Structures, Thermochemical Properties, and Bonding of Mixed

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Structures, Thermochemical Properties and Bonding of Mixed Earth-Alkali Silicon Trimers Si3M+/0/- with M = Be, Mg, Ca Tran Dieu Hang, Huynh Minh Hung, Huyen Thi Nguyen, and Minh Tho Nguyen J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b02492 • Publication Date (Web): 20 May 2015 Downloaded from http://pubs.acs.org on May 25, 2015

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The Journal of Physical Chemistry

Structures, Thermochemical Properties and Bonding of Mixed Earth-Alkali Silicon Trimers Si3M+/0/- with M = Be, Mg, Ca Tran Dieu Hang, Huynh Minh Hung, Huyen Thi Nguyen, Minh Tho Nguyen 1,* Department of Chemistry, University of Leuven, B-3001 Leuven, Belgium (Abstract) The ground state geometries, electronic structures and thermochemical properties of binary earth-alkali silicon clusters Si3M with M = Be, Mg, Ca in neutral, cationic and anionic states were investigated using quantum chemical computations. Lowest-lying isomers of the clusters were determined on the basis of the composite G4 energies. Along with total atomization energies, thermochemical parameters were determined for the first time by means of the G4 and coupled-cluster theory with complete basis set CCSD(T)/CBS approaches. The most favored equilibrium formation sequences for Si3M clusters emerge as follows: all Si3M+/0/- clusters are formed by attaching the M atom into the corresponding cation, neutral and anion silicon trimer Si3+/0/-, except for the Si3Mg+ and Si3Ca+ where the metal cations are bound to the neutral Si3. The resulting mixed tetramers exhibit geometrical and electronic features similar to the pure silicon tetramer Si4+/0/-. Electron localization function (ELF) and ring current analyses point out that the σ-aromatic character of silicon tetramer remains unchanged upon substituting one Si atom by one earth-alkali atom.

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Email: [email protected] 1

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Keywords: Silicon clusters, Binary alloy silicon clusters, Heats of formation, Total atomization energies, σ-Aromaticity, Ring current, Electron Localization Function

1. Introduction Small silicon clusters have received continuing attention in part due to their potential use as building blocks for nanomaterials in optoelectronic devices.1–5 A good interpretation about their geometrical, electronic structures and bonding nature is thus important to designing new compounds. Si3 and Si4 are the simplest silicon clusters, but there is a sharp difference in their electronic states and the singlet-triplet separation gap (ΔEST). As a matter of fact, while both singlet (1A1, C2v) and triplet (3A2’, D3h) states of Si3 were found to be quasi degenerate,6–9 Si4 displays a singlet rhombic structure (1Ag, D2h) located at ~0.9 eV below the triplet counterpart.10,11 Concerning the electronic property, the singlet Si3 ring has been reported to have a paratropic ring current, whereas its interaction with a proton (giving Si3H+) or a Li+ cation (yielding Si3Li+) reinforces the anti-aromatic character of the ring.9 Several theoretical studies have been investigated on the aromatic character12–15 of Si4 in various charge states. Using molecular orbitals 2


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(MO), Zhai et al.16 previously reported that the neutral Si4, possessing 16 valence electrons, is σ anti-aromatic and π aromatic. In contrast, our recent results11 pointed out that the singlet tetramer Si4 is a σ-aromatic four-membered ring17,18 without substantial contribution of its π electrons using the ring current approach. Molecular and electronic properties of clusters can essentially be improved upon mixing and doping.19–22 With the continuing efforts to reduce nanomaterial sizes, silicon-based clusters, especially mixed metal-silicon clusters, turn out to be promising in numerous technological applications.2,23,24 It would therefore be of interest to investigate the effects of a simple attachment of an ion or an atom of other groups on the properties of the simplest silicon cluster, namely Si 3. The properties of interest include the electronic structure, singlet-triplet (or low spin – high spin) energy gap, chemical bonding and aromatic feature. A dopant with suitable properties could have a role of linker for further assembly of clusters. Our previous results revealed that Li+ cations are the linkers connecting Ge9 building blocks to form GenLim nanowires.25 It is therefore useful to address the question as to whether an M+ cation could significantly stabilize both the singlet and the triplet of silicon trimer. This is associated with a possible assemblage such as [Si3-M+-Si3-M+]n where the cationic metal atoms serve as linkers connecting the triatomic clusters to generate wiretype materials in either low- or high-spin state. Only a few investigations on alkaline-earth containing silicon clusters have been reported. The structural and electronic properties of Be2Si and Mg2Si were determined using local density approximation (LDA),26 but these are not silicon clusters. The BenSin and Be2nSin (n = 1-4) clusters were studied27 using ab initio wavefunction calculations. Both the neutral and anionic MSin0/clusters with n = 2-10 and M = Be, Mg, Ca, were also theoretically studied using the G3 3



