On-the-fly ab initio semiclassical evaluation of absorption spectra of polyatomic molecules beyond the Condon approximation

To evaluate vibronic spectra beyond the Condon approximation, we extend the on-the-fly ab initio thawed Gaussian approximation by considering the Herzberg-Teller contribution due to the dependence of the electronic transition dipole moment on nuclear coordinates. The extended thawed Gaussian approximation is tested on electronic absorption spectra of phenyl radical and benzene: Calculated spectra reproduce experimental data and are much more accurate than standard global harmonic approaches, confirming the significance of anharmonicity. Moreover, the extended method provides a tool to quantify the Herzberg-Teller contribution: we show that in phenyl radical, anharmonicity outweighs the Herzberg-Teller contribution, whereas in benzene, the Herzberg-Teller contribution is essential, since the transition is electronically forbidden and Condon approximation yields a zero spectrum. Surprisingly, both adiabatic harmonic spectra outperform those of the vertical harmonic model, which describes the Franck-Condon region better. Finally, we provide a simple recipe for orientationally averaging spectra, valid beyond Condon approximation, and a relation among the transition dipole, its gradient, and nonadiabatic coupling vectors.Comment: Final form available via open access in J. Phys. Chem. Lett.: https://pubs.acs.org/doi/10.1021/acs.jpclett.8b00827. Last 11 pages contain the Supporting Informatio

2024: anticipating record-breaking performances in front crawl swimming through mathematical analysis

Introduction: This study presented a novel approach to predict future front crawl swimming world records (WRs) by employing a methodology that integrated performance data from both running and front crawl swimming.Methods: By extracting the top one running and swimming performances from 1995 to 2023 and applying a model that correlates physiological characteristics such as maximum aerobic power, anaerobic capacity, the decrement in maximum power with prolonged effort, and performance speed and duration, it was possible to project the potential record-breaking performances in 2024 across various swimming distances for both male and female athletes. Furthermore, this approach was expected to be less susceptible to the influence of the full-body swimsuit era, which may have disrupted the typical trajectory of swimming performance progression.Results: The average relative error between the top one and estimated speeds in front crawl swimming (50–1,500 m, from 1995 to 2023, and for male and female) was 0.56% ± 0.17%. For male, WR in longer distances have been predicted with new WR in the 400 and 800 m. A more ambitious prediction was noted among female, with twice as many WR as among male illustrated by new WR in the 50, 200, 400 and 800 m.Discussion: This study illustrated that the utilization of a prediction model based on physiological parameters yielded plausible time estimates. Additionally, the research accentuated the ongoing trajectory of surpassing existing WR into 2024, illustrating the competitive zeal fueled by an emerging framework of exceptional swimmers

Predicting Temporal Gait Kinematics: Anthropometric Characteristics and Global Running Pattern Matter

Equations predicting stride frequency (SF) and duty factor (DF) solely based on running speed have been proposed. However, for a given speed, kinematics vary depending on the global running pattern (GRP), i.e., the overall individual movement while running, which depends on the vertical oscillation of the head, antero-posterior motion of the elbows, vertical pelvis position at ground contact, antero-posterior foot position at ground contact, and strike pattern. Hence, we first verified the validity of the aforementioned equations while accounting for GRP. Kinematics during three 50-m runs on a track (n = 20) were used with curve fitting and linear mixed effects models. The percentage of explained variance was increased by ≥133% for DF when taking into account GRP. GRP was negatively related to DF (p = 0.004) but not to SF (p = 0.08), invalidating DF equation. Second, we assessed which parameters among anthropometric characteristics, sex, training volume, and GRP could relate to SF and DF in addition to speed, using kinematic data during five 30-s runs on a treadmill (n = 54). SF and DF linearly increased and quadratically decreased with speed (p < 0.001), respectively. However, on an individual level, SF was best described using a second-order polynomial equation. SF and DF showed a non-negligible percentage of variance explained by random effects (≥28%). Age and height were positively and negatively related to SF (p ≤ 0.05), respectively, while GRP was negatively related to DF (p < 0.001), making them key parameters to estimate SF and DF, respectively, in addition to speed

PIMP Your Stride: Preferred Running Form to Guide Individualized Injury Rehabilitation

Despite the wealth of research on injury prevention and biomechanical risk factors for running related injuries, their incidence remains high. It was suggested that injury prevention and reconditioning strategies should consider spontaneous running forms in a more holistic view and not only the injury location or specific biomechanical patterns. Therefore, we propose an approach using the preferred running form assessed through the Volodalen(®) method to guide injury prevention, rehabilitation, and retraining exercise prescription. This approach follows three steps encapsulated by the PIMP acronym. The first step (P) refers to the preferred running form assessment. The second step (I) is the identification of inefficiency in the vertical load management. The third step (MP) refers to the movement plan individualization. The answers to these three questions are guidelines to create individualized exercise pathways based on our clinical experience, biomechanical data, strength conditioning knowledge, and empirical findings in uninjured and injured runners. Nevertheless, we acknowledge that further scientific justifications with appropriate clinical trials and mechanistic research are required to substantiate the approach

Using statistical parametric mapping to assess the association of duty factor and step frequency on running kinetic

Duty factor (DF) and step frequency (SF) were previously defined as the key running pattern determinants. Hence, this study aimed to investigate the association of DF and SF on 1) the vertical and fore-aft ground reaction force signals using statistical parametric mapping; 2) the force related variables (peaks, loading rates, impulses); and 3) the spring-mass characteristics of the lower limb, assessed by computing the force-length relationship and leg stiffness, for treadmill runs at several endurance running speeds. One hundred and fifteen runners ran at 9, 11, and 13 km/h. Force data (1000 Hz) and whole-body three-dimensional kinematics (200 Hz) were acquired by an instrumented treadmill and optoelectronic system, respectively. Both lower DF and SF led to larger vertical and fore-aft ground reaction force fluctuations, but to a lower extent for SF than for DF. Besides, the linearity of the force-length relationship during the leg compression decreased with increasing DF or with decreasing SF but did not change during the leg decompression. These findings showed that the lower the DF and the higher the SF, the more the runner relies on the optimization of the spring-mass model, whereas the higher the DF and the lower the SF, the more the runner promotes forward propulsion

Using statistical parametric mapping to assess the association of duty factor and step frequency on running kinetic

Duty factor (DF) and step frequency (SF) were previously defined as the key running pattern determinants. Hence, this study aimed to investigate the association of DF and SF on 1) the vertical and fore-aft ground reaction force signals using statistical parametric mapping; 2) the force related variables (peaks, loading rates, impulses); and 3) the spring-mass characteristics of the lower limb, assessed by computing the force-length relationship and leg stiffness, for treadmill runs at several endurance running speeds. One hundred and fifteen runners ran at 9, 11, and 13 km/h. Force data (1000 Hz) and whole-body three-dimensional kinematics (200 Hz) were acquired by an instrumented treadmill and optoelectronic system, respectively. Both lower DF and SF led to larger vertical and fore-aft ground reaction force fluctuations, but to a lower extent for SF than for DF. Besides, the linearity of the force-length relationship during the leg compression decreased with increasing DF or with decreasing SF but did not change during the leg decompression. These findings showed that the lower the DF and the higher the SF, the more the runner relies on the optimization of the spring-mass model, whereas the higher the DF and the lower the SF, the more the runner promotes forward propulsion