A Study of Negative Force Constants: A Method to Obtain Force Constants by Electronic Structures

Abstract

The potential of negative force constants appearing in the valence-force model is discussed from the viewpoint of electronic structures. Prior to discussing this, a general procedure for obtaining force constants by the first-principles calculations is given, while simpler examples are worked out. For the strongest bond-stretching force, it is almost always calculable without ambiguity by using the breathing type deformation. For non-central forces, such as angle-bending forces, there is a practical difficulty in estimation. The expansion of the adiabatic potential obtained by the first-principles calculations involves so many force constants other than the bond-stretching and angle-bending forces that the values of angle-bending force constants so obtained usually exhibit large errors. Only for more simple molecules is it possible to evaluate the noncentral forces without ambiguity. In such a case, negative values of the angle-bending force constants appear, depending on the electronic configuration. How the Jahn–Teller effect participates in negative force constants has been investigated. The Jahn–Teller effect can contribute, but not all negative forces are ascribed to this effect.