http://www.uic.edu/classes/phys/phys461/phys450/ANJUM03/lecture_notes3_aa.htm
Non-covalent interactions
www.uic.edu/.../lecture_notes3_aa.htm
Many molecules are electrically neutral but have a permanent dipole because of an asymmetric distribution of the electron cloud around the positively charged ...
University of Illinois at Chicago
Loading...
Molecular Interactions (Noncovalent Interactions)
ww2.chemistry.gatech.edu/~lw26/structure/molecular.../mol_int.html
Sep 21, 2015 - Molecular Interactions (Noncovalent Interactions) ..... structures present an oversimplified view of the electronic structure of a .... Moderate hydrogen bonds, which are the most common, are formed between neutral donors and ...[PDF]Understanding of Noncovalent Interactions ... - Springer
www.springer.com/.../9783662457559...
Noncovalent interactions play a pivotal role in the design of a new material with .... electronic properties and stability of the compound resulting in increased resistance ..... It was observed that in case of the neutral molecular fragment, the.
Springer Science+Business Media
Loading...
Kaplan MCAT Biochemistry Review: Book + Online
https://books.google.com/books?isbn=1625231253
Kaplan - 2015 - Study Aids
... of PAGE but adds SDS, a detergent that disrupts all noncovalent interactions. ... The pIis the pH at which the protein or amino acid is electrically neutral, with ...Principles of Metabolic Control in Mammalian Systems
https://books.google.com/books?isbn=1461330068
Herman - 2013 - Science
Kollman (1977a) has defined noncovalent interactions as those in which the ... electrically neutral atoms approach one another, the instantaneous positions of ...Nanometer-Size Polyoxometalate Anions Adsorb Strongly ...
pubs.acs.org/doi/pdf/10.../acs.jpcc.5b06273
American Chemical Society
Loading...
by B Naskar - 2015
Aug 17, 2015 - noncovalent interactions on polar electrically neutral surfaces covered by ... adsorption (salting-in property) of POMs on soft, neutral, and.Biochemistry and Molecular Biology - Page 37 - Google Books Result
https://books.google.com/books?isbn=0199609497
... by noncovalent interactions between amino acid residues of the polypeptide. ... Although a covalent bond is overall electrically neutral, the bond can have a ...[PPT]13-miller-chap-2-lecture.ppt - ResearchGate
https://www.researchgate.net/file.PostFileLoader.html?id...
Noncovalent interactions are weak electrical bonds between molecules. Types of ... The a-amino and a-carboxyl groups are charged at neutral pH. There are ...
ResearchGate
Loading...
Solvents and Solvent Effects in Organic Chemistry
https://books.google.com/books?isbn=3527642137
Christian Reichardt, Thomas Welton - 2011 - Science
These noncovalent interactions are also called van der Waals forces, since the Dutch ... Electrically neutral molecules with an unsymmetrical charge distributionBiomaterials for Delivery and Targeting of Proteins and ...
https://books.google.com/books?isbn=0203492323
Ram I. Mahato - 2004 - Medical
subunits associate in a specific way through noncovalent interactions among the ... Waals forces including dipole-dipole interaction of electrical neutral residues.
