 → Al(NC)2 + NCCN

0.38

−

Al(NC)5 → Al(NC)3 + NCCN

−0.07

Al(NC)3 → AlNC + NCCN

ΔE(eV)

channel

0.85

→ Al(CN)3 + e

− −

−3.20

Al(CN)2 2 − → Al(CN)2− + e− Al(CN)3

2−

2−

→ Al(CN)3 + e

−2.25

−

−3.35

Al(NC)4 → Al(NC)3 + (NC)

4.24

Al(CN)4

Al(NC)5−

2.13

Al(NC)52 − →Al(NC)4− + (NC)−

→

Al(NC)3−

+ NCCN

−

→ Al(CN)4 + e

→

Al(CN)5−

−

+e

−1.55

−

+0.89

Table 12. EA (in eV) of AlXn (X = CN or NC) and VDE (in eV) of AlXn− Calculated Using Two Levels of Theory AlX

AlX2

AlX3

AlX4

AlX4

method

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

EA (ADE)

VDE

B3LYP OVGF

0.57 (0.85)

0.86 0.73

2.81 (2.81)

3.35 3.51

2.38 (2.65)

3.53 3.51

5.84 (6.86)

6.87 7.96

3.44 (3.44)

4.58 4.42

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(3) The stability and electronic properties of the dianions were also studied in the gas phase. The results show that while some of the dianions studied here are stable against autoejection of an electron, they all are metastable against fragmentation. However, when compared between the halogens and pseudohalogens bound to a metal atom, the dianions composed of pesudohalogens are more stable than those composed of halogens. This is because the second electron in a dianion containing CN moieties finds a larger phase space to delocalize as opposed to those containing Cl. The results compare well with available experimental and theoretical data. The studies reveal that there are a number of ways where new superhalogens can be created and these can be useful in synthesizing new salts and oxidizing agents.

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ASSOCIATED CONTENT

S Supporting Information *

Energy differences between two low lying spin configurations for the systems (NaCln, MgCln, AlCln, NaX, MgX, AlX, and NaX22− (where X = CN or NC) calculated using B3LYP and CCSD(T) methods and 6-311++G(3df) basis set (Tables S1− S7) and the electronic states (Table S8). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by grants from the Department of Energy and Defense Threat Reduction Agency (Grant No. HDTRA1-09-1-0025). This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0205CH11231. 5616



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Stability and Spectroscopic Properties of Singly and Doubly Charged

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