2D Nmr: Density Matrix and Product Operator Treatment

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The density matrix operator at each stage of the experiment is labelled with numbers. For the analytical descriptions of the experiment, we have written a computer program in Mathematica which is very flexible for the implementation and the evolutions of the product operators under the Hamiltonians [20]. Evolutions of density matrix operator for each labelled point are obtained:.

Density Matrix and Product Operator Treatment Spectroscopy 2D Nmr

In Equation 9 , , , and. In density matrix operator theory, only the last term of Equation 9 contributes to the signal as acquisition is taken along y-axes. It is necessary to obtain the values of observable product operators indicated by O. Using values and making trigonometric. Figure 1.

Optimum t value is. BB: Broad band decoupling [6]. This equation shows that the spin—spin coupling information appears on F1 axis and represents two coherences for I nucleus with phase of. Therefore, they give doublets signals with opposite direction and no signal for central peak. The signals coordinate are , and with intensity distribution of —, respectively.

For IS 2 spin system, is the density matrix operator at thermal equilibrium:.

Density Matrix and Product Operator Treatment Spectroscopy 2D Nmr rnogmaseazanet.tk

Using values;. This equation represents five signals at the coordinates of , , , and with the relative intensities of —2:—, respectively. As seen in this equation, there exist seven signals at , , , , , and coordinates with the relative intensities of —3:—6:—, respectively.


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A computer program was written by Kanters et. M using Maple. Farrar , John E. A Handbook of Nuclear Magnetic Resonance. Ray Freeman.

Quantum Theory, Lecture 9: Quantum Statistical Mechanics. Density Matrices. Ensembles.

Principles of nuclear magnetic resonance in one and two dimensions Thomas W. Two-dimensional NMR methods for establishing molecular connectivity : a chemist's guide to experiment selection, performance, and interpretation Gary E.


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by Mateescu, Gheorghe D.; Valeriu, Adrian

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