R. K. Moitra

Correlation problem in open-shell atoms and molecules. A non-perturbative linked cluster formulation

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

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

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.

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

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.

Extended states in one-dimensional lattices : application to the quasiperiodic copper-mean chain

The question of the conditions under which one-dimensional systems support extended electronic eigenstates is addressed in a very general context. Using real-space renormalization-group arguements we discuss the precise criteria for determining the entire spectrum of extended eigenstates and the corresponding eigenfunctions in disordered as well as quasiperiodic systems. For purposes of illustration we calculate a few selected eigenvalues and the corresponding extended eigenfunctions for the quasiperiodic copper-mean chain. So far, for the infinite copper-mean chain, only a single energy has been numerically shown to support an extended eigenstate [J. Q. You, J. R. Yan, T. Xie, X. Zeng, and J. X. Zhong, J. Phys.: Condens. Matter 3, 7255 (1991)]: we show analytically that there is in fact an infinite number of extended eigenstates in this lattice which form fragmented minibands.

Renormalization-group analysis of extended electronic states in one-dimensional quasiperiodic lattices

We present a detailed analysis of the nature of electronic eigenfunctions in one-dimensional quasi-periodic chains based on a clustering idea recently introduced by us [Sil et al., Phys. Rev. {\bf B 48}, 4192 (1993) ], within the framework of the real-space renormalization group approach. It is shown that even in the absence of translational invariance, extended states arise in a class of such lattices if they possess a certain local correlation among the constituent atoms. We have applied these ideas to the quasi-periodic period-doubling chain, whose spectrum is found to exhibit a rich variety of behaviour, including a cross-over from critical to an extended regime, as a function of the hamiltonian parameters. Contrary to prevailing ideas, the period-doubling lattice is shown to support an infinity of extended states, even though the polynomial invariant associated with the trace map is non-vanishing. Results are presented for different parameter regimes, yielding both periodic as well as non-periodic eigenfunctions. We have also extended the present theory to a multi-band model arising from a quasi-periodically arranged array of

On the nature of eigenstates of quasiperiodic lattices in one dimension

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Extended electronic states in disordered 1-d lattices: an example

-function potentials on the atomic sites. Finally, we present a multifractal analysis of these wavefunctions following the method of Godreche and Luck [ C. Godreche and J. M. Luck, J. Phys. A :Math. Gen. {\bf 23},

TWO-BAND FIBONACCI QUASICRYSTAL WITH HYBRIDIZATION: EXACT LOCAL GREEN’S FUNCTION USING THE RENORMALIZATION-GROUP METHOD

Abstract We re-examine the conventional idea of determining the nature of the electronic eigenfunctions (extended, critical or localised) of a Fibonacci lattice from a study of the invariant associated with the trace map. We demonstrate that this is insufficient, and a more detailed study of the renormalisation group transformation itself is required to ascertain the nature of the eigenfunctions. Suitable examples are provided.

Exact local Green function for phonons in a Fibonacci chain: a new real-space renormalisation group approach

Abstract We discuss a very simple model of a 1-d disordered lattice, in which all the electronic eigenstates are extended. The nature of these states is examined from several viewpoints, and it is found that the eigenfunctions are not Bloch functions although they extend throughout the chain. Some typical wavefunctions are plotted. This problem originated in the earlier study of extended states in the quasiperiodic copper-mean lattice of Sil, Karmakar, Moitra and Chakrabarti [Phys. Rev. B (1993)]. In the present investigation extended states are found to arise from a different kind of correlation than that of the well-known dimer-type.