Dialog Box: Manual Angle Force List [Forces menu]
This is for locating sets of angles using individual generated atoms rather than overall specifications based on type (atomic number) and length limits. For "automatic" angle specification of the latter type, see Angles. This type of angle is not applicable to crystals or polymers.
The upper list gives the current 3-atom valence angle coordinates. The data for each one is in a single line in the scrolling list or spreadsheet. To add a new entry, press the down arrow key while the focus is on the last row, or click the Add button. The lower list gives the specifications for each force constant in terms of atom types - an unlimited number of specifications is allowed (there must be at least one).
Each entry in the upper list is an "fcon" or force constant - this pertains to a set of actual angles, specified by the list of triplets of atom numbers in the lower list. This set may or may not be equivalent by symmetry, and whether or not a set of angles conforms with symmetry is up to you, when you specify the individual atom triplets (automatic angles specified in the Angles dialog always conform with symmetry). All members of a symmetry-equivalent set should be included in one manual angle in this list, but one manual angle is not limited to a single symmetry-equivalent set - there may be several chemically similar angles included.
No. This is the number in the angle list. Do not use this number for specifying automatic interactions.
Fcon This is the number in the overall force constant list. Use this number for specifying automatic interactions.
Force. Note that angle forces may be specified in either in md-A or in md/A. This choice is made with the Units for angle forces radio box (below).
Nspc. Number of atom type specifications for this angle (lower list).
Lst Sq. If this box is checked, this force constant will be included in least-squares refinement.
Type. Calculations based on internal coordinates for highly symmetric molecules typically do not need to consider angle-bending in more than one plane and there may be only one internal coordinate or force constant per angle. When using Cartesian coordinates, especially in cases of lower symmetry, it is often necessary or convenient to include the complete force field, requiring two internal coordinates.
VIBRATZ supports three types of force constants for 3-atom valence angles - standard in-plane forces or internal coordinates, forces perpendicular to the plane of the bond, and forces in two perpendicular directions but with the same force constant. Standard in-plane forces are appropriate in situations in which it is not necessary to consider out-of-plane bending - for example in small molecules like H2O, in which out-of-plane bending can be resolved into in-plane bending and rotation of the molecule; or in cases in which bending is symmetrically degenerate and only one of the two directions is calculated. In-plane forces alone are also conventionally used where there is a redundancy of angle coordinates, such as X-C-X angles in non-planar CXn polyhedra with more than 3 X ligands. The second and third radio buttons in this group are for situations in which it is necessary to consider forces in more than one plane, which indeed is the general case in large molecules and crystals. Out-of-plane 3-atom angle bending may be used in many situations in place of psi (bond-plane) angles (see the CO3A example). If a given angle is not 180 degrees and out-of-plane forces are to be considered, the force constants for in-plane and out-of-plane bending are presumably different and two separate angle coordinates should normally be defined. The third option, which generates forces in two perpendicular directions, is primarily for 180 degree angles - i.e. linear configurations of three atoms (see the Ni(CO)4 and Fe(CO)5 examples). If the angle is 180 degrees, the actual displacement directions are arbitrary. This option will generate two coordinates for each angle. See below for definitions of the displacement or s-vectors for in-plane and out-of-plane coordinates and Forces - General Considerations for further discussion of the selection of force-constant models.
Again, the out-of-plane angle forces used in VIBRATZ may in some cases take the place of tau and/or psi forces used in calculations on molecules with internal coordinates.
The Atom numbers in the specifications in the lower list or spreadsheet must be the numbers of actual generated atoms in the molecule. These are best obtained from the Atoms Window - in fact you can select bonds involving atoms which have been clicked in succession with the mouse. Note that when you click on three atoms defining an angle the central atom is second, but in this list the central atom is first. This process, after a query (), will bring up this dialog. Generated atom numbers with coordinates can also obtained from the Output Window. The numbers entered here are not necessarily the Input Atoms as entered in the Input menu, although the lists of input and generated atoms will be the same if there is no symmetry. If there is symmetry, there will be more generated atoms than input atoms.
Note that for Urey-Bradley forces, angles involving adjacent ligands for the relevant polyhedra (X-C-X angles) must be defined in this dialog, even if there are not considered to be any true valence bending forces. That is, the force constants for these angles specified in this dialog may be zero.
Once specifications have been entered, the force-constant values and least-squares flags for angles may be changed in the overall Forces List, accessible from the Control Window.
The Units for angle forces radio buttons determine the units of force constants and the way they are interpreted. Force constants for bonds are always in md/A (millidynes per Angstrom), but those involving angles may be expressed in either of two ways - in md-A (per radian squared) or in md/A. Published values may be given either way, and it is absolutely necessary to choose the appropriate option if such values are to be used or compared. See the Basic Parameters dialog (Setting menu) for more details.
Orientation of coordinates for 180-degree angles and definition of in-plane and out-of-plane coordinates. Angles in the equilibrium position are always 0 to 180 degrees. In the case of 180 degree angles it is necessary to specify arbitrarily the direction of the displacement or s-vectors (see WDC, p. 54). For in-plane coordinates the s-vectors are obtained from the cross-product of the bond vectors and the y-axis, or the cross-product of the bond vectors and the z-axis if the bond vectors are nearly parallel to y. This ensures that there is a component of displacement in the x-direction, which may be the only direction calculated for many degenerate species (this is the default direction selected by the basis functions in most cases). Since the non-central atoms of 3-atom angles are considered to be interchangable (and these atoms are often of the same type or chemical species), the sign of the s-vectors must also be specified arbitrarily. If the s-vectors of the outer atoms (which are identical for 180 degree angles) have a significant z component, this is made to be positive; if the z component is very small, then x is made to be positive, and if the s-vectors are nearly parallel to y, then the y-component is made to be positive.
For the out-of-plane coordinates of 180 degree angles, the s-vectors are perpendicular to the in-plane s-vectors and the bond vectors. The same procedure is used to determine sign as for the in-plane coordinates.
In the case of non-180-degree angles, the s-vectors for in-plane coordinates are obtained in the standard way (WDC, p. 56), and the s-vectors for out-of-plane coordinates are perpendicular to the plane of the angle. The sign is determined as above.
After the solution of the secular equation and determination of atomic motions, it is necessary to resolve the atomic motions into in-plane and out-of-plane angle bending, for partitioning of the potential energy. In practice the displaced atom coordinates are projected onto two planes, one of which is the original plane of the angle (if the angle is not 180 degrees), and the other of which is a plane perpendicular to the plane of the angle, passing through the two non-central atoms. These two projections give the in-plane and out-of-plane angle changes, respectively.
Interactions involving out-of-plane angle coordinates or either type of coordinate for 180 degree angles may be questionable because of the arbitrary direction and/or sign of the displacements. Of course this depends on the particular geometry and symmetry.
Once specifications have been entered, the force-constant values and least-squares flags may be changed in the overall Forces List, accessible from the Control Window.