The article information
 Haoqi Chen, Huan Shan, Aidi Zhao, Bin Li
 陈浩琪, 单欢, 赵爱迪, 李斌
 FirstPrinciples Study of Two Dimensional Transition Metal PhthalocyanineBased MetalOrganic Frameworks in Kagome Lattice
 二维kagome晶格过渡金属酞菁框架的第一性原理研究
 Chinese Journal of Chemical Physics, 2019, 32(5): 563571
 化学物理学报, 2019, 32(5): 563571
 http://dx.doi.org/10.1063/16740068/cjcp1810227

Article history
 Received on: October 15, 2018
 Accepted on: November 1, 2018
b. Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Twodimensional metalorganic frameworks (MOFs) have attracted great attention for their intriguing properties. Compared with the existed 2D organic systems [15], especially the carbonbased sheets, many 2D MOFs not only exhibit great capacity of conductivity and lightharvesting, but also manifest applications in other regions as catalysis, gas storage, and particular magnetism attributed to the coordinating with metal atoms [611]. Transition metal phthalocyaninebased 2D MOFs are one of such materials that have long been studied in order to achieve tunable electronic, optical, and magnetic properties through substitution of transition metal (TM) atoms. In the structure of TMPc, the TM atoms are located at center of the host phthalocyanine (Pc) and coordinated with four nitrogen atoms, so they are prevented from clustering when the TMPc molecules form 2D structure. For the TMPc, the magnetism is owing to the unfilled d shell of the TM atom, and the optical properties are generally determined mainly by the ligands. Successfully synthesizing 2D periodic TMPcbased monolayer in experiment [12, 13] provided a novel synthetic method for exploring polyTMPc structures with fascinating properties, and new types of 2D MOFs based on the TMPcs and their derivatives have been synthesized subsequently [1418]. In addition, theoretical studies predicted potential applications of these 2D TMPcbased MOFs in hydrogen storage [19], CO
In order to expand family of 2D TMPcbased MOFs and further explore their properties and applications, here we propose an intriguing TMPcbased porous monolayer with geometric frustrated kagome lattice. The spin ordering of kagome systems are of interest and are investigated intensively due to the existence of spin frustration [2528]. The kagome lattice is composed of interlaced equilateral triangles, so that if the spins on the vertices prefer to be antiferromagnetic (AFM) coupling, the structural arrangement of spins precludes simultaneous satisfaction of the nearestneighbor interactions. Especially, the
In this work, by employing firstprinciples calculations, we have systematically investigated the electronic structure, magnetic behaviors, and optical properties of freestanding 2D kagTMPc frameworks. Both the 2D metalfree (MF) and TM phthalocyanine frameworks are taken into account and the kagMFPc framework could be regarded as the host structure. For the kagTMPc frameworks, we choose 3d TM atoms varying from Cr to Zn in the periodic table. The 2D kagMFPc framework is a nonmagnetic semiconductor with a direct band gap of 1.25 eV. When the TM atoms (Cr, Mn, Fe, Co, Ni, Cu, Zn) are introduced, the magnetic moments per unit cell of the kagTMPc are approximate to 4, 3, 2, 1, 0, 1, and 0 μ
Our firstprinciples calculations based on spinpolarized density functional theory (DFT) are carried out in the framework of the projector augmented wave (PAW) method [30, 31] with the PerdewBurkeErnzerhof type generalized gradient approximation [32], implemented in Vienna Ab initio Simulation Package (VASP) [33]. All selfconsistent calculations are performed with an energy cutoff of 400 eV for the planewave expansion of electron wavefuctions. The Brillouin zone integration is generated in a grid of 5
The MF phthalocyanine is always regarded as the host material of abundant TMPc derivates. Comprehension of intrinsic properties of organic ligand parts separated from the TM atoms in this type of system is of significance and can inform us the specific characters related to H, C, and N. For an MF phthalocyanine monomer, i.e., H
Next we will discuss the situations of 3d TM atoms coordinated frameworks. The TM atoms are located at the center of the Pc pores, and each TM atom donates two 4s electrons to the Pc ligands so that it is bonded with the adjacent nitrogen and remains in the +2 valence state. Structural optimization shows that the TM atoms are dispersed uniformly on the kagome vertices, and the lattice constants of the 2D kagTMPc frameworks (TM atom varying from Cr to Zn) are shown in FIG. 6 and Table Ⅰ. The bond length between the TM atom and its adjacent N atom increases along the association direction of TMPc units (
