Covalent vs Ionic Bonding in Al-C Clusters


lone pair attractors outside the Al atoms accord with the antibonding orbitals MO-32, ... there is no bonding attractor between C atoms and the side A...
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Covalent vs Ionic Bonding in Al-C Clusters Ning Du, Huihui Yang, and Hongshan Chen J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 03 May 2017 Downloaded from http://pubs.acs.org on May 9, 2017

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The 3s(Al) and 2s2p(C) form bonding and antibonding orbitals, corresponding to the covalent C-Al bonds and lone pair electrons respectively.

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Covalent vs ionic bonding in Al-C clusters

Ning Du, Huihui Yang and Hongshan Chena) College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China The low-energy structures of AlnCm (n=4, 6; m=1-4) are determined by using the genetic algorithm combined with density functional theory and the QCISD models. The electronic structures and bonding features are analyzed through the density of states (DOS), valence molecular orbitals (MOs) and electron localization function (ELF). The results show that the carbon atoms tend to aggregate and sit at the center of the clusters. The C-C bond lengths in most cases accord with the double C=C bond. Due to the large difference between the electronegativities of carbon and aluminum atoms, almost all the 3p electrons of Al transfer to C atoms. The 3s orbitals of Al and the 2s2p orbitals of C form bonding and antibonding orbitals; the bonding orbitals correspond to the covalent C-Al bonds and the antibonding orbitals form lone pair electrons at the outer side of Al atoms. The lone pair electrons form large local dipole moments and enhance the electrostatic interactions between C and Al atoms. Planar geometry and multi-connection are prominent structural patterns in small AlnCm clusters. However, the multi-connection does not correspond to multi-center chemical bonding. There are multi-center bonds but they are much weaker than the  C-Al bonds.

1. INTRODUCTION Metal clusters have fascinating physical and chemical properties determined by their sizes and compositions. Doping with other metal or nonmetal atoms in the metal clusters can tune their properties for different purpose of applications. Aluminum is a lightweight and cheap material and the Al-based clusters have been extensively investigated. In recent years, aluminum-carbon clusters have attracted increasing a)

Author to whom correspondence should be addressed. Email: [email protected] 1

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attention as a new class of materials, and quite many experimental and theoretical investigations1-15 have been carried out. Wang and co-workers studied the small neutral and anionic AlnCm clusters using photoelectron spectroscopy and ab initio calculations.1-4,6 They found Al2C2 has a quasilinear (acetylenic) structure,1 and Al3C2 is formed by attaching a third aluminum on the side of Al2C2.2 Al3C- and Al3C clusters are found to have a planar triangular structure and a distorted triangular structure respectively.3 Al4C- anion has a planar tetra-coordinated structure and Al4C has a tetrahedral structure,4 which is confirmed later by Zubarev et al.5 Both Al5C and Al5Care found to have planar structures that are related to the planar square Al4C- by adding one Al+ ion or Al atom to an edge of the square.6 Zhao et al.7 carried out both experimental and computational studies on AlnC- clusters and demonstrated the pronounced stability of Al7C-. Naumkin8 investigated CnAlm (n=2-3, m=2-8) clusters at MP2 level, and concluded that these systems exhibit hyper-coordinated planar structures, which supports the similarity to CnBm clusters. Wu et al.9 studied C2E4 (E=Al, Ga, In and TI) clusters using B3LYP method, and the results show that C2E4 has planar structures with double tetra-coordinated carbon atoms. The features of planar structure and multi-coordination are also demonstrated in the lowest-energy structures of AlnCm (n=0-5, m=0-5) clusters.10 Inspired by this theoretical finding, Dai11and Li12 investigated AlxC (x=1/3, 1, 2 and 3) monolayers containing the planar multi-coordinated carbon. Recently, Irving et al.13 studied two series of ‘Al-kanes’ (CnAl2n+2) and ‘Al-kenes’ (CnAl2n) (n=1-5), and suggested that all the systems beyond CAl4 are structurally different from their stoichiometric hydrocarbon counterparts (with an equal number of hydrogen atoms) and the close-packing of the constituent aluminum atoms seems to be best accommodated. The close-packed structures are also found in the low-energy isomers of Al6C.14 Dong et al.15 measured neutral AlmCn and AlmCnHx (m=2-6, n=2-4, x=1-8) clusters experimentally and performed theoretical calculations. The results indicate that the structures containing C=C bonds are energetically favorable for small neutral AlmCn and AlmCnHx clusters. The electronic configuration of Al is [Ne]3s23p1. The 3s and 3p levels are separated by 4.0 eV, and aluminum has been found to behave as a monovalent atom in 2

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small clusters.16,17 The structure motifs of AlnCm clusters suggest they are combined through covalent C-Al bonds. It should be made clear how the 3s3p orbitals of Al atoms overlap with the hybrid 2s2p orbitals of C atoms to form C-Al bonds. The difference in electronegativities of carbon and aluminum is quite large. How do the electronegativities affect the nature of the bonding? Is the covalent C-Al bonds also strongly ionic (polarized)? The planar geometry and multi-connection are the prominent structural patterns in small AlnCm clusters.8-10 How is the multi-connection related to the saturation of covalent bonding? And does the multi-connection correspond to multi-center chemical bonding? The present study aims to address these issues. We have carefully searched the global-minimum energy structures of AlnCm (n=4, 6; m=1-4), and analyzed in detail their electronic structures and bonding features.

