Internal Rotation Axis Research Articles

Simulation and analysis of 13C spin-rotation nuclear magnetic resonance relaxation rates of methyl groups

This work analyzes the nuclear spin–rotation contribution to the nuclear magnetic resonance relaxation of methyl groups from 10 rigid compounds (eight benzene derivatives with one, two, or three methyl groups and two bicyclic molecules) with internal rotation axes not aligned to the smallest molecular moment of inertia via molecular dynamics simulation and ab initio calculation. The molecular dynamics simulation and ab initio calculation of nuclear spin-rotation coupling constants reproduce the experimental behavior in selected systems. The presented methodology can help in the analysis and interpretation of experimental relaxation data.

Structure of Tris[2-(4-pyridyl)ethyl]phosphine, Tris[2-(2-pyridyl)ethyl]phosphine, and Their Chalcogenides in Solution: Dipole Moments, IR Spectroscopy, and DFT Study.

Tris(hetaryl)substituted phosphines and their chalcogenides are promising polydentate ligands for the design of metal complexes. An experimental and theoretical conformational analysis of tris[2-(4-pyridyl)ethyl]phosphine, tris[2-(2-pyridyl)ethyl]phosphine, and their chalcogenides was carried out by the methods of dipole moments, IR spectroscopy and DFT B3PW91/6-311++G(df,p) calculations. In solution, these compounds exist as an equilibrium of mainly non-eclipsed (synclinal or antiperiplanar) forms with a predominance of a symmetrical conformer having a gauche-orientation of the Csp3-Csp3 bonds of pyridylethyl substituents relative to the P=X bond (X = lone pair, O, S, Se) and a gauche-orientation of the pyridyl rings relative to the zigzag ethylene bridges. Regardless of the presence and nature of the chalcogen atom (oxygen, sulfur, or selenium) in the studied molecules with many axes of internal rotation, steric factors-the different position of the nitrogen atoms in the pyridyl rings and the configuration of ethylene bridges-determine the realization and spatial structure of preferred conformers.

Comparison of crystal structure and DFT calculations of triferrocenyl trithiophosphite’s conformance

A triferrocenyl trithiophosphite was studied by X-ray single-crystal diffraction. Triferrocenyl trithiophosphite has nine axes of internal rotation: three P-S bonds, three C-S bonds and three Fe-cyclopentadienyl axes. Rotation around the P-S bonds results in a totally asymmetric structure with three ferrocenylthio groups exhibiting different orientations towards the phosphorus lone electron pair (LEP). A comparison of DFT calculations and X-ray diffraction data is presented, herein we show which conformations are preferred for a given ligand.

A generalized framework for determination of functional musculoskeletal joint coordinate systems

Establishing anatomical coordinate systems (CS) from anatomical landmarks is sensitive to landmark selection. Vastly different results can be obtained amongst observers which can greatly affect the resulting joint kinematics. The aim of this study is to introduce an objective method for calculating functional CS definitions for bones in joints that observe three-cylindrical-joint kinematic chain decomposition methods and to apply the method on tibiofemoral joint specimens. This method is driven by low resistance joint motion during loading profiles and not from anatomical landmark selection. Two anatomical CS definitions were established from points collected by five observers, for twelve knees. The knees underwent passive flexion and internal/external rotation using the anatomical CSs. The kinematics from these profiles were used in linear least squares minimization of off-axis motions to redefine the tibia and femur origins, the femur flexion axis and the tibia internal rotation axis. Significant improvements in reproducibility of 7.4 mm (tibia origin, p < 0.001), 3.4 mm (femur origin, p < 0.001), and 2.9° (femur FE-axis, p < 0.001) between the two functional CSs compared to the two anatomical CSs were observed.Functional CSs led to significant decreases in off-axis motion during discrete passive flexion profiles. This new strategy for establishing functional CSs provides an objective approach that will reduce the effects of observer error in establishing CSs. Additionally, functional CSs allow for better interpretations of kinematic responses due to loading because effects of kinematic cross-talk is minimized.

