Structures and electronic properties of B₂Si₆^−/0/+: anion photoelectron spectroscopy and theoretical calculations

Abstract

We measured the photoelectron spectrum of B₂Si₆⁻ anion and investigated the structures and electronic properties of B₂Si₆⁻ anion as well as those of its neutral and cationic counterparts with quantum chemical calculations. The vertical detachment energy (VDE) of the B₂Si₆⁻ anion has been measured to be 2.40 ± 0.08 eV. Through global minimum searches and CCSD(T) calculations, we have identified that the lowest-energy structures of B₂Si₆^q (q = −1, 0, +1) are peculiar structures with a Si atom hanging over a distorted bowl-like B₂Si₅ framework. Quasi-planar or planar isomers have also been identified for the B₂Si₆ cluster at −1, 0, and +1 charge states. The quasi-planar and planar isomers are higher in energy than their bowl-like counterparts by at least 0.20 eV. The symmetries of the quasi-planar isomers varied at different charge states, ranging from C_s to C_2h, then to D_2h respectively for the −1, 0, and +1 charge states. The reducing of the symmetry from +1 charge state to −1 charge state is more likely due to the Jahn–Teller effect upon the addition of electrons.

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1. Introduction

Silicon-based compounds have attracted tremendous attention because of their importance in the semiconductor industry.^1–4 They have aromaticity, size-dependent structural characteristics, as well as distinctive physiochemical properties.⁵ In particular, they have been used as one of the most important p-type dopants in crystalline silicon.^6,7 Boron-silicon compounds have high melting points and high hardness. Their conductivity increases with the increasing concentration of boron.^5,8,9 Compared with carbon, silicon is more reluctant to form unsaturated compounds.^10–14 Although the synthesis and isolation of stable unsaturated silicon compounds are a great challenge, some silicon–silicon multiple-bonded compounds were identified in the last decades. In 1981, a Si=Si double-bonded compound, silaethene, was isolated by Brook et al.¹⁵ In the same year, West et al.¹⁰ synthesized and isolated a stable compound containing a Si=Si double bond, tetramesityldisilene. Since then, many other interesting stable unsaturated silicon compounds have been investigated extensively.^16–24

Scientists have made great efforts to search for compounds with planar aromatic six-membered silicon rings (c-Si₆) over the past decades because they may be used as highly stable two-dimensional (2D) aromatic nanomaterial. The cyclotrisilenylium ion²⁵ and cyclobutadiene dianion²⁶ have been found to be the potentially aromatic compounds based on the planar three-membered or four-membered silicon rings. As the silicon analogues of benzene, compounds with planar aromatic c-Si₆ have been of great interest in the silicene field.^27,28 The planar D_6h c-Si₆ unit in Si₆H₆ is less stable than the chair-like D_3d structure due to the pseudo-Jahn–Teller effect.^29,30 The dark green crystals of an isomer of Si₆H₆ with the proposed dismutational aromaticity³¹ were synthesized by Abersfelder et al.²² It has a chair-like conformation in line with the theoretical results.^29,30 Subsequently, a cage isomer of hexasilabenzene was investigated experimentally by Abersfelder et al.^32,33 and Kratzert et al.³⁴ In addition, several planar D_6h c-Si₆ structures have been suggested by theoreticians. These planar benzene-like structures can be formed by substituting Si atoms by C atoms in silabenzenes.³⁵ It has also been proposed that anionic systems c-Si₆²⁻, c-Si₆⁴⁻, and c-Si₆⁶⁻ could be planar.^36–38 Zdetsis et al.²⁷ have predicted that Si₆Li₆ with D_2h symmetry could be formed by the reduction of the c-Si₆⁶⁻ anion in the presence of lithium. Recently, the c-BSi₃ silicene containing planar aromatic D_6h c-Si₆ rings has been predicted by theory to be the global minimum of the BSi₃ monolayer and possesses metallic character.³⁹