2. COMPUTATIONAL METHODS The lowest-energy isomers of AlnCm (n=4, 6; m=1-4) clusters are determined through three steps. Firstly, randomly generated structures are globally searched by genetic algorithm (GA)18-21 combined with the semi-empirical method PM3.22 The low-energy isomers from the first step are taken as the initial structures of the second GA searching combined with the density functional theory PBE.23 For the third step, the low-energy isomers obtained from the GA procedures are further optimized using the hybrid density functional model B3LYP24 and configuration interaction method QCISD.25 In the present work, the GA procedures start with an initial population of 16 structures. With 50% probability, two individuals in the population are chosen as parents to produce a new offspring via a “cut and splice” mating operation. With another 30% probability, small changes are successively made in each atomic coordinate of a selected cluster (mutation operation). With the rest of probability, the types of two randomly selected atoms in a cluster are exchanged (exchange operation). The structures of the offsprings generated by the above three operators are relaxed to their local minima using semi-empirical method PM3 (MOPAC 7 package26) or density functional theory PBE (implemented in the Dmol3 code27, 28). For the PBE 3

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optimization, the double numerical basis including d-polarization function is used. The convergence criterion for the self-consistent field calculations is 10-6 Ha. Orbital cut off is chosen as 4.8 Å. The convergence criteria for the optimization are set as a maximum force of 0.002 Ha/Å and a maximum displacement of 0.005 Å. In order to maintain the diversity of the structures in the population pool, we use the following criteria to choose the “child” and update the population pool. (1) If the energy of a “child” is higher than all the existing “parents”, it will be discarded. (2) If the energy of a “child” is lower than some of the existing individuals and its structure is different from all the existing isomers, it will replace the highest energy isomer in the population pool. We employ the pseudo rotational inertia of a cluster ( I   mi ri 2 , mi is set as 1 and 2 for Al and C atoms) to identify whether the structures of two clusters are different. After the structural comparison and selection, the GA iteration continues until the convergence criterion is achieved. In this study, the convergence criterion is that the lowest-energy isomer keeps unchanged continuously in 2000 generations, or the maximum number of iteration exceeds 5000. The low-energy isomers obtained from the global searching processes are further optimized using the hybrid density functional theory B3LYP and configuration interaction method QCISD. The split basis set with polarization and diffuse function 6-311+G(d)29-31 is used. The B3LYP and QCISD calculations are performed using the Gaussian 09 package.32 All the cluster geometries are fully optimized without any symmetry constraint, and energy minima have been verified by vibrational frequency calculations. We checked the ground state multiplicities for the lowest-energy structures and part of the isomers with close energies. The singlet state is lowest in energies for all the structures.

3. RESULTS AND DISCUSSION 3.1 The low-energy structures and stability of AlnCm (n=4, 6; m=1-4) clusters The low-energy isomers of AlnCm clusters are shown in Figures 1 and 2. Except for a few isomers (which relax to the lower-energy isomers when optimized by QCISD model), the low-energy structures optimized by B3LYP and QCISD models are in good agreement. Table 1 lists the average C-C, C-Al and Al-Al bond lengths in 4

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the most stable isomers. Table 2 presents the binding energies of AlnCm (n=4, 6; m=1-4) clusters calculated using B3LYP and QCISD models. 3.1.1. The low-energy structures of Al4Cm (m=1-4) The lowest-energy isomer Al4C-a is a tetrahedron with Td symmetry. At the B3LYP/6-311+G(d) level, the C-Al bond is 2.01 Å and the four Al atoms are 3.28 Å away from one another. When optimized by QCISD model, the C-Al bond is 1.99 Å. The next isomer Al4C-b is a diamond-like structure with C2v symmetry. Its energy is 0.81 eV higher than Al4C-a at the QCISD level. The isomer Al4C-c at the B3LYP level is a planar structure with C2v symmetry. The C atom is located in the middle of an Al4 trapezoid. This structure relaxes to isomer Al4C-a when optimized using QCISD model. The most stable structure of Al4C2 has D2h symmetry. Two Al atoms are located at the opposite sides of a linear AlCCAl chain. The C-C bond is 1.32/1.33 Å (optimized by B3LYP/QCISD models), matching double C=C bond length. The two carbon atoms sit 2.00 Å away from the terminal Al atoms, and 2.16 Å from the side ones. The four Al atoms are 3.36 Å away from one another. The isomer Al4C2-b is a planar structure, and the C-C bond length is only 1.28 Å. The structure of Al4C2-c has C2 symmetry, with one C atom located at the interior of a distorted Al4C pentagon. The binding energies in Table 2 illustrate that Al4C2-a is much more stable than the other two isomers. The lowest-energy isomer Al4C3-a resemble propadiene with hydrogen atoms being replaced by Al. The two couples of Al atoms are perpendicularly located at the two sides of the linear C3 chain. The C-C bond is 1.32 Å and the C-Al bond is 1.98 Å. This structure with D2d symmetry is a stable energy minima at B3LYP, but it changes slightly at QCISD level. The energy of the deformed structure is, however, only 0.009 eV lower. In the isomer Al4C3-b, two Al atoms and three C atoms form a slightly bended chain with Al atoms at the two ends. The other two Al atoms lie under this C3Al2 unit. The C-C bond is 1.31 Å. Vibrational frequency calculation suggests this structure is a transition state and it relaxes to Al4C3-a after removing the imaginary frequency (at both B3LYP and QCISD levels). As the lowest-energy isomer at 5

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PBE0/aug-cc-pvtz level is similar to this structure,8 we also present it in Figure 1. The structure of Al4C3-c has Cs symmetry, and three C atoms form a triangle. Its energy is much higher (by 1.62/1.38 eV at the QCISD level) than the other two isomers. In the most stable structure of Al4C4, two linear AlCCAl chains form a distorted parallelogram; the C atoms in each chain also connect to one Al atom in the other chain. The structure has symmetry C2h. The C-C bond is only 1.25 Å, very close to triple C≡C bond pattern. The two C atoms sit 2.04 Å away from the terminal Al atoms, and 2.18/2.43 Å away from the Al atom in the other chain. The isomer Al4C4-b with C2h symmetry contains a bended AlC4Al chain; the other two Al atoms sit at the opposite sides of the C4 unit. The isomer Al4C4-c has a kite-like structure with symmetry Cs. Al4C4-d is approximately a planar structure, which consists of three triangles and one pentagon. Al4Cm clusters have been investigated using different methods in previous literatures. For Al4C, the isomer Al4C-a is the lowest-energy structure reported by Wang et al.4 (at B3LYP/6-311+G*, MP2/6-311+G* and CCSD(T)/6-311+G* levels). Al4C2-a, Al4C3-a and Al4C4-a are the most stable isomers given by Loukhovitski10 (at B3LYP/6-311+G* level). Al4C2-a is also reported by Dong15 (at MP2/6-311+G* levels). 3.1.2. The low-energy structures of Al6Cm (m=1-4) The lowest-energy structure of Al6C is a carbon-centered triangular prism in symmetry D3h. The bond length of the side Al-Al edges is 2.73 Å and the bond length in the triangles is 2.83 Å. The C-Al bond is 2.13 Å. The six aluminum atoms in the isomer Al6C-b form a tetragonal bipyramid. The C atom is located in one of the pyramids; it is 1.96 Å away from the ‘top’ Al atom and 2.04 /2.22 Å from the Al atoms in the tetragon. The isomer Al6C-c has a saddle-like structure with symmetry C2. The saddle C atom connects to four Al atoms, sitting 1.97 Å away from the terminal atoms and 2.03 Å from the side ones. The energies of these three isomers are very close at B3LYP level. The lowest-energy structure of Al6C2 can be described as sitting two other Al atoms above the distorted Al4C2-a. Compared to Al4C2-a, the C-C bond (1.35 Å) is 6

