Yu
Wang
^{a},
Man
Qiao
^{a},
Yafei
Li
*^{a} and
Zhongfang
Chen
*^{b}
^{a}Jiangsu Collaborative Innovation Centre of Biomedical Functional Materials, Jiangsu Key Laboratory of New Power Batteries, School of Chemistry and Materials Science, Nanjing Normal University, Nanjing, 210023, China. E-mail: liyafei@njnu.edu.cn
^{b}Department of Chemistry, Institute for Functional Nanomaterials, University of Puerto Rico, Rio Piedras Campus, San Juan, PR 00931, USA. E-mail: zhongfangchen@gmail.com

Received
22nd June 2017
, Accepted 22nd January 2018

First published on 22nd January 2018

The prediction of new materials with peculiar topological properties is always desirable to achieve new properties and applications. In this work, by means of density functional theory computations, we extend the rule-breaking chemical bonding of planar pentacoordinate silicon (ppSi) into a periodic system: a C_{2v} Ca_{4}Si_{2}^{2−} molecular building block containing a ppSi center is identified first, followed by the construction of an infinite CaSi monolayer, which is essentially a two-dimensional (2D) network of the Ca_{4}Si_{2} motif. The moderate cohesive energy, absence of imaginary phonon modes, and good resistance to high temperature indicate that the CaSi monolayer is a thermodynamically and kinetically stable structure. In particular, a global minimum search reveals that the ppSi-containing CaSi monolayer is the lowest-energy structure in 2D space, indicating its great promise for experimental realization. The CaSi monolayer is a natural semiconductor with an indirect band gap of 0.5 eV, and it has rather strong optical absorption in the visible region of the solar spectrum. More interestingly, the unique atomic configuration endows the CaSi monolayer with an unusually negative Poisson's ratio. The rule-breaking geometric structure together with its exceptional properties makes the CaSi monolayer quite a promising candidate for applications in electronics, optoelectronics, and mechanics.

## Conceptual insightsChemical bonding is one of the most basic concepts of chemistry, and many established bonding rules are the foundations for the understanding of the structure and electronic properties of molecules and solids. Therefore, designing new materials with rule-breaking chemical bonding, e.g. planar hypercoordinate motifs, would be of both theoretical and practical importance. Based on multi-scale simulations, we demonstrate that a two-dimensional CaSi monolayer, in which each Si atom binds with five ligands to form a moiety of quasi-planar pentacoordinate silicon, is thermodynamically, dynamically and thermally stable. Our designed CaSi monolayer is the global minimum structure in 2D space; it possesses a moderate band gap and exhibits an unusually negative Poisson's ratio. |

As another group-14 element, silicon (Si) has distinct bonding characters from those of carbon. For instance, Si tends to utilize all three of its 3p orbitals to adopt the tetrahedral sp^{3} hybridization, whereas the planar hybridization of silicon is rather rare in nature. Extensive studies of planar hypercoordinate carbon have also motivated scientists to explore molecules with planar hypercoordinate silicon, especially considering that the planar tetracoordination is fundamentally easier to realize with silicon than with carbon.^{19} In 1979 Schleyer et al. predicted theoretically the first molecule containing a planar tetracoordinate silicon (ptSi) center, i.e. orthosilicic acid ester.^{20} Afterwards, many ptSi-containing molecules were designed computationally, such as tetraazafenestrane^{21} and Si(CO)_{4}.^{22} However, none of these molecules have been realized experimentally. The breakthrough occurred in 2000; Boldyrev et al.^{23} detected the first ptSi-containing molecule SiAl_{4}^{−} by a joint experimental and theoretical study. In 2004, Li et al.^{24} proposed a scheme to incorporate ptSi, planar pentacoordinate silicon (ppSi) and hexacoordinate silicon (phSi) in C_{2v}-B_{n}E_{2}Si (E = CH, BH, or Si; n = 2–5). Islas et al.^{25} designed several planar hypercoordinate silicon species by enclosing Si atoms in boron wheels. These studies significantly enriched the family of planar hypercoordinate silicon moieties. However, at present there are few studies focusing on planar hypercoordinate silicon, and global minimum structures with planar hypercoordinate silicon are rather rare.

