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- Archibald, M., et al.
(författare)
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Finding the hole in a wall
- 2020
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Ingår i: Journal of Mathematical Chemistry. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 58:10, s. 2313-2323
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Tidskriftsartikel (refereegranskat)
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| 3. |
- Arteca, Gustavo A., et al.
(författare)
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Constructing quantum mechanical models from diabatic schemes : external field modulation of effective energy barriers for bond breaking/formation processes
- 2014
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Ingår i: Journal of Mathematical Chemistry. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 52:9, s. 2395-2410
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Tidskriftsartikel (refereegranskat)abstract
- We have recently proposed an approach where chemical transformations can be described as quantum processes involving the modulation of entangled states by an applied external field (Arteca and Tapia in Phys Rev A 84:012115, 2011). In practical implementations, we gain insight into these processes by using simple quantum-mechanical models derived from diabatic schemes. In this context, reactant, product, and, eventually, intermediate species, are assigned to diabatic basis functions, and then entangled by an external field into a quantum state from which all observable properties of the chemical reaction should emerge. Here, we extend our previous model for bond breaking/formation in diatomic molecules (Arteca et al. in J Math Chem 50:949, 2012). We consider the entire manifold of semiclassical models defined by only two diabatic basis functions: a harmonic well for the "molecular" bound state, and an exponential potential energy function for the asymptotically separated fragments (the "product" channel). Using a two-parameter space to describe all models, we determine how the topology of the total energy function is affected by the shape of the applied field. We show that strong and weak local couplings with the external field modify substantially the occurrence of energy barriers, in contrast to using the uniform (i.e., space-invariant) coupling employed in previous works.
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| 4. |
- Arteca, Gustavo A., et al.
(författare)
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Constructing quantum mechanical models starting from diabatic schemes : Quantum states for simulations bond break/formation-I. Feshbach-like quantum states and electronuclear wave functions
- 2012
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Ingår i: Journal of Mathematical Chemistry. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 50:4, s. 949-970
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Tidskriftsartikel (refereegranskat)abstract
- A quantum description adapted to scrutinize chemical reaction mechanisms obtains by implementing an electronuclear separation via quantum numbers method; truly diabatic base states obtain that sustain quantum states expressed as linear superpositions. A proto-type bond breaking/formation case: H-2(+) double left right arrow H(1s) + H+ test possibilities via mathematical modeling. Asymptotic states (vertical bar H > circle times vertical bar H+>) and (vertical bar H+> circle times vertical bar H >) and basis states for quantized electromagnetic radiation complete the model; Feshbach-resonance-like quantum states obtain that play pivotal roles gating association/dissociation processes. A fixed grid of floating Gaussian orbitals permits actual computations compatible with this method. The information therefrom gleaned is used to construct model Hamiltonians easily adaptable to second quantization formalisms. Theoretical developments and non-routine computations results can directly be related to experiment.
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| 9. |
- Belkic, D, et al.
(författare)
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Derivative NMR spectroscopy for J-coupled multiplet resonances using short time signals (0.5 KB) encoded at low magnetic field strengths (1.5T). Part I: water suppressed
- 2021
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Ingår i: JOURNAL OF MATHEMATICAL CHEMISTRY. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 59:2, s. 364-404
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- The theme of this study is within the realm of basic nuclear magnetic resonance (NMR) spectroscopy. It relies upon the mathematics of signal processing for NMR in analytical chemistry and medical diagnostics. Our objective is to use the fast Padé transform (both derivative and nonderivative as well as parametric and nonparametric) to address the problem of multiplets from J-coupling appearing in total shape spectra as completely unresolved resonances. The challenge is exacerbated especially for short time signals (0.5 KB, no zero filling), encoded at a standard clinical scanner with the lowest magnetic field strengths (1.5T), as is the case in the present investigation. Water has partially been suppressed in the course of encoding. Nevertheless, the residual water content is still more than four times larger than the largest among the other resonances. This challenge is further sharpened by the following question: Can the J-coupled multiplets be resolved by an exclusive reliance upon shape estimation alone (nonparametric signal processing)? In this work, the mentioned parametric signal processing is employed only as a gold standard aimed at cross-validating the reconstructions from nonparametric estimations. A paradigm shift, the derivative NMR spectroscopy, is at play here through unprecedentedly parametrizing total shape spectra (i.e. solving the quantification problem) by sole shape estimators without fitting any envelope.
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| 10. |
- Belkic, D, et al.
(författare)
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Derivative NMR Spectroscopy for J-Coupled Multiplet Resonances using Short Time Signals (0.5KB) Encoded at Low Magnetic Field Strengths (1.5T). Part II: Water Unsuppressed
- 2021
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Ingår i: JOURNAL OF MATHEMATICAL CHEMISTRY. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 59:2, s. 405-443
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- The topic of this work is on reliable resolving of J-coupled resonances in spectral envelopes from proton nuclear magnetic resonance (NMR) spectroscopy. These resonances appear as multiplets that none of the conventional nonderivative shape estimators can disentangle. However, the recently formulated nonconventional shape estimator, the derivative fast Padé transform (dFPT), has a chance to meet this challenge. In the preceding article with a polyethylene phantom, using the time signals encoded with water suppressed, the nonparametric dFPT was shown to be able to split apart the compound resonances that contain the known J-coupled multiplets. In the present work, we address the same proton NMR theme, but with sharply different initial conditions from encodings. The goal within the nonparametric dFPT is again to accurately resolve the J-coupled resonances with the same polyethylene phantom, but using raw time signals encoded without water suppression. The parallel work on the same problem employing two startlingly unequal time signals, encoded with and without water suppression in the preceding and the current articles, respectively, can offer an answer to a question of utmost practical significance. How much does water suppression during encoding time signals actually perturb the resonances near and farther away from the dominant water peak? This is why it is important to apply the same dFPT estimator to the time signals encoded without water suppression to complement the findings with water suppression. A notable practical side of this inquiry is in challenging the common wisdom, which invariably takes for granted that it is absolutely necessary to subtract water from the encoded time signals in order to extract meaningful information by way of NMR spectroscopy.
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