Treating linear molecules in calculations of rotation-vibration spectra

In this article, a numerical implementation of the exact kinetic energy operator (KEO) for triatomic molecules (symmetric of XY2-type and asymmetric of YXZ-type) is presented. The implementation is based on the valence coordinates with the bisecting (XY2-type molecules) and bond-vector (YXZ) embeddings and includes the treatment of the singularity at linear geometry. The KEO is represented in a sum-of-product form. The singularity caused by the undetermined angle at the linear configuration is resolved with the help of the associated Legendre and Laguerre polynomials used as parameterized bending basis functions in the finite basis set representation. The exact KEO implementation is combined with the variational solver theoretical rovibrational energies, equipped with a general automatic symmetry-adaptation procedure and efficient basis step contraction schemes, providing a powerful computational solver of triatomic molecules for accurate computations of highly excited ro-vibrational spectra. The advantages of different basis set choices are discussed. Examples of specific applications for computing hot spectra of linear molecules are given

Artificial Symmetries for Calculating Vibrational Energies of Linear Molecules

Linear molecules usually represent a special case in rotational-vibrational calculations due to a singularity of the kinetic energy operator that arises from the rotation about the a (the principal axis of least moment of inertia, becoming the molecular axis at the linear equilibrium geometry) being undefined. Assuming the standard ro-vibrational basis functions, in the 3N−6 approach, of the form ∣∣ν1,ν2,νℓ33;J,k,m⟩ , tackling the unique difficulties of linear molecules involves constraining the vibrational and rotational functions with k=ℓ3 , which are the projections, in units of ℏ, of the corresponding angular momenta onto the molecular axis. These basis functions are assigned to irreducible representations (irreps) of the C2v (M) molecular symmetry group. This, in turn, necessitates purpose-built codes that specifically deal with linear molecules. In the present work, we describe an alternative scheme and introduce an (artificial) group that ensures that the condition ℓ3=k is automatically applied solely through symmetry group algebra. The advantage of such an approach is that the application of symmetry group algebra in ro-vibrational calculations is ubiquitous, and so this method can be used to enable ro-vibrational calculations of linear molecules in polyatomic codes with fairly minimal modifications. To this end, we construct a—formally infinite—artificial molecular symmetry group D∞h (AEM), which consists of one-dimensional (non-degenerate) irreducible representations and use it to classify vibrational and rotational basis functions according to ℓ and k. This extension to non-rigorous, artificial symmetry groups is based on cyclic groups of prime-order. Opposite to the usual scenario, where the form of symmetry adapted basis sets is dictated by the symmetry group the molecule belongs to, here the symmetry group D∞h (AEM) is built to satisfy properties for the convenience of the basis set construction and matrix elements calculations. We believe that the idea of purpose-built artificial symmetry groups can be useful in other applications

Testing covariance models for MEG source reconstruction of hippocampal activity

Beamforming is one of the most commonly used source reconstruction methods for magneto- and electroencephalography (M/EEG). One underlying assumption, however, is that distant sources are uncorrelated and here we tested whether this is an appropriate model for the human hippocampal data. We revised the Empirical Bayesian Beamfomer (EBB) to accommodate specific a-priori correlated source models. We showed in simulation that we could use model evidence (as approximated by Free Energy) to distinguish between different correlated and uncorrelated source scenarios. Using group MEG data in which the participants performed a hippocampal-dependent task, we explored the possibility that the hippocampus or the cortex or both were correlated in their activity across hemispheres. We found that incorporating a correlated hippocampal source model significantly improved model evidence. Our findings help to explain why, up until now, the majority of MEG-reported hippocampal activity (typically making use of beamformers) has been estimated as unilateral

Interference suppression techniques for OPM-based MEG: Opportunities and challenges

One of the primary technical challenges facing magnetoencephalography (MEG) is that the magnitude of neuromagnetic fields is several orders of magnitude lower than interfering signals. Recently, a new type of sensor has been developed – the optically pumped magnetometer (OPM). These sensors can be placed directly on the scalp and move with the head during participant movement, making them wearable. This opens up a range of exciting experimental and clinical opportunities for OPM-based MEG experiments, including paediatric studies, and the incorporation of naturalistic movements into neuroimaging paradigms. However, OPMs face some unique challenges in terms of interference suppression, especially in situations involving mobile participants, and when OPMs are integrated with electrical equipment required for naturalistic paradigms, such as motion capture systems. Here we briefly review various hardware solutions for OPM interference suppression. We then outline several signal processing strategies aimed at increasing the signal from neuromagnetic sources. These include regression-based strategies, temporal filtering and spatial filtering approaches. The focus is on the practical application of these signal processing algorithms to OPM data. In a similar vein, we include two worked-through experiments using OPM data collected from a whole-head sensor array. These tutorial-style examples illustrate how the steps for suppressing external interference can be implemented, including the associated data and code so that researchers can try the pipelines for themselves. With the popularity of OPM-based MEG rising, there will be an increasing need to deal with interference suppression. We hope this practical paper provides a resource for OPM-based MEG researchers to build upon

