Effective electron displacements: A tool for time-dependent density functional theory computational spectroscopy

Abstract

We extend our previous definition of the metric Δr for electronic excitations in the framework of the time-dependent density functional theory [C. A. Guido, P. Cortona, B. Mennucci, and C. Adamo, J. Chem. Theory Comput. 9, 3118 (2013)], by including a measure of the difference of electronic position variances in passing from occupied to virtual orbitals. This new definition, called Γ, permits applications in those situations where the Δr-index is not helpful: transitions in centrosymmetric systems and Rydberg excitations. The Γ-metric is then extended by using the Natural Transition Orbitals, thus providing an intuitive picture of how locally the electron density changes during the electronic transitions. Furthermore, the Γ values give insight about the functional performances in reproducing different type of transitions, and allow one to define a "confidence radius" for GGA and hybrid functionals.

Describing excited states of [n]cycloparaphenylenes by hybrid and double-hybrid density functionals: from isolated to weakly interacting molecules

“…Figure 6 shows how this is indeed the case for the states numbered as S 3 and S 4 , in both parallel-like and tubular-like configurations, largely exceeding the values of the calculated ∆r the threshold of 1.5 − 2.0Å previously proposed as a cutoff for confirming a (marked) charge-transfer excitation [84]. These charge-transfer states can be viewed as those having an electron in one molecule and a hole on the other, and are always difficult to describe by routine TD-DFT calculations [93].…”

“…The use of some metrics to characterize the nature of an excited-state has revealed recently as a highly useful tool [78][79][80][81][82][83], and actually a threshold for ∆r of 1.5 − 2.0Å is proposed as a sign of having a (marked) charge-transfer excitation or not [84]. This is easily understood if one considers the ∆r value as a kind of exciton free path.…”

Circular Dichroism and TDDFT Investigation of Chiral Fluorinated Aryl Benzyl Sulfoxides

“…To properly investigate the nature of the relevant transitions and to estimate the associated effective electronic displacement during the excitation, an analysis based on the recently proposed Γ-index [42,43] was carried out, particularly in its natural transition orbital (NTO) version. This procedure permits one to identify the "principal components" of the transition electron density (by using NTO's) and provides a measure of the interaction distance of the holeparticle pairs.…”

Communication: Exciton analysis in time-dependent density functional theory: How functionals shape excited-state characters

“…The search for tools to diagnose the failures of TDDFT in combination with different functionals is an ongoing challenge and several descriptors measuring orbital overlaps [14][15][16] and centroid distances [17][18][19] have been proposed. However, some cases like extended symmetric π-conjugated systems, e.g., acenes, cause significant but hard-to-detect errors.…”