Ellipsoid Parameters

Dialog Box: Ellipsoid Parameters [ Input2 Menu ]

This dialog controls plotting parameters for the Thermal Ellipsoid and 3D display modes, set in the Display Mode sub-menu in the Display menu or in the Dialog Bar - Left

The following parameters are those which are in the various instruction series of ORTEP.

NPLANE - drawing of ellipses = 0, no ellipsoid components = 1, boundary ellipse only = 3, principal ellipses only

= 4, boundary + principal ellipses NDOT - back side of principal ellipses < 0, solid line back side

= 0, back side omitted = 3, 4 dots on back side = 4, 8 dots on back side = 5, 16 dots on back side = 6, 32 dots on back side

NLINE - forward principal axes and shading (cut-out octant) = 0, no forward axes or shading

= 1, forward principal axes only = N, forward axes + (N-1) line shading NDASH - dashed reverse principal axes = 0, no reverse axes

= N, dashed reverse axes with N dashes NBOND - bond type for stick bonds

= 0, no bonds

= 1, 2, 3, 4, 5 give lines at 180, 90, 45, 22.5 or 11.25 degrees apart, bonds ending at ellipsoids

= -1 to -5, same, bonds ending at atom centers TAPER - bond taper. The bond radius is

R = R0 +- TAPER * ABS( COS(THETA) )

where theta is the angle between the bond and the view direction. The bond radius is set in the Bond Data dialog (Input1 menu).

SCAL2 - ellipsoid probability scaling factor.

This controls the size of ellipsoids. A value of 0.76 gives 10% probability, 1.54 gives 50% probability, 3.36 gives 99% probability, etc. See the table in the original ORTEP instructions.

DISP - retrace resolution.

When lines are retraced to emphasize certain ellipsoids or make the width a function of depth, this is the separation.

A0 and A1 - depth function parameters.

Lines may be retraced to give wider lines for closer ellipsoids.

dR(x) = AO + A1 * x

where dR is the width of the line and x is the height in Angstroms.

Use b/w shades. If this box is checked, ellipsoids in black-and-white display and output will be filled with the b/w shade or color specified in the Input Atom Data dialog (Input1 menu). If it is not checked, they are filled with white before drawing ellipsoid

components.

Show iso as spheres. If this box is checked, isotropic atoms are shown as spheres (i.e.

circles) without the principal planes, which can give a false impression of anisotropy.

Default radius. This is the mu value which is given to atoms with no valid entered temperature factors; it is 0.1 by default.

If DISP is 0.0, lines are not retraced. For one-dot lines on typical screens, DISP should be about 0.01 inch, but it can be much smaller for output. Note that x is measured from

the zero of coordinates, not the rear-most atom

Line widths for atoms are set independently in the Line Widths dialog (Input2 menu), and the value of DISP should take account of these settings if wide lines are used.

For color display and output, depth is probably best shown by front-back fading of color (Shading dialog, Input2 menu) rather than line retracing.

3D Mode. If the Show in 3D mode box is checked, and if temperature factor data have been entered, atoms will be shown as ellipsoids in the 3D Display Mode. If NLINE is greater than 0, the "forward axes" or cutout octant is shown as in ORTEP (except in 3D files - see below). If NPLANE is greater than 1, the trace of the principal planes will be shown as stripes or three-dimensional bands just outside the ellipsoids. The Width of principal- plane stripes gives the width of these bands. The Radius Factor for stripes gives the height or extent to which the curves for the principal planes are outside the ellipsoid itself; this should always be larger than 1.0. By increasing this factor and decreasing SCAL2, the principal planes can be made to dominate the representation, as elliptical disks.

For direct screen and print rendering, the bonds between ellipsoids are the same size as shape as in ORTEP drawing, and the TAPER parameter is applicable. In 3D files (VRML and POV-Ray), bonds are always strictly cylindrical. Also in these files, the ellipsoids are always complete and do not have the cutout octant as possible in ORTEP drawing. When Polyhedra are present, and ligand atoms are not shown at the corners, bonds to these corners are always cylindrical, not tapered. Note that the option to show corner atoms as spheres of constant size is not applicable to the 3D mode - such atoms are either absent, or shown as thermal ellipsoids. Of course, the atoms could be converted to isotropic temperature factors of appropriate size.

The SCAL2 parameter above determines the size of the ellipsoids as in the Ellipsoid drawing mode. Apart from SCAL2, TAPER, NLINE and NPLANE the ORTEP parameters above are not applicable to 3D drawings.

The 3D Material parameters used for both the cutout octant and the principal-plane bands are those for polyhedra - this is to avoid distracting specular reflections from large flat surfaces (although polyhedra may be assigned large specular reflection components as well).

