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Hydrogen Bond, Molecular Orbital

Orbitals Orbital Energy Levels It becomes very difficult to solve the Schrodinger equation numerically for molecule with many electrons. An approximate method called Molecular Orbital Theory (MO for short) has been developed for constructing reasonably accurate molecular structure (the wave functions and energy levels) with reasonably computational time. The MO starts with a linear combination of the wave functions for the electrons of each atom as shown in the left side of Figure 12-13a. The energy of the system is minimized with respect to the coefficients of the linear combination at different inter-atomic separation. The final result yields the wave functions (probability

Figure 12-13a Orbitals

Figure 12-13b Orbital Energy Levels

amplitude) for the molecule as shown in the right side of Figure 12-13a as well as the molecular energy levels as shown in Figure 12-13b. The isosurface shown in Figure 12-13a is called atomic or molecular orbitals. It is defined as the surface
N<sub>2</sub> Orbital Image N<sub>2</sub> Orbital Calculated within which the probability of finding the electron has some definite value, say 90%. The molecular orbital designated with an " * " is the unstable antibonding state, otherwise, it is the stable bonding state. The + or - sign signifies a positive or negative value for the wave function. Each orbital can accommodate two electrons with opposite spin direction. Recently (in 2005), a method has been developed to take image of a molecule by using a short laser pulse lasting just 3 x 10-14 second. Figure 12-14a shows a electron orbital of a nitrogen molecule as imaged by such technique. It agrees quite well with the orbital as calculated from theoretical models (Figure 12-14b). The colours represent the amplitude of the wave function - the

Figure 12-14a N2 Image [view large image]

Figure 12-14b N2 Model

electron is most likely to be found at the red and dark blue areas. Producing a three-dimensional image requires repeating the process at different angles, like a hospital CT scanner.

H2O Energy Levels Hydrogen Bond In the H2O molecule, the electric field around the oxygen atom is stronger than that around the hydrogen. The electrons from the hydrogen atoms are drawn close to the oxygen. This leaves the hydrogen atoms positively charged at one end. The four pairs of valence electrons around the oxygen atom (six contributed by the O atom -- 2 in the 2s, 4 in the 2p states; and one each by the H atoms in the 1s state) occupy four sp3 orbitals that form a tetrahedral pattern. The energy levels for these four pairs of electrons are lower than the original levels in separated atoms as shown in Figure 12-15a (MO1 - MO4). Since the positively charged atomic nucleus for

Figure 12-15a H2O Energy Levels [view large image]

Figure 12-15b Hydrogen Bond [view large image]

the hydrogen is partially exposed, it often attracts to other negatively charged orbitals such as the electron pairs of the oxygen atom in another H2O molecule (see Figure 12-15b).

Water This is called hydrogen bond. It is different from the covalent bond since there is no orbital overlap; it is not an ionic bond since there is no charge transfer from one atom to another. The strength of the hydrogen bond is about 10 times weaker than the covalent and ionic bonds. Hydrogen bonds are important in fixing properties such as solubilities, melting points, and boiling points, and in determining the form and stability of crystalline structures. Molecules such as water carrying hydrogen bonds are called polar molecules. They play a crucial role in biological systems.

Figure 12-16 Water
[view large image]

    Water has some special properties crucial to the existence of life courtesy to the hydrogen bond:

  1. Heat Capacity - Water has high heat capacity (needs more heat to rise the temperature) and boiling point by virtue of the additional hydrogen bonds that keep the water molecules packed together with extra strength (see Figure 12-16a, white bar represents covalent bond, grey and blue bars for hydrogen bond). This property moderates the temperature of the environment. Lack of water turns the land into desert. The same hydrogen bonds also pull water up a tree, in a phenomenon called capillary action, and maintain surface tension, which enables small bugs to walk on water.
  2. Ice - When water cools to below 4oC, it suddenly becomes less dense. It is because the thermal agitation cannot overcome the hydrogen bonds and solid ice begins to form. The angle subtended by the two hydrogen atoms then increase from 105 to 109 degrees resulting a less tightly packed configuration (Figure 12-16b). That's why ice can float on water and protects the water beneath from frozen allowing fish to live in the polar regions or creatures under the icy surface of Europa (Figure 12-16f).
  3. Solution - Water is a good solvent able to dissolve many polar substances (Figure 12-16c). That's why water-based liquids, like blood, are perfect transporters of essential substances such as salt, sugars and hormones.
  4. Protein folding - Some amino acids are hydrophobic (repelled by water); while others are hydrophilic (attracted to water). In a a liquid environment such as the inside of cells, these properties dictate how a protein "assembles", or folds (Figure 12-16d). DNA too, depends on water. Experiments have shown that the double helix would fall to pieces without water. This is because water molecules help form hydrogen bonds between DNA's phosphate groups.
  5. DNA binding site - Some biochemists think that water molecules may play an active role in guiding enzymes to certain spots on the DNA (Figure 12-16e). It is found that water molecules spend more time around certain areas of DNA when cell divides. Such tendency seems to suggest that water is needed for the expression of genes - a process that is kick-started by binding the transcription factor to the gene switch.
  6. Origin of Water on Earth - Water molecules are one of the components in interstellar dust. It would be incorporated into the primordial Earth naturally. Water as many other gaseous materials are trapped by the Earth's gravity when it acquired a sufficient amount of mass. It might be in the form of solid when the temperature was too low in the very beginning, and in the form of gas when it was covered with magma produced by planetesimal impacts. Only in a very narrow window of temperature (from 0oC to 100oC) it turned into liquid state suitable for life. Later on more water are added via the impacts of comets, which contain a lot of water and the impacts occurred more often in the past.
  7. Search for ET - All known life on Earth depends on water. Typical enzymes, just like DNA, need to be surrounded by water to function properly. Nobody know if enzymes can function in another liquid, or there might be fundamentally different life-forms in other parts of the universe - a possibility that would not be ruled out by many scientists. Nevertheless, NASA has chosen the strategy of "Follow the Water" in its programs to search for extra-terrestrial life (to Europa for example, see Figure 12-16f).
See more in "Molecular Orbital Theory".

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