Molecular physics: study of physical properties of molecules and molecular dynamics.
Areas: physical chemistry, chemical physics and quantum chemistry.
Experiments techniques: spectroscopy and scattering.
Bohr model:
Energy levels of electrons with different distance from nucleus. (n - quantum number)
Electron can absorb photon and change the own level. For example from 2 to 3
if electron return from 3 to 2 it emmit new photon.
En = -hc * R * Z2/n2
En - energy of electron
h,c -Plank constant, Light speed constant
R - Rydberg constnat
Z - atomic number
n - quantum number
E = hν = hc/λ
=> ΔE = 1 / λ = RZ2 (1/n12 - 1/n22)
n2 - electron from (initial, begins)
ΔEelectron = Ephoton
Occupied orbitals (l - quantum
number)
s orbital : l = 0
p orbital : l = 1
d orbital : l = 2
f orbital : l = 3
l = 0, 1 , 2 , ... , n - 1
* all orbitals with included ( n - 1)
if n = 3; => l = 0, 1, 2
ml= -l ... l - specific orbital
if l = 2
ml = -2, -1, 0, 1, 2
ms - spin number +1/2 οr -1/2
To write electronic
configuration - Aufbau principle:
s - 2 electrons maximum
p - 6
d - 10
f - 14
Hunds rule can show magnetic properties
Also Pauli's principle, Hunds rule
Molecular Orbital Theory
Bonding orbitals
*when waves interfere constructively, the amplitude increases where they overlap
* when wavefunctions interfere desctructively the amplitude decreases
Valence bond theory
Bonds result from the pairing of unpaired electrons from valence shell atomic orbitals
H(1 e) + H(1 e) = H2
*promotion of electrons occurs cuz it would increase the number of unpaired electrons
*two p - orbitals forming a π - bond
Motion associated with rotational and vibrational energy levels within a molecule. Different rotational and vibrational levels correspond to different rates of rotation or oscillation.
In general, the goals of molecular physics experiments are to characterize shape and size, electric and magnetic properties, internal energy levels, and ionization and dissociation energies for molecules. In terms of shape and size, rotational spectra and vibrational spectra allow for the determination of molecular moments of inertia, which allows for calculations of internuclear distances in molecules. X-ray diffraction allows determination of internuclear spacing directly, especially for molecules containing heavy elements. All branches of spectroscopy contribute to determination of molecular energy levels due to the wide range of applicable energies (ultraviolet to microwave regimes).
PSI function
Ψ*(operator)Ψ - sort of a dot product
Ψ*Ψ = |Ψ|2
Probability of existance in x: <Ψ|x| Ψ>
to describe orbitals Ψnlm(r, Θ, φ)
n - shell (energy level)
l - subshell (shape of orbital)
m - orbital orientation (specific orbital)
3D shape (r, Θ, φ):
Ψnlm( r, Θ, φ) = Rnl(r) * Ylm( Θ, φ)
Rnl(r) - radial Ψ
Ylm( Θ, φ) - angular Ψ
Z - for hydrogen arom is 1
* white lines(and red) on plots are Nodes, no probability
* RPD - radius probablity density
Valency: how many electrons on the last shell(on highest energy level)
When bond is creatings - release of energy, usually to heat.
When bond is destroyings - need energy to make it.
bond energies possible to find by enthalpy and in the tables
But:
When the two 1s wave functions combine out-of-phase, the regions of high electron probability do not merge. In fact, the orbitals act as if they actually repel each other. Notice particularly that there is a region of space exactly equidistant between the nuclei at which the probability of finding the electron is zero(nodal surface).
We see, then, that whenever two orbitals, originally on separate atoms, begin to interact as we push the two nuclei toward each other, these two atomic orbitals will gradually merge into a pair of molecular orbitals - σ orbital.
Carbon has four outer-shell electrons, two 2s and two 2p. For two carbon atoms, we therefore have a total of eight electrons, which can be accommodated in the first four molecular orbitals. The lowest two are the 2s-derived bonding and antibonding pair, so the “first” four electrons make no net contribution to bonding. The other four electrons go into the pair of pibonding orbitals, and there are no more electrons for the antibonding orbitals— so we would expect the dicarbon molecule to be stable, and it is.
The electron configuration of oxygen is 1s22s22p4. In O2, therefore, we need to accommodate twelve valence electrons (six from each oxygen atom) in molecular orbitals. As you can see from the diagram, this places two electrons in antibonding orbitals. Each of these electrons occupies a separate π* orbital because this leads to less electron-electron repulsion (Hund's Rule).
Check existing:
He2 : 1/2 ( 2 - 2) = 0 no bond ( 2 - bonding electrons, 2 - antibonding electrons)
H2 : 1/2 ( 2 - 0) = 1 bond ( 2 - bonding electrons, 0 - antibonding electrons)
more order more stable
Hartree-Fock method
self-consistent field method (SCF)
the Hartree equation as an approximate solution of the Schrödinger equation
Hamiltonian for NZ
Hartree idea:
Hartree's trial wave function is a product of single particle orbitals, one for each electron.
h - here position and momentum of particle i ( approximation )
d3r - triple integral
*
Because of symmetry:
Add Lagrange multiplyer to normalize function:
Эλ - Lagrange multiplyer
The Hartree equations (33) have the form of a set of pseudo-Schr¨odinger equations for the orbitals uλ(r), in which the Lagrange multiplier эλ plays the role of an eigenvalue. The potential energy includes the potential of the nucleus, −Z/r, as well as the potential Vλ(r). The latter is physically the electrostatic potential produced at field point r by the charge clouds of all the other orbitals µ 6= λ, as may be seen from Eq. (34). The exclusion of the orbital λ from this sum is what makes the sum depend on λ; the electron with orbital λ is not acted upon by its own charge cloud.
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