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approach.28–30 Recently, studies of Ca2Sin with n = 1-11 clusters were conducted using the density function theory.31 Although geometric structures were reported, neither high accuracy data nor deep analysis of the chemical bonding phenomena of these binary alloy silicon clusters were available. More recently, we have also studied the effects of some cations, namely H+, Li+, Na+ and K+ on the singlet-triplet gap of Si3.9 The calculated results revealed that whereas the lighter cations, including H+, Li+, Na+ are likely to favor the singlet state, the K+ cation prefers the triplet state. Nevertheless, the change in the values of ΔEST is insignificant. In this context, we set out to further investigate the effects of different neutral and ionic earth-alkaline attachments on the S-T gap, or low - high spin state gap, as well as some basic properties of silicon trimer. Furthermore, these mixed Si3M can be considered as silicon tetramer Si4 derivatives where a Si atom is replaced by neutral and ionic earth-alkaline elements. The equilibrium geometry of each cluster in both electronic states and their thermochemical parameters are determined using high levels of theory. The bonding and aromatic character of Si3M with M = Be, Mg, Ca is subsequently explored using the canonical molecular orbitals (MOs) analysis, electron localization function (ELF) and ring current approaches. 2. Computational Methods. All electronic structure calculations are carried out using the Gaussian 09 32 and Molpro 201233 suites of programs. Our recent studies pointed out that thermochemical parameters of silicon clusters calculated using the composite G4 method are very close to the coupled-cluster

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CCSD(T)/CBS data (CBS stands for complete basis set).8 Both G4 and CCSD(T)/CBS methods are thus used in the present work to obtain energetic values. In the composite G4 procedure34 geometry optimizations and vibrational analyses are performed using the popular hybrid B3LYP functional in conjunction with the 6-31+G(2df,p) basis set, followed by single-point electronic energy computations using coupled-cluster theory CCSD(T) and different additivity corrections for the basis sets. In the CCSD(T)/CBS protocol, electronic energies are computed using the correlation consistent aug-cc-pVnZ with n = Q and 5 (denoted as aVnZ), and in some cases cc-pVnZ basis sets35 on the basis of CCSD(T)/aug-cc-pVTZ or CCSDT(T)/cc-pVTZ optimized geometries. The CCSD(T) energies are then extrapolated to the CBS energies using expression (1)36: E(x) = ECBS + B/x3

(1)

where x = 4 and 5 for the aVQZ and aV5Z basis sets, respectively, ECBS is the extrapolated CBS energy and B is a fitting parameter. Zero-point energies (ZPE) are calculated from CCSD(T)/aug-cc-pVTZ harmonic vibrational analyses at corresponding equilibrium geometries. For open-shell species, the unrestricted formalism (UHF, UCCSD) is employed. The electron localization function (ELF) technique37 for a partition of the total electron density into basins, and ring current approaches38,39 along with the ipsocentric model40–42 are used to analyze the electron distribution. Unless otherwise stated, the ELF and ring current maps reported in this paper are constructed using B3LYP/6311+G(d) densities. The ring current maps are plotted in the molecular plane of each system considered. 5



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3. Results and Discussion In the following sections, we successively describe the geometries, thermochemical parameters and chemical bonding of the tetraatomic systems considered. 3.1. Structures of the Lowest-lying Isomers of Si3M+/0/- with M = Be, Mg, Ca Equilibrium structures and symmetry point groups of the neutral Si3M, cationic Si3M+ and anionic Si3M¯ systems containing M = Be, Mg, Ca, along with their G4 relative energies are displayed in Figures 1, 2 and 3. Owing to a large number of isomers located on these potential energy surfaces, we only present some stable isomers of each cluster type whose relative energies are within ~180 kJ/mol from the corresponding ground state. As for a convention, each structure depicted hereafter is denoted by a label of M-x-y in which M is alkaline earth metal Li, Na and K, x = n, c, a stands for a neutral, cation or anion, respectively, and y = 1, 2,... numbers the different isomers in an increasing relative energy ordering. Therefore, the structure labeled with the number y = 1 (M-x-1) invariably states to the energetically lowest-lying structure obtained from G4 calculations. The main characteristics of the Si3M+/0/- clusters in terms of geometry, electronic state, symmetry point group, and relative energy are described according to the metal M. The relative energy values mentioned hereunder for each Si3M system are consistently referred to the corresponding global minimum M-x-1. 3.1.1. Si3Be +/0/- Clusters Each of the Si3Be clusters in different charge states has a low spin state with a planar C2v structure in the most energetically stable isomer. The electronic states of Si3Be and Si3Be+/- are thus 1A1 and 2A1, respectively (Figure 1). Both Be-n-1 and Be-n-3 correspond to an attachment 6


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that keeps the Si3 frame unchanged. The Be atom is bridged to a Si-Si bond in Be-n-1, whereas it is bonded with only one Si atom in Be-n-3. Moreover, Be-n-1 can be regarded as being derived from the rhombic Si48 by replacing a Si atom with a Be, and it thus is a substitution structure. Ben-2 with Cs symmetry in the triplet ground state also follows the substitution pattern, but the substitution site is different from that of Be-n-1. The former is 109 kJ/mol less stable than the latter. Similarly, the most stable structure for the cation Si3Be+ Be-c-1 can also be considered as both an attachment and a substitution structure. For Be-c-2B, Be bridges over three Si atoms to form a tetrahedral Cs structure with a high spin 4A’ state. This isomer lies much higher in energy than the ground state (82 kJ/mol). The high spin Be-c-3 (C2v, 4A2) is by 128 kJ/mol higher in energy than Be-c-1, and can be seen as a substitution or attachment pattern. Six lower-lying isomers of the anion Si3Be¯ are shown in Figure 1. Be-a-1 (C2v, 2A1), Bea-2 (Cs, 2A’’), Be-a-4 (C2v, 4B1) and Be-a-6 are not only attachment but also substitution structures. Both Be-a-3 and Be-a-5 are attachment structures and possess Cs symmetry. In summary, the lowest-energy structures of Si3Be+/0/- clusters in all states belong to not only bridge-type attachment structure but also substitution structure, and are structurally similar to those of Si4+/0/-clusters.8 3.1.2. Si3Mg+/0/- Clusters The low spin structures Mg-n-1, Mg-c-1 and Mg-a-1 are the ground states of the neutral, cationic and anionic clusters Si3Mg+/0/-, respectively (Figure 2). Similar to Si3Be+/0/-, they have each a rhombic geometry. Of the three lower-lying isomers of Si3Mg, Mg-n-1 results from the attachment of an Mg atom to the Si‒Si bond of Si3 to form a planar C2v (1A1) species. It can also be considered as a substitution isomer from Si4 whose rhombic singlet is similar to Si3Mg. Mg-n7