Conformations and Low-Frequency Intramolecular Motions of 1-Butanol, 1-Butanethiol, Iso-butanol, and Iso-butanethiol Investigated by Fourier Transform Microwave Spectroscopy Combined with Quantum Chemical Calculations.

The rotational spectra of 1-butanol (1-BuOH), 1-butanethiol (1-BuSH), 2-methyl-1-propanol (iso-BuOH), and 2-methyl-1-propanethiol (iso-BuSH) were measured by Fourier transform microwave spectroscopy in the frequency region from 3.7 up to 25 GHz. The observed spectral lines were assigned by observation of the deuterium substitution effect and by ab initio or density functional theory calculations at the levels of MP2/6-311++G(d,p) or B3LYP and cam-B3LYP, respectively. For 1-BuOH and 1-BuSH, seven of the 14 conformations, anticipated to exist as stable, were detected, whereas four and three among the five possible conformations were identified for iso-BuOH and iso-BuSH, respectively. We further found that, of the seven conformers of 1-BuOH, five were trans and two gauche, with respect to the internal rotation axis: the C2-C3 bond, while three of iso-BuOH existed in gauche and one in trans. The most stable conformer of the two BuOH molecules was trans with respect to the C-O bond, while all the sulfur analogues were gauche to the C-S axis. The rare isotopomers examined included 13C and OD of 1-BuOH and OD of iso-BuOH, 34S, 13C, and SD of the two sulfur molecules, and the rotational constants obtained on these isotopomers were employed in the molecular structure derivation. The potential barrier to CH3 internal rotation and the deuterium quadrupole coupling constant, where available, were also derived from the spectral analysis, and the molecular parameters thus obtained were compared with those derived using quantum-chemical calculations; the values derived using cam-B3LYP/6-311++G(d,p) were in better agreement with the observed than those derived using MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p). The TTg form of 1-BuOH and of 1-BuSH and the Tg form of iso-BuSH exhibited additional spectral splittings, which were interpreted as caused by the OH or SH group tunneling between the symmetric and antisymmetric states. Some of the J = 8 rotational levels of 1-BuSH happened to be near-degenerate with others, and the splittings in them caused by mutual repulsion could be precisely determined by the observation of the transitions involving those split levels. Such splittings were determined for 1-BuSH, 1-BuSD, and iso-BuSH to be 1694.1731 (22), 56.3174 (16), and 6.4678 (14) MHz, respectively. A natural bond orbital analysis was performed to show that the most stable conformation of the primary and secondary alcohols is Gt because of the charge transfer from the lone-pair electron of the oxygen atom to the antibonding orbital of the C-H bond in 1-BuOH, whereas in iso-BuOH, the charge transfer to the antibonding orbital of the C1-C2 bond.

The low-barrier methyl internal rotation in the rotational spectrum of 3-methylphenylacetylene

The rotational spectrum of 3-methylphenylacetylene has been recorded in the 2–8 GHz region using a chirped-pulse broadband microwave spectrometer. Torsion-rotation transition splittings are observed from a tunneling motion along the methyl internal rotation axis. The XIAM program was used to characterize the splitting, yielding an internal rotation barrier, V3, of 11.4259722±0.00002 cm−1. While this barrier is considered low, fits of A-state only transitions yield a quality, rigid-rotor fit, and are compared to the combined A/E fits. Computationally predicted barriers are estimated between 14.4 and 28.9 cm−1.

Internal methyl rotation and molecular structure of trifluorotoluenes: microwave rotational spectra of 2,3,4- and 2,4,5-trifluorotoluene

The microwave rotational spectra of 2,3,4- and 2,4,5-trifluorotoluenes, along with all13C isotopic species in natural abundance, have been recorded in the frequency range 8–27 GHz employing pulsed-jet Fourier transform microwave spectroscopy. The analysis of the spectra in the lowest torsional state has yielded the rotational constants, centrifugal distortion constants, three-fold barrier to methyl rotation, and the direction of the internal rotation axis in the moment of inertia principal axes systems of these trifluorotoluenes. For both molecules, the molecular constants of their eight isotopologues have been used to obtain the substitution rsstructures of the ring and the methyl-carbon. The potential barriers hindering the internal rotation of the methyl top in 2,3,4- and 2,4,5-trifluorotluene are 2.5878(80) and 2.2809(23) kJ/mol, respectively.