There have been many experimental and theoretical investigations on the structural and electronic properties of small size Si_nB_m clusters.^8,9,39–50 Cline et al.^8,9 have reported the existence of two new silicon borides SiB₄ and SiB₆ in silicon-boron systems. Bernardo and Morrison⁴⁰ performed a theoretical study on the structures and binding energies of SiB_n⁺ (n = 1–4) and suggested that SiB_n⁺ (n = 1–4) cluster cations prefer planar boron networks with silicon located at the edge site. The high- and low-spin states of BSi were calculated by Boldyrev and Simons⁴¹ and were confirmed by Knight et al.⁴² using electron spin resonance (ESR) spectroscopy technology. Verhaegen et al.⁴³ and Viswanathan et al.⁴⁴ have studied the thermochemistry of BSi, BSi₂, and BSi₃. Yamauchi et al.⁴⁵ have investigated the geometric and electronic properties of B₁₂ in silicon crystalline and found that the lowest-lying isomer of B₁₂ in silicon crystalline is icosahedral. The low-lying excited electronic states and structures of BSi₂, B₂Si, and B₂Si₂ were investigated by Davy et al. using the B3LYP method.⁴⁶ Sun et al.⁴⁷ have investigated BSi_m⁻ (m = 1–6) cluster anions using time-of-flight mass spectrometry and quantum chemical calculations. Tam et al.⁵⁰ studied the structures, thermochemical properties and growth mechanism of Si_nB^q (n = 1–10; q = −1, 0, +1) and found that Si₉B and Si₁₀B exhibit endohedral structures. Dai et al.⁵¹ conducted a first-principle theoretical study on the structures of 2D boron-silicon compounds, and found that B_nSi (n = 1–3, 5, 6) and BSi_m (m = 3, 4) clusters prefer planar sp²-Si structures. Recently, Dopfer and co-workers reported a combined infrared-ultraviolet two-color ionization (IR-UV2CI) spectroscopy and quantum chemical study on BSi₆, and found that the most stable structure of BSi₆ is a distorted pentagonal bipyramid.⁵²

In order to get insight into the structural and electronic properties of boron-doped silicon clusters, in this work we carried out a combined photoelectron spectroscopy and quantum chemical study on B₂Si₆^−/0/+.

2. Experimental and theoretical methods

2.1 Experimental method

The experiments were carried out on a home-built apparatus consisting of a time-of-flight mass spectrometer and a magnetic-bottle photoelectron spectrometer, which has been described elsewhere.⁵³ The B₂Si₆⁻ anion was produced by laser vaporization of rotating and translating disk targets (13 mm diameter; B/Si molar ratio of 1 : 2) with the second harmonic (532 nm) of a nanosecond Nd:YAG laser (Continuum Surelite II-10). Helium gas with a backing pressure of 5.0 atm. was delivered through a pulsed valve into the laser ablation source to cool the formed B₂Si₆⁻ anion. The B₂Si₆⁻ anion was mass-selected and then photodetached with the fourth harmonic light beam from another Nd:YAG laser (Continuum Surelite II-10, 266 nm). The resultant electrons were energy-analyzed by the magnetic-bottle photoelectron spectrometer. The photoelectron spectrum was calibrated using the spectrum of Cu⁻ anion taken at the similar conditions. The resolution of the photoelectron spectrometer was approximately 40 meV for electrons with 1 eV kinetic energy.

2.2 Theoretical method

The theoretical calculations of B₂Si₆^q (q = −1, 0, +1) were performed using the Becke 3-parameter-Lee–Yang–Parr (B3LYP) density functional method as implemented in the GAUSSIAN 09 program package.⁵⁴ Global minimum searches were carried out using the basin-hopping (BH) method⁵⁵ at the DFT level. Low-lying structures were fully optimized using the B3LYP method with the aug-cc-pVTZ basis set. We tested the theoretical method by calculating the bond length of B–Si (1.917 Å, ⁴Σ⁻), which is in good agreement with the bond length calculated with the MP2 method in the literature (1.905 Å).⁴² The vibrational frequencies were calculated to confirm whether their structures are real local minima. The zero-point energies (ZPEs) corrections were included for all calculated energies. For more reliable energies, the CCSD(T) single-point calculations were performed using the Molpro2012 program⁵⁶ at the B3LYP/aug-cc-pVTZ geometries. The first VDE was calculated based on the energy difference between the neutral and anion at the ground state geometry of the anion. The excited-state energies of the neutrals were calculated by using the time-dependent density functional theory (TD-DFT) method.⁵⁷ The statistical average of orbital potentials (SAOP) functional was employed and all-electron basis sets TZ2P were used for B and Si. Simultaneously, the higher VDE values were also approximated using the generalized Koopman's theorem⁵⁸ at the DFT/CAMY-B3LYP⁵⁹ level. The TD-DFT and DFT/CAMY-B3LYP⁵⁹ calculations were carried out on these clusters using Amsterdam Density Functional program (ADF 2013.01).^60–62

