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Deformation of Tetrahedron Structures Via Doping Two Atoms with Elements

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Deformation of Tetrahedron Structures Via Doping Two Atoms with Elements J. Chem. Sci. (2019) 131:37 © Indian Academy of Sciences https://doi.org/10.1007/s12039-019-1613-x REGULAR ARTICLE Deformation of E4 (E = P, As, Sb) tetrahedron structures via doping two atoms with elements from group 13: a study of the pseudo-Jahn–Teller effect ALI REZA ILKHANIa,b,∗ aDepartment of Chemistry, Yazd Branch, Islamic Azad University, Yazd, Iran bDepartment of Chemistry, University of Alberta, Edmonton, AB T6G 2G2, Canada E-mail: [email protected] MS received 9 January 2019; revised 22 February 2019; accepted 3 March 2019; published online 2 May 2019 Abstract. White phosphorus and yellow arsenic are the most famous inorganic four-membered tetrahedral molecules in nature. Due to the recent application of the tetrahedron-based system as a carrier in drug delivery, the manipulation of the E4 (E = P, As, Sb) tetrahedron structure by replacing two of the E atoms by elements from group 13 (D = Al, Ga, In) has been computationally explored. The symmetry-breaking phenomenon induced by the pseudo-Jahn–Teller effect was reported in the E2D2 tetrahedral structure. State averaging of the four low-lying electronic states along the a2 deformation normal coordinate for the series in CASSCF(4,4)/cc– pVTZ–(PP) was carried out to formulate the (1A1 + 2A1 + 1A2) ⊗ a2 PJTE problem and their corresponding coupling constants estimated by fitting the obtained state energies. Moreover, the deformed C2v tetrahedral configuration of E2D2 can be restored by i) the protonation of the D atoms or ii) trapping a noble gas dication in the center cavity cage of the systems. Furthermore, the calculated thermodynamic properties of the E2D2 show that the protonation reaction acts as a spontaneous process fulfilling the G < 0 conditions and the considered series obeys the Bronsted–Lowry base behaviors. Keywords. Pseudo-Jahn–Teller interaction; APES; electronic state mixing; deformed tetrahedron. 1. Introduction and the high-temperature instability and photoelec- + + tron spectrum of the P4 and As4 tetrahedron were 3 An important aspect of drug delivery relies on dosage investigated. The P4 tetrahedron is an air-sensitive control and managing the side effects. A portion of hydrophobic system that can be quelled by encapsu- this can be circumvented with the use of nano drug lating it in a tetrahedral assembly of iron (II) ions and 4 carriers. This can help combat the issues of drug resis- short organic chains. The P4 tetrahedron and the P8 tance and uptake inefficiencies common in conventional cubic structures have been computed and the phospho- deployment. The tetrahedron is one of the stable platonic rus strain rings between them were compared. 5,6 The structures in chemistry that are being paid recent atten- MNDO calculation was employed to show stability in 1 tion in DNA tetrahedron-based drug delivery systems. the P4 tetrahedron as well as the forbidden dissocia- ( = , , ) 7 The presence of a cavity cage in the P4 E P As Sb tion from the Td to the D2d symmetry. Although the tetrahedron systems makes them interesting as carriers P8 cubic structure has not been identified as a stable of other substances in the field of computational chem- P allotrope, yet in reality, the MNDO calculations dis- istry. Despite the high angle strain found in tetrahedrons, played that the P8 cubical structure is more stable than ( ) ( ) 8 white phosphorus P4 and yellow arsenic As4 are the P4 tetrahedron in gaseous media. The decomposi- existing tetrahedral allotropes of P and As. Even for tion pathway from P4 to P2 has been studied through the element phosphorus, the P4 tetrahedron is defined as calculating thermochemical properties as well as a ther- the standard state. mal and photolysis reaction. 9–11 The decomposition constant of the P4 tetrahedron into The Jahn-Teller (JT) problem has been treated for the 2 + two P2 in the gas phase was experimentally tracked P4 tetrahedral structure and the linear coupling con- + stant for E4 (E = P, As, Sb) corroborated with the *For correspondence experimental spectra. 12 Moreover, the combination of 1 37 Page 2 of 9 J. Chem. Sci. (2019) 131:37 + JT and pseudo-Jahn-Teller effects (PJTE) of the P4 tetrahedral structure was studied by Koppel 13 and the + JT effect of P4 tetrahedral structure was formulated as 2 14 T2 ⊗ (t2+ e) problem. The PJTE is the only source to explain the ori- gin of structural instability and spontaneous symmetry breaking in any unstable symmetrical system. 