Non-covalent interactions We have learnt that all biological macromolecules are linear polymers in which repeating subunits are covalently linked together. The free energy associated with a covalent bond is ~ 100 � 150 kBT. These bonds are therefore not disrupted by thermal fluctuations. There are many, much weaker, non-covalent interactions that are responsible for the 3-dimensional configuration that the biological polymers adopt. These interactions also play a very important role in the flexibility of the macromolecules, their interactions with each other and with other molecules in the cell. The various non-covalent interactions can be classified as: 
where k is a constant 
, in vacuum, where 
= 8.85x10-12 C2/N.m2 is the permittivity of free space. (k = 9x109 N.m2/C2). The potential energy U of two charges is defined as the work required to bring the two charges to a distance r apart if they are initially infinitely far away:
The potential energy is negative when the force is attractive (q1 and q2 have opposite signs), and positive when the force is repulsive. The gradient of the potential energy function is a measure of the force:
or, more generally, 
. The potential energy for the simple Coulomb interaction falls off rather gradually, as 1/r, and hence it is also referred to as a long-range interaction. In vacuum, U ~ 30 kBT for two charges q1 = q2 = e- (1.6x10-19C) separated by r ~ 2nm. In water, which is the appropriate medium inside the cells, the Coulomb interactions are reduced by a factor which is equal to the dielectric constant of water. Water molecules have a permanent dipole; they align in the direction of the local electric field and effectively screen the charges. The dielectric constant of bulk water is 
80 at room temperature. Therefore, in water, U ~ 0.4 kBT for two ions carrying unit charges separated by ~ 2 nm. Distance dependence of the apparent dielectric constant The screening property from aligned dipoles is expected to decrease as the distance between the two ions decreases, and in the limit that the two ions are right next to each other, the apparent dielectric constant is 1. The following graph gives an empirical estimate of the apparent dielectric constant of water as a function of the distance from an ion: 
At a distance of r = 0.5 nm, the apparent dielectric constant is ~ 20, and the potential energy of two unit charges is U5 kBT. For decreasing value of r, the potential energy U increases both because of the 1/r dependence as well as a smaller value for the apparent dielectric constant. There is another very important screening effect that arises from free ions in solution and which will cluster around charged objects (thus the name counter-ions) and further reduce the strength and range of the Coulomb interactions. These counter-ions can be associated with the charged objects with energies in excess of 5 kBT and hence are not easily shaken off by thermal energy.
Charge-dipole and dipole-dipole interactions Many molecules are electrically neutral but have a permanent dipole because of an asymmetric distribution of the electron cloud around the positively charged nuclei. For example, in HCl, the valence electron of the H atom is donated to the Cl atom, with H carrying a net positive charge, and Cl a net negative charge. Similarly, water has a permanent dipole because the electron density is greater near the more electronegative O atom. The dipole moment is defined as
where d is the separation between 2 charges +q and �q. p is a vector and points in the direction from �q to +q. When a molecule with a dipole moment p is placed in an electric field E, the dipole has a potential energy 
where 
is the angle between the vectors p and E. Charge-dipole interactions 
The electric field from a single point charge at a distance r from the charge is
, and the electric field vector points away from the charge (for positive charges) and toward the charge (for negative charges). The potential energy of a charge-dipole system is 
. The potential energy now falls off as 1/r2, more rapidly than the charge-charge system. In the absence of thermal motion, the dipole will align with the E field, which corresponds to =0. Thermal averaging Because of random collisions with the molecules of the surrounding medium, the dipole will undergo Brownian motion. Here we will consider only the change in the orientation of the dipole as a result of random collisions, and write down the Boltzmann probability that the dipole makes an angle with the E field as: Probability 
The average value of the potential energy, averaged over all possible orientations whose probability is given by the Boltzmann distribution, can be written as 
where Z is the normalization constant, 
, and 
is the incremental solid angle between two cones swept by the p vector as it makes an angle and 
with respect to the E vector. You should be able to work out the integrals and show that 
which, in the limit pU << kBT, simplifies to 
Substituting for the electric field due to a point charge q at a distance r from the charge, we get 
With thermal averaging, the charge-dipole interaction falls off as 1/r4. The minus sign indicates that the interaction is always attractive.
Dipole-dipole interactions The interaction energies between two dipoles p1 and p2 have a more complicated angular-dependence, since there are now two dipoles, each one of which can be oriented in any direction. Here we will write down the form of the solution without worrying about the details of the calculations.
The potential energy has the form
where E1 is the electric field from dipole p1and 
depends on the angular position of p2 relative to p1 and their relative orientations. The distance dependence 1/r3 comes from the radial dependence of the electric field E1 of dipole p1. The thermal averaging with Boltzmann probabilities, in the limit U<< kBT, gives: 
Note that the potential energy between two dipoles falls off as 1/r6 power. Dipole-dipole interactions are short-range interactions
Van der waals interactions Perhaps the most important class of dipole-dipole interactions are the ones where one or both molecules do not have a permanent dipole. These interactions are valid for any two atoms that come into close contact with each other, and are called Van der Waals interactions. Dipole-induced dipole interactions A molecule with a permanent dipole p1 can induce a dipole in another polarizable molecule. In this case the induced dipole moment p2* points in the same direction as the inducing electric field E1. The potential energy of interaction between p1 and p2* takes the form
where the minus sign indicates that the interaction is always attractive, since the induced dipole always follows the direction of the instantaneous electric field. defines the angular position of p2* relative to p1and the electric field E1 is independent of the azimuthal angle 
. The magnitude of p2* depends upon the strength of the electric field at position 
, 
where 
is the polarizability of the second molecule. The interaction potential is given by: 
where again we have a 1/r6 dependence. The above result is in the absence of thermal averaging. Thermal averaging Since p2*, in this case, always follows the instantaneous direction of the electric field E1, thermal averaging requires that we simply average over the dependence, with all orientations of p1 equally likely. The average value 
gives a numerical constant. The average potential energy 
has a 1/r6 dependence as in the thermally averaged dipole-dipole case. Induced dipole-induced dipole interactions A fluctuating electric field environment around each atom induces a fluctuation dipole moment that is proportional to the polarizability of the atom. This instantaneous dipole can then induce a dipole in a neighboring atom, resulting in an attractive potential that also has a 1/r6 dependence.
