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Related Concept Videos

Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
Coordination Number and Geometry02:57

Coordination Number and Geometry

For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
Interference: Path Lengths01:10

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.

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Correlative Microscopy for 3D Structural Analysis of Dynamic Interactions
13:43

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Published on: June 24, 2013

Explicitly correlated multireference configuration interaction with multiple reference functions: avoided crossings

Toru Shiozaki1, Hans-Joachim Werner

  • 1Institut für Theoretische Chemie, Universität Stuttgart, Stuttgart, Germany.

The Journal of Chemical Physics
|May 17, 2011
PubMed
Summary
This summary is machine-generated.

We developed an advanced multireference configuration interaction method (MRCI-F12) for complex molecular electronic structures. This method accurately models systems near conical intersections and avoided crossings, crucial for understanding chemical reactions.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Molecular Electronic Structure Theory

Background:

  • Accurate modeling of molecular electronic structures is essential for understanding chemical phenomena.
  • Near conical intersections and avoided crossings, electronic states strongly mix, posing challenges for standard computational methods.
  • Existing multireference configuration interaction methods may not efficiently handle these complex electronic structures.

Purpose of the Study:

  • To develop an explicitly correlated multireference configuration interaction method (MRCI-F12) applicable to nearly degenerate molecular electronic structures.
  • To generalize the MRCI-F12 method to handle multiple reference functions, crucial for systems with strongly mixed electronic states.
  • To introduce a singles correction for CASSCF reference energies to improve multi-state calculations.

Main Methods:

  • Development of an explicitly correlated multireference configuration interaction method (MRCI-F12) with multiple reference functions.
  • Utilization of the F12b approximation for computationally efficient formulas.
  • Expansion of the doubly external wave function in terms of internally contracted configurations from all reference functions.
  • Inclusion of a singles correction to CASSCF reference energies for multi-state calculations.

Main Results:

  • The developed MRCI-F12 method is routinely applicable to nearly degenerate molecular electronic structures.
  • The method successfully models systems near conical intersections and avoided crossings.
  • Numerical results are presented for the avoided crossing of LiF, excited states of ozone, and the H(2) + OH reaction.

Conclusions:

  • The generalized MRCI-F12 method provides an accurate and efficient approach for studying complex molecular electronic structures.
  • This method is particularly valuable for systems exhibiting strong mixing of electronic states, such as those near conical intersections.
  • The inclusion of a singles correction enhances the applicability to multi-state calculations.