Diatomic molecules internal energy

These results do not agree with experimental results. At room temperature, while the translational motion of diatomic molecules may be treated classically, the rotation and vibration have quantum attributes. In addition, quantum mechanically one should also consider the electronic degrees of freedom. However, typical electronic excitation energies are very large compared to k T (they are of the order of a few electronvolts, and 1 eV corresponds to 10 000 K). Such internal degrees of freedom are considered frozen, and an electronic cloud in a diatomic molecule is assumed to be in its ground state f with degeneracy g. The two nuclei A and... 

The energy of a diatomic molecule can be divided into translational and internal contributions = (/ik) /(2A7)... 

These electronic energies dependence on the positions of the atomic centres cause them to be referred to as electronic energy surfaces such as that depicted below in figure B3.T1 for a diatomic molecule. For nonlinear polyatomic molecules having atoms, the energy surfaces depend on 3N - 6 internal coordinates and thus can be very difficult to visualize. In figure B3.T2, a slice tln-oiigh such a surface is shown as a fimction of two of the 3N - 6 internal coordinates. 

For a diatomic molecule, for example, there is only one internal coordinate and the energy as a function of configuration (inter-nuclear distance) will look something like the following ... 

A linear molecule, such as any diatomic molecule, carbon dioxide, and ethyne (acetylene, HC=CH), can rotate about two axes perpendicular to the line of atoms, and so it has two rotational modes of motion. Its average rotational energy is therefore 2 X jkT = kT, and the contribution to the molar internal energy is NA times this value ... 

The relationships between bond length, stretching force constant, and bond dissociation energy are made clear by the potential energy curve for a diatomic molecule, the plot of the change in the internal energy AU of the molecule A2 as the internuclear separation is increased until the molecule dissociates into two A atoms ... 

The potential energy function U(R) that appears in the nuclear Schrodinger equation is the sum of the electronic energy and the nuclear repulsion. The simplest case is that of a diatomic molecule, which has one internal nuclear coordinate, the separation R of the two nuclei. A typical shape for U(R) is shown in Fig. 19.1. For small separations the nuclear repulsion, which goes like 1 /R, dominates, and liniR >o U(R) = oo. For large separations the molecule dissociates, and U(R) tends towards the sum of the energies of the two separated atoms. For a stable molecule in its electronic ground state U(R) has a minimum at a position Re, the equilibrium separation. 

In addition to the processes just discussed that yield vibrationally and rotationally excited diatomic ions in the ground electronic state, vibrational and rotational excitations also accompany direct electronic excitation (see Section II.B.2.a) of diatomic ions as well as charge-transfer excitation of these species (see Section IV.A.l). Furthermore, direct vibrational excitation of ions and molecules can take place via charge transfer in symmetric ion molecule collisions, as the translational-to-internal-energy conversion is a sensitive function of energy defects and vibrational overlaps of the individual reactant systems.312-314... 

Photoionization is a special case of a two-body dissociation where Me Ma. thus, the photoelectron receives essentially all of the KER and the atom or molecule (e.g., from a photodissociation event) essentially retains its initial velocity as it is ionized. For photodissociation of a homonuclear diatomic the KER is equally shared between the two product atoms (A and A ). The sum of the internal energies in the product atoms can be determined from the measured KER (l/2mAVA + l/2mA.VA) and from... 

Vibrational Predissociation, in this section we discuss the case of a transition from a predissociative state to the photofragment state that occurs on a single adiabatic pes. Such processes cannot occur for diatomic molecules, but they can be observed for polyatomic systems. The transition is caused by intramolecular energy transfer, that is, by internal redistribution of vibrational energy. 

Rotational energy contributes to the internal energy of a diatomic molecule, and classically any rotational speed is possible. We will return to rotational properties in Chapter 8, when we discuss quantum mechanics, which imposes restrictions on the rotational energy we will find that transitions between allowed rotational states let us measure bond lengths or cook food in microwave ovens. 

The whole of this section has been concerned with the problem of transforming the potential energy V from a representation in geometrically defined internal co-ordinates H to dimensionless normal co-ordinates q, a transformation achieved in the single equation (14) for a diatomic molecule. It will be clear to the reader that programming this transformation is a considerable part of the task of performing an anharmonic calculation on any polyatomic molecule. 

F s, parameter that can be calculated knowing the mass of the recoiling atom and the bond dissociation energy. When the -particles are ejected with relativistic energies, Monahan (1958) derived the following expression to calculate the maximum internal energy available for bond rupture in a diatomic molecule ... 

The total energy of a diatomic molecule may be separated into translational energy and internal energy. We are concerned here with the internal energy which can be expressed to a good approximation by where E, is the electronic... 

For AT diatomic molecules that have only a single internal vibration the partition function is easily determined from the approximate formula for the energy levels... 

The outer distorted surface II corresponds to a molecule that has much greater internal energy but less than the critical energy. The diagonal arrows indicate the directions along which dissociation into an atom and a diatomic molecule would take place. 

Dissociation of diatomic molecules (and halogens in particular) in shock waves has been extensively studied. ° ° A lingering intriguing problem has been the unexpectedly low Arrhenius activation energy of such processes.Among the factors that have been considered as contributing to the observed kinetic behavior have been the enhancement of the rate of collisional dissociation by internal excitation of the diatomic molecules and the possible role of multiquantum transitions in which the molecule gains several vibrational quanta per collision.107... 

A diatomic molecule has only the internuclear distance Q as an internal coordinate (F = I). Unless //, vanishes because d>, and are of different symmetry, it is in general impossible to find a value of Q that would satisfy simultaneously both conditions. The energies , and E, therefore are different, and in one dimension, two states of the same electronic symmetry cannot cross. In a system with two independent internal coordinates Q, and Q2 (F = 2), for... 

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