Application of Berlin's Theorem to Bond-Length Changes in Isolated Molecules and Red- and Blue-Shifting H-Bonded Clusters

2008 ◽  
Vol 73 (6-7) ◽  
pp. 862-872 ◽  
Author(s):  
Weizhou Wang ◽  
Pavel Hobza
Keyword(s):  
Bond Length ◽  
Electron Density ◽  
Chemical Bond ◽  
Length Change ◽  
Molecular Cluster ◽  
Analysis Method ◽  
Electrostatic Forces ◽  
Binding Region ◽  
Electron Density Difference ◽  
Length Changes

The origin of the bond-length change in molecule or molecular cluster has been investigated at the MP2/aug-cc-pVDZ level of theory using the electrostatic potential or the electron density difference analysis method. Our results have clearly shown that the bond-length change of a chemical bond is determined mainly by the balance of the electrostatic forces exerted by electrons on the two nuclei. The factors that affect the balance of the electrostatic forces include four parts: (i) The abstraction of the electron density from Berlin's binding region between the two nuclei. (ii) The accumulation of the electron density in Berlin's antibinding regions. (iii) The accumulation of the electron density in Berlin's binding region between the two nuclei. (iv) The abstraction of the electron density from Berlin's antibinding regions. Using the change of the electron density around the two nuclei of a chemical bond, we have succeeded in explaining two important chemical phenomena: (i) breakdown of bond length-bond strength correlation; (ii) the bond-length change in the hydrogen bond.

Negative hyperconjugation and red-, blue- or zero-shift in X–Z⋯Y complexes

2015 ◽  
Vol 177 ◽  
pp. 33-50 ◽  
Author(s):  
Jyothish Joy ◽  
Eluvathingal D. Jemmis ◽  
Kaipanchery Vidya
Keyword(s):  
Bond Length ◽  
Electron Density ◽  
Lone Pair ◽  
Length Change ◽  
Length Variation ◽  
Computational Studies ◽  
Zero Shift ◽  
Negative Hyperconjugation ◽  
Exchange Repulsion ◽  
Major Factors

A generalized explanation is provided for the existence of the red- and blue-shifting nature of X–Z bonds (Z = H, halogens, chalcogens, pnicogens, etc.) in X–Z⋯Y complexes based on computational studies on a selected set of weakly bonded complexes and analysis of existing literature data. The additional electrons and orbitals available on Z in comparison to H make for dramatic differences between the H-bond and the rest of the Z-bonds. The nature of the X-group and its influence on the X–Z bond length in the parent X–Z molecule largely controls the change in the X–Z bond length on X–Z⋯Y bond formation; the Y-group usually influences only the magnitude of the effects controlled by X. The major factors which control the X–Z bond length change are: (a) negative hyperconjugative donation of electron density from X-group to X–Z σ* antibonding molecular orbital (ABMO) in the parent X–Z, (b) induced negative hyperconjugation from the lone pair of electrons on Z to the antibonding orbitals of the X-group, and (c) charge transfer (CT) from the Y-group to the X–Z σ* orbital. The exchange repulsion from the Y-group that shifts partial electron density at the X–Z σ* ABMO back to X leads to blue-shifting and the CT from the Y-group to the σ* ABMO of X–Z leads to red-shifting. The balance between these two opposing forces decides red-, zero- or blue-shifting. A continuum of behaviour of X–Z bond length variation is inevitable in X–Z⋯Y complexes.

Theoretical study of H bonds of HArF and HF with isoelectronic systems N2, CO, and BF

2010 ◽  
Vol 88 (4) ◽  
pp. 352-361
Author(s):  
An Yong Li ◽  
Li Juan Cao ◽  
Hong Bo Ji
Keyword(s):  
Frequency Shift ◽  
Bond Length ◽  
Electron Density ◽  
Electrostatic Interaction ◽  
Theoretical Study ◽  
Blue Shift ◽  
Length Change ◽  
Red Shift ◽  
P Value ◽  
Small Contribution

