A spectroscopic ruler for intermediate-zone FRET measurements

It is well known that Fluorescence Resonance Energy Transfer (FRET), the most common mechanism for electronic energy to migrate between molecular chromophores, has a predominantly inverse sixth power dependence on the rate of transfer as a function of the distance R between the chromophores. However, the unified theory of electronic energy transfer, derived from quantum electrodynamics, predicts an additional contribution with an R-4 dependence on distance. This intermediate-zone term becomes especially important when the chromophore spacing is similar in magnitude to the reduced wavelength (ƛ= λ 2π ) associated with the mediated energy. In previous theoretical studies we have suggested that inclusion of the intermediate term, through rate equation and quantum dynamical calculations, may be important for describing the exciton diffusion process in some circumstances, and in particular when the distance between the chromophores exceeds 5 nm. In this paper, we focus of the role of the intermediate-zone contribution to distance measurements between chromophores made through the application of spectroscopic ruler techniques. One of the major assumptions made in employing these experimental techniques is that the R−6dependence is valid. In this work, we reformulate the spectroscopic ruler principles for intermediate distances to include the inverse fourth power rate component, and compare the results of this reformulation to experimental FRET results from the literature. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

A quantum dynamical comparison of the electronic couplings derived from quantum electrodynamics and Förster theory:Application to 2D molecular aggregates

The objective of this study is to investigate under what circumstances Förster theory of electronic (resonance) energy transfer breaks down in molecular aggregates. This is achieved by simulating the dynamics of exciton diffusion, on the femtosecond timescale, in molecular aggregates using the Liouville–von Neumann equation of motion. Specifically the focus of this work is the investigation of both spatial and temporal deviations between exciton dynamics driven by electronic couplings calculated from Förster theory and those calculated from quantum electrodynamics. The quantum electrodynamics (QED) derived couplings contain medium- and far-zone terms that do not exist in Förster theory. The results of the simulations indicate that Förster coupling is valid when the dipole centres are within a few nanometres of one another. However, as the distance between the dipole centres increases from 2 nm to 10 nm, the intermediate- and far-zone coupling terms play non-negligible roles and Förster theory begins to break down. Interestingly, the simulations illustrate how contributions to the exciton dynamics from the intermediate- and far-zone coupling terms of QED are quickly washed-out by the near-zone mechanism of Förster theory for lattices comprising closely packed molecules. On the other hand, in the case of sparsely packed arrays, the exciton dynamics resulting from the different theories diverge within the 100 fs lifetime of the trajectories. These results could have implications for the application of spectroscopic ruler techniques as well as design principles relating to energy harvesting materials

Interpreting angular momentum transfer between electromagnetic multipoles using vector spherical harmonics

The transfer of angular momentum between a quadrupole emitter and a dipole acceptor is investigated theoretically. Vector spherical harmonics are used to describe the angular part of the field of the mediating photon. Analytical results are presented for predicting angular momentum transfer between the emitter and absorber within a quantum electrodynamical framework. We interpret the allowability of such a process, which appears to violate conservation of angular momentum, in terms of the breakdown of the isotropy of space at the point of photon absorption (detection). That is, collapse of the wavefunction results in loss of all angular momentum information. This is consistent with Noether’s Theorem and demystifies some common misconceptions about the nature of the photon. The results have implications for interpreting the detection of photons from multipole sources and offers insight into limits on information that can be extracted from quantum measurements in photonic systems

Polariton mediated resonance energy transfer in a fluid

The focus of this work is on a microscopic quantum electrodynamical understanding of cumulative quantum effects in resonance energy transfer occurring in an isotropic and disordered medium. In particular, we consider quantum coherence, defined in terms of interferences between Feynman pathways, and analyze pure-amplitude and phase cross terms that appear in the Fermi golden rule rate equation that results from squaring the matrix element for mediated energy transfer. It is shown that pure-amplitude terms dominate in the near-zone when chromophores are close in proximity to one another (within a few nanometers), and phase cross terms dominate toward the far-zone when phase differences between different Feynman pathways begin to emerge. This can be understood in terms of physical attributes of the mediating photon, whose character becomes more real at long distances, coinciding with vanishing longitudinal components of the field, as transverse components begin to dominate

Spectral Filtering as a Tool for Two-Dimensional Spectroscopy: A Theoretical Model

Two-dimensional optical spectroscopy is a powerful technique for the probing of coherent quantum superpositions. Recently, the finite width of the laser spectrum has been employed to selectively tune experiments for the study of particular coherences. This involves the exclusion of certain transition frequencies, which results in the elimination of specific Liouville pathways. The rigorous analysis of such experiments requires the use of ever more sophisticated theoretical models for the optical spectroscopy of electronic and vibronic systems. Here we develop a non-impulsive and non-Markovian model which combines an explicit definition of the laser spectrum, via the equation of motion-phase matching approach (EOM-PMA), with the hierarchical equations of motion (HEOM). This theoretical framework is capable of simulating the 2D spectroscopy of vibronic systems with low frequency modes, coupled to environments of intermediate and slower timescales. In order to demonstrate the spectral filtering of vibronic coherences, we examine the elimination of lower energy peaks fromthe 2D spectra of a zinc porphyrin monomer on blue-shifting the laser spectrum. The filtering of Liouville pathways is revealed through the disappearance of peaks from the amplitude spectra for a coupled vibrational mode