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slightly stretched by adding two more Al atoms. The two C atoms sit 1.97/2.28 Å away from the terminal/side Al atoms ‘underneath’, and 2.23 Å from the ‘top’ Al atoms. The two ‘top’ Al atoms are 2.67 Å apart, and they are 2.78 Å and 2.85 Å away from the side and terminal Al atoms ‘underneath’. The geometry of the Al6C2-c is similar to ethane but compressed along the C-C axis. The C-C bond is 1.49 Å, obviously stretched by 0.14 Å relative to that in Al6C2-a. The isomer Al6C2-b is generated by turning one Al atom to the direction of C-C bond in Al6C2-c. The structure of Al6C2-d has symmetry D2h, and it is formed by two Al4C tetrahedrons via sharing two Al atoms. Al6C2-d is a energy minima at QCISD level, but it’s a TS at B3LYP level. After removing the imaginary frequency, the structure changes slightly (to symmetry D2), but the energy lowers only 0.00027 eV. The geometry of Al6C3-a is a planar structure with D2h symmetry. The three C atoms bonding linearly sit in an Al6 hexagon. The C-C bond is 1.33 Å, slightly stretched by 0.01 Å relative to that in Al4C3-a. The distance from the ‘outer’ carbon atoms to the ‘terminal’ and ‘side’ Al atoms are 2.00 Å and 2.10 Å respectively. The structure of Al6C3-b consists of an Al4C tetrahedron and a linear AlCCAl chain. The isomer Al6C3-c is a planar structure generated by turning the two top Al atoms in Al6C3-b. This structure relaxes to Al6C3-b when optimized using QCISD model. The isomer Al6C3-d has a C3 core; the C-C bond is 1.42 Å and the C-C-C bond angle is 119.73º. Each C atom connects to four Al atoms tetrahedrally. The ‘outer’ carbon atoms sit 1.96 Å away from the terminal Al atoms, and 2.18/2.24 Å from the side/ ‘out-plane’ Al atoms. The distances from the middle carbon atom to the side and ‘out-plane’ Al atoms are 2.18 Å and 2.35 Å respectively. The stability order based on B3LYP and QCISD results is reversed. The B3LYP result shows the isomer Al6C3-a is the most stable, while the QCISD result shows the isomer Al6C3-d is the most stable. The isomers Al6C4-a and -b are formed by replacing the C2 unit in Al6C3-b and -c with a C3 unit. The structure of Al6C4-b also relaxes to Al6C4-a when optimized using QCISD model. The structures of Al6C4-c and -d are generated by adding two Al atoms at the opposite sides of the C2 unit in Al4C4-c and -a, respectively. For Al6C cluster, the isomer Al6C-c is the lowest-energy structure given by 7

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Ashma (at PBE level).33 For Al6C2 cluster, the isomer Al6C2-a is the lowest-energy structure predicted by Dong15 (at B3LYP/6-311+G* and MP2/6-311+G* levels). No global searching has been performed for Al6C3 and Al6C4 clusters. Except for the structures Al4C-c, Al6C3-c and Al6C4-b, which relax to the lowerenergy isomers after optimized by QCISD model, the geometries of AlnCm clusters optimized by B3LYP and QCISD models agree well. Table 1 presents the average C-C, C-Al and Al-Al bond lengths in the lowest-energy isomers of AlnCm clusters. The C-C and Al-Al bond lengths calculated using B3LYP model are slightly shorter than that calculated using QCISD, but the C-Al bond lengths calculated by B3LYP are slightly longer. For most structures, the differences in the bond length determined by these two models are within 0.03 Å. The binding energies at QCISD level are 4.87, 3.15 and 1.17 eV for C2, AlC and Al2 dimmers. It indicates that the C-C interaction is much stronger than C-Al and Al-Al interaction. The structures in Figures 1 and 2 show that the C atoms tend to sit at the center of the clusters and form more C-C and C-Al bonds, and the C-C bond lengths are much shorter than the C-Al and Al-Al bonds. The C-C bond in Al4C4-a is only 1.25 Å, very close to the triple C≡C bond length. The C-C bond in Al6C3-d is the longest, and the value 1.42 Å is between double C=C and single C-C bond lengths. In other structures, the C-C bond lengths are around 1.32 Å, according with double C=C bond pattern. 3.1.3. The stability of the AlnCm (n=4, 6; m=1-4) The stability of the clusters can be judged by the binding energy, which is defined as the difference in the energies of the cluster and its component atoms. E b  E (Al n C m )  nE (Al)  mE (C)

where the E(AlnCm), E(Al) and E(C) are the total energies of the AlnCm clusters, aluminum and carbon atoms, respectively. Table 2 lists the binding energies of all the isomers involved in this work. The binding energies (the magnitude) calculated using B3LYP are slightly larger than those calculated using QCISD. Except for the Al4C2-b and -c and the four isomers of Al6C3, the stability order of the isomers determined by these two models is consistent. For the isomers of Al6C3, the stability order 8