The H bonds of HArF and HF with N2, CO, and BF were studied at the MP2(full)/6-311++G(2d, 2p) level. The results show that only the complexes WY···HArF (WY = N2, OC) and WY···HF (WY = N2, OC, FB) are stable, the H-bonding WY···HArF leads to contraction of the HAr bond with a concomitant frequency blue shift, but the H-bonding WY···HF causes the HF bond to elongate with a frequency red shift. A quantity P is defined to measure polarization of the HX bond; the H bonding causes the P value of the HX bond (X = Ar, F) to increase. The HX bond length change and frequency shift in the H-bonding WY···HArF and WY···HF are mainly caused by intermolecular hyperconjugation, n(Y) → σ*(HX) (X = Ar, F), where electrostatic interaction has only a small contribution. In HArF, the strong intramolecular hyperconjugation, n(F) → σ*(HAr), can adjust electron density on σ*(HAr); upon formation of H bonding, the HAr stretching frequency blue shift is caused by a decrease of intramolecular hyperconjugation and an increase of the s character of the Ar hybrid in the HAr bond, induced by the intermolecular hyperconjugation. In the H bonds of HF without intramolecular hyperconjugation, the intermolecular hyperconjugation, n(Y) → σ*(HF), leads to a red shift of the HF bond, although there is also large rehybridization.

scholarly journals Medial collateral ligament reconstruction graft isometry is effected by femoral position more than tibial position

2021 ◽  
Author(s):  
Christoph Kittl ◽  
James Robinson ◽  
Michael J. Raschke ◽  
Arne Olbrich ◽  
Andre Frank ◽  
...  
Keyword(s):  
Medial Collateral Ligament ◽  
Knee Flexion ◽  
Length Change ◽  
Collateral Ligament ◽  
Complex Behaviour ◽  
Femoral Attachment ◽  
Attachment Sites ◽  
Custom Made ◽  
Length Changes ◽  
Graft Length

Abstract Purpose The purpose of this study was to examine the length change patterns of the native medial structures of the knee and determine the effect on graft length change patterns for different tibial and femoral attachment points for previously described medial reconstructions. Methods Eight cadaveric knee specimens were prepared by removing the skin and subcutaneous fat. The sartorius fascia was divided to allow clear identification of the medial ligamentous structures. Knees were then mounted in a custom-made rig and the quadriceps muscle and the iliotibial tract were loaded, using cables and hanging weights. Threads were mounted between tibial and femoral pins positioned in the anterior, middle, and posterior parts of the attachment sites of the native superficial medial collateral ligament (sMCL) and posterior oblique ligament (POL). Pins were also placed at the attachment sites relating to two commonly used medial reconstructions (Bosworth/Lind and LaPrade). Length changes between the tibiofemoral pin combinations were measured using a rotary encoder as the knee was flexed through an arc of 0–120°. Results With knee flexion, the anterior fibres of the sMCL tightened (increased in length 7.4% ± 2.9%) whilst the posterior fibres slackened (decreased in length 8.3% ± 3.1%). All fibre regions of the POL displayed a uniform lengthening of approximately 25% between 0 and 120° knee flexion. The most isometric tibiofemoral combination was between pins placed representing the middle fibres of the sMCL (Length change = 5.4% ± 2.1% with knee flexion). The simulated sMCL reconstruction that produced the least length change was the Lind/Bosworth reconstruction with the tibial attachment at the insertion of the semitendinosus and the femoral attachment in the posterior part of the native sMCL attachment side (5.4 ± 2.2%). This appeared more isometric than using the attachment positions described for the LaPrade reconstruction (10.0 ± 4.8%). Conclusion The complex behaviour of the native MCL could not be imitated by a single point-to-point combination and surgeons should be aware that small changes in the femoral MCL graft attachment position will significantly effect graft length change patterns. Reconstructing the sMCL with a semitendinosus autograft, left attached distally to its tibial insertion, would appear to have a minimal effect on length change compared to detaching it and using the native tibial attachment site. A POL graft must always be tensioned near extension to avoid capturing the knee or graft failure.

An origin of excess vibrational entropies at grain boundaries in Al, Si and MgO: a first-principles analysis with lattice dynamics

2021 ◽  
Author(s):  
T. Yokoi ◽  
K. Ikawa ◽  
A. Nakamura ◽  
K. Matsunaga
Keyword(s):  
Bond Length ◽  
Grain Boundaries ◽  
First Principles ◽  
Lattice Dynamics ◽  
Excess Entropy ◽  
First Principle ◽  
Length Changes

Excess vibrational entropies are examined by performing first-principle lattice dynamics for grain boundaries in MgO, Al and Si. Bond-length changes are critical for excess entropy, although their bonding nature is originally very different.

The location and mechanism of electromotility in guinea pig outer hair cells

1993 ◽  
Vol 70 (2) ◽  
pp. 549-558 ◽  
Author(s):  
R. Hallworth ◽  
B. N. Evans ◽  
P. Dallos
Keyword(s):  
Guinea Pig ◽  
Hair Cells ◽  
Outer Hair Cell ◽  
Length Change ◽  
Opposite Polarity ◽  
Outer Hair Cells ◽  
Response Amplitude ◽  
Change Function ◽  
Length Changes ◽  
Diameter Change

1. The microchamber method was used to examine the motile responses of isolated guinea pig outer hair cells to electrical stimulation. In the microchamber method, an isolated cell is drawn partway into a suction pipette and stimulated transcellularly. The relative position of the cell in the microchamber is referred to as the exclusion fraction. 2. The length changes of the included and excluded segments were compared for constant sinusoidal stimulus amplitude as functions of the exclusion fraction. Both included and excluded segments showed maximal responses when the cell was excluded approximately halfway. Both segments showed smaller or absent responses when the cell was almost fully excluded or almost fully included. 3. When the cell was near to, but not at, the maximum exclusion, the included segment response amplitude was zero, whereas the excluded segment response amplitude was nonzero. In contrast, when the cell was nearly fully included, the excluded segment response amplitude was zero, but the included segment response amplitude was still detectable. A simple model of outer hair cell motility based on these results suggests that the cell has finite-resistance terminations and that the motors are restricted to a region above the nucleus and below its ciliated apex (cuticular plate). 4. The function describing length change as a function of command voltage was measured for each segment as the exclusion fraction was varied. The functions were similar at midrange exclusions (i.e., when the segments were about equal length), showing nonlinearity and saturability. The functions were strikingly different when the segment lengths were different. The effects of exclusion on the voltage to length-change functions suggested that the nonlinearity and saturability are local properties of the motility mechanism. 5. The diameter changes of both segments were examined. The segment diameter changes were always antiphasic to the length changes. This finding implies that the motility mechanism has an active antiphasic diameter component. The diameter change amplitude was a monotonically increasing function of exclusion for the included segment, and a decreasing function for the excluded segment. 6. The voltage to length-change and voltage to diameter-change functions were measured for the same cell and exclusion fraction. The voltage to diameter-change function was smaller in amplitude than the voltage to length-change function. The functions were of opposite polarity to each other, but were otherwise similar in character. Thus it is likely that the same motor mechanism is responsible for both axial and diameter deformations.

Redshift or Adduct Stabilization—A Computational Study of Hydrogen Bonding in Adducts of Protonated Carboxylic Acids

2009 ◽  
Vol 15 (2) ◽  
pp. 239-248 ◽  
Author(s):  
Solveig Gaarn Olesen ◽  
Steen Hammerum
Keyword(s):  
Hydrogen Bond ◽  
Hydrogen Bonds ◽  
Bond Strength ◽  
Bond Length ◽  
Carboxylic Acids ◽  
Computational Study ◽  
Proton Affinities ◽  
Oh Groups ◽  
Hydrogen Bond Strength ◽  
Length Changes

It is generally expected that the hydrogen bond strength in a D–H•••A adduct is predicted by the difference between the proton affinities (Δ PA) of D and A, measured by the adduct stabilization, and demonstrated by the infrared (IR) redshift of the D–H bond stretching vibrational frequency. These criteria do not always yield consistent predictions, as illustrated by the hydrogen bonds formed by the E and Z OH groups of protonated carboxylic acids. The Δ PA and the stabilization of a series of hydrogen bonded adducts indicate that the E OH group forms the stronger hydrogen bonds, whereas the bond length changes and the redshift favor the Z OH group, matching the results of NBO and AIM calculations. This reflects that the thermochemistry of adduct formation is not a good measure of the hydrogen bond strength in charged adducts, and that the ionic interactions in the E and Z adducts of protonated carboxylic acids are different. The OH bond length and IR redshift afford the better measure of hydrogen bond strength.

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