Quantum Chemistry

Quantum ChemistryQuantum Chemistry

Dr. Ron RusayDr. Ron Rusay

Atomic Structure and Periodicity Electromagnetic Radiation The Nature of Matter The Atomic Spectrum of Hydrogen The Bohr Model The Quantum Mechanical Model of the Atom Quantum Numbers Orbital Shapes and Energies Electron Spin and the Pauli Principle Polyelectronic Atoms The History of the Periodic Table The Aufbau Principles and the Periodic Table Periodic Trends in Atomic Properties The Properties of a Group: The Alkali Metals

Quantum TheoryQuantum Theory Based on experimental observations of Based on experimental observations of

light and particleslight and particles Development progressed through rigorous Development progressed through rigorous

mathematical computationsmathematical computations It bridges physics and chemistry It bridges physics and chemistry It is described generally as quantum It is described generally as quantum

mechanicsmechanics

Electromagnetic RadiationElectromagnetic Radiation(“Light”)(“Light”)

Energy that exhibits wave-like Energy that exhibits wave-like behavior. behavior.

In a vacuum, electromagnetic energy In a vacuum, electromagnetic energy travels through space at the speed of light.travels through space at the speed of light.

It is described by the Electromagnetic It is described by the Electromagnetic Spectrum.Spectrum.

Nature of EM EnergyNature of EM Energy

Demonstrating Light’sDemonstrating Light’sWave NatureWave Nature

Frequency & Wave lengthFrequency & Wave length

WavesWaves http://chemistry.beloit.edu/BlueLight/waves/index.html http://chemistry.beloit.edu/BlueLight/waves/index.html

Waves have 4 primary characteristics:Waves have 4 primary characteristics: 1.1. WavelengthWavelength: distance between two : distance between two

peaks in a wave.peaks in a wave.

2.2. FrequencyFrequency: number of waves per : number of waves per second that pass a given point in space.second that pass a given point in space.

3.3. AmplitudeAmplitude: the height of the wave.: the height of the wave.

4. 4. SpeedSpeed: speed of light is 2.9979 : speed of light is 2.9979 10 1088 m/s. m/s.

WavesWaves http://chemistry.beloit.edu/BlueLight/waves/index.htmlhttp://chemistry.beloit.edu/BlueLight/waves/index.html

Focus on 2 of the primary characteristics:Focus on 2 of the primary characteristics: 1.1. Wavelength:Wavelength: distance between two distance between two

peaks in a wave.peaks in a wave.

2.2. Frequency:Frequency: number of waves per number of waves per second that pass a given point in space.second that pass a given point in space.

3.3. AmplitudeAmplitude: the height of the wave.: the height of the wave.

4. 4. SpeedSpeed: speed of light is 2.9979 : speed of light is 2.9979 10 1088 m/s. m/s.

Wavelength and frequencyWavelength and frequency

= = c c / / = frequency (s= frequency (s11)) = wavelength (m)= wavelength (m) c = speed of light (m sc = speed of light (m s11))

QUESTIONQUESTION

ANSWERANSWER 5 –

B) 4.12 10 s1

The smaller the frequency of light, the longer the wavelength.

Planck’s ConstantPlanck’s Constant

EE = change in energy, in J = change in energy, in J hh = Planck’s constant, 6.626 = Planck’s constant, 6.626 10 103434 J s J s = frequency, in s= frequency, in s11

= wavelength, in m= wavelength, in m cc = speed of light = speed of light

Ehhc = = νλTransfer of energy is quantized, and can Transfer of energy is quantized, and can only occur in discrete units, called quanta.only occur in discrete units, called quanta.

Planck’s Equation (Interactive)Planck’s Equation (Interactive)Ehhc = = νλ

Electromagnetic EnergyElectromagnetic Energy

EM SpectrumEM Spectrum : Chem Connections : Chem Connections http://chemistry.beloit.edu/Stars/EMSpectrum/index.htmlhttp://chemistry.beloit.edu/Stars/EMSpectrum/index.html

Energy and MassEnergy and Mass

Energy has massEnergy has mass

EE = = mmcc22

EE = energy = energy mm = mass = mass cc = speed of light = speed of light

Energy and MassEnergy and Mass”Duality””Duality”Ehcphoton = mhcphoton =

(Hence the (Hence the dualdual nature of light.) nature of light.)

