Molecules

Contents

Quantum Theory^1,2, Blackbody Radiation

Molecules are small objects not susceptible of direct observation even under the most powerful microscope. However, their properties can be deduced indirectly from experiments. These objects are different on the conceptual level as well. Classical physics can no longer offer a consistent description. It is replaced by quantum theory, which describes the objects only in term of probability, energy levels, and other quantum numbers. A well-defined orbit such as the path of a planet around the Sun becomes the probability of finding the object at a certain location in the microscopic world. Thus, all the illustrations related to these objects would be just a schematic diagram conveying some ideas, they should never be taken literally as the real thing.

Historically, the quantum theory began with the attempt to account for the discrepancy between the theoretical and observational blackbody radiation. The classical theory of Rayleigh-Jeans failed to fit the observation of the radiation energy distribution from a blackbody at high frequency. In searching for a modification that would reduce the contribution of the high frequencies to the energy, Planck was led to make an assumption: The energy of the radiation with frequency is restricted to integral multiples of a basic unit hv (a quantum), i.e., E = nh where h = 6.625x10-27 erg-sec is the Planck constant and n is an integer. With this assumption, Planck obtained an exact fit to the observed distribution of radiation energy. According to classical theory, electromagnetic radiation is a wave phenomenon. The Planck's assumption endows a particle aspect to the same entity. Such wave-particle duality requires radical changes in the fundamental concepts of the properties of matter and energy. An introduction on the subject of "wave" can be found in the appendix: Wave, Sound, and Music.

Figure 12-01 Blackbody Radiation

Correspondence Principle

The first difference is that whereas classical theory always deals with continuously varying quantities, quantum theory must also deal with discontinuous or indivisible processes (e.g., the unit of energy packed in a quantum). The second difference is that whereas classical theory completely determines the relationship between variables at an earlier time and those at a later time, quantum laws determine only probabilities of future events in terms of given conditions in the past.

The Correspondence Principle states that the laws of quantum physics must be so chosen that in the classical limit, where many quanta are involved (e.g., n is a large integer in E=nh), the quantum laws lead to the classical equations as an average. This requirement combined with indivisibility, and incomplete determinism define the quantum theory in an almost unique manner.

Uncertainty Principle

and time/energy (including the rest mass energy mc2), it is impossible to have a precisely determined value of each member of the pair at the same time. This statement is illustrated with a schematic diagram in Figure 12-02. The corresponding formula is: x px > , where denotes the uncertainty, x is the position of the point mass m along the x-axis, px = m vx is the momentum along the x-axis, vx is the velocity along the x-axis, and = h/2 = 1.054x10-27 erg-sec. A similar relation exists for the uncertainty of the time t and energy E, e.g.,

Figure 12-02 Uncertainty Principle [view large image]

t E > . In case of heavy mass (such as a macroscopic object), the uncertainties and thus the quantum effect becomes very small, classical physics is applicable once more.

Many quantum phenomena such as superposition, probability density (or wave), vacuum fluctuation, and virtual particles are related to the uncertainty principle:


• By definition, a state consists of all the information needed to completely describe a system at an instant of time. Since the quantum state is specified by momentum, energy, angular momentum, or spin and there is an uncertainty in determining their value, it implies that a particle can occupy many quantum states (with different probability). This is called superposition. Figure 12-03a illustrates a very simple superposition of two spin states - one parallel and the

	other anti-parallel to the direction of a magnetic field, where |a|2 and |b|2 are probabilities of finding the particle in the corresponding state. It is only when the state of the particle, e.g. the spin in this case, is measured that it settles into a definite state. But as soon as we stop monitoring its behavior, the particle dissolves into a superposition again.
Figure 12-03a Superposition [view large image]	Note : Probability = |Probability Amplitude|2, e.g., a and b in Figure 12-03a are the probability amplitudes, the corresponding probabilities are |a|2 and |b|2.

• The uncertainty in space and time is interpreted as the probability of finding the particle at a certain time and place. For example, the electron within the confine of the nucleus exhibits a certain probability pattern. Figure 12-03b shows the probability distribution of an electron in the 3d state (m_l=0) of the hydrogen atom. When the electron moves in free space with a certain momentum p, the probability pattern displays a wave-like form with the wavelength = h/p, which is known as the de Broglie wavelength. Since there is a spread of momentum according to the uncertainty principle, the electron wave is described by a wave packet, which is the combination from waves of different

		wavelengths and amplitudes (Figure 12-03c). If an object's wavelength is of a similar order to the size of the objects around it, the wave nature comes to the fore. The wavelength of a macroscopic object such as a moving car is something around 10-36 cm; thus it takes some pretty tiny objects to expose the car's wavelike properties. Only
Figure 12-03b Probability Pattern [view large image]	Figure 12-03c de Broglie Wave [view large image]	microscopic objects such as electron has a large enough wavelength to show its wavelike property with objects in manageable size. For example, the de Broglie wavelength for a 75 ev electron is 2 x 10-8 cm, thus the spacing between atoms in a crystal is a good diffraction grating for such electron.

In classical physics, empty space-time is called the vacuum. The classical vacuum is utterly featureless. However, in quantum mechanics, the vacuum is a much more complex entity. It is far from featureless and far from empty. The quantum vacuum is just one particular state of a quantum field. It is the quantum mechanical state in which no field quanta are excited, that is, no real particles are present. Hence, it is the "ground state" of the quantum field, the state of minimum energy. Figure 12-03d illustrates the kind of activities going on in a quantum vacuum. It shows virtual particle pairs appear, lead a brief existence, and then annihilate one another in accordance with the Uncertainty Principle.

Figure 12-03d Vacuum Fluctuation [view large image]

• There are two kinds of virtual particle. One kind are particles produced out of the vacuum as mentioned above. Many such particles can be produced only in virtual pairs (as shown in Figure 12-03d) in order to preserve the existing balance of properties such as electric charge in the Universe. But particles, which are not constrained by these conservation laws, notably photons, can be produced without any mirror image counterpart (such as in the Casimir effect below).
  
  The particles which join the vertices in a Feynman diagram (Figure12-03e) are also virtual particles and can never be detected directly, even though they are of key importance in determining the way "real" particles interact. This kind of virtual particle can be generated in violation of conservation laws, which are obeyed overall during the interaction. All quantum particles can be thought of as being surrounded by a cloud of virtual particles (and pairs) of various kinds, which are being created and (usually) reabsorbed by the parent particle. The lifetime of each of these virtual particles

	(and therefore the distance it can travel from its parent particle) depends on its mass-energy and the leeway allowed by the uncertainty principle. Interactions occur when a real particle come close enough (as in high energy collision) for one or more of the virtual particles in the cloud to be absorbed by the other real particle.
Figure 12-03e Feynman Diagram

Since the virtual photons in between two parallel metal plates placed a short distance apart can exist only when they can form a standing wave, there are fewer photons in each cubic centimeter of vacuum between the plates than there are in the vacuum outside. So, in effect, there is an excess pressure from outside pushing the plates together. This is known as Casimir effect (see Figure 12-03f). The resulting force is very small, but it has been measured (for plates separated by gaps of a few nanometers), proving that quantum fluctuations of the vacuum are a real phenomenon.

Figure 12-03f Casimir Effect [view large image]

Complemetarity Principle

"double-slit" experiment, but with a lens on the far side of the pinhole screen. The lens refocuses the spreading beams onto two mirrors, which reflect them onto two photon detectors tracking the path of the photons as particles. The interference pattern (wave property) is observed indirectly by placing wires in front of the lens at the "would be" positions of the dark fringes. It is argued that if the photons do not interfere, there will be no dark fringes and the wires will block some of the photons hitting the lens, reducing the photon count at the detectors. Since no such dip in the signal is seen, it implies that the light does form an interference pattern, violating the complementarity principle. Such claim has

Figure 12-03g Particle and Wave [view large image]

raised a storm of criticism initially in 2004, but the publication of the research in 2007 has forced a more cool-headed discussion now.

