Localized diabatization applied to excitons in molecular crystals

Abstract

Traditional ab initio electronic structure calculations of periodic systems yield delocalized eigenstates that should be understood as adiabatic states. For example, excitons are bands of extended states which superimpose localized excitations on every lattice site. However, in general, in order to study the effects of nuclear motion on exciton transport, it is standard to work with a localized description of excitons, especially in a hopping regime; even in a band regime, a localized description can be helpful. To extract localized excitons from a band requires essentially a diabatization procedure. In this paper, three distinct methods are proposed for such localized diabatization: (i) a simple projection method, (ii) a more general Pipek-Mezey localization scheme, and (iii) a variant of Boys diabatization. Approaches (i) and (ii) require localized, single-particle Wannier orbitals, while approach (iii) has no such dependence. These methods should be very useful for studying energy transfer through solids with ab initio calculations.

Theoretical Modeling of Singlet Fission

“…Computational characterization of the CT or CR mixing in adiabatic wave functions might be a non trivial task, in particular for CR contributions in symmetric systems where the measure of the static dipole moment of the state is not appropriate and diabatization schemes − or decomposition techniques ,, are required. The need for the characterization and quantification of CT content in electronic transitions has generated a variety of computational techniques. − The CT nature of S 1 can be assessed by standard charge population analysis, spatial overlap measure between ground and excited states, by means of the attachment/detachment density analysis, or employing other tools for the quantitative analysis of excited states .…”

Diabatic States at Construction (DAC) through Generalized Singular Value Decomposition

“…Diabatic representation of potential energy surfaces (PESs) is widely used in studies of charge transfer and nonadiabatic dynamic simulations of photochemical reactions involving conical intersections or locally avoided crossings . It provides diabatic coupling elements of the Hamiltonian operator, which are scalar and smoothly varying with nuclear coordinates. − On the other hand, the nonadiabatic coupling or derivative coupling vectors of the adiabatic PES are not smooth and exhibit singularities in regions near conical intersection. , Consequently, numerous techniques have been developed for constructing diabatic states. ,,,− However, diabatic states are not unique, and most methods involve an orthogonal transformation of the adiabatic surfaces with restraints by desired properties or minimization of the nonadiabatic coupling vectors. These approaches, known as diabatization methods, may be classified as the adiabatic-to-diabatic (ATD) category because the adiabatic PESs are determined first and the diabatic states that are constructed through an ATD transformation are admixtures of the corresponding valence bond (VB) configurations of the asymptotic dissociation products.…”

“…Most ATD transformations, − whether orbital- and property-dependent or -independent, direct or indirect, focus on finding the transformation X to obtain diabatic energies, but in GDAC, we emphasize optimization of the wave functions of diabatic states such that Φ ds will have the maximum resemblance of the valence characters that the diabatic states represent. The transformation matrix X becomes a natural consequence of the optimized Φ ds .…”

Diabatic Hamiltonian construction in van der Waals heterostructure complexes

“…Many of them were mainly designed to build the diabatic wavefunctions for molecular systems when the adiabatic wavefunctions are available. 17,[19][20][21][22][23][24][25][39][40][41] Alternatively, it is also possible to build the diabatic states directly by assuming the smooth property constrain of the diabatic electronic wavefunction. 26,[28][29][30][31][32][42][43][44] Although many diabatic methods have been well established, it is still not easy to construct the diabatic Hamiltonian for the large or extended systems, if many-electro n wavefunctions that are the linear combination of the slater determinants are considered .…”

“…[65][66] Recently, Subotnik and coworkers proposed several protocols (includ ing the projection approach) to construct the localized diabatic excitonic states in molecular crystal systems. 20 In this work, we extended the wavefunction projection method to construct the diabatic Hamiltonian for vdW heterostructure complexes within the single-partic le picture. For broad applications, the projection method is combined with the widelyused electronic structure calculations with plane wave basis sets.…”