ARTICLE pubs.acs.org/JPCA
Ab Initio Investigation on a New Class of Binuclear Superalkali Cations M2Li2kþ1þ (F2Li3þ, O2Li5þ, N2Li7þ, and C2Li9þ) Jing Tong, Ying Li, Di Wu,* Zhi-Ru Li, and Xu-Ri Huang Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, Changchun 130023, People’s Republic of China
bS Supporting Information ABSTRACT: Superalkalies with low ionization potentials (IPs) can exhibit behaviors reminiscent of alkali atoms and hence be considered as potential building blocks for the assembly of novel nanostructured materials. A new series of binuclear superalkali cations M2Li2kþ1þ (M = F, O, N, C) has been studied using ab initio methods. The structural features of such cations are found to be related to the central atoms. In the preferred structures of F2Li3þ, O2Li5þ, and N2Li7þ, two central atoms are bridged by lithium atoms. While in the global minima of C2Li9þ, two central carbon atoms directly link each other and the CC unit extends to the surface of the whole system. These M2Li2kþ1þ species exhibit very low vertical electron affinities of 2.74-4.61 eV at the OVGF/6-311þG(3df) level and hence should be classified as superalkali cations.
’ INTRODUCTION Superalkalies characterized by lower ionization potentials (IPs) than those (5.39-3.89 eV)1 of alkali-metal atoms have been of considerable interest in recent years.2-7 Thus far the superalkalies investigated have been hyperalkalized molecules of the MLkþn type (where L is an alkali metal atom, k is the maximal formal valence of the central atom M, and n g 1). The first evidence of this kind of superalkalies is the Li3O molecule, which was experimentally discovered by Wu et al.8 and later indicated to be quite stable thermodynamically toward dissociation or loss of an electron by Schleyer et al.9 Since then, a number of mononuclear superalkalies of the type MLkþn have been investigated by theoretical approaches and experimental techniques, such as XLi2 (X = F, Cl, Br, I),10-13 OM3 (M = Li, Na, K),7,14,15 NLi4,7 BLi6,16 etc. Superalkalies are of great importance in chemistry since they can be used for the synthesis of unusual charge-transfer salts, which contains an alkaline moiety and another moiety possessing relatively low electron affinity. A crystal salt Li3OþNO2- containing a singly charged superalkali cation, Li3Oþ, has been known for 70 years.17 Interestingly, superalkalies can mimic the characteristics of alkali metals and maintain their structural and electronic integrities when assembled with other species. Lately, Khanna and co-workers18 theoretically demonstrated a kind of superatom compound formed by combining superalkalies (K3O and Na3O) and superhalogens Al13. It is found that the same chemical principles, working for the atomic cluster, can be extended to a cluster with superatom motifs. Subsequent theoretical work by Li et al.19 predicted a series of superalkalisuperhalogen compounds which exhibit special bonding nature r 2011 American Chemical Society
and extraordinarily large nonlinear optical (NLO) responses. These investigations indicate that superalkalies may serve as potential building blocks for the assembly of novel nanostructured materials with special properties. Hence, exploring various new superalkali species should be a meaningful project. In our previous work, a new type of binuclear superalkali B2Li11 and its corresponding cation B2Li11þ were theoretically introduced.20 The vertical electron affinities for the binuclear superalkali cations B2Li11þ are in the range of 3.40-3.73 eV, which is not only lower than the IP of the Cs atom but also lower than the IP of the mononuclear superalkali BLi6. These findings support the viewpoint that the potential of creating new species classified as superatoms is limitless and thereby generates further interest in systematically characterizing more binuclear superalkali cations with low electron affinities. In the present work, a series of binuclear superalkali cations according to M2Li2kþ1þ (M = F, O, N, C for k = 1, 2, 3, 4, respectively, where M represents a nonmetal atom in the second row of the periodic table, and k is the maximal formal valence of the central atom M) is investigated in detail. These cations exhibit superalkali nature with low vertical electron affinities of 2.74-4.61 eV. We obtained the various structures of these isoelectronic analogues (F2Li3þ, O2Li5þ, N2Li7þ, and C2Li9þ), and explored the evolution of their respective preferred geometries along with the changing of the central atoms.
