Related Experiment Video
Updated: Jul 16, 2026
14:42
Remote Magnetic Actuation of Micrometric Probes for in situ 3D Mapping of Bacterial Biofilm Physical Properties
Published on: May 2, 2014
Can ring strain be realized in momentum space?
P Balanarayan1, Shridhar R Gadre
1Contribution from the Department of Chemistry, University of Pune, Pune 411007, India.
Journal of the American Chemical Society
|August 17, 2006
Summary
Increased electron momentum density at low momentum indicates ring strain in molecules. This finding aids in analyzing strained hydrocarbons and their analogues using computational methods.
Area of Science:
- Quantum Chemistry
- Computational Chemistry
- Molecular Spectroscopy
Background:
- Ring strain significantly influences molecular properties.
- Electron momentum density (EMD) provides insights into electronic structure.
- Previous studies have explored EMD but not specifically for strained systems.
Purpose of the Study:
- To establish electron momentum density (EMD) at low momentum as a reliable indicator of ring strain.
- To analyze the impact of strain on molecular EMDs using a specific computational approach.
- To investigate the EMD signatures of strain in various strained hydrocarbons and their derivatives.
Main Methods:
- Application of a p-space Hirshfeld atomic partitioning scheme.
- Calculation and analysis of electron momentum densities for strained and unstrained molecules.
- Comparison of EMD profiles to identify strain-induced changes.
Main Results:
- An increased EMD at low momentum was observed and linked to ring strain.
- The Hirshfeld partitioning revealed increased electron population on strained carbons.
- Hydrogens bonded to strained carbons showed a more positive character.
Conclusions:
- Low-momentum EMD is a valid indicator for detecting ring strain in molecules.
- The Hirshfeld partitioning method effectively visualizes strain effects on atomic electron densities.
- This approach is applicable to a range of strained cage-like hydrocarbons and their nitrogen-substituted analogues.
Related Concept Videos
01:09Conservation of Angular Momentum
A system's total angular momentum remains constant if the net external torque acting on the system is zero. Considering a system that consists of n tiny particles, the angular momentum of any tiny particle may change, but the system's total angular momentum would remain constant. The principle of conservation of angular momentum only considers the net external torque acting on the system. While there are internal forces exerted by different particles within the system that also produce internal...
01:18Conservation of Angular Momentum: Application
A system's total angular momentum remains constant if the net external torque acting on the system is zero. Examples of such systems include a freely spinning bicycle tire that slows over time due to torque arising from friction, or the slowing of Earth's rotation over millions of years due to frictional forces exerted on tidal deformations. However in the absence of a net external torque, the angular momentum remains conserved. The conservation of angular momentum principle requires a change...
01:11Angular Momentum about an Arbitrary Axis
Imagine a rigid body with a mass denoted as 'm', which has its center of mass at point G and is rotating around an inertial reference frame. The angular momentum at an arbitrary point P can be calculated by taking the cross product of the position vector and linear momentum vector for each individual mass element.
The velocity of a mass element comprises its translational velocity and the relative velocity instigated by the body's rotation. Substituting the velocity equation into the angular...
The velocity of a mass element comprises its translational velocity and the relative velocity instigated by the body's rotation. Substituting the velocity equation into the angular...
01:12Equation of Motion for a Rigid Body
The movement of a rigid object can be understood through the equations that explain both translational and rotational motion about the center of mass of the object, point G. This center of mass is the point where the equation of motion for translational motion comes into play, as per Newton's Second Law.
The combined moments generated about the center of mass of the object are equal to the rate of change of the angular momentum of the body. An external force, when applied at a different point...
The combined moments generated about the center of mass of the object are equal to the rate of change of the angular momentum of the body. An external force, when applied at a different point...
01:07Conservation of Mass in Fixed, Nondeforming Control Volume
The principle of conservation of mass is fundamental in fluid dynamics and is crucial for analyzing flow within fixed control volumes, such as pipes or ducts. This principle states that the total mass within a control volume remains constant unless altered by the inflow or outflow of mass through the control surfaces. This results in a vital relationship for steady, incompressible flow where the mass entering a system equals the mass leaving it.
In the case of a sewer pipe, which can be modeled...
In the case of a sewer pipe, which can be modeled...
01:14Conservation of Mass in Moving, Nondeforming Control Volume
Stormwater detention basins are essential in managing runoff during heavy rainfall, particularly in urban areas where impervious surfaces increase the risk of flooding. Understanding the conservation of mass in these systems allows engineers to optimize basin performance, balancing inflow, outflow, and water storage.
In the context of a detention basin, the conservation of mass states that the total mass of water entering the basin must equal the mass leaving the basin plus any accumulation of...
In the context of a detention basin, the conservation of mass states that the total mass of water entering the basin must equal the mass leaving the basin plus any accumulation of...