It is known that the properties of a material are mainly determined by its structure, and the unique geometric structures usually lead to exotic physicochemical properties. Therefore, it is desirable to extend the bonding arrangements of planar hypercoordinate carbon and silicon into periodic solids and nanostructures, which would bring some unique structures and peculiar potentials for a wide range of applications. The past decade has witnessed the rapid development of this field.^{26–28} In particular, stimulated by the isolation of graphene and two dimensional (2D) inorganic materials, there has been growing interest in the design of 2D materials containing planar hypercoordinate carbon or silicon, e.g. ptC-containing B_{2}C,^{29} TiC,^{30} and Al_{2}C monolayers,^{31,32} ppC-containing Be_{5}C_{2} monolayers,^{33} phC-containing Be_{2}C monolayers,^{34} and ptSi-containing SiC_{2} monolayers.^{35} The novel geometric structures endow these 2D materials with many intriguing properties. For example, Wang et al.^{33} demonstrated that a Be_{5}C_{2} monolayer is semimetallic and has an unusually negative Poisson's ratio in the in-plane direction; thus it is appealing for specific applications in electronics and mechanics. The 2D Cu_{2}Si monolayer with phSi bonding was theoretically predicted by Yang et al. in 2015,^{36} and was just synthesized by Feng et al.^{37} Besides the unique bonding, Cu_{2}Si presents intriguing Dirac nodal line fermions, which open new avenues to realize high-speed low-dissipation devices.^{37} Nevertheless, to the best of our knowledge, there is no attempt at designing nanostructures with ppSi, which may be due to the difficulty in finding a suitable type of ligand to electronically or mechanically fit the ppSi in periodic systems.

Here, inspired by the bonding pattern of our newly discovered ppSi species Ca_{4}Si_{2}^{2−}, we recognize that calcium (Ca) is a promising ligand to construct ppSi-containing solids. Along this line, we computationally designed a new ppSi-featuring 2D material, namely the CaSi monolayer, in which each Si atom binds with four Ca atoms and one Si atom in almost the same plane to form a quasi ppSi moiety. The ppSi-containing CaSi monolayer has good thermodynamic, kinetic, and mechanical stabilities and is the global minimum structure in 2D space. Due to its exotic geometric structure, the CaSi monolayer presents rather attractive electronic, optical, and mechanical properties.

The bonding pattern of the CaSi monolayer was analyzed utilizing the Solid State Adaptive Natural Density Partitioning (SSAdNDP) method,^{47} which is an extension of the AdNDP method to periodic systems and as such was derived from periodic implementation of the Natural Bond Orbital (NBO) analysis. SSAdNDP allows the interpretation of chemical bonding in systems with translational symmetry in terms of classical lone pairs and two-center bonds, as well as multi-center delocalized bonds.

The thermal stability of the CaSi monolayer was assessed utilizing first principles molecular dynamics (FPMD) simulations within the PBE functional as implemented in VASP. The initial configuration with a 3 × 4 supercell was annealed at three temperatures. Each FPMD simulation (NVT ensemble) lasted for 10 ps with a time step of 1.0 fs. Temperature control is fulfilled using the Nosé–Hoover method.^{48}

The global minimum search for the lowest-energy structure of 2D CaSi was conducted using the particle-swarm optimization (PSO) method within the evolutionary scheme as implemented in the CALYPSO code.^{49} The population size and the number of generations were set to be 30 in all PSO simulations. We did three structural searches with the unit cell of CaSi monolayers containing 4, 8, and 16 atoms, respectively. The structure relaxations during the PSO simulation were performed using the PBE functional as implemented in VASP. All the structures obtained from the CALYPSO search were re-optimized using VASP.

The natural population analysis (NPA) charges and the Wiberg bond index (WBI) were then computed at the M06-2X/cc-pVTZ level of theory to understand the bonding characteristics of Ca_{4}Si_{2}^{2−}. According to our computations, the ppSi atom is negatively charged (NPA charge −1.55) and the natural electron configuration is 3s^{1.52}3p_{x}^{1.05}3p_{y}^{1.60}3p_{z}^{1}.^{34} These results suggest that ppSi in Ca_{4}Si_{2}^{2−} is mainly stabilized by the σ-donation of Ca atoms and the delocalization of silicon 3p_{z} electrons. The WBI values for ppSi−Ca bonds are 0.29 and 0.30, respectively, while the WBI of the Si−Si bond is 1.90, resulting in a total WBI of 3.08 for the ppSi center.

