Critical assessment of density functional theory for computing vibrational (hyper)polarizabilities

Can Short- and Middle-Range Hybrids Describe the Hyperpolarizabilities of Long-Range Charge-Transfer Compounds?

“…This is the idea behind long-range corrected (LC)-DFT functionals, [29][30][31][32][33][34] which have been shown to provide an improved description of long-range properties (including CT excitations and hyperpolarizabilities) as compared to global hybrids and GGAs. [35][36][37][38][39][40][41][42][43][44][45][46][47][48] Furthermore, the range-separation parameter of LC-DFT can be optimized ab initio for the system of interest by demanding that the molecule, and its corresponding anion, obey the Coulomb operator is divided in three parts). However, these functionals are rarely used in hyperpolarizability calculations since it is believed that the incorrect asymptotic behavior of the exchange potential would lead to catastrophic overshooting of GGAs.…”

“…The 1/ R term can be recovered by separating the Coulomb operator into complementary short- and long-range parts, and evaluating the exchange energy in the long-range with pure HF exchange. This is the idea behind long-range corrected (LC)-DFT functionals, − which have been shown to provide an improved description of long-range properties (including CT excitations and hyperpolarizabilities) as compared to that by global hybrids and GGAs. − Furthermore, the range-separation parameter of LC-DFT can be optimized ab initio for the system of interest by demanding that the molecule, and its corresponding anion, obey Koopman’s theorem, so that ϵ a A – ϵ i D approximates IP D – EA A . − This methodology, often referred to as gap tuning or optimally tuned LC-DFT, further improves the accuracy in predictions of CT energies and first-order hyperpolarizabilities − (if the system is not very large, , because the tuning procedure is not size extensive). A recent review on tuned LC-DFT is available in ref .…”