Using OPMs to measure neural activity in standing, mobile participants

Optically pumped magnetometer-based magnetoencephalography (OP-MEG) can be used to measure neuromagnetic fields while participants move in a magnetically shielded room. Head movements in previous OP-MEG studies have been up to 20 cm translation and ∼30° rotation in a sitting position. While this represents a step-change over stationary MEG systems, naturalistic head movement is likely to exceed these limits, particularly when participants are standing up. In this proof-of-concept study, we sought to push the movement limits of OP-MEG even further. Using a 90 channel (45-sensor) whole-head OP-MEG system and concurrent motion capture, we recorded auditory evoked fields while participants were: (i) sitting still, (ii) standing up and still, and (iii) standing up and making large natural head movements continuously throughout the recording - maximum translation 120 cm, maximum rotation 198°. Following pre-processing, movement artefacts were substantially reduced but not eliminated. However, upon utilisation of a beamformer, the M100 event-related field localised to primary auditory regions. Furthermore, the event-related fields from auditory cortex were remarkably consistent across the three conditions. These results suggest that a wide range of movement is possible with current OP-MEG systems. This in turn underscores the exciting potential of OP-MEG for recording neural activity during naturalistic paradigms that involve movement (e.g. navigation), and for scanning populations who are difficult to study with stationary MEG (e.g. young children)

Transformation Properties under the Operations of the Molecular Symmetry Groups G36 and G36(EM) of Ethane H3CCH3

In the present work, we report a detailed description of the symmetry properties of the eight-atomic molecule ethane, with the aim of facilitating the variational calculations of rotation-vibration spectra of ethane and related molecules. Ethane consists of two methyl groups CH3 where the internal rotation (torsion) of one CH3 group relative to the other is of large amplitude and involves tunnelling between multiple minima of the potential energy function. The molecular symmetry group of ethane is the 36-element group G36, but the construction of symmetrised basis functions is most conveniently done in terms of the 72-element extended molecular symmetry group G36(EM). This group can subsequently be used in the construction of block-diagonal matrix representations of the ro-vibrational Hamiltonian for ethane. The derived transformation matrices associated with G36(EM) have been implemented in the variational nuclear motion program TROVE (Theoretical ROVibrational Energies). TROVE variational calculations are used as a practical example of a G36(EM) symmetry adaptation for large systems with a non-rigid, torsional degree of freedom. We present the derivation of irreducible transformation matrices for all 36 (72) operations of G36(M) (G36(EM)) and also describe algorithms for a numerical construction of these matrices based on a set of four (five) generators. The methodology presented is illustrated on the construction of the symmetry-adapted representations both of the potential energy function of ethane and of the rotation, torsion and vibration basis set functions

Modelling optically pumped magnetometer interference in MEG as a spatially homogeneous magnetic field

Here we propose that much of the magnetic interference observed when using optically pumped magnetometers for MEG experiments can be modeled as a spatially homogeneous magnetic field. We show that this approximation reduces sensor level variance and substantially improves statistical power. This model does not require knowledge of the underlying neuroanatomy nor the sensor positions. It only needs information about the sensor orientation. Due to the model's low rank there is little risk of removing substantial neural signal. However, we provide a framework to assess this risk for any sensor number, design or subject neuroanatomy. We find that the risk of unintentionally removing neural signal is reduced when multi-axis recordings are performed. We validated the method using a binaural auditory evoked response paradigm and demonstrated that removing the homogeneous magnetic field increases sensor level SNR by a factor of 3. Considering the model's simplicity and efficacy, we suggest that this homogeneous field correction can be a powerful preprocessing step for arrays of optically pumped magnetometers

Optically pumped magnetoencephalography in epilepsy

We demonstrate the first use of Optically Pumped Magnetoencephalography (OP-MEG) in an epilepsy patient with unrestricted head movement. Current clinical MEG uses a traditional SQUID system, where sensors are cryogenically cooled and housed in a helmet in which the patient's head is fixed. Here, we use a different type of sensor (OPM), which operates at room temperature and can be placed directly on the patient's scalp, permitting free head movement. We performed OP-MEG recording in a patient with refractory focal epilepsy. OP-MEG-identified analogous interictal activity to scalp EEG, and source localized this activity to an appropriate brain region

Effect of floor type on the performance, physiological and behavioural responses of finishing beef steers

peer-reviewedBackground:The study objective was to investigate the effect of bare concrete slats (Control), two types of mats [(Easyfix mats (mat 1) and Irish Custom Extruder mats (mat 2)] fitted on top of concrete slats, and wood-chip to simulate deep bedding (wood-chip placed on top of a plastic membrane overlying the concrete slats) on performance, physiological and behavioral responses of finishing beef steers. One-hundred and forty-four finishing steers (503 kg; standard deviation 51.8 kg) were randomly assigned according to their breed (124 Continental cross and 20 Holstein–Friesian) and body weight to one of four treatments for 148 days. All steers were subjected to the same weighing, blood sampling (jugular venipuncture), dirt and hoof scoring pre study (day 0) and on days 23, 45, 65, 86, 107, 128 and 148 of the study. Cameras were fitted over each pen for 72 h recording over five periods and subsequent 10 min sampling scans were analysed. Results: Live weight gain and carcass characteristics were similar among treatments. The number of lesions on the hooves of the animals was greater (P < 0.05) on mats 1 and 2 and wood-chip treatments compared with the animals on the slats. Dirt scores were similar for the mat and slat treatments while the wood-chip treatment had greater dirt scores. Animals housed on either slats or wood-chip had similar lying times. The percent of animals lying was greater for animals housed on mat 1 and mat 2 compared with those housed on concrete slats and wood chips. Physiological variables showed no significant difference among treatments. Conclusions: In this exploratory study, the performance or welfare of steers was not adversely affected by slats, differing mat types or wood-chip as underfoot material