Short-range repulsive interaction As the atoms get too close, at some point there is a strong repulsion from overlapping electron clouds and Pauli�s exclusion principle whereby filled electron shells of an atom cannot accommodate any more electrons. Lennard-Jones potential A commonly used analytical form that lumps together all dipole-dipole interactions and includes both the attractive and the repulsive terms is the Lennard-Jones potential where the repulsive term is approximated as having a 1/r12 dependence:
This form of the potential energy function has a minimum at r = ro with 
. 
The atoms can be treated as spheres defined by a Van der Waals radius that is a measure of how close another atoms can come before a strong, very short range, repulsive force kicks in. Some typical Van der Waals radii of atoms are hydrogen ~ 1.2 A , oxygen ~ 1.4 A , nitrogen ~ 1.6 A , and carbon ~ 2 A .
Hydrogen bonds A very important interaction responsible for the structure and properties of water, as well as the structure and properties of biological macromolecules, is the hydrogen bond. A hydrogen bond is an interaction between a proton donor group D-H and a proton acceptor atom A. D-H is stongly polar, which means that the electron density is primarily around the electronegative atom (examples, F-H, O-H, N-H, S-H in order of decreasing polarity). The acceptor atom A is also strongly electronegative. The hydrogen bond interaction is more than just an ionic or dipole-dipole interaction between the donor and the acceptor groups. The distance between the H and A in a hydrogen bond is less than the sum of their respective Van der Waals radii. Hydrogen bonds are usually shown as
although the strength of the interaction 
can sometimes be as strong as 
. The hydrogen bond is strongest when the three atoms D, H, and A have a collinear geometry. The strength of the hydrogen bonds in biological macromolecules ranges from ~ 2 kBT to ~ 5kBT. Hydrogen bonding network in water 
Hydrophobic interactions Another very important interaction is the hydrophobic interaction. As the term hydrophobic suggests, this interaction is an effective interaction between two nonpolar molecules that tend to avoid water and, as a result, prefer to cluster around each other. Unlike all the other interactions that we have studied so far and which are pairwise interactions between atoms or parts of molecules, the nature of the hydrophobic interaction is very different. It involves a considerable number of (water) molecules, and does not arise as a result of a direct force between the nonpolar molecules. Nonpolar molecules are not good acceptors of the hydrogen bond. When a nonpolar molecule is placed in water, the hydrogen bonding network of water is disrupted. The water molecules therefore reorganize around the solute and make a sort of cage, similar to the structure of water in ice, in order to gain back the broken hydrogen bonds. This reorganization results in a considerable loss in the configurational entropy of water and therefore an increase in the free energy G. If there are two or more such nonpolar molecules, the configuration in which they are spatially together (clustered together) is preferred because now the hydrogen bonding network of water is disrupted in one (albeit bigger) pocket, rather than in several small pockets. Therefore, the entropy of water is larger when the nonpolar molecules are clustered together, leading to a decrease in the free energy. At equilibrium, the configuration with the lower free energy and which has a higher Boltzmann probability, is the preferred configuration. Hydrophobic interactions have strengths of a few kBT and are comparable in energy to hydrogen bonds.