To further understand how the ppSi is stabilized in Ca_{4}Si_{2}^{2−}, we scrutinized the canonical molecular orbitals of Ca_{4}Si_{2}^{2−}. As shown in Fig. 1b, the most occupied molecular orbitals correspond to the σ bonding of ppSi and those between the peripheral Ca and Si atoms. In particular, HOMO−3 is a highly delocalized π orbital and HOMO−4 is a delocalized σ orbital, which could intrinsically help maintain the planar configuration. Interestingly, the number of π electrons in Ca_{4}Si_{2}^{2−} satisfies the Hückel (4n + 2) π-electron rule (n = 0), revealing the aromaticity of Ca_{4}Si_{2}^{2−}. Moreover, the considerable HOMO–LUMO gap (2.12 eV) also suggests the high stability of Ca_{4}Si_{2}^{2−}. Interestingly, the Ca_{4}Si_{2}^{2−} anion can be neutralized by two protons (H^{+}) to form a neutral molecule of Ca_{4}Si_{2}H_{2}, which is a local minimum with the lowest vibrational frequency of 26.4 cm^{−1}. In contrast to Ca_{4}Si_{2}^{2−}, Ca_{4}Si_{2}H_{2} has a slightly buckled rather than planar configuration (Fig. S1, ESI†).

Similar to our previously designed phC-containing Be_{2}C monolayer^{34} and ppC-containing Be_{5}C_{2} monolayer,^{33} the CaSi monolayer is not purely planar. As can be seen from the side view (Fig. 2a), the Ca atoms of the CaSi monolayer are buckled into two different atomic layers, which are 0.38 Å above or below the Si atomic layer, respectively. The sum of the three Ca–Si–Ca angles and two Ca–Si–Si angles associated with one ppSi is 364.44°, which is quite close to the ideal 360°, indicating the good planarity of ppSi moieties in the 2D CaSi monolayer. The lengths of the Si–Ca (2.97 Å, 3.04 Å) and Si–Si bonds (2.27 Å) of the CaSi monolayer are quite close to those of Ca_{4}Si_{2}^{2−}, whereas the Ca–Ca bond lengths (3.61 Å, 3.98 Å) depart a little from those of Ca_{4}Si_{2}^{2−}. Interestingly, the CaSi monolayer can be entirely planar by applying a biaxial tensile strain of 3.4%. However, this purely planar structure is 16 meV per atom higher in energy than the buckled one. According to the Hirshfeld charge population analysis, in the CaSi monolayer, the Si and Ca atoms possess −0.25 |e| and 0.25 |e| charge, respectively. The out-of-plane buckling in the CaSi monolayer could minimize the repulsive interactions between Ca cations and maintain the intensities of the in-plane Si–Ca and Si–Si bonds, which are favorable for the stabilization of the whole structure.

To understand the unique chemical bonding and the stabilizing mechanism of ppSi moieties in the 2D CaSi monolayer, we first plotted its deformation electronic density, which is defined as the difference between the total electronic density and the electronic densities of the isolated Si and Ca atoms. Significant electron transfer occurs from the 4s orbital of the Ca atoms to Si atoms (Fig. 2b), which are delocalized over the Si–Si and Ca–Si bonds, contributing to the stabilization of the ppSi moieties. Moreover, some electrons are also extracted from the 3p_{z} of the Si atoms to further stabilize the ppSi moieties. A similar stabilization mechanism has also been revealed in other 2D nanomaterials with planar hypercoordinate motifs.^{29–37}

To give a more robust analysis of chemical bonding and to understand in more detail how the lattice bonds of the CaSi monolayer are formed, we further employed the recently developed SSAdNDP method to analyze the CaSi monolayer. According to the SSAdNDP analysis (Fig. S2, ESI†), one unit cell of the CaSi monolayer contains two 2c-2e Si–Si bonds, eight 3c-2e σ bonds on eight Ca–Si–Ca triangles, and two 4c-2e π bonds on two Ca–Si–Ca–Si rhombuses, accounting for 24 valence electrons per unit cell. Noteworthily, the two Si atoms and two Ca atoms involved in a 4c-2e π bond are exactly in the same plane. The deduced bonding picture is consistent with the symmetry of the 2D network. Therefore, it is the existence of multicenter delocalized σ and π bonds that help in maintaining the quasiplanar configuration of the CaSi monolayer.

