Vibronic coupling

Encyclopedia

In theoretical chemistry

, the

Vibronic coupling is large in the case of two adiabatic potential energy surface

s coming close to each other (that is, when the energy gap between them is of the order of magnitude of one oscillation quantum). This usually happens in the neighbourhood of an avoided crossing

of potential energy surface

s corresponding to distinct electronic states of the same spatial and spin symmetry. However, vibronic coupling also exists at real crossings. In this case the adiabatic or Born–Oppenheimer approximation fails and non-adiabatic terms (the so-called vibronic coupling terms) have to be taken into account. The vibronic coupling terms are usually difficult to evaluate. This is because they are proportional to the first and second derivatives of the electronic wave function with respect to the molecular coordinates

. A simpler way to solve this problem is to switch from the adiabatic to the diabatic

representation of the potential energy surface

s. The vibronic terms are responsible for example for surface hopping or the Berry phase. The Berry phase has been discovered by Longuet-Higgins

in this context. The vibronic coupling becomes infinite in the neighbourhood of a conical intersection

. This singularity in the potential energy landscape is the origin of the Berry phase.

Perhaps the earliest examples of the importance of vibronic coupling were found during the 1930s. In 1934 Renner wrote about the vibronic coupling in an electronically excited Π-state in CO

of benzene

by Sklar in 1937 (with the valence bond method) and later in 1938 by Goeppert-Mayer and Sklar (with the molecular orbital

method) demonstrated a correspondence between the theoretical predictions and experimental results of the benzene spectrum

. The benzene spectrum was the first qualitative computation of the efficiencies of various vibrations at inducing intensity absorption.

Theoretical chemistry

Theoretical chemistry seeks to provide theories that explain chemical observations. Often, it uses mathematical and computational methods that, at times, require advanced knowledge. Quantum chemistry, the application of quantum mechanics to the understanding of valency, is a major component of...

, the

**vibronic coupling**terms, (which are neglected within the Born–Oppenheimer approximation), are proportional to the interaction between electronic and nuclear motions of molecules. The term "vibronic" originates from the concatenation of the terms "vibrational" and "electronic". The word coupling denotes the idea that in a molecule, vibrational and electronic interactions are interrelated and influence each other.Vibronic coupling is large in the case of two adiabatic potential energy surface

Potential energy surface

A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems...

s coming close to each other (that is, when the energy gap between them is of the order of magnitude of one oscillation quantum). This usually happens in the neighbourhood of an avoided crossing

Avoided crossing

[Image:Avoided_crossing.png|thumb|right|300px|An avoided energy level crossing in a two level system subjected to an external magnetic field. Note the energies of the diabatic states, \scriptstyle...

of potential energy surface

Potential energy surface

A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems...

s corresponding to distinct electronic states of the same spatial and spin symmetry. However, vibronic coupling also exists at real crossings. In this case the adiabatic or Born–Oppenheimer approximation fails and non-adiabatic terms (the so-called vibronic coupling terms) have to be taken into account. The vibronic coupling terms are usually difficult to evaluate. This is because they are proportional to the first and second derivatives of the electronic wave function with respect to the molecular coordinates

Molecular geometry

Molecular geometry or molecular structure is the three-dimensional arrangement of the atoms that constitute a molecule. It determines several properties of a substance including its reactivity, polarity, phase of matter, color, magnetism, and biological activity.- Molecular geometry determination...

. A simpler way to solve this problem is to switch from the adiabatic to the diabatic

Diabatic

A diabatic process is one in which heat transfer takes place, which is the opposite of an adiabatic process. In quantum chemistry, the potential energy surfaces are obtained within the adiabatic or Born-Oppenheimer approximation...

representation of the potential energy surface

Potential energy surface

A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems...

s. The vibronic terms are responsible for example for surface hopping or the Berry phase. The Berry phase has been discovered by Longuet-Higgins

H. Christopher Longuet-Higgins

Hugh Christopher Longuet-Higgins FRS was both a theoretical chemist and a cognitive scientist. He was born on April 11, 1923 in Kent, England and died on March 27, 2004....

in this context. The vibronic coupling becomes infinite in the neighbourhood of a conical intersection

Conical intersection

In quantum chemistry, a conical intersection of two potential energy surfaces of the same spatial and spin symmetries is the set of molecular geometry points where the two potential energy surfaces are degenerate . Conical intersections are ubiquitous in both trivial and non-trivial chemical...

. This singularity in the potential energy landscape is the origin of the Berry phase.

Perhaps the earliest examples of the importance of vibronic coupling were found during the 1930s. In 1934 Renner wrote about the vibronic coupling in an electronically excited Π-state in CO

_{2}. Calculations of the lower excited levelsExcited state

Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....

of benzene

Benzene

Benzene is an organic chemical compound. It is composed of 6 carbon atoms in a ring, with 1 hydrogen atom attached to each carbon atom, with the molecular formula C6H6....

by Sklar in 1937 (with the valence bond method) and later in 1938 by Goeppert-Mayer and Sklar (with the molecular orbital

Molecular orbital

In chemistry, a molecular orbital is a mathematical function describing the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The term "orbital" was first...

method) demonstrated a correspondence between the theoretical predictions and experimental results of the benzene spectrum

Spectroscopy

Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

. The benzene spectrum was the first qualitative computation of the efficiencies of various vibrations at inducing intensity absorption.