Wavelength and MassWavelength and Mass

= wavelength, in m= wavelength, in m hh = Planck’s constant, 6.626 = Planck’s constant, 6.626 10 103434 J J ..s s

= kg m= kg m22 s s11

mm = mass, in kg = mass, in kg = frequency, in s= frequency, in s11

= hmde Broglie’s Equationde Broglie’s Equation

Atomic Spectrum of HydrogenAtomic Spectrum of Hydrogen

Continuous spectrumContinuous spectrum: Contains : Contains allall the wavelengths of light.the wavelengths of light.

Absorbtion vs.EmissionAbsorbtion vs.Emission http://chemistry.beloit.edu/BlueLight/pages/elements.htmlhttp://chemistry.beloit.edu/BlueLight/pages/elements.html

Line (discrete) spectrumLine (discrete) spectrum: Contains : Contains only some only some of the wavelengths of light. of the wavelengths of light.

http://chemistry.beloit.edu/BlueLight/pages/color.html

Absorption & Emission

Emissions: Flame TestsEmissions: Flame Tests

Electromagnetic EnergyElectromagnetic EnergyVisible Light / Color Visible Light / Color : ChemConnections : ChemConnections http://chemistry.beloit.edu/Stars/applets/emission/index.htmlhttp://chemistry.beloit.edu/Stars/applets/emission/index.html

The Perception of ColorsThe Perception of Colorshttp://chemconnections.org/organicchem227/227assign-06.html#vision

Atomic Emission Spectrum of HAtomic Emission Spectrum of H22

The Bohr ModelThe Bohr Model

EE = energy of the levels in the H-atom = energy of the levels in the H-atom z z = nuclear charge (for H, z = 1)= nuclear charge (for H, z = 1) nn = an integer = an integer

E = 2.178 10J (182−↔−zn/)2““The electron in a hydrogen atom moves around the The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.”nucleus only in certain allowed circular orbits.”

X X

The Bohr ModelThe Bohr Model

Ground StateGround State: The : The lowest possible energy state lowest possible energy state for an atom (n = 1).for an atom (n = 1).

Energy Changes in the Hydrogen Energy Changes in the Hydrogen AtomAtom

E = EE = Efinal statefinal state E Einitial stateinitial state = hcEΔ

Heisenberg Uncertainty Heisenberg Uncertainty PrinciplePrinciple

The more accurately we know a The more accurately we know a particle’s position, the less accurately we can particle’s position, the less accurately we can know its momentum or vice versa.know its momentum or vice versa.

Quantum Entanglement/SuperpositionQuantum Entanglement/SuperpositionSchrödinger’s Cat: Alive or Dead?Schrödinger’s Cat: Alive or Dead?

Can something be in two places at the same time?Can something be in two places at the same time?

In quantum microstates, YES.In quantum microstates, YES.

Science, 272, 1132 (1996)Science, 272, 1132 (1996)

Quantum Numbers (QN) for ElectronsQuantum Numbers (QN) for Electrons(Solutions for the Schrödinger Equation: (Solutions for the Schrödinger Equation: = = ) )

Where: Where: = Wave function = Wave function

1.1. Principal QN Principal QN ( integer ( integer nn = 1, 2, 3, . . .) : = 1, 2, 3, . . .) : relates to relates to sizesize and and energyenergy of the orbital. of the orbital.

2.2. Angular Momentum QN Angular Momentum QN ( integer ( integer ll oror )= 0 )= 0 to n to n 1) : relates to 1) : relates to shapeshape of the orbital. of the orbital.

3.3. Magnetic QN Magnetic QN (integer (integer m m l l oror mm = + l to = + l to l) : l) :

relates to relates to orientationorientation of the orbital in space of the orbital in space relative to other orbitals.relative to other orbitals.

