Pseudo Jahn-Teller origin of puckering in C₄ H₄ ²⁺, Si₄ H₄²⁺, and C₄ F₄²⁺dications

The Pseudo Jahn-Teller Effect (PJTE) is employed to explain the origin of the puckered structure of cyclobutadiene dication (C₄ H ₄²⁺) and rationalize its difference from the less-folded Si₄H₄²⁺ and planar C₄ H ₄²⁺ analogs. It is found that in the highest-symmetry D_4h configuration of all three dications, the vibronic coupling between the ground state ¹A_1g and excited state ¹B_2u, i.e., the PJTE problem (¹A_1g + ¹B_2u) ⊗ b_2u, is the reason of puckering instability. In C₄ H₄²⁺ the PJTE interaction is very strong breaking the D_4h symmetry to form a stable D _2d puckered geometry, whereas in Si₄H₄ ²⁺ it is relatively weak resulting in a less-folded structure. Compared with C₄ H₄²⁺ and Si₄H ₄²⁺, the PJTE interaction in C₄F ₄²⁺ is very weak due to the extremely large energy gap of 9.64 eV between the two coupling states, so no puckering instability occurs.