Received: November 1, 2010 Revised: January 18, 2011 Published: February 21, 2011 2041
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Figure 1. Three equilibrium structures of binuclear superalkali cation F2Li3þ. Color legend: F, cyan; Li, purple.
Figure 4. Five equilibrium structures of binuclear superalkali cation C2Li9þ. Color legend: C, gray; Li, purple.
Figure 2. Six equilibrium structures of binuclear superalkali cation O2Li5þ. Color legend: O, red; Li, purple.
Table 1. Symmetry Point Group, Relative Energies, Erel (in kcal/mol), Lowest Vibrational Frequencies (υ1, in cm-1), HOMO-LUMO Gaps (in eV), Binding Energies per Atom, Eb (in eV), Vertical Electron Affinities, EAvert (in eV), NBO Charges on Central F Atoms, and F-F Distances [RF-F, in Angstroms] of the F2Li3þ Cations isomer symmetry Erel υ1 gap
Eb EAvert
qF1
qF2
qF1þF2 RF-F
1Aþ
D¥h
1Bþ
C2v
8.22 96 14.39 3.311 4.00 -0.884 -0.903 -1.788 2.687
1Cþ
D3h
13.24 314 15.90 3.268 3.76 -0.881 -0.881 -1.762 2.368
0.00 56 15.92 3.383 3.00 -0.905 -0.905 -1.810 3.471
energies per atom (Eb) of M2Li2kþ1þ were obtained at the CCSD(T)/6-311þG(3df) level, where þ Eb ðM2 Liþ 2k þ 1 Þ ¼ ½2EðMÞ þ 2kEðLiÞ þ EðLi Þ
- EðM2 Liþ 2k þ 1 Þ=ð2k þ 3Þ
All calculations were performed using the GAUSSIAN 03 program package.28 Dimensional plots of the molecular structures were generated with the GaussView program.29 Figure 3. Seven equilibrium structures of binuclear superalkali cation N2Li7þ. Color legend: N, blue; Li, purple.
’ CALCULATION DETAILS The potential energy surfaces of the M2Li2kþ1þ (M = F, O, N, C) cations were explored using the Saunders “kick” method with little thought or effort.21-23 All atoms are initially placed at a common point in geometrical space and then kicked in random directions within a box of chosen dimensions. Such “zero” input structure can avoid biasing the search. The kick size employed here ranges from 2 to 10 Å in the cubic box. Several hundred starting geometries were obtained at the B3LYP/6-31G(d) level until no new minimum appeared. Afterward, much larger kicks were performed to do an intensive search for additional minima in the region of one kicked structure. The minima at the B3LYP/ 6-31G(d) level are then reoptimized at the MP2/6-311þG(3df) level, followed by vibrational frequency calculations. In addition, the CCSD(T)/6-311þG(3df) single-point computations on these stable points were carried out. The vertical electron affinities (EAvert) of these M2Li2kþ1þ cations were obtained and assigned on the basis of the restricted outer valence Green function (OVGF) method24-26 with the 6-311þG(3df) basis set. Natural bond orbital (NBO)27 analyses were performed at the MP2/6-311þG(3df) level. The binding
’ RESULTS AND DISCUSSIONS The optimized geometries of various isomers of F2Li3þ, O2Li5þ, N2Li7þ, and C2Li9þ are shown in Figures 1, 2, 3, and 4, respectively. The binding energy values, highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps, NBO charges on central M atoms, and MM distances of these cations are gathered in Tables 1, 2, 3, and 4, respectively. The vertical electron affinities (EAvert) for the M2Li2kþ1þ (M = F, O, N, C) cations, which can also reflect the IP of their corresponding neutral species,20 are also collected in Tables 1, 2, 3, and 4, respectively. As expected, these binuclear cations exhibit very low EAvert values, which are lower than the IP = 5.14 eV of the Na atom.1 Therefore, all M2Li2kþ1þ species investigated can be considered as binuclear superalkali cations. In the following subsections, the structural features together with the EAvert values of the isomers for each M2Li2kþ1þ cation are discussed in detail. A. F2Li3þ. Three structures were identified for F2Li3þ with D¥h, C2v, and D3h symmetries (see Figure 1), which are identical to those reported by Yokoyama et al. at the B3LYP level.11,30 The linear isomer 1Aþ is the lowest energy structure of F2Li3þ at the MP2/6-311þG(3df) level of theory. Two central fluorine atoms 2042
