R. K. Moitra

Bio: R. K. Moitra is an academic researcher from Saha Institute of Nuclear Physics. The author has contributed to research in topics: Fibonacci number & Hamiltonian (quantum mechanics). The author has an hindex of 12, co-authored 29 publications receiving 950 citations.

Correlation problem in open-shell atoms and molecules

Abstract: In this paper we present a non-perturbative approach to the calculation of correlation energies of open-shell systems. The formulation utilizes an Ursell-type expansion about a multi-determinant starting wavefunction. We have proved a theorem which enables us to derive an effective hamiltonian for the system consisting entirely of linked terms. In the symmetry-degenerate case this effective hamiltonian acts within the subspace of a set of symmetry-degenerate functions, and generates the energy eigenvalues of the system. The present theory has been cast in a diagrammatic language which facilitates the analysis of the correlation problem. The workability of the theory has been tested on a 4 π electron problem, transbutadiene, for which we have calculated the lowest π-π* singlet and triplet energies. The agreement between the results of the present theory and that found from a full CI calculation is excellent. The desirable feature of the theory is that the effective hamiltonian is energy-independent. We hav...

Applications of a non-perturbative many-body formalism to general open-shell atomic and molecular problems: calculation of the ground and the lowest π-π* singlet and triplet energies and the first ionization potential of trans-butadiene

Abstract: In this paper we explore the feasibility of widening the scope of the non-perturbative open-shell many-body formalism recently developed by us [1], which utilizes an Ursell type of cluster expansion about certain starting wavefunctions spanning a model space. We show that, by generalizing the definition of the cluster expansion operator, we can incorporate into the model space (a) determinants differing widely in energy and (b) determinants differing in their number of electrons. This flexibility is useful for the calculation of difference energies of interest, like transition energies and ionization potentials of atomic and molecular systems. The generalized scheme has been tested on the 4π-electron problem trans-butadiene for which, by choosing a very general model space, we have calculated the energies of the ground, the lowest π-π* singlet and triplet and the first ionization potential by choosing a single composite cluster expansion operator for all states. Results for some more restricted choice of ...

A non-perturbative open-shell theory for atomic and molecular systems: Application to transbutadiene

Abstract: A non-perturbative theory is proposed in this article in which an energy independent effective Hamiltonian is obtained for open-shell systems. We have given a diagrammatic version of theory to facilitate the analysis of the problem. The theory has been applied to a model 4-π electron problem, for calculating the lowestπ-π* singlet and triplet energy levels of transbutadiene. Comparison with full Cl calculation indicates the excellent workability of the theory.

A non-perturbative open-shell theory for ionisation potential and excitation energies using HF ground state as the vacuum

Abstract: The authors' recently developed (1975) non-perturbative open-shell theory is adapted for direct evaluation of ionisation potential and excitation energies. Separating the 'core' contribution from the 'valence' part through the use of a multiple-cluster-expansion operator, the method provides a systematic way of including various core-valence interaction and core relaxation components. HF orbitals have been used as the basis for facilitating detailed comparison of the method with perturbative and propagator techniques. It has been shown that the method encompasses all the important second-order contributions of the latter formalisms and certain other classes of diagrams in a compact manner. An application to a simple 4 pi electronic problem is discussed to illustrate how this method works for real systems.

Role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice.

Abstract: A new type of correlated disorder is shown to be responsible for the appearance of extended electronic states in one-dimensional aperiodic systems like the Thue-Morse lattice. Our analysis leads to an understanding of the underlying reason for the extended states in this system, for which only numerical evidence is available in the literature so far. The present work also sheds light on the restrictive conditions under which the extended states are supported by this lattice.

Cluster expansion of the wavefunction. Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory

Abstract: The symmetry‐adapted‐cluster (SAC) expansion of an exact wavefunction is given. It is constructed from the generators of the symmetry‐adapted excited configurations having the symmetry under consideration, and includes their higher‐order effect and self‐consistency effect. It is different from the conventional cluster expansions in several important points, and is suitable for applications to open‐shell systems as well as closed‐shell systems. The variational equation for the SAC wavefunction has a form similar to the generalized Brillouin theorem in accordance with the inclusion of the higher‐order effect and the self‐consistency effect. We have expressed some existing open‐shell orbital theories equivalently in the conventional cluster expansion formulas, and on this basis, we have given the pseudo‐orbital theory which is an extension of open‐shell orbital theory in the SAC expansion formula.

Use of Cluster Expansion Methods in the Open-Shell Correlation Problem

Abstract: Publisher Summary This chapter discusses the developments of the open-shell many-body cluster expansion theories. Interpretation of most of the spectroscopic and dynamical phenomena, involving excited or ionized molecules and molecular fragments require models for open-shell states transcending the simple orbital description. The language of occupation number representation, coupled with the hole-particle description of the operators, the use of Wick's theorem and the attendant diagrammatic depiction of the various terms makes the many-body approach a very attractive alternative to the traditional CI-based theories. The open-shell many-body perturbation theory (MBPT) and the propagator or the Green's function methods have now developed into vast computational technology, generating softwares that are cost-effective and competitive with the CI-based codes. The cluster expansion based open-shell many-body formalisms possess even greater potentiality since they not only share and embed all the desirable features and technical advantages of the open-shell MBPT or propagator theories, but also are inherently non-perturbative in nature. They provide more compact descriptions of the electron correlation and are more flexible. Moreover, the cluster expansion of the open-shell functions provides valuable insight regarding the structure of general many-electron wave-functions.