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 origin of structural instability and spontaneous symmetry breaking in any unstable symmetrical system. 15,16 It was specifically employed to answer why some systems 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 frequency 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 systems 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 deformation 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 dihedral 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. (2019) 131:37 Page 3 of 9 37 ) 2 C ( 2 Deformed Ga 2 ) As 2v 0609 0567 – . . C systems in unstable ( 0 0 2 ± ± Tetrahedral Ga 2 ) 2 C ( and As ) 2 Deformed In In , 2 P ) Ga 2v 1128 – 0304 . . = C ( 0 0 D ± ± ( Tetrahedral 2 D 2 ) P 2 C ), ( Sb 2 Deformed , Ga As 2 , P ) P 2v 1057 – 0470 . . C = ( 0 0 E ± ± ( Tetrahedral 2 Al 2 ) 2 C ( 2 Deformed Al 2 lower symmetry. ) 2 Sb 2v 0273 – 1232 . . C ( 0 0 ± ± Tetrahedral ) 2 C ( 2 Deformed Al 2 ) As 2v 1167 0420 – . . C ( 0 0 ± ± Tetrahedral ) 2 C ( 2.8802.2952.294 3.081 2.40245.98 2.40188.0451.13 3.42651.11 2.618 46.9277.75 2.617 86.19 50.11 2.953 50.08 2.32367.23 47.23 79.80 2.32173.40 83.8470.40 48.83 2.490 48.82 2.521 67.86 45.09 82.35 2.520 73.23 89.84 70.47 50.51 2.655 50.52 2.863 68.24 42.44 78.97 2.862 72.84 90.12 70.50 53.01 53.04 67.89 44.86 79.05 73.21 89.88 70.42 52.11 53.13 68.25 76.52 71.83 70.44 68.80 72.48 70.48 2 Deformed Al 2 P ) 2v 0995 – 0867 . . C 3.26 2.66 2.89 2.48 2.10 2.03 2.72 2.20 3.46 2.63 2.40 1.62 0 0 ( 2.399 3.189 2.535 3.282 2.810 3.662 2.459 3.279 2.68270.53 3.720 70.39 2.596 70.53 3.592 70.42 70.53 70.45 70.53 70.47 70.53 70.46 70.53 70.48 246.7 – 217.6 – 215.0 – 242.2 – 155.2 – 194.7 – 60.00 45.97 60.00 46.89 60.00 47.21 60.00 45.08 60.00 42.43 60.00 44.83 symmetry) and deformed equilibrium structure with C ± ± Tetrahedral 2v 3 1 4 4 2 2 –E –E –E –D –D –D 3 4 4 3 2 1 4 4 4 3 4 4 3 1 2 2 2 2 4 –E –E –D –D –D –E –E –D –E –E –D –D –D –E –D –D –D –D 3 4 4 D 3 4 3 3 4 3 3 4 3 4 1 2 3 4 1 1 1 2 2 2 − –D –D –E –E –D –E –D –E –E –D –D –D –E –D –D –E –E –D –D –D –D –D –D 3 3 3 4 3 3 D E 1 1 2 1 2 1 2 1 2 1 1 1 2 1 2 1 2 1 E E E E E E E D E D E D E E E E E E D D D E E E Y X Geometry parameters, imaginary frequencies, normal modes, and dipole moment of E ) 1 − cm freq. ( length (Å) angle (deg) modes in Cartesian moment (Debye) tetrahedral configuration (C Imaginary Table 1. Geometry parameters Bond Angle (deg) Dihedral Normal Dipole 37 Page 4 of 9 J. Chem. Sci. (2019) 131:37

Table 2. Main electronic conﬁguration and their coefﬁcients in the E2Al2 (E = P, As, Sb), P2D2 (D = Ga, In) and As2Ga2 systems.