Exclusion Principle

The Pauli Exclusion Principle states that identical fermions -- one type of fundamental matter with 1/2 integer spin quantum number -- cannot be in the same place at the same time and with the same orientation (i.e., cannot have the same quantum state). It is this Exclusion Principle that requires the electrons in an atom to occupy different energy levels instead of all congregating in the lowest energy level. Chemistry would be very different without this rule. The exclusion principle is also responsible for the degenerate pressure, which prevents the White Dwarf from complete collapse. The other type of matter, bosons (particles with integer spin quantum number), do not have this property. The boson gas can form Bose-Einstein condensate near absolution zero temperature. They are all in the same quantum state, and behave like a single entity. Figure 12-04 shows the bosons bunch together, while the fermions keep their distance at temperature a few hundreds billionths of a degree above absolution zero (nanoKelvin=nK). Superfluidity refers to frictionless flow of spin 0 boson, e.g.,

Figure 12-04 Fermions and Bosons

helium-4 at low temperature.

Path Integral3, Transition to Quantum Theory

Each history has associated with it a number, called the amplitude, which defines the probability of that particular path being followed. While the classical path (the dash line) occurs with higher probability, the probability for the other paths vary according to a weighting factor. The probability of going from "here" to "there" is the sum of the probability for all paths. This formulism was originally devised by Richard Feynman for his PhD thesis in early 1940s. Twenty years earlier the transition from classical to quantum had to be formulated with a postulation which can be shown to be equivalent to the method of path integral (see mathematical detail).

Figure 12-05 Path Integral [view large image]

First Quantization, Schrodinger Equation4

It was postulated that the momentum p and position q are no longer mere numbers but are operators satisfying the commutative relation:

(qp - pq) = i.

This is called the canonical quantization. The fact that the particle is endowed with wave property is referred to as first quantization. Actually only p is treated as an operator - a differential operator acting on the wave function (q), q remains to be a c-number. The commutative relation can be viewed as a mathematical statement for the Uncertainty Principle. Since it implies that p cannot be a function of q (because it would mean p and q can be determined precisely at the same time), p can be related to q only in the form of an operator such as - i d/dq, where i = . The commutative relation is the direct result of such interpretation. Application of this rule for p and q to the equation relating the total energy E to the kinetic energy p²/2m and the potential energy V(q), e.g., E = p²/2m + V(q), yields the time-independent Schrodinger Equation for one particle with mass m and interacting potential V (i.e., it describes the stationary states with well-defined energy E corresponding to E 0, and t in the uncertainty relation t E > ) : For a given interacting potential V the problem is to find the Energy E and the corresponding wave function . The wave function is the probability amplitude of finding the particle at certain position (again do not confuse this amplitude with the state vector amplitude in superposition). The absolute square of the amplitude is the probability density. It turns out that the imaginary factory i in the quantization of p is crucial in describing a waveform for the case of E > V; otherwise, will be just an exponential function not compatible with observation. This form of Schrodinger Equation can be used to find out the structure of the atom or molecule. However, the generalization to system of many particles and more than one source of interaction becomes rapidly un-manageable and is solvable only through methods of approximation. The Schrödinger Equation for a poly-atomic molecule with N atomic nucleus and n electrons can be written down as :

{(²/2)[(/m) + (/M_k)] + E - (e²)[(1/2)(1/|r_i - r_j|) - (Z_k/|r_i - R_k|) + (1/2)(Z_kZ_l/|R_k - R_l|)]} = 0

where m is the mass of electron, M_k is the mass of the k^th atomic nucleus with number of positive charge Z_k, E is the total energy of the system, and . Since the atomic nucleus move much slower than the electrons, the Born-Oppenheimer approximation can be adopted to separate the wave function into = _{electrons nuclei} and the resulting equations are solved separately - the part for the electrons yields the electronic configuration while the vibrational and rotational states (of the nuclei) are obtained from the nuclear part. This method makes the equation more or less solvable but the task is still formidable with increasing number of particles. The Molecular Orbital Theory is used further to alleviate the computational difficulty in calculating the molecular structure (the nuclear part).

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Quantum Interpretations

• Copenhagen Interpretation - The mathematics of quantum theory dictates that quantum system exists in superposition of states. It is proposed that a certain state reveals its identity only through the measurement. This kind of interpretation is something extraneous to the mathematical formulaion - something that tacks on to the theory. Such situation does not bother practical physicists, who just carry out routine calculations or experiments, as long as the rules of quantum theory yield consistent results, and it is kept in mind that mathematical models do not always make sense to our everyday experience. It is the pure theorists and philosophers, who are very un-comfortable with such arbitrary rule. Schrodinger himself was particularly distressed about two things -- the idea that a quantum system could be in a superposition of states, and the requirement of an intelligent observer to "collapse the wave function" and force a quantum system to take up an unique state. He used a "thought experiment" to demonstrate the absurdity of such an interpretation, which could result in a cat half alive and half dead. This is known as the "Schrodinger's cat paradox". According to the idea of superposition of states, a radioactive nucleus could be half decayed and half not decayed, unless its state is measured. Schrodinger pointed out that the radioactive substance could be sealed in a box with a

  detector to monitor it. The detector is wired up to release a cloud of poison gas if the radioactive material decays; while the famous cat is kept inside. If the box is sealed and nobody looks into it, then the radioactive nucleus is in a fifty-fifty superposition of states, so are the poison gas (has and has not been released) and the cat (has and has not been killed, see Figure 12-06a). Thus, everything remains in limbo until an intelligent observer looks into the box. At this point, the superposition collapses and the cat becomes either dead or alive. But in spite of such nonsense as this paradox, the Copenhagen interpretation is still enshrined in most textbooks as the standard interpretation, and no cat has ever been put through such indignities.

  Figure 12-06a Schrodinger's Cat [view large image]

  Decoherence - It is suggested that coupling between a quantum system in a superposition and the environment in which it is embedded leads the system to 'collapse' or decay over time into one state or another. This is because in a large collection of atoms it is impossible for the quantum waves (in the superposition) to overlap sufficiently to allow them to combine into a state known as "coherence", in other words, they don't interfer with each other any more as shown in Figure 12-06b. The rate of decoherence depends on the size of the quantum system. Physicists can now create and maintain quantum particles such as atoms or photons in superpositions for significant periods of time, if the coupling to the environment is weak. For a system as big as a cat, however, comprised of billions upon billions of atoms, decoherence happens almost instantaneously, so that the cat can never be both alive and dead for any measurable instant (Figure 12-06b). The obvious problem with this argument is that nobody knows where to draw the line. Thus, the boundary between the two extremes, where a quantum system

  Figure 12-06b Decoherence [view large image]

  have just enough contact with the outside world to start behaving like a classical object, is currently a subject of active research.

  The thought experiment of the Schrodinger's cat can now be implemented in its miniaturized version with an atom moving left or right to represent the dead or alive of the cat (quantum cat or qcat) and the radioactive trigger becomes the distance of the electron (yellow circle in Figure 12-06c) to the nucleus (red circle): closer separation mimics the decayed state while that further away is the un-decayed state. By using lasers to manipulate the atom, the motion and

  separation can be coupled (entangled) as shown in Figure 12-06c. Thus, the qcat is both dead and alive until a measurement of the atomic state is performed. Other experiments scale up this basic idea, so that huge numbers of atoms become entangled and enter states that classical physics would deem impossible. A small leap of imagination extends the same to the very special kind of large, warm system - life. Preliminary investigation suggests that migratory bird's eye has a type of molecule in which two electrons form

  Figure 12-06c Quantum Cat [view large image]

  an entangled pair with zero total spin. It would responses to the inclination of the Earth's magnetic field to direct the path of migration (through a sequence of bio-chemical processes).

