Systems, methods and media for computationally determining chemical properties of a molecule

A method of partitioning a first molecule into at least one functional region to determine a property between chemical bonds of the molecule in order to design a second molecule by constructing one or more special charge density gradient paths of the first molecule to identify an irreducible bundle of the first molecule, the method comprising:

• defining a constant charge isosurface in said first molecule based on charge density data for the first molecule, the isosurface forming one or more closed, two dimensional surfaces;
• determining a magnitude of at least one charge density gradient vector of the charge density data and mapping the magnitude of the vector onto the constant charge isosurface;
• identifying one or more minima, maxima, and/or saddle points of said charge density gradient vectors on said isosurface, wherein the minima, maxima and saddle points describe the charge density topologically and are defined in terms of an index which is the number of positive curvatures minus the number of negative curvatures;
• constructing a special charge density gradient path by connecting said one or more minima, maxima, and/or saddle points along a gradient path to a corresponding critical point, wherein each special charge density gradient path represents a path of least steep, steepest or saddle descent that corresponds to an edge of an irreducible bundle;
• combining said special charge density gradient paths to construct the irreducible bundle, the irreducible bundle comprising polyhedra formed from a bundle of gradient paths with a common origin and terminus, wherein a vertex of the irreducible bundle is a critical point, an edge of the irreducible bundle is a special gradient path connecting two critical points and a face of the irreducible bundle is a two dimensional ridge and is a minimum area surface of zero flux in the gradient of the charge density that is bounded by special gradient paths;
• partitioning the molecule into non-overlapping unions of irreducible bundles, which are space filling regions, each region containing a single bond point and producing a graphical representation of the union of irreducible bundles to visualize that region of the molecule and associate that region with a property of the molecule, wherein each property of the region represents a property of the bond;
• and
• producing the second molecule with desired properties by applying the information about the property of the first molecule and correlating the property with elements of molecular structure and bonding to design the second molecule.

A system of partitioning a first molecule into at least one functional region to determine a property between chemical bonds of the molecule in order to design a second molecule by constructing one or more special charge density gradient paths of the first molecule to identify an irreducible bundle of the first molecule, the system comprising:

• a memory for storing computer readable code;
• and a processor operatively coupled to the memory, the processor configured to:
• define a constant charge isosurface in said first molecule based on charge density data for the first molecule, the isosurface forming one or more closed, two dimensional surfaces;
• determine a magnitude of at least one charge density gradient vector of the charge density data and mapping the magnitude of the vector onto the constant charge isosurface;
• identify one or more minima, maxima, and/or saddle points of said charge density gradient vectors on said isosurface, wherein the minima, maxima and saddle points describe the charge density topologically and are defined in terms of an index which is the number of positive curvatures minus the number of negative curvatures;
• construct a special charge density gradient path by connecting said one or more minima, maxima, and/or saddle points along a gradient path to a corresponding critical point, wherein each special charge density gradient path represents a path of least steep, steepest or saddle descent that corresponds to an edge of an irreducible bundle;
• combine said special charge density gradient paths to construct the irreducible bundle, the irreducible bundle comprising polyhedra formed from a bundle of gradient paths with a common origin and terminus, wherein a vertex of the irreducible bundle is a critical point, an edge of the irreducible bundle is a special gradient path connecting two critical points and a face of the irreducible bundle is a two dimensional ridge and is a minimum area surface of zero flux in the gradient of the charge density that is bounded by special gradient paths;
• partition the molecule into non-overlapping unions of irreducible bundles, which are space filling regions, each region containing a single bond point and producing a graphical representation of the union of irreducible bundles to visualize a region of the molecule and associate a region with a property of the molecule, wherein each property of the region represents a property of the bond;
• and
• produce the second molecule with desired properties by applying the information about the property of the first molecule and correlating the property with elements of molecular structure and bonding to design the second molecule.

A method of partitioning a first molecule into at least one functional region to determine a property between chemical bonds of the molecule in order to design a second molecule by identifying an irreducible bundle of the first molecule, the method comprising:

• finding one or more minima, maxima or saddle points of a charge density associated with the first molecule wherein these points describe the charge density topologically and are defined in terms of an index which is the number of positive curvatures minus the number of negative curvatures;
• identifying one or more special charge density gradient paths constituting a one-dimensional ridge that passes through one or more minima, maxima, saddle points of index +1 or saddle points of index −1 of the charge density;
• combining the special charge density gradient paths to construct an irreducible bundle, the irreducible bundle comprising polyhedra formed from a bundle of gradient paths with a common origin and terminus, wherein a vertex of the irreducible bundle is a critical point, an edge of the irreducible bundle is a special gradient path connecting two critical points and a face of the irreducible bundle is a two dimensional ridge and is a minimum area surface of zero flux in the gradient of the charge density that is bounded by special gradient paths;
• partitioning the molecule into non-overlapping unions of irreducible bundles, which are space filling regions, each region containing a single saddle point of index −1 and producing a graphical representation of the union of irreducible bundles to visualize that region of the molecule and associate that region with a property of the molecule, wherein each property of the region represents a property of the bond;
• and
• producing the second molecule with desired properties by applying the information about the property of the first molecule and correlating the property with elements of molecular structure and bonding to design the second molecule.