State symmetry Electronic conﬁguration Coefﬁcients

P2Al2 As2Al2 Sb2Al2 P2Ga2 P2In2 As2Ga2

2 2 1A1 1a1 1b1 0.9169 0.9399 0.8679 0.9360 0.9467 0.8687 2 2 1a1 1a2 −0.0840 −0.0554 0.1571 −0.0184 −0.0857 0.2258 2 2 1b1 1a2 −0.1726 −0.1490 −0.3999 −0.2414 −0.1956 −0.5389 2 2 2A1 1a1 1b1 −0.0893 0.1032 0.4382 0.2027 0.1470 0.5888 2 2 1a1 1a2 0.7351 −0.6537 −0.5456 −0.6100 −0.4865 −0.5232 2 2 1b1 1a2 −0.6057 0.6793 0.6657 0.7089 0.5751 0.8041 2 1 −1 1B1 1a1 1b1 1a2 0.6453 0.6482 0.6644 0.6297 0.6678 0.6720 2 1 −1 1a1 1b1 1a2 −0.6453 −0.6482 −0.6644 −0.6297 −0.6678 −0.6720 1 1 −1 −1 1a1 2a1 1b1 1a2 0.2019 0.1992 0.1758 0.1847 0.1721 0.1627 −1 −1 1 1 1a1 2a1 1b1 1a2 0.2019 0.1992 0.1758 0.1847 0.1721 0.1627 −1 2 1 1A2 1a1 1b1 1a2 −0.5157 −0.5567 −0.6480 −0.6297 −0.6584 −0.6656 1 2 −1 1a1 1b1 1a2 0.5157 0.5567 0.6480 0.6297 0.6584 0.6656 2 1 −1 1a1 2a1 1a2 −0.3998 −0.3569 −0.2367 −0.2718 −0.2139 −0.2033 2 −1 1 1a1 2a1 1a2 0.3998 0.3569 0.2367 0.2718 0.2139 0.2033

series correspondingly increases the D–E–D angles as Table 2 shows that the highest coefficient in the 2 2 opposed to the imaginary frequency magnitude, as well 1A1 ground state belongs to the 1a1 1b1 electronic as the D–D–E–E dihedral angels, across both the series. configuration which indicates that four active electrons Furthermore, the dipole moment value decreases from are placed in the HOMOs with a1 and b1 symmetries. −1 2 1 1 2 −1 the C2v tetrahedral configuration to the C2 equilibrium Additionally, the 1a1 1b1 1a2 and 1a1 1b1 1a2 in the structure in all the E2D2 systems. 1A2 excited state electronic configurations demonstrate Hence, the size of an atom is a very important fac- an electron excitation from HOMO with a1 symmetry tor in the chemical behavior of its included systems, to a LUMO with a2 symmetry. By tracking the sym- thereby requiring the effect of atoms size in deformation metry of the orbitals in the electronic configurations, of the E2D2 series to be explored. Due to the imagi- only two LUMOs with a1 and a2 symmetries contributed nary frequency magnitudes in Table 2, when P atoms in the electron configurations. In the other words, two instead with larger atoms (As or Sb) are explored, the HOMOs (1a1, and 1b1) with two LUMOs (2a1, and 1a2) instability in the E2Al2 series decreases from 246.7 to compose the (4,4) active space that was employed in −1 215.0cm . In a similar way, replacing Al by Ga and the SA–CASSCF calculations of the 1A1 ground and In atoms reduced the imaginary frequency to 242.2 and three 1B1,2A1, 1A2, low–lying excited states in the −1 155.2cm in P2Ga2 and P2In2 systems, respectively E2D2systems. (except in the P2Ga2 and As2Ga2 series, in which it is Comparing the molecular orbital energies in the series the opposite). to find the similarities in their electronic configurations guides us to choose an appropriate active state for the 3.2 Electron configurations and excitation CASSCF calculation. This helps to reduce the number of independent parameters of the calculation in the study.

Electronic calculations were done for the 1A1 ground Consequently, based on observed symmetry breaking state and three low–lying excited states (1B1, 2A1, 1A2) phenomena from a C2v tetrahedral configuration to the corresponding to the tetrahedral configuration of the equilibrium structure with C2 symmetry, an active space considered E2D2 series. Here, 2, 1 and −1 super- that at least concludes an a1 andana2 in the HOMOs and scripts denote pair–electrons and an electron in different LUMOs should be chosen for the calculation. Indeed, orientations, respectively. Whereas, 1 and 2 prefixes the chosen active space must have potential with a suffi- indicate the first and second orbitals in similar symme- cient electron excitation, which matches with the PJTE try. The main electronic configurations and their related in the series. Whereas in the systems under considera- coefficients for the mentioned states are provided in tion, the HOMO and HOMO−1areina1 and b1 while Table 2. the LUMO and LUMO+1 are in a2 and a1 symmetries J. Chem. Sci. (2019) 131:37 Page 5 of 9 37