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Table 2. Symmetry Point Group, Relative Energies, Erel (in kcal/mol), Lowest Vibrational Frequencies (υ1, in cm-1), HOMO-LUMO Gaps (in eV), Binding Energies per Atom, Eb (in eV), Vertical Electron Affinities, EAvert (in eV), NBO Charges on Central O Atoms, and O-O Distances [RO-O, in Angstroms] of the O2Li5þ Cations isomer symmetry Erel υ1 gap
Eb EAvert qO1
qO2 qO1þO2 RO-O
2Aþ
D3h
0.00 133 10.56 3.715 2.94 -1.647 -1.647 -3.295 2.675
2Bþ
C2v
13.56 43 8.51 3.631 3.24 -1.672 -1.641 -3.313 2.969
2Cþ
D2d
20.44 49 9.69 3.588 2.74 -1.671 -1.671 -3.342 3.594
2Dþ 2Eþ
Cs Cs
115.03 82 6.04 3.002 2.96 -0.842 -0.842 -1.685 1.538 115.21 98 5.93 3.001 3.04 -0.859 -0.803 -1.662 1.535
2Fþ
Cs
125.35 40 5.98 2.939 2.83 -0.820 -0.820 -1.640 1.560
Table 3. Symmetry Point Group, Relative Energies, Erel (in kcal/mol), Lowest Vibrational Frequencies (υ1, in cm-1), HOMO-LUMO Gaps (in eV), Binding Energies per Atom, Eb (in eV), Vertical Electron Affinities, EAvert (in eV), NBO Charges on Central N Atoms, and N-N Distances [RN-N, in Angstrsoms] of the N2Li7þ Cations isomer symmetry Erel υ1 gap Eb EAvert
qN1
qN2
qN1þN2 RN-N
3Aþ
C2
0.00 12 6.90 2.815 3.08 -2.196 -2.196 -4.393 3.011
3Bþ
C3v
23.74 55 5.19 2.700 3.75 -2.215 -2.135 -4.350 3.064
3Cþ 3Dþ
Cs Cs
25.28 91 4.86 2.693 3.29 -1.385 -1.381 -2.767 1.504 41.83 93 1.72 2.613 4.61 -1.543 -1.528 -3.071 1.555
3Eþ
C2
50.97 81 5.43 2.569 3.47 -0.687 -0.687 -1.373 1.252
3Fþ
C5v
52.01 49 5.43 2.564 3.39 0.024
0.117
0.141 1.114
3Gþ
Cs
59.02 19 5.12 2.530 3.61 -0.014 0.125
0.111 1.113
Table 4. Symmetry Point Group, Relative Energies, Erel (in kcal/mol), Lowest Vibrational Frequencies (υ1, in cm-1), HOMO-LUMO Gaps (in eV), Binding Energies per Atom, Eb (in eV), Vertical Electron Affinities, EAvert (in eV), NBO Charges on Central C Atoms, and C-C Distances [RC-C, in Angstrsoms] of the C2Li9þ Cations isomer symmetry Erel υ1 gap Eb EAvert
qC1
qC2
qC1þC2 RC-C
4Aþ
C2v
0.00 92 5.11 2.516 3.40 -0.728 -0.728 -1.457 1.269
4Bþ
C1
4.42 68 4.88 2.499 3.41 -0.783 -0.734 -1.517 1.269
4Cþ
Cs
9.64 62 4.56 2.478 3.19 -1.047 -0.902 -1.949 1.310
4Dþ
D3h
33.23 86 5.21 2.385 3.30 -2.551 -2.551 -5.102 3.205
4Eþ
Cs
41.52 11 4.42 2.353 3.48 -1.656 -1.526 -3.182 1.491
in 1Aþ are linked via one Li atom, and each F atom is coordinated with two lithium atoms. The end F1-Li1 bond of 1.661 Å is slightly shorter than the middle F1-Li2 bond of 1.736 Å. The next stable isomer 1Bþ, which can be viewed as a Li-tail structure,30 is found to be higher in energy by 8.22 kcal/mol than 1Aþ. In 1Bþ, the F1-Li1 and F2-Li2 bond lengths are 1.690 and 1.706 Å, respectively, while the F2-Li1 bond of 1.948 Å is relatively long. Thus, isomer 1Bþ can be viewed as constituted by FLi2þ and FLi units. The 1Cþ form exhibits a trigonal bipyramidal geometry with two apex F atoms bridged by three Li atoms, where the F-Li bond distance is 1.849 Å. Interestingly, the highsymmetrical 1Cþ is estimated to be less stable by 13.24 kcal/mol than 1Aþ. Note that two F atoms are bridged by Li atoms in all three isomers. This may be because the fluorine atom is the most
