Diatomic molecules defined

If, for instance, species a corresponds to a diatomic molecule defined by... 

The data of paramagnetic diatomic molecules (defined as those wifli a paramagnetic ground state) will appear later in subvolume 11/29E1. The reader will find, however, the chemical sum formulae of investigated paramagnetic diatomic species listed already in subvolume A1 in alphabetic order, together with some references to pertinent literature. 

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

The advantages of INDO over CNDO involve situations where the spin state and other aspects of electron spin are particularly important. For example, in the diatomic molecule NH, the last two electrons go into a degenerate p-orbital centered solely on the Nitrogen. Two well-defined spectroscopic states, S" and D, result. Since the p-orbital is strictly one-center, CNDO results in these two states having exactly the same energy. The INDO method correctly makes the triplet state lower in energy in association with the exchange interaction included in INDO. 

The rotational temperature is defined as the temperature that describes the Boltzmann population distribution among rotational levels. For example, for a diatomic molecule, this is the temperature in Equation (5.15). Since collisions are not so efficient in producing rotational cooling as for translational cooling, rotational temperatures are rather higher, typically about 10 K. 

The geometry of a diatomic molecule such as Cl2 or HCl can be described very simply. Because two points define a straight line, the molecule must be linear. 

The sample on the left contains a collection of eight diatomic molecules. All the molecules have the same composition, so this Is a pure substance. The molecules in the sample are distributed evenly through the entire volume of the container. This is the defining characteristic of a gas. 

The total number of spatial coordinates for a molecule with Q nuclei and N electrons is 3(Q + N), because each particle requires three cartesian coordinates to specify its location. However, if the motion of each particle is referred to the center of mass of the molecule rather than to the external spaced-fixed coordinate axes, then the three translational coordinates that specify the location of the center of mass relative to the external axes may be separated out and eliminated from consideration. For a diatomic molecule (Q = 2) we are left with only three relative nuclear coordinates and with 3N relative electronic coordinates. For mathematical convenience, we select the center of mass of the nuclei as the reference point rather than the center of mass of the nuclei and electrons together. The difference is negligibly small. We designate the two nuclei as A and B, and introduce a new set of nuclear coordinates defined by... 

The first derivative U HRe) vanishes because the potential is a minimum at the distance R. The second derivative U XR ) is called the force constant for the diatomic molecule (see Section 4.1) and is given the symbol k. We also introduce the relative distance variable q, defined as... 

From the analogue of Saha s equation for the dissociation of a diatomic molecule AB, one can define a dissociation constant depending only on temperature... 

Let us also consider the application of these transformations to diatomic molecules. We note that the density transformations carry the initial prolate spheroidal coordinates (C, t], (j)) into the transformed coordinates (C, j/p, 4>)- The equations that define these transformations are [119] ... 

Problem 9-1. The bond order of a diatomic molecule is defined as [number of electrons in binding orbitals - number of electrons in antibonding orbitals]. Show that the following values are correct ... 

Vibrational energy and transitions As seen in Fig. 3.2a, the bond between the two atoms in a diatomic molecule can be viewed as a vibrating spring in which, as the internuclear distance changes from the equilibrium value rc, the atoms experience a force that tends to restore them to the equilibrium position. The ideal, or harmonic, oscillator is defined as one that obeys Hooke s law that is, the restoring force F on the atoms in a diatomic molecule is proportional to their displacement from the equilibrium position. 

For a molecule in a given electronic and vibrational state, it is convenient to define the permanent dipole operator d = (i/r // i/r), where v/) is a product of the electronic and vibrational states. This vector operator depends on the angles that specify the orientation of the molecule with respect to the external field axis. For diatomic molecules, d is directed along the intermolecular axis. The Stark shifts of the molecule in a DC electric field can (almost always) be found by treating the molecule as a rigid rotor and diagonalizing the matrix of the operator... 

Several important conclusions can be drawn from Figure 4.38. It appears that in general a simple catalytic reaction, which includes the dissociation of a diatomic molecule, will have this dissociation as the rate-determining step, when the reaction takes place under conditions close to equilibrium. This agrees well with the ammonia synthesis being dissociation rate-determined, as this process is the prototype of an equilibrium-limited reaction [128]. When the reaction is taking place far from equilibrium, the actual approach to equilibrium becomes unimportant, and the volcano plot very closely follows the volcano defined by the minimum value among the maximal possible rates for all reaction steps. 

Historically the first application of symmetry to potential energy surfaces was to prove the so-called non-crossing rule. In its simplest form this may be stated as potential energy curves for states of diatomic molecules of the same symmetry do not cross . We have already seen in section 2 that this should be qualified to apply to adiabatic curves, as in some situations it may be convenient to define diabatic curves wdiich do cross. 

Analogous to (4.31) for the diatomic molecule, the rotational constants of a polyatomic molecule are defined as... 

---