A practical and efficient diabatization that combines Lorentz and Laplace functions to approximate nonadiabatic coupling terms

Abstract

A fixed relation of α × β = 1.397 between the α- and β-parameters of a Lorentz function and a Laplace function that approximates nonadiabatic coupling terms and maximizes the overlap area between the two functions was found. The mixing angle corresponding to the geometric average between the potential couplings calculated using the individual path-integral of the two functions was then used in the construction of diabatic states and the coupling of the states. Employing the new method, the actual computation of nonadiabatic coupling terms at just a few geometries before and after the guessed conical intersection is enough, and the remaining steps are straightforward and almost automatic. The new method was tested for the one-dimensional LiF system and the two-dimensional space of the collinear case of NH3Cl, and promising results were achieved.

Construction of Vibronic Diabatic Hamiltonian for Excited-State Electron and Energy Transfer Processes

“…Generally, there are two categories of methods for performing the diabatization, i.e., the direct diabatic-state construction ,− and the adiabatic-to-diabatic transformation. ,− In the first approach, the diabatic states are constructed explicitly before the calculations of the adiabatic electronic wave functions. For example, in the description of excited-state ET and EET processes, one approach is to take individual fragments as building blocks of the whole system.…”

“…Although there are many researches on diabatization and various diabatization methods were proposed, we still see that some works focus on this topic in recent years. ,,,− ,,, This implies that diabatization is still very challenging. Recently, Tamura, Burghardt, and co-workers , developed a rather practical diabatization method based on the wave function projection approach for time-dependent density functional theory (TDDFT).…”

An ab initio study of the rovibronic spectrum of sulphur monoxide (SO): diabatic vs. adiabatic representation

“…The Lorentzian was shown to provide a good description of the ab initio NACs around the crossing point 48,49,51,52 (see Fig. 7) but diverges at large distances R from R c causing improper shaped diabatic PECs by decaying too slowly.…”

“…An alternative approach is to transform the electronic Hamiltonian to the diabatic basis, where electronic states are coupled via off-diagonal potential energy terms, termed diabatic couplings (DCs). 33,34,37 The transformation from the adiabatic to the diabatic basis is described by a unitary matrix U , which is parametrically dependent on the NAC term,where the mixing angle β ( R ) is obtained by integrating the functional form of the non-adiabatic derivative coupling 35,47–49 with | ψ 1 〉 and | ψ 2 〉 as the lower and upper energy electronic wavefunctions in the adiabatic representation.…”

Simulating Coherent Multidimensional Spectroscopy of Nonadiabatic Molecular Processes: From the Infrared to the X-ray Regime

“…In practice, the conditions in eq are approximated to yield a quasi-diabatization. , The choice of the mixing angle is then not unique and depends of the employed method. For a selection of possible quasi-diabatization methods see refs and − . A system where the electronic populations follow the adiabatic states during the time evolution is commonly labeled adiabatic, while a system that preserves its electronic character by following a single diabatic state is called diabatic.…”