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2 (Cs 1A’) is an attachment structure where the Mg atom connects with only one Si atom to form a bond (cf. Figure 2). The triplet Mg-n-3 (C2v, 3A1) is also found but this structure is very unstable with a relative energy of 179 kJ/mol. Four lower-lying isomers of the cationic cluster Si3Mg+ are shown in Figure 2. Similar to Si3Be+, a C2v structure related to Mg-c-1 has an imaginary frequency of b2 mode, indicating the distortion tendency to lower symmetry. The system therefore undergoes a Jahn-Teller distortion to give the global minimum Mg-c-1 (Cs). The two isomers Mg-c-2 (C1, 2

A) and Mg-c-4 (C1, 4A) belong to the attachment pattern in which a Mg atom bridges over three

Si atoms, but with a large doublet - quartet gap of 103 kJ/mol. Mg-c-3 has neither attachment nor substitution pattern, and displays Cs (2A’) symmetry. The latter structures are much less favored, lying at least 61 kJ/mol above Mg-c-1. The anionic cluster Si3Mg¯ has more close lying isomers than the cation with at least eight isomers having relative energies smaller than 180 kJ/mol. The ground state isomer Mg-a-1 (C2v, 2

A1) again has a low spin state. The remaining isomers are much less favored lying from 72

kJ/mol above. Resembling the shape of Mg-a-1, the high spin isomer Mg-a-7 (Cs, 4A’’) is less stable by 156 kJ/mol. Mg-a-2 (C2v, 2A1) is an attachment derivative in which the Mg atom connects with only one silicon atom. Mg-a-8 has rather a similar structure in the higher spin state but it undergoes Jahn-Teller distortion to give actually a Cs symmetry structure (cf. Figure 2). Both isomers Mg-a-3 and Mg-a-6 are classified as attachment adducts in which the Mg is capped on three Si atoms, and display Cs point group in both doublet and quartet states. Energetically, they are higher than Mg-a-1 by 77 and 135 kJ/mol, respectively. The C2v substitution structure Mg-a4 (2B1) and Mg-a-5 (4B1) that have identical structure but in two spin states are quasi degenerate, with an energy gap of only 2 kJ/mol.

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3.1.3. Si3Ca+/0/- Clusters Of the four lower-lying isomers of the neutral Si3Ca displayed in Figure 3, the most stable Ca-n-1 and the least stable isomer Ca-n-4 belong to both attachment and substitution types, whereas Ca-n-2 and Ca-n-3 are from the former type. Similar to Si3Be and Si3Mg, the ground state of Si3Ca Ca-n-1 adopts a C2v ((1A1) ground state. The other isomers of Si3Ca turn out to be >100 kJ/mol higher. Of the cations Si3Ca+, Ca-c-1 (C2v, 2A1) has a low-lying 2A2 excited state Ca-c-3 which is 144 kJ/mol higher. Ca-c-2 belongs to an attaching pattern, and its Cs 4A’ state is 115 kcal/mol less stable than Ca-c-1. For the anions Si3Ca¯, the lowest-energy structure Ca-a-1 has a rhombus shape which is similar to Si3Be¯ and Si3Mg¯. Both structures Ca-a-2 (C1, 2A) and Ca-a-4 (C1, 4A) are attachment type with a doublet - quartet separation gap of only 7 kJ/mol. Meanwhile, both isomers Ca-a-3 and Ca-a-5 are generated by replacing one Si atom of the rhombus Si4¯ by one Ca atom. Ca-a-3 (Cs 2A’’) is more stable than Ca-a-5 (Cs 4A’’) by only 6 kJ/mol. In summary, an attachment of the earth alkali atoms, cations and anions into the silicon trimer results in a clear-cut stabilization of the low spin state with an increasing singlet-triplet separation gap (for species with an even number of electrons). The calculated singlet-triplet gaps (ΔEST) are indeed quite large as compared to the degeneracy of both states of Si3, but similar to that of Si4. Moreover, the resulting tetramers exhibit geometrical and electronic features similar to the pure silicon tetramers Si4+/0/-. In the following sections, we compare some properties of both Si3M and Si4 systems to identify the effects of replacement.