Figure 2. The adiabatic potential energy surface cross-sections (in eV) for the ( = , , ), E2Al2 E P As Sb P2D2 (D = Ga, In) and As2Ga2 systems along the Qa2 instability directions. Note the changing energy scale in the profiles. that justify why four electrons in four active orbitals are deformed C2 structure. Additionally, the 1A2 excited suitable for this study. state demonstrates stability along the Qa2 that corrob- orates with the condition of effective mixing between states via the expected PJTE (1A1 +1A2)⊗a2 problem. 3.3 Adiabatic potential energy cross-sections The symmetry of the A1,andA2 states in C2 deformed structure in all E D series is A symmetry. Thus, any Based on observations of an electron excitation from a 2 2 1 other low-lying excited states with a similar symmetry to a molecular orbitals, and regarding the normal modes 2 that is placed lower than 1A states in the APES must of the imaginary frequencies of the E D series oriented 2 2 2 be added in the (1A +1A +···) ⊗a PJTE problem. in the a direction that was given in Table 1, the origin 1 2 2 2 Hence, the second excited state in Figure 2 has an A of the SBP in the series is a PJTE (1A + 1A ) ⊗ a 1 1 2 2 symmetry. It should be contributed as a modified form of problem. In other words, the SBP in the E D series is 2 2 the (1A +2A +1A ) ⊗a PJTE problem. Although, caused by mixing the unstable 1A ground state with 1 1 2 2 1 the first excited sate (1B ) is located between the 2A negative curvature and a stable low-lying A excited 1 1 2 and 1A , it is specifically very close to the 1A ground state which should show a positive curvature along the 2 1 state in the P Al , due to its B symmetry and is not to a normal coordinate. State averaging CASSCF calcu- 2 2 2 be added in the problem. lations via the (4,4) active space were accomplished for the ground (1A1), and low-lying excited (2A1, 1B1, and ) 1A2 states corresponding to the E2D2 series considered. 3.4 The pseudo Jahn-Teller effect due to deformation The obtained adiabatic potential energy surface (APES) cross-sections of the energy states around the Qa2 insta- Following the procedure of the general theory that has ble directions were illustrated in Figure 2. been introduced by Bersuker, 15,16 the wavefunction of The APES cross sections in Figure 2 reveals that all the ground and two low-lying excited states with A sym- considered E2D2 (E = P, As, Sb) systems are unstable metry were assumed as |1A1, |2A1 and |1A2 and the in their 1A1 ground state, which is shown by a neg- interval energies between the 1A1 ground and 2A1 and ative curvature, from tetrahedral C2v configuration to 1A2 excited states by the and , respectively. Thus, 37 Page 6 of 9 J. Chem. Sci. (2019) 131:37

Table 3. The second order corrections, K1 − p1, K2 − p2, and K3 − p3; the PJTE coupling constants, F, and G; and interval energies , for the E2Al2 (E = P, As, Sb), P2D2 (D = Ga, In) and As2Ga2 systems series obtained by ﬁtting Equation (7) to the calculated the APES proﬁles in Figure 2. Systems K − p eV K − p eV K − p eV F eV G eV (eV) (eV) 1 1 Å2 2 2 Å2 3 3 Å2 Å Å

P2Al2 2.14 5.05 2.09 1.99 4.12 0.80 1.07 As2Al2 1.78 −0.59 1.92 1.85 −2.11 0.97 1.03 Sb2Al2 1.31 −1.48 1.63 1.72 −1.16 1.46 1.52 :P2Ga2 1.10 −1.63 1.84 1.88 −1.93 1.34 1.39 P2In2 1.43 −1.11 1.45 1.61 −1.44 1.48 1.68 Ga2As2 1.29 −1.70 1.64 1.69 −1.63 1.65 1.66