15,16 It was specifically employed to answer why some sys- tems in their high-symmetry are unstable and deform Figure 1. Illustration of the symmetry breaking phenom- to lower-symmetry stable structures, called symmetry 17–24 ena and deformation of the C2v tetrahedral configuration to breaking phenomena, in several types of research. the equilibrium structure with C2 symmetryinP2Ga2 system. The PJTE has also been applied to rationalize the reason for instability in two-dimensional materials 25–29 as well as tracking the origin of puckering in unstable planar atoms with geometry optimization and following fre- 30–32 systems. Another application of the PJTE is to find quency calculations for E2Al2 (E = P, As, Sb) series a way to restore the planarity of distorted molecules. To computed. An imaginary frequency along a2 normal do this, nonplanar puckered molecules were coordinated coordinate was observed for E2Al2. It was proven that by rings, atoms, or ions, which suppresses the PJTE in the considered systems are unstable in their tetrahedral 33–38 complexed systems. C2v configuration. Indeed, observing the imaginary fre- quency in E2Al2 series points to the occurrence of the 2. Methods and computational details symmetry breaking phenomena (SBP) from C2v high symmetry to the equilibrium structure C2 lower sym- Due to the importance of accurate structural models of carriers metry. in drug delivery, with the goal of understanding parameters Subsequently, Al atoms in E2Al2 series were replaced that may affect carrier structure, the E4 (E = P, As, Sb) tetra- with other elements from group 13 along with geometry hedron were manipulated by replacing two of the E atoms and frequency calculations. All E2D2 (E = P, As, Sb; D from group 13 elements (D = Al, Ga, In) and the result- = Ga, In) systems with a tetrahedral structure show sim- ing E2 D2 tetrahedral structure has been computationally ilarity in an imaginary frequency along the a2 instability explored. Geometry optimizations and follow up frequency normal coordinate. Hence, P Ga , P In ,andAsGa calculations for both the tetrahedron C symmetry and 2 2 2 2 2 2 2v were specifically explored due to their higher imagi- deformed (C2) configurations in all E2D2 considered sys- tems were accomplished using the density functional theory nary frequency values. The SBP from high–symmetry with the B3LYP method 39 at the cc–pVTZ 40–42 basis set. the C2v tetrahedral configuration to the C2 equilibrium Whereas Sb and In atoms are restricted in the cc–pVTZ basis structure for P2Ga2 as representative of the E2D2 sys- set, the cc-pVTZ–PP pseudopotential basis set 43–45 is used tems are illustrated in Figure 1. Normal modes in X and instead in the computation of the Sb2Al2 and P2In2 systems. Y Cartesian axis for Ga and P atoms are differentiated The state average-complete active space self–consistent field by different colors and directions. 46–48 (SA–CASSCF) wave-function method was employed to To compare the effect of deformation in the E2D2 compute the ground and low-lying excited states along the a2 series under consideration, geometrical parameters in deformation normal coordinate and to provide correspond- the form of bond lengths (Å), angles, and dihedral angles ing adiabatic potential energy surface (APES) cross-sections. (degrees), imaginary frequencies (cm−1), and dipole According to the frequency calculations of the E2D2 systems, moment (Debye) for both unstable tetrahedral con- the four active electrons and four active orbitals that composes figurations (C symmetry) and deformed equilibrium the CAS(4,4) active space was chosen on account of ratio- 2v structures of the E2Al2 (E = P, As, Sb), P2D2 (D = nalizing electronic configurations, molecular orbital energies , ) and symmetry elements of the systems. The MOLPRO 2015 Ga In and As2Ga2 systems are provided in Table 1. package 49 carried out all computations in this article. Table 1 shows that all geometrical parameters in C2v tetrahedral configuration change due to deforma- tion in the E2D2 systems. Particularly, the E–D–E and 3. Results and Discussion D–E–D angles expand significantly from tetrahedral to deformed equilibrium structures in all compounds of 3.1 Tetrahedral and deformed configurations the series. In addition, E–D–D–E and D–E–E–D dihe- dral angles also contract slightly from the C2v to the Initially, the E4 (E = P, As, Sb) tetrahedron structure C2transition. Moreover, increasing the size of either E was manipulated by replacing two vertices with Al or D atoms in both of the manipulated E2Al2 and P2D2 J. Chem. Sci. Table 1. Geometry parameters, imaginary frequencies, normal modes, and dipole moment of E2Al2 (E = P, As, Sb), P2D2 (D = Ga, In) and As2Ga2 systems in unstable tetrahedral configuration (C2v symmetry) and deformed equilibrium structure with C2 lower symmetry. P2Al2 As2Al2 Sb2Al2 P2Ga2 P2In2 As2Ga2 Tetrahedral Deformed Tetrahedral Deformed Tetrahedral Deformed Tetrahedral Deformed Tetrahedral Deformed Tetrahedral Deformed Geometry (2019) 131:37 parameters (C2v) (C2) (C2v) (C2) (C2v) (C2) (C2v) (C2) (C2v) (C2) (C2v) (C2) Bond E1–E2 2.399 3.189 2.535
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