Does Alkaline-Earth-Metal-Based Superalkali Exist? - ACS Publications

Subscriber access provided by NEW YORK UNIV

Article

Does Alkaline-Earth-Metal Based Superalkali Exist? Jia-Yuan Liu, Yongjie Xi, Ying Li, Siyi Li, Di Wu, and Zhi-Ru Li J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b10555 • Publication Date (Web): 06 Dec 2016 Downloaded from http://pubs.acs.org on December 6, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Does Alkaline-Earth-Metal Based Superalkali Exist? Jia-Yuan Liu,a Yong-Jie Xi,b Ying Li,a Si-Yi Li,a Di Wu,*a Zhi-Ru Lia a

Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China

b

Department of Chemistry, National University of Singapore, 117543, Singapore

ABSTRACT: A series of MkF2k-1+ (M = Mg, Ca; k = 2, 3) cations have been theoretically investigated to make a new attempt to design superalkali species. As expected, most of these cations were identified as pseudo-alkali or even superalkali cations in view of their low electron affinities (EAs). The stability of these cationic clusters is indicated by considerable HOMO-LUMO gaps and positive dissociation energies. More intriguingly, these alkaline-earth-metal-based cations have advantages over alkali-metal-based superalkalis in two aspects: 1) they possess much larger binding energy values; 2) they can keep the chemical stability along with the increasing cluster size. Therefore, it is proposed here that the alkaline-earth-metal atoms could partner with halogens to construct stable cations of low EA value, which may add new candidates to the superalkali family.

*

Corresponding author; e-mail address: [email protected]

ACS Paragon Plus Environment

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 29

1. INTRODUCTION Specific clusters which exhibit similar chemical behaviors to atoms in the periodic table are regarded as superatoms.1 In recent years, the field of superatoms has drawn numerous attention from both experimental and theoretical research groups and a great deal of superatoms have been characterized.2-7 The seminal works by Castleman, Khanna, and Jena et al. have confirmed the idea that superatoms can behave as composite entities in chemistry, which consequently broadened the traditional periodic table to a third dimension.6, 8 That superatoms can serve as building blocks to construct nanoscale assemblies9-11 suggests a new way through which materials with desired functionality might be designed. A well-known subset of superatom is superalkalis,12 which feature lower ionization potentials (IPs) than those of alkali-metal atoms (5.39-3.89 eV).13 Accordingly, their daughter cations possess very low electron affinities. Owing to their excellent reducibility and size advantage, superalkalis play an important part in chemistry. They can be used to reduce species that possess low electron affinity and enable the synthesis of unusual charge-transfer salts.14, 15 They are superior to alkali metal atoms in forming cluster-assembled compounds where steric hindrance is remarkable for the latter.16,

17

Another fact, showing the application prospect of

superalkalis, is that they can serve as potential building blocks of novel nanostructured materials and at the same time keep their own electronic and structural integrity.17-21 Therefore, designing and characterizing various superalkali species should be an exciting project. During the past 30 years, the theoretical and experimental attemps to identiy various superalkali clusters,22-33 especially their cations,24,

26, 30, 33-40

have yielded

abundant results. Most reported superalkalis are mononuclear clusters, in accord with the MLk+n formula which was introduced by Gutsev and Boldyrev.12 Very recently, plenty of efforts have been devoted to exploring superalkalis of new type. So far the research area of superalkali has been developed to include dinuclear30,

35

and

polynuclear38, 40 species. Combining the concepts of aromaticity and superatom, Sun


2

Page 3 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


et al. have designed a series of aromatic superalkali cations by using inorganic/organic aromatic clusters as central cores.37 More interestingly, Hou et al. have proposed the possibility of using hydrogen as ligands in creating an unusual type of superalkalis, thereby introducing nonmetallic members into the superalkali family.41 In retrospect, the studies of superalkalis mainly focused on alkali metal compounds12,

24, 28, 30-33, 35, 36, 38

while the alkaline-earth metal compounds did not

attract any attention. This may be due to the larger first IP of alkaline-earth metal than that of alkali metal. For example, the Li2F molecule has a low IP of 3.8 eV29 which characterizes its superalkali nature, while the MgF molecule possesses IP up to 7.85 eV42 and cannot be qualified as a superalkali species. Nevertheless, as we found in previous studies, dinuclear superalkalis show lower IP values when compared with their corresponding mononuclear ones.30 Thus, we wonder if larger polynuclear alkaline-earth metal halides have lower IPs than MgF and even exhibit superalkali features. In the present contribution, a series of cationic MkF2k-1+ (M = Mg, Ca; k = 2, 3) compounds were investigated to verify whether the superalkalis can be derived from the alkaline-earth-metal-based species. We theoretically obtained various structures of the MkF2k-1+ cations and their vertical electron affinities (EAvert). As expected, most of these MkF2k-1+ cations exhibit pretty low EAvert values. Three of them present superalkali nature, while the rest can be regarded as pseudo-alkali species. In particular, the EAvert value of 3.26 eV for Ca3F5+ (isomer 4-I) is much lower than that of Cs+ cation (3.89 eV). Such superalkalis involving alkaline-earth metals not only provide potential candidates to the research on superalkalis but reflect the limitless potential of creating new species classified as superatoms. 2. COMPUTATIONAL METHODS The stochastic search procedure43,

44

was adopted to search all the minimum

structures of the MkF2k-1+ cations. In this procedure, a mass of initial structures were generated inside a sphere by randomly kicking all atoms out from the center of the


3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

sphere. All the starting geometries were optimized at the B3LYP/3-21G level to rule out the irrational structures. Afterwards, much more hunts were conducted to search for new minima in the vicinity of each stationary point found above. This process had been repeated until no new minimum appeared. Then, all the resulting minimum structures were reoptimized at the MP2/6-311+G(3df) level. Frequency analysis was performed at the same level. In order to evaluate the computational method, we compare the optimized geometrical parameter of MgF2 with the experimental value. The Mg-F bond length of MgF2 is 1.761 Å at the MP2/6-311+G(3df) level, which is in good agreement with the experimental value of 1.771 Å.13 Thus, the MP2/6-311+G(3df) treatment is considered reliable for predicting the structures of the MkF2k-1+ cations. The vertical electron affinities (EAvert) of the MkF2k-1+ cations were obtained by two means. Firstly, the direct computation method, namely the restricted outer valence Green function (OVGF)45-49 method, was adopted with the 6-311+G(3df) basis set. For all the investigated cations, the pole strengths (PSs) are greater than 0.80-0.85,50 justifying the validity of OVGF approximation. Secondly, the EAvert value of an MkF2k-1+ cation is indirectly computed as the energy difference between itself and its neutral at the cation’s geometry by using the CCSD(T) and MP2 methods. For comparison, we also obtained the adiabatic electron affinity (EAad) of each MkF2k-1+ cation which is computed as the difference in total energy between the MkF2k-1+ cation and its neutral at their respective optimized geometries with zero-point vibrational energy corrections. The zero-point-corrected dissociation energies (∆E), natural bond orbital (NBO)51 charges and the binding energies per atom (Eb) of the MkF2k-1+ cations were obtained at the MP2/6-311+G(3df) level, where Eb (M k F2+k -1 ) = [(k − 1) E (M) + E (M 2 + ) + (2k − 2) E (F) + E (F− ) − E (M k F2+k -1 )] / 3k − 1 All calculations were performed using the GAUSSIAN 09 program package.52

3. RESULTS AND DISCUSSION The MP2 optimized structures of various minimum energy isomers of Mg2F3+,


4

Page 4 of 29

Page 5 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Mg3F5+, Ca2F3+, and Ca3F5+ are shown in Figures 1 and 2, respectively. For comparison, their corresponding neutral geometries also have been optimized at the MP2/6-311+G(3df) level and are shown in Figures 3 and 4, respectively. Besides, the singly occupied molecular orbitals of the neutral MkF2k-1 species are provided in Figures S1 and S2 to assist in understanding their electronic structure. The nomenclature uses Arabic numerals from 1 to 4 to represent the Mg2F3+, Mg3F5+, Ca2F3+, and Ca3F5+ cations, respectively, followed by Roman numerals differentiating the isomers with zero-point corrected total energies increasing in the order of I < II < III < …. For example, 2-II denotes the second favorable configuration of Mg3F5+. As for the neutral MkF2k-1 species, their structures are named after corresponding cationic ones. For example, 2-II′ represents the corresponding neutral configuration of 2-II. Gathered in Tables 1-4 are lowest vibrational frequencies, relative energies, highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gaps, binding energy per atom (Eb), and NBO charges on Mg or Ca atoms of these cations, respectively. The vertical electron affinities (EAvert) of the MkF2k-1+ cations, obtained by using the MP2, CCSD(T) and OVGF methods, respectively, are collected in Tables 5, in which the EAad values at the MP2 level are also listed. To explore the thermodynamic stability of the MkF2k-1+ cations, two possible dissociation channels are considered, namely MkF2k-1+ → Mk-1F2k-3+ + MF2 and MkF2k-1+ → Mk-1F2k-1− + M2+. Their zero-point-corrected dissociation energies (∆E1 and ∆E2, respectively) are listed in Tables 1-4, respectively. From the results, only the last isomer of Ca3F5+ has a relatively small dissociation energy of 8.4 kcal/mol upon losing a CaF2 molecule. Otherwise, the dissociation reactions are highly endothermic with dissociation energies of 34.0 ~ 427.8 kcal/mol, reflecting the stability of the MkF2k-1+ cations, especially when it comes to the loss of an M2+ ion. The structural features, electron affinity values, as well as stability of the MkF2k-1+ cations are elaborated in the following subsections.


5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3.1 Mg2F3+ Three isomers have been identified for the Mg2F3+ cation. From Figures 1 and 3, the Mg2F3+ isomers and their corresponding neutral Mg2F3 structures generally share similar structural features. The D3h-symmetric trigonal bipyramid structure 1-I is the global minimum of Mg2F3+. Two magnesium atoms are linked via three fluorine atoms in 1-I, where the Mg-F bond length is 1.913 Å. As for neutral 1-I′, the Mg-F bond length is 1.940 Å, reflecting the fact that the loss of an electron from 1-I′ hardly affects its structure. The second lowest-energy isomer 1-II has a planar kite-like structure, which is higher in energy than 1-I by 14.4 kcal/mol. With two Mg and two F atoms in its quasi-rhombic part and one F forming its tail, the configuration of 1-II is of C2v symmetry. In this configuration, the Mg1-F1 and Mg2-F3 bond lengths are 1.825 and 1.742 Å, respectively, which are relatively shorter compared with the Mg2-F1 bond of 1.993 Å. According to NBO analysis, the charges on the Mg1F2 and Mg2F3 subunits are 0.125 and 0.875|e|, respectively. Thus, isomer 1-II may be viewed as composed of MgF2 and MgF+ units. Even though the geometry of 1-II′ is very similar to 1-II, the Mg1-F1 bond length of 1.946 Å is a bit longer in the former case. Isomer 1-III possesses a linear D∞h-symmetric structure, which is 23.3 kcal/mol less stable than 1-I. Two Mg atoms are linked by a fluorine atom in this structure, and each Mg atom is coordinated with two F atoms. The middle Mg1-F2 bond of 1.884 Å is slightly longer than the end Mg1-F1 bond of 1.728 Å. In contrast, the neutral 1-III′ possesses a “seagull”-shaped C2v configuration. The angle of ∠Mg1F2Mg2 is 101.7°. Interestingly, the Mg1-F1 (1.765 Å) and Mg1-F2 (1.901 Å) bond lengths of 1-III′ are very close to those of 1-III, respectively. It is noteworthy that the two Mg atoms are separated by F atoms in all the three Mg2F3+ isomers. Besides, the more bridge F atoms there are, the higher stability the isomer has. The HOMO-LUMO energy gap is considered to be a useful quantity for measuring the electronic stability and chemical inertness of clusters. From Table 1, the HOMO-LUMO energy gaps (11.57~15.34 eV) of Mg2F3+ are quite large,