The natural bond orbital (NBO 5.0)^63,64 analyses of B₂Si₆^q (q = −1, 0, +1) were also performed to gain insights into the natural electron configurations of the valence orbitals and natural charges of these clusters. To further understand the nature of B–Si bonds in these boron-silicon complexes, we analyzed the density of state and adaptive natural density partitioning (AdNDP⁶⁵) using the Multiwfn 2.6.1 package.⁶⁶

3. Experimental results

The photoelectron spectrum of B₂Si₆⁻ anion obtained with 266 nm photons is shown in Fig. 1. The spectral features are labeled with letters (X, A, B, and C), which correspond to the transitions from the ground state of B₂Si₆⁻ anion to the ground and excited states of B₂Si₆ neutral. The adiabatic detachment energy (ADE) and vertical detachment energies (VDEs) estimated from the photoelectron spectrum are summarized in Table 1. The spectrum of B₂Si₆⁻ anion is characterized by a small peak centered at 2.40 eV, a small shoulder centered at 3.61 eV, a broad feature centered at 3.90 eV, followed by a sharp peak centered at 4.27 eV. Because the instrumental resolution shows a significant influence on the broadening of the photoelectron spectrum, the ADE was determined by adding the instrumental resolution to the onset of the first peak in the spectrum. The onset of the first peak was determined by drawing a straight line along the leading edge of that peak across the baseline of the spectrum. The ADE of B₂Si₆⁻ anion estimated from the experimental spectrum is 2.15 eV.

Fig. 1 (a) Photoelectron spectrum of B₂Si₆⁻ anion recorded with 266 nm photons. (b) Simulated spectrum of B₂Si₆⁻ anion using the generalized Koopmans' theorem. (c) Simulated spectrum of B₂Si₆⁻ anion using the TD-DFT method. The simulations were conducted by fitting the distribution of the VDE values with unit-area Gaussian functions of 0.1 eV full width at half maximum.

Table 1 Experimental VDEs and ADE of B₂Si₆⁻ anion measured from the 266 nm photoelectron spectrum

	VDE^a (eV)				ADE^a (eV)
	X	A	B	C
a The numbers in parentheses indicate the uncertainties in the last digit.
B2Si6^−	2.40(8)	3.61(8)	3.90(8)	4.27(8)	2.15(8)

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4. Theoretical results

The structures of the typical low-lying isomers of the B₂Si₆⁻ anion are shown in Fig. 2, and those of their corresponding neutral and cationic clusters are also shown in Fig. 2. The simulated spectra of B₂Si₆⁻ anion using the generalized Koopmans' theorem and TD-DFT method were constructed by fitting the distribution of the VDE values with unit-area Gaussian functions of 0.10 eV full width at half maximum (Fig. 1). The relative energies, VDEs, ADEs, term energies, and NPA charges of these isomers from our calculations are summarized in Tables 2–5.

Fig. 2 Structures and relative energies of the low-lying isomers of B₂Si₆^q (q = −1, 0, +1). The bond distances are in angstroms. The relative energies outside the parentheses are from the DFT/B3LYP method, and those in parentheses from the CCSD(T) method.

Table 2 Relative energies, VDEs and ADEs of the low-lying isomers of B₂Si₆⁻ anion obtained by DFT and CCSD(T) calculations

	Isomers	Sym.	State	ΔE (eV)		ADE (eV)		VDE (eV)
				B3LYP	CCSD(T)	Theo.	Expt.	Theo.	Expt.
B2Si6^−	1a	C1	^2A	0.00	0.00	2.00	2.15	2.30	2.40
	1b	C2h	^2Bu	0.41	0.31	2.88		2.98
	1c	Cs	^2A′	0.51	0.63	2.16		2.52