  
  Mathematically, the property of superposition of states is directly related to the special form of linear differential equation, which governs the behaviour of a single particle in quantum theory. When this particle interacts with other particles (as in a macroscopic object) or the detecting device or its environment, the equation becomes nonlinear implying no more superposition and hence the "collapse" of the particle to a definite state. If the interaction is small then the solution would consist of a lowest order term corresponding to one of the "interaction-free" states plus some higher order terms as prescribed by the "perturbation theory"
  
  

  Recently in 2004, half-a-dozen experiments have been designed to determine the boundary between the classical and quantum world. One experiment shown in Figure 12-06d fires C70 (70 carbon atoms in the soccerball-like crystal of about 1 nm across) fullerene balls at 190 m/sec toward two diffraction gratings. The first grating creates the matter wave from the fullerenes. The wave is then diffracted by the second grating and the interference pattern is formed on the detecting screen demonstrating the wave property of the fullerenes. However, the interference pattern fades away if the fullerenes are heated by a laser heater (to about 2700oC) or collide with gas (leaking into the vacuum chamber of the experiment). No one has a definitive answer for how the striking photons or molecules switch between quantum and classical behavior. One explanation is that the interaction causes an uncertainty in the position of the fullerenes,

  Figure 12-06d Matter-Wave Experiment and quantum-classical boundary [view large image]

  blurring the interference pattern. Another argument asserts that the disappearance of the quantum property is caused by entanglement between the photons/molecules, the fullerenes, and the rest of the world (via the wall of the chamber).

  
  
  Report in 2007 indicates that quantum effects have been detected in objects as large as buckyballs, but not viruses. The boundary seems to be located at about 10 nm (see Figure 12-06d). It is found that beside decoherence, the coarseness of detecting instruments also plays a role to induce transition from quantum to classical reality.
  
  

  Hidden Variables - This interpretation is based on the assumption that all the usual versions of quantum mechanics are incomplete, and that there is an underlying layer of reality which contains additional information about the world. This additional information is in the form of the hidden variables. If physicists knew the values of these hidden variables, the arguments goes, they could predict the precise outcomes of particular measurements, not just the probabilities of getting particular results. A helpful analogy can be made with a deck of playing cards prepared by a cheating card dealer (Figure 12-06e). He knows precisely the sequence in the deck; only the ignorant gamblers insist that the chance of picking a particular card is 1 in 52.

  Figure 12-06e Hidden Variables [view large image]

  The idea on hidden variables can be traced back to the 1920s and 1930s in the form of EPR (Einstein-Podolsky-Rosen) paradox. These scientists had a lot of problems with quantum mechanics in general and entanglement in particular.

  Entanglement occurs for example, in the decay of the pi meson into an electron-positron pair (Figure 12-06f). Since the spin for the pi meson is 0, the spin for the electron-positron pair must be opposite according to the conservation of angular momentum. Therefore, no matter how far apart are the members of this pair, if the spin is flipped for one of the member, the spin for the other member will also be flipped to the opposite at precisely the same moment. This non-local influence (non-locality) occur instantaneously, as if some form of communication, which Einstein called a "spooky action at a distance", operates not just faster than the speed of light, but infinitely fast. According to EPR, all the weird aspects come about due to our lack of the complete understanding of the subatomic world. No faster-than-light signaling between the entangled pair need be invoked if their properties had been set from the start. These well-defined properties, which quantum mechanics does not describe, are known as "hidden variables". Then a seminal paper by John Bell in 1964 showed that if EPR were correct, the results found by two widely separated detectors measuring certain properties of the two entangled particles (such as the spin orientations about various randomly

  chosen detecting axes) would have to agree (match) more than 50% of the time - this is known as the Bell's theorem, or Bell's inequality. Starting in early 1970s, technology has improved significantly to enable the required experiments for resolving the paradox. It culminated in the early 1980s, when the Aspect experiment firmly established that measurements from the two detectors do not agree more than 50% of the time. Quantum mechanics survived the test and entanglement will stay with us into the quantum computing age.

  Figure 12-06f Entanglement [view large image]

  A theory published in Nature Physics 2012 asserted that the wave function cannot be interpreted as the result of missing information (and hence the association with probability). Similar to the Bell's theorem, it shows that theories that treat the wave function in terms of lack of knowledge of a system's physical state will also fail to reproduce the predictions of quantum mechanics. Experimental checking of this new theorem is being arranged.

  
  

  Many Worlds - This interpretation states that whenever the world is faced with a choice at the quantum level, the universe divides into many, so that all possible options are followed, i.e., all the states are realized. Originally, it was suggested that we might think of the experiment with two slits in terms of two different realities, in one of which the electron goes thought slit 1 while in the other it goes through slit 2. Our world is a recombination of the two possibilities (the two worlds merge to become one again, see double slit pattern in Figure 12-06g),

  Figure 12-06g Double-Slit Experiment [view large image]

  producing interference between the two worlds. When we look to see which slit the electron goes through, we make one world real while the other disappears, so there is no interference (see single slit pattern in Figure 12-06g).

  The idea has been expanded further to include each possible outcome in the large-scale everyday world, and they all occur in different "parallel" universes. We only experience the copy for our own world. It has been shown that such interpretation leads to exactly the same predictions for the outcome of experiments as the other interpretations. The only problem is that there is no way to test, and it is difficult to imagine the mind-boggling idea of 10100 slightly imperfect copies of oneself all constantly splitting into further copies (see Figure 12-06h). However, some cosmologists find it useful to get around the puzzle, which is insurmountable in the Copenhagen interpretation (it requires an outside observer to work), of explaining what observation can collapse the wave function of the entire Universe and bring it into reality. Such interpretation has

  Figure 12-06h Quantum Worlds [view large image]

  received a boost in 2007 from the research which links the branching structure of the multiverse to the probability interpretation of the wave function in quantum mechanics, and thus provides an explanation for the origin of the empirical rule.

  
  

  Penrose Interpretation - Recently in 2005, Roger Penrose comes up with a new quantum interpretation. According to his theory each quantum event would create its own distortions in space-time, which requires energy to sustain. Since the stability of a system depends on the amount of energy involved (the lesser the easier to maintain), a macroscopic object tends to settle down in only one location (producing only one distorted space-time). According to his calculation, for microscopic objects such as electrons, atoms, and molecules the distortion is negligible; they can persist with the many quantum states (superposition) essentially forever as standard quantum theory predicts. Large objects, on the other hand, create such significant gravitational fields that the duplicate states vanish almost at once. For a dust speck, the process takes nearly a second - long enough that it might be possible to measure. Figure 12-06i shows a tabletop version of the more expensive and technically more difficult experiment for verifying the Penrose interpretation (in outer space). It directs a laser beam (separated by a beam splitter) toward a very tiny mirror to check if it can be in two states at the same

  Figure 12-06i Penrose Interpretation

  time. Until now, the experiment is running with a significantly smaller mirror than needed to test Penrose's theory. If the Penrose interpretation is correct, the two quantum states of the mirror (moved and unmoved) now consisting of a fullerene ball (a collection of seventy carbon atoms) will gradually change to just one state as the size of mirror increases to a dust speck. Figure 12-06i is a pictorial summary of the different kinds of interpretation.

  Figure 12-06j Interpretations

  In an article commemorates the 50th anniversary of the "New Scientist" magazine, Roger Penrose suggests that there are three kinds of reality: the physical, the mental and the mathematical, with something (as yet unknown) profoundly mysterious in the relations between them. According to this view, the various "Quantum Interpretations" are attempts to link the mathematical reality to the physical or mental reality. Figure 12-06k shows the mathematical reality as the patterns of interference computed from a mathematical formula, while the physical reality is in the form of photographic plate with the darker strip corresponding to the higher value of the curve. The mental reality is the image of dark and white strips formed in the retina and perceived by our consciousness.

  Figure 12-06k Reality [view large image]

  Another scheme is to consider the physical reality as primary, while the mental and mathematical realities as secondary. In this view, some processing steps are required to arrive at the secondary reality such as neuro-activity and com- putation. But the secondary reality does not always produce a corresponding primary reality. For examples, dreams and other altered mental states are not real; and mathematical formulas can generate result, which has no match in reality (unless the concept of multiverse is invoked).