Spin polarization calculations are carried out to investigate the magnetism in the 2D kagTMPc frameworks. The calculation results show that except for the kagNiPc and kagZnPc frameworks which are nonmagnetic, all the other kagTMPc frameworks have spinpolarized ground states. The magnetic moments per unit cell of the 2D kagTMPc frameworks are 12, 9, 6, 3, and 3 μ
Since the 4s electrons of the central TM atoms have been involved in the chemical bonding between the TM atoms and the nearest N atoms, the local magnetism in the 2D kagTMPc framework is considered to originate from spinsplitting of the 3d electrons of the central TM atoms. Due to the kagome crystalline field and D
To learn about the magnetic coupling interactions and magnetic ground state of the 2D kagTMPc systems, we have considered and calculated their electronic states with both the FM and AFM coupling between the TM atoms. In the FM state, all the spins on the TM atoms are parallel. But in the AFM state, it is noteworthy that there possibly exists spin frustration, since each unit cell contains three TM atoms located on the equilateral triangle and the AFM coupling between arbitrarily two adjacent TM atoms can't be satisfied simultaneously. So we reverse one spin of each unit cell in the FM state and obtain a spin frustrated (SF) magnetic state which is considered to represent the AFM state. The calculated magnetic exchange energy
Since the 2D kagMnPc framework exhibits stable FM ordering, we have explored the magnetic behaviors under finite temperature by performing the MC simulations. Without an external field, the Hamiltonian of the Heisenberg model can be written as:
$ \begin{eqnarray} H =  \sum\limits_{\langle {i, j}\rangle } {{J_\alpha} {\textbf{S}_i}\cdot{\textbf{S}_j}} \end{eqnarray} $  (1) 
where exchange integral
$ \begin{eqnarray*} {J_1}={E_\rm{ex}}/(8S^2) \end{eqnarray*} $ 
Therefore, we estimate that the exchange integral
$\begin{eqnarray*} {C_\rm{V}}={\mathop {\lim }\limits_{\Delta T \to 0} \frac{\Delta E_T}{\Delta T}} \end{eqnarray*} $ 
Here
The spin ordering of kagome antiferromagnets is very attractive because of various unique features in their phase transitions. Messio et al. [25] provided the regular magnetic orders in frustrated kagome lattice and discussed relative stability of various possible magnetic orders, with the second and thirdneighbor exchange interactions being also taken into account. The geometries of various exchange paths in our 2D kagCrPc framework are defined in FIG. 4(a), and we try to analyze its magnetic ordering in the ground state by adopting the
So we employ the
$ \begin{eqnarray} H =  \sum\limits_{\langle {i, j}\rangle } {J({\textbf{S}_i^x}{\textbf{S}_j^x} + {\textbf{S}_i^y}{\textbf{S}_j^y} + \Delta {\textbf{S}_i^z}{\textbf{S}_j^z})} \end{eqnarray} $  (2) 
where
The TMPc compounds and relevant derivatives are well known for their extensive applications as optical materials. Especially, the 2D ZnPcbased metal organic framework has also been proven to have an appropriate absorber gap and interface band alignment as the donor and acceptor so that it is promising for high efficiency solar cell [21], which motivates us to study the optical properties of the 2D kagTMPc frameworks in depth. The electronic density of states (DOS) of the H
To explore the specific performance in light absorption, we carry out the calculations of the absorption coefficients of the TMPc molecules and the corresponding 2D kagTMPc frameworks. The frequency dependent dielectric function
$ \begin{eqnarray} \alpha (\omega ) = \sqrt 2 \omega {\left[ {{\varepsilon _1} + {{\left( {{\varepsilon _1}^2(\omega ) + {\varepsilon _2}^2(\omega )} \right)}^{1/2}}} \right]^{1/2}} \end{eqnarray} $  (3) 
In order to compare the intensities of optical absorptions between the TMPc molecules and TMPc based frameworks, we divide the absorption coefficient
By employing the firstprinciples calculations, we have systematically studied the electronic, magnetic, and optical properties of the 2D TMPcbased kagome metalorganic frameworks. Our calculations indicate that the 2D kagMnPc framework is an FM semiconductor with narrow band gap of 0.09 eV and the Curie transition temperature is about 125 K, and the easymagnetization axis is perpendicular to the framework plane. The 2D kagCrPc framework is an
This work was supported by the National Key Research & Development Program of China (No.2016YFA0200604 and No.2017YFA0204904), the National Natural Science Foundation of China (No.21473174), the Fundamental Research Funds for the Central Universities (No.WK2340000074 and No.WK2060190084). The computational resources of Supercomputing Center of University of Science and Technology of China, Supercomputing Center of Chinese Academy of Sciences, Tianjing, and Shanghai Supercomputer Centers are also acknowledged.
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b. 中国科学技术大学量子信息与量子科技前沿协同创新中心，合肥 230026