The two major areas of research have been:
(a) Quantum Chemistry and
(b) Nonlinear dynamics in Chemistry and Biology.
In the 1970’s and 1980’s developed accurate atomic and molecular potential fields from ab initio principles. Demonstrated its successful use in calculations of various atomic and molecular structure properties. These developments were the forerunner of the present day Density Functional Theory widely used by Chemists and Physicists in molecular property computations. Relativistic and electron correlation effects were successfully incorporated into the formalism in later years.
In the 1980’s a quantum mechanical definition of chemical valency was introduced and developed in further work. This concept enables the quantitative rationalization of electronic and geometric structure of molecules. The concept of valency was generalized for molecular orbitals.
The preferred course of chemical reactions could be predicted using this concept of valency.
In recent years our attention is focused on experimental and modeling studies of nonlinear dynamical phenomena in chemistry, biochemistry and physiology. Based on rigorous analysis of extensive experimental data on human ECG and EEG, we have established the “chaotic” nature of the human cardiac and brain systems.
The concept of Unstable Periodic Orbits (UPO) spectrum has been introduced to analyse the dynamics of such systems. It is shown that the UPO spectrum clearly distinguishes several cardiac pathologies and states of consciousness of the brain
We have shown recently that complex biochemical reaction networks can be quantitatively modeled efficiently using Dealy Differential Equations . Many parts of the network can be represented by time delays. Our technique has been applied to model circadian rhythms and cell division cycles.
A simple two-variable nonlinear delay equation model can describe quantitatively the circadian protein oscillations in the fungus Neurospora crassa. We have also found that external “noise” can generate and amplify circadian oscillations. This is an instance of the occurrence of “stochastic resonance” phenomenon in a biological rhythm.
In our latest work, we have applied nonlinear dynamical model to explain the oscillations of CO2 gas over melting ice, observed in our laboratories. This observation and its theory are expected to have deep geological and environmental implications.