The kinetic stability of the CaSi monolayer can be confirmed by the phonon curves where no appreciable imaginary phonon mode is observed (Fig. 3). Remarkably, the highest frequency of the CaSi monolayer (475 cm^{−1}) is even higher than those in a MoS_{2} monolayer (473 cm^{−1})^{53} and Cu_{2}Si monolayer (420 cm^{−1}),^{36} but lower than that of silicene (550 cm^{−1}).^{54} According to the analysis of the phonon density of states, the highest frequency modes of the CaSi monolayer mainly correspond to the Si–Si bonds. Note that the purely planar CaSi monolayer achieved by a biaxial tensile strain of 3.4% is also dynamically stable as all phonon branches are positive in the entire Brillouin zone (Fig. S3, ESI†).

Fig. 3 Phonon spectrum (left) and phonon density of states (right) of the CaSi monolayer computed using the PBE functional. |

Moreover, we also performed first-principles molecular dynamics (FPMD) simulations to evaluate the thermal stability of the CaSi monolayer. Three independent FPMD simulations (900, 1200, and 1500 K) were carried out using a 3 × 4 supercell. As shown in Fig. S4 (ESI†), the CaSi monolayer can retain its structural integrity with slight out-of-plane distortions throughout a 10 ps FPMD simulation up to 1200 K, suggesting that the ppSi-featuring 2D CaSi phase can be separated by an enough barrier from other minimum structures on the potential energy surface, indicative of good thermal stability. In addition, we performed geometry optimizations starting from the distorted structures by FPMD at 900 K and 1200 K and found that these two structures can easily recover to their initial configurations, indicative of high phase stability.

The aforementioned results can guarantee that the CaSi monolayer is at least a good local minimum structure on the potential energy surface. Experimentally, the global minimum structures have more opportunities to be synthesized than other local minima. Is the ppSi-containing CaSi monolayer the global minimum? To address this issue, we performed a global minimum search for CaSi in the whole 2D space employing the particle-swarm optimization (PSO) method as implemented in the CALYPSO code. As a benchmark, CALYPSO predicted the graphene and h-BN monolayer structures with two-atom hexagonal unit cells by only one generation, suggesting the reliability and efficiency of the PSO algorithm in predicting stable 2D structures.

For 2D CaSi, we obtained three low-energy isomers within 30 generations, which are labeled as CaSi-I, CaSi-II, and CaSi-III (Fig. S5, ESI†). Actually, CaSi-I is just the ppSi-containing CaSi monolayer as discussed above. The structure of CaSi-II can be described as Si tetramers embedded in distorted Ca octagons. Interestingly, all the Si atoms in CaSi-II are also quasi ppSi. In contrast to CaSi-I and CaSi-II, each Si atom in CaSi-III binds with four neighboring Ca atoms to form a ptSi moiety. According to DFT computations, CaSi-I is 86 and 392 meV per atom lower in energy than CaSi-II and CaSi-III, respectively. Therefore, our designed CaSi monolayer is actually the global minimum structure in 2D space, which is the first global minimum of ppSi-containing species. We propose that a CaSi monolayer may be grown on suitable substrates by the chemical vapor deposition (CVD) or molecular beam epitaxy (MBE) method, similar to growing silicene^{50} and germanene^{51} on metal or metal oxide surfaces.

