Molecular energy total

Torsional strain refers to the component of total molecular energy that results from nonoptimal arrangement of vicinal bonds, as in the eclipsed conformation of ethane. The origin and stereoelectronic nature of torsional strain were discussed in Section 1.1.1. The... 

The total molecular energy is invariant to all transformations involving basis orbitals, just as any physical event is invariant under any transformation of coordinates. But just as the proper choice of coordinates helps in visualizing physical events, so the choice of the proper orbital basis is helpful in visualizing molecular properties. 

All conclusions drawn from the above reasoning depend on the assumption (among others) that two-electron properties may be neglected. In particular, conclusions on total molecular energies drawn from MO inspection are sensitive to this point. The reader s attention is however drawn to the following points ... 

Under the Born-Oppenheimer scheme it is reasonable to assume that the total molecular energy is partitioned as a sum of contributions... 

In order to leam more about the nature of the intermolecular forces we will start with partitioning of the total molecular energy, AE, into individual contri butions, which are as close as possible to those we defined in intermolecular perturbation theory. Attempts to split AE into suitable parts were undertaken independently by several groups 83-85>. The most detailed scheme of energy partitioning within the framework of MO theory was proposed by Morokuma 85> and his definitions are discussed here ). This analysis starts from antisymmetrized wave functions of the isolated molecules, a and 3, as well as from the complete Hamiltonian of the interacting complex AB. Four different approximative wave functions are used to describe the whole system ... 

In the valence molecular calculations, the total molecular energy can be decomposed as follows ... 

Typically, the simplest parameters to detennine from experiment are ab and Dab- With these two parameters available, (Zab can be determined from Eq. (2.8), and thus the cubic and quartic force constants can also be determined from Eqs. (2.4) and (2.7). Direct measurement of cubic and quartic force constants requires more spectral data than are available for many kinds of bonds, so this derivation facilitates parameterization. We will discuss parameterization in more detail later in the chapter, but turn now to consideration of other components of tlie total molecular energy. 

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. 

With each electronic state, we have a series of vibration-rotation levels. See Fig. 4.3. The total molecular energy (excluding translation) for a given state of electronic and nuclear motion is the sum of the equilibrium electronic energy Ue, the vibrational energy vib, and the rotational energy... 

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... 

The Bom-Oppenheimer principle (Bom-Oppenheimer approximation) [1] says that the electrons in a molecule move so much faster than the nuclei that the two kinds of motion are independent the electrons see the nuclei as being stationary, and so each electron doesn t have to adjust its motion to maintain a minimized electron-nucleus interaction energy. Thus we can calculate the purely electronic energy of a molecule, then the intemuclear repulsion energy, and add the separate energies to get the total molecular energy. 

The polarizabilities are calculated from the electrical field dependence of either the total molecular energy or the dipole moment the y2 ]ki in crystals obey the laws of crystal symmetry and are measured using powerful laser sources. 

The total electronic energy of a particular system is taken to be the sum of the orbital energies, e, times their occupation numbers. For a closed-shell system elect = 2 c The total molecular energy can be written as... 

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... 

Since the lowest total molecular energy was calculated at R -... 

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