Table 12-01 Status of Various Quantum Interpretations

Hydrogen Atom^5,6

		quantum number respectively; the probability densities have either spherical symmetry or rotational symmetry about the z axis. When the electron jumps from a higher energy level En+1 to a lower one En, a photon with frequency = (En+1 - En)/h is released (see the atomic transition series in Figure 12-07a). Excitation is the reversed process when the electron in energy level En absorbs a
Figure 12-07a Energy Levels [view large image]	Figure 12-07b Probability Density [view large image]	photon with frequency . Incidentally, the semi-classical Bohr model of H atom can also account for such H atom structure as well. The theory

Covalent Bond, Hydrogen Molecule7

		When two hydrogen atoms approach each other, the final configuration depends on the spin of the two electrons (a consequence of the Exclusion Principle). If the spin of the two electrons is parallel as shown in the right side of Figure 12-08, the two atoms remain separated. However, if the spin of the two electrons is antiparallel as shown in the left side of Figure 12-08, the two atoms combine to form a hydrogen molecule. There is a high probability
Figure 12-08 H2 Wave Function [view large image]	Figure 12-09 H2 Potential Curve [view large image]	of finding the electrons in between the atomic nuclei and this "electron cloud" tends to keep them from breaking up. This kind of binding is

		configuration of high probability with a final one of high probability as shown by the green line in Figure 12-10b. Transitions are also governed by selection rules, which usually allow transitions to occur only between change of the rotational or vibrational quantum number by an amount 1. The former is related to the initial and final states of the molecule, which favors the one step change in the rotational configuration. While the latter is linked to the oscillating state of the molecule, which occurs only at certain resonant energy so that the emitting or absorbing photon can carry only
Figure 12-10a Vibrational and Rotational Energy Levels [view large image]	Figure 12-10b Transition [view large image]	that amount - one step at a time.

Ionic Bond8, Atomic Shells

The most stable electron configuration of an atom consists of closed shells -- 2 for the n =1 shell; 8 for the n = 2 shell; ... (See Figure 12-11.) Thus He with 2 electrons and Ne with 10 electrons are among the most stable chemical elements. Atoms with incomplete outer shells tend to gain or lose electrons in order to attain stable configuration, becoming negative or positive ions in the process. For example, it requires 5.1 ev to ionize (remove) the outer shell electron from the sodium (Na); while adding an electron to the incomplete shell of chlorine (Cl) releases 3.8 ev. Thus the formation of a Na+ ion and a Cl- ion by the donation of one electron of Na to Cl requires just 5.1 - 3.8 = 1.3 ev.

Figure 12-11 Atomic Shells [view large image]

Figure 12-12 shows the decrease in potential energy as the Na+ and Cl- ions approaching each other. For very small separation of the ions, however, there is a strong repulsion due to the Exclusion Principle. The minimum in the potential curve occurs at r = 0.24 nm. At this separation the mutually attractive and repulsive forces on the ions exactly balance, and the system is in equilibrium with the creation of an ionic bond. To dissociate a NaCl molecule into Na and Cl atoms requires an energy of 4.2 ev, breaking it up into Na+ and Cl- ions requires an additional energy of 1.3 ev.

Figure 12-12 Ionic Bond [view large image]

Table 12-02 Properties of Ionic and Covalent Compounds

Hydrogen Bond⁹, Molecular Orbital¹⁰

		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
Figure 12-13a Orbitals [vli]	Figure 12-13b Orbital Energy Levels [view large image]	yields the wave functions (probability 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

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

		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
Figure 12-15a H2O Energy Levels [view large image]	Figure 12-15b Hydrogen Bond [view large image]	separated atoms as shown in Figure 12-15a (MO1 - MO4). Since the positively charged atomic nucleus for the hydrogen is partially exposed, it often attracts to

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

Figure 12-16 Water [view large image]

such as water carrying hydrogen bonds are called polar molecules. They play a crucial role in biological systems.

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 4^oC, 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 0^oC to 100^oC) 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).

van der Waals Force11, Dipole-Dipole Interaction

		of liquids into solids. Such familiar aspects of the behavior of matter in bulk as friction, surface tension, viscosity, adhesion, cohesion, and so on also arise from van der Waals forces. The interaction is between dipole-dipole. It can be the interaction between a permanent and an induced dipole as shown in Figure 12-17 or between a time average dipole (due to fluctuations of charge) and an induced dipole as shown in Figure 12-18. The van der Waals interaction is about 10 times weaker than hydrogen
Figure 12-17 van der Waals Interaction [view large image]	Figure 12-18 van der Waals, Nonpolar [view large image]	bond. The stronger hydrogen bond can be considered as interaction between permanent dipoles.

Physical Chemistry

• Thermochemistry - It is the application of the first law of thermodynamics (conservation of energy) to processes such as: chemical reactions, phase changes, e.g., boiling and melting, and the formation of solutions. The first

  	thermochemistry law (proposed in 1780) states that: the quantity of heat required to decompose a compound into its elements is equal to the heat evolved when that compound is formed from its elements. The second law of thermochemistry (discovered experimentally in 1840, also known as Hess law). It states that the heat change in a chemical reaction is the same whether it takes place in one or
  Figure 12-19 Hess Law [view large image]	several stages. That is, the heat change depends on the initial and final states only (Figure 12-19).

  Chemical Kinetics - Chemical kinetics study reaction rates in a chemical reaction. It is measured by the amount of reactant used up, or the amount of product formed, in a certain period of time. Reactions with low activation energies go faster than reactions with high activation energies. The rate of a reaction can be affected by the temperature, the amounts of reactants in the container, and catalysts (Figure 12-20). Reactions almost always go faster at higher temperatures, because the increase in kinetic energy makes the reactants move faster and collide more often. The rate of a reaction also increases when reactants are added (resulting in higher concentration)

  Figure 12-20 Reaction Rate [view large image]

  since there are more collisions between the reactants. Another way to speed up a reaction is to lower the energy of activation. This can be done by adding a catalyst, which speeds up the reaction but is not itself changed or used up.

  
  
  
• Solution - A solution is a mixture in which one substance called the solute (the component that changes state upon dissolving in smaller amount) is uniformly dispersed in another substance called the solvent. Because the solute and the solvent do not react with each other, they can be mixed in varying proportions (see Figure 12-21). Solutes and solvents may be solids, liquids, or gases (see Figure 12-22). Gases form solutions easily because their particles are moving so

  		rapidly that they are far apart and attractions to the other gas particles are not important. When solids or liquids form solutions, there must be an attraction between the solute particles and the solvent particles. Otherwise, the particles do not mix and no solution forms. Compounds containing nonpolar molecules such as iodine, oil, or grease do not dissolve in water because water is polar. The polarities of a solute and a solvent must be similar in order to form a solution. It is found as early as the 1800s that whenever a
  Figure 12-21 Solution	Figure 12-22 Types of Solution [view large image]	substance is dissolved in a liquid the vapor pressure (the pressure at which the rate of evaporation is equal to the rate of condensation) of the latter is lowered. Such

  behaviour has the effect of rising the boiling point and lowering the freezing point of the solution. It also produces osmosis, which is the flow of a solvent, usually water, through a semipermeable membrane into a solution of higher solute concentration, i.e., diluting the solution.



• Electrochemistry - For the subject of physical chemistry the most important conductors are those of the electrolytes; they are distinguished from electronic conductors, such as metals, by the fact that the passage of an electric current is accompanied by the transfer of matter. There are two main groups of electrolytic conductors; the first consists of pure

  		substances, e.g., fused salts, and the second of solutions. The most thoroughly studied examples of the latter are solutions of acids, bases and salts in water. Sodium chloride (NaCl) is a strong electrolyte, which dissociates in water into hydrated ions of Na+(aq) and Cl-(aq). As shown in Figure 12-23a, the light bulb glows as these ions provide a path for current flow in a circuit of : light bulb - battery - electrolytic solution - light bulb. HF is a weak electrolyte only generates a dim light. While nonelectrolytic substances such as sugar block the
  Figure 12-23a Electro- lyte [view large image]	Figure 12-23b Battery [view large image]	passage of electricity altogether. Figure 12-23b shows the essential parts of a lead storage battery. When the switch in the battery circuit is closed, reactions take place at the anode

  and the cathode as shown in the diagram. The battery can store energy because the system of lead, lead dioxide, and sulfuric acid is in a higher energy state than those of the chemical substances they can react to form, namely, lead sulfate and water. When fully charged, the voltage between the terminals of a lead storage battery is 2.0 volts. Most automobile starters require either 6 or 12 volts to function, so the car batteries consists of 3 or 6 individual lead cells connected together to provide the proper voltage. By connecting the terminals of the battery to a source of direct current, which forces electric flow in the direction opposite to that of normal battery current, the battery can be recharged. (see also "modern rechargable battery")
  