nonmetallic and electronegative element in the periodic table and thus prefers to form a strong ionic bond with the Li ligand. The gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is a useful quantity for examining the stability of clusters. It is found that systems with larger HOMO-LUMO energy gaps are less reactive. As listed in Table 1, the HOMO-LUMO gaps of F2Li3þ are in the range of 14.39-15.92 eV, which are significantly larger than the experimental HOMO-LUMO gap in C60 (1.9 eV)31 and also much larger than those of other binuclear superalkali cations (i.e., O2Li5þ, N2Li7þ, C2Li9þ, B2Li11þ). Furthermore, the binding energies per atom (Eb) of F2Li3þ are 3.268-3.383 eV, which are larger than those of F2Li3 species (2.026-2.197 eV) at the same computational level. It suggests the enhanced stability of F2Li3þ. As can be seen from Table 1, the EAvert values for the F2Li3þ cations are greatly lower than the IP = 5.39 eV of the Li ligand. Among the three F2Li3þ cations, isomer 1Aþ exhibits the lowest EAvert value of 3.00 eV, which might be related to its linear structure, resulting in a more even distribution of the excess positive charge. The EAvert value of isomer 1Bþ is predicted to be 4.00 eV. Note that the recent measured ionization energy (IE) of neutral F2Li3 (4.2 ( 0.2 eV)32 is close to the calculated EAvert value for the second stable isomer 1Bþ and not for the most stable isomer 1Aþ. This observation is consistent with the prior investigation.11,30,32 The EAvert value of 3.76 eV for 1Cþ is lower than that of 1Bþ; this is because the more symmetrical structure of 1Cþ benefits a more even distribution of the excess positive charge. B. O2Li5þ. Six forms of superalkali cations O2Li5þ are illustrated in Figure 2. The D3h symmetrical 2Aþ is the most stable structure and can be viewed as a trigonal bipyramidal Li5 cluster33 with one oxygen atom locating in each pyramid. Two central oxygen atoms in 2Aþ are bridged by three Li atoms, and the OLi1 bond length is 1.862 Å, while the O-Li2 bond distance (1.703 Å) is slightly shorter. The less favorable structure of O2Li5þ, 2Bþ, is higher in energy by 13.56 kcal/mol than 2Aþ. In isomer 2Bþ of C2v symmetry, two central oxygen atoms are linked via two Li atoms. The O-Li bond lengths of 2Bþ are 1.678-1.751 Å except that the O1-Li1 and O1-Li2 bonds of 1.937 Å are relatively long. This indicates that the structure is composed of OLi2 and OLi3þ units. Isomer 2Cþ is 6.88 kcal/mol less stable than 2Bþ. This structure can be regarded as two OLi2 molecules linked by a Liþ cation and resulting in a higher D2d symmetry. The middle O1-Li1 bond of 1.797 Å is 0.108 Å longer than the end O2-Li2 bond of 1.689 Å, which also verifies the (OLi2)2Liþ description of 2Cþ. In the following three structures 2Dþ, 2Eþ, and 2Fþ, two central O atoms are linked together and the O-O distances are short (1.535-1.560 Å). From Table 2, the NBO charges on the O-O unit are from -1.640 to -1.685 au; so, isomers 2Dþ, 2Eþ, and 2Fþ are peroxides and can be regarded as the O22- ion bounded to different Lin structural units. From NBO and molecular orbitals analyses, isomer 2Dþ can be characterized as LiþO22-Li42þ, and the O22- unit attaches to one face of the tetrahedral Li42þ cation. This description is also valid for isomer 2Eþ, which has a similar geometry to 2Dþ. Hence, the difference in total energy between 2Dþ and 2Eþ is only 0.18 kcal/mol. From another viewpoint, structures 2Dþ and 2Eþ can also be considered as two oxygen atoms inserted into one pyramid of trigonal bipyramidal Li5 cluster. The least favorable structure of O2Li5þ is isomer 2Fþ (Cs), which is 10.14 kcal/mol higher in energy than 2Eþ. This species can be 2043
