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What is Morse equation?

What is Morse equation?

[′mȯrs i‚kwā·zhən] (physical chemistry) An equation according to which the potential energy of a diatomic molecule in a given electronic state is given by a Morse potential.

What is depth of Morse potential?

The Morse potential energy function is of the form. Here is the distance between the atoms, is the equilibrium bond distance, is the well depth (defined relative to the dissociated atoms), and controls the ‘width’ of the potential (the smaller is, the larger the well).

What does the Morse potential do?

The Morse potential is a useful approximation for vibration of diatomic molecules.

What is D in Morse potential?

The potential energy, V(R), of a diatomic molecule can be described by the Morse potential: where De is the well depth, R is internuclear distance, Re is the equilibrium internuclear distance (bond length), and. νe is the vibrational constant and μ is the reduced mass.

Why is Morse potential more accurate?

One such approach is the Morse potential, named after physicist Philip M. Morse, and a better approximation for the vibrational structure of the molecule than the harmonic oscillator because it explicitly includes the effects of bond breaking and accounts for the anharmonicity of real bonds (Figure 5.3.

What is beta in Morse potential?

The Morse potential U(r – re) is given by De{1 – exp[–β(–r – re)]} 2, where De is the dissociation energy at the minimum of the curve (i.e. when r=re) and β is a constant. The Morse potential was used by the US physicist Philip M. Morse in 1929 in solving the Schrödinger equation.

What features of the Morse potential makes it suitable for modeling dissociation of a diatomic molecule?

What feature of the Morse potential makes it suitable for modeling dissociation of a diatomic molecule? In contrast to the harmonic potential, the Morse potential levels off as the bond length becomes large. This is necessary to model dissociation.

What is the meaning of anharmonicity?

In classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator. If the anharmonicity is large, then other numerical techniques have to be used. In reality all oscillating systems are anharmonic, but approximate the harmonic oscillator the smaller the amplitude of the oscillation is.

Will a Morse potential lead to thermal expansion?

It is symmetric about equilibrium bond distance. Thus, Morse potential varies directly with bond length after equilibrium value, so it can lead to thermal expansion.

What is anharmonic oscillator potential?

Anharmonic oscillation is defined as the deviation of a system from harmonic oscillation, or an oscillator not oscillating in simple harmonic motion. Anharmonic oscillation is described as the restoring force is no longer proportional to the displacement.

What is the Morse potential?

The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule. It is a better approximation for the vibrational structure of the molecule than the QHO ( quantum harmonic oscillator) because it explicitly includes the effects…

How do you write the Morse potential equation?

Since the zero of potential energy is arbitrary, the equation for the Morse potential can be rewritten any number of ways by adding or subtracting a constant value. V ( r ) = V ′ ( r ) − D e = D e ( 1 − e − a ( r − r e ) ) 2 − D e {displaystyle V(r)=V'(r)-D_{e}=D_{e}(1-e^{-a(r-r_{e})})^{2}-D_{e}}.

What is the difference between Morse potential and harmonic potential?

The Morse potential (blue) and harmonic oscillator potential (green). Unlike the energy levels of the harmonic oscillator potential, which are evenly spaced by ħω, the Morse potential level spacing decreases as the energy approaches the dissociation energy.

What is the value of K E in Morse potential?

where k e {displaystyle k_{e}} is the force constant at the minimum of the well. Since the zero of potential energy is arbitrary, the equation for the Morse potential can be rewritten any number of ways by adding or subtracting a constant value.