Extended Mulliken–Hush Method with Applications to the Theoretical Study of Electron Transfer

Abstract

A novel adiabatic-to-diabatic (ATD) transformation strategy, namely, the extended Mulliken–Hush (XMH) method, is proposed to evaluate diabatic properties including electronic couplings, potential energy surfaces, and their crossings. The XMH method is developed by adopting our recently proposed ATD transformation formula of a general vectorial physical observable, in which a useful ATD transformation is further determined by using an auxiliary dipole between localized frontier orbitals as a simple approximation of the diabatic transition dipole. The XMH method is simple and practical that provides a flexible way to construct diabatic states. To some extent, it can be regarded as an extension of the generalized Mulliken–Hush (GMH) method since the latter takes a stronger approximation, in which the diabatic transition dipole is assumed to be vanishing. Test calculations on the HeH2 + system show that the electronic couplings predicted by the XMH method are closer to the ones calculated by the valence bond block-diagonalization approach than the GMH ones since the XMH method takes into account both the magnitude and direction of the diabatic transition dipole, which is consistent with the properties of this molecule. In the study of electron transfer in the two kinds of donor-bridge-acceptor systems, the XMH method maintains the simplicity of the GMH method and gives reasonable results even when the latter fails, wherein the diabatic transition dipole is nearly perpendicular to the difference of the initial and final adiabatic dipoles. More importantly, the XMH method can be easily combined with high-level electronic structure methods, in which the properties of the ground and excited states may be more accurately calculated, and hence, one may expect that further development of the XMH method would result in a general computational model for studying electron transfer reactions.

Diabatic States of Molecules

“…Early work on property-unblending diabatization was designed to obtain diabatic bases for electron-transfer processes, − and one diagonalized the component of the dipole property matrix along the direction of the donor-to-acceptor axis. − Examples of this approach are the generalized Mulliken–Hush (GMH) method, , the extended GMH method, , the fragment charge difference method, , and the fragment excitation and spin difference method. , This approach was later generalized into the form summarized in eqs and , which do not require selecting a directional component of vector properties since they employ the norm.…”

The three kingdoms—Photoinduced electron transfer cascades controlled by electronic couplings

“…78 Additionally, the electronic couplings were obtained based on the GMH method as well as with the fragment charge difference (FCD) approach, which are widely applied to study intermolecular and intramolecular electron transfer processes. [79][80][81][82][83][84] These simulations were performed at the B3LYP/def2-SVP level of theory using Q-Chem. 85 Solvent effects (CH 2 Cl 2 ) were taken into account using the conductor-like polarizable continuum model.…”

Optical and dielectric response of two‐dimensional WX2 (X = Cl, O, S, Se, Te) monolayers: A comprehensive study based on density functional theory

“…The WX 2 is also promising for different gas adsorption, such as SO 2 . [ 14 ] The WX 2 ‐based materials exhibit excellent catalytic performance for hydrogen and oxygen evolution reactions for water‐splitting applications. [ 15–17 ] However, it is crucial from a physics perspective to dig into these materials' physical properties to understand the electronic, dielectric, and optical responses.…”