New perspectives on ACL injury: On the role of repetitive sub-maximal knee loading in causing ACL fatigue failure.

ABSTRACTIn this paper, we review a series of studies that we initiated to examine mechanisms of anterior cruciate ligament (ACL) injury in the hope that these injuries, and their sequelae, can be better prevented. First, using the earliest in vitro model of a simulated single‐leg jump landing or pivot cut with realistic knee loading rates and trans‐knee muscle forces, we identified the worst‐case dynamic knee loading that causes the greatest peak ACL strain: Combined knee compression, flexion, and internal tibial rotation. We also identified morphologic factors that help explain individual susceptibility to ACL injury. Second, using the above knee loading, we introduced a possible paradigm shift in ACL research by demonstrating that the human ACL can fail by a sudden rupture in response to repeated sub‐maximal knee loading. If that load is repeated often enough over a short time interval, the failure tended to occur proximally, as observed clinically. Third, we emphasize the value of a physical exam of the hip by demonstrating how limited internal axial rotation at the hip both increases the susceptibility to ACL injury in professional athletes, and also increases peak ACL strain during simulated pivot landings, thereby further increasing the risk of ACL fatigue failure. When training at‐risk athletes, particularly females with their smaller ACL cross‐sections, rationing the number and intensity of worst‐case knee loading cycles, such that ligament degradation is within the ACL's ability to remodel, should decrease the risk for ACL rupture due to ligament fatigue failure.© 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:2059–2068, 2016.

Microwave spectra of the SiH4-H2O complex: A new sort of intermolecular interaction

Microwave spectral patterns observed for the silane-water complex were found much different from those of the methane-water complex. The SiH4-H2O complex is likely to have a tightly bound structure. The effective rotational and centrifugal distortion constants: B = 3621.1193 (45) MHz and DJ = 49.84 (30) kHz led to the distance between the Si and O atoms in the complex to be 3.3 Å, much shorter than the C and O separation in the CH4-H2O of 3.7 Å, and to the silane-water stretching force constant and stretching frequency to be 2.88 N/m and 65 cm−1, respectively, which are to be compared with 1.52 N/m and 55 cm−1 of the CH4-H2O. The characteristic features of the spectra observed for the main species 28SiH4-H2O are common to those of isotopic species: 29SiH4-H2O, 30SiH4-H2O, 28SiH4-H218O, 28SiH4-D2O, 29SiH4-D2O, 30SiH4-D2O, 28SiH4-HDO, 29SiH4-HDO, 30SiH4-HDO, 28SiD4-H2O, 28SiD4-D2O, and 28SiD4-HDO. The observed spectra also indicate that the silane executes a threefold internal rotation about one of its four Si–H bonds, while the C2 symmetry axis of the water is bent away from the internal-rotation axis. An internal axis method analysis yielded an estimate of the internal-rotation potential barrier V3 to be 140 ± 50 cm−1, and those based on diagonalization of a principal axis method Hamiltonian matrix and on the extended internal axis method resulted in V3 ranging from 180 to 100 cm−1, depending on the isotopic species studied. All the measurements were done by using a pulsed nozzle Fourier transform microwave spectrometer, and the spectral assignments were made with the aid of the Stark effect, which yielded the dipole moment to be 1.730 (10) D. Transitions in higher energy states of the SiH4 internal rotation were observed, clearly resolved from the main lines, when the carrier gas was replaced from Ar to Ne.

Global Dynamics and Exchange Kinetics of a Protein on the Surface of Nanoparticles Revealed by Relaxation-Based Solution NMR Spectroscopy.

