Rudolf Polák

On the definition of the atomic charge in a molecule

Atomic charges calculated by various methods for model two-center molecules have been compared with corresponding electron-count functions. Varying the overlap and polarity conditions in the model system, it could be found out under what conditions the individual definitions fail to predict physically reasonable values of atomic charges.

A study of the nonadiabatic effects in the Li−Li 2 + system: Typical minimum energy paths for the reaction Li+Li 2 + →Li 3 +

Mutual arrangement and nonadiabatic coupling between the lowest two singlet potential energy surfaces of the Li3+ system are studied along typical ground-state minimum energy paths for the reaction Li+Li2+→ Li3+. The potentials and nonadiabatic coupling matrix elements are obtained using the diatomics-in-molecules method. The relative Li−Li2+ motion along the pathways is predicted to be inefficient in causing nonadiabatic transitions from the ground state to the first excited state of the system.

The Time-Independent Schrödinger Equation

It is important to remember that the Schrodinger equation, similar to the principal thermodynamic laws, cannot be derived from the general principles of physics. It is true that we can proceed from the classical law of conservation of energy and, through a number of modifications (some of them inconceivable from the point of view of classical mechanics), arrive at the Schrodinger equation (“derive it”). However, this procedure does not possess the character of derivation by deduction that is considered normal in classical physics. The only method of determining whether the equation obtained has physical significance, i.e. whether it gives a true picture of the real behaviour of particles, will lie in comparison of values for quantities calculated using this equation with experimentally obtained values.

Study of nonadiabatic effects in the Li-Li 2 + system. Location of nonadiabatic regions

Nonadiabatic coupling between the lowest two singlet potential energy surfaces of the Li-Li2+system is calculated using the diatomics-in-molecules method. Location of nonadiabatic regions in the configuration space of Li-Li 2+and their analysis is used to estimate those inner and translational states of the reactants which can lead to nonadiabatic behavior.

Magnetic Properties of Molecules

In this chapter some magnetic properties of systems with closed electronic shells1–4, namely, the magnetic susceptibility and the anisotropy of this susceptibility will be discussed very briefly. Proton behaviour under NMR conditions has already been mentioned (Section 13.2.4).

Atomic Orbitals (AO) and Molecular Orbitals (MO)

The solution of the Schrodinger equation for the hydrogen atom can rarely be used directly in more complex chemical problems. This solution nevertheless forms a basis for the study of more complicated atoms and even for molecules. The possible modes of graphical representation of the radial and angular parts of hydrogen-type functions — the atomic orbitals — have already been described. Thus only a few remarks will be given here in this connection: (i) The application of computers permits information on the graphical representation of complete AO’s to be obtained1. (ii) Frequently, the graphical representation of the angular part is particularly useful. It should be noted that the contours in Fig. 3–10b indicate the regions in space in which the electron can be found (with the given probability). This figure is not to be understood as describing a “smearing out” of the electron charge in space. (iii) The sign of the wave function (+ or −) in the individual AO parts must be specified. This is important when analyzing the symmetry of the studied formations and in the calculation of some integrals. The sign of the wave function is, however, of no physical importance (in the sense of comparison with a physical quantity).

Basic Approximations in the Theory of the Chemical Bond

The modern theory of the chemical bond is based on the quantum mechanics of systems composed of electrons and atomic nuclei, assuming that solution of the fundamental quantum mechanical equation leads to a complete description of the system. As follows from the two preceding chapters, difficulties lie not in the formulation of the Schrodinger equation, but in its solution. As even three-particle systems are not exactly solvable, problems interesting for chemists must be simplified by conversion into model systems. The mere fact that, as a rule, an isolated system is treated (an atom, a molecule, a solid or a system of several partial subsystems) is a kind of abstraction, as the influence of the surrounding medium, for example the influence of a solvent, is frequently ignored.

Thermochemical Properties and Molecular Stability

The enthalpy of formation of one mole of compound A m B n C o from its elements under standard conditions is called the heat of formation (∆H f):

Calculation Methods in the Theory of the Chemical Bond

mA + nB + oC \to {{A}_{m}}{{B}_{n}}{{C}_{o}} \ldots \Delta {{H}_{f}}