Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra

Abstract

We recently showed that the dephasing representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that further acceleration is possible with cellularization [M. Šulc and J. Vaníček, Mol. Phys. 110, 945 (2012)]. Here, we focus on increasing the accuracy of this approximation by first implementing an exact Gaussian basis method, which benefits from the accuracy of quantum dynamics and efficiency of classical dynamics. Starting from this exact method, the DR is derived together with ten other methods for computing time-resolved spectra with intermediate accuracy and efficiency. These methods include the Gaussian DR, an exact generalization of the DR, in which trajectories are replaced by communicating frozen Gaussian basis functions evolving classically with an average Hamiltonian. The newly obtained methods are tested numerically on time correlation functions and time-resolved stimulated emission spectra in the harmonic potential, pyrazine S 0 /S 1 model, and quartic oscillator. Numerical results confirm that both the Gaussian basis method and the Gaussian DR increase the accuracy of the DR. Surprisingly, in chaotic systems the Gaussian DR can outperform the presumably more accurate Gaussian basis method, in which the two bases are evolved separately.

Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics

“…In this test case, there does not appear to be any benefit from the use of time-displacement, i.e., trains, to increase the size of the nuclear basis set. However, there may be advantages to time-displacement in other cases or for more sensitive properties than the electronic population (e.g., the absorption spectrum 60,61 or multi-dimensional spectroscopies). …”

Communication: GAIMS—Generalized Ab Initio Multiple Spawning for both internal conversion and intersystem crossing processes

“…For more information on these approximations, the interested reader is referred to different reviews on AIMS. 9,22,37,38 To summarize, GFMS is a generalization to the in principle exact method FMS for the description of both IC and ISC processes. The GAIMS technique, which is amenable to molecules, is obtained by applying the IFG and saddle-point approximations to GFMS.…”

Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics

“…Also, a possibility of adding a decoherence correction 93,94 to the underlying FSSH dynamics may be considered. Finally, the accuracy and efficiency of the method may be improved by implementing a prefactor amplitude correction, 24,25 cellularization, 19,25 or by replacing the trajectories with evolving Gaussian basis functions, 26 i.e., ideas that have been used successfully in the Born-Oppenheimer DR. 19,[24][25][26] setting of mixed states, arbitrary couplings between electronic states, and arbitrary pulse shapes.…”

“…23 Recently, the application of the DR to BornOppenheimer spectra was developed further by improving the accuracy and efficiency using a semiclassical prefactor, 24,25 cellularization, 19,25 and Gaussian basis expansion. 26 Kocia and Heller have extended the method in order to compute the off-diagonal elements of the evolution operator, allowing its use as a general semiclassical propagator. 27 During a revision of our paper, Petit and Subotnik 28 have published a paper in which they compute linear absorption spectra of onedimensional model potentials using a geometric average of correlation functions computed with phase averaging using trajectories propagated on either the ground or excited electronic surface, sometimes obtaining results that are even more accurate than those based on trajectories propagated on the average surface.…”

“…The pyrazine molecule exhibits a conical intersection between the first (S 1 ) and second (S 2 ) bright excited states, which influences the dynamics after excitation and the resulting vibronic spectra. Because the pyrazine molecule provides an almost ideal benchmark, its vibronic spectra have been extensively studied both experimentally [37][38][39][40][41][42][43][44][45][46] and theoretically, 6,25,26,31,[47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] giving us an opportunity not only to assess the accuracy of the MSDR in relation to experiment but also to compare it with exact quantum calculations on simplified models developed by others. In addition, due to efficiency of the MSDR, we were able to go beyond simplified model systems and to compute the absorption spectrum using the ab initio electronic structure computed on the fly in all 24 dimensions.…”