- Ionic interactions
- Van der waals interactions
- Hydrogen bonds
- Hydrophobic interactions
where k is a constant , in vacuum, where = 8.85x10-12 C2/N.m2 is the permittivity of free space. (k = 9x109 N.m2/C2). The potential energy U of two charges is defined as the work required to bring the two charges to a distance r apart if they are initially infinitely far away: The potential energy is negative when the force is attractive (q1 and q2 have opposite signs), and positive when the force is repulsive. The gradient of the potential energy function is a measure of the force:
or, more generally, . The potential energy for the simple Coulomb interaction falls off rather gradually, as 1/r, and hence it is also referred to as a long-range interaction. In vacuum, U ~ 30 kBT for two charges q1 = q2 = e- (1.6x10-19C) separated by r ~ 2nm. In water, which is the appropriate medium inside the cells, the Coulomb interactions are reduced by a factor which is equal to the dielectric constant of water. Water molecules have a permanent dipole; they align in the direction of the local electric field and effectively screen the charges. The dielectric constant of bulk water is 80 at room temperature. Therefore, in water, U ~ 0.4 kBT for two ions carrying unit charges separated by ~ 2 nm. Distance dependence of the apparent dielectric constant The screening property from aligned dipoles is expected to decrease as the distance between the two ions decreases, and in the limit that the two ions are right next to each other, the apparent dielectric constant is 1. The following graph gives an empirical estimate of the apparent dielectric constant of water as a function of the distance from an ion: At a distance of r = 0.5 nm, the apparent dielectric constant is ~ 20, and the potential energy of two unit charges is U
5 kBT. For decreasing value of r, the potential energy U increases both because of the 1/r dependence as well as a smaller value for the apparent dielectric constant. There is another very important screening effect that arises from free ions in solution and which will cluster around charged objects (thus the name counter-ions) and further reduce the strength and range of the Coulomb interactions. These counter-ions can be associated with the charged objects with energies in excess of 5 kBT and hence are not easily shaken off by thermal energy. Charge-dipole and dipole-dipole interactions Many molecules are electrically neutral but have a permanent dipole because of an asymmetric distribution of the electron cloud around the positively charged nuclei. For example, in HCl, the valence electron of the H atom is donated to the Cl atom, with H carrying a net positive charge, and Cl a net negative charge. Similarly, water has a permanent dipole because the electron density is greater near the more electronegative O atom. The dipole moment is defined as
where d is the separation between 2 charges +q and �q. p is a vector and points in the direction from �q to +q. When a molecule with a dipole moment p is placed in an electric field E, the dipole has a potential energy where is the angle between the vectors p and E. Charge-dipole interactions The electric field from a single point charge at a distance r from the charge is
, and the electric field vector points away from the charge (for positive charges) and toward the charge (for negative charges). The potential energy of a charge-dipole system is . The potential energy now falls off as 1/r2, more rapidly than the charge-charge system. In the absence of thermal motion, the dipole will align with the E field, which corresponds to =0. Thermal averaging Because of random collisions with the molecules of the surrounding medium, the dipole will undergo Brownian motion. Here we will consider only the change in the orientation of the dipole as a result of random collisions, and write down the Boltzmann probability that the dipole makes an angle with the E field as: Probability The average value of the potential energy, averaged over all possible orientations whose probability is given by the Boltzmann distribution, can be written as where Z is the normalization constant, , and is the incremental solid angle between two cones swept by the p vector as it makes an angle and with respect to the E vector. You should be able to work out the integrals and show that which, in the limit pU << kBT, simplifies to Substituting for the electric field due to a point charge q at a distance r from the charge, we get With thermal averaging, the charge-dipole interaction falls off as 1/r4. The minus sign indicates that the interaction is always attractive. Dipole-dipole interactions The interaction energies between two dipoles p1 and p2 have a more complicated angular-dependence, since there are now two dipoles, each one of which can be oriented in any direction. Here we will write down the form of the solution without worrying about the details of the calculations.
The potential energy has the form
where E1 is the electric field from dipole p1and depends on the angular position of p2 relative to p1 and their relative orientations. The distance dependence 1/r3 comes from the radial dependence of the electric field E1 of dipole p1. The thermal averaging with Boltzmann probabilities, in the limit U<< kBT, gives: Note that the potential energy between two dipoles falls off as 1/r6 power. Dipole-dipole interactions are short-range interactions Van der waals interactions Perhaps the most important class of dipole-dipole interactions are the ones where one or both molecules do not have a permanent dipole. These interactions are valid for any two atoms that come into close contact with each other, and are called Van der Waals interactions. Dipole-induced dipole interactions A molecule with a permanent dipole p1 can induce a dipole in another polarizable molecule. In this case the induced dipole moment p2* points in the same direction as the inducing electric field E1. The potential energy of interaction between p1 and p2* takes the form
where the minus sign indicates that the interaction is always attractive, since the induced dipole always follows the direction of the instantaneous electric field. defines the angular position of p2* relative to p1and the electric field E1 is independent of the azimuthal angle . The magnitude of p2* depends upon the strength of the electric field at position , where is the polarizability of the second molecule. The interaction potential is given by: where again we have a 1/r6 dependence. The above result is in the absence of thermal averaging. Thermal averaging Since p2*, in this case, always follows the instantaneous direction of the electric field E1, thermal averaging requires that we simply average over the dependence, with all orientations of p1 equally likely. The average value gives a numerical constant. The average potential energy has a 1/r6 dependence as in the thermally averaged dipole-dipole case. Induced dipole-induced dipole interactions A fluctuating electric field environment around each atom induces a fluctuation dipole moment that is proportional to the polarizability of the atom. This instantaneous dipole can then induce a dipole in a neighboring atom, resulting in an attractive potential that also has a 1/r6 dependence. Short-range repulsive interaction As the atoms get too close, at some point there is a strong repulsion from overlapping electron clouds and Pauli�s exclusion principle whereby filled electron shells of an atom cannot accommodate any more electrons. Lennard-Jones potential A commonly used analytical form that lumps together all dipole-dipole interactions and includes both the attractive and the repulsive terms is the Lennard-Jones potential where the repulsive term is approximated as having a 1/r12 dependence:
This form of the potential energy function has a minimum at r = ro with . The atoms can be treated as spheres defined by a Van der Waals radius that is a measure of how close another atoms can come before a strong, very short range, repulsive force kicks in. Some typical Van der Waals radii of atoms are hydrogen ~ 1.2 A , oxygen ~ 1.4 A , nitrogen ~ 1.6 A , and carbon ~ 2 A . Hydrogen bonds A very important interaction responsible for the structure and properties of water, as well as the structure and properties of biological macromolecules, is the hydrogen bond. A hydrogen bond is an interaction between a proton donor group D-H and a proton acceptor atom A. D-H is stongly polar, which means that the electron density is primarily around the electronegative atom (examples, F-H, O-H, N-H, S-H in order of decreasing polarity). The acceptor atom A is also strongly electronegative. The hydrogen bond interaction is more than just an ionic or dipole-dipole interaction between the donor and the acceptor groups. The distance between the H and A in a hydrogen bond is less than the sum of their respective Van der Waals radii. Hydrogen bonds are usually shown as
although the strength of the interaction can sometimes be as strong as . The hydrogen bond is strongest when the three atoms D, H, and A have a collinear geometry. The strength of the hydrogen bonds in biological macromolecules ranges from ~ 2 kBT to ~ 5kBT. Hydrogen bonding network in water Hydrophobic interactions Another very important interaction is the hydrophobic interaction. As the term hydrophobic suggests, this interaction is an effective interaction between two nonpolar molecules that tend to avoid water and, as a result, prefer to cluster around each other. Unlike all the other interactions that we have studied so far and which are pairwise interactions between atoms or parts of molecules, the nature of the hydrophobic interaction is very different. It involves a considerable number of (water) molecules, and does not arise as a result of a direct force between the nonpolar molecules. Nonpolar molecules are not good acceptors of the hydrogen bond. When a nonpolar molecule is placed in water, the hydrogen bonding network of water is disrupted. The water molecules therefore reorganize around the solute and make a sort of cage, similar to the structure of water in ice, in order to gain back the broken hydrogen bonds. This reorganization results in a considerable loss in the configurational entropy of water and therefore an increase in the free energy G. If there are two or more such nonpolar molecules, the configuration in which they are spatially together (clustered together) is preferred because now the hydrogen bonding network of water is disrupted in one (albeit bigger) pocket, rather than in several small pockets. Therefore, the entropy of water is larger when the nonpolar molecules are clustered together, leading to a decrease in the free energy. At equilibrium, the configuration with the lower free energy and which has a higher Boltzmann probability, is the preferred configuration. Hydrophobic interactions have strengths of a few kBT and are comparable in energy to hydrogen bonds. 
No comments:
Post a Comment