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3.2. Thermochemical Properties of Clusters 3.2.1. Total Atomization Energies and Heats of Formation The heats of formation of all species considered are directly derived from their total atomization energies (TAE), along with the heats of formation of the elements ΔfHo (Si) and ΔfHo (M) with M = Be, Mg, Ca. The ΔfHo values at 0 K of the elements are 448.5, 319.75, 145.9 and 177.3 kJ/mol for Si, Be, Mg and Ca, respectively. Calculated results for the neutrals are summarized in Table 1. At a first glance, there is a good agreement between both sets of G4 and CBS results. The heat of formation at 0 K and 298 K obtained by the composite G4 approach are somewhat smaller than those obtained applying the CBS method. The difference varies in the range of 10-15 kJ/mol. In order to check the reliability of the G4 and CBS results, we first compare the previously calculated G4 TAEs8 and enthalpies of formation with those for the Si3 and Si4 clusters whose experimental values are available (Table 1).43–46 Let us mention that for the singlet-triplet energy gap of Si3, the composite G4 method yields a value of 4 kJ/mol in favor of the singlet state, which is close to the value of < 1 kJ/mol obtained using different CCSD(T)/CBS approaches.8 The experimental values for the heat of formation of Si3 and Si4 are also characterized by large error margins (Table 1). In this context, we would expect an error margin of ± 8 kJ/mol for the computed values. 3.2.2. Electron Affinities (EAs) and Ionization Energies (IEs) The adiabatic EA/IE of each neutral Si3M cluster is calculated as the difference between the total energies of the corresponding neutral and anionic/cationic optimized structures. As 10


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expected for relative quantities in which intrinsic errors of the methods employed can mutually be cancelled, the EA and IE values given in Table 2 again confirm a reasonable agreement between both CBS and G4 methods. The maximum difference between the two sets of the EA values amounts to only 0.03 eV, whereas the differences in the IEs of Si3X (X = Be, Mg) and Si3Ca are larger, 0.18 and 0.29 eV, respectively. Such differences in the energetics of Si 3M obtained from both G4 and CBS methods can be explained by the differences in the ways of determining the geometries and of calculating electronic energies. As stated above, the CCSD(T)/CBS protocol uses the (U)CCSD(T)/aug-cc-pvTZ (cc-pvTZ for Ca) geometry optimizations, whereas in the composite G4, geometries are optimized at (U)B3LYP/6-31+G(2df,p) level. The larger differences in the IE values of the Si3M clusters are due to the fact that their electronic energies are calculated using different basis sets, namely the aug-cc-pVnZ for Si3X and cc-pVnZ (n = 3,4,5) for Si3Ca. As far as we are aware of, no experimental values are available for these mixed clusters. Therefore, the previously computed EAs and IEs of the Sin clusters (n = 2-5)8 are used to check the reliability of the G4 and CBS values by comparing them with available experimental data. Results collected in Table 2 reveal a good agreement between the calculated data at both levels and experiment, with the maximum absolute deviation of less than ± 0.1 eV. The EA (Si3Ca) is smaller than those of Si3Mg and Si3Be (Table 2). The IEs given in Table 2 gradually decrease from Si3Be to Si3Ca. The ionization energies of metal atoms in the same main group in fact tend to decline with the increasing of atomic number. Namely, the ordering of IEs are Ca < Mg < Be. As it is easier to remove electron from Ca, the net charge of Si 3 in Si3Ca is more negative than that in Si3Mg and Si3Be (cf. Table 3 listing the Mulliken charges on atoms of neutral Si3M).

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The ability of capturing electron from Si3Ca is weaker than from Si3Mg and Si3Be. However, the EA of Si3Mg is larger than that of Si3Be. Although the net charge of Si3 in Si3Mg is more negative than that in Si3Be, the electronegativity () actually decreases upon descending a main group. Because (Be) > (Mg), a metallic bond is more important in Si3Be, whereas for Si3Mg an ionic bond is more dominant. 3.3. Relative Stability of Clusters and Dissociation Energies In an attempt to probe the intrinsic stabilities of the clusters considered with respect to fragmentations, their average binding energies (Eb) are calculated. The Eb values can be defined as follows (eqs. (2) – (4)): Eb (Si3M) = [3E(Si) + E(M) - E(Si3M)] / 4

(2)

Eb (Si3M -) = [2E(Si) + E(Si-) + E(M) - E(Si3M-)] / 4

(3)

Eb (Si3M +) = [2E(Si) + E(Si+) + E(M) - E(Si3M+)] / 4

(4)

where E(M), E(Si), E(Si+) and E(Si-) are the total energies of the M atom (with M = Be, Mg, Ca), Si atom, the anion Si- and the cation Si+, respectively. For their part, E(Si3M), E(Si3M-) and E(Si3M+) are total energies of the neutral Si3M, anionic Si3M- and cationic Si3M+ structures, respectively. Calculated results using G4 total energies and listed in Table 4 point out that Beclusters are more stable than Mg-counterparts with respect to fragmentations, whereas the Mgmixed clusters are less stable than Ca-derivatives. The reasons for such a trend could be understood as follows.

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All Si3M+/0/- clusters can be seen as ionic compounds in which the bonds are basically defined by electrostatic interaction forces. Therefore, the radius of the ions is shorter, the ionic bond is stronger. Because the radius of beryllium atom is smaller than that of magnesium, the average binding energies of the Si3Be+/0/- are getting larger than that of the corresponding Si3Mg+/0/. In the case of Si3Ca+/0, despite the fact that the Mg has a smaller atomic radius than Ca atom, the Ca atom includes 3d electrons. The shape of d orbitals is more easily distorted and disposed to ionic polarization. The resulting ionic polarization tends to increase the bond constituents, and thereby strengthening of Ca-Si bonds in Si3Ca+/0/- clusters. The average binding energies of Si3Ca+/0/- thus become larger than those of Si3Mg+/0/- clusters. In order to evaluate further the thermodynamic stability, dissociation energies (De) for different fragmentation channels of the Si3M clusters are computed. Results obtained from total G4 energies are given in Table 5. Dissociation energies of the neutral Si3M (M = Be, Mg, Ca) for the Si-loss channel (1) Si3M → Si2M + Si come across to be larger than those for the M-elimination channel (2) Si3M → Si3 + M. Similar observations are found for the anionic Si3M¯ clusters that have a tendency to be fragmented to form one M element and the corresponding anion Si3¯ along the fragmentation channel (6) Si3M¯→ Si3¯ + M. However, for positively charged clusters Si3M+, the smallest De are found for the fragmentation channels (9) Si3M+ → Si3 + M+ except for Si3Be+ which is detached giving Be and Si3+. This indicates that both Si3Mg+ and Si3Ca+ clusters prefer to decompose forming the corresponding cluster Si3 plus the ion M+ (M = Mg, Ca) counterpart. Proceeding in the opposite direction, these values correspond to the Mg+ and Ca+ affinities of Si3. 3.4 Chemical Bonding

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We now carry out an analysis of the electron distribution in the Si tetramer and Si3M with M = Be, Mg, Ca. As mentioned above, we first make use of the electron localization function (ELF) technique to locate the electrons and thus to identify the chemical bonds. Figure 4 shows the ELF plots of Si4 at high bifurcation values of 0.85 of Si4 in both singlet and triplet states. The large bifurcation value lets us to have a better view on the electron densities. The ELF is a simple measure of the electron localization in a molecular system, and thereby provides information about the spaces of molecule, called basins, in which electrons tend to occupy. It is valuable to address localization domains corresponding to bonding or lone pairs. In the Si tetramer, four monosynaptic domains V(Si) and four disynaptic domains V(Si,Si) can obviously be identified in both states. Populations of the lone pairs are rather comparable in both spin states, being around 2.3 – 2.6 electrons, whereas each Si-Si bond is occupied by ~1.5 electrons. Let us note that in Si4 there is a population of ~0.5 and 0.6 electrons for the shorter diagonal Si-Si bond in the singlet and triplet state, respectively. In the neutral Si3M series, a charge transfer is, as expected, operated from the metal atom to the trimer. Thus, the positive charges centered on the Be, Mg and Ca amount to 0.3, 0.4 and 0.7 electrons, respectively, in the singlet state (Table 3). The localization domains located at bifurcation values of 0.86 and 0.9 of Si3M in both spin states are displayed in Figures 5 and 6. In the singlet Si3Be, two basins are observed in the region between Be and Si atoms implying that two Be-Si bonds are actually formed upon attaching. Population analysis demonstrates the existence of two disynaptic V(Si,Be) basins, each occupied by 2.2 electrons, while the V(Si1) and V(Si3) basins are filled each by 1.9 electrons. In comparison 14


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to the monosynaptic V(Si) lone pair and disynaptic V(Si, Si) basins of the bare singlet tetramer, the electron population is reduced by ~0.4 and 0.2 electrons, respectively, when the Be atom is involved. The basin pattern of the high spin Si3X clusters is similar to that of the low spin state, except for the electron number of both V(Si,Be) basins which is now reduced to ~1.9 electrons, while that of both V(Si) basins remains populated each at ~2.1 electrons. Particularly, a trisynaptic basin V(Si1,Si3,Be) with a population of ~1.9 electrons is located illustrating a certain three-centre bond covering Si and Be atom. Prompt electron excitation apparently leads to an electron loss in the Si-Be bonds, and that is a reason for a lower stability of the triplet Si3Be. Similarly, Si3Mg also possesses in both spin states two bonded Si-Mg basins. The electron population of each V(Si,Mg) basin of low spin Si3Mg amounts to ~3.3 electrons, whereas the V(Si,Mg) basins of the high state Si3Mg is reduced to 1.7 electrons. Electron population of the disynaptic V(Si,Si) basin in both spin states of Si3Mg has a higher value of 2.2 electrons as compared to that of the disynaptic V(Si,Si) basins of Si4. In a similar way, trisynaptic basins V(Si1,Si3,Mg) with a population of ~2.2 electrons are observed in the triplet Si3Mg. Such an electron distribution results in a weaker interaction of Mg with triplet Si3 moiety, and thereby a low stability of the tetratomic triplet. As a consequence, the singlet-triplet separation gap of Si3Mg has the largest value (179 kJ/mol) as compared to that of Si3Be (109 kJ/mol). In the case of Ca, although population analysis reveals no disynaptic V(Si,Ca) basin, the singlet state exhibits two localization domains located between both Ca and Si atoms. The Ca atom forms two highly polar Si-Ca bonds. The two V(Si) basins near Ca are occupied each by 3.2 electrons in low spin state, while it is up to 3.5 electrons in the high spin state. Electrons of Ca are 15



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Page 16 of 43

thus transferred into the Si lone pair basins. Reduction of electron population in Si-Ca bonds following excitation reduces the stability of triplet Si3Ca, and as a result, the Ca attachment also induces a substantial change of the singlet – triplet energy gap, being now at 113 kJ/mol. 3.5 Ring Current and Aromaticity The aromatic character of the tetramer Si4 was examined in detail in previous reports.11,16 Our recent study11 pointed out that the singlet Si4 exhibits characteristic of a σ-aromatic fourmembered ring, and does not follow the classical Hückel counting rule. As the silicon clusters attached by earth alkali metal atoms have a rhombic form, which is similar to that of Si4, a question of interest concerns their eventual aromaticity. To probe this characteristic, the ipsocentric model is used.42,47 Accordingly, ring current stems from electron excitations between occupied and unoccupied MOs. When the product of the irreducible representations of both occupied and unoccupied MOs contains an in-plane translational (rotational) symmetry, a diatropic (paratropic) current occurs. In addition, the spatial distribution of a pair of MOs has an influence on the magnitude of a symmetry-allowed contribution. This model is simple for planar molecules. The maps given in Figure 7 display the σ, π and total current densities for the singlet Si3Be, Si3Mg and Si3Ca. The ring currents are calculated using the SYSMO package48 implemented in the Gamess-UK program.49 Total electron density of a molecular system can be partitioned in terms of σ, π… MOs. The total current normally includes contributions from all core, π, σ… MOs. In the Si3Be or Si3Mg and Si3Ca, π electrons appear to make a small contribution to the total current. In each singlet species, the total ring current is, as expected, diatropic and mainly comes from contributions of delocalized σ electrons.