the (1A1 + 2A1 + 1A2) ⊗ a2 PJTE problem makes the Here, F1n, F2n, F3n are referred to as the vibronic cou- 1A1 ground state unstable and the necessary condition pling constants between the 1A1 2A1, 1A2 (as first, of instability around the Qa2 normal coordinate yield in second, third A symmetry) states and the n high–energy Equation (1): excited state and E is corresponded to their energies. × 2 The 3 3 secular Equation (2) can be simplified by < F using f, g, a, b,andc denotations to Equation (6). − (1) K3 p3 a − ε 0 f And the secular matrix equation of the problem is for- 0 b − ε g = 0(6) mulated as Equation (2): fgc− ε (K −p ) 1 1 Q2−ε 0 FQ After the Equation (6) expansion, the mathematical 2 ( − ) K2 p2 2+−ε = solutions are provided as Equation (7). 0 2 Q GQ 0 (K −p ) ⎧ FQ GQ 3 3 Q2+− ε 2 ⎨ ε1 + ε2 + ε3 = a + b + c (2) ε ε + ε ε + ε ε = + + − 2 − 2 ⎩ 1 2 2 3 1 3 ab ac bc f g (7) ε ε ε = abc + cf 2 + bg2 where, primary force constants and the vibronic cou- 1 2 3 , , , ) pling constants are K1 K2 K3 (for 1A1 2A1,1A2 Accordingtothe(1A1+2A1+1A2)⊗a2 problem in E2D2 and F, G, respectively. Those mentioned constants can systems, f, g, a, b,andc variables were fitted from the be introduced in the following Equations (3)and(4). obtained energies in the APES cross-sections profiles in Figure 2 and their related PJTE coupling constants (F K =1A | ∂2 H/∂ Q2 |1A , 1 1 0 1 and G), as well as of the perturbation corrected force K =2A | ∂2 H/∂ Q2 |2A , constant parameters (K − p , K − p ,andK − p ) 2 1 0 1 1 1 2 2 3 3 = | ∂2 /∂ 2 | were estimated and revealed in Table 3. K3 1 A2 H Q 0 1A2 (3) F =1A | (∂ H/∂ Q) |1A , 1 0 2 3.5 Restoring tetrahedral structure = | (∂ /∂ ) | G 2A1 H Q 0 1A2 (4) With the goal of restoring the tetrahedral structure and In addition, H is electronic Hamiltonian with respect quenching the PJTE in the E2D2 systems under consid- to the Q instability direction and p , p , p are a2 1 2 3 eration, protonation of D atoms and trapping a noble gas the second-order perturbation corrections from all the dication at the center of the cavity cage of the systems , , higher excited A symmetry states to 1A1 2A1 1A2 were explored and the plausibility of these methods was states, respectively. These perturbation corrections are examined. given by Equation (5): |F |2 3.5a Protonation of D atoms: In the first effort of sup- − 1n 2 =− 2, ( +) 2 Qa2 p1 Qa2 pressing the PJTE, two protons H are placed at the n En − E1 apexes of the E2D2 deformed tetrahedral pyramid (same |F |2 − 2n 2 =− 2, as the positions that hydrogens located in tetrahedrane 2 Qa2 p2 Qa2 n En − E2 structure). The geometrical optimization and frequency 2 2+ |F | calculation of the simulated E2D2H2 revealed that the −2 3n Q 2 =−p Q 2 (5) a2 3 a2 complexes restore their C tetrahedral configuration n En − E3 2v J. Chem. Sci. (2019) 131:37 Page 7 of 9 37