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The Journal of Physical Chemistry A characterized as (Liþ)2O22-Li3þ with the O22- unit bound to an apex of triangular Li3þ ion. The O-Li1 bond length of 1.819 Å is slightly shorter than the O-Li2 bond length of 1.884 Å. Differently from F2Li3þ, the isomers with directly linked central O atoms appear for binuclear superalkali cations O2Li5þ. Because of the high electronegativity of the oxygen atom, the structures with separate O atoms have larger stabilities than those with O-O units. In addition, the more bridge Li atoms there are, the larger stability the isomer exhibits. For the three most favorable isomers with separate O atoms, the preferential order is bridged by three Li atoms (2Aþ) > by two Li atoms (2Bþ) > by one Li atom (2Cþ). From Table 2, the HOMO-LUMO gaps of superalkali cations O2Li5þ are in the range of 5.93-10.56 eV. Note that the structures with separated O atoms possess much larger gaps than those of other structures with O-O units. It confirms the fact that the central O atoms prefer forming ionic bonds with Li ligands to bonding together. Except the HOMO-LUMO gaps, the large Eb values of 2.939-3.715 eV also indicate the stabilities of binuclear superalkali cations O2Li5þ. As shown in Table 2, the EAvert values for the O2Li5þ cations are in the 2.74-3.24 eV range, which are all lower than the IP = 3.89 eV of the Cs atom and greatly lower than the IP of Li ligand. Interestingly, it is found that the distribution of Li ligands is closely related to the EAvert value of the isomer. That is, the more symmetrical the localization of the electropositive lithium ligands, the lower electron affinity the isomer shows. Among all six O2Li5þ cations, isomer 2Cþ shows the lowest EAvert value of 2.74 eV, which may profit from its high molecular symmetry (D2d) and even distribution of Li ligands. From Figure 2, isomer 2Fþ has a similar arrangement of Li ligands to that of 2Cþ and shows the second lowest EAvert value of 2.83 eV. As one can notice, the distributions of Li ligands in isomers 2Aþ, 2Dþ, and 2Eþ are all near to trigonal bipyramidal Li5 cluster. As a result, their EAvert values are very close to each other, that is, 2.94, 2.96, and 3.04 eV, respectively. Isomer 2Bþ is found to exhibit the highest EAvert value of 3.24 eV among the six O2Li5þ cations. This may be due to its asymmetrical arrangement of Li ligands, which is a disadvantage for 2Bþ to evenly disperse the excess positive charge. C. N2Li7þ. Seven structures are identified for superalkali cations N2Li7þ, which are illustrated in Figure 3. The 3Aþ form is the most stable isomer of N2Li7þ and exhibits a typical capsule geometry. In this structure with C2 symmetry, each N atom is coordinated with five Li ligands and two central nitrogen atoms are linked by three Li atoms. The N-Li bond lengths of 3Aþ are in the 1.828-2.065 Å range. The N-Li bonds in the N-Li-N linking fragment are longer (by 0.1-0.2 Å) than those that involve only two atoms (i.e., one Li and one N atom). In a quite recent paper, Roy et al.34 theoretically revealed the mechanisms for the ready reactions of N2 with various model Lin clusters. They found that N2 was only reduced to a single bond length of 1.487 Å by Li6 cluster in the global N2Li6 minimum, while eight Li atoms could cleave the triple-bonded nitrogen completely, and the fully reduced nitrido product with well-separated N atoms (rNN = 3.023 Å) was the global minimum of N2Li8. Note that complete N-N cleavage (rNN = 3.011 Å) appears in the lowest energy structure of N2Li7þ, indicating that N2 can be fully reduced by the Li7þ cluster cation. The less favorable structure 3Bþ with C3v symmetry is 23.74 kcal/mol higher in energy than 3Aþ. In this structure, two central N atoms are also separated and bridged by three Li atoms and the
