Saroj Mukhopadhyay

Bio: Saroj Mukhopadhyay is an academic researcher from Indian Association for the Cultivation of Science. The author has contributed to research in topics: Coupled cluster & Ground state. The author has an hindex of 5, co-authored 5 publications receiving 447 citations.

Aspects of separability in the coupled cluster based direct methods for energy differences

Abstract: In this paper we have discussed in detail the aspects of separability of the energy differences obtained from coupled cluster based “direct” methods such as the open-shell Coupled Cluster (CC) theory and the Coupled Cluster based Linear Response Theory (CC-LRT). It has been emphasized that, unlike the state energiesper se, the energy differences have a semi-local character in that, in the asymptotic limit of non-interacting subsystemsA, B, C, etc., they are separable as ΔE A , ΔE B , ΔE A + ΔE B , etc. depending on the subsystems excited. We classify the direct many-body methods into two categories: core-extensive and core-valence extensive. In the former, we only implicitly subtract the ground state energy computed in a size-extensive manner; the energy differences are not chosen to be valence-extensive (separable) in the semi-local sense. The core-valence extensive theories, on the other hand, are fully extensive — i.e., with respect to both core and valence interactions, and hence display the semi-local separability. Generic structures of the wave-operators for core-extensive and core-valence extensive theories are discussed. CC-LRT is shown to be core-extensive after a transcription to an equivalent wave-operator based form. The emergence of valence disconnected diagrams for two and higher valence problems are indicated. The open-shell CC theory is shown to be core-valence extensive and hence fully connected. For one valence problems, the CC theory and the CC-LRT are shown to be equivalent. The equations for the cluster amplitudes in the Bloch equation are quadratic, admitting of multiple solutions. It is shown that the cluster amplitudes for the main peaks, in principle obtainable as a series inV from the zeroth order roots of the model space, are connected, and hence the energy differences are fully extensive. It is remarkable that the satellite energies obtained from the alternative solutions of the CC equations are not valence-extensive, indicating the necessity of a formal power series structure inV of the cluster amplitudes for the valence-extensivity. The alternative solutions are not obtainable as a power series inV. The CC-LRT is shown to have an effective hamiltonian structure respecting “downward reducibility”. A unitary version of CC-LRT (UCC-LRT) is proposed, which satisfy both upward and downward reducibility. UCC-LRT is shown to lead to the recent propagator theory known as the Algebraic Diagrammatic Construction. It is shown that both the main and the satellite peaks from UCC-LRT for the one valence problems are core-valence extensive owing to the hermitized nature of the underlying operator to be diagonalized.

Advances in methods and algorithms in a modern quantum chemistry program package

Abstract: Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space

Abstract: The equation-of-motion coupled-cluster (EOM-CC) approach is a versatile electronic-structure tool that allows one to describe a variety of multiconfigurational wave functions within single-reference formalism. This review provides a guide to established EOM methods illustrated by examples that demonstrate the types of target states currently accessible by EOM. It focuses on applications of EOM-CC to electronically excited and open-shell species. The examples emphasize EOM's advantages for selected situations often perceived as multireference cases [e.g., interacting states of different nature, Jahn-Teller (JT) and pseudo-JT states, dense manifolds of ionized states, diradicals, and triradicals]. I also discuss limitations and caveats and offer practical solutions to some problematic situations. The review also touches on some formal aspects of the theory and important current developments.

Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method

Abstract: The theory for analytic energy derivatives of excited electronic states described by the equation‐of‐motion coupled cluster (EOM‐CC) method has been generalized to treat cases in which reference and final states differ in the number of electrons. While this work specializes to the sector of Fock space that corresponds to ionization of the reference, the approach can be trivially modified for electron attached final states. Unlike traditional coupled cluster methods that are based on single determinant reference functions, several electronic configurations are treated in a balanced way by EOM‐CC. Therefore, this quantum chemical approach is appropriate for problems that involve important nondynamic electron correlation effects. Furthermore, a fully spin adapted treatment of doublet electronic states is guaranteed when a spin restricted closed shell reference state is used—a desirable feature that is not easily achieved in standard coupled cluster approaches. The efficient implementation of analytic gradien...

Equation of motion coupled cluster method for electron attachment

Abstract: The electron attachment equation of motion coupled cluster (EA‐EOMCC) method is derived which enables determination of the various bound states of an (N+1)‐electron system and the corresponding energy eigenvalues relative to the energy of an N‐electron CCSD reference state Detailed working equations for the EA‐EOMCC method are derived using diagrammatic techniques for both closed‐shell and open‐shell CCSD reference states based upon a single determinant The EA‐EOMCC method is applied to a variety of different problems, the main purpose being to establish its prospects and limitations The results from EA‐EOMCC calculations are compared to other EOMCC approaches, starting from different reference states, as well as other theoretical methods and experimental values, where available We have investigated electron affinities for a wide selection of both closed‐shell and open‐shell systems Excitation spectra of atoms and molecules with an odd number of electrons are obtained, taking the closed‐shell ground state of the ion as a reference in the EA‐EOMCC calculation Finally we consider excitation spectra of some closed‐shell systems, and find in particular that the electron attachment approach is capable of yielding accurate triplet excitation energies in an efficient way