Eur. Phys. J. Plus (2022) 137: 803
https://doi.org/10.1140/epjp/s13360-022-02971-6

Regular Article

Theoretical investigation of lithium-based clusters Li_n (where n = 3, 5, 7) with remarkable electronic and frequency-dependent NLO properties

Department of Chemistry, COMSATS University Islamabad, Abbottabad Campus, 22060, Abbottabad, KPK, Pakistan

^b khurshid@cuiatd.edu.pk

Received: 5 May 2022
Accepted: 17 June 2022
Published online: 11 July 2022

Abstract

Herein, we report the theoretical insight into electronic and nonlinear optical (NLO) properties of pure lithium clusters Li_n (where n = 3, 5, 7) using MP2/6–311++G(d,p) and DFT theory. The optimization of clusters is carried out at MP2/6–311++G(d,p), while spectral, electronic, and NLO properties are at CAM-B3LYP functional. The studied superalkali clusters are thermodynamically stable, and their binding energies per atom range from − 8.15 to − 15.49 kcal mol⁻¹. The calculated vertical ionization potentials (VIP) and FMOs analysis suggest their superalkali and excess electrons nature. These clusters have significantly reduced HOMO–LUMO gaps (2.78–3.41 eV). The displayed total density of states (TDOS) spectra also provide a more comprehensive picture of electronic characteristics. Being excess electron clusters, the static hyperpolarizability (β_o) value is up to 7.77 × 10⁴ au for Li₅ where its second hyperpolarizability (γ_o) significantly increased up to 2.7 × 10⁶ au. There is an excellent correlation between total hyperpolarizability and the computed vector part of hyperpolarizability (β_vec). The two-level model (β_tl) reveals that excitation energy is the main influencing factor to hyperpolarizability. Besides, dynamic hyperpolarizabilities β(ω) show remarkable values (3.2 × 10⁶ au) for EOPE β( − ω;ω,0) effect at 532 nm. Similarly, the second-harmonic generation (SHG) phenomenon is also much more pronounced at a small dispersion frequency (ω = 532 nm). The dynamic second hyperpolarizability γ(ω) value increases up to 1.2 × 10¹¹ au, and the results are much more pronounced at a larger dispersion frequency (1064 nm). Additionally, the dynamic NLO properties at the applied frequency of 1300 nm are much more pronounced than those of 1900 nm. The significant scattering hyperpolarizability (β_HRS) is recorded up to 1.3 × 10⁴ au for Li₃ cluster. Hence, the studied lithium-based superalkali clusters are novel candidates for excellent electronic and NLO properties.