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determined by these two models is reversed. The structures and bonding features are quite different in these four isomers. The different stability order might stem from different consideration of electron correlation in different methods. The average binding energies per atom Ea  Eb ( n  m ) calculated using QCISD are plotted in Figure 3. The binding energies (the magnitude) increase with the number of C atoms. The Al4Cm clusters are more stable than Al6Cm clusters with the same m. Generally, the binding energies increase with the cluster size because each atom can form more chemical bonds when the atoms increase. While in this instance, the stability of AlnCm recedes by adding Al atoms. It indicates that the stability of AlnCm depends on the C/Al ratio. As the C-C and C-Al interaction is much stronger than Al-Al interaction, doping carbon in aluminum clusters enhance the stability considerably. 3.2. The electronic structure and bonding features of AlnCm (n=4, 6; m=1-4) According to the Koopmans’ theorem, the highest occupied molecular orbital (HOMO) level can be approximately regarded as the first ionization energy. The HOMO levels of Al and C atoms calculated using QCISD are -5.83 eV and -11.97 eV respectively, which agree well with the corresponding ionization energies (5.99 eV and 11.26 eV, listed in the NIST database34). The following analyses are based on the QCISD calculations. 3.2.1. The charge distribution The present study is aimed to discuss the bonding feature of AlnCm clusters in detail. While the geometries of AlnCm clusters suggest the chemical bonds in AlnCm clusters possess obvious characters of covalent bonding. It is expected that the electrons transfer from aluminum to carbon atoms due to the large difference between the electronegativities of Al and C, and the C-Al interactions in AlnCm clusters are strongly ionic. We perform population analysis using the AIM (atoms in molecules) and NBO (natural bond orbital) models. The AIM model proposed by Bader35 defines the region for each atom in a molecule by the surface on which the gradient of electron density is zero, and it offers a partition of the electron density with a clear 9

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physical meaning. The NBO analysis,36 based on the localized orthonormal orbitals generated from the canonical orbitals by a unitary transformation, has been widely used and is considered to provide a satisfactory result. The calculated charge on Al/C atoms are given in Table 3. The relative values of the NBO and AIM charge on Al/C atoms agree well except for the isomers Al4C3-a, Al6C3-a and Al6C4-a which contain a linear C3 unit. The NBO charges on the middle C atoms in the C3 units are small positive or negative value but the AIM charges are close to -1.0. It is possible that linear dependence might occur during the unitary transformation to build the localized atomic orbitals, we think the AIM results are reasonable. Based on AIM analysis, the charge on the hexa-coordinated carbon in Al6C-a is -3.99, very close to its saturated valence -4. The charges on the carbon coordinated with four Al atoms in Al4C-a and Al6C4-a are around -3.20. In all other isomers, the charges on carbon atoms increase with the number of connected Al atoms and the Al/C ratio in the clusters. In isomers Al4C-a, Al4C2-a and Al4C3-a, the charges on Al atoms are around 0.80. In isomer Al4C2-a, the charges on the terminal Al atoms are larger than the value on the side ones. In isomer Al4C4-a, the charges on the Al atoms connecting to three C atoms are 1.02 and the charges on the other two Al atoms connecting to one C atom are 0.82. In isomer Al6C2-a, the charges on the ‘top’ and ‘bottom’ Al atoms are 0.64 and 0.79, respectively. In isomer Al6C3-a, the charges on the terminal and side Al atoms are 0.74 and 0.69. In isomer Al6C3-d, the charges on Al atoms are around 0.85. The Al atoms in the middle of isomer Al6C4-a connect to three C atoms, and the charges on them are much larger than the value on other Al atoms. Except for the three coordinated Al atoms in Al4C4-a and Al6C4-a, the Al atoms have charge values about 0.8. This indicates that aluminum behaves as a monovalent atom in small Al-C clusters. 3.2.2. Comparing Al4C, Al4C3 with CH4 and C3H4. The Td symmetry of Al4C-a suggests the 2s2p orbitals of carbon atom hybridize in sp3 manner. The 1:4 of the C/Al ratio means the Al atoms behave as a monovalent atom. By intuition, the four lobes of C sp3 orbitals will overlap with Al 3p and form four polarized C-Al bonds in the isomer Al4C-a. However, the real scenarios are quite different. We calculate the total and partial density of states (DOS) using the Multiwfn 10

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program37 and the energy levels are represented by Gaussian distribution with a half width of 0.27 eV. The DOS of Al4C and CH4 is given in Figure 4; it illustrates Al4C has two single states and two triply degenerated states. The valence molecular orbitals of Al4C and CH4 are presented in Figure 5. It shows the four orbitals (MO-22 and the triply degenerated MO-23, 24, 25) with the lower energies in Al4C resemble the valence orbitals in CH4, except that the orbitals in Al4C are obviously contracted. The MO-26 and triply degenerated MO-27, 28, 29 are located mainly at the outer side of Al atoms. The DOS in Figure 4 shows only the triply degenerated HOMO consists of small components of Al 3p. The above results mean that the 3s orbitals of the four Al atoms and the sp3 hybrid orbitals of C form four bonding orbitals and four antibonding orbitals. The 3p orbitals of Al atoms make only small contributions to the antibonding orbitals, so the 3p orbitals of Al are nearly left unoccupied. This is in agreement with the population analysis; the charges on Al atoms are close to 1.0. To have a visual description of the bonding characters, we have calculated the electron localization function (ELF).The concept of ELF was proposed by Becke and Edgecombe38 and developed by Savin and coworkers.39 It depends on the total electron density, its gradient  and the kinetic energy density  i i , 2

2     1  i  i 2  1   2 8  ELF  1   23 3 3 2  5 3   10   

 

      

2

      

