Theoretical model size-extensivity

It is of some note that many of the models may be (and often were) obtained by-passing the derivational approach here. Basically each model may be viewed as represented by the first terms in a graph-theoretic cluster expansion [80]. Once the space on which the model to be represented is specified, the interactions in the orthogonal-basis cases are just the simplest additive few-site operators possible. For the nonorthogonal bases the overlaps are just the simplest multiplicative operators possible, while the associated Hamiltonian operators are the simplest associated derivative operators. These ideas lead [80] to proper size-consistency and size extensivity. Similar sorts of ideas apply in developing wavefunction Ansatze or ground-state energy expansions for the various models. 

Atomic level simulations and electronic structure calculations are necessary to understand the mechanisms and physical properties for these molecule/bulk interfacial CTs. However, unfortunately, a simple extension of standard theoretical models for homogeneous CTs is not always useful. While there are several difficulties in developing theoretical models (ideally possible to combine ah initio techniques) for interfacial CTs, the fundamental difficulties result from (i) the total system size often being (semi-) infinite (ii) the coexistence of locality and nonlocality in excited electron... 

Debashis Mukherjee is a Professor of Physical Chemistry and the Director of the Indian Association for the Cultivation of Science, Calcutta, India. He has been one of the earliest developers of a class of multi-reference coupled cluster theories and also of the coupled cluster based linear response theory. Other contributions by him are in the resolution of the size-extensivity problem for multi-reference theories using an incomplete model space and in the size-extensive intermediate Hamiltonian formalism. His research interests focus on the development and applications of non-relativistic and relativistic theories of many-body molecular electronic structure and theoretical spectroscopy, quantum many-body dynamics and statistical held theory of many-body systems. He is a member of the International Academy of the Quantum Molecular Science, a Fellow of the Third World Academy of Science, the Indian National Science Academy and the Indian Academy of Sciences. He is the recipient of the Shantiswarup Bhatnagar Prize of the Council of Scientihc and Industrial Research of the Government of India. 

For these theories, the present work provides a numerical calibra-tion for the argon model by yielding values for constants that must otherwise be treated as arbitrary parameters and by determining how closely the theoretical predictions are followed by the model system. The well behaved dependence of the decay rates and capture cross sections upon cluster size indicates that it may not be necessary to perform such calculations for larger clusters. A direct extension of the present type of study could supply all of the rate coefficients necessary to reformulate the steady-state nucleation rate in terms of quantities which could be either directly calculated or approximated with reasonable accuracy by use of the theoretical models. 

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