6

Page 6 of 29

Page 7 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


especially for the global minimum 1-I, whose gap value is almost the same with that of stable MgF2 molecule (15.42 eV at the MP2/6-311+G(3df) level). The NBO charges on Mg and F atoms are in the range of 1.727-1.851|e| and 0.852-0.891|e|, respectively, indicating the formation of Mg-F ionic bonds. Besides, the Mg atoms in these cations are more positively charged compared with those in alkali-metal-based superalkali cations, so the atoms involved in such alkaline earth-based cations are bound together more tightly. As shown in Table 1, the binding energies (Eb) of the Mg2F3+ cations range from 5.99 to 6.19 eV, which are much larger than those of binuclear superalkali cations F2Li3+ (3.27–3.38 eV)35, showing the advantage of the alkaline earth-based cations with respect to stability. According to the OVGF results, the EAvert values of the three Mg2F3+ isomers are 5.34-6.77 eV (see Table 5). Herein, the EAvert value of 5.34 eV for the global minimum isomer 1-I is slightly lower than the IP of Li atom (5.39 eV),13 and thus 1-I is eligible to be considered as a pseudoalkali cation. The EAvert values of isomers 1-II and 1-III are predicted to be 6.77 and 5.50 eV, respectively. Isomer 1-II exhibits a relatively larger EAvert value because the higher symmetries of I-I and I-III benefit more even distribution of the excess positive charge. Nevertheless, the Mg2F3+ cations exhibit much lower EAvert values compared with that of the MgF+ cation (7.61 eV at the OVGF/6-311+G(3df) level). Thus, it is highly expected that the transition from Mg2F3+ to the larger Mg3F5+ species is a promising way to further decrease the EAvert values. From Table 5, the EAvert values calculated by the MP2 and CCSD(T) methods agree very well with the OVGF results, either in value or in sequence. Note that the same case has also been reported in our previous study.33 As for the EAad values, they are very close to the EAvert values for isomers 1-I and 1-II. However, the difference between EAvert and EAad values is as large as 0.72 eV for 1-III, which can be attributed to the different geometries of 1-III and 1-III′.

3.2 Mg3F5+ The structures of the neutral Mg3F5 species are similar to corresponding Mg3F5+


7


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

cations except 2-V′ and 2-VI′ (see Figures 1 and 3). From Figure 1, the D3h-symmetric isomer 2-I is the lowest-energy structure of Mg3F5+. In 2-I, an equilateral triangle formed by three Mg atoms is enclosed by a bigger equilateral triangle composed of three F atoms, and the six atoms are coplanar with two additional fluorine atoms respectively lying above and below this plane. The in-plane and out-of-plane Mg-F bond lengths are 1.936 Å and 2.009 Å, respectively. The geometry of neutral 2-I′ isomer very much resembles 2-I in view of the fact that the in-plane and out-of-plane Mg-F bond lengths of 2-I′ are 1.958 Å and 2.021 Å, respectively. Besides, another five isomers were obtained for Mg3F5+. The less favorable structure of Mg3F5+ is 2-II, which is higher in energy by 11.4 kcal/mol than 2-I. The C2v-symmetric 2-II looks like a combination of a planar MgF3 unit and a folded Mg2F2 rhombus. The two parts are connected by two Mg-F bonds of 1.847 Å. The neutral 2-II′ not only has exactly the same shape as 2-II, but possesses similar structural parameters. The Mg-F bond length show little difference (no more than 0.06 Å) between the two structures. The C3v-symmetric structure 2-III looks like an MgF2 molecule apex-bound to structure 1-I, which is 29.8 kcal/mol higher in energy than 2-I. In 2-III, the Mg2F3+ and MgF2 units are bridged by the Mg2-F2 bond of 1.903 Å. Note that the Mg-F bonds which contain Mg2/F2 bridge atom are lengthened compared with corresponding those in isolated 1-I or MgF2 molecule, while the opposite is discerned for the other Mg-F bonds. For example, the Mg3-F2 and Mg3-F3 bond lengths are 1.850 Å and 1.733 Å, respectively, the former is longer whereas the latter is shorter than that (1.761 Å) of free MgF2 molecule. Similarly, the Mg2-F1 bond of 1.952 Å is elongated compared with that of structure 1-I, while the Mg1-F1 bond behaves reversely. As for the neutral structure 2-III′, the Mg3-F2 and Mg3-F3 bond lengths are 1.812 Å and 1.743 Å, respectively, which get closer to that of free MgF2 molecule. Meanwhile, the bridge Mg2-F2 bond of 2-III′ is 0.037 Å longer than that of 2-III. Isomer 2-IV can also be regarded as composed of a 1-I structure and an MgF2


8

Page 8 of 29

Page 9 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


molecule, and the two subunits are linked together by two Mg-F bonds. This configuration is 34.1 kcal/mol higher in energy than 2-I. Although it looks similar to its corresponding neutral isomer 2-IV′, they have different structural features. To be specific, the F1-Mg2-F2 and Mg2-F3-Mg3 planes are perpendicular to each other in

2-IV, whereas are coplanar in 2-IV′. The least two favorable structures of Mg3F5+ are 2-V and 2-VI, which are 34.7 and 36.6 kcal/mol less stable than 2-I, respectively. From Figure 1, both of the structures are planar and can be regarded as a combination of structure 1-II and an MgF2 molecule, but the way how these two subunits are linked to each other yields the difference between 2-V and 2-VI. As shown in Figure 1, the MgF2 molecule is bound to the 1-II unit by two Mg-F bonds in structure 2-V but via a Mg-F bond in

