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.