16


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Figure 8 gives the individual contributions of four valence MOs of Si3M (M = Be, Mg, Ca) and their corresponding magnetic responses. The lower-lying σ-MOs also do not take part in the current, and their behaviors are given in the Supporting Information file (ESI). The π-MOs b1 contributes insignificantly to total current density (as already revealed in Figure 7). Only the three σ-MOs b2 and a1 have substantial contributions to the diatropic current density. Figure 9 schematically displays the HOMO-LUMO transitions responsible for the ring currents in Si3Be. This simple model based on orbital contributions provides a reasonable elucidation for the magnetic responses properties in both circumstances. In Si3Be, four excitations from the HOMOs to the LUMOs are allowed by translational transitions, namely T(y) and T(x), which gives rise to a diamagnetic ring current, and a rotational transition R(z) from a1 to a2 MOs leads to a paratropic current density (Figure 9). Consequently, the total current density could be either diamagnetic or paramagnetic. In this case, the diamagnetic current turns out to be predominant as the forbidden R(z) transition is less important. It is expected due to its larger energy denominator, and the high cancellation effect in the transition moment resulting from the more complex nodal structure of the target orbital, (cf. Figure 9). This view is consistent with the results shown in Figure 8 that indicate the contributions of the HOMO's in both systems to the ring currents. Similar transitions are found in the cases of Si3Mg and Si3Ca. The jmax values50, which is measure of the maximum strength of the current density per unit inducing field, of the ring current in Si3M (M = Be, Mg, Ca) system are summarized in Table 6.. For example, the total calculated π-electron current of benzene has jmax = 0.077.51 The electron delocalization and thus the current strength are, by definition, controlled by the jmax values which are higher for stronger currents irrespective of the current direction. 17



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Two main results emerge from values of Table 6. In each molecule, the σ-electron current is consistently much stronger than that of π-electrons. Regarding the total jmax values for Si3M cluster, they turn out to be slightly smaller than the sum of the corresponding jmax(σ) + jmax(π) values. A small paratropic contribution to the total current (jmax having a different sign) thus occurs, and causes a partial cancellation of the jmax (total) values. Overall, attachment of an earth-alkali metal to Si3 forming a rhombic four-membered ring tends to induce a diatropic response of its electron density, and thereby an aromatic feature (cf. Figure 9). Indeed, each Si3M cluster exhibits an σ-aromatic character which is similar to that of the pure Si4. 4. Concluding Remarks In the present theoretical study, geometries and electronic properties of the mixed earthalkali silicon clusters Si3M with M = Be, Mg, Ca, in the cationic, neutral and anionic states, were examined using high accuracy quantum chemical calculations. The most stable isomers of the clusters considered were determined on the basis of G4 energies. We predicted the total atomization energies, enthalpies of formation, average binding energy, and dissociation energies for the first time using both G4 and CCSD(T)/CBS methods. Moreover, the analysis of the chemical bonding using the electron localization function (ELF) and the magnetic ring currents, conducted for the first time, gives more insight into the aromatic character of Si3M clusters. From the computed results, the main conclusions have emerged as follows: i) Each of the neutral and negatively charged earth-alkali attached silicon clusters Si3M0/is formed by attaching the M atom into the corresponding silicon cluster Si30/-. The cationic Si3Be+ 18


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cluster is also derived by attaching a Be atom into the corresponding Si3+ whereas Si3Mg+ and Si3Ca+ are attaching structures in which the Mg+ and Ca+ cation are bound to Si3. ii) Attachment of earth-alkali atoms and cations to the silicon trimer induces a stabilizing interaction with the singlet Si3 and a destabilizing interaction with the triplet Si3 unit. They tend to increase the stability of the low spin state and thus enlarge substantially the singlet-triplet energy gaps of the binary clusters like the case of silicon tetramer. The resulting tetramers exhibit geometrical and electronic features similar to the pure silicon tetramer Si4+/0/-. iii) Similar to silicon tetramer, the rhombic four-membered mixed clusters Si3M (M = Be, Mg, Ca) exhibit an σ-aromatic character. Thus, when substituting one Si of the rhombus Si4 by one earth-alkali metal, the aromatic character remains unchanged. Acknowledgments. The authors are grateful to the Vietnam Ministry of Education and Training (Program 911) for doctoral scholarships. We are indebted to the KU Leuven Research Council (GOA and IDO programs and IRO scholarship) for continuing support. Supporting Information: Tables containing the Cartesian coordinates of the lowest-lying structures considered. Figures displaying the molecular orbitals and ring current maps of some σ-MOs of Si3M (M = Be, Mg, Ca). This material is available free of charge via the Internet at http://pubs.acs.org.

19



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Table 1. Total Atomization Energy (TAE, kJ/mol) and Heats of Formation (ΔfH, kJ/mol) at 0 K and 298 K of the Lowest-lying Isomers of Neutral Clusters Si3M (M = Be, Mg, Ca) Using G4 and CBS Approaches.