2-VI. Compared to corresponding cations, neutral isomers 2-V′ and 2-VI′ show obvious structural differences. There is a six-member ring in 2-V′, which is composed of alternating Mg and F atoms. In 2-VI′, the Mg2-F3-Mg3 and F1-Mg2-F2 planes are perpendicular to each other. The angle of ∠Mg2F3Mg3 is 101.0°, which is quite close to the Mg1F2Mg2 angle of the 1-III′ isomer. As listed in Table 2, the HOMO−LUMO gaps of Mg3F5+ are in the range of 12.87−16.37 eV, and the most stable isomer 2-I exhibits the largest gap value among these Mg3F5+ species. From previous works, it is found that the gaps of binuclear superalkali cations B2Li11+ (1.36 ~ 2.14 eV)30 are smaller than that of 2.36 eV53 for mononuclear superalkali cation BLi6+. In contrast, the gap values of the Mg3F5+ cations are approximate to or even larger than those of Mg2F3+, and the binding energies of Mg3F5+ are only slightly lower than those of Mg2F3+, indicating that such MgkF2k-1+ cations can keep the chemical stability along with the increasing size. The OVGF results in Table 5 show that the EAvert values of Mg3F5+ are in the range of 4.34-5.75 eV. Except for 2-IV and 2-V, all the rest isomers possess smaller EAvert values than the IP of lithium atom. Therefore, 2-I, 2-II, 2-III, and 2-VI can be classified as pseudoalkali cations. Particularly, the EAvert value of 2-I (4.34 eV) is equal to the IP of potassium atom.13 From Table 5, the difference between EAad and


9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

EAvert values is pretty small for isomers 2-I, 2-II, 2-III, and 2-IV. However, the discrepancies between EAad and EAvert values are as large as 0.99 eV and 0.83 eV for

2-V and 2-VI, respectively. This is reasonable if we take into account the obvious structural discrepancy between 2-V and 2-VI and their corresponding neutral species, respectively.

3.3 Ca2F3+ Although the EAvert values of some MgkF2k-1+ (k = 2, 3) isomers are lower than the IP of lithium, they are still above the IP of cesium (3.89 eV).13 In view of the lower first IP of calcium than that of magnesium, the Ca2F3+ and Ca3F5+ cations are expected to perform better than Mg2F3+ and Mg3F5+ in yielding lower EAvert values. Two optimized configurations of Ca2F3+ were obtained in our work (see Figure 2). The more stable isomer 3-I is similar to the structure of 1-I and also has D3h symmetry. The Ca-F bond length is 2.148 Å. The other isomer 3-II possesses a C2-symmetric structure, which can be regarded as two CaF2 molecules sharing a common F atom. The terminal Ca-F bonds of 1.940 Å are shorter than those (2.161 Å) involved in the Ca–F–Ca linking fragment. The geometry of neutral isomer 3-I′ very much resembles

3-I, only the Ca-F bond length (2.172 Å) is slightly longer (see Figure 4). In contrast, 3-II′ possesses a Zig-zag geometry, which is more like 1-III′ than 3-II. The angle of ∠Ca1F3Ca2 is 113.3°. Unlike the case of Mg2F3+, both the kite-like and linear configurations were not found for Ca2F3+. This may result from the different geometries of MgF2 and CaF2 molecules, namely, linear structure for the former and V-shaped geometry for the latter.54 In Table 3, the HOMO−LUMO gaps of Ca2F3+ are in the range of 14.08−15.30 eV, indicating that the Ca2F3+ cations possess high chemical stability. It is also found that the most stable isomer 3-I possesses larger gap value compared with isomer 3-II. The EAvert values of 3-I and 3-II are 3.92 and 4.26 eV, respectively, both of which are much lower than that of 1-I, not only suggesting the pseudoalkali characteristics of the Ca2F3+ cations, but also proving our assumption that larger


10

Page 10 of 29

Page 11 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


alkaline-earth ligand M may bring decreased EAvert value of MkF2k-1+. The EAad values of two Ca2F3+ isomers are also listed in Table 5. The lowest-energy isomer 3-I has almost the same EAvert and EAad values. However, the difference between EAvert and EAad values is as large as 0.70 eV for isomer 3-II because its corresponding neutral isomer 3-II′ has a quite different structure.

3.4. Ca3F5+ Ca3F5+ has six minimum energy structures (see Figure 2). The D3h-symmetric 4-I, which resembles the structure of 2-I, is the most stable isomer of Ca3F5+. Similar to

2-I, there are two types of Ca-F bonds in 4-I and the out-of-plane Ca-F bonds of 2.265 Å are ca. 0.1 Å longer than the in-plane ones. The neutral isomer 4-I′ also possesses D3h symmetry, where the out-of-plane and in-plane Ca-F bond lengths are 2.268 Å and 2.192 Å, respectively. Isomer 4-II has no analogue in the Mg3F5+ species. It possesses C2v symmetry and is 16.6 kcal/mol higher in energy than 4-I. As is illustrated in Figure 2, the geometry of 4-II resembles a basket with a Ca1-F1-Ca3 segment forming the handle part. Interestingly, the neutral 4-II′ looks like a squashed 4-II, where the Ca2-F1 distance shortened from 3.524 Å to 2.483 Å. The next isomer 4-III is 29.4 kcal/mol less stable than 4-I. It shows similar structural characteristics to 2-II, only it has Cs symmetry and possesses a tilted Ca1F3 motif. Isomer 4-IV can be described as a slightly distorted 4-III, in which the Ca1F3 unit bent upward towards the folded-rhombic Ca2F2 unit, with the intersecting angle between the Ca1-F2-F3 and F2-F3-Ca3-Ca2 planes varying from 166.4° to 125.3°. Hence, the difference in total energy between 4-IV and 4-III is only 0.2 kcal/mol, and they are likely to coexist in gas phase. Besides, they correspond to the same neutral configuration 4-III′ (4-IV′). The least two favorable configurations of Ca3F5+ are 4-V and 4-VI, which resemble the structures of 2-IV and 2-VI, respectively. The planar 4-VI is 44.2 kcal/mol less stable than 4-V, indicating that the Ca3F5+ cations prefer the


