Direct energy minimization of excited singlet states

Abstract

A general method is developed which permits the minimization of the energy of an excited singlet or triplet state. The conditions for energy minimization are obtained without introduction of Lagrange multipliers by a highly concise matrix formulation. The method is applicable to excited states expressed as linear combinations of an unlimited number of singly excited configurations. The method reduces to an iterative system of matrix diagonalizations and is thus equivalent to a pseudoeigenvalue problem. Calculations for the lowest n→π* and π→π* states of thiazole and 2-methylthioimidazole are reported.

Thiazole and the Diazines Pyrazine and Pyrimidine as Sensitizers for Lanthanide Luminescence from VIS to NIR

“…Therefore, also the photoluminescence spectra of the respective ligands were recorded (Figure ), which underline the absence of the typical ligand fluorescence [pyrazine: λ = 320–435 nm; ( λ max = 356 nm), pyrimidine λ = 335–490 nm ( λ max = 354 nm), and thiazole λ = 330–460 nm ( λ max = 376 nm)] in the products. A population of ligand triplet states by ISC can also be assumed as intermediate states before energy transfer, as the lowest triplet levels T 1 of thiazole (26045 cm –1 ), pyrazine (26553 cm –1 ), and pyrimidine (28300 cm –1 ) are relevant for a population the 5 D 3 and 5 D 4 states of Tb 3+ (26273, 20500 cm –1 ) . Different from the Tb emission, the emission of Er 3+ is in the NIR, which gives a large distance >20000 cm –1 to the emissive states.…”

“…A population of ligand triplet states by ISC can also be assumed as intermediate states before energy transfer, as the lowest triplet levels T 1 of thiazole (26045 cm -1 ), pyrazine (26553 cm -1 ), and pyrimidine (28300 cm -1 ) [23] are relevant for a population the 5 D 3 and 5 D 4 states of Tb 3+ (26273, 20500 cm -1 ). [24] Different from the Tb emission, the emission of Er 3+ is in the NIR, which gives a large distance Ͼ20000 cm -1 to the emissive states. But, as Er 3+ also provides excited 4f-states around the triplet levels of the ligands such as 2 G 11/2 , 5 G 5,6 , and thereby within the preferable gap to excited 4f-states, also the energy transfer in 2 and 5 is reasonable.…”

Luminescent coordination polymers for the VIS and NIR range constituting LnCl3 and 1,2-bis(4-pyridyl)ethane

“…The energetic position of the triplet level T 1 was reported at 26 045 cm −1 around 380 nm. 28 The two Gd 3+ -compounds, 6 and 13, are good examples to observe the effects of ligand-centered luminescence in compounds isostructural to other lanthanides without the participation of Gd 3+ in the luminescence, as the respective 4ftransition at 307 nm is not populated. Accordingly, the emission is ligand centred fluorescence (e.g.…”