  
• Phase Change - The term phase as used here relates to the fact that matter exists either as a solid, liquid, or gas such as ice, water, and steam for H₂O. Transitions from one phase to another are accompanied by the absorption or liberation of heat and usually by a change in volume. Figure 12-24 uses H₂O as an example to illustrate the process of phase change. The experiment puts ice (at -25^oC) into a container, which is surrounded by a heating coil (generating an uniform heating rate). Temperature of the ice rises from a to b until it reaches 0^oC - the melting point. Ice turns into water from b to c. The heat spent for the phase change (per unit mass) is called the heat of fusion. The temperature

  remains constant during the change of phase. Once the conversion is complete, the temperature of the water starts to rise again from c to d with a different rate since the specific heat (capacity to absorb heat) of water is greater than that of ice. Similar phase change occurs from d to e for water changing into steam. It takes longer time for the phase change from d to e, because the heat of vaporization (~ 540 cal/gm) is about 7 times higher than the heat of fusion. If the heating process continues from e to f, the gas would be called "superheated steam". The process reversed when heat is removed from the container.

  Figure 12-24 Phase Change [view large image]

• Surface Tension - A molecule in the interior of a liquid is completely surrounded by other molecules, and so, on the average, it is attracted equally in all directions. On a molecule in the surface, however, there is a resultant attraction inwards, because the number of molecules is greater in the bulk of the liquid than in the vapor. As a consequence of

  this inward pull the surface of a liquid always tends to contract to the smallest possible area; it is for this reason that drops of liquid and bubbles of gas in a liquid become spherical, a needle floats on the top of water, certain water bugs can travel across the surface of a pond or lake (see Figure 12-25a). When compounds called surfactants (Figure 12-05b) are added to water, they disrupt the hydrogen bonding between the water molecules. As a result, the surface tensions decreased and the water spreads out rather than forming drops or curved surface (Figure 12-25c).

  Figure 12-25a Surface Tension [view large image]

  Soap, detergents, shampoos, and fabric softeners, are example of surfactants we use every day.

  Surfactant is a class of organic chemicals call amphiphiles (amphi-, meaning both), which has a hydrophilic (water

  		loving) head and a hydrophobic (water hating) tail. An example of sodium dodecyl sulfate (SDS) molecule is shown in Figure 12-25b. When these molecules are dissolved in water the tails manage to avoid the water molecules by either forming a thin layer on the surface with the tail sticking out or wrapping into a sphere with the head facing the water molecules (Figure 12-25c). Oils and fats, which dislike contact with water, are easily
  Figure 12-25b Surfactant [view large image]	Figure 12-25c Surfactant in Water [view large image]	incorporated into the sphere and washed away in our daily cleaning actions.

Inorganic Chemistry¹²

• Periodic Table - A molecule is a compound composed of a group of two or more atoms held together by chemical bonds. A molecular formula is a symbolic representation of the composition of a compound in terms of its constituent elements (e.g., H₂O, CH₄, C₆H₁₂O₆, ... etc. where the integers represent the number of the particular element in the molecule). The periodic table (see Figure 12-26) is a structured list of all known elements, arranged in order of their

  atomic numbers. The horizontal rows are called periods. All elements in a period have the same number of shells of electrons. Each element across the row has an increment of one outer electron from left to right. The vertical columns are called groups. Elements within the same group all have the same number of electrons in their outer shell. They therefore tend to have similar chemical properties. Elements in the table can be classified as metals, non-metals, or metalloids. Metals have certain properties, which distinguish them from non-metals. These include generally high melting points, a shiny appearance, and good malleability (flatten into sheets), ductility (drawn into wires) and conductivity of electricity and heat. Some elements have both metallic and non-metallic properties. They are known as metalloids.

  Figure 12-26 Periodic Table, Traditional [view large image]

• Valence - The concept of valence is very important in determining if a chemical reaction can proceed or not. The valence numbers (oxidation numbers or states) for all the elements are listed on the top right of the symbol name in Figure 13-01a. The valence of a free atom is zero, but in a chemical compound, the value has some positive or negative value. For example, when carbon burns, the reaction is
  C + O₂ CO₂
  the carbon atom starts with zero valence and becomes +4 in CO₂; the valence of each oxygen atom is -2, so that the net valence of CO₂ is zero - a requirement for the chemical reaction to proceed. The increase in valence number from 0 to +4 (for the carbon atom in CO₂) is referred to as oxidation reaction.
  Another example is the reduction reaction:
  CuO + H₂ Cu + H₂O
  where the valence of Cu changes from +2 (in CuO) to zero, i.e., there is a decrease in the valence of Cu in this reaction. Thus, the rule for classifying reactions is: an element is oxidized when its valence number (oxidation number) increases;

  and is reduced when its valence number decreases. Figure 12-27 shows the valence for some common chemical elements. The value for electronegativity is a number that indicates the relative ability of an element to attract electrons. The rule for forming chemical compounds is to complete the shell by either accepting electrons or to denote depending on which way is easier to achieve. In Figure 12-27 the

  Figure 12-27 Valence [view large image]

  number of electrons to form a complete shell is two for hydrogen, and eight for carbon and oxygen. Thus oxygen tends to accept two more electrons and has a higher value for electronegativity. Further detail can be found in the topic on Atom.

  
  
  
• Classification - Inorganic compounds are classified into acids, bases, salts, and oxides as shown in Table 12-03 below:
  
  

  Substance	Properties	Classification
  Acids	Dissolve in water and produce H+. Taste - sour, feel - may sting.	Oxygenless: HCl Oxoacids: H2SO4
  Bases	Accept acids' H+ such as NaOH and MgO. Taste - bitter, feel - slippery.	Alkalis: soluble such as NaOH Insouble Base: Cu(OH)2
  Salts	Ionic compounds consist of metal and nonmetal ions. Form crystal, hard and brittle, hight melting/boiling points, conduct electricity when dissolved or melted, may react with water to form neutral, acid or basic solution.	Insoluble: attraction between ions > with water - PbCl2 Neutral: dissolves into hydrated ions - (H2O)(Na+)(H2O)(H2O)(Cl-)(H2O) Medium: dissolves into metal cations and anions of acid radical - (Na+)2(SO42-) Acid: dissolves into metal cations, hydrogen and acid radical anions - (Na+)(H+)(CO32-) Basic: dissolves into metal cations, hydroxyl and acid radical anions - (Zn2+)(OH-)(Cl-) Double: dissolves into two cations and one anion - ( K+)(Al3+)(SO42-)2 Mixed: dissolves into one cations and two anion - ( Ca2+)(Cl-)(OCl-) Complex: dissolves into complex cations or anions - [Ag(NH3)2+](Br-), (Na+)[Ag(CN)2-]
  Oxides	Consist of two elements, one of which is oxygen. The oxide group contains the greatest variations of physical properties. Some are hard, some soft. Some have a metallic luster; others are clear and transparent.	Non-salts: CO, NO, N2O (see general rules) Basic: salts with metal oxidation number +1, to +3 - MgO Amphoteric: salts with oxidation # +2, to +4 - Al2O3 Acid: salts with metal oxidation number +3, to +7 - SiO2

  Table 12-03 Classification of Inorganic Compounds

• Chemical Reactions - Table 12-04 is a list of the reactions between different classes of inorganic compounds :
  
  

  Reactants	Products	Example
  metal + non-metal	salt	Hg + S HgS
  basic oxide + acid oxide	salt	MgO + CO2 Mg CO3
  base + acid	salt	Ca(OH)2 + 2HCl CaCl2 + 2H2O
  metal + oxygen	basic oxide	2Mg + O2 2MgO
  non-metal + oxygen	acid oxide	4P + 5O2 2P2O5
  basic oxide + water	base	Na2O + H2O 2NaOH
  acid oxide + water	acid	SO3 + H2O H2SO4
  acid + salt	salt + acid	H2SO4 + BaCl2 BaSO4 + 2HCl
  acid + metal	salt	6HCl + 2Al 2AlCl3 + 3H2
  base + salt	salt + base	Ba(OH)2 + K2SO4 BaSO4 + 2KOH
  base + acid oxide	acid salt	KOH + CO2 KHCO3

  Table 12-04 Reactions of Inorganic Compounds

  Many of the most commonly used metals, such as iron and silver, belong to a group called transition metals, found in the middle of the periodic table. They have more than one valence. The compounds that they form are often brightly coloured. Many metals react with water, with dilute acids and with the oxygen in the air. They can be listed in order of how reactive they are. This is known as the reactivity series and is shown in Figure 12-28 with the most reactive on top and the least reactive on the bottom.

