1. Interatmic distance: The user clicks on any two molecules on the screen when requested. The program returns the distance between the atoms in angstroms. The display is either in a message box, or, if the bond rotate routine is in effect, displays the value in a text box at the top of the screen which is updated as the bond rotates.

Incidentally, here are some of the references used to determine the correct bond lengths:

1) CRC's Handbook of Chemistry and Physics (69th edition p. F-158)

2) The bond order-bond length relationship by J.P. Paolini (J. Computational Chem., 11: 1160-1163)

3) Valency and Molecular Structure, Fourth edition, by F. Cartmell and G.W.A. Fowles, Butterworths (from this was found, besides bond lengths for various pairs a calculation method called the Schomaker-Stevenson relationship which allows the calculation of bond lengths when they are not known):

bond length = r(a) + r(b) -0.09*(difference in electronegativity)

where r(a) and r(b) are the covalent radii of the atoms and electronegativity values of elements are from Pauling.

2. Angle: Three atoms are clicked on (the center atom in the angle is clicked on second) when requested by the program. The program will return the value in an information box, or, if bond rotation is activated, will return the answer (in degrees) in a text box at the top right and update the value as the bond rotates.

3. Dihedral angle: Four atoms are clicked on when requested by the program. The program will return the value in an information box, or, if bond rotation is activated, will return the answer (in degrees) in a text box at the top right and update the value as the bond rotates. The dihedral angle is the angle formed between the plane formed by the atoms selected first, second and third and the plane formed by atoms 2,3 and 4.

Strain energy due to deviation from ideal bond lengths, bond angles, dihedral angles, unbonded atom overlap and hybrid strain are calculated. The MOLY force field parameters are used. MOLY uses a classical mechanical force field (reference 1 below) and looks up values in tables of literature values to determine ideal bond lengths, angles and dihedral angles for the different combinations of atoms and bonds. It adds together the components to obtain the strain energy:

E_total = E_bond + E_angle + E_nonbonded + E _tor + E_hyb

The bond-length and bond angle strain terms are calculated using standard Hooke's law type functions. The default method of calculating unbonded strain is:

where d is the overlap = (radius of i + radius of j) - the distance from i to j))

The torsional function tries to stagger butane-type interactions, keep double bonds, amides and esters planar, allenes perpendicular etc. The hybridization term is used to keep strained carbonyls flat and to automatically increase the angle between the appendages of strained rings. This minimizer is a modification of the MOLY minimizer (1) which was itself a descendent of one developed by Wipke et.al. (2).

Molecular weight: The molecular weight of all of the molecules is supplied in a box. This property is as exact as the atomic weights reported in the literature.

Molecular volume/density: The molecular volume in cubic angstroms is displayed for all of the molecules. Volume is calculated using the method of A. Bondi (J. Phys. Chem. 68:441), 1964. The program also calculates surface area using the same elementary 3-D geometry principles and calculates density. Density is calculated by dividing molecular weight by volume and then correcting for fragments found with an algorithm I derived from solvents. Individual volumes and surface contributions of each atom are also listed.

Dimensions: This operation displays three values for all of the molecules: the length along the x axis, the width along the y axis and the depth along the z axis in angstroms. After this the user is asked if he would like to do some time-consuming calculation involving dimensions. First you will be asked if you would like to calculate the global maximum and minimum dimensions. If so, the molecule will be rotated in 5 degree increments along the y and z axes for 360 degrees and the maximum and minimum dimensions found will be reported. Then you will be asked if you want to orient the maximum dimension along the x axis. If you answer yes to this you will also be given the option of finding and orienting the molecule's maximum width along the y axis (the maximum length remains on x).

The partial charges are calculated using DelRe's method (G. Del Re, J. Chem. Soc., (1958), 4031-4040; Biochem. et Biophys. Acta 75:153-182 (1963); D. Polland and H. Sheraga, Biochemistry 6:3791-3800 (1967) and partly with values obtained by trial and error on conformationally constrained molecules with known dipole moments. The partial charges of Del Re were further modified so that they too resulted in dipole moments reported in the literature. Some account of pi bond (as well as sigma bond) is taken into account by MMEd, so this method is no longer equivalent to Del Re's. The program for calculating partial charge and dipole moment is included in the sample Display program included with MMEd.

With version 3.1 two PEOE (partial equalization of orbital electronegativity) methods are introduced for the calculation of partial charge. The first of these methods uses Gasteiger and Marsili's method for finding the sigma contribution and adds one quarter of the pi contribution to charge calculated by Huckel Theory. The second method (MPEOE) is an attempt to improve on this method.

References:

hydrophilic surface area: the surface area that tends to be associated with water instead of repelling it.

Percent hydrophilic surface area: the percentage of the surface area of the molecule that is hydrophilic.

This calculation is performed from the Calculate menu.

This calculation is selected from the Calculate menu. This calculation could be used in conjunction with chemical analysis by a mass spectrometer. The molecular formula and mass percent for each atom is listed molecule by molecule. The mass percent is calculated by Multiplying the atomic weight of an atom by the number of atoms of that type per molecule, and then dividing the result by the molecular weight.

This item is found in the Calculate menu.

The center of mass, moments of inertia and the rotational constants (used in microwave spectroscopy) are calculated for the molecule. The moments of inertia are calculated as the principle components of the momentum tensor. The rotational constants are calculated by dividing 505379.055 by the moments of inertia. The moments of inertia ideally contain terms for vibrational motion from quantum mechanics. The method found on the Calculate menu uses only classical mechanics and can be referred to as a rigid rotor approximation. If you wish to include the effects of vibrational motion used the alternative method found in MOPAC.

Both MOPAC and CNDO calculate partial atomic charges, HOMO and LUMO values and dipole moment. In addition there are a number of other calculations of molecular properties calculated by these programs.

CNDO: Three additional values not part of the original CNDO program are returned: hydrogen bond acceptor, hydrogen bond donor and log of the octanol water partition coefficient (log P). All of these properties are derived from partial atomic charges and log P uses molecular volume as an additional determinant.

MOPAC: There are some additional molecular properties calculated by MOPAC. These include heat of formation, ionization potential and moments of inertia. In addition the THERMO key word gives some thermodynamics calculations as described below.

THERMO - Thermodynamics calculations can be performed on molecules. The key words FORCE and ROT also must be included. The combination of these three key words will give the user additional thermodynamic property calculations: internal energy, heat capacity, partition function and entropy for translation, rotation and vibrational energy over a range of temperatures.

To get a more complete understanding of the capabilities of MOPAC, which is a very large program in its own right, you should download the MOPAC version 6 manual from the internet. Search for MOPAC and Manual to obtain a URL.