2. COMPUTATIONAL DETAILS
Geometries of neutral and charged endohedral M@C20H20 (M = Li, Na, Mg) species were optimized in Ih symmetry using density functional theory combined with B3LYP functional at aug-cc-pVTZ basis set.48,49 Their cartesian coordinates and harmonic vibrational frequencies are reported in the Electronic Supplementary Information (ESI) (Tables S1and S2). Single point MP2 (second-order Møller–Plesset perturbation theory)50 calculations were performed using B3LYP geometries [MP2(FC)//B3LYP] to obtain adiabatic ionization energies (AIEs). AIE of M@C20H20 = Energy of optimized M@C20H20+/2+ − Energy of optimized M@C20H20. The unrestricted Hartree-Fock spin contamination for open shell species did not exceed 0.0011. Renormalized partial third-order quasiparticle electron propagator method (P3+)51–53 was used to obtain vertical ionization energies (VIEs) of Li@C20H20, Na@C20H20, and Mg@C20H20. For this purpose, vertical electron binding energies (VEBE) of Li@C20H20+, Na@C20H20+, Mg@C20H20+, and Mg@C20H202+ were calculated (−VEBE = VIE) using the B3LYP optimized geometries of MC20H20 (M = Li, Na, Mg).
Excited states of MC20H20 (M = Li, Na, Mg+) were investigated at diagonal second-order approximation (D2), partial third-order quasiparticle (P3), and P3+ electron propagator methods.51–54 The accuracy of these methods increases in the order of D2, P3, and P3+.55 These techniques were used to calculate vertical electron attachment energies of MC20H20 (M = Li+, Na+, Mg2+) and their differences were calculated to obtain vertical excitation energies of MC20H20 (M = Li, Na, Mg+). In each case, B3LYP optimized geometries of MC20H20 (M = Li, Na, Mg+) were employed.
Various correlation consistent basis set combinations [cc-pVTZ (≡TZ), aug-cc-pVTZ (≡ATZ), d-aug-cc-pVTZ (≡DATZ)] were tested to study excited states of Li@C20H20.48,49,56They are, (1) Li:TZ, C:TZ, H:TZ, (2) Li:TZ, C:TZ, H:ATZ, (3) Li:TZ, C:ATZ, H:TZ, (4) Li:ATZ, C:TZ, H:TZ, (5) Li:TZ, C:ATZ, H:ATZ, (6) Li:ATZ, C:TZ, H:ATZ, (7) Li:ATZ, C:ATZ, H:TZ, (8) Li:ATZ, C:ATZ, H:ATZ, (9) Li:TZ, C:TZ, H:DATZ. Results indicate that the (9)th basis set (Li:TZ, C:TZ, H:DATZ) provides the most accurate results and therefore was used to carry out vertical electron attachment calculations for the Na@C20H20+ and Mg@C20H202+. The pole strengths related to electron attachment energies of all the species are greater than 0.950.
All calculations were performed using Gaussian 16 package57. GaussView58 and Molden59 software packages were used to plot Dyson orbitals.