1

The ELF is fundamentally related to the electron pair probability and it can illustrate the core, the bonding and the lone pair regions effectively; the spatial distribution of the localization attractors (local maxima of ELF) provides a well-defined classification of chemical bonds, allowing an absolute characterization of covalency versus ionicity. The bonding attractors lie between the core attractors (which surround the nuclei) and characterize the covalent interactions. It can be seen in Figure 6 that there are bonding attractors between the C atom and Al atoms. It clearly indicates the covalent character of the C-Al bonds. The large attractors at the outer side of Al atoms 11

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show the region of the lone pair electrons. It accords with the feature of the four antibonding orbitals. The structure of Al4C3-a is similar to propadiene (C3H4). The DOS of Al4C3-a and C3H4 is also given in Figure 4. It shows the eight states at the lower end in Al4C3 contain similar components of C atoms with the states in C3H4. These orbitals consist of 3s orbitals but nearly no 3p orbitals of Al atoms. The four states with the highest energies are dominated by 3s orbitals of Al; only the doubly degenerated HOMO contains components of Al 3p. The valence molecular orbitals of Al4C3 and C3H4 are given in Figure S1 of the supporting information, and it shows the eight orbitals with the lower energies in Al4C3 resemble the valence orbitals in C3H4. These orbitals in Al4C3 are also contracted considerably, and the energy order of the doubly degenerated MO-27, 28 and MO-29 is reversed (relative to MO-7 and MO-8, 9 in C3H4). The extra four orbitals with the highest energies are located obviously at the outer side of Al atoms. MO-4, 5 and MO-10, 11 in C3H4 mean two double C=C bonds, and MO-6, 7, 8, 9 mean the C-H bonds formed by sp2 hybrid orbitals of C and 1s orbitals of H atoms. Compared with MO-10,11 in C3H4, MO-30,31 in Al4C3-a have quite large components of Al 3s and the π-type lobs corresponding to the C=C bonding are obviously smaller. It suggests weaker C=C bonds in Al-C clusters. The contracted MO-26, 27, 28, 29 indicate the electrons in these orbitals concentrate between the atoms, so strong covalent C-Al bonds. The ELF of Al4C3-a is shown in Figure 6. It clearly shows the C-C and C-Al bonding attractors. Due to the orbital contraction, the electron densities accumulate obviously between the two terminal Al atoms, and the C-Al bonding can also be considered as a three-center bond. The large lone pair attractors outside the Al atoms accord with the antibonding orbitals MO-32, 33, 34, 35. 3.2.3. The bonding features of Al4C2 and Al6C3 The isomer Al4C2-a is a planar structure. Combining the DOS (given in Figure S2 of the supporting information) and the valence molecular orbitals (in Figure 7), we can conclude that MO-23 originates from the bonding interactions between the 2s orbitals of carbon atoms, and MO-27 is the π orbital formed by the C 2p orbitals 12

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perpendicular to the molecule plane. These two orbitals form the double C=C bond like that in ethene. MO-24 is dominated by the antibonding interactions between two C 2s orbitals. The MO-25, 26 are composed of C 2p and Al 3s. MO-25 forms the three-center bonds between C and the side Al atoms. Although MO-24 is formed by C 2s, it localizes between C and the terminal Al atoms. This orbital and MO-26 form strong  C-Al bonds. The MO-28, 29, 30 are dominated by Al 3s and the MO-31, 32 are formed by C 2p and Al 3s3p. The MO-29, 30 correspond to the lone pair electrons outside the terminal Al atoms and the MO-28, 32 correspond to the lone pair electrons outside the side Al atoms. The ELF of Al4C2-a is shown in Figure 8. It shows clearly the bonding attractors for the C-C and axial C-Al bonds. Only one orbital corresponds to two three-center bonds, and the electron pair probability is smaller than 0.5, so there is no bonding attractor between C atoms and the side Al atoms. Due to the contribution of MO-31, however, the axial C-Al bonding attractor extends toward the side Al atoms. So this attractor can be regarded as a four-center bonding. The valence MOs and ELF indicate that the interaction between C and the terminal Al atoms is much stronger than the interaction between C and the side Al atoms. This explains the C-Al bond lengths in Al4C2-a (2.00 Å for the terminal C-Al, 2.16 Å for the side C-Al). The large attractors outside the Al atoms show the region of the lone pair electrons. The isomer Al6C3-a is also a planar structure. The bonding feature of Al6C3-a resembles that in Al4C2-a. The valence molecular orbitals of Al6C3-a is shown in Figure S3 of the supporting information. The C 2s orbitals (MO-34, 35) and 2p orbitals (MO-40,45) perpendicular to the molecule plane form two double C=C bonds; but MO-35 and 45 are obviously extended along the axis. The 2p orbitals of C and 3s orbitals of the terminal Al atoms form two strong C-Al bonds (MO-36, 38). MO-37 and MO-39 are formed by C 2p and Al 3s and correspond to the multi-center bonds. The rest orbitals are dominated by Al 3s and correspond to the lone pair electrons at the outside of Al atoms. The ELF is also given in Figure 8. It clearly shows the C-C and axial C-Al bonding attractors, but no attractors for the side Al-C boding. The Al-C bonding attractors in this structure extend obviously toward the side Al atoms and have a polysynaptic shape, and they are actually four-center bonds. 13

