Internal conversion of singlet and triplet states employing numerical DFT/MRCI derivative couplings: Implementation, tests, and application to xanthone

Abstract

We present an efficient implementation of nonadiabatic coupling matrix elements (NACMEs) for density functional theory/multireference configuration interaction (DFT/MRCI) wave functions of singlet and triplet multiplicity and an extension of the Vibes program that allows us to determine rate constants for internal conversion (IC) in addition to intersystem crossing (ISC) nonradiative transitions. Following the suggestion of Plasser et al. [J. Chem. Theory Comput. 12, 1207 (2016)], the derivative couplings are computed as finite differences of wave function overlaps. Several measures have been taken to speed up the calculation of the NACMEs. Schur’s determinant complement is employed to build up the determinant of the full matrix of spin-blocked orbital overlaps from precomputed spin factors with fixed orbital occupation. Test calculations on formaldehyde, pyrazine, and xanthone show that the mutual excitation level of the configurations at the reference and displaced geometries can be restricted to 1. In combination with a cutoff parameter of tnorm = 10−8 for the DFT/MRCI wave function expansion, this approximation leads to substantial savings of cpu time without essential loss of precision. With regard to applications, the photoexcitation decay kinetics of xanthone in apolar media and in aqueous solution is in the focus of the present work. The results of our computational study substantiate the conjecture that S1 T2 reverse ISC outcompetes the T2 ↝ T1 IC in aqueous solution, thus explaining the occurrence of delayed fluorescence in addition to prompt fluorescence.

Ultrafast Intersystem Crossing in Xanthone from Wavepacket Dynamics

“…330 ps. Recently, Bracker et al extended the use of Fermi’s golden rule for both the internal conversion and the ISC . Their results suggested that 1 ππ*– 3 ππ* ISC and 1 ππ*– 1 nπ* IC are competitive processes from which a branched mechanism was inferred.…”

Large Inverted Singlet–Triplet Energy Gaps Are Not Always Favorable for Triplet Harvesting: Vibronic Coupling Drives the (Reverse) Intersystem Crossing in Heptazine Derivatives

“…A further advantage of the Fourier transform approach is that it is easily extended to include temperature effects by assuming a Boltzmann population of the vibrational levels in the initial electronic state. 35,41,42 To speed up the numerical integration, a Gaussian damping function is introduced. The width of the damping function, the integration interval, and the number of grid points are technical parameters that have to be chosen with great care.…”

“…For IC, only the linear coupling terms of the nonadiabatic corrections were taken into account. The gradients of the matrix elements and the derivative couplings were obtained by distorting the nuclear framework along dimensionless normal modes using a step size of 0.5 units, utilizing averaged two-point finite difference techniques. , The phases of these gradients are arbitrary and need to be aligned properly by relating the phases of the molecular orbitals and of the DFT/MRCI wavefunctions to a reference calculation as performed in earlier work . Evaluation of nonradiative rate constants in the energy domain according to is not practicable for molecules as large as those investigated here because the density of vibrational states is too high.…”

“…To this end, the Dirac δ function is expressed as the Fourier integral In the harmonic oscillator approximation, analytical expressions for the generating functions of ISC and IC rate transitions including a Duschinsky transformation of the respective normal coordinates can be derived. ,− In the VIBES program, correlation functions were implemented, which use the normal coordinates of the initial state as a common basis for evaluating the FC factors and the nuclear coupling terms. ,− ISC, RISC, and IC rate constants are then obtained by numerically integrating the resulting correlation functions in the time domain. A further advantage of the Fourier transform approach is that it is easily extended to include temperature effects by assuming a Boltzmann population of the vibrational levels in the initial electronic state. ,, To speed up the numerical integration, a Gaussian damping function is introduced. The width of the damping function, the integration interval, and the number of grid points are technical parameters that have to be chosen with great care.…”

Removing the Deadwood from DFT/MRCI Wave Functions: The p-DFT/MRCI Method

“…The method was originally conceived as a means to calculate singlet and triplet valence excited states of organic molecules. However, the scope of the method has recently been significantly widened to include multiplicity-independent formulations, , a parameterization tuned to the description of transition-metal complexes, the treatment of core-excited states, and the calculation of spin–orbit and nonadiabatic couplings ,, and diabatic potentials …”