Semiclassical Approach to Photophysics Beyond Kasha’s Rule and Vibronic Spectroscopy Beyond the Condon Approximation. The Case of Azulene

Abstract

Azulene is a prototypical molecule with an anomalous fluorescence from the second excited electronic state, thus violating Kasha's rule, and with an emission spectrum that cannot be understood within the Condon approximation. To better understand photophysics and spectroscopy of azulene and other non-conventional molecules, we develop a systematic, general, and efficient computational approach combining semiclassical dynamics of nuclei with ab initio electronic structure. First, to analyze the nonadiabatic effects, we complement the standard population dynamics by a rigorous 1 arXiv:2001.08414v2 [physics.chem-ph] measure of adiabaticity, estimated with the multiple-surface dephasing representation.Second, we propose a new semiclassical method for simulating non-Condon spectra, which combines the extended thawed Gaussian approximation with the efficient single-Hessian approach. S 1 ← S 0 and S 2 ← S 0 absorption and S 2 → S 0 emission spectra of azulene, recorded in a new set of experiments, agree very well with our calculations. We find that accuracy of the evaluated spectra requires the treatment of anharmonicity, Herzberg-Teller, and mode-mixing effects.

A Computational Protocol to Predict Anti-Kasha Emissions: The Case of Azulene Derivatives

“…The vibronic features of the experimental S 2 absorption and emission spectra are only recovered after the inclusion of HT effects (Figure 3c). The relevance of HT effects on the S 2 emission of azulene have also been proved by Prlj et al 77 In Ref. 77 they combined a semiclassical approach with ab initio calculations to account for the anomalous emission in azulene.…”

Dual Emission: Classes, Mechanisms, and Conditions

“…[71,73] Thel arge DE(S 2 ÀS 1 )v alue should effectively slow down IC in as imple FGR framework;i nf act, am ore thorough treatment with CI reaches the same conclusions. [15,73] Further examples of compounds showing steady-state non-Kasha emission in solution are cyclo [3.3.3]azines [74] as well as triphenylmethane-(TPM-), [75] porphine-, [76] thioketone-, [67] tricarbocyanine (TCC)-, [77] and phenanthroimidazole-type [78] dyes, which show very large f 2 values and also large DE(S 2 ÀS 1 )v alues on the order of 1eV, thus emphasizing the crucial role of alarge energy spacing DE(S 2 ÀS 1 )for the observation of non-Kasha behavior. For new compounds,t his should be crosschecked with quantum-chemical calculations, [79] and by analyzing the PLE spectrum (see Section 2).…”

Duale Emission: Klassen, Mechanismen und Bedingungen

“…[69] Dieses Verhalten wird durch die besondere elektronische Struktur des Azulens (und seiner Derivate) bedingt, [72] die eine große Energielücke DE(S 2 ÀS 1 ) % 1.7 eV und gleichzeitig eine große Oszillatorstärke f 2 des S 2 !S 0 -Übergangs im Vergleich mit f 1 fürS 1 !S 0 erzeugt. [71,73] Die große S 2 ÀS 1 -Energielücke bedingt bereits im einfachen FGR-Modell eine Verlangsamung der IC;auch die genauere CI-Behandlung kommt zur selben Schlussfolgerung. [15,73] Weitere Beispiele fürS teady-State-non-Kasha-Emission in Lçsung sind Cyclo [3.3.3]azin-, [74] Tr iphenylmethan (TPM)-, [75] Porphin-, [76] Thioketon-, [67] Tr icarbocyanin (TCC)- [77] und Phenanthroimidazol-basierte [78] Farbstoffe,d ie ausreichend große f 2 -Oszillatorstärken und gleichzeitig große DE(S 2 ÀS 1 )-Separation in der Grçßenordnung von 1eVaufweisen;d ies unterstreicht wiederum die zentrale Role einer großen S 2 ÀS 1 -Energielücke fürd as Auftreten des Non-Kasha-Verhaltens.…”

“…[71,73] Die große S 2 ÀS 1 -Energielücke bedingt bereits im einfachen FGR-Modell eine Verlangsamung der IC;auch die genauere CI-Behandlung kommt zur selben Schlussfolgerung. [15,73] Weitere Beispiele fürS teady-State-non-Kasha-Emission in Lçsung sind Cyclo [3.3.3]azin-, [74] Tr iphenylmethan (TPM)-, [75] Porphin-, [76] Thioketon-, [67] Tr icarbocyanin (TCC)- [77] und Phenanthroimidazol-basierte [78] Farbstoffe,d ie ausreichend große f 2 -Oszillatorstärken und gleichzeitig große DE(S 2 ÀS 1 )-Separation in der Grçßenordnung von 1eVaufweisen;d ies unterstreicht wiederum die zentrale Role einer großen S 2 ÀS 1 -Energielücke fürd as Auftreten des Non-Kasha-Verhaltens. Fürn eue Verbindungen sollte dies mithilfe quantenchemischer Berechnungen [79] sowie durch eine Analyse des PLE-Abbildung 3.…”