The global motions and exchange kinetics of a model protein, ubiquitin, bound to the surface of negatively charged lipid-based nanoparticles (liposomes) are derived from combined analysis of exchange lifetime broadening arising from binding to nanoparticles of differing size. The relative contributions of residence time and rotational tumbling to the total effective correlation time of the bound protein are modulated by nanoparticle size, thereby permitting the various motional and exchange parameters to be determined. The residence time of ubiquitin bound to the surface of both large and small unilamellar liposomes is ∼20 μs. Bound ubiquitin undergoes internal rotation about an axis approximately perpendicular to the lipid surface on a low microsecond time scale (∼2 μs), while simultaneously wobbling in a cone of semiangle 30-55° centered about the internal rotation axis on the nanosecond time scale. The binding interface of ubiquitin with liposomes is mapped by intermolecular paramagnetic relaxation enhancement using Gd(3+)-tagged vesicles, to a predominantly positively charged surface orthogonal to the internal rotation axis.

Analysis of the effects of high tibial osteotomy on tibial rotation.

Limited literature reports on internal and external rotation of the distal fragment in the context of valgus open wedge (OW) high tibial osteotomy (HTO). In the authors clinical observation, the distal fragment was always rotated internally in relation to the proximal fragment by the end of the surgical procedure. The purpose was to evaluate the influence of valgus OW-HTO on post-operative tibial torsion. Prospective case series. Fifty patients (10 female, 40 male; mean age 42.1 ± 9.4years) underwent valgus OW- HTO. The osteotomy was spread and fixed with a locking plate at the posteromedial aspect of the proximal tibia. The osteotomy of the tibial tuberosity was performed either proximally or distally dependent on the patello-femoral findings. Two independent observers measured axial tibial rotation using K-wires placed into the anterior margin of the tibia proximal and distal to the osteotomy. An overall mean of 4.4 ± 2.8° internal rotation of the distal tibia has been shown. In four patients with additional single step double bundle ACL-replacement after harvesting ipsilateral autologous hamstring grafts, the distal tibia rotated internally by 0.1 ± 0.3°, accordingly in the other 46 patients by 4.8 ± 2.6°. Valgus OW-HTO produces significant internal axial rotation of the distal tibia. This might be caused by soft tissue tension of the medial hamstrings/soft tissue structures and the location of the lateral tibial hinge. Surgeons have to take into consideration that valgus OW HTO might result in significant 3D changes of the tibia. Higher degrees of internal torsion of the tibia might influence overall gait mechanics and specifically alternate patellofemoral kinematics.

Restriction in hip internal rotation is associated with an increased risk of ACL injury.

Evidence suggests that femoroacetabular impingement (FAI) in athletes may increase the risk of anterior cruciate ligament (ACL) injury. This study correlates ACL injury with hip range of motion in a consecutive series of elite, contact athletes and tests the hypothesis that a restriction in the available hip axial rotation in a dynamic in silico model of a simulated pivot landing would increase ACL strain and the risk of ACL rupture. Three hundred and twenty-four football athletes attending the 2012 NFL National Invitational Camp were examined. Hip range of internal rotation was measured and correlated with a history of ACL injury and surgical repair. An in silico biomechanical model was used to study the effect of FAI on the peak relative ACL strain developed during a simulated pivot landing. The in vivo results demonstrated that a reduction in internal rotation of the left hip was associated with a statistically significant increased odds of ACL injury in the ipsilateral or contralateral knee (OR 0.95, p=0.0001 and p<0.0001, respectively). A post-estimation calculation of odds ratio for ACL injury based on deficiency in hip internal rotation demonstrated that a 30-degree reduction in left hip internal rotation was associated with 4.06 and 5.29 times greater odds of ACL injury in the ipsilateral and contralateral limbs, respectively. The in silico model demonstrated that FAI systematically increased the peak ACL strain predicted during the pivot landing. FAI may be associated with ACL injury because of the increased resistance to femoral internal axial rotation during a dynamic maneuver such as a pivot landing. This insight may lead to better interventions to prevent ACL injury and improved understanding of ACL reconstruction failure. Cohort study, Level IV.

Microwave spectrum of formic acetic anhydride

Rotational transitions of formic acetic anhydride (HCO–O–COCH3) have been measured with angular momenta J = 2 to 6 between 11 and 26 GHz. All transitions showed splittings of up to 60 MHz due to the hindered internal rotation of the methyl group. The frequencies of observed transitions have been fitted to those calculated numerically for the simultaneous overall and internal rotation of formic acetic anhydride. Three moments of inertia, the barrier to internal rotation and the angle between the internal rotation axis and the principal axis a have been determined, but the moment of inertia of the methyl group had to be assumed. The moments of inertia are consistent with all nuclei lying in a symmetry plane except of two hydrogen nuclei in the methyl group.

