Diatomic Molecules as a simple Anharmonic Oscillator

Diatomic Molecules as a simple Anharmonic Oscillator

1. ASSIGNMENT ON DIATOMIC MOLECULES AS A SIMPLE ANHARMONIC OSCILLATOR

2. Made By: Anita Malviya

3. Diatomic Molecules Diatomic molecules  are molecules composed of only two atoms, of either the same or different chemical elements. The prefix  di-  is of Greek origin, meaning "two ". Ifa diatomic molecule consists of two atoms of the same element, such as hydrogen (H 2 ) or oxygen (O 2 ), then it is said to be homonuclear.    If a diatomic molecule consists of two different atoms, such as carbon monoxide (CO) or nitric oxide (NO), the molecule is said to be  heteronuclear .

4. Molecular vibration A   molecular vibration  occurs when atoms in a molecule are in periodic motion while the molecule as a whole has constant translational and rotational motion. The frequency of the periodic motion is known as a vibration frequency, and the typical frequencies of molecular vibrations range from less than 10 12  to approximately 10 14  Hz . A diatomic molecule has one normal mode of vibration. The normal modes of vibration of polyatomic molecules are independent of each other but each normal mode will involve simultaneous vibrations of different parts of the molecule such as different chemical bonds . the motion in a normal vibration can be described as a kind of simple harmonic motion. In this approximation, the vibrational energy is a quadratic function (parabola) with respect to the atomic displacements and the first overtone has twice the frequency of the fundamental .

5. Anharmonic Oscillator A harmonic oscillator obeys Hooke's Law and is an idealized expression that assumes that a system displaced from equilibrium responds with a restoring force whose magnitude is proportional to the displacement. In nature, idealized situations break down and fails to describe linear equations of motion. Anharmonic oscillation is described as the restoring force is no longer proportional to the displacement. Anharmonic oscillators can be approximated to a harmonic oscillator and the anharmonicity can be calculated using perturbation theory.

6. Vibrational Energy Levels J. Michael Hollas, Modern Spectroscopy , John Wiley & Sons, New York, 1992. Selection Rules: Must have a change in dipole moment (for IR). 2) D v = 1

7. Potential energy from period of oscillations Let us consider a potential well . Assuming that the curve  is symmetric about the -axis, the shape of the curve can be implicitly determined from the period  of the oscillations of particles with energy  according to the formula:

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