Author
Mangala Sunder Krishnan
Other affiliations: McGill University, Université de Montréal, Queen's University
Bio: Mangala Sunder Krishnan is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Hamiltonian (quantum mechanics) & Quantum entanglement. The author has an hindex of 8, co-authored 28 publications receiving 186 citations. Previous affiliations of Mangala Sunder Krishnan include McGill University & Université de Montréal.
Papers
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TL;DR: In this article, van Vleck's contact transformation method was used for the study of time-dependent interactions in solid state nuclear magnetic resonance (NMR) by Floquet theory. But the authors did not consider the effect of the contact transformation on the dynamics of a dipolar coupled spin (I=1/2) system.
Abstract: In this article, we propose to use van Vleck’s contact transformation method for the study of time-dependent interactions in solid state nuclear magnetic resonance (NMR) by Floquet theory [A. Schmidt and S. Vega, J. Chem. Phys. 96, 2655 (1992)]. Floquet theory has been used for studying the spin dynamics of magic angle spinning (MAS) NMR experiments. The contact transformation method is an operator method in time-independent perturbation theory and has been used to obtain effective Hamiltonians in molecular spectroscopy. Here the above method is combined with Floquet theory to study the dynamics of a dipolar coupled spin (I=1/2) system. In order to determine the frequencies and intensities of bands in MAS spectra, we need to diagonalize the Floquet–Hamiltonian matrix. This is generally done numerically, by truncating the infinite dimensional Floquet–Hamiltonian matrix. Here we propose an effective Floquet–Hamiltonian for the system. We demonstrate the application of the above method to a homonuclear dipolar coupled spin system (I=1/2). The eigenvalues obtained from the above are compared with those obtained using numerical diagonalization. The eigenvalues of the effective Hamiltonian compare quite well with those computed using numerical diagonalization of Floquet matrices.
49 citations
TL;DR: In this paper, the effect of radiofrequency pulses in nuclear quadrupole resonance (NQR) spectroscopy was examined, where both rotating and counter-rotating radiofrequency field components are retained.
Abstract: The effect of radiofrequency pulses in nuclear quadrupole resonance (NQR) spectroscopy is examined. The description is different from that needed in nuclear magnetic resonance (NMR) spectroscopy. In particular, both rotating and counter-rotating radiofrequency field components are retained. Pulses in NQR spectroscopy are selective and cause transitions between two pairs of levels (±M) → ±(M + 1), other transitions are not normally excited. The formulation of pulses is then described for any spin I by two 2 × 2 rotation matrices, one causing an M → M + 1 transition and the other causing a - (M + 1) → -M transition. Calculations on resonance for spins with an axially symmetric nuclear quadrupole for up to three pulses are presented for spins I = 1 and I = 3/2. The results agree with the work of Reddy, R. and Narasimhan, P. T., 1991, Molec. Phys., 72, 491, in the appropriate limits.
19 citations
TL;DR: In this article, the subduced mapping from the sixtyfold symmetric group onto for is considered in the context of nuclear magnetic resonance (NMR) coherence transfer networks over coherent superpositional (CSP)-forms of Liouville space bases within p ˇ-4 of the Liouvillian SU2 for high order multiple quantum processes.
Abstract: The absence of any single pair of nuclei on any one of the three representative Cl, l = 2, 3, 5 (subduced) icosahedral rotational symmetry axes of [13C]60, leads to a virtually unique case of the invariance hierarchy over M(SO(2))-weights reducing to a purely combinatorial problem. Aspects of the subduced mapping from the sixtyfold symmetric group onto for are considered in the context of nuclear magnetic resonance (NMR) coherence transfer networks over practical coherent superpositional (CSP)-forms of Liouville space bases within p ˇ- 4 of Liouvillian SU2 for high order multiple quantum processes. The number of equivalent sites under each type of rotational operation provides a highly structured invariance set. The use (of necessity) of a largely character-free algebra within the simply reducible (SR) {[λ]} ≡ [λ] ⊗ [n - 1, 1], or non-SR {[λ′]} ≡ [n - 2, 2] ⊗ [n - 2, 2], group aspects and additional properties allows the tertiary [n - r, r - r′, r′] () partitions to be correlated with their subduced irrep...
18 citations
04 Jul 2012
TL;DR: This panel presents views from different countries on the development of open educational resource initiatives at a global level.
Abstract: In recent years, the term Open Educational Resources (OER) has emerged, aiming to promote open access to digital educational resources that are available online for everyone at a global level. This panel presents views from different countries on the development of open educational resource initiatives.
14 citations
TL;DR: In this article, a homodesmotic reaction scheme coupled with density functional theory has been used to estimate theoretically strain energies and heats of formation of cyclic [n]paraphenyleneacetylenes ([n]CPPAs) for molecular electronics.
Abstract: Cyclic [n]paraphenyleneacetylenes ([n]CPPAs) are potentially useful compounds for molecular electronics In this article, a homodesmotic reaction scheme coupled with density functional theory has been used to estimate theoretically strain energies and heats of formation of [n]CPPAs Calculations have been done for a series of [n]CPPAs, containing up to ten phenylacetylene units Strain energies of [n]CPPAs decrease, while heats of formation increase steadily with the increase in the number of phenylacetylene units using homodesmotic reaction schemes B3LYP and mPW1PW91 functionals have been used with the Pople basis set 6-31G* to analyze the trends The results are sensitive to the scheme of homodesmotic reaction chosen, thereby necessitating careful chemical consideration before spending considerable computational resources for higher [n]CPPAs not considered here Computational estimates for the ring diameter of [n]CPPAs and absolute entropy have also been obtained here The HOMO-LUMO gaps of the belt sh
13 citations
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TL;DR: A software library incorporating recent research into efficient simulation algorithms for large spin systems is introduced, and Liouville space simulations of most liquid-state NMR experiments on 40+ spin systems can now be performed without effort on a desktop workstation.
357 citations
TL;DR: This review gives a comprehensive and strictly chronological treatment of literature reports from the inception of the field, with emphasis on both synthesis and properties of CPPs and related nanohoops.
Abstract: The first synthesis of a cyclic oligophenylene possessing a radial π system was reported in 2008. In the short period that has elapsed since, there has been an ever-increasing level of interest in molecules of this type, as evidenced by the volume of publications in this area. This interest has been driven by the highly unusual properties of these molecules in comparison to their linear oligoarene analogues, as well as the diverse array of potential applications for them. Notably, CPPs and related structures were proposed as viable templates for the bottom-up synthesis of single-walled carbon nanotubes (SWCNTs), a proposition which has recently been realised. This review gives a comprehensive and strictly chronological (by date of first online publication) treatment of literature reports from the inception of the field, with emphasis on both synthesis and properties of CPPs and related nanohoops. (The scope of this review is restricted to molecules possessing a radial π system consisting entirely of subunits which are aromatic in isolation, e.g. CPPs, but not cycloparaphenyleneacetylenes or cyclopolyacetylenes).
319 citations
TL;DR: A selective classified bibliography of symbolic computation in some areas of chemistry is provided together with some examples of computer algebra algorithms and techniques to facilitate future joint work of chemists and computer scientists.
Abstract: A selective classified bibliography of symbolic computation in some areas of chemistry is provided together with some examples of computer algebra algorithms and techniques to facilitate future joint work of chemists and computer scientists. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
240 citations
TL;DR: The structures and strain energies of cycloparaphenylenes (CPPs) have been determined by DFT calculation at the B3LYP/6-31G(d) level of theory and it was found that benzene rings of [12]CPP can rotate rather freely at room temperature.
207 citations
144 citations