Intersystem crossing driven by vibronic spin–orbit coupling: a case study on psoralen

Abstract

For 7H-furo[3,2-g][1]benzopyran-7-one (psoralen), intersystem crossing (ISC) rate constants have been computed. Employing the Fermi golden rule, the harmonic approximation, and a pure-spin Born-Oppenheimer basis, both direct and vibronic spin-orbit (SO) coupling has been taken into account. Necessary data on electronic excitation energies and potential energy hypersurfaces originate from correlated all-electron calculations applying (time-dependent) density functional theory and the density functional theory/multireference configuration interaction approach. SO coupling has been treated by means of the one-center mean-field approximation. Vibronic SO couplings have been evaluated via numerical differentiation of SO matrix elements. Accounting only for direct SO coupling, rate constants of the order of k(ISC) approximately 10(10) s(-1) result for S2(n --> pi*) --> T1(pi --> pi*) ISC, whereas the rates of the channels S1 (pi --> pi*) --> {1,2 3} (pi --> pi*) do not exceed k(ISC) approximately 10(5) s(-1). Including vibronic SO coupling, rate constants of k(ISC) approximately 3 x 10(8) s(-1) are obtained for the S1 (pi --> pi*) --> T1 (pi --> pi*) ISC. The radiationless transition from the S1(pi --> pi*) state to the nearly degenerate T3(pi --> pi*) state has been estimated to be slightly less efficient (k(ISC) approximately 10(7) s(-1)). Based on our computed rates of ISC and excited state solvent shifts, we conclude that the experimentally observed appreciable triplet quantum yields of psoralen in polar protic media are primarily due to S1(pi --> pi*) --> T (pi --> pi*) channels. For heteroaromatic systems, (pi --> pi*)/(pi --> pi*) ISC driven by vibronic SO coupling is expected to be a common triplet state population mechanism.

Intersystem crossing rates of S1 state keto-amino cytosine at low excess energy

“…Earlier theoretical investigations of ISC between El-Sayed forbidden transitions such as 1 ππ * 3 ππ * suggest that the Condon approximation might not be sufficient and that vibronic spin-orbit coupling might play an essential role in such cases. 58,60 We tested the influence of these higherorder coupling terms on the S 1 T 1 ISC rate and found virtually no effect. The reason is probably the already quite substantial n O π * contribution to the S 1 wave function.…”

“…56,57 With the electronic coupling matrix elements, vibrational frequencies and wave functions at hand, intersystem crossing (ISC) rates were calculated using the VIBES program. [58][59][60][61] The calculation of rates makes use of the Fermi golden-rule and harmonic multimode approximation including Dushinsky rotations. Theoretical details of the method are provided elsewhere.…”

A general method to describe intersystem crossing dynamics in trajectory surface hopping

“…This methodology is especially well suited to investigate ultrafast ISC (on timescales up to a few ps), because long timescales are usually too expensive for nuclear dynamics approaches. In this regard, our methodology can be considered complementary to other nondynamical treatments of ISC, [76][77][78][79] which are not well applicable to ultrafast processes, but work well for slower reactions. Our methodology has been recently implemented in a completely new SHARC surface hopping dynamics code.…”

“…Another strength of on-the-fly methods is that they allow going beyond the so-called linear vibronic coupling [133,134] and linear vibronic spin-orbit coupling [77,135] approaches, where the relevant matrix elements are only approximated by some truncated power series around a reference geometry. In trajectory surface hopping methods, the availability of the full geometry dependence of the electronic properties makes it automatically possible to describe effects like the promotion of SOC by excitation of symmetry-reducing vibrational modes.…”

“…For relatively slow ISC processes, the calculation of ISC rate constants using Landau-Zener theory, [75] Fermi's golden rule [76,77] or Marcus-Jortner theory [76,78,79] is well established. For ultrafast ISC processes-where the system is very far from equilibrium-a dynamical treatment describing the motion on the PES and taking into account the kinetic processes that lead the system toward the relevant crossing region is mandatory.…”