Spartan 5.1 User's Guide

Chapter 6: The Geometry Menu

This section reviews the features and functions available under the Geometry menu.

Selection of Geometry results in display of the following menu:

Distance
Angle
Dihedral

Freeze Center

Constrain Distance
Constrain Angel
Constrain Dihedral

Define Point
Define Plane

Surface Area
Volume

Report Symmetry
Report Chirality

(Keystroke equivalents are given by the underlined letter in the menu entry.)

Except for Volume, Surface Area and Report Symmetry, these functions require selection of one or more atoms, or one or more bonds, or a previously-defined constraint. This is accomplished by clicking on the atom(s) or bond(s) or the constraint. Except for Freeze Center, as atoms are selected, each will be identified by a small yellow sphere. ("Frozen atoms" are identified by magenta colored markers.) As bonds are selected, the two atoms connected by the bond will be identified by small yellow spheres. Selection of a distance constraint results in two atoms being identified by yellow spheres, an angle constraint in three atoms identified, and a dihedral constraint in four atoms being identified. A miss on an atom or a bond or a constraint is signaled by a bell. Selection of any entry under the Geometry menu results in replacement of whatever model type is presently displayed by a ball-and-wire model. The original model is restored after all requests have been satisfied.


Section 6.1: Distance

Obtains and displays the distance (in Ångstroms) between two atoms, whether or not they are bonded. Selection results in a message in the menu bar.

Clicking on the two atoms (or the bond) results in a dialog.

To obtain another distance, click on another pair of atoms or alternatively on a bond. To exit the dialog, click on Done or select any other menu entry.

If the selected molecule is a member of a list, a different dialog is presented.

This is identical to the original dialog, except that it incorporates a Post button. Clicking on Post enters the selected distance for every member of the list into the next available column in the associated spreadsheet.*


Section 6.2: Angle

Obtains and displays the angle (in degrees) involving three (unique) atoms, two connected bonds or, if an angle has previously been constrained, a constraint vector. Selection results in a message in the menu bar.

Clicking on the appropriate atoms or bonds in the proper order results in a dialog.

To obtain another angle, repeat the operations. To exit, click on Done or select any other menu entry.

If the selected molecule is a member of a list, a different dialog is presented.

This is identical to the original dialog, except that it incorporates a Post button. Clicking on Post enters the selected angle for every member of the list into the next available column in the associated spreadsheet.

This function also handles angles involving user-defined points (see Define Point below) or planes (see Define Plane below).


Section 6.3: Dihedral

Obtains and displays the dihedral angle (in degrees) involving four (unique) atoms, three connected bonds or, if a dihedral angle has previously been constrained, a constraint vector. Note that the dihedral angle is defined as the angle between the plane made by the first three atoms (or the first two bonds) specified and the plane made by the last three atoms (or the second two bonds) specified. Selection results in a message in the menu bar.

Clicking on the appropriate atoms or bonds in the proper order or on the constraint vector results in a dialog.

To obtain another dihedral angle, repeat the above operations. To exit, click on Done or select any other menu entry.

If the selected molecule is a member of a list, a different dialog is presented.

This is identical to the original dialog, except that it incorporates a Post button. Clicking on Post enters the selected dihedral angle for every member of the list into the next available column in the associated spreadsheet.

This function also handles dihedral angles involving user-defined points (see Define Point below).


Section 6.4: Freeze Center

Allows "freezing" of one or more atoms during minimization in Spartan's builders or (optionally) during geometry optimization, transition-state optimization or conformation searching using molecular mechanics, semi-empirical, density functional or ab initio methods. The latter needs to be explicitly indicated in the appropriate setup dialogs; see Sections 8.2 to 8.5. Atom freezing is not available for calculations performed using Gaussian 94.

Atom freezing is especially useful in a number of situations, among them obtaining approximate transition structures for derivative reactions using geometry optimization rather than transition-state optimization. Such structures might later be used as guesses for full transition-state optimizations or perhaps even be suitable on their own. For example, a good guess at the transition state for pyrolysis of cyclohexyl formate might be obtained by modifying the transition state for pyrolysis of ethyl formate, freezing all but the modified sections (designated in bold in the figure below) and then performing geometry optimization instead of transition-state optimization.

Selecting Freeze Center results in a message in the menu bar.

In addition, a dialog appears on screen.

Atoms may be frozen one at a time by clicking on them and, once frozen, may be thawed by clicking a second time. Frozen atoms are marked. All freezes all atoms and None thaws all atoms. Once all desired atoms have been frozen, clicking on Save or selecting any other menu entry exits the dialog. Clicking on Cancel also exits the dialog, but any freeze/thaw operations have been lost.


Section 6.5: Constrain Distance


Section 6.6: Constrain Angle


Section 6.7: Constrain Dihedral

Allow introduction of one or more geometrical constraints during minimization and transition-state optimization as well as conformer searching (see Section 7.2) and (implicitly) for coordinate driving (see Section 7.5). That is, they specify conditions which the optimization procedure must satisfy in addition to meeting the usual demands on the gradient and energy. Constraints may be used in conjunction with any of the methods available in Spartan, including molecular mechanics, semi-empirical and ab initio molecular orbital and density functional methods. Whereas any specified constraints are automatically imposed for minimization inside Spartan's builders, constraints need to be explicitly "turned on" (inside the appropriate setup dialogs) for operations outside the builders. Discussion is provided in Sections 8.2 to 8.5. Constraints are not available for calculations performed using Gaussian 94.