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N-N distance is 3.064 Å. The N-Li bond lengths are in the range of 1.812-1.849 Å except that the N1-Li1(2,3) bonds of 2.319 Å are much longer than the others. This suggests that isomer 3Bþ consists of NLi3 and NLi4þ units, which is also supported by the NBO analyses. The next stable isomer 3Cþ is only 1.54 kcal/mol less stable than 3Bþ. In this Cs structure, two central N atoms directly link each other and N2 is reduced to a single-bond length of 1.504 Å. According to NBO and molecular orbitals analyses, isomer 3Cþ can be characterized as (Liþ)3N24-Li42þ, in which the N24- unit attaches to one face of the tetrahedral Li42þ cation. Isomer 3Dþ is found to be 16.55 kcal/mol higher in energy than 3Cþ. It can be viewed as a N2 molecule inserted into the equatorial section of pentagonal bipyramidal Li7 cluster, and two central nitrogen atoms are also linked together by a single bond of 1.555 Å. Isomer 3Eþ is of C2 symmetry and exhibits a boat geometry, featuring two N atoms located in the bottom. In this form, N2 is reduced to a double-bond length of 1.252 Å. The least two favorable structures of N2Li7þ are 3Fþ and 3Gþ, which are 1.04 and 8.05 kcal/mol less stable than 3Eþ, respectively. From Figure 3, both of the structures have N2 bound to an apex of the Li7 cluster. The N-N bond lengths in 3Fþ and 3Gþ are 1.114 and 1.113 Å, respectively, which are quite near that in bare N2 (1.097 Å), suggesting the triple-bond character of N-N bonds in 3Fþ and 3Gþ. In previous work, two stable structures of Li7 are predicted, namely, a C3v ground-state geometry formed by capping three of the faces of a Li4 tetrahedron and a pentagonal bipyramidal form (D5h).33 In isomer 3Fþ of C5v symmetry, N2 links to the D5h isomer of Li7 and the N-Li bond length is 2.117 Å. While in isomer 3Gþ with Cs symmetry, N2 links to the C3v isomer of Li7 and the N-Li bond length is 2.177 Å, which is 0.06 Å longer than that in 3Fþ. From the above results, the stabilities of isomers of N2Li7þ are closely related to the N-N distance. The preferred structure for N2Li7þ is 3Aþ, and the second is structure 3Bþ, in both of which the two central N atoms are cleaved completely and bridged via three Li atoms. As for the other isomers, two N atoms directly link to each other, and the preferential order is linked by a single bond (3Cþ, 3Dþ) > by a double bond (3Eþ) > by a triple bond (3Fþ, 3Gþ). Except isomer 3Dþ, the binuclear superalkali cations N2Li7þ have large HOMO-LUMO gaps of 4.86-6.90 eV, which are shown in Table 3. The binding energies per atom (Eb) of N2Li7þ are in the range of 2.530-2.815 eV, which are slightly smaller compared with those of O2Li5þ cations. It is confirmed theoretically that the N2Li7þ species have very low vertical electron affinities in the range of 3.08-3.75 eV except that isomer 3Dþ shows a relatively higher EAvert value of 4.61 eV. From the NBO results, the lowest unoccupied molecular orbital (LUMO) energy of 3Dþ is -0.15797 au, which is considerably lower compared to those of other isomers (ca. -0.1 au). As a result, the electron affinity of 3Dþ is higher than the other N2Li7þ species. D. C2Li9þ. Five structures were identified for superalkali cation C2Li9þ (Figure 4). Different from the above binuclear superalkali cations, C2Li9þ has an interesting global minimum structure 4Aþ in which the C-C unit extends to the surface of the whole system and can be regarded as bound to the C4v isomer of the Li9 cluster.33 In this C2v geometry, the C-Li1 bond of 2.205 Å is longer than the C-Li2 bond of 2.052 Å. Although the C-C distance of 4Aþ is predicted to be 1.269 Å, which exceeds that in acetylene (1.21 Å), the linear C2Li2 has a very similar 2044
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The Journal of Physical Chemistry A C-C bond length of 1.260 Å at the same computational level. Hence, two C atoms in 4Aþ are considered to be linked by a triple bond. The second isomer 4Bþ, which is only 4.42 kcal/mol less stable than 4Aþ, presents similar structural characteristics. The C-C unit occupies an external position of the whole structure of 4Bþ, and the C-C bond length is also 1.269 Å, indicating the triple-bond character. Isomer 4Cþ possesses Cs point group, in which two carbon atoms are linked directly to each other while the C-C bond length of 1.310 Å is slightly longer than those of former two isomers. In this structure, Li1, Li2, Li3, Li4, Li5, and two C atoms are coplanar, featuring the other four Li atoms symmetrically distributed on both sides of this plane. 4Cþ is found to be higher in energy by 5.22 kcal/mol than 4Bþ, along with elongation of the C-C bond. The capsule structures of C2Li9þ, 4Dþ and 4Eþ, are found to be 33.23 and 41.52 kcal/mol less stable than 4Aþ, respectively. 4Dþ has relative higher symmetry as D3h, in which two central carbon atoms are bridged by three Li atoms and each C atom is coordinated with six Li ligands. The C-Li1 and C-Li2 bond lengths are 2.130 and 2.000 Å, respectively. As for isomer 4Eþ with Cs symmetry, two carbon atoms are linked together. This structure is quite similar to the global minimum of B2Li11þ. The C-C bond length is 1.491 Å, and the C-Li bond lengths are in the range of 1.8862.300 Å. From Table 4, the C2Li9þ cations also show large HOMOLUMO gaps ranging from 4.42 to 5.21 eV. The Eb values of C2Li9þ are in the range of 2.353-2.516 eV, which are smaller compared with those of N2Li7þ cations but larger than those (1.656-1.688 eV) of B2Li11þ cations.20 The vertical electron affinities for the C2Li9þ cations range from 3.19 to 3.48 eV (see Table 4), which are low enough to guarantee the studied species can be classified as superalkali cations. Among the five isomers, 4Cþ shows the lowest EAvert of 3.19 eV, which might be related to its incompact geometry, which helps to disperse the excess positive charge and therefore reduce the repulsion interaction. Isomers 4Aþ and 4Bþ with extended C-C units show similar EAvert values, namely, 3.40 and 3.41 eV, respectively. Isomers 4Dþ and 4Eþ both have capsule structures; however, the lower EAvert value of 3.30 eV for 4Dþ profits from its highly symmetrical structure (D3h), which allows for a more even distribution of the excess positive charge. Isomer 4Eþ is found to exhibit the highest EAvert value of 3.48 eV among all the C2Li9þ cations. This is due to its packed capsule structure, which is a disadvantage for 4Eþ to disperse the excess positive charge. E. Geometries of Neutral M2Li2kþ1 Species. For comparisons with the cations, the optimized geometries of the neutral M2Li2kþ1 species and their relative energies at the B3LYP/6311þG(3df) level are presented in the Supporting Information, Figures S1-S4 and Tables S1-S4. From Figure S1, three minimum energy structures were found for F2Li3. The total energies of