Gaussian focus

Figure 2.4. Pages 45-46. Ray diagrams illustrating (a) Gaussian focus, (b) underfocus by decreasing the object distance, (c) underfocus by increasing the focal length, and (d) overfocus by decreasing the focal length.

Fig. 1. The imaginary part of the phase contrast transfer function, sinX, plotted as a function in reciprocal space for a microscope operating at 200 kV with a spherical aberration coefficient of 1.2 mm a) Gaussian focus b) 325A underfocus c) 65OA underfocus.

It is apparent from the ray diagram of Fig. 3.3 that there is a plane, A-A, nearer to the lens than the geometrical or Gaussian focus plane, where the resolution is improved. It is called the plane of least confusion or Scherzer focus [3, 4, 7], and it is close to where the rays from the outermost parts of the lens intersect the axis. From Fig. 3.3 the distance 6Z between this plane and the Gaussian image plane is approximately the radius of the image disc in the Gaussian plane divided by a. The radius is Ma C and a = ajM, so... 

It is important to remember that image resolution depends on the interaction volume, which may be much greater than the probe diameter (see Section 2.3 and Section 3.2.2). Because brightness B is fixed by the electron source, the geometric (or Gaussian) focused spot size can be given in terms of the probe current i using Eq. (3.14). 

Semi-empirical methods are characterized by their use of parameters derived from experimental data in order to simplify the approximation to the Schrbdinger equation. As such, they are relatively inexpensive and can be practically applied to very, very large molecules. There are a variety of semi-empirical methods. Among the best known are AMI, PM3 and MNDO. Gaussian includes a variety of semi-empirical models, and they are also the central focus or present in many other programs including AMPAC, MOPAC, HyperChem and Spartan. 

The molecules considered in both the worked examples in the text and the exercises have been chosen to minimize the amount of CPU time necessary to complete a non-trivial calculation of each type. We ve deliberately chosen systems that, for the most part, can be modeled with minimal cost because our goal here is to focus on the chemistry, rather than on Gaussian s features and research capabilities. Note, however, that although the molecules we will consider are relatively small, the methods you will... 

In this context, we should focus the reader s attention on the process of specifications of boundary conditions by doing Gaussian elimination along the rows for oj yj and along the columns for When p, happens to be... 

The electric field of a focused Gaussian beam in TEM00 at cylindrical coordinates z and r is given by [59],... 

The present chapter reviews applications in biocatalysis of the ONIOM method. The focus is on studies performed in our research group, in most cases using the two-layer ONIOM(QM MM) approach as implemented in Gaussian [23], The studied systems include methane monooxygenase (MMO), ribonucleotide reductase (RNR) [24, 25], isopenicillin N synthase (IPNS) [26], mammalian Glutathione peroxidase (GPx) [27,28], Bi2-dependent methylmalonyl-CoA mutase [29] and PLP-dependent P-lyase [30], These systems will be described in more detail in the following sections. ONIOM applications to enzymatic systems performed by other research groups will be only briefly described. 

Chapter 1 gives a short description of ab initio methods, Hartree-Fock and post-Hartree-Fock, focusing on the Gaussian computer programs. Chapter 2 describes semi-empirical calculations and their applications to biological systems. Chapter 3 addresses itself to electrostatic properties of molecules, as determined by quantum-chemical methods. The density functional method is discussed in chapter 4. Chapter 5 compares theoretically obtained parameters to experimental data. 

As an example of an experimental setup needed for the kind of experiments discussed above, we give now a brief overview of a recent experiment carried out by our group at the SLIC facility at CEA in Saclay (France) [10]. The laser system was the UHI-10 Ti Sa laser, which delivered 65 fs pulses with energy up to 0.7 J. The laser beam was focused by an //5 off-axis parabolic mirror, producing a quasi-gaussian spot where the field parameter ao = c/l aser/mec2,... 

As the disc spins, a protein edge passes through a focused Gaussian beam that has a beam radius p0. At the moment when the optic axis coincides with the protein edge in the near field, there is a quadrature condition in the far field set by... 

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