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Table 3 Term energies of the lowest-energy isomer of B₂Si₆⁻ anion calculated with the generalized Koopmans' theorem (GKT) and TD-DFT method

Term energies	Expt. (eV)	GKT (eV)	TD-DFT (eV)
X ← A	1.21	1.59	1.36
X ← B	1.50	1.82	1.62
X ← C	1.87	1.97	1.92

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Table 4 Relative energies, symmetries and electronic states of the low-lying isomers of B₂Si₆ neutral and B₂Si₆⁺ cation obtained by the DFT/B3LYP and CCSD(T) calculations

	Isomers	Sym.	State	ΔE (eV)
				B3LYP	CCSD(T)
B2Si6	2a	C1	^1A	0.00	0.00
	2b	C2h	^1Ag	0.66	0.33
	2c	C2h	^1Ag	1.30	0.45
B2Si6^+	3a	C1	^2A	0.00	0.00
	3b	D2h	^2B1g	0.00	0.20
	3c	C2h	^2Au	0.76	0.93

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Table 5 NPA charges and spin density distributions of the most stable isomers (bowl-like isomers) and the quasi-planar isomers of B₂Si₆^q (q = −1, 0, +1)

	NPA charges					Spin density distributions
	B2Si6^+ (3a, C1)	B2Si6^+ (3b, D2h)	B2Si6 (2a, C1)	B2Si6 (2b, C2h)	B2Si6^− (1a, C1)	B2Si6^+ (3a, C1)	B2Si6^+ (3b, D2h)	B2Si6^− (1a, C1)
B1	−0.62	−0.77	−1.04	−0.73	−1.02	0.00	−0.05	0.00
B2	−0.48	−0.77	−1.04	−0.73	−1.07	0.15	−0.05	0.08
Si3	0.46	0.36	0.52	0.26	0.40	0.21	0.06	0.00
Si4	0.34	0.36	0.37	0.26	0.07	0.08	0.06	0.11
Si5	0.47	0.55	0.26	0.21	0.16	0.45	0.43	0.00
Si6	0.28	0.36	0.31	0.26	0.26	0.04	0.06	0.00
Si7	0.39	0.36	0.57	0.26	0.17	0.00	0.06	0.73
Si8	0.16	0.55	0.05	0.21	0.03	0.07	0.43	0.08

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4.1 B₂Si₆⁻

For the B₂Si₆⁻ anion, the most stable isomer 1a can be viewed as one Si atom located on the top of the distorted bowl-like B₂Si₅ framework. The distance between B1 and Si8 is ∼2.274 Å. The Si3–Si4, Si4–Si5, Si5–Si6 and Si6–Si7 bond lengths are ∼2.455 Å. The B–B bond distance is ∼1.682 Å, close to the B–B bond lengths (∼1.710 Å) in the compounds of the a-B (a-rhombohedral boron) type.⁶⁷ The first VDE and ADE of isomer 1a are calculated to be 2.30 eV and 2.00 eV at the DFT/B3LYP level, respectively, in reasonable agreement with the experimental values (2.40 eV and 2.15 eV). The first term energies ΔE (B₂Si₆(X) ← B₂Si₆(A)) obtained from the generalized Koopmans' theorem and TD-DFT calculations are 1.59 eV and 1.36 eV, respectively, in reasonable agreement with the experimental value (1.21 eV). The second term energies ΔE (B₂Si₆(X) ← B₂Si₆(B)) obtained from the generalized Koopmans' theorem and TD-DFT calculations are 1.82 eV and 1.62 eV, respectively, also in reasonable agreement with the experimental measurement (1.50 eV). The second detachment channels correspond to the transitions to the two ³A final states with electrons detached from HOMO−1 and HOMO−2 of B₂Si₆⁻ anion. The third term energies ΔE (B₂Si₆(X) ← B₂Si₆(C)) obtained from the generalized Koopmans' theorem and TD-DFT calculations are 1.97 eV and 1.92 eV, respectively, also in good agreement with the experimental value (1.87 eV). The simulated spectra of the bowl-like isomer 1a from the generalized Koopmans' theorem and TD-DFT calculations can reasonably explain all the observed photoelectron spectrum bands (Fig. 1). Isomer 1b is a C_2h distorted oblique prism with the ²B_u electronic state. The theoretical VDE of isomer 1b is calculated to be 2.98 eV, which does not match with the experimental value. Isomer 1c is a quasi-planar structure with a boron dimer surrounded by six Si atoms. It is of C_s symmetry with the ²A′ electronic state. The VDE and ADE of isomer 1c are calculated to be 2.52 eV and 2.16 eV, respectively. Isomers 1b and 1c are less stable than isomer 1a by 0.41 eV and 0.51 eV at the DFT/B3LYP level, respectively. The CCSD(T)/aug-cc-pVTZ results show that isomers 1b and 1c are higher in energy than isomer 1a by 0.31 eV and 0.63 eV, respectively. Therefore, the existence of isomers 1b and 1c in the experiments can be ruled out, and isomer 1a corresponds to the major peaks observed in the spectrum of the B₂Si₆⁻ anion.

