Selective Gaussian

Berger (1989) anticipated the solution to the problem of needing experimental access to selective heteronuclear shift connectivities with the development of a selective ID analog of the HMQC experiment to which he gave the acronym SELINCOR. Simply, SELINCOR replaces the final 90° carbon pulse of the HMQC experiment (see Fig. 1) with a selective Gaussian 90° pulse applied to the C resonance of interest. SELINCOR has had no practical applications but was certainly of interest in a developmental sense. 

Figure 2 NMR spectra from the brain of a healthy 43 year old male human volunteer. The upper spectrum is from the cerebellum and the lower spectrum is from the occipital cortex. The spectrum was measured at 170 MHz using a 4T magnet with a 15 cm diameter semi-volume coil. Localization was achieved using a pulse sequence based on the STEAM method with a nominal volume of 27 mL. Water peak suppression used selective Gaussian pulses. Cho - choline groups, Cr - creatine, NAA - N-acetylaspartate. Reproduced with permission from Seaquist ER and Gruetter R (1998) Identification of a high concentration of scyllo-inositol in the brain of a healthy human subject using and NMR. Magnetic Resonance in Medicine 39 313-316.

As usual there is the question of the initial conditions. In general, more than one frozen Gaussian function will be required in the initial set. In keeping with the frozen Gaussian approximation, these basis functions can be chosen by selecting the Gaussian momenta and positions from a Wigner, or other appropriate phase space, distribution. The initial expansion coefficients are then defined by the equation... 

The two sources of stochasticity are conceptually and computationally quite distinct. In (A) we do not know the exact equations of motion and we solve instead phenomenological equations. There is no systematic way in which we can approach the exact equations of motion. For example, rarely in the Langevin approach the friction and the random force are extracted from a microscopic model. This makes it necessary to use a rather arbitrary selection of parameters, such as the amplitude of the random force or the friction coefficient. On the other hand, the equations in (B) are based on atomic information and it is the solution that is approximate. For ejcample, to compute a trajectory we make the ad-hoc assumption of a Gaussian distribution of numerical errors. In the present article we also argue that because of practical reasons it is not possible to ignore the numerical errors, even in approach (A). 

The original paper defining the Gaussian-2 method by Curtiss, Raghavachari, Trucks and Pople tested the method s effectiveness by comparing its results to experimental thermochemical data for a set of 125 calculations 55 atomization energies, 38 ionization potentials, 25 electron affinities and 7 proton affinities. All compounds included only first and second-row heavy atoms. The specific calculations chosen were selected because of the availability of high accuracy experimental values for these thermochemical quantities. 

This directs the program to save the input you typed in to a file. Select the desired directory location in the standard Windows save dialog box, and give the input file the name H20.GJF. GJF is the extension used for Gaussian input files on Windows systems (standing for Gaussian fob File). 

Select and drag the desired input file from the File Manager into the Gaussian 94W main program window or on top of its minimized icon. The... 

To better understand this, let s create a set of data that only contains random noise. Let s create 100 spectra of 10 wavelengths each. The absorbance value at each wavelength will be a random number selected from a gaussian distribution with a mean of 0 and a standard deviation of 1. In other words, our spectra will consist of pure, normally distributed noise. Figure SO contains plots of some of these spectra, It is difficult to draw a plot that shows each spectrum as a point in a 100-dimensional space, but we can plot the spectra in a 3-dimensional space using the absorbances at the first 3 wavelengths. That plot is shown in Figure 51. 

The potential energy curves (Fig. 1), the non-adiabatic coupling, transition dipole moments and other system parameters are same as those used in our previous work (18,19,23,27). The excited states 1 B(0 ) and 2 B( rio) are non-adiabatically coupled and their potential energy curves cross at R = 6.08 a.u. The ground 0 X( Eo) state is optically coupled to both the and the 2 R( nJ) states with the transition dipole moment /ioi = 0.25/xo2-The results to be presented are for the cw field e(t) = A Yll=o cos (w - u pfi)t described earlier. However, for IBr, we have shown (18) that similar selectivity and yield may be obtained using Gaussian pulses too. 

Gaussian pulses are frequently applied as soft pulses in modern ID, 2D, and 3D NMR experiments. The power in such pulses is adjusted in milliwatts. Hard" pulses, on the other hand, are short-duration pulses (duration in microseconds), with their power adjusted in the 1-100 W range. Figures 1.15 and 1.16 illustrate schematically the excitation profiles of hard and soft pulses, respectively. Readers wishing to know more about the use of shaped pulses for frequency-selective excitation in modern NMR experiments are referred to an excellent review on the subject (Kessler et ai, 1991). 

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