  Figure 12-28 Reactivity Series [view large image]

  Chemical reactions can also be classified by the process involved in the reaction such as combustion, decompostition, photoreduction, etc. There is a very good website in Ref. 13, where it offers plenty of demonstrations for the various types of process in chemical reactions.



• Nomenclature of Binary Molecules (compounds of only two elements, e.g., H₂O, HCl) :
  1. For covalent molecules, element to the left and below in the periodic table (see Figure 12-19) is named first. For example, in HCl hydrogen is named first, and in BrCl bromine is named first. For ionic molecules, cation (positively charged element) is named first.
  2. For covalent molecules, the other element is named with "-ide" ending. For example, HCl is named hydrogen chloride, and BrCl is named bromine chloride. For ionic molecules, anion (negatively charged element) is ended with "-ide".
  3. When two non-metals form more than one compound from each other, Greek prefixes are used. (Note: mono- is not affixed to first element of compound if there is only one atom per molecule, e.g., CO₂ is carbon dioxide, not monocarbon dioxide). For example, the prefix for one=mono-, two=di-, three=tri-, four=tetra-, five=penta-, six=hexa-, seven=hepta-, eight=octa-, nine=nona-, and ten=deca-. Therefore, the names for the following compounds are: NO - nitrogen monoxide, N₂O - dinitrogen monooxide, NO₂ - nitrogen dioxide, N₂O₃ - dinitrogen trioxide, N₂O₄ - dinitrogen tetroxide, N₂O₅ - dinitrogen pentoxide, PCl₅ - phosphorus pentachloride, P₂O₅ - diphosphorus pentoxide, SF₆ - sulfur hexafluoride, and Cl₂O₇ - dichlorine heptoxide.

Organic Chemistry

• Covalent Bonds - Since a carbon atom has four valence electrons, which can be shared with other atoms to achieve an octet (a stable closed atomic shell). In all organic molecules, all carbon atoms always have four covalent bonds. In

organic compounds, carbon atoms are most likely to bond with hydrogen, oxygen, nitrogen, sulfur, and halogens such as chlorine. Hydrogen with one valence electron forms a single covalent bond. An octet is achieved by nitrogen forming three covalent bonds and so on. Figure 12-29 lists the covalent bonds for these elements in organic compounds. The solid line denotes a bond with two sharing electrons in between the atoms, while the dot represents the electron not in a bond.

Figure 12-29 Covalent Bonds [view large image]

• Structure and naming convention - In most organic molecules, a carbon atom is boned to four other atoms. Study

indicates that the four bonds are arranged as far apart as possible, and they have a tetrahedral shape as shown in diagram (a), Figure 12-30 for methane and ethane. Other three dimensional representations can be in the form of (b) the ball-and-stick model, (c) space-filling model, (d) wedges (toward the reader) and dashes (away from the reader). Diagram (e) depicts the structural formula, which shows how the atoms in a molecule are bonded together in two dimensions, (f) is the chemical formula in one dimension showing just the

Figure 12-30 Organic Compounds [view large image]

constituent atoms. Table 12-05 explains the naming convention for organic compounds. It serves to bring some order into the mind-boggling variety of organic compounds.





# of Carbon Atoms (n)	CnH2n+2	CnH2n	CnHn	CnH2n+1OH	Examples
n = 1,       meth-	-ane	--	-yne	-anol	chloro-methane, meth-oxy-methane, methane-thiol
n = 2,       eth-	-ane	-ene	-yne	-anol	eth-ane, eth-ene, eth-yne, eth-anol, ethan-amide
n = 3,       prop-	-ane	-ene	-yne	-anol	prop-ane

Table 12-05 Naming Convention for Organic Compounds

Note 1: The hydrogen atoms can be replaced by other atoms with corresponding number of bonds. For example, two
             hydrogen atoms with one bond each can be replaced by one oxygen atom carrying two bonds (ethanal).
             But then the resulting compound would be categorized into another class and may not follow exactly the same
             convention in the table (see Figure 12-32).
Note 2: Structural formula for the examples can be found in Figure 12-32.


• Polarity - A covalent bond between two carbon atoms is nonpolar because the electrons are shared equally. However, when a carbon atom bonds to a different atom, the bond is polar covalent because the center of charge for the distribution of the electrons does not coincide exactly with the center of positive charges from the atomic nuclei. Most of the elements found in organic compounds are more electronegative (element with the greater electronegativity value pulls

the shared electron closer to its nucleus) than carbon, with the exception of hydrogen (see Figure 12-31). A bond between identical atoms is nonpolar. A polar bond forms between atoms of different electronegativity values. However, when molecules consist of several polar bonds, the arrangement of the bonds determines whether it is a polar or nonpolar molecule. If a molecule contains a symmetrical arrangement of polar bonds so that the dipoles cancel out, the molecule is nonpolar. Figure 12-31 shows the polar and nonpolar configurations of some molecules.

Figure 12-31 Polarity [view large image]

The polarities of molecules have a strong influence on the physical and chemical behavior of organic compounds. Organic compounds containing carbon and hydrogen have covalent bonds and form nonpolar molecules. As a result, the attractions between molecules are weak, which accounts for the low melting and boiling points of carbon compounds. Most organic compounds are not soluble in water. But small organic compounds with oxygen or nitrogen atoms are somewhat soluble because the electronegative atom forms hydrogen bonds with water. Table 12-06 below compares the differences between inorganic and organic compounds.



Inorganic Compounds	Organic Compounds
A few compounds with carbon atom, e.g., CO2	All organic compounds are carbon base
Elements joined by ionic or covalent bonds	Elements joined exclusively by covalent bonds
Most are ionic or polar covalent	Nonpolar, unless a more electronegative atom is present
Dissolve in water, may produce ions	Not soluble, unless a polar group is present or in organic liquids
High melting and boiling points	Low melting and boiling points
Vaporize at high temperature	Decompose by heat more easily
Flammability low	Flammability high
Reaction proceed quicker as solutions of the reactants are brought together	Reaction proceed at much slower rates in hours or days (except in living cell with enzymes)
Do not exhibit isomerism	May exist as isomers

Table 12-06 Difference Between Inorganic and Organic Compounds

Note: Isomers are chemical compounds with identical chemical formula but different arrangements of elements.


• Functional Groups - Organic compounds number in the millions and more are synthesized every day. It might seem that the task of learning organic chemistry would be over-whelming. However, within this vast number of compounds, there are characteristic structural features called functional groups, which are a certain group of atoms that react in a predictable way. They are the reactive sites in the carbon compounds. Compounds with the same functional group undergo similar chemical reactions. The identification of functional groups allows us to classify organic compounds according to their structure and to name compounds within each family. While the naming convention is listed in

Table 12-05, Figure 12-32 shows the classification of organic compounds into fourteen functional groups. The hydrocarbons, which contain only carbon and hydrogen, are the simplest of the organic compounds. The alkanes (a functional group) contain only carbon-carbon single bonds. They are also called saturated hydrocarbons because they cannot add any more hydrogen atoms to the structure. The alkanes are not very reactive compared to compounds in other functional groups, but they serve as a basic structure for the rest of the organic molecules. Hydrocarbons with double or triple bonds are called unsaturated hydrocarbons, because they can add atoms of hydrogen, oxygen, or a halogen. The alkenes contain a functional group that is a double bond between two adjacent carbon atoms; one of these bond can be linked to other atoms. Alkynes contain a triple bond. The alkenes and the alkynes are much more reactive than the single-bonded alkanes. Usually the addition of other molecules such as oxygen, sulfur,

Figure 12-32 Functional Groups [view large image]

nitrogen, phosphorus or halogen would make the compound more reactive. The structural formula for all the functional groups is shown in Figure 12-32.

• Some common organic compounds -
  
  
  • Plastics - Polymers are organic compounds which contain enormously long chains of atoms. These chains are made up of small repeating units of molecules called monomers. Some polymers, such as plastics are a large group of synthetic polymers which have had a tremendous impact on our everyday lives. All plastics have a number of useful qualities in common. They are strong as well as being light and flexible, easily colored and molded into shape. In addition, they are good heat insulators and are rot and corrosion-proof. The alkene, and ethene form the basis of many important plastics. For example, under the right conditions, ethene molecules will

    		react with each other, opening up their double bonds and joining together to form the polymer (poly)ethene, or polythene (Figure 12-33). Most plastics are made from raw materials derived from crude oil. They are difficult to recycle, most plastics cannot be burned as they release toxic fumes. The non-biodegradable rubbish is buried in huge holes dug deep into the ground called landfill sites. The plastics in there will give off methane gas, and form toxic slime leaking into underground water supplies.
    Figure 12-33 Plastics [view large image]	Figure 12-34 Foods [view large image]

  • Fuels - Hydrocarbons, particularly alkanes, are the compounds that make up natural gas, motor oils, gasoline, and other fuels. The coal and crude oil that provides these hydrocarbons was formed 200 million years ago from the pressures on buried organic matter deep in the earth. Because the hydrocarbons are flammable we use compounds such as methane (CH₄), propane (C₃H₈), and butane (C₄H₁₀) as energy sources.
  • Alcohol - Ethyl alcohol (C₂H₅OH) is the alcohol found in alcoholic beverage. Isopropyl alcohol (C₃H₇OH) is another alcohol commonly used to disinfect skin before giving injections and to treat cuts.
  • Solvent - Acetone is used as an organic solvent because it dissolves a wide variety of organic substances.
  • Food flavorings - Ketones and aldehydes are used in food industry to produce artificial flavorings such as vanilla, cinnamon, and spearmint. These substances are usually dissolved in alcohol because they are not very soluble in water. The aldehyde butyraldehyde (C₄H₈O) adds a "buttery" taste to foods and margarine.
  • Vinegar and juices - The sour tastes of vinegar and fruit juices and the pain from ant stings are all due to carboxylic acids. Acetic acid is the carboxylic acid that makes up vinegar. Aspirin also contains a carboxylic acid group. Esters found in fruits produces the pleasant aromas and tastes of bananas, oranges, pears, and pineapples (Figure 12-34). Esters are also used as solvents in many household cleaners, polishes, and glues.
  • Fish - One of the characteristics of fish is their odor, which is due to amines. Amines are produced when proteins decay, they give off a particularly pungent and offensive odor (Figure 12-34).
  • Dried foods - Since carbohydrates and proteins in death organisms decay via hydrolysis. Foods can be preserved by removing the water within. This method was used extensively in the past when preservative and refrigeration were not available.
  • Stimulants - Alkaloids are biologically active amines synthesized by plants to ward off insects and animals. Some typical alkaloids include caffeine, nicotine, and histamine. Many are painkillers and hallucinogens such as morphine, LSD, marijuana, and cocaine. Certain parts of our neurons have receptor sites that respond to the various alkaloids. By modifying the structures of certain alkaloids to eliminate side effects, chemists have synthesized painkillers and drugs such as Novocain, Codeine, and Valium.
  
  
  
• Organic compounds in living organisms -
  
  
  • Carbohydrates - In plants, photosynthesis combines CO₂ and water to form monosaccharides such as glucose and polysaccharides such as starch and cellulose. Glucose has a six-carbon chain with an aldehyde group and several hydroxyl groups. When glucose molecules join by ether links, long polymers of complex carbohydrates call polysaccharides are formed, which are known as starch and cellulose. A difference in the direction of the bond between the glucose molecules allows us to digest the starches in our cereals and bread, but not the cellulose in their packaging.
  • Lipids - Lipids containing carbon, hydrogen, and oxygen make up a variety of components in our body such as body fat. Body fat is composed of fatty acids, which are carboxylic acids with long carbon chains, bonded to glycerol by ester bonds. Because most lipids are insoluble, they play a major role in the structure of cell walls, which separate cell contents from aqueous fluids outside the cells.
  • Protein - Proteins are composed of carbon, hydrogen, oxygen, and nitrogen. These large polymers consist of small molecules called amino acids that have both amine and carboxylic acid functional groups. The order of amino acids in a protein determines the structure and function of the protein in the body. There are proteins such hemoglobin that transport oxygen to the cells, contract our muscles, form antibodies, make up hair, skin, and enzymes that catalyze biological reactions.
  • Nucleic acids - Nucleic acids are long chains of nucleotides, which contain a carbohydrate called ribose, a nitrogen base, and a phosphate group. The nucleic acids carry the messages for the production of all the proteins in the cells. It contains the genetic material for the reproduction of next generation.

Soft Matter

		"mesoscopic matter" since the size of the basic constituents ranges from a few nano-meters to about one micro-meters (Fiugre 12-35a) - at the boundary between quantum and classical objects (Figure 12-35b). It is the properties and interactions of these mesoscopic structures that determine the macroscopic
Figure 12-35a Soft Matter [view large image]	Figure 12-35b Length Scale [view large image]	behavior of the material; the quantum effect in the atomic or molecular scale are unimportant. Some examples for the soft matter are listed below.

Colloids - A very simple example is to mix dust into a glass of water. Smoke in the air is called aerosol. In general a colloidal system consists of nano size particles (dispersed phase) in a continuous medium, both of them can be in solid, liquid, or gaseous phase. Table 12-07a lists the various combinations between the two kinds (in Microsoft Word 97-2003 Document Format). Detail of the examples can be accessed by doing a ctrl-click on the subject.

Table 12-07a Colloids [view table]

Polymers - Polymers are large molecules whose molecular weight can range from the thousands to millions (in reference to the mass of hydrogen atom). They are built up by the repetition of low molecular weight units called monomers (Figure 12-35c, diagram a). For example: polyethylene is assembled by joining a long chain of many ethylene (ethlene) molecules together (Figure 12-35c, diagram b, c). When dissolved

Figure 12-35c Polymer Structure [view large image]

in a liquid, these chains wind into little balls. In the presence of large numbers of chains and depending on the process of production, they can grow intertwined into a kind of solid like the plastics shown in Figure 12-35c, diagram d and Figure 12-35a.

In glassy state polymers can be classified as amorphous or crystalline with different properties (see Figure 12-35d).

		Most polymers are in either amorphous or semi-crystalline forms. Depending on temperature, they can also exist in rubbery and melt states (Figure 12-35d). Thermo-plastics do not undergo chemical change in their composition when heated and can be
Figure 12-35d Polymer Properties [view large image]	Table 12-07b Plastics Families [view table]	moulded repeatedly. Thermosets type plastics can melt and take shape once; they stay solid after solidification.

Mass of common thermoplastics range from 20,000 to 500000 amu (atomic mass unit = 1.6x10^-24 gm), while thermosets are assumed to have infinite molecular weight. Table 12-07b (in Microsoft Word 97-2003 Document Format) lists the four families of plastics in declining quality from top row to bottom. Detail of some examples can be accessed by doing a ctrl-click on the subject.

		Micelles, Vesicles, and Emulsions - Micelle is an aggregate of surfactant molecules dispersed in liquid. Surfactant is a class of organic chemicals call amphiphiles, which has a hydrophilic (water loving) head and a hydrophobic (water hating) tail (see surfactant for more detail).
Figure 12-35e Vesicle [view large image]	Figure 12-35f Emulsion [view large image]	Vesicle is a double layers sphere made from surfactant molecules with the hydrophilic heads facing the aqueous solutions on the outside and inside (Figure 12-35i).

