Molcharge - Partial Charges¶
Introduction¶
The assignment of appropriate atomic partial charges, both to small molecule ligands and to biopolymers (such as proteins and nucleic acids) is essential to getting meaningful results from any electrostatics calculation.
A molecule may be considered a collection of atomic nuclei and the electrons that surround them. The number of protons in each nucleus defines its atomic number/element. If the number of electrons exactly matches the number of protons in these nuclei, the molecule is neutral and has no net charge. If there are more electrons than protons, the molecule has a net negative charge, and if there are less, the molecule has a net positive charge.
It is both the atomic nuclei and the net charge that define the identity of a molecule. Indeed, this is a representation common to quantum chemistry. Adding or removing electrons (or atoms) from a molecule produces a different molecule.
In the discrete world of chemoinformatics, valence bond theory allows the electrons present in a system to be represented in terms of bonds with formal bond orders, and formal charges assigned to particular atoms. The sum of the formal charges is equal to the net charge on the molecule, but which atoms are assigned which formal charges is to some extent arbitrary, i.e., the same molecule may be represented by similar connection tables, but with formal charges assigned to different sets of atoms.
For example, guanidinium may be expressed as either N[C+](N)N with the formal charge assigned to the carbon, or as [NH2+]=C(N)N with the formal charge assigned to an arbitrarily to one of the otherwise equivalent nitrogens. A similar example is a thiocarboxylate group, where either C(=O)[S-] or C(=S)[O-] are both equally appropriate representations of the same chemical functionality.
A zwitterion is an electrically neutral molecule that is represented as containing atoms with positive formal charge as well as atoms with negative formal charge.
Perhaps the most important fact to appreciate when considering formal charges is that they are all a myth. A figment of a chemist’s fevered imagination. Valence bond theory is an exceptionally useful and powerful discretized model of the universe. But as with any model of reality, it has its limitations. Formal charges, for all their numerous benefits to mankind, unfortunately, do not exist.
The limitations of describing formal charges with valence bond theory is
apparent even within chemoinformatics. Sydnones, for example, are a class of
heterocyclic compound that cannot be written using normal covalent bonds
without introducing and arbitrarily assigning both positive and negative
charges. Similarly, in inorganic chemistry, the ditechnetium cation,
, causes similar problems where the +5 formal charge
cannot be assigned to both technetium atoms without breaking symmetry.
A better model, or approximation, of the wave function describing the distribution of electron density around a molecule is the use of atomic partial charges. A partial charge is a floating point value assigned to each atomic center intended to model the distribution of electrons over a molecule.
Atomic partial charge is yet another approximation, much like the formal charges described above. However, partial charges provide a much better model to describe the electric field, dipole moment and other observable properties of a molecule.
A common limitation of the use of partial charges is the assumption that they are conformationally invariant. Unfortunately, the distribution of electrons around a molecule depends upon the spatial configuration of its nuclei. Some partial charge assignment algorithms, such as the method of Goddard and Rappé, consider these conformational effects, whilst others that are based on quantum mechanics, such as the RESP and AM1BCC methods of Bayly et al., go to great lengths to eliminate conformational effects, for example, by restraining and symmetrizing symmetric atom positions.
Theory¶
Marsili-Gasteiger Partial Charges¶
Marsili-Gasteiger partial charges are assigned using a two stage algorithm. In the first stage, seed charges are assigned to each atom in the molecule. For example, carboxylate oxygens are each assigned the value -0.5. During the second stage, these initial charges are then shared across bonds, moving a certain amount of charge from one atom to another. The partial charge moved and its direction is determined by difference in electronegativities of the atoms on each end of the bond. The relaxation algorithm is then iterated several times (by default eight passes), attenuating the charge moved with each iteration. OpenEye does not recommend use of this charge model. However, it is included for comparison.
MMFF94 Partial Charges¶
The partial charges used by the MMFF94 and MMFF94s force fields are assigned using a four stage algorithm. In the first stage, each atom of the molecule is assigned an MMFF94 atom type. In the second stage, an initial seed partial charge is assigned to each atom based upon it’s atom type. For a few atom types, the initial partial charge also depends upon the local environment. In the third stage, the initial charges assigned to aromatic rings are shared between all atoms of the aromatic ring. Finally, in the fourth stage, a table of bond charge increments (BCI) is used to move charges across bonds based upon the bond type of the bond (single, double, triple) and the atom types of the atoms at each end.
AM1 Charges¶
AM1 charges are a set of Mulliken-type charges derived from a semi-empirical quantum-mechanical calculation. For further discussion of this method, please see Dewar et. al.
AM1BCC Charges¶
AM1BCC charges start with partial charges derived from the AM1 wave-function. In a second stage, bond-charge corrections (BCC) are applied to the partial charges on each atom to generate the final partial charges. For further discussion, please see the work of Chris Bayly.
The method of assigning AM1BCC charges to a set conformations was proposed by Chris Bayly and colleagues. It is based on the following procedure: Coulomb electrostatic energy is calculated for every conformer using MMFF94 absolute values partial charges (original negative charges are replaced with their absolute values). The standard AM1BCC calculation is then performed for the lowest electrostatic energy conformer determined in previous step, and the AM1BCC charges obtained are assigned to all conformers.
OpenEye considers AM1BCC charges to be the best partial charge model currently available.