11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

three-dimensional structures rather than the planar ones, which is also true for the Mg3F5+ cations. There is great structural difference between 4-V/4-VI and corresponding neutral 4-V′/4-VI′. The plane composed by Ca2, F1 and F2 atoms is same to the plane Ca1, Ca2, and F3 atoms in 4-V′. In 4-V, the former plane is perpendicular to the latter plane. Generally, 4-V′ can be viewed as the Ca1F1Ca2F2 quadrangle rotated 90° along the Ca1-Ca2 axis in structure 4-V. Compared with 4-VI, the angle of ∠Ca2-F3-Ca3 became bent in 4-VI′, which is similar to the case of

2-VI′. From Table 4, the HOMO−LUMO gaps of Ca3F5+ are in the range of 11.56−15.86 eV, and the largest and the lowest gap values belong to the most stable isomer 4-I and the least favorable isomer 4-VI, respectively. Similar to the case of Mg3F5+ species, the HOMO-LUMO gap and binding energy values of the Ca3F5+ cations are, respectively, close to those of Ca2F3+. So the CakF2k-1+ cations can also keep the stability along with the increasing size. Moreover, as can be seen from Table 5, isomers 4-I, 4-II, 4-III show lower EAvert values than the IP of Cs atom (3.89 eV),13 and consequently, can be classified as novel superalkali cations. The EAvert values of isomers 4-IV, 4-V, 4-VI are lower than the IP of Li atom (5.39 eV)13 but higher than the IP of Cs atom, therefore they can be termed as pseudo-alkali cations. The low EAvert values of the Ca3F5+ cations reflect the excellent ability of their corresponding neutral species to serve as electron donors. The EAad values of Ca3F5+ are also listed in Table 5, and they are close to the EAvert values for isomers 4-I, 4-II, 4-III, 4-IV and 4-V. For isomer 4-VI, the EAad value is much larger than the EAvert value, which is due to the large structural difference between the neutral and cationic species. As to why such alkaline-earth-metal-based cations possess low EAs, we may get a clue by looking over the electronic structure of their neutral parents. From Figures S1 and S2, the singly occupied molecular orbitals of the MkF2k-1 molecules are dominated by loosely bound s electron from M atom(s). Besides, the electron cloud protrudes out of the molecule due to the repulsion from F− ligands. Therefore, the


12

Page 12 of 29

Page 13 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


MkF2k-1 molecules are apt to lose the SOMO electron, and consequently, their daughter cations feature low EAvert values.

4 CONCLUSION A new kind of cations with formula MkF2k-1+ (M = Mg, Ca; k = 2, 3), which are expected to have low electron affinities, have been proposed and investigated. Seventeen structures of MkF2k-1+ have been identified and thirteen of which can be considered as pseudoalkali or even superalkali cations. Owing to the large binding energies, wide HOMO-LUMO gaps, and high dissociation energies, such alkaline-earth-metal-based cations exhibit enhanced stabilities compared with previously reported binuclear superalkalis M2Li2k+1+. In addition, the EAvert values of the lowest-energy MkF2k-1+ isomers decrease in the order 5.34 eV (1-I, Mg2F3+) > 4.34 eV (2-I, Mg3F5+) > 3.92 eV (3-I, Ca2F3+) > 3.26 eV (4-I, Ca3F5+), indicating that increasing either the size of the cation itself or the atomic number of alkaline-earth-metal atoms involved is an effective way to achieve lower EAvert values.


13


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ASSOCIATED CONTENT Supporting Information Complete citation for reference 52 and the HOMOs of the neutral MkF2k-1 molecules. This Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org/

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (D.W.).

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant Nos. 21173098, 21573089, 21303066) and State Key Development Program for Basic Research of China (Grant No. 2013CB834801).

REFERENCES (1) Khanna, S. N.; Jena, P. Assembling Crystals from Clusters Phys. Rev. Lett. 1992, 69, 1664−1667. (2) Bergeron, D. E.; Castleman, A. W., Jr.; Morisato, T.; Khanna, S. N. Formation of Al13I−: Evidence for the Superhalogen Character of Al13 Science 2004, 304, 84−87. (3) Bergeron, D. E.; Roach, P. J.; Castleman, A. W., Jr.; Jones, N. O.; Khanna, S. N. Al Cluster Superatoms as Halogens in Polyhalides and as Alkaline Earths in Iodide Salts Science 2005, 307, 231−235. (4) Reveles, J. U.; Khanna, S. N.; Roach, P. J.; Castleman, A. W., Jr. Multiple Valence Superatoms Proc. Natl. Acad. Sci. 2006, 103, 18405−18410. (5) Das, U.; Raghavachari, K. Al5O4: A Superatom with Potential for New Materials Design J. Chem. Theory Comput. 2008, 4, 2011−2019. (6) Castleman, A. W., Jr. From Elements to Clusters: The Periodic Table Revisited J. Phys. Chem. Lett. 2011, 2, 1062−1069.