Emulsion is formed from two immiscible liquids that do not separate readily as shown in the middle of Figure 12-35f. It is created when energy is added to the mixture (by shaking for example). Some emulsions like milk are quite stable and will take a long time to separate since the nano-size particles is small enough to be suspended by brownian movement. Others may part quite quickly like the salad dressing of oil and vinegar (figure 12-35g). The emulsion itself consists of small droplets of one liquid within the body of a second liquid. Emulsions can fail in four basic ways: (i) Coalescence is the forming of bigger spheres until the two liquid are separated completely. (ii) Flocculation is the forming of clumps instead of larger spheres. (iii) Creaming is for the less dense liquid to float to the top. (iv) Breaking is the combined action of coalescence and creaming (see Figure 12-35g).

Figure 12-35g Emulsion Examples [view large image]

		Liquid Crystals - Liquid crystals are in the "meso-phase" between solid and liquid. The transition can be induced by temperature (thermotropic) as shown in Figure 12-35h or by dissolving the material in a liquid. Liquid crystals have the ability of in a form of orderly orientation but yet are in dynamic motion. Such special property is the result of structural anisotropy, e.g., rod-shape (calamatic), disc-shaped (discotic), and board-like (sanidic), and forced alignment by interaction
Figure 12-35h Liquid Crystal Phase [view large image]	Figure 12-35i Liquid Crystal Examples [view large image]	between the molecules. Actually, in the meso-phase the 3-dimensional ordering has been reduced to 1 or 2-dimensional ordering (Figure 12-35h). Figure 12-35i shows the various types of liquid crystals.

Liquid crystals find wide use in liquid crystal displays, which rely on an electric field to control its orientation. Polarization of the light depends in turn on the orientation so that it is either blocked or transmitted by a second polarization filter (polarizer) perpendicular to the first one (Figure 12-35j). The liquid crystal in this application is usually the nematic type (rod-shaped) in twisted form at relaxing state.

Figure 12-35j LC Display

Legend for Figure 12-35j: L - light, P1 - horizontal polarizer, P2 - vertical polarizer, E1, E2 - electrodes, LC - liquid crystals, G -grid, V - voltage supply, S - switch, I - image.

		Biomolecules - The biomolecuels of life is made from organic compounds, but not all organic compounds are related to life. Figures 12-35k and 12-35l happen to show the same thing with different perspective. In general the biomolecules in a living system are more complicated. For examples: 1. In the case of protein, it is not simply a polymer but a more complicated polymer makes from 20 different kinds of monomers (the amino acids). Every specific amino acid sequence gives a unique shape, and this in turn gives the molecule a single, well-defined function.
Figure 12-35k Bio-molecules	Figure 12-35l Organic Compounds [view large image]	2. DNA and RNA are also polymers made from nucleotides (the monomers). In a biological system the combination of the mono-mers cannot be at random. It has to be very specific and coiled up into chromosomes, otherwise the organism would not survive.

Nano-technology

achieved significant scientific successes. This field is characterized by the need to use the microscopic laws of quantum mechanics, while, on the other hand, the samples can be made and operated by essentially ordinary macroscopic methods. This involves linear size scales from a few to thousands of atoms, and reliable fabrication and analysis methods exist down to the scale of about fifty atoms. The term "nano" usually denotes the low end of this range. Figure 12-36a shows (left) scale of 10 micron with a circuit board element

Figure 12-36a Nano Domain [view large image]

comparing to a human hair, and (right) 0.1 micron, where a small stat-of-the-art transistor is compared with one commercially available in 2001.

Methods based on extremely powerful scanning tunneling microscope (STM, Figure 12-36b) that allows control of both fabrication and analysis on the scale of single atoms are being developed. Controlling man-made molecular structures on the level of individual atoms (including position and orientation) is possible in principle, and physical measurements such as that of the local (atomic scale) density of electronic states near an appropriate defect in a superconductor have been made. A variety of surface probes can measure, for example, the local electrostatic potential on a sample's surface with a resolution approaching 10 nm.

Figure 12-36b STM [view large image]

There are two distinct approaches to manufacture small-scale devices. Microelectronics starts with a large system and then divides it, reducing its dimensions by a variety of well-controlled methods. For example, shapes are printed onto the surface of silicon, which is then etched away to make microscopic wheels or micromotors. The smallest feature capability that can be achieved, appear to be around the 10 nm scale. Other methods work with individual atoms to make even smaller objects. An example of such large-scale preparation of high-quality materials is provided by the MBE (molecular-beam-epitaxy) method (Figure 12-36c), which can be used to grow individual lattice layers and extra-thin metallic layers.

Figure 12-36c MBE [view large image]

The graphite phase of carbon provides some interesting nano materials such as carbon nanotubes and buckyballs (Figrure 13-36d). Nanotubes are produced by rolling a layer of two-dimensional graphite, called graphene, into a hollow cylinder parallel to the z axis and having a nanmeter-scale diameter. Graphene is a poor conductor, but the nanotube becomes metallic or semiconducting depending on the details of how exactly the graphene sheet is wound and connected to itself. Spherical fullerene (buckyball) contains 60 or 70 carbon atoms in the soccerball-like crystal of about 1 nm across. As of the early 21st century, the chemical and physical properties of fullerenes are still under heavy study. Fullerenes are not very reactive due to the stability of the graphite-like bonds, and are also sparingly soluble in many solvents. The buckyball has been used to run tests on determining the boundary between classical and quantum domains since its size is close to the transitional zone. Scientists are also working on building very small structures such as the nanorobot (Figure 12-36d), which can check out a patient's blood cells. The microgears were made by etching silicon in the same way as a microchip. Sixty of them would fit on the head of a pin.

Figure 12-36d Nano Objects [view large image]

The Future of Chemistry

academic institutions. The strongly synthetic character of chemistry sets it apart from the "discovery" sciences such as physics, biology, astronomy and the Earth sciences. "Chemistry creates its object" as a French chemist wrote in 1860. The downside of this focus on making stuff is that chemists can be portrayed as inveterate tinkers - tweaking the molecular world to satisfy their curiosity, sometimes for fun and sometimes for profit. And it makes it especially hard to see where industrial chemistry ends and academic chemistry

Figure 12-37 Future of Chemistry [view large image]

begins. Recently in 2006, the Nature magazine asked many leading chemists what are the field's big questions. They have come up with six very important subjects in the arena of chemistry (Figure 12-37):

1. How do we design molecules with specific functions and dynamic?
2. What is the chemical basis of the cell?
3. How do we make the materials needed for the future, in energy, aerospace or medicine?
4. What is the chemical basis of thought and memory?
5. How did life on Earth begin, and how and where might it begin on other world?
6. How can we explore all the possible permutations of all the elements?

Table 12-08 Ten Priorities in Chemistry

Table 12-09 Ten Unsolved Mysteries in Chemistry

References:

1. Quantum Theory, Overview -- http://www.levity.com/mavericks/quantum.htm
2. Quantum Theory, more detail -- http://www.srikant.org/core/node12.html
3. Path Integral -- http://www.chem.unc.edu/lectures/2003Hermans/notes3/pathintegral.pdf
4. Schrodinger Equation -- http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schr.html#c1
5. Hydrogen Atom, Schrodinger Equation -- http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html#c2
6. Hydrogen Atom, Energy and Wave Functions -- http://www.kw.igs.net/~jackord/bp/i6.html
7. Covalent Bond, Hydrogen Molecule -- http://hyperphysics.phy-astr.gsu.edu/hbase/molecule/hmol.html
8. Ionic Bond -- http://207.10.97.102/chemzone/lessons/03bonding/mleebonding/ionic_bonds.htm
9. Hydrogen Bond -- http://207.10.97.102/chemzone/lessons/03bonding/mleebonding/hydrogen_bonds.htm
10. Molecular Orbitals -- http://www.chm.davidson.edu/ChemistryApplets/MolecularOrbitals/
11. van der Waals Force -- http://207.10.97.102/chemzone/lessons/03bonding/mleebonding/van_der_waals_forces.htm
12. Inorganic Compounds -- http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/compound.html#c2
13. Chemical Reactions -- http://boyles.sdsmt.edu/subhead/types_of_reactions.htm

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