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Considering the isomer Al6C3-d is the lowest-energy structure determined by QCISD, and the center C atom is hexa-coordinated, we also analyzed its bonding feature. The DOS is given in Figure S2 of the supporting information. Compared with Al6C3-a, the orbital composition are similar, but the valence orbital levels in Al6C3-d move down to lower energies. The valence molecular orbitals of Al6C3-d are shown in Figure S4. MO-34, 35 are similar to those in Al6C3-a, and correspond to the C-C bonds formed by C 2s orbitals. The orbitals (MO-36, 37, 38, 40) originated from C 2p and ‘in-plane’ Al 3s form the multi-center bonds and axial C-Al bonds in the CCC plane. MO-39 and 42 are dominated by the C 2p orbitals perpendicular to the CCC plane, but they concentrate among the ‘outer’ C and ‘out-plane’ Al atoms (It is similar to the MO-24 in Al4C2-a; the MO is formed by C 2s but corresponds to the C-Al bond). To show clearly their localization, we offer two views for MO-39 and 42. The rest orbitals dominated by Al 3s correspond to the lone pair electrons at the outside of Al atoms. The bonding feature in this Al6C3-d is best described by the ELF in Figure 9. Figure 9(a) shows the ELF in the CCC plane. There are two attractors for C-C bonds, two attractors for C-Al bonds and one attractor for the three-center Al-C-Al bond in this plane. The large attractors outside the Al atoms also show the region of the lone pair electrons. Figure 9(b) shows the ELF in the plane defined by center C atom and two ‘out-plane’ Al atoms. It shows there is no attractor between these C and Al atoms, so the center C atom does not bond with the ‘out-plane’ Al atoms. Figure 9(c) shows the ELF in the plane defined by one ‘outer’ C atom and two ‘out-plane’ Al atoms. The 0.75 bonding attractor means there exist weak three-center bonds among the ‘outer’ C and ‘out-plane’ Al atoms in Al6C3-d. As discussed above, Al-C clusters don’t form multi-center bonding as the geometric structures suggest. When it forms, the multi-center bonds corresponding to the multi-connected Al atoms are much weak. Only one orbital in Al4C2-a and two orbitals in Al6C3-a corresponds to the multi-coordinated side Al atoms. For Al6C3-d, each C atom connects to four Al atoms in geometry. However, the center C atom forms planar tetra-coordination with two outer C atoms and two side Al atoms; it does not form bonds with the ‘out-plane’ Al atoms. The ‘outer’ C atoms form 14

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penta-coordination with the center C atom, one side Al atom, one terminal Al atom and two ‘out-plane’ Al atoms. Here we would like to make a short summary on the bonding natures presented above. The partial DOS shows that only the occupied orbitals near HOMO have small components of Al 3p. It suggests that almost all the 3p electrons of aluminum transfer to carbon atoms. This is consistent with the charge distribution analysis. The valence MOs and ELF show clearly that Al 3s orbitals form bonding orbitals and antibonding orbitals with C 2s2p orbitals hybrid in different manners. Generally, the canonical orbitals which are the eigen-functions of the Hamiltonian operator are delocalized and form a basis for an irreducible representation of the point group of the systems. By unitary transformation of the canonical orbitals, we can obtain localized orbitals corresponding to the covalent bonds. In AlC clusters, most of the bonding orbitals presented in Figures 5, 7 are localized and correspond directly to the covalent C-C and C-Al bonds. Similar to the hydrocarbon molecules, Al-C clusters having two or more carbon atoms form double C=C bonds in planar or tetra-coordinated structures. Compared with the C-H bonds in hydrocarbons, the C-Al bonds formed by Al 3s and C 2s2p are contracted obviously. It implies these electrons concentrate between the C and Al atoms and the covalent bonding is strong. In contrast to the C-H bonds, the antibonding orbitals form lone pair electrons at the outer side of the Al atoms. Except for the lone pair electrons, the positive charge on Al atom is close to +3. The lone pair electrons form large local dipole moments and they will contribute considerably to the electrostatic interaction between Al and C atoms. It means the C-Al bonds are both strongly covalent and strongly ionic. It interprets the significantly enhanced stability by doping carbon in aluminum clusters.

4. CONCLUSIONS The low-energy structures of AlnCm (n=4, 6; m=1-4) are determined by using global optimization technique GA combined with density functional theory. The lowenergy isomers are also optimized using QCISD model. The structures obtained by B3LYP and QCISD models are generally in good agreement. Some of the lowest15

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energy isomers are consistent with the structures reported in previous literatures, and we also obtain a number of new low-energy isomers. The main results can be concluded as the following: (1) In the lowest-energy structures, carbon atoms tend to form C2 and C3 units and sit at the center of the clusters. The C-C bond lengths in most cases accord with the double C=C bond pattern. Analyses on valence molecular orbitals confirm that the neighbor C atoms form double C=C bonds in the planar structures. (2) The planar structures and tetrahedrally coordinated C atoms indicate the AlnCm clusters are combined together through covalent chemical bonds. The valence MOs and ELF show that the 3s orbitals of Al form bonding orbitals and antibonding orbitals with the C 2s2p orbitals hybrid in different manners. The bonding orbitals form covalent C-Al bonds. The antibonding orbitals are located mainly at the outer side of the Al atoms and form lone pair electrons. (3) The population analysis shows the charge state of Al is close to the +1 cation, and the DOS shows that only small components of Al 3p contribute to the states near HOMO. It means almost all the 3p electrons of Al transfer to the C atoms. The positive charges on Al and the lone pair electrons sitting opposite to C atoms form large local dipole moments, and they enhance the electrostatic interaction between C and Al atoms. (4) From the point of view of geometry, there is multi-connection in AlnCm clusters. However, the multi-connection does not mean multi-center chemical bonding. There exist multi-center bonds, but they are usually much weaker.

ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11164024 and No.11164034). We appreciate Jijun Zhao for offering the GA code. We also thank National Supercomputer Centre in Guangzhou and in Shenzhen for computational resources.

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REFERENCES (1) Cannon, N. A; Boldyrev, A. I.; Li, X.; Wang, L. S. The electronic structure and chemical bonding of aluminum acetylide: Al2C2 and Al2C2−: An experimental and theoretical investigation. J. Chem. Phys. 2000, 113, 2671-2679 . (2) Li, X.; Wang, L. S.; Cannon, N. A ; Boldyrev, A. I. Electronic structure and chemical boning in nonstoichiometric molecules: Al3X2− ( X= C, Si, Ge ). A photoelectron spectroscopy and ab initio study . J. Chem. Phys. 2002,116, 1330-1338. (3) Boldyrev, A. I.; Simons, J.; Li, X.; Chen, W.; Wang, L. S. Combined photoelectron spectroscopy and ab initio study of the hypermetallic Al3C molecule. J. Chem. Phys. 1999, 110, 8980-8985. (4) Li, X.; Wang, L. S. ; Chen, W, Boldyrev, A. I.; Simons, J. Tetracoordinated Planar Carbon in the Al4C- Anion. A Combined Photoelectron Spectroscopy and ab Initio Study. J. Am. Chem. Soc. 1999, 121, 6033-6038. (5) Zubarev, D. Y. ; Boldyrev, A. I. Appraisal of the performance of nonhybrid density functional methods in characterization of the Al4C molecule. J. Chem. Phys. 2005, 122, 144322-1-144322-7. (6) Boldyrev, A. I.; Simons, J.; Li, X.; Wang, L. S. The electronic structure and chemical bonding of hypermetallic Al5C by ab initio calculations and anion photoelectron spectroscopy. J. Chem. Phys. 1999, 111, 4993-4998. (7) Zhao, J. J.; Liu, B. C.; Zhai, H. J. ; Zhou, R. F.; Ni, G. Q.; Xu, Z. Z. Mass spectrometric and

first principles study of AlnC- clusters. Solid State Commun. 2002, 122, 543-547. (8) Naumkin, F. Y. Flat-structural Motives in Small Alumino-Carbon Clusters CnAlm (n = 2-3, m =2-8) . J. Phys. Chem. A. 2008, 112, 4660-4668. (9) Wu, Y. B.; Lu, H. G.; Li, S. D.; Wang, Z. X. Simplest Neutral Singlet C2E4 (E =Al, Ga, In, and Tl) Global Minima with Double Planar Tetracoordinate Carbons: Equivalence of C2 Moieties in C2E4 to Carbon Centers in CAl42-and CAl5+. .J. Phys. Chem. A. 2009, 113, 3395-3402. (10) Loukhovitski, B. I.; Sharipov, A. S. ; Starik, A. M. Physical and Thermodynamic Properties of AlnCm Clusters: Quantum-Chemical Study. J. Phys. Chem. A. 2015, 119, 1369-1380. (11) Dai, J.; Wu, X. J.; Yang, J. L.; Zeng, X. C. AlxC Monolayer Sheets: Two-Dimensional Networks with Planar Tetracoordinate Carbon and Potential Applications as Donor Materials in 17

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Solar Cell. J. Phys. Chem. Lett. 2014, 5, 2058-2065. (12) Li, Y. F.; Liao, Y. L.; Paul von Ragu´e Schleyer; Chen, Z. F. Al2C monolayer: the planar tetracoordinate carbon global minimum. Nanoscale. 2014, 6, 10784-10791. (13) Irving, B. J.; Naumkin, F. Y. A computational study of ‘Al-kanes’ and ‘Al-kenes’. Phys. Chem. Chem. Phys. 2014, 16, 7697-7709. (14) Yang, H. H.; Zhang, Y.; Chen, H. S. Dissociation of H2 on carbon doped aluminum cluster Al6C. J. Chem. Phys. 2014, 141, 064302-1- 064302-7. (15) Dong, F.; Heinbuch, S.; Xie, Y.; Rocca, J. J.; Bernstein, E. R. Experimental and theoretical study of neutral AlmCn and AlmCnHx clusters. Phys. Chem. Chem. Phys. 2010, 12, 2569-2581. (16) Rao, B. K.; Jena, P. Energetics and electronic structure of carbon doped aluminum clusters. J. Chem. Phys. 2001, 115, 778-783. (17) Kawamata, H.; Negishi, Y.; Nakajima, A.; Kaya, K. Electronic properties of substituted aluminum clusters by boron and carbon atoms (AlnBm−/AlnCm−); new insights into s–p hybridization and perturbed shell structures. Chem. Phys. Lett. 2001, 337, 255-262. (18) Deaven, D. M. ; Ho, K. M. Molecular Geometry Optimization with a Genetic Algorithm. Phys. Rev. Lett. 1995, 75, 288-291. (19) Zhao, J. J.; Xie, R. H. Genetic algorithms for the geometry optimization of atomic and molecular clusters. J. Comput. Theor. Nanosci. 2004, 1, 117-131. (20) Johnston, R. L. Evolving better nanoparticles: Genetic algorithms for optimising cluster geometries. Dalton Trans. 2003, 22, 4193-4207. (21) Zhao, J. J.; Huang, X. M.; Shi, R. L.; Tang, L. L.; Su, Y.; Sai, L. W. Ab initio global optimization of clusters. Chem. Modell. 2016, 12, 249-292. (22) Stewart, J. J. P. Optimization of parameters for semiempirical methods I. Method. J. Comp. Chem. 1989, 10, 209-220. (23) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. (24) Lee, C.; Yang, W.; Parr, R. G. Development of the Colic-Salvetti Correlation-energy Formula into a Functional of the Electron Density. Phys. Rev. B. 1988, 37, 785−789. (25) Pople, J. A.; Head-Gordon, M.; Raghavachari. K. Quadratic configuration interaction. A general technique for determining electron correlation energies. J. Chem. Phys. 1987, 87, 18

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5968-5975. (26) Stewart, J. J. P. MOPAC: A semiempirical molecular orbital program. J. ComputerAided Mol. Des. 1990, 4, 1-105. (27) Delley, B. An allelectron numerical method for solving the local density functional for polyatomic molecules. J. Chem. Phys. 1990, 92, 508-517. (28) Delley, B. From molecules to solids with the DMol3 approach. J. Chem. Phys. 2000, 113, 7756-7764. (29) McLean, A. D.; Chandler, G. S. Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=11–18. J. Chem. Phys. 1980, 72, 5639-5648. (30) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. Efficient diffuse function-augmented basis sets for anion calculations. III.* The 3-21+G basis set for first-row elements, Li–F. J. Comput. Chem. 1983, 4, 294-301. (31) Frisch, M. J.; Pople, J. A.; Binkley, J. S. Selfconsistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets. J. Chem. Phys. 1984, 80, 3265-3269. (32) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B. et al. GAUSSIAN 09 (Revision D.01), Gaussian, Inc., Wallingford CT, 2013. (33) Ashman, C.; Khanna, S. N.; Pederson, M. R. Reactivity of AlnC clusters with oxygen: search for new magic clusters. Chem. Phys. Lett. 2000, 324, 137-142. (34) NIST Chemistry WebBook, http://webbook.nist.gov/chemistry/,(accessed 19 May 2016). (35) Bader, R. F. W. A quantum theory of molecular structure and its applications. Chem. Rev. 1991, 91, 893-928. (36) Reed, A. E.; Weinstock, R. B.; Wenihold, F. Natural population analysis. J. Chem. Phys. 1985, 83, 735-746. (37) Lu, T.; Chen, F. Multiwfn: A multifunctional wavefunction analyzer. J. Comput. Chem. 2012, 33, 580-592. (38) Becke, A. D.; Edgecombe, K. E. A simple measure of electron localization in atomic and molecular systems. J. Chem. Phys. 1990, 92, 5397-5403. (39) Savin, A.; Nesper, R.; Wengert, S.; Fässler, T. F. ELF: The Electron Localization Function. Angew. Chem. Int. Ed. 1997, 36, 1808-1831. 19

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Table 1. The average bond length in AlnCm calculated using different models. Isomer

B3LYP/6-311+G(d)

QCISD/6-311+G(d)

RC-C (Å)

RC-Al (Å)

RAl-Al (Å)

RC-C (Å)

RC-Al (Å)

RAl-Al (Å)

Al4C-a

---

2.01

---

---

1.99

---

Al4C2-a

1.32

2.11

---

1.33

2.08

---

Al4C3-a

1.32

1.98

---

1.33

1.98

---

Al4C4-a

1.25

2.09

2.93

1.26

2.09

3.01

Al6C-a

---

2.13

2.79

---

2.13

2.80

Al6C2-a

1.35

2.19

2.82

1.41

2.12

2.89

Al6C3-a

1.33

2.07

2.86

1.35

2.06

2.87

Al6C3-d

1.42

2.24

---

1.43

2.22

---

Al6C4-a

1.31

2.09

2.95

1.32

2.08

2.96

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Table 2. Binding energy of AlnCm (n=4, 6; m=1-4) clusters calculated using different models. Isomer

symmetry

Al4C-a

Eb (eV) B3LYP/6-311+G(d)

QCISD/6-311+G(d)

Td

-12.67

-12.50

Al4C-b

C2v

-12.30

-11.69

Al4C-c

C2v

-12.20

---

Al4C2-a

D2h

-19.36

-18.46

Al4C2-b

Cs

-18.59

-17.41

Al4C2-c

C2

-18.47

-17.48

Al4C3-a

D2d

-25.83

-24.36

Al4C3-b

C2v

-25.51

-24.13

Al4C3-c

Cs

-24.10

-22.74

Al4C4-a

C2h

-31.75

-29.86

Al4C4-b

C2h

-31.74

-29.67

Al4C4-c

Cs

-31.39

-29.58

Al4C4-d

C1

-31.28

-29.25

Al6C-a

D3h

-16.34

-15.94

Al6C-b

Cs

-16.32

-15.82

Al6C-c

C2

-16.32

-15.78

Al6C2-a

C2

-23.50

-22.61

Al6C2-b

Cs

-23.33

-22.48

Al6C2-c

D3d

-23.28

-22.48

Al6C2-d

D2h

-22.91

-22.34

Al6C3-a

D2h

-29.76

-27.89

Al6C3-b

C2v

-29.45

-28.11

Al6C3-c

C2v

-29.35

---

Al6C3-d

C2v

-29.30

-28.26

Al6C4-a

C2v

-36.35

-34.29

Al6C4-b

C2v

-36.16

---

Al6C4-c

Cs

-35.90

-34.04

Al6C4-d

Cs

-35.56

-33.74 21

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Table 3. The AIM and NBO charge in AlnCm calculated by QCISD/6-311+G(d). Isomer

AIM charge (e)

NBO charge (e)

Al

C

Al

C

Al4C-a

0.82

-3.28

0.81

-3.22

Al4C2-a

0.81/ 0.78

-1.58

0.75/0.69

-1.44

Al4C3-a

0.84

-1.18/-1.01

0.81

-1.67/0.13

Al4C4-a

1.02/0.82

-0.91/-0.93

0.81/0.73

-0.94/-0.59

Al6C-a

0.66

-3.99

0.53

-3.20

Al6C2-a

0.79/0.64

-2.22

0.76/0.48

-2.00

Al6C3-a

0.74/0.69

-1.60/-1.03

0.59/0.63

-1.79/-0.13

Al6C3-d

0.84/0.89/0.83

-2.04/-1.03

0.84/0.83/0.79

-1.99/-0.95

Al6C4-a

1.53/0.84/0.82

-3.16/-1.16/-0.89

1.22/0.83/0.77

-2.90/-1.42/0.10

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Figure 1. Low-energy isomers of Al4Cm(m=1-4) 175x155mm (120 x 120 DPI)

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Figure 2. Low-energy isomers of Al6Cm(m=1-4) 162x162mm (120 x 120 DPI)

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Figure 3. The average binding energy of AlnCm (n=4, 6; m=1-4) clusters 117x92mm (120 x 120 DPI)

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Figure 4. Comparison of the density of states (DOS) of Al4C, CH4 and Al4C3, C3H4.

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Figure 5. Comparison of the valence molecular orbitals of Al4C and CH4

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Figure 6. The contour maps of ELF of Al4C-a and Al4C3-a. Interval of 0.05 is set for the contour lines.

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The Journal of Physical Chemistry

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Figure 7. The valence molecular orbitals of Al4C2-a 263x121mm (120 x 120 DPI)

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The Journal of Physical Chemistry

Figure 8. The contour maps of ELF of Al4C2-a and Al6C3-a. Interval of 0.05 is set for the contour lines.

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The Journal of Physical Chemistry

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Figure 9. The contour maps of ELF of Al6C3-d. (a) in the CCC plane; (b) in the plane of center C and ‘outplane’ Al atoms; (c) in the plane of outer C and ‘out-plane’ Al atoms. Interval of 0.05 is set for the contour lines.

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