If the molecule has more than two atoms, then things get more complicated. Suppose just one more atom is added so now there are three atoms like in water HO where the two hydrogen atoms are both attached to the central oxygen atom. Remember with hydrogen there was one kind of stretching, but in water there are two kinds of stretching and four other kinds of vibration called bending vibrations as shown below.
The atoms in a CH group or molecules like water can vibrate in six different ways: symmetric and antisymmetric stretching, scissoring, rocking, wagging and twisting:
symmetric stretching: when the two attached atoms move away and toward the central atom at the same time.
antisymmetric stretching: When the two attached atoms do not move away and toward the central atom at the same time.
scissoring: Just like the name says scissoring is when the two atoms move away and toward each other
rocking: This motion is like a pendulum on a clock going back and forth only here an atom is the pendulum and there are two instead of one.
wagging: If a person holds up their hand in front of them and puts there two fingers in a "V" sign and bend there wrist toward and away from them. Here the tips of the fingers are the attached atoms and the wrist is the central atom.
twisting: This motion is like a person is walking on a treadmill where their waist is the central atom and their feet are the two attached atoms
Molecules with more than three atoms are even more complicated and have even more vibrations which are sometimes called "vibrational modes". Each new vibrational mode is basically a different combination of the six shown above. The more atoms in the molecule the more ways they can be combined. For most molecules with N atoms the number of possible vibrations for that molecule is 3N - 6 while linear molecules, or molecules with there atoms in a straight line, have 3N-5 vibrational modes.
Using Newtonian mechanics the vibrations of a molecule can be calculated by treating the bonds like springs. This is useful because like a spring, a bond requires energy to stretch it out and it also takes energy to squeeze it together. The energy needed to stretch or squeeze the bond is dependent on the stiffness of the bond, which is represented by the "spring constant" k, and the reduced mass, or "center of mass" of the two atoms attached to either end denoted by "μ". The formula used to relate the energy needed to cause a vibration in the bond is:
"h": is planck's constant
ν: is frequency and represents the rate at which the bond is squished together and pulled apart again. The larger ν the faster this rate becomes.
Ε: is the energy required to push and pull the bond together.
"μ": The reduce mass is the two masses of the atoms multiplied together and divided by their addition:
Using quantum mechanics, the formula that describes the spring is exactly the same as the Newtonian mechanics version except only certain energies or energy levels are allowed. Think of the energy levels as steps on a ladder where a person can only go up or down one rung at a time. Just as that person can't stand on the space between rungs so the bond can not have an energy between energy levels. This new formula becomes:
where "n" is a quantum number or "energy level" that can take values of 0, 1, 2 ...
The statement that energy levels can only go up or down one level at a time is known as a selection rule which states that the only allowed transitions between energy levels are:
where \Delta n is the energy transition.
When light of a certain frequency hits a molecule that has a vibration whose motion corresponds to the same frequency then the light gets absorbed into the molecule and the energy from the light causes the bonds to move in that specific vibrational motion. By checking for light that gets absorbed, scientists can tell if a certain kind of molecular bond is there and match it against a list of molecules that have that bond.
However, some molecules like helium and argon have only one atom and don't have any bonds. This means that they won't absorb any light in the same way a molecule with more than one atom can.
The specific fields of chemistry that use molecular vibrations in their studies include infrared spectroscopy (IR) and Raman spectroscopy (Raman) with IR being more widely used and having three subfields of its own. These subfields are known as Near IR, Mid IR and Far IR spectroscopy. The following is a general list of these fields and real world applications
Near IR: quantitative determination of species such as proteins, fats, low low-molecular-weight hydrocarbons and water. Further use is obtained in the agricultural products, food, petroleum and chemical industries
Mid IR:The most popular of the IR fields, is used in determining structure of organic and biochemical compounds.
Far IR: this field is less popular though it has found uses in inorganic studies
Raman: Is used for the qualitative and quantitative study of inorganic, organic and biological systems often as a complimentary technique to IR.
Four Asian Tigers
The Four Asian Tigers or Asian Dragons are the highly developed economies of Hong Kong, Singapore, South Korea and Taiwan. These regions were the first newly industrialized countries. They are known because they had very high growth rates (they became rich very fast) and fast industrialization between the early 1960s and 1990s. Four economies are currently well rich economies (developed countries).
All four Asian Tigers have a highly educated and productive work force compared to others in the region.
The economic success of South Korea and Taiwan were known as the "Miracle on the Han River" and the "Taiwan Miracle" respectively.
The four tigers has accomplished rapid economical growth in a short period of time.
All the Asian Tigers tried to export (sell) products to rich industrialized nations. They grew rich very quickly (they had double-digit economic growth) for decades. Each nation was not a democracy, and people were not very free in the early years. All of these countries later became freer, and people now think Taiwan and Korea are liberal democracies.
BRICS
BRICS is used to talk about the countries of Brazil, Russia, India, China and South Africa. Many economists think that all these countries are at a similar stage of economic development. When people write about these countries, they usually write "BRICS" or the "BRICS countries".
The acronym was invented by Jim O'Neill, an economist who worked for Goldman Sachs. In 2001, he wrote an article that he called "Building Better Global Economic BRICs".
Mexico and South Korea were the only other countries with economies that are like the BRICs. But O'Neill did not include these countries because they were considered already more developed, as they were already members of the OECD.
Shih Tzu
The Shih Tzu is a breed of dog weighing with long silky hair. The breed originated in China and is among the earliest breeds. Shih Tzu were officially recognized by the American Kennel Club in 1969
The Shih Tzu has a short muzzle and big, brown dark eyes. They have a silky, very long double coat. Some other Shih Tzu have shorter, more curly hair. ([Wikipedia Shih Tzus] Their fur comes in many colors.
These dogs are tiny, but they have a big personality. They are known for being affectionate, playful, and happy. They want to be your best friend. This tiny pup loves attention and is a perfect companion dog. If you are feeling sad, or need a hug, the Shih Tzu will always fluff you down with puppy hugs and kisses. [akc.org Shih Tzu] This dog requires a lot of attention, due to their connections to royalty.
The Shih Tzu is a good quality dog because of the shiny, welll groomed, silky coat and the Chinese valued Shih Tzu the most. [Wikipedia Shih Tzus] The coat colors come in light brown, black, white, black and white, black and gold, white and gold, dark brown, gold, red and black, and brown and white.