14

Page 14 of 29

Page 15 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(7) Medel, V. M.; Reveles, J. U.; Khanna, S. N.; Chauhan, V.; Sen, P.; Castleman, A. W., Jr. Hund’s Rule in Superatoms with Transition Metal Impurities Proc. Natl. Acad. Sci. 2011, 108, 10062−10066. (8) Khanna, S. N.; Jena, P. Atomic Clusters: Building Blocks for a Class of Solids Phys. Rev. B 1995, 51, 13705−13716. (9) Castleman, A. W., Jr.; Khanna, S. N.; Sen, A.; Reber, A. C.; Qian, M.; Davis, K. M.; Peppernick, S. J.; Ugrinov, A.; Merritt, M. D. From Designer Clusters to Synthetic Crystalline Nanoassemblies Nano Lett. 2007, 7, 2734−2741. (10) Castleman, A. W., Jr.; Khanna, S. N. Clusters, Superatoms, and Building Blocks of New Materials J. Phys. Chem. C 2009, 113, 2664−2675. (11) Claridge, S. A.; Castleman, A. W., Jr.; Khanna, S. N.; Murray, C. B.; Sen, A.; Weiss, P. S. Cluster-Assembled Materials Acs Nano 2009, 3, 244−255. (12) Gutsev, G. L.; Boldyrev, A. I. DVM Xα Calculations on the Electronic Structure of “Superalkali” Cations Chem. Phys. Lett. 1982, 92, 262−266. (13) Lide, D. R. CRC Handbook of Chemistry and Physics. 89th ed.; CRC press: Boca Raton, Florida, 2008. (14) Zintl, E.; Morawietz, W. Orthosalze von Sauerstoffsäuren Z. Anorg. Allg. Chem. 1938, 236, 372−410. (15) Jansen, M. Neue Untersuchungen an Na3NO3 Z. Anorg. Allg. Chem. 1977, 435, 13−20. (16) Clayborne, P.; Jones, N. O.; Reber, A. C.; Reveles, J. U.; Qian, M. C.; Khanna, S. N. Superatoms and Their Assemblies Based on Alkali and Super-alkali Motifs J. Comput. Methods Sci. Eng. 2007, 7, 417−430. (17) Reber, A. C.; Khanna, S. N.; Castleman, A. W., Jr. Superatom Compounds, Clusters, and Assemblies: Ultra Alkali Motifs and Architectures J. Am. Chem. Soc. 2007, 129, 10189−10194. (18) Wang, F. F.; Li, Z. R.; Wu, D.; Sun, X. Y.; Chen, W.; Li, Y.; Sun, C. C. Novel Superalkali Superhalogen Compounds (Li3)+(SH)− (SH = LiF2, BeF3, and BF4) with Aromaticity: New Electrides and Alkalides ChemPhysChem 2006, 7, 1136−1141. (19) Li, Y.; Wu, D.; Li, Z. R. Compounds of Superatom Clusters: Preferred Structures and Significant Nonlinear Optical Properties of the BLi6−X (X = F, LiF2, BeF3, BF4) Motifs Inorg. Chem. 2008, 47, 9773−9778.


15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(20) Yang, H.; Li, Y.; Wu, D.; Li, Z. R. Structural Properties and Nonlinear Optical Responses of Superatom Compounds BF4−M (M = Li, FLi2, OLi3, NLi4) Int. J. Quantum Chem. 2012, 112, 770−778. (21) Giri, S.; Behera, S.; Jena, P. Superalkalis and Superhalogens as Building Blocks of Supersalts J. Phys. Chem. A 2014, 118, 638−645. (22) Schleyer, P. v. R.; Wuerthwein, E. U.; Kaufmann, E.; Clark, T.; Pople, J. A. Lithium Carbide (CLi5), Lithium Carbide (CLi6), and the Related Effectively Hypervalent First Row Molecules, CLi5−nHn and CLi6−nHn J. Am. Chem. Soc. 1983, 105, 5930−5932. (23) Wu, C. H. The Stability of the Molecules Li4O and Li5O Chem. Phys. Lett. 1987, 139, 357−359. (24) Rehm, E.; Boldyrev, A. I.; Schleyer, P. v. R. Ab Initio Study of Superalkalis. First Ionization Potentials and Thermodynamic Stability Inorg. Chem. 1992, 31, 4834−4842. (25) Zakrzewski, V. G.; Niessen, W. v.; Boldyrev, A. I.; Schleyer, P. v. R. Green Function Calculation of Ionization Energies of Hypermetallic Molecules Chem. Phys. 1993, 174, 167−176. (26) Lievens, P.; Thoen, P.; Bouckaert, S.; Bouwen, W.; Vanhoutte, F.; Weidele, H.; Silverans, R. E.; Navarro-Vázquez, A.; Schleyer, P. v. R. Ionization Potentials of LinO (2 ≤ n ≤ 70) Clusters: Experiment and Theory J. Chem. Phys. 1999, 110, 10316−10329. (27) Gutsev, G. L.; Boldyrev, A. I. The Theoretical Investigation of the Electron Affinity of Chemical Compounds Advances in Chemical Physics, 1985, 61, 169−221. (28) Li, Y.; Wu, D.; Li, Z. R.; Sun, C. C. Structural and Electronic Properties of Boron-Doped Lithium Clusters: Ab Initio and DFT Studies J. Comput. Chem. 2007, 28, 1677−1684. (29) Veličković, S. R.; Koteski, V. J.; Belošević Čavor, J. N.; Djordjević, V. R.; Cvetićanin, J. M.; Djustebek, J. B.; Veljković, M. V.; Nešković, O. M. Experimental and Theoretical Investigation of New Hypervalent Molecules LinF (n = 2–4) Chem. Phys. Lett. 2007, 448, 151−155. (30) Tong, J.; Li, Y.; Wu, D.; Li, Z. R.; Huang, X. R. Low Ionization Potentials of Binuclear Superalkali B2Li11 J. Chem. Phys. 2009, 131, 164307−164311. (31) Anusiewicz, I. The Na2X Superalkali Species (X = SH, SCH3, OCH3, CN, N3) as Building Blocks in the Na2XY Salts (Y = MgCl3, Cl, NO2). An Ab Initio Study of the Electric Properties of the Na2XY Salts Aust. J. Chem. 2010, 63, 1573−1581. (32) Zein, S.; Ortiz, J. V. Interpretation of the Photoelectron Spectra of Superalkali Species: Na3O and Na3O− J. Chem. Phys. 2012, 136, 224305.