4.4. Electron Spin QN : Electron Spin QN : ((mmss = + = +11//22, , 11//22) : relates ) : relates

to the to the spin state spin state of the electron.of the electron.

ElectronProbability = ||2

||2 = (double integral ofwave function )

““ORBITAL”:ORBITAL”:

Periodic Table ClassificationsPeriodic Table ClassificationsElectron Configurations & Quantum NumbersElectron Configurations & Quantum Numbers

Representative Elements Representative Elements (A (A Groups): Groups): s (l=0)s (l=0) and and p (l=1)p (l=1) (N, C, Al, Ne, (N, C, Al, Ne, F, O)F, O)

Transition ElementsTransition Elements: : d (l=2)d (l=2) orbitals orbitals (Fe, Co, Ni, etc.)(Fe, Co, Ni, etc.)

Lanthanide and Actinide Series Lanthanide and Actinide Series (inner transition elements): (inner transition elements): f (l=3) f (l=3) orbitals (Eu, Am, Es)orbitals (Eu, Am, Es)

Valence ElectronsValence Electrons

AtomValence ElectronsCa 2N 5Br 7Valence electrons are the outermost electrons in the Valence electrons are the outermost electrons in the highest principal quantum level of an atom. They are highest principal quantum level of an atom. They are found in the s- and p- orbitals and are the bonding found in the s- and p- orbitals and are the bonding electrons.electrons.

Inner electrons are called Inner electrons are called corecore electrons. electrons.

QUESTIONQUESTION

ANSWERANSWER

l n ml

B) 4

Orbitals are designated by m . For = 2, has four values.

QUESTIONQUESTION

ANSWERANSWER

l f l

A) 0

For n = 3, can be 0, 1, or 2. An orbital has an = 3.

Quantum Numbers : l, mQuantum Numbers : l, mll

Orbital Shape & OrientationOrbital Shape & Orientation

Magnetic Spin mMagnetic Spin mss

ElectronProbability = ||2

||2 = (double integral ofwave function )

Atomic OrbitalsAtomic Orbitals

See the following Web page:See the following Web page:

Identify the unknown orbitals by comparing Identify the unknown orbitals by comparing their shapes to the known orbitals and their shapes to the known orbitals and assign quantum numbers to each orbital.assign quantum numbers to each orbital.

http://chemconnections.org/general/chem120/atomic-orbitals/orbitals.html

Multi-electron AtomsMulti-electron AtomsElectron ConfigurationElectron Configuration

Aufbau PrincipleAufbau Principle As protons are added one by one As protons are added one by one

to the nucleus to build up the elements, to the nucleus to build up the elements, electrons are similarly added to these electrons are similarly added to these hydrogen-like orbitals.hydrogen-like orbitals.

Full electron Full electron configurationconfiguration(Spectroscopic (Spectroscopic notation) --->notation) --->

QUESTIONQUESTION

ANSWERANSWER

2

-

B) [Xe] 6s

[Xe] denotes a shorthand version of the electron configuration for Xe. Noble gas configurations are used to reduce writing time.

Pauli Exclusion PrinciplePauli Exclusion Principle

In a given atom, no two electrons In a given atom, no two electrons can have the same set of four quantum can have the same set of four quantum numbers ( numbers ( n, l, mn, l, ml l , m, mss ).).

Therefore, an orbital can hold only Therefore, an orbital can hold only two electrons, and they must have two electrons, and they must have opposite spins.opposite spins.

QUESTIONQUESTION

ANSWERANSWER

l ml – – –

C) 14

For = 3, = 3, 2, 1, 0, 1, 2, 3 and each of these orbitals can hold two electrons.

Hund’s RuleHund’s Ruleorbital diagramsorbital diagrams

The lowest energy configuration for an The lowest energy configuration for an atom is the one having the atom is the one having the maximum number maximum number of unpaired electrons of unpaired electrons allowed by the Pauli allowed by the Pauli principle in a particular set of degenerate principle in a particular set of degenerate orbitals.orbitals.

Orbital Diagram ->Orbital Diagram ->

Periodic Table ClassificationsPeriodic Table ClassificationsElectron ConfigurationsElectron Configurations

Representative Elements Representative Elements (A (A Groups): fill Groups): fill ss and and pp orbitals (Na, Al, Ne, orbitals (Na, Al, Ne, O)O)

Transition ElementsTransition Elements: fill : fill dd orbitals orbitals (Fe, Co, Ni)(Fe, Co, Ni)

Lanthanide and Actinide Series Lanthanide and Actinide Series (inner transition elements): fill (inner transition elements): fill 4f 4f and and 5f 5f orbitals (Eu, Am, Es)orbitals (Eu, Am, Es)

Valence ElectronsValence Electrons

AtomValence ElectronsCa 2N 5Br 7Valence electrons are the outermost electrons in the Valence electrons are the outermost electrons in the highest principal quantum level of an atom. They are highest principal quantum level of an atom. They are found in the s- and p- orbitals and are the bonding found in the s- and p- orbitals and are the bonding electrons.electrons.

Inner electrons are called Inner electrons are called corecore electrons. electrons.

QUESTIONQUESTION

ANSWERANSWER

E) none

Atoms in the same group have the same number of valence electrons. None of the sets of atoms have members all from the same group.

QUESTIONQUESTION

ANSWERANSWER

+ 2+ 2

B) K , Ca , Ar, S–

All of the species in an isoelectronic series must have the same number of electrons with the same electron configurations.

Two ways of showing the formation of lithium fluoride: LiF; [Li+ and F -]

using electron configurations & diagrams

QUESTIONQUESTION

ANSWERANSWER

–

E)

N ion has an extra electron that must be paired. It is isoelectronic with oxygen.

Paramagnetism & DiamagnetismParamagnetism & Diamagnetism Electron Configuration & Magnetic PropertiesElectron Configuration & Magnetic Properties

•Diamagnetic materials have all electrons Diamagnetic materials have all electrons paired and are not attracted to a magnetic paired and are not attracted to a magnetic field.field.

•Paramagnetic materials have unpaired Paramagnetic materials have unpaired electrons and the magnetic attraction electrons and the magnetic attraction (magnetism) is generally proportional to the (magnetism) is generally proportional to the number of unpaired electrons. (Note: not all number of unpaired electrons. (Note: not all metals follow this rule.) metals follow this rule.)

Electron DiagramsElectron Diagrams Magnetic Properties Magnetic Properties

#1 = #1 = HH22O(l)O(l) # 2 = # 2 = FeFe22OO33(s)(s) # 3 = # 3 = FeO(s)FeO(s) #4= #4= Fe(s)Fe(s)

Transition Metal Ions (B Groups) Transition Metal Ions (B Groups) Oxidation Numbers (States)Oxidation Numbers (States)

Isoelectronic atoms and ions have the same electron configurations

Apparatus Used to Apparatus Used to Measure Measure ParamagnetismParamagnetismNOTE: NOTE: OO22 is is

paramagnetic, Nparamagnetic, N22 is is

not! Also, not! Also, Ferromagnetic Ferromagnetic effects are much, effects are much, much stronger than much stronger than ParamagneticParamagnetic

Electron DiagramsElectron Diagrams Magnetic Properties Magnetic Properties

•Ground state configurations of nitrogen (N) and oxygen (O) Ground state configurations of nitrogen (N) and oxygen (O) have 3 and 2 unpaired electrons in their electron diagrams have 3 and 2 unpaired electrons in their electron diagrams respectively, what can be going on in the video? respectively, what can be going on in the video? •Ground state diagrams do work very well for the Transition Ground state diagrams do work very well for the Transition metals but not many others because of bonding, which metals but not many others because of bonding, which forms pairs of electrons. forms pairs of electrons. (molecular orbitals vs. atomic (molecular orbitals vs. atomic orbitals)orbitals).Eg. water, nitrogen and oxygen..Eg. water, nitrogen and oxygen.

Molecular Orbital DiagramsMolecular Orbital Diagrams

Summary: Information from the Summary: Information from the Periodