Total Molecular Equations

In the case of reacting MgSO and NaOH, we can use the solubihty rules to answer the first question. The ions that are 

Using that information we can now write a balanced equation for the reaction that took place  

This is an example of what chemists call a total molecular equation. A total molecular equation shows all of the reactant species as molecular species. 

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In the total molecular equation, the presence of ions was implicit. In the total ionic equation, the ions are shown expUcitly. You can see at a glance which species are present as ions and which species are present as molecules. 

Throughout the remainder of this book we will usually write net ionic equations for reactions that take place in aqueous solution. For reactions occurring in the gas phase, or between liquids other than water, we will continue to write total molecular equations. 

J. B. Goebel (Zeitschr. physik. Chem., 53, 213, 1905 54, 314, 1906 71, 652, 1910) has found an empirical equation for the depression of freezing-point in aqueous solutions of total molecular concentration n ... 

Thus, local softness contains the same information as the Fukui function fir) plus additional information about the total molecular softness, which is related to the global reactivity with respect to a reaction partner, as stated in HSAB principle. Thus, the Fukui function may be thought of as a normalized local softness. Atomic softness values can easily be calculated by using Equation 32.4, namely... 

Inserting this expression into the total molecular Schrodinger equation, and using the fact that the electronic eigenfunctions are... 

Essentially Chapter 9 is concerned with the solution of the nuclear equation (eqn(8-2.3)), which involvesthe subject of molecular vibrations, and Chapter 10 deals with examples of the solution of the electronic equation (eqn (8-2.2)). The reader will have observed that the eigenvalues of the electronic equation Eel which occur in Fnu0 are normally required before the nuclear equation can be solved, the latter equation providing the final total molecular energy E. 

In dealing with the MO-LCAO wave function no additional assumptions concerning the vibronic matrix elements are necessary. The evaluation of the total molecular energy exactly copies the lower sheet of the adiabatic potential. This is a consequence of the well-known fact that the Hartree-Fock equations are equivalent to the statement of the Brillouin theorem the matrix elements of the electronic Hamiltonian between the ground-state and... 

In order to illustrate electronic transitions we discuss the simple two-dimensional model of a linear triatomic molecule ABC as depicted in Figure 2.1. R and r are the appropriate Jacobi coordinates to describe the nuclear motion and the vector q comprises all electronic coordinates. The total molecular Hamiltonian Hmoi, including all nuclear and electronic degrees of freedom, is given by Equation (2.28) with Hei and Tnu being the electronic Hamiltonian and the kinetic energy of the nuclei, respectively. 

According to Equation (2.29), in the adiabatic representation (index a) one expands the total molecular wavefunction F(R, r, q) in terms of the Born-Oppenheimer states Ej (q R, r) which solve the electronic Schrodinger equation (2.30) for fixed nuclear configuration (R,r). In this representation, the electronic Hamiltonian is diagonal,... 

As Dewar points out in ref. [30a], this derivation is not really satisfactory. A rigorous approach is a simplified version of the derivation of the Hartree-Fock equations (Chapter 5, Section 5.2.3). It starts with the total molecular wavefunction expressed as a determinant, writes the energy in terms of this wavefunction and the Hamiltonian and finds the condition for minimum energy subject to the molecular orbitals being orthonormal (cf. orthogonal matrices, Section 4.3.3). The procedure is explained in some detail in Chapter 5, Section 5.2.3)... 

We add the operator —p, ER to the total molecular Hamiltonian. According to Eq. (3.1), the electronic Hamiltonian of the molecule in the field due to the solvent is then He — p ER. The electronic Schrodinger equation is then solved using this modified Hamiltonian. This leads to a self-consistent solution where the electronic wave function and the electronic energy are modified due to the solvent field. Thus, polarization of the molecular electronic density (as described approximately above) is automatically included in this approach. 

This type of equation can be called the total equation. (A total equation is sometimes referred to as a molecular equation because the compounds in it are written as if they were molecules. )... 

It can be seen that although both the relativistic and the NRL calculations predict the molecule to be bound at R — 3.877 au the predicted NRL D is about 3.5 times larger than the relativistic prediction. However, the calculated relativistic total molecular energy at R - 3.877 au is lower by 2165.19 au (58916eVI). We shall use the four-component functions defined through the equations (3.5a - 3.5d) of Malli and Pyper (14) in order to express the calculated valence RMOs in terms of the large components of the i mg> functions, where d mg> and f mg> functions have... 

Thus the total molecular dipole moment can be equated to a sum of atomic charges and first moments. The first term in eqn (6.47), /i, is the contribution from the interatomic charge transfer, while the second term, / , arises from the polarizations of the individual atomic distributions. In general, both terms are important in determining /i (Bader et al. 19876). 

Most of the ingredients of the model described above have been formerly postulated in treatments of unimolecular reactions. In particular, the model for the barrier dynamics is inherent in the usual TST for unimolecular reactions involving polyatomic molecules, while taking the total molecular energy Ej as the important dynamic variable in the well is the underlying assumption in theories that use a master or a diffusion equation for Ej- as their starting point. 

The basis of the use of quantum mechanics is that we can construct a total molecular wave function using which a time independent non-relativistic Schrbdinger equation of the form. 

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