What would compel a composer to set the same poem twice? Ludwig van Beethoven first set the text of Christoph Tiedge’s “An Die Hoffnung” (to Hope) between 1804 and 1805, and would later set the poem again, using even more of the text in 1815. While seeking context clues from what is known of his biography is crucial, another avenue of study lies within the pieces themselves. Through the study of key characteristics during Beethoven’s lifetime in addition to what biographical information we know, we can infer Beethoven’s intentions with each setting of the text and how this reflects his changing relationship to the text of “An Die Hoffnung”.

The interband transitions of urania (UO2) are validated independently through cathode luminescence of UO2. A picture emerges consistent with density functional theory. While theory is generally consistent with experiment, it is evident that the choice of functional can significantly alter the band gap and some details of the band structure, in particular at the conduction band minimum. Strictly ab initio predictions of the optical properties of the actinide compounds, based on density functional theory alone continues to be somewhat elusive.