The introduction of constraints is essential in a number of situations, among them:

  1. "Mapping" of conformational energy profiles where one or more dihedral angles need to be fixed while other geometrical variables are optimized. Mapping energy profiles, in one dimension, can be automated inside of Spartan using Coordinate Driving (see Section 7.5). This operates independently of, and perhaps in conjunction with, the constraint features discussed here.
  2. Structure optimization in which the values of certain key parameters are known, for example, optimization of the geometry of a molecule with an intramolecular hydrogen bond or a disulfide linkage.
  3. Building molecules with "unusual" geometrical parameters, e.g., very long bonds, as for example required in the construction of transition states.

Selecting Constrain Distance results in a message in the menu bar.

Selection occurs by clicking on each of the atoms in turn or, if they are bonded, on the bond connecting them or, if a distance constraint has already been defined, on the constraint vector. A magenta colored line will be drawn between the two atoms (if the atoms were bonded, a magenta colored line will replace the original bond). In addition, a dialog appears on screen.

This displays the current distance, and provides for specification that the selected parameter is to be constrained to this or some other value (or alternatively that an existing constraint is to be removed). Assuming that this is the first entry for a particular distance, Constrain Distance will be "off". Turning Constrain Distance "on" results in a box where the distance constraint will be placed (upon first entry it contains the original "unconstrained" distance). This distance can be changed (this is optional as the existing distance may be used if desired).

Sigma indicates the weighting of the constraint relative to other requirements in the overall minimization. The default value may be changed. The larger the value the closer the constraint will be satisfied (at the expense of the other requirements). Sigma has meaning only in mechanics and semi-empirical calculations where constraints are introduced via penalty functions. It does not have meaning for ab initio and density functional calculations where a general Lagrange multiplier method is employed.

As many distance constraints as desired may be introduced (or existing constraints modified or removed) simply by repeating the above sequence of operations. When completed, clicking on Save or selecting any other menu entry removes the dialog with any constraints added, modified or removed. Clicking on Cancel also removes the dialog, but whatever actions have been taken are lost.

Angle and dihedral angle constraints are handled in a similar manner. Selection of Constrain Angle results in a message in the menu bar.

Selection results in display of an on-screen dialog.

This is handled in an analogous manner to the dialog previously described under Constrain Distance.

Similarly, selection of Constrain Dihedral results in a message in the menu bar.

Selection results in display of an on-screen dialog.

This is handled in an analogous manner to the dialog previously described under Constrain Distance.


Section 6.8: Define Point

Defines a point as the geometric (unweighted) center of a selected group of atoms. Selection results in a message in the menu bar.

Clicking on a series of atoms in any order, with the end of the series signaled by clicking on an atom which has already been selected, defines a point and exits the dialog. For wire and ball-and-wire models only, the point will appear as a magenta asterisk. It is treated as an "atom" for measurements under the Geometry menu (Distance, Angle, Dihedral), but it may not be used for defining constraints. As many points as desired can be defined.

Point definitions are lost following closing and reopening a molecule. There is also no mechanism available for removing a point in Spartan's main screen. Points defined inside Spartan's builders may be removed using Delete (inside the builders).


Section 6.9: Define Plane

Defines and displays a reference plane. Selection results in a message in the menu bar.

Clicking on three or more (non-colinear) atoms in any order, with the end of the series signaled by clicking on an atom which has already been selected, defines a plane and exits the dialog.

Three atoms uniquely define a plane, and the plane resulting from selection of more than three atoms represents a "best fit".

For wire and ball-and-wire models only, the plane will appear as a magenta colored disk. It can be used for Distance and Angle operations under the Geometry menu, but it may not be used for defining constraints. As many planes as desired may be defined.

Plane definitions are lost following closing and reopening a molecule. There is also no mechanism for removing a plane in Spartan's main screen. Planes defined inside Spartan's builders may be removed using Delete (inside the builders).


Section 6.10: Surface Area

Reports the surface area of a space-filling model (in Å2) of the selected molecule.

If the selected molecule is a member of a list, a different dialog is presented.

This is identical to the original dialog, except that it incorporates a Post button. Clicking on Post enters the surface area for each and every member of the list into the next available column in the associated spreadsheet.

The surface area of an electron density surface (representing overall molecular size and shape) may also be obtained (see Section 9.2.6).


Section 6.11: Volume

Reports the volume of a space-filling model (in Å3) of the selected molecule.

If the selected molecule is a member of a list, a different dialog is presented.

This is identical to the original dialog, except that it incorporates a Post button. Clicking on Post enters the volume for each and every member of the list into the next available column in the associated spreadsheet.

The volume of an electron density surface (representing overall molecular size and shape) may also be obtained (see Section 9.2.6).


Section 6.12: Report Symmetry

Reports the symmetry point group of the selected molecule.

It is useful to check for symmetry after molecule building and minimization.


Section 6.13: Report Chirality

Selection results in R/S designation of all chiral centers in a molecule.


Notes

* This function and related Angle and Dihedral functions under the Geometry menu, as well as Charges under the Properties sub-menu (Display menu) and Align under the Molecule menu (in the spreadsheet) assume that atoms are labelled in a consistent manner. This will generally be the case for lists of molecules resulting from conformational searching (see Section 7.2), vibration sequencing (see Section 7.4), coordinate driving (see Section 7.5) or a combinatorial study (see Section 7.6), but will not generally be true for user defined lists (as, for example, from Group As under the File menu). In the latter case, it will be necessary to relabel the molecules in the list. This may be accomplished using Edit Labels under the Model menu (see Section 5.9).


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