A further breakthrough occurred upon the advent of modern (" ab initio ") electronic structure calculations whereby the relevant parameters characterising JT systems can be reliably determined from first principles. Thus one could go beyond studies of model systems that explore the effect of parameter variations on the PES and vibronic energy levels; one could also go on beyond fitting these parameters to experimental data without clear knowledge about the significance of the fit. Instead, well-founded theoretical investigations became possible which greatly improved the insight into the phenomena at hand and into the details of the underlying mechanisms.