Fostering Motivation toward Chemistry through Augmented Reality Educational Escape Activities. A Self-Determination Theory Approach

There is little doubt that motivation influences the extent to which individuals engage with online learning experiences. With the increasing role of digital technologies within chemistry higher education, this study illustrates how an augmented reality (AR)-supported educational escape activity (EEA), based on topics of inorganic stereochemistry, can be employed within an online environment. The design aspects of our activity were guided by principles of Self-Determination Theory (SDT)─an intrinsic-extrinsic theory of motivation. We sought to actively support the fundamental needs of competency, autonomy, and relatedness. Our control group was provided with a copy of our EEA that utilized two-dimensional drawings. Reported measures of competency were seen as a positive predictor of intrinsic motivation. However, in this study, this was not observed to be a positive predictor of academic performance. The introduction of AR, over and above the EEA, did not result in any significant differences in reported intrinsic motivation or post-test scores on our stereochemistry test instrument. Collected qualitative data suggest that participants found the activity to be useful and engaging. Through students’ discussions, we have provided evidence of how design aspects of the EEA support the psychological needs satisfaction outlined by SDT. The design of our EEA provides one approach to implementing this style of learning activity, in a way that supports virtual presence and is scalable to large student cohorts

Augmented reality and worked examples: Targeting organic chemistry competence

Instructional guidance, provided using worked examples, helps the inexperienced learner cope with complex information, that may be difficult to process in limited capacity working memory. For students of chemistry, such complex information can pertain to the visualisation of structural changes in molecules throughout chemical reactions. This can be alleviated through the affordances of augmented reality (AR) technology. 3D structures are important as they have a crucial impact on the chemical and physical properties of molecules. Within a framework of Cognitive Load Theory, this study illustrates how AR-supported worked examples may enhance learning of electrophilic aromatic substitution. The participant cohort were FHEQ level 5 undergraduate students studying a module of organic chemistry. In addition, the achievement motivation of learner's was also explored, and how this may be impacted by the provision of AR technology and worked examples. The control group was provided with a copy of our worked examples that contained 2D reaction mechanism drawings. Data was collected using a combination of quantitative instruments and qualitative surveys/interviews. For this cohort of students, significant intragroup improvements, and greater normalised change values, in conceptual understanding were observed in the AR group. This was not observed in the control group. No significant intergroup differences in reported cognitive load or achievement motivation of students were found. This was unaffected when introducing prior relevant chemistry experience as a covariate. Student feedback and subsequent thematic analysis show not only the positive impacts on student engagement, but also how students convey their understanding of electrophilic aromatic substitution principles

Exploring the effect of augmented reality on cognitive load, attitude, spatial ability, and stereochemical perception

Augmented reality (AR) has the capacity to afford a virtual experience that obviates the reliance on using two-dimensional representations of 3D molecules for teaching stereochemistry to undergraduate students. Using a combination of quantitative instruments and qualitative surveys/interviews, this study explored the relationships between students’ attitudes, perceived cognitive load, spatial ability, and academic performance when engaging in an asynchronous online stereochemistry activity. Our activity was designed using elements of game-based learning, and integrated AR technologies. The control group was provided with a copy of our activity that used two-dimensional drawings, whereas the AR group completed an activity using the AR technologies. For this cohort of students, results indicated significant improvement in academic performance in both the control and AR groups. The introduction of AR technologies did not result in the AR group outperforming the control group. Participants from both groups displayed significant improvements in spatial ability throughout the research period. Further, a moderate correlation (rs = 0.416) between students’ spatial ability and academic performance was found. No significant intergroup differences in the perceived cognitive loads of students were observed. A significant difference was observed on one item of the Intellectual Accessibility subscale of the ASCI (V2), Complicated–Simple. We found no correlation for student attitude or cognitive load with academic performance. The findings of this study provide insights for future AR-related studies to explore the role of spatial ability, student attitude, and cognitive load in learning performance

One- to Two-Exciton Transitions in Perylene Bisimide Dimer Revealed by Two-Dimensional Electronic Spectroscopy

The excited-state energy levels of molecular dimers and aggregates play a critical role in their photophysical behavior and an understanding of the photodynamics in such structures is important for developing applications such as photovoltaics and optoelectronic devices. Here, exciton transitions in two different covalently bound PBI dimers are studied by two-dimensional electronic spectroscopy (2DES), a powerful spectroscopic method, providing the most complete picture of vibronic transitions in molecular systems. The data are accurately reproduced using the equation of motion-phase matching approach. The unambiguous presence of one-exciton to two-exciton transitions are captured in our results and described in terms of a molecular exciton energy level scheme based on the Kasha model. Furthermore, the results are supported by comparative measurements with the PBI monomer and another dimer in which the interchromophore distance is increased