Disentangling the Puzzle of Hydrogen Bonding in Vitamin C.

Fast-passage Fourier transform microwave spectroscopy in combination with a laser ablation source has been successfully applied to probe vitamin C (l-ascorbic acid) in the gas phase. Its ethyldiol side chain and two hydroxyl groups around the γ-lactone ring provide five internal rotation axes, enabling vitamin C to assume a wide variety of nonplanar 3D cooperative hydrogen bond networks that can also include the keto and ether functions. The rotational constants extracted from the analysis of the spectrum unequivocally identify the existence of three dominant conformers stabilized by different intramolecular hydrogen bonding motifs forming five-, six-, or seven-membered rings.

Comparative Matrix Isolation Infrared Spectroscopy Study of 1,3- and 1,4-Diene Monoterpenes (α-Phellandrene and γ-Terpinene)

In the present work, γ-terpinene (a 1,4-diene derivative) and α-phellandrene (1,3-diene derivative) were isolated in cryogenic argon matrices and their structures, vibrational spectra, and photochemistries were characterized with the aid of FTIR spectroscopy and quantum chemical calculations performed at the DFT/B3LYP/6-311++G(d,p) level of approximation. The molecules bear one conformationally relevant internal rotation axis, corresponding to the rotation of the isopropyl group. The calculations provide evidence of three minima on the potential energy surfaces of the studied molecules, where the isopropyl group assumes the trans, gauche+, and gauche- conformations (T, G+, G-). The signatures of all these conformers were identified in the experimental matrix infrared spectra, with the T forms dominating, in agreement with the theoretical predicted abundances in gas phase at room temperature. In situ UV (λ > 200 nm) irradiation of matrix-isolated α-phellandrene led to its isomerization into an open-ring species. The photoproduct was found to exhibit the ZE configuration of its backbone, which to be formed from the reactant molecule does not require extensive structural rearrangements of both the reagent and matrix. γ-Terpinene was photostable when subjected to irradiation under the same experimental conditions. In addition, the liquid compounds at room temperature were also investigated by FTIR-ATR and FT-Raman spectroscopies.

Knee Rotation and Loading during Spin and Step Turn

The tibia axial rotation and knee joint valgus torque may increase anterior cruciate ligament (ACL) tension in direction changes during daily activities. The purpose of the study was to compare knee joint rotation and torque between step turn and spin turn in direction change following walking downstairs. The knee joint axial rotation and valgus torque were quantified from 20 healthy subjects. Significant differences were found between 2 turn strategies and between 2 legs. Spin turn showed significantly greater internal tibia rotation (13.5°±5.9°), greater tibia rotation range of motion (-15.1°∼13.5°) than step turn (5.1°±5.2° and -11.5°∼5.1°) for both legs. Significantly greater peak valgus torque during spin turn (-0.91±0.33 Nm/kg) was found than that during step turn (-0.25±0.32 Nm/kg) for the left leg, while there was no significant difference between 2 turn strategies for the right leg (spin turn: -0.44±0.23 Nm/kg, and step turn: -0.40±0.27 N/kg). Excessive internal axial rotation combined with higher valgus torque may make the ACL and ACL graft more vulnerable to injury. The study indicated that, for right dominant people, turning with right leg or using step turn might reduce the stress on the ACL or ACL graft after ACL reconstruction.