The partial DOS analysis demonstrates that the electronic states near the Fermi level of the CaSi monolayer are mainly contributed by the Si-3p and Ca-3d orbitals. It manifests that the empty Ca-3d orbitals split in the CaSi monolayer, and there is a finite probability for Si to back donate some of its received electrons to the low-lying 3d orbitals of Ca, leading to a partial occupancy of 3d orbitals and strong p–d hybridization. This electron donation/back-donation mechanism essentially helps in stabilizing the 2D CaSi network. We also plotted the partial charge densities associated with the VBM and CBM of the CaSi monolayer to give a more explicit picture of its electronic structure. As shown in Fig. 4b and c, the VBM and CBM of the CaSi monolayer are mainly contributed by the multicenter bonding and anti-bonding between Si and Ca atoms, respectively.

The moderate band gap would make the CaSi monolayer a suitable candidate for optoelectronics. To give an intuitive demonstration of the optical properties, we also computed the imaginary part of the dielectric function (ε_{2})^{61} of the CaSi monolayer using the HSE06 functional (the PBE results are shown in Fig. S8, ESI†). As shown in Fig. 5, the optical absorption of the CaSi monolayer along the x and y directions covers both the visible and ultraviolet light regions. Remarkably, the absorption along the y direction is much stronger than that of the x direction. In comparison to the x and y directions, the optical absorption along the z direction is much less pronounced. The above results indicate that the CaSi monolayer possesses good capacity for light-harvesting and has unique optical anisotropy.

U_{ε} = E_{ε} – E_{0} = ½C_{11}ε_{x}^{2} + ½C_{22}ε_{y}^{2} + C_{12}ε_{x}ε_{y} + 2C_{66}ε_{xy}^{2} | (1) |

On the basis of derived elastic constants, the in-plane Young's modulus (Y) of the CaSi monolayer can be computed by Y_{x} = (C_{11}C_{22} − C_{12}C_{21})/C_{22} = 21.83 N m^{−1} and Y_{y} = (C_{11}C_{22} − C_{12}C_{21})/C_{11} = 24.61 N m^{−1}, which are much lower than those of graphene (∼341 N m^{−1})^{63} and a MoS_{2} monolayer (∼128 N m^{−1}),^{64} suggesting that the CaSi monolayer is a rather soft material with good flexibility. The small difference in Young's modulus in different directions indicates that the CaSi monolayer is mechanically anisotropic to a rather small extent.

Remarkably, the negative C_{12} of the CaSi monolayer leads to negative Poisson's ratios of −0.15 (C_{21}/C_{22}) and −0.16 (C_{12}/C_{11}) in the x and y directions, respectively. Physically, the Poisson's ratio is defined as the negative ratio of the transverse contraction to the longitudinal extension. In nature, most common materials have positive Poisson's ratios as they will become thinner in cross section when they are stretched. Materials with negative Poisson's ratios, which are known as auxetic materials,^{65} can expand laterally when stretched. As a verification, we found that the equilibrium lattice constant of the CaSi monolayer in the y(X) directions is stretched by ∼0.3% when the lattice is subjected to a tensile strain of 2% in the x(y) direction (Fig. 6), confirming the negative Poisson's ratio of the CaSi monolayer.

The negative Poisson's ratio would endow the CaSi monolayer with multiple merits, such as enhanced toughness, self-adaptive vibrational damping and improved shear stiffness. With so fascinating mechanical properties, the CaSi monolayer can be utilized in many specific fields, e.g. superior dampers, piezocomposites, and nanoauxetic materials. Recently, 2D black phosphorus has been first predicted theoretically^{66} and then observed experimentally^{67} to have a negative Poisson's ratio. Some hypothetical 2D nanostructures, including but not limited to penta-graphene,^{68} borophane,^{69} silica^{70} and our previously designed Be_{5}C_{2} monolayer,^{33} were also revealed to possess a negative Poisson's ratio. Note that the negative Poisson's ratios of black phosphorus and borophane were observed in the out-of-plane direction, while the negative Poisson's ratio of our CaSi monolayer was found in the in-plane direction. Remarkably, the negative Poisson's ratio of the CaSi monolayer is much higher than those of black phosphorus, penta-graphene and borophane, and is comparable to those of silica and a Be_{5}C_{2} monolayer. No doubt, the unusually negative Poisson's ratios in these 2D structures should be derived from their novel atomic configurations.

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## Footnote |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7nh00091j |

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