Surface Second Harmonic Generation - Applications - Molecular Orientation - Calculation of Molecular Orientation

Calculation of Molecular Orientation

When dealing with adsorbed molecules on a surface, it is typical to find a uniaxial distribution of the molecules, resulting in x- and y- coordinate terms to be interchangeable. When analyzing the second-order susceptibility tensor χ(2), the quantities χXYZ = -χYXZ must be 0 and only three independent tensor terms remain: χzzz, χzxx, and χxxz. The intensities of the s and p polarizations in the second harmonic are given by following relationships:

where γ is the polarization angle with γ = 0 corresponding to p-polarized light. The si terms depend on the experimental geometry are functions of the total internal reflection angles of the incident and second harmonic beams and the linear and nonlinear Fresnel factors respectively which relate the electric field components at the interface to incident and detected fields.

The second-order susceptibility tensor, χ(2), is the parameter which can be measured in second order experiments, but it does not explicitly provide insight to the molecular orientation of surface molecules. To determine molecular orientation, the second-order hyperpolarizability tensor β, must be calculated. For adsorbed molecules in a uniaxial distribution, the only independent hyperpolarizability tensor terms are βz’z’z’, βz’x’x’, and βx’x’z’ where ’ terms denote the molecular coordinate system as opposed to the laboratory coordinate system. β can be related to χ(2) through orientational averages. As an example, in an isotropic distribution on the surface, χ(2) elements are given by.

where Ns is the surface number density of the adsorbed molecules, θ and Ψ are orientational angles relating the molecular coordinate system to the laboratory coordinate system, and represents the average value of x. In many cases, only or two of the molecular hyperpolarizability tensor are dominant. In these cases, the relationships between χ and β can be simplified. Bernhard Dick presents several of these simplifications.

Read more about this topic:  Surface Second Harmonic Generation, Applications, Molecular Orientation

Other articles related to "molecular":

Trihydrogen Cation - History
... Using an early form of mass spectrometry, he discovered a large abundance of a molecular ion with a mass-to-charge ratio of 3 ... Klemperer in 1973 that H3+ is responsible for the formation of many observed molecular ions ... medium (ISM) by Geballe Oka in two molecular interstellar clouds in the sightlines GL2136 and W33A ...
Journal Of Molecular Biology
... The Journal of Molecular Biology is a peer-reviewed scientific journal published weekly by Elsevier ... concerning studies of organisms or their components at the molecular level ...
... Molecularity in chemistry is the number of colliding molecular entities that are involved in a single reaction step ... A reaction involving one molecular entity is called unimolecular ... A reaction involving two molecular entities is called bimolecular ...
Molecular Term Symbol
... In molecular physics, the molecular term symbol is a shorthand expression of the group representation and angular momenta that characterize the state of a molecule, i ... quantum state which is an eigenstate of the electronic molecular Hamiltonian ... to any exact symmetry of the electronic molecular Hamiltonian ...

Famous quotes containing the words calculation of, orientation and/or calculation:

    “To my thinking” boomed the Professor, begging the question as usual, “the greatest triumph of the human mind was the calculation of Neptune from the observed vagaries of the orbit of Uranus.”
    “And yours,” said the P.B.
    Samuel Beckett (1906–1989)

    Institutions of higher education in the United States are products of Western society in which masculine values like an orientation toward achievement and objectivity are valued over cooperation, connectedness and subjectivity.
    Yolanda Moses (b. 1946)

    Common sense is the measure of the possible; it is composed of experience and prevision; it is calculation appled to life.
    Henri-Frédéric Amiel (1821–1881)