On the Physical Reasons for the Extension of Symmetry Groups in Molecular Spectroscopy

Several situations of general interest, in which the symmetry groups usually applied to spectroscopy problems need to be extended, are reviewed. It is emphasized that any symmetry group of geometrical operations to be used in Molecular Spectroscopy should be extended for completeness by considering the time reversal operator, as far as the Hamiltonian is invariant with respect to the inversion of the direction of motion. This can explain the degeneracy of pairs of vibrational and rotational states spanning the so-called separably degenerate irreducible representations, in symmetric tops of low symmetry, and Kramers degeneracy in odd electron molecules in the absence of magnetic fields. An extension with account of time reversal is also useful to determine relative phase conventions on vibration-rotation wavefunctions, which render all vibration-rotation matrix elements real. An extension of a molecular symmetry group may be required for molecules which can attain different geometries by large amplitude periodical motions, if such motions are hindered and are not completely free. Special cases involving the internal rotation are discussed in detail. It is observed that the symmetry classification of vibrational modes involving displacements normal to the internal rotation axis is not univocal, but can be done in several ways, which actually correspond to different conventions on the separation of vibration and internal rotation in the adopted basis functions. The symmetry species of the separate vibrational and torsional factors of these functions depend on the adopted convention.

Knee model sensitivity to cruciate ligaments parameters: A stability simulation study for a living subject

If the biomechanic function of the different anatomical sub-structures of the knee joint was needed in physiological conditions, the only possible way is a modelling approach. Subject-specific geometries and kinematic data, acquired from the same living subject, were the foundations of the 3D quasi-static knee model developed. Each cruciate ligament was modelled by means of 25 elastic springs, paying attention to the anatomical twisting of the fibres. The sensitivity of the model to the cross-sectional area was performed during the anterior/posterior tibial translations, the sensitivity to all the cruciate ligaments parameters was performed during the internal/external rotations. The model reproduced very well the mechanical behaviour reported in literature during anterior/posterior translations, in particular considering 30% of the mean insertional area. During the internal/external tibial rotations, similar behaviour of the axial torques was obtained in the three sensitivity analyses. The overlapping of the ligaments was assessed at about 25° of internal axial rotation. The presented model featured a good level of accuracy in combination with a low computational weight, and it could provide an in vivo estimation of the role of the cruciate ligaments during the execution of daily living activities.

The microwave and submillimeterwave spectrum of 13C 1-methyl formate in its ground torsional state (H 13COOCH 3)

The rotational spectrum of 13C 1 methyl formate (H 13COOCH 3) has been observed in the frequency range 7–610 GHz. Two hundred and ninety one transitions up to J=58 ( K max=24) were assigned to the A-species of the ground torsional state. They could be fitted to a standard Watsonian involving 19 parameters (up to one decic centrifugal distortion constant). About 260 E-transitions were also assigned. A global analysis of all these transitions using the internal axis method gave a satisfactory fit permitting to determine the three internal rotation parameters ( I α =3.132(4) μÅ 2, V 3=4912(6) J/mol and ∠( i, a)=52.30(5)°, which is the angle between the principal axis a and the internal rotation axis i) and allowing us to make an accurate prediction of the rotational spectrum.

Isokinetic dynamometry in assessment of external and internal axial rotation strength of the shoulder: Comparison of two positions

Background: Measuring isokinetic strength of the shoulder complex is potentially an important clinical tool in both diagnosis and management of injury and pathology. However, a clinically relevant position is yet to be established. Objectives: To establish an appropriate and repeatable protocol to evaluate the functional strength of both internal and external rotators of the glenohumeral joint to enable assessment of clinical injury management and training related developments in upper limb strength. Methods: A population cross-sectional study of shoulder internal and external rotational strengths of 17 normal, healthy volunteers (11 males, 6 females) aged 21 to.45 years were measured both isokinetically and isometrically. Two test positions: seated and supine, were compared by way of reliability and repeatability analyses. Humeral rotation was performed at 45° of abduction in the scapular plane seated, and at 90° of abduction in the supine position. Results: Throughout concentric testing, when the population was considered as a whole the left shoulder data appeared more repeatable than the right shoulder. This however, was not evident when the study population was divided into single sex groupings. Equally, whilst the repeatability trend of sitting vs. supine position was skewed towards the former, more evident in the left shoulder, this was less apparent when sexes were analysed separately. All comparative measures were statistically insignificant. Conclusion: The findings of this study suggest that measurements of isokinetic shoulder rotation strength are highly prone to both joint specific and non-specific errors.