Structure Si3 (1A1, C2v)

TAE (kJ/mol) G4 Exptl.a (CBS) 723.9 705  16 (717.8) 1151  22

ΔfH (kJ/mol) G4 (CBS) 0 K 621.7 (627.8)

G4 (298 K)

Exptl.b (298K)

624.7 (630.7)

631.3  7.9

629.3 (633.0)

632.8 (636.5)

634.8  8.3

Si4 (1Ag, D2h)

1164.9 (1161.1)

Be-n-1 (1A1, C2v)

985.0 (972.5)

680.3 (692.9)

681.7 (694.2)

Mg-n-1 (1A1, C2v)

901.1 (890.7)

590.4 (600.7)

596.5 (606.7)

Ca-n-1 (1A1, C2v)

966.5 (951.5)

556.4 (571.4)

563.5 (578.6)

a

Experimental values taken from refs. 43,44.

b

Experimental values taken from refs. 45,46.

Values in parentheses were calculated using CCSD(T)/CBS approach. Values of Si3 and Si4 were reported in ref. 9.

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Table 2. Adiabatic Electron Affinities (EA) and Ionization Energy (IE) of Sin (n = 2-5) and Si3M (M = Be, Mg, Ca) Using both G4 and CCSD(T)/CBS Approaches.

a

Neutral

Anion

Cation

(state)

(state)

(state)

Si2 (3  g )



(2  g )

Si3 (1A1)

EA (eV)

IE (eV)

G4

CBSa

Exptl.b

G4

CBSa

Exptl.c

(4  g )

2.29

2.23

2.20  0.01

7.89

7.85

7.92  0.05

(2A1)

(2A1)

2.31

2.31

2.29  0.002

8.29

8.12

8.12  0.05

Si4 (1Ag)

(2Bg)

(2Bg)

2.18

2.14

2.13  0.001

8.00

7.95

8.20  0.10

Si5 (1A1’)

(2A2’’)

(2A2’’)

2.50

2.47

2.59  0.02

8.17

8.09

7.92  0.07

Si3Be (1A1)

(2A1)

(2A1)

1.91

1.89

8.27

8.20

Si3Mg (1A1)

(2A1)

(2A)

1.93

1.92

7.52

7.34

Si3Ca (1A1)

(2A1)

(2A1)

1.75

1.78

6.41

6.12





Based on CCSD(T) energies extrapolated using Eq. (1) with aug-cc-pVQZ and aug-cc-pV5Z

basis sets at CCSD(T)/aug-ccpVTZ optimized geometries for Si3Be and Si3Mg and with cc-pVQZ and cc-pV5Z basis sets at CCSD(T)/cc-pVTZ optimized geometries for Si3Ca. b

Experimental values taken from refs. 51–53.

c

Experimental values taken from ref. 54.

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Table 3. Mulliken Net Charges q (electrons) on the Metal and Si Atoms of Neutral Si3M Obtained Using B3LYP Functional (within G4 method).

Si3Be

Si3Mg

Si3Ca

q (Si1 = Si2)

-0.16

-0.16

-0.29

q (Si3)

-0.02

-0.12

-0.13

q (M4)

0.32

0.45

0.71

Table 4. Average Binding Energies (Eb in eV) of Si3M, Si3M+ and Si3M¯ (M = Be, Mg, Ca) Using G4 Approach.

Si3M

Eb (Si3M+)

Eb (Si3M)

Eb (Si3M¯)

M = Be

2.52

2.55

2.69

M = Mg

2.49

2.33

2.48

M = Ca

2.93

2.50

2.61

27



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Table 5. Dissociation Energies (De, kJ/mol) for Various Fragmentation Channels of Sin (n = 3, 4) and Si3M (M = Be, Mg, Ca) in Neutral, Cationic and Anionic States (G4 calculations). Neutrals

Anions

Cations

Si3M De(1)

De(2)

De(3)

De(4)

De(5)

De(6)

De(7)

De(8)

De(9)

De(10)

Si3Be

403.3

261.1

485.7

457.6

454.0

222.0

381.8

390.2

365.4

262.4

Si3Mg

391.5

177.2

479.9

447.7

384.6

140.0

359.4

450.8

191.4

250.9

Si3Ca

378.1

242.6

506.9

417.2

410.1

188.4

385.8

545.0

209.3

423.9

Table 6. Values of jmax (au) Related to the Ring Currents of the Singlet Si3M (M = Be, Mg, Ca) jmax

jmax

jmax

total

σ-electrons

π-electrons

Si3Be

0.086

0.084

0.006

Si3Mg

0.053

0.048

0.006

Si3Ca

0.055

0.053

0.006

Structure

28


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Figure Captions Figure 1. Shapes, electronic states and G4 relative energies (ΔE, kJ/mol) of the lower-lying isomers Si3Be at the neutral, cationic, and anionic states. Figure 2. Shapes, electronic states, and G4 relative energies (ΔE, kJ/mol) of the lower-lying isomers Si3Mg at the neutral, cationic, and anionic states. Figure 3. Shapes, electronic states, and G4 relative energies (ΔE, kJ/mol) of the lower-lying isomers Si3Ca at the neutral, cationic, and anionic states. Figure 4. ELF isosurface plots of Si4 in both singlet and triplet states (B3LYP/6-311+G(d)) at bifurcation value ELF = 0.9. Figure 5. ELF localization domains identified at bifurcation value of 0.86 of Si3M (M = Be, Mg, Ca) in both low and high spin states (B3LYP/6-311+G(d)). Figure 6. ELF localization domains identified at bifurcation value of 0.9 of Si3M (M = Be, Mg, Ca) in both low and high spin states (B3LYP/6-311+G(d)). Figure 7. Current density maps of the singlet Si3M (M = Be, Mg, Ca) using B3LYP/6-311+G(d) densities. Figure 8. Current density maps from 8 valence occupied orbitals of the singlet Si3M (M = Be, Mg, Ca) using B3LYP/6-311+G(d) densities. Figure 9. Electron excitation responsible for the ring current of Si3Be. Black arrows: translational transitions forming diatropic current, white arrow: rotational transition forming paratropic current.

