Vibronic coupling | EPFL Graph Search

Vibronic coupling (also called nonadiabatic coupling or derivative coupling) in a molecule involves the interaction between electronic and nuclear vibrational motion. The term "vibronic" originates from the combination of the terms "vibrational" and "electronic", denoting the idea that in a molecule, vibrational and electronic interactions are interrelated and influence each other. The magnitude of vibronic coupling reflects the degree of such interrelation. In theoretical chemistry, the vibronic coupling is neglected within the Born–Oppenheimer approximation. Vibronic couplings are crucial to the understanding of nonadiabatic processes, especially near points of conical intersections. The direct calculation of vibronic couplings used to be uncommon due to difficulties associated with its evaluation, but has recently gained popularity due to increased interest in the quantitative prediction of internal conversion rates, as well as the development of cheap but rigorous ways to analytically calculate the vibronic couplings, especially at the TDDFT level. Vibronic coupling describes the mixing of different electronic states as a result of small vibrations. The evaluation of vibronic coupling often involves complex mathematical treatment. The form of vibronic coupling is essentially the derivative of the wave function. Each component of the vibronic coupling vector can be calculated with numerical differentiation methods using wave functions at displaced geometries. This is the procedure used in MOLPRO. First order accuracy can be achieved with forward difference formula: Second order accuracy can be achieved with central difference formula: Here, is a unit vector along direction . is the transition density between the two electronic states. Evaluation of electronic wave functions for both electronic states are required at N displacement geometries for first order accuracy and 2*N displacements to achieve second order accuracy, where N is the number of nuclear degrees of freedom. This can be extremely computationally demanding for large molecules.

How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

Jiri Vanicek, Seonghoon Choi

Diabatization of the molecular Hamiltonian is a standard approach to remove the singularities of nonadiabatic couplings at conical intersections of adiabatic potential energy surfaces. In general, it is impossible to eliminate the nonadiabatic couplings entirely—the resulting “quasidiabatic” states are still coupled by smaller but nonvanishing residual nonadiabatic couplings, which are typically neglected. Here, we propose a general method for assessing the validity of this potentially drastic approximation by comparing quantum dynamics simulated either with or without the residual couplings. To make the numerical errors negligible to the errors due to neglecting the residual couplings, we use the highly accurate and general eighth-order composition of the implicit midpoint method. The usefulness of the proposed method is demonstrated on nonadiabatic simulations in the cubic Jahn–Teller model of nitrogen trioxide and in the induced Renner–Teller model of hydrogen cyanide. We find that, depending on the system, initial state, and employed quasidiabatization scheme, neglecting the residual couplings can result in wrong dynamics. In contrast, simulations with the exact quasidiabatic Hamiltonian, which contains the residual couplings, always yield accurate results.

2021

Rational Design of Hole Transport Materials: Tools and Structure-Packing-Property Relationships

Kun-Han Lin

The growing demand for low-cost, large-scale and flexible electronics has led to a boost in research on organic semiconductors (OSC). Understanding structure-packing-property relationships (SPPR) and the role of molecular building blocks in charge transport enables the development of effective rational design strategies, which helps in accelerating the search of promising of OSCs. Therefore, the original work presented in this thesis addresses these two aspects, with a focus on organic hole transport materials (HTM) utilized in perovskite solar cells. In the first part of this thesis, we place emphasis on revealing the SPPR of triphenylamine (TPA)-based HTMs utilizing multi-scale simulations involving molecular dynamics, density-functional theory and kinetic Monte-Carlo techniques. In the first example, we investigated the role of heteroatoms, presence of hexyl chains and substitution positions on charge transport for truxene derivatives. In particular, the impact of the presence of hexyl chain on hole mobility (ÃÅ) was identified, where hexyl-substituted truxene compounds possess hole mobilities an order of magnitude lower than those of their bare-core counterparts. The lower mobility originates primarily from the steric effect of hexyl chains, which prevents the truxene dimer from adopting a face-to-face arrangement. Due to the crucial role of the hexyl chain, we further investigated the effect of alkyl chain length on charge transport. As the alkyl chain is elongated, the reorganization energy (Î») remains unchanged, while the electronic coupling (V) and energetic disorder (ÃÂ) decrease simultaneously. Since V decreases much faster than ÃÂ does, ÃÅ gradually decreases with increasing alkyl chain length. Finally, we reveal the underlying mechanism of the multiarm effect on ÃÅ. By increasing the number of carbazole arms substituted on the TPA core, all transport parameters are decreased, which overall leads to an increase in ÃÅ. The second part focuses on the development of a fragment-based decomposition scheme for reorganization energy (FB-REDA) and electronic coupling (FB-ECDA). The total ÃÂ» of a molecule is partitioned into fragment reorganization energies utilizing local fragment vibrational modes. We demonstrate the usefulness of FB-REDA by successfully reduce the ÃÂ» of a dopant-free HTM (TPA1PM, ÃÂ» = 213 meV) by nearly 50% (TPD3PM, ÃÂ» = 108 meV) using rational design strategies based on the FB-REDA results. Similarly, the total V between two molecules in a dimer was decomposed into fragment-fragment electronic coupling terms using FB-ECDA. Combined with percolation and dimer composition analysis, we successfully established the relationship between molecular packing and electronic coupling for two series of molecules.

EPFL2020

FB-ECDA: Fragment-based Electronic Coupling Decomposition Analysis for Organic Amorphous Semiconductors

Kun-Han Lin

We present a fragment-based decomposition analysis tool (FB-ECDA) for the electronic coupling of charge transfer processes. This tool provides insight on the sophisticated relationship between molecular packing, electronic coupling, and the molecular transport network present in organic amorphous semiconductors. On the basis of atomic orbitals, FB-ECDA decomposes the total electronic coupling into individual electronic coupling terms arising from each molecular building blocks in a straightforward manner. The usefulness of this approach is demonstrated by revealing the structure-packing-property relationships for two series of molecules differing by the number of arm substituents and acene core length. Overall, we provide insight on the design of organic semiconductors exhibiting efficient charge transport network through achieving a subtle balance between molecular packing and electronic structure. We expect FB-ECDA to be a valuable tool for understanding sophisticated charge transfer processes in amorphous systems and guiding the rational design of organic semiconductors.

AMER CHEMICAL SOC2020

Rational Design of Hole Transport Materials: Tools and Structure-Packing-Property Relationships

Kun-Han Lin

EPFL2020