As was mentioned in Equation (1), must be less 2 than F , as the necessary condition for instability K3−p3 of the ground state in the series. By both the trapping of an inert gas dication and the di-protonation efforts for E2D2 series, the interval energies between the 1A1 ground and all three, low–lying excited states (1B1, 2A1, 1A2) changes. Specifically, the energy gap Figure 3. Representative of restoring the Ga P tetrahedral between the ground and A2 excited states, , is signifi- 2 2 ( = structure (C2v symmetry) from the deformed configuration cantly increased. For examples, the in the E2Al2 E with C2 symmetry through the protonation of Ga atoms. Other P, As, Sb) series increases from 1.07, 1.03, 1.57 eV to + + E2D2 deformed systems considered also demonstrate that the 5.86, 5.76, 3.46 when trapping He2 (He2 @E Al ) 2+ 2 2 E2D2H2 complexes restoration. and 7.32, 6.02, 4.94 eV with Al atoms di-protonated 2+ (E2Al2H2 ). Therefore, increasing the magnitude of increases stability in the A1 ground state, quenching the PJTE in the E2Al2 systems. However, di-protonation to E atoms in E2Al2 (E = P, As, Sb) series increases the value of the imaginary frequencies in the series from 246.7, 217.6, and 215.0 to 448.4, 409.0, and 421.9cm−1. In other words, pro- tonating E atoms of E2Al2 will increase the PJTE, Figure 4. Representative of restoring the Ga2P2 tetrahedral the instability of C2v tetrahedral configuration, in the structure (C2v symmetry) from the deformed configuration series. To explain the reason, exploring the molecu- 2+ with C2 symmetry through trapping Ne inside the tetrahe- lar orbital energies of E2Al2 and di-protonated to Al dron cage. Other deformed In2P2 and Ga2As2 configurations 2+ ) 2+ 2+ atoms (H2 E2Al2 complexes is useful. Due to the demonstrate analogous restoration with Ne or He . 2+ number of electrons in the P2Al2, P2Al2H2 and 2+ He @E2Al2 systems being the same, all of these follow without a disrupted structure (Figure 3) and do not show the same configuration of 12a1, 7b1, 6b2, 3a2 HOMOs. 2+ any imaginary frequency. In the H2 P2Al2 system, however, the HOMOs re- In addition, the calculated thermochemical param- arrange as 12a1, 7b1, 5b2, 4a2. Here, the highest electron eters at standard temperature and pressure for the pair in the b2 symmetry change to a2 symmetry elec- protonation reaction in the considered E2D2 systems trons. In other words, the electronic configuration in 2+ 2+ return a negative G value from –12.45 KJ/mol in P2Al2 H2 P2Al2 is different with respect to P2Al2, P2Al2H2 2+ to –5.83 KJ/mol in P2In2.Infact,theE2D2 protonation and He @E2Al2 systems and thus, the energy gap 2+ process, as well as the formation of the E2D2H2 com- between the highest a1 HOMO and a2 LUMO is affected. plexes is a spontaneous reaction, thermodynamically. Similarly, in the di-protonation of P in P2Al2 system, 2+ Based on the general definition of Bronsted-Lowry, H2 E2Al2 (E = As, Sb) also show re-arrangement + a base refers to the compound that behaves as an H between the b2 and a2 symmetries HOMO electrons. proton acceptor. Although group 13 elements are poten- tially familiar with accepting electron-pairs (Lewis acid concept), the E2D2 systems become stable by protona- 4. Conclusions 2+ tion of the D atoms in the E2D2H2 complexes which are in conflict with our expectations. According to the application of tetrahedron structures as a carrier in drug delivery and toward developing effi- 3.5b Trapping noble gas dication inside E2 D2 cage: ciency in targeted drugs, the manipulation of white phos- 2+ In the second attempt to quenching the PJTE, He and phorus and its family group series E4(E = P, As, Sb) 2+ Ne were trapped in the center hole of the E2D2 were explored by replacing two E atoms by group 13 (D) systems. No imaginary frequency was observed for elements. Consequences of the state averaging CASSCF 2+ 2+ He @E2D2 or Ne @E2D2 cages, from the opti- calculations, electron excitation, and the corresponded mization and following frequency calculations (see APES reveal that the (1A1 +2A1 +1A2)⊗a2 problem is 2+ the Ne @P2Ga2 trapped system illustrates in Fig- the reason for the origin of deformation, as well as the 2+ ure 4). Consequently, the PJTE in the He @E2D2 or symmetry breaking phenomena, in the E2D2 systems. 2+ Ne @E2D2 cages was suppressed and the E2D2 sys- Moreover, calculation results present the protonation of tems restore their tetrahedral structure. the D atoms and trapping a noble gas dication in center 37 Page 8 of 9 J. Chem. Sci. (2019) 131:37 of the cage in the systems as two successful efforts for 15. Bersuker I B 2006 The Jahn–Teller Effect (Cambridge: restoring the tetrahedral structure and suppressing the Cambridge University Press) p. 110 PJTE in the E D systems. 16. Bersuker I B 2013 Pseudo Jahn–Teller effect—A two- 2 2 state paradigm in formation, deformation, and transfor- mation of molecular systems and solids Chem. Rev. 113 Acknowledgements 1351 The author wishes to acknowledge the Yazd Branch, Islamic 17. 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