these structures increased in the order 1A < 1B < 1C (see Table S1, Supporting Information). Herein, isomers 1B and 1C show much resemblance to 1Bþ and 1Cþ, respectively. The global minimum structure 1A exhibits a bent geometry with C2v symmetry, while 1Aþ adopts a linear structure that helps to reduce the mutual repulsion interaction inside the cation. Six structures were identified for O2Li5. The total energies of these isomers increased in the order 2A < 2B < 2C < 2E < 2D < 2F (see Table S2, Supporting Information). From Figure S2, Supporting Information, structures 2A, 2B, 2C, 2D, and 2F generally coincide with those of the cationic species, respectively,
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except that the straight O-Li-O bond in 2Cþ becomes bent in 2C. Isomer 2E exhibits a new structure that is different from all the O2Li5þ cations. N2Li7 has seven minimum structures, and the total energy order is 3A < 3B < 3C < 3D < 3E < 3G < 3F (see Table S3, Supporting Information). From Figure S3, Supporting Information, structures 3A-3F are fairly similar to structures 3Aþ-3Fþ, respectively. However, isomer 3G exhibits a different structure compared to those of the N2Li7þ cations. The five structures of C2Li9 (4A-4E) totally coincide with their corresponding cations 4Aþ-4Eþ, respectively (see Figure S4, Supporting Information). From Table S4, Supporting Information, the total energies of these isomers increased in the order 4A < 4B < 4C < 4E < 4D. From the above analysis, we find that the lowest energy structures of M2Li2kþ1þ correspond to the global minimum structures of neutral M2Li2kþ1 species, respectively.
’ CONCLUSIONS We extended the study on binuclear superalkali cations to the M2Li2kþ1þ (M = F, O, N, C) species. The geometries and energetic properties of these cations were obtained theoretically. It is noteworthy that the structural characteristics of the global minima of binuclear superalkali cations are related to the electronegativities of central atoms. For C2Li9þ and B2Li11þ with relatively lower electronegativities of the central atoms, the lowest energy structures feature two central atoms linked directly to each other, while for the F2Li3þ, O2Li5þ, and N2Li7þ cations the relatively bigger electronegativities of their central F, O, and N atoms lead to the preference for central atom-ligand interaction over the central atom-central atom interaction. As a result, two central atoms are bridged by some Li atoms in the global minimum structures of F2Li3þ, O2Li5þ, and N2Li7þ cations. The vertical electron affinities (EAvert) for these binuclear superalkali cations at the OVGF/6-311þG(3df) level are much lower than the IP = 5.39 eV of the ligand Li atom. Furthermore, the lowest energy isomers of these cations exhibit remarkably low EAvert values of 2.94-3.40 eV, which is even lower than the IP = 3.89 eV of the Cs atom. Hence, the studied M2Li2kþ1þ species should be classified as superalkali cations, which also reflect the superalkali nature of the neutral M2Li2kþ1 species. Our results presented in this work may add candidates to the research on superalkalies and offer references to future investigation on other polynuclear superatoms. ’ ASSOCIATED CONTENT
bS
Supporting Information. Optimized geometries of various isomers, symmetry point group, relative energies, and lowest vibrational frequencies of M2Li2kþ1 (k = 1, 2, 3, 4 for M = F, O, N, C, respectively). This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (Grant Nos. 21043003, 21073075). 2045
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