16

Page 16 of 29

Page 17 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(33) Tong, J.; Li, Y.; Wu, D.; Wu, Z. J. Theoretical Study of Substitution Effect in Superalkali OM3 (M = Li, Na, K) Chem. Phys. Lett. 2013, 575, 27−31. (34) Alexandrova, A. N.; Boldyrev, A. I. σ-Aromaticity and σ-Antiaromaticity in Alkali Metal and Alkaline Earth Metal Small Clusters J. Phys. Chem. A 2003, 107, 554−560. (35) Tong, J.; Li, Y.; Wu, D.; Li, Z. R.; Huang, X. R. Ab Initio Investigation on a New Class of Binuclear Superalkali Cations M2Li2k+1+ (F2Li3+, O2Li5+, N2Li7+, and C2Li9+) J. Phys. Chem. A 2011, 115, 2041−2046. (36) Tong, J.; Li, Y.; Wu, D.; Wu, Z. J. Theoretical Study on Polynuclear Superalkali Cations with Various Functional Groups as the Central Core Inorg. Chem. 2012, 51, 6081−6088. (37) Sun, W. M.; Li, Y.; Wu, D.; Li, Z. R. Designing Aromatic Superatoms J. Phys. Chem. C 2013, 117, 24618−24624. (38) Tong, J.; Wu, Z. J.; Li, Y.; Wu, D. Prediction and Characterization of Novel Polynuclear Superalkali Cations Dalton. Trans. 2013, 42, 577−584. (39) Hou, N.; Wu, D.; Li, Y.; Li, Z. R. Lower the Electron Affinity by Halogenation: an Unusual Strategy to Design Superalkali Cations J. Am. Chem. Soc. 2014, 136, 2921−2927. (40) Liu, J. Y.; Wu, D.; Sun, W. M.; Li, Y.; Li, Z. R. Trivalent Acid Radical-Centered YLi4+ (Y = PO4, AsO4, VO4) Cations: New Polynuclear Species Designed to Enrich the Superalkali Family Dalton. Trans. 2014, 43, 18066−18073. (41) Hou, N.; Li, Y.; Wu, D.; Li, Z. R. Do Nonmetallic Superalkali Cations Exist? Chem. Phys. Lett. 2013, 575, 32−35. (42) Sikorska, C.; Skurski, P. The IP vs. VDE Competition as a Key Factor Determining the Stability of the MgBX5 (X = F, Cl) Compounds Chem. Phys. Lett. 2010, 500, 211−216. (43) Saunders, M. Stochastic Search for Isomers on a Quantum Mechanical Surface J. Comput. Chem. 2004, 25, 621−626. (44) Bera, P. P.; Sattelmeyer, K. W.; Saunders, M.; Schaefer, H. F., III; Schleyer, P. v. R. Mindless Chemistry J. Phys. Chem. A 2006, 110, 4287−4290. (45) Cederbaum, L. S. One-Body Green’s Function for Atoms and Molecules : Theory and Application J. Phys. B: At. Mol. Phys. 1975, 8, 290−303. (46) Ortiz, J. V. Electron Binding Energies of Anionic Alkali Metal Atoms from Partial Fourth Order


17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Electron Propagator Theory Calculations J. Chem. Phys. 1988, 89, 6348−6352. (47) Zakrzewski, V. G.; Ortiz, J. V. Semidirect Algorithms for Third-Order Electron Propagator Calculations Int. J. Quantum. Chem. 1995, 53, 583−590. (48) Zakrzewski, V. G.; Ortiz, J. V.; Nichols, J. A.; Heryadi, D.; Yeager, D. L.; Golab, J. T. Comparison of Perturbative and Multiconfigurational Electron Propagator Methods Int. J. Quantum Chem. 1996, 60, 29−36. (49) Ortiz, J. V. The Electron Propagator Picture of Molecular Electronic Structure, in Computational Chemistry: Reviews of Current Trends; World Scientific: Singapore, 1997. (50) Zakrzewski, V. G.; Dolgounitcheva, O.; Ortiz, J. V. Electron Binding Energies of TCNQ and TCNE J. Chem. Phys. 1996, 105, 5872−5877. (51) Honer, J.; Löw, R.; Weimer, H.; Pfau, T.; Büchler, H. P. Artificial Atoms Can Do More than Atoms: Deterministic Single Photon Subtraction from Arbitrary Light Fields Phys. Rev. Lett. 2011, 107, 093601−093605. (52) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Revision D01; Gaussian, Inc: Wallingford, CT, 2009. (53) Li, Y.; Liu, Y. J.; Wu, D.; Li, Z. R. Evolution of the Structures and Stabilities of Boron-Doped Lithium Cluster Cations: Ab Initio and DFT Studies Phys. Chem. Chem. Phys. 2009, 11, 5703−5710. (54) Hargittai, M. Molecular Structure of Metal Halides Chem. Rev. 2000, 100, 2233−2301.


18

Page 18 of 29

Page 19 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure captions:

Figure 1. The equilibrium structures and symmetries of Mg2F3+ and Mg3F5+. Color legend: F, cyan; Mg, yellowish green

Figure 2. The equilibrium structures and symmetries of Ca2F3+ and Ca3F5+. Color legend: F, cyan; Ca, earth yellow

Figure 3. The corresponding neutral equilibrium structures of Mg2F3+ and Mg3F5+. Color legend: F, cyan; Mg, yellowish green. The relative energies Erel (in kcal/mol) are also shown.

Figure 4. The corresponding neutral equilibrium structures of Ca2F3+ and Ca3F5+. Color legend: F, cyan; Ca, earth green. The relative energies Erel (in kcal/mol) are also shown.


