Atoms spring-like bond

IR absorption (or Raman shift) is caused by a quantum transition between two energy levels, and so band positions ought to be defined in terms of energy units. However, atoms can be treated as oscillating under the influence of spring-like bonds obeying Hooke s law, so the terms vibration and vibrational frequency are habitually used. The vibrational frequency is considered to be equal to the frequency of absorbed radiation (or frequency difference in the... 

A polyatomic molecule, such as a sugar, may be regarded as a system of masses joined by bonds having spring-like properties. The vibration of each of the masses (atoms) can be resolved into components parallel to the x, y, and z axis of a Cartesian system of coordinates. This means that each atom has three degrees of freedom, and a system of N nuclei has 3 N... 

The atoms in a molecule vibrate and the bonds between the atoms act like springs. A given molecule has a specific set of vibrational frequencies, which are in the same range as the IR frequencies of electromagnetic vibration. 

In a classical picture, a molecule is often seen as collection of N atoms, connected by chemical bonds that are formed by light electrons orbiting the heavy atomic nuclei. The particular geometrical configuration of the molecule is determined by type and character of the chemical bonds, which are seen as spring-like elastic connections between the atoms, and the kind of atoms involved. As a consequence of the elasticity of the inter-atomic bonds, the molecule can vibrate, i.e., the atoms can perform periodic motions relative to each other. Within a harmonic approximation, these vibrations can be expressed as superpositions of A — 6 (A — 5 for linear... 

The forces which hold atoms together (the interatomic bonds) which act like little springs, linking one atom to the next in the solid state (Fig. 4.1). 

As we showed in Chapter 4, atoms in crystals are held together by bonds which behave like little springs. We defined the stiffness of one of these bonds as... 

Mathematically, the movement of vibrating atoms at either end of a bond can be approximated to simple-harmonic motion (SHM), like two balls separated by a spring. From classical mechanics, the force necessary to shift an atom or group away from its equilibrium position is given by... 

In ball-and-stick models, balls with holes drilled at appropriate angles are used to represent the atoms, and sticks or springs are used for the bonds to link them. The resultant model is rather like the framework model, but has representations of the atoms. Models tend to look better than the framework type, but in practice tend to be bigger and less user friendly. 

The equations above assume that only one end of the spring moves. If both ends can move (as will happen if, for example, the spring is really a chemical bond connecting two atoms with similar masses m i and m ) the expression becomes slightly more complicated. If all we are interested in is the relative motion of the two masses, the solutions looks exactly like Equations 3.21 to 3.23 with the mass replaced by // = OT1OT2/(ni + m2). 

The atoms of a covalent bond never sit still, even at absolute zero. They are constantly vibrating, somewhat like balls connected by springs. The energies of the vibrations, like all energies on a molecular scale, are quantized. At room temperature, most molecules are in the lowest vibrational energy level. The separation between the energy levels... 

AC — D (carbon-deuterium) bond is electronically much like a C — H bond, and it has a similar stiffness, measured by the spring constant, k. The deuterium atom has twice the mass (m) of a hydrogen atom, however. 

In a diatomic molecule, the masses mv and m2 vibrate back and forth relative to their centre of mass in opposite directions, as shown in the following figure. The two masses reach the extremes of their respective motions at the same time. The diatomic molecule has only one vibrational degree of freedom, i.e., it has only one frequency, called the fundamental vibrational frequency. During vibrational motion, the bond of the molecule behave like a spring and the molecule exhibits a simple harmonic motion provided the displacement of the nuclei from the equilibrium configuration is not too much. At the two extremes of motion which correspond to extension and compression of the chemical bond between the two atoms, the potential energy is maximum. On... 

As we have seen, a molecule can be approximated as a collection of atoms held together by bonds. In describing the vibrations in a molecule, we can compare the bond between a given pair of atoms to a spring attached to two masses. As the atoms move apart in a vibrational motion, the bond—like a spring—provides a restoring force that pulls the atoms back toward each other. 

Covalent bonds are not static. They are more like springs with weights on each end. When two atoms are bonded to each other, the bond stretches back and forth. When three or more atoms are joined together, bonds can also bend. These bond stretching and bending vibrations represent the different vibrational modes available to a molecule. 

Even where the promotion is to a lower vibrational level, one which lies wholly within the E2 curve (e.g., Vi or V2), the molecule may still cleave. As Fig. 7.2 shows, equilibrium distances are greater in excited states than in the ground state. The Franck-Condon principle states that promotion of an electron takes place much faster than a single vibration (the promotion takes 10 s a vibration 10 s). Therefore, when an electron is suddenly promoted, even to a low vibrational level, the distance between the atoms is essentially unchanged and the bond finds itself in a compressed condition like a pressed-in spring this condition may be relieved by an outward surge that is sufficient to break the bond. 

A covalent bond is more like a flexible spring than a rigid ruler, because the atoms can vibrate back and forth. 

Bonds between atom-like partieles are viewed as springs. 

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