29



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Be-n-1 (1A1, C2v) 0

Be-n-2 (3A’’, Cs) 109

Page 30 of 43

Be-n-3 (1A1, C2v) 157

The neutral Si3Be cluster

Be-c-1 (2A1, C2v) 0

Be-c-2 (4A’, Cs) 82

Be-c-3 (4A2, C2v) 128

The cationic Si3Be+ cluster

Be-a-1 (2A1, C2v) 0

Be-a-2 (2A’’, C2v) 44

Be-a-3 (2A’’, Cs) 57

30


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Be-a-4 (4B1, C2v) 98

Be-a-5 (4A’’, Cs) 148

Be-a-6 (4A’’, Cs) 159

The anionic Si3Be¯ cluster Figure 1.

31



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Mg-n-1 (1A1, C2v) 0

Mg-n-2 (1A’, Cs) 100

Page 32 of 43

Mg-n-3 (3A2, C2v) 179

The neutral Si3Mg cluster

Mg-c-1 (2A’, C1) 0

Mg-c-2 (2A, C1) 61

Mg-c-3 (2A’, Cs) 87

Mg-c-4 (4A, C1) 164

The cationic Si3Mg+ cluster

Mg-a-1 (2A1, C2v) 0

Mg-a-2 (2A1, C2v) 72

Mg-a-3 (2A’’, Cs) 77

Mg-a-4 (2B1, C2v) 125

32


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Mg-a-5 (4B1, C2v) 127

Mg-a-6 (4A’’, Cs) 135

Mg-a-7 (4A’’, Cs) 156

Mg-a-8 (4A’’, Cs) 174

The anionic Si3Mg¯cluster

Figure 2.

33



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Ca-n-1 (1A1, C2v) 0

Ca-n-2 (1A1, C2v) 102

Page 34 of 43

Ca-n-3 (3A’’, Cs) 113

Ca-n-4 (3B1, C2v) 129

The neutral Si3Ca cluster

Ca-c-1 (2A1, C2v) 0

Ca-c-2 (4A’, Cs) 115

Ca-c-3 (2A2, C2v) 144

The cationic Si3Ca+ cluster

Ca-a-1 (2A1, C2v) 0

Ca-a-2 (2A, C1) 111

Ca-a-3 (2A’’, Cs) 114 34


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Ca-a-4 (4A, C1) 118

Ca-a-5 (4A’’, Cs) 120

The anionic Si3Ca¯ cluster

Figure 3.

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V(Si)=2.3 V(Si,Si)=1.5

Page 36 of 43

V(Si)=2.3

V(Si)=2.3 V(Si)=2.6

singlet

V(Si,Si)=1.5

triplet

Figure 4.

36


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Singlet

Triplet V(Si)=2.1

V(Si)=1.9 V(Si,Si)=1.7

V(Si,Be)=2.2

V(Si,Si)=1.9

V(Si,Be)=1.9

Si3Be

V(Si)=1.9

V(Si)=2.4

V(Si)=2.0

V(Si,Mg)=3.3 V(Si,Si)=2.2

V(Si,Si)=2.2

V(Si,Mg)=1.7

V(Mg)=0.6

Si3Mg

V(Si)=1.8

V(Si)=2.4 V(Si)=3.2 V(Si,Si)=1.8

V(Si)=3.5 V(Si,Si)=2.2

Si3Ca

V(Si)=2.4

V(Si)=2.5

Figure 5. 37



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

Singlet

Triplet V(Si)=2.1

V(Si)=1.9 V(Si,Be)=2.2

V(Si)=2.4

Page 38 of 43

V(Si,Be)=1.9

V(Si)=1.9

Si3Be

V(Si,Mg)=3.3

V(Si)=2.0

V(Si)=2.4

V(Si, Mg)=1.7

V(Mg)=0.6 Si3Mg

V(Si)=3.2 V(Si)=2.3

V(Si)=3.5 V(Si)=2.5

Si3Ca

Figure 6. 38


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Total

-MOs

-MOs

Si3Be

Si3Mg

Si3Ca

Figure 7. 39



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Page 40 of 43

Si3 Be

HOMO a1

HOMO-1 b1

HOMO-2 b2

HOMO-3 a1

Si3 Mg

HOMO a1

HOMO-1 b2

HOMO-2 b1

HOMO-3 a1 40


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Si3 Ca

HOMO a1

HOMO-1 b2

HOMO-2 a1

HOMO-3 b1

Figure 8

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Page 42 of 43

b2

-0.07 T(y)

R(z)

a2

b1 a1

-0.11 T(y)

T(x) T(y)

a1

-0.23

b1 b2

Si3Be Figure 9.

42


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Si3M species are σ-aromatic.

81x43mm (300 x 300 DPI)


Structures, Thermochemical Properties, and Bonding of Mixed

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