19


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1


20

Page 20 of 29

Page 21 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2


21


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3


22

Page 22 of 29

Page 23 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4


23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 29

Table 1. Relative energies Erel (in kcal/mol), HOMO–LUMO gaps (in eV), the lowest vibrational frequencies (υ1, in cm-1), binding energies per atom (Eb, in eV), NBO charges on Mg atoms (qMg, in |e|) and zero-point-corrected dissociation energies (in kcal/mol) of Mg2F3+ → MgF+ + MgF2 (∆E1) and Mg2F3+ → Mg2+ + MgF3- (∆E2) of the Mg2F3+ cations.

Isomer

Erel

gap

υ1

Eb

qMg1

qMg2

∆E1

∆E2

1-I

0.0

15.34

292

6.190

1.785

1.785

83.3

356.5

1-II

14.4

11.57

62

6.065

1.851

1.727

69.5

342.7

1-III

23.3

14.30

37

5.988

1.807

1.807

61.1

334.2


24

Page 25 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Relative energies Erel (in kcal/mol), HOMO–LUMO gaps (in eV), the lowest vibrational frequencies (υ1, in cm-1), binding energies per atom (Eb, in eV), NBO charges on Mg atoms (qMg, in |e|) and zero-point-corrected dissociation energies (in kcal/mol) of Mg3F5+ → Mg2F3+ + MgF2 (∆E1) and Mg3F5+ → Mg2+ + Mg2F5- (∆E2) of the Mg3F5+ cations.

Isomer

Erel

gap

υ1

Eb

qMg1

qMg2

qMg3

∆E1

∆E2

2-I

0.0

16.37

200

5.730

1.721

1.721

1.721

78.3

358.7

2-II

11.4

12.87

34

5.669

1.725

1.769

1.769

67.7

348.1

2-III

29.8

14.50

25

5.569

1.775

1.673

1.802

49.6

330.0

2-IV

34.1

12.93

26

5.546

1.837

1.579

1.762

45.0

325.4

2-V

34.7

13.39

30

5.542

1.737

1.779

1.737

45.0

325.4

2-VI

36.6

13.00

19

5.532

1.722

1.752

1.805

43.3

323.7


25


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 29

Table 3. Relative energies Erel (in kcal/mol), HOMO–LUMO gaps (in eV), the lowest vibrational frequencies (υ1, in cm-1), binding energies per atom (Eb, in eV), NBO charges on Ca atoms (qCa, in |e|) and zero-point-corrected dissociation energies (in kcal/mol) of Ca2F3+ → CaF+ + CaF2 (∆E1) and Ca2F3+ → Ca2+ + CaF3- (∆E2) of the Ca2F3+ cations.

Isomer

Erel

gap

υ1

Eb

qCa1

qCa2

∆E1

∆E2

3-I

0.0

15.30

231

6.049

1.749

1.749

188.6

427.8

3-II

39.5

14.08

10

5.707

1.763

1.763

172.0

411.1


26

Page 27 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4. Relative energies Erel (in kcal/mol), HOMO–LUMO gaps (in eV), the lowest vibrational frequencies (υ1, in cm-1), binding energies per atom (Eb, in eV), NBO charges on Ca atoms (qCa, in |e|) and zero-point-corrected dissociation energies (in kcal/mol) of Ca3F5+ → Ca2F3+ + CaF2 (∆E1) and Ca3F5+ → Ca2+ + Ca2F5- (∆E2) of the Ca3F5+ cations.

Isomer

Erel

gap

υ1

Eb

qCa1

qCa2

qCa3

∆E1

∆E2

4-I

0.0

15.86

146

5.777

1.689

1.689

1.689

88.3

339.0

4-II

16.6

15.00

34

5.687

1.730

1.649

1.738

72.1

322.8

4-III

29.4

12.94

15

5.618

1.705

1.738

1.738

59.8

310.6

4-IV

29.6

12.56

36

5.617

1.638

1.748

1.748

59.4

310.2

4-V

37.9

13.19

93

5.571

1.836

1.602

1.768

34.0

284.8

4-VI

82.1

11.56

64

5.332

1.757

1.785

1.818

8.4

259.2


27


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 29

Table 5. Vertical electron affinities EAvert (in eV) at the OVGF, MP2 and CCSD(T) levels, and adiabatic electron affinities EAad (in eV) of the MkF2k-1+ (M = Mg, Ca; k = 2, 3) cations. Pole strengths (PS) in parentheses.

EAvert

EAad

isomer OVGF(PS)

MP2

CCSD(T)

MP2

1-I

5.34 (0.987)

5.35

5.43

5.37

1-II

6.77 (0.988)

6.81

6.85

7.02

1-III

5.50 (0.988)

5.52

5.59

6.22

2-I

4.34 (0.985)

4.36

4.46

4.38

2-II

5.02 (0.986)

5.04

5.13

5.15

2-III

4.52 (0.988)

4.56

4.63

4.94

2-IV

5.75 (0.989)

5.80

5.84

6.10

2-V

5.52 (0.984)

5.54

5.63

6.53

2-VI

5.10 (0.985)

5.12

5.20

5.94

3-I

3.92 (0.989)

3.97

4.05

3.97

3-II

4.26 (0.989)

4.30

4.35

4.96

4-I

3.26 (0.988)

3.29

3.41

3.30

4-II

3.37 (0.989)

3.39

3.62

3.53

4-III

3.78 (0.988)

3.81

3.88

4.23

4-IV

4.00 (0.988)

4.04

4.11

4.23

4-V

4.29 (0.989)

4.35

4.38

4.57

4-VI

4.49 (0.986)

4.54

4.58

5.61


28

Page 29 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic


29

Does Alkaline-Earth-Metal-Based Superalkali Exist? - ACS Publications

Recommend Documents