Interference orbitals

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2 but m somewhat different ways Both assume that electron waves behave like more familiar waves such as sound and light waves One important property of waves is called interference m physics Constructive interference occurs when two waves combine so as to reinforce each other (m phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2 2) Recall from Section 1 1 that electron waves m atoms are characterized by their wave function which is the same as an orbital For an electron m the most stable state of a hydrogen atom for example this state is defined by the Is wave function and is often called the Is orbital The valence bond model bases the connection between two atoms on the overlap between half filled orbifals of fhe fwo afoms The molecular orbital model assembles a sef of molecular orbifals by combining fhe afomic orbifals of all of fhe atoms m fhe molecule... 

The characteristic feature of valence bond theory is that it pictures a covalent bond between two atoms in terms of an m phase overlap of a half filled orbital of one atom with a half filled orbital of the other illustrated for the case of H2 m Figure 2 3 Two hydrogen atoms each containing an electron m a Is orbital combine so that their orbitals overlap to give a new orbital associated with both of them In phase orbital overlap (con structive interference) increases the probability of finding an electron m the region between the two nuclei where it feels the attractive force of both of them... 

To improve our model we note that s- and /7-orbitals are waves of electron density centered on the nucleus of an atom. We imagine that the four orbitals interfere with one another and produce new patterns where they intersect, like waves in water. Where the wavefunctions are all positive or all negative, the amplitudes are increased by this interference where the wavefunctions have opposite signs, the overall amplitude is reduced and might even be canceled completely. As a result, the interference between the atomic orbitals results in new patterns. These new patterns are called hybrid orbitals. Each of the four hybrid orbitals, designated bn, is formed from a linear combinations of the four atomic orbitals ... 

FIGURE U5 When two ls-orbitals overlap in the same region of space in such a way that their wavefunctions have the same signs in that region, their wavefunctions (red lines) interfere constructively and give rise to a region of enhanced amplitude between the two nuclei (blue line). 

In molecular hydrogen, where we are building LCAO-MOs from two atomic orbitals, we expect two molecular orbitals. In the second molecular orbital, the two atomic orbitals interfere destructively where they overlap. This orbital has the form... 

Molecular orbitals are formed by combining atomic orbitals when atomic orbitals interfere constructively, they give rise to bonding orbitals when they interfere destructively, they give rise to antibonding orbitals. N atomic orbitals combine to give N molecular orbitals. 

Quite generally, we will find that the magnitude and direction of these chiral dissymmetries varies greatly with both electron energy and initial orbital. The prediction or interpretation of such characteristics falls beyond the capability of the simple, intuitive analogy presented in II.B.l, so that we must now turn to consider the quanmm interference effects that control the observable distributions in order to enhance our predictive abilities. A reader wishing to pass over these details at first encounter will find a summary of the deductions made at the start of the subsequent Section, IV. 

In the expressions for the BED and BEB cross sections for each orbital the first log term represents large impact parameter collisions dominated by the dipole interaction. The remaining terms represent low-impact parameter collisions, described by the augmented Mott cross section. The second log function describes interference between direct and exchange scattering which is included in the Mott cross section. 

Electronic factors related to orbital overlap also appear to interfere significantly in the dynamics of concerted electron transfer/bond breaking reactions in donor-spacer-cleaving acceptor systems.94... 

De Broglie s work clearly shows that a moving electron can be considered as a wave. If it behaves in that way, a stable orbit in a hydrogen atom must contain a whole number of wavelengths, or otherwise there would be interference that would lead to cancellation (destructive interference). This condition can be expressed as... 

In order to reveal the mechanism of this molecular half-adder, the T(E) spectra of the molecule are presented in Fig. 26b. When perpendicular to the plane of the molecule, each NO2 contributes a very sharp resonance which does not participate in the overall conductance. When rotated by 90°, an NO2 introduces a supplementary resonance in the gap of the molecule. Due to its asymmetrical delocalization over the atomic orbitals, this resonance increase the conduction between the drive and the XOR electrode, but not between the drive and the AND electrode. This insures a 1 output for the former and a 0 for the latter. When the two NO2S are rotated, the two resonances they introduce create a deep interference between the drive and the XOR electrode. Located on the Fermi energy of the molecule, this interference leads to a low conductance state and a 0 logical output for the XOR gate. In contrast, the two resonances do not interfere destructively between the drive and the AND electrode, leading to a high conductance state and a 1 logical output. 

According to De Broglie an electron in a Bohr orbit is associated with a standing wave. To avoid self destruction by interference an integral number of wavelengts are required to span the orbit of radius r, which implies n — 2nr, or nh/2n = pr, which is the Bohr condition. As a physical argument the wave conjecture is less plausible, but not indefensible. One possible interpretation considers the superposition of several waves rather than a single monochromatic wave to simulate the behaviour of a particle. 

In Sect. 4.3, we discussed the role of ionization potential in harmonic phase Ip [8,11], As the geometric structures of the atomic or molecular valence orbitals should give additional effects to the harmonic phases [26,55], by measuring the harmonic phases as well as intensities from a pair of atoms and/or molecules with the same Jp such as H2-D2 [12], N2-Ar, and CO2-KX [12,30], the net effects due to the structures of them and their dynamics can be extracted [11] (Fig. 4.5). The main advantage of the present method, which we call heterodyne interferometry, is that it makes use of the interference of harmonics, and faint signals from the dynamics in the atoms and molecules can be observed. 

A further approach to correction for broad band interference utilizes the Zeeman effect. Under the effect of a strong magnetic field atomic orbitals can be split into sets with energies higher or lower than the original. The orbitals responsible for the broad band absorption remain largely unaffected. 

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