4.2 B₂Si₆

The lowest-energy structure of B₂Si₆ (isomer 2a) with no symmetry is similar to isomer 1a of B₂Si₆⁻ anion. The Si3–Si4, Si4–Si5, Si5–Si6, and Si6–Si7 bond lengths are also ∼2.455 Å. The B–B bond distance is 1.637 Å, close to the B–B bond length of isomer 1a. But the Si7–Si8 bond length is ∼2.795 Å in isomer 2a, much shorter than that (∼3.820 Å) of isomer 1a. Isomer 2b is of C_2h symmetry in ¹A_g electronic state with a boron dimer surrounded by six Si atoms. It is less stable in energy than isomer 2a by 0.66 eV from the B3LYP/aug-cc-pVTZ calculations, while CCSD(T) calculations show that the energy difference is 0.33 eV. Isomer 2c also has a C_2h symmetry with the ¹A_g electronic state and it is higher in energy than isomer 2a by 1.30 eV and 0.45 eV from the B3LYP and CCSD(T) calculations, respectively. It is worth mentioning that we also considered the highly symmetric D_2h structure of isomer 2b, however, it is unstable.

To understand the stabilities of the isomers 2a and 2b of B₂Si₆, we searched the possible transition barriers between them by Berny method. The transition-state structure obtained by us was confirmed to connect the correct reactants (isomer 2a) and products (isomer 2b) by intrinstic reaction coordinate (IRC). The transition state is determined for the conversion pathway, with a conversion barrier of 0.48 eV calculated at the CCSD(T) level. It indicates that the bowl-like structure of B₂Si₆ neutral (isomer 2a) is highly stable.

4.3 B₂Si₆⁺

The low-lying isomers of B₂Si₆⁺ cation (3a and 3b) are degenerated in energy from the B3LYP results. However, the CCSD(T) results show that isomer 3b is higher than isomer 3a by 0.20 eV in energy. The structure of isomer 3a is similar to isomer 2a of B₂Si₆. The Si7–Si8 and Si4–Si8 bond lengths are slightly elongated in isomer 3a relative to those of isomer 2a. Isomer 3b has a perfectly planar hexagon structure with a large HOMO–LUMO gap of 2.35 eV. It has a D_2h symmetry with the ²B_1g electronic state. The Si–Si distances are somewhat different in isomer 3b. The Si4–Si5, Si5–Si6, Si6–Si7, and Si3–Si4 bond distances are ∼2.500 Å, slightly shorter than the Si7–Si8 and Si4–Si8 bonds (∼2.900 Å) in the same isomer. The B–B bond length in isomer 3b is ∼1.666 Å, close to the B–B distances in the quasi-planar isomers of the negative and neutral charge states. Isomer 3c has a C_2h symmetry with the ²A_u electronic state and it is higher in energy than isomer 3a by 0.76 eV and 0.93 eV from the B3LYP and CCSD(T) calculations, respectively, indicating that the preference of isomer 3a is the largest. It is worth mentioning that, for the quasi-planar or planar structures, the symmetries of the negatively charged B₂Si₆⁻ (1c, C_s) and neutral B₂Si₆ (2b, C_2h) are lower than that of the positively charged B₂Si₆⁺ (3b, D_2h), indicating that the Jahn–Teller effect caused by the increased electrons might be the major factor contributing to the lowing of the symmetry.