Polyhedra in Ellipsoid mode (non-3D) group. In the Ellipsoid display mode, you can either show polyhedra with flat, opaque faces (last option), or you can show the ligand-ligand "bonds" which are the edges of polyhedra, and also the central-ligand-ligand bonds. Both of these types of "bonds" are as defined in the Polyhedra input in the Input1 menu, not the Bonds input. The ligand-ligand "bonds" or edges will have the fill and edge colors which are specified for the given polyhedron in the Polyhedron Data dialog, and the

central-ligand "bonds" will have the edge and fill colors of the central atom

(Input Atom Data dialog). Both these bond types will have a uniform radius, as specified in the edit box.

The intersections of the solid polyhedra with the corner ellipsoids are not solved exactly, but approximated assuming the corner atoms are spheres. The size of these spheres is determined by the settings in the Polyhedra dialog (Input1 menu). This approximation will be less acceptable as the ellipsoids deviate further from sphericity.

All the atoms involved in polyhedra, except for the central atom in the case of solid polyhedra, will be shown as elllipsoids.

The central-ligand and ligand-ligand "bonds", if used, must be added to the bond list during calculation, so changes in this option may require Recalculation, rather than just replot.

3.2.3.12 3D General

Dialog Box: 3D General [ Input2 Menu ]

In the 3D drawing mode, crystal edges (Crystal Edges and Faces dialog), structure axes (Crystal Axes dialog) or unit-cell edges (Unit Cell dialog) may either be lines or

cylinders. If they are lines, the width is set in the Line Widths dialog (Input2 menu).

Rims of atoms and bonds and edges of polyhedra are never shown, so the relevant values are for edges (which include axes and unit cell) and bonds (which include skeletal bonds.

Width of lines in VRML files cannot be controlled. Wide lines in 3D generally do not look good, so if width is to be more than one pixel, cylinders are better.

Spheres (atoms) and cylinders (bonds or vectors) are actually drawn as assemblages of planar polygons, the number of which is determined by the Subdivisions... setting (below).

If the Thermal ellipsoids box is checked, and if temperature factor data have been entered, atoms will be shown as ellipsoids in the 3D Display Mode. Some of the parameters in the Ellipsoid Parameters dialog may need to be adjusted - see that dialog for further details.

Subdivisions per quadrant... Spheres or ellipsoids (atoms) and cylinders (bonds or other lines) are drawn as assemblages of flat faces, and this parameter determines the fineness of the subdivisions. The default value of 5 may need to be increased for very large atoms. This parameter replaces the Slices and Stacks parameters in V4.0 of ATOMS - in V4.0 files, values of Subdivisions will be obtained from the sphere Slices number. The Slices for spheres and cylinders number is 4 times the Subdivisions, and Stacks for spheres is 2 times the Subdivisions. Cylinders have only one stack. Ellipsoids

are distorted spheres (it could also be said that spheres are special ellipsoids) and they use the same subdivision parameters.

Bonds between ellipsoids, which are drawn in ORTEP style, have either 4 or 8

Subdivisions per quadrant, according to whether the value entered is less than, or equal to or greater than 6.

3.2.3.13 3D Light Sources

Dialog Box: 3D Light Sources [ Input2 Menu ]

There may be as many as 8 light sources in the 3D drawing mode, and each may have a different color.

Each light may be either Directional, in which case all rays are parallel in a given direction; it may be Positional, in which case all rays emanate from a given point; or it may be Ambient, in which case the rays bathe all objects uniformly - there is no directional quality. If the light is Directional, the x, y and z coordinates in the Position/Direction box give the direction vector. If the light is Positional, the

coordinates give the location of the light source, in Angstroms in the Observer coordinate system. Ambient light is neither directional or positional and these coordinates are not used.

There may be only one ambient light.

Each light has only one color. For non-ambient lights, the diffuse and specular components have the same color and intensity. The absolute values of the RGB

components determine the intensity of the light - for example, 0.2, 0.2, 0.2 gives a white light of one/fifth the maximum intensity.

Since the colors and Material properties for each atom, etc. are specified individually, the Ambient, Diffuse and Specular Colors should normally be white (1.0, 1.0, 1.0).

However, they can be changed for special effects or to correct color distortions in display or output devices.

The color of a given object is the resultant of the colors of the various lights, the color specified for the object itself in the dialogs of the Input1 and Input2 menus, and the

Material coefficients. See Lighting Equation for details.

Attenuation. The incident intensity from a light source is itself subject to attenuation according to the equation

Ii = Ii(0) / (Kc + Kl d + Kq d^2 )

Where d is the distance of the point in question from the (positional) light and Kc, Kl and Kq are the constant, linear and quadratic attenuation coefficents respectively. Constant attenuation is essentially a brightness coefficient. Values larger than 1.0 simply darken the scene. Values smaller than 1.0 may add a white component and/or increase the specular contribution. Linear and quadratic attenuation apply only to Positional lights.

3.2.3.14 3D Fog

Dialog Box: 3D Fog (Fading) [ Input2 Menu ]

Fog in the 3D drawing mode is similar to fading (Shading dialog) in the Standard

drawing mode - it contributes to the illusion of depth by changing the color as a function of distance from the eye. It blends the specified foreground color for the atom, bond or other object with the given background or other specified color, on a pixel-by-pixel basis.

This can be according to one of three equations, selected with the radio buttons in the upper left of the dialog.

Linear: f = (end - z) / (end - start) Exp: f = exp[-density * z]

Exp2: f = exp[(-density * z) ^2]

where z is the distance from the eye and f is the fraction of the initial color, the remainder being the fog color specified in the lower part of the dialog. Note that the color in this case is specified by RGB components varying from 0.0 to 1.0 (floating point) rather than 0 to 255.

ATOMS sets the parameters start and end at the foremost and rearmost atoms, or calculates the density, using the specified Fraction of intensity at rear. That is, the foremost atom will always have the pure (non-fogged) color (f = 1.0), and the rearmost atom will have the specified fraction (f) of the pure color and the remainder the fog color.

For example, if the rearmost atom is to blend into the background, i.e. disappear, set the Fraction of intensity at rear at 0.0 and check the Use background radio button. If the fog color is not the current background (Background Color dialog, Input2 Menu), it will usually be black (0.0, 0.0, 0.0).

Fog or fading may also be referred to as depth-cueing.

3.2.3.15 3D Material Properties

Dialog Box: 3D Material Properties [ Input2 Menu ]

In the 3D drawing mode the material properties of objects determine the way the objects interact with the light sources.

The color observed at a given point is a resultant of the light source(s) (3D Lighting) and the material properties; that is, the RGB coefficients of the Ambient, Diffuse and Specular components of the light source(s) are multiplied by the specified colors of the objects, and by the material coefficients in this dialog, then the results are limited to the range 0.0-1.0. See Lighting Equation for details.

Ambient light has no direction or origin and is considered to bathe all objects uniformly.

Having a significant ambient component causes non-illuminated parts of objects to be other than black. It thus "softens" the illumination in a somewhat similar way to the Darkest Shade and Darkness Angle parameters (Shading dialog) in the Standard display mode. Note that there must be a separate ambient light to show this component.

Diffuse color is usually the main component of the appearance of objects. The intensity of the color is dependent on the angle between the light ray and the normal to the surface in question.

Specular reflection only occurs when the normal to the surface in question is close to bisecting the angle between the incident light and the vector from the point on the surface to the eye. It produces bright highlights on a curved surface. The larger the

Shininess coefficient, the smaller will be the bright specular highlight on a curved surface. The shininess coefficient has a maximum of 128 because of computational restrictions, but values on the order of 5-30 are usually realistic.

In ATOMS, specular reflection is always white, that is it does not depend on the color of the object, only the color of the light source(s). Specular reflection does not work well for polyhedra because faces at the reflection angle will give an essentially solid white appearance, rather than a bright spot. This is because the angle is calculated for the corners of the face, and interpolated for each point in the interior of the face.

When thermal ellipsoids are shown in the 3D mode (see Ellipsoid Parameters), the material parameters used for both the cutout octant and the principal-plane bands are those for polyhedra - this is to avoid distracting specular reflections from large flat surfaces.

Emission is similar to ambient, except that there is no dependence on the color of any light source. A high value of emission makes an object look like is is glowing.

3.2.3.16 3D Polyhedra

Dialog Box: 3D Polyhedra [ Input2 Menu ]

This dialog specifies some special ways of displaying polyhedra in the 3D display mode which are not available in non-3D modes.

The Polyhedron Mode can be:

1) Completely opaque. This is similar to Standard display mode (but edges cannot be shown);

2) Skeletal, no bonds or 3) Skeletal, with bonds. The skeletal modes show the ligand-ligand bonds or polyhedral edges, with the central atom as a sphere.

4) Translucent, no bonds or 5) Translucent, with bonds. The polyhedron faces may all be translucent, in which case objects behind show through, or you may check the Back faces opaque box, in which case the interior may be seen, but nothing behind the

polyhedron. Complete translucency may be confusing if there are many polyhedra, i.e.

polyhedra behind polyhedra.

Translucency may increase computation time. Support for translucency may depend on the platform and output mode. VRML files do not support Back faces opaque.

Viewers for these files may not support translucency.

The Opacity (1.0-transmission) for the translucent modes may be specified, but again system software and file viewers may not support a complete range.

Ligands may be shown as spheres, or only as intersections of the ligand-ligand bonds.

Planar polyhedra are shown as plates with a finite thickness, with or without the central atom.

Im Dokument ATOMS for Windows and Macintosh (Seite 110-117)