330 terms Flashcards
Normalization
Finding A (amplitude) of a soln to the Schrodinger equation since the sum of all the probabilities must be equal to 1
Zeeman effect
Describes how the energy of an electron changes in the presence of an electric field
What does m quantum number refer to ?
Magentic property
Hartree Fock approximation aka orbital approximation
Mathimatically assumes that each electron has its own wavefunction and that the total wavefunction is a seperable product of inidividual wavfunctions
Issues with HF approx
HF ALWAYS overestimates energy!
Zero point energy
The zero point energy is the ground state energy for the harmonic oscillator E=h(nu). Given the uncertainty principal , if E=0 here, then there would be certain position and certain momentum (since velocity=0).
Postulate 1 of Quantum mechanics
All the info ab a quantum mechanical system is contained in the wavefunction
psi is an indepterminate model (psi cannot predict the future)
Postulate 2 of Quantum mechanics
Every observable in classical mechanics corresponds with a linear operator
a linear operator is distributive
psi must be single valued,continuous, finite,
(end behavior that gpes to zero)
Postulate 3 of Quantum mechanics
Any measurement associated with an observable associated with the operator A, only values that can ever be observed are the eigenvalues from A psi =a psi
Postulate 4 of Quantum Mechanics
The average value for any observable is <a>= (integral over all space) psi (complex conj) * Ahat * psi</a>
If you constrain a wave you get
Quantized states! can on get interger values of full wavelengths that fit between 2 points.
What to orbitals represent?
Probabilites that you find an electronin an area in space
A typical molecule has ___ degrees of freedom
3N-6 internal (vibrational degrees of freedom)
Anharmonicity
asymetric potential
Pauli principal arrise from 2 properties of e-
1) electrons are indistinguisable
2) electrons are
Born Oppenhiemer approximation
electrons treat nuclei as frozen and fixed
nuclei see electrons as delocalized
this assumption allows us to multiply electron energy and nuclear energy
Define Hermitian
Hermitian means A operator operating on complex conjugate is equal to A operating on the function
Eigenfunctions of the Hermitian operator
MUST be real (not imaginary) because all obeservables are observable
Commutator
When 2 operators commute they can be simultaneously defined for a system
Orthogonal definition
Independent or not overlapping,
can use symmetry argument:
Why wavelength and frequency inversely related?
Frequency quantifies the energy per photon
(we could also increase the number of the photons)
Photoelectric effect
Ephoton= threshold energy + KE (0.5 mv^2)
de Broglie wavelength
=h/p=h/mv
we can determine the wavelength of a piece of matter
How does treating matter as wave lead to quantized states ?
Because you contrain a wave such that interger values of the wavelength exist between 2 points
Uncertainty for PIB
position
momentum
Linear operators
Position : x(hat)= x
Momentum: p(hat)=-ih(bar) d/dx
Kinetic Energy: T(hat)= -h^2/2m d^2/dx^2
Energy: Hamiltonian
Resonance criteria
If energy of light wave matches the frequency of chemical processes (spacing of energy levels), then the light can be absorbed
Limitation of PIB (from pset)
-the repulsion of other electrons in the system
-ignores nuclei
-finite walls (molecule can be oxidized)
EM spectrum
low E
radiowave (excites spin)
microwave (excites rotations)
IR (excites molecular vibrations and nuclear motions)
Vis/Uv (excites electrons)
high E
Postulate 4 QM
average value is the integral (over all space) of psi* A psi
Postulate 5 QM
Time independent Schrodinger equation
All Qm operators must be
Hermitian
Eigenfunctions of any hermitian operator must be
orthogonal
Tunneling region
Intersection of V(x) and the eigenstate, particle can “jump” over an energy barrier
Vibrational degrees of freedom
3N-6 for to specify the conformation of bc we subtract away rotations and traslations that don’t change bond length
Transition states
Most unstable, 3N-7 degees of freedom
force constant is negative, and so there is an imaginary frequency meaning that the molecule cannot oscillate, so that it cannot feel a restoring force and so a slight distruption to the bond pushes the molecule to fall to stable product
Rigid Rotor
answers following question: what are the likely angular rotations of a diatomic molecule
Assumptions of RR model
-Fixed bond length and so as a result mass is constrained to live somewhere on a 2D surface of a sphere
-center of mass coordinates
order of magnitude for visible light spectrum
400nm-700nm
Frequencies of visible light
10^-14 to 10^-15
I (moment of inertia)
I= μR^2
Reduced mass
m1*m2/(m1+m2)
Frank Condon Principal
Over the course of excitation, nuclei do not move
Microwave spectrum (rotational energy) features
-regularly spaced CHANGE in energy levels
-gap in middle- fundemental frequency
-R- branch peaks closer together than P branch (positive delta J) peaks
Angular momentum (Lx, Ly, Lz) and L^2)
Can only define one component at a time(carves out curve of uncertainty)
ONE exception to this is when L^2 is zero- then each component is zero but for the uncertainty prinicpal to be met ther must be uncertainty in postion (spherical so knoe r but could be anywher on the surface)
Only model with regularly spaced energy levels?
The 1D harmonic oscillator
Why HF a not great approximation?
e- are moving to the average of the other postion (lots of unceratinty) so HF is always an over approximation
Average position of PIB graphically?
Where psi squared is symmetric
Can superpostion for H atom have well defined energy?
Yes- in the case of degereracy- ex psi 200 and psi 211 , both have the same energy