5. Discussion

5.1 NPA charges and spin density distributions of B₂Si₆^q (q = −1, 0, +1)

As shown in Table 5, the effective atomic charges of the most stable structures of B₂Si₆^q (q = −1, 0, +1) indicate that both B atoms in the clusters are negatively charged, Q_B < 0. It is obvious that some electrons are transferred to the B atoms, partly because of the larger Pauling electronegativity of B (2.04) as compared to Si (1.90).⁶⁸ The electron is mainly detached from the p orbitals of Si(4) and lateral Si(7) atoms when B₂Si₆⁻ anion with a C₁ symmetry was photodetached. Inversely, the electron is taken off from the B atoms when the lowest-energy isomer of B₂Si₆ neutral loses one electron. The spin density distributions of B₂Si₆⁻ anion (1a, C₁) have shown that its spin densities are mainly located on lateral Si(7) and slightly located on B(2), Si(4), and Si(8). For B₂Si₆⁺ cation (3a, C₁), the spin densities are mainly located on B(2), Si(3), and Si(5). For planar B₂Si₆⁺ cation (3b, D_2h), the unpaired electron is mainly located on the C₂ axis of Si(5) and Si(8).

5.2 Molecular orbitals of B₂Si₆ (2a, C₁)

Using the ‘adaptive density partitioning’ approach,⁶⁵ one can also approximately extract 9 delocalized valence MOs of approximate “s” and “p” symmetry for the remaining 30 electrons in the B₂(2s²2p¹)–Si₆(3s²3p²) valence shell of B₂Si₆ (2a, C₁) (Fig. 3), in addition to the 6 lone pair electrons of six Si atoms, 9 delocalized MOs include one 2c-2e BSi σ bond (electronic occupation is equal to 1.88 |e|), three 3c-2e B₂Si or BSi₂ σ bonds (electronic occupation is equal to 1.89 |e|), three 4c-2e BSi₃ σ bonds (electronic occupation is equal to 1.90 |e|), and two 5c-2e B₂Si₃ MOs (electronic occupation is equal to 1.91 |e|). The 15 electron pairs of these 30e systems cannot be localized symmetrically. The two 5c-2e B₂Si₃ MOs contain the σ plus π double delocalization. The Si7–Si8 bond length in isomer 2a is shortened by 1.025 Å relative to that of isomer 1a, most likely due to the forming of the 4c-2e BSi₃ σ bonds.

Fig. 3 Molecular orbitals of the bowl-like isomer of B₂Si₆ (2a, C₁). Six lone pairs of Si atoms and nine optimally localized MOs (contour values ψ = ±0.038 au) are from the AdNDP⁶⁵ method (ON = electronic occupation).

6. Conclusions

We measured the photoelectron spectrum of B₂Si₆⁻ anion and investigated its anionic, cationic and neutral structures with density functional theory (B3LYP) and wave function theory (CCSD(T)) approaches. By comparing the calculated VDEs with the experimental measurements, the structure of B₂Si₆⁻ anion is determined. The CCSD(T) results reveal that the lowest-lying isomers of B₂Si₆^q (q = −1, 0, +1) have a peculiar structure with a Si atom hanging over a distorted bowl-like B₂Si₅ framework. The Si7–Si8 distance in the lowest-lying isomer 2a of B₂Si₆ neutral is shortened by 1.025 Å relative to that of the lowest-lying isomer 1a of B₂Si₆⁻ anion. Isomer 2a is characterized with σ or π delocalization in chemical bonding. In addition to the bowl-like structures, we also found low-lying quasi-planar or planar structures for B₂Si₆^q (q = −1, 0, +1), which are higher in energy than the corresponding bowl-like structures by at least 0.20 eV. The planar B₂Si₆⁺ cation has a D_2h symmetry and is highly aromatic. For the quasi-planar or planar structures, the symmetries of the negatively charged B₂Si₆⁻ (1c, C_s) and neutral B₂Si₆ (2b, C_2h) are lower than that of the positively charged B₂Si₆⁺ (3b, D_2h), more likely due to the Jahn–Teller effect upon the addition of electrons.

Acknowledgements

This work was supported by the Natural Science Foundation of China (Grant No. 21103202 and 21501114) and Natural Science Foundation of Shanxi Province (Grant No. 2015021048).

Notes and references

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