Debasis Mukhopadhyay

Bio: Debasis Mukhopadhyay is an academic researcher from University of Calcutta. The author has contributed to research in topic(s): Diabatic & Coupled cluster. The author has an hindex of 15, co-authored 43 publication(s) receiving 791 citation(s). Previous affiliations of Debasis Mukhopadhyay include Indian Association for the Cultivation of Science & Princeton University.

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.

The construction of a size-extensive intermediate Hamiltonian in a coupled-cluster framework

Abstract: A size-extensive formulation for an intermediate Hamiltonian H int , furnishing size-extensive energies for the main roots, is presented. The working model space, comprised of the main and intermediate space, is taken as complete. The starting point is a shifted Bloch equation derived by us, involving shift operators generated by the projector spanned by the intermediate eigenvectors of H int . It is shown that a manifestly size-extensive H int can be constructed in the coupled-cluster framework provided we choose the shift operator explicitly as additively separable and the associated intermediate wave operator R as multiplicatively separable.

Applications of open-shell coupled cluster theory using an eigenvalue-independent partitioning technique: Approximate inclusion of triples in IP calculations

Abstract: Using our eigenvalue-independent partitioning (EIP) approach for the calculation of open-shell coupled cluster (CC) energy differences, we have computed the ionization potentials of HF and H 2 O using basis sets with and without polarization functions. Our results include the three-body cluster operator for the ionized states at the lowest order of approximation. It is found that a CCSD calculation for the ground state, followed by a CCSD calculation for the ionized states - with additional inclusion of triples using the converged CCSD amplitudes - produces results that are accurate up to third order and recovers the relaxation and differential correlation energies consequent on ionization in a balanced and compact manner.

Size-extensive effective Hamiltonian formalisms using quasi-Hilbert and quasi-Fock space strategies with incomplete model spaces

Abstract: An open-shell coupled cluster (CC) theory is developed using an incomplete model space (IMS) that works entirely within one particular n -valence Hilbert space sector. It is proved that the theory is size-extensive since both H eff and the energies obtained therefrom are connected. The method may be viewed as the Fock space CC theory for an IMS projected onto a given Hilbert space, and is denoted here as a “quasi-Hilbert” space theory. A “quasi-Fock“ formalism is also outlined where additional information on the lower valence model spaces are deliberately retained.

Molecular-exciton approach to spin-charge crossovers in dimerized hubbard and excitonic chains

Abstract: The crossover from band to correlated states in half-filled quantum cell models is studied in a molecular-exciton framework based on a chain of dimers. Crystal states with one or several excited dimers yield analytical excitation energies to first order in interdimer Coulomb interactions V(p,p') for excitonic chains or interdimer electron transfer ${\mathit{t}}_{\mathrm{\ensuremath{-}}}$=t(1-\ensuremath{\delta}) for Hubbard chains. Molecular-exciton analysis of excitations and transition moments rationalizes exact numerical solutions of oligomers with arbitrary intradimer correlations U, ${\mathit{V}}_{1}$, and electron transfer ${\mathit{t}}_{+}$=t(1+\ensuremath{\delta}), including the number, positions, and transition moments of low-lying excitations. Short correlation lengths of infinite chains with large alternation \ensuremath{\delta}\ensuremath{\ge}0.6 lead to converged crystal states for oligomers containing N=4--7 dimers. The present approach provides a detailed picture of excited-state crossovers with increasing U, ${\mathit{V}}_{1}$, and V(p,p'). Quite generally, the lowest singlet excitation ${\mathit{S}}_{1}$ is one-photon allowed (1B) on the band side of the spin-charge crossover and two-photon allowed (2A) on the correlated side. Intermediate correlations and large \ensuremath{\delta} reveal different crossovers in Hubbard chains, where 1B involves charge transfer between dimers, and excitonic chains, where 1B has an excited dimer.We also obtain two-photon transition moments M and extend vanishing M(2A) in the band limit up to U=2${\mathit{t}}_{+}$, the \ensuremath{\delta}\ensuremath{\sim}1 crossover of Hubbard chains. We find finite M(2A) on the correlated side, however, where 2A contains two triplet dimers in either alternating Hubbard or excitonic chains. Their different spin-charge crossovers appear as an abrupt and continuous increase, respectively, of two-photon intensity on going from the correlated to the band side. The greater delocalization (\ensuremath{\delta}\ensuremath{\sim}0.07--0.33) realized in conjugate polymers is consistent with excitonic chains. The potential V(p,p') in the Pariser-Parr-Pople model for conjugated hydrocarbons distinguishes strongly fluorescent polymers with ${\mathit{S}}_{1}$=1B from others with ${\mathit{S}}_{1}$=2A. We also relate our results at large \ensuremath{\delta} to other approximations for nonlinear optical spectra of conjugated polymers.

Coupled-cluster theory in quantum chemistry

Abstract: Today, coupled-cluster theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules. Though it was originally proposed for problems in physics, it has seen its greatest development in chemistry, enabling an extensive range of applications to molecular structure, excited states, properties, and all kinds of spectroscopy. In this review, the essential aspects of the theory are explained and illustrated with informative numerical results.

STARK SPECTROSCOPY: Applications in Chemistry, Biology, and Materials Science

Abstract: Stark spectroscopy has been applied to a wide range of molecular systems and materials. A generally useful method for obtaining electronic and vibrational Stark spectra that does not require sophisticated equipment is described. By working with frozen glasses it is possible to study nearly any molecular system, including ions and proteins. Quantitative analysis of the spectra provides information on the change in dipole moment and polarizability associated with a transition. The change in dipole moment reflects the degree of charge separation for a transition, a quantity of interest to a variety of fields. The polarizability change describes the sensitivity of a transition to an electrostatic field such as that found in a protein or an ordered synthetic material. Applications to donor-acceptor polyenes, transition metal complexes (metal-to-ligand and metal-to-metal mixed valence transitions), and nonphotosynthetic biological systems are reviewed.

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...

Density Matrix Analysis and Simulation of Electronic Excitations in Conjugated and Aggregated Molecules

Abstract: Predicting the electronic structure of extended organic molecules constitutes an important fundamental task of modern chemistry. Studies of electronic excitations, charge-transfer, energy-transfer, and isomerization of conjugated systems form the basis for our understanding of the photophysics and photochemistry of complex molecules1-3 as well as organic nanostructures and supramolecular assemblies.4,5 Photosynthesis and other photochemical biological processes that constitute the basis of life on Earth involve assemblies of conjugated chromophores such as porphyrins, chlorophylls, and carotenoids.6-8 Apart from the fundamental interest, these studies are also closely connected to numerous important technological applications.9 Conjugated polymers are primary candidates for new organic optical materials with large nonlinear polarizabilities.10-19 Potential applications include electroluminescence, light emitting diodes, ultrafast switches, photodetectors, biosensors, and optical limiting materials.20-27 Optical spectroscopy which allows chemists and physicists to probe the dynamics of vibrations and electronic excitations of molecules and solids is a powerful tool for the study of molecular electronic structure. The theoretical techniques used for describing spectra of isolated small molecules are usually quite different from those of molecular crystals, and many intermediate size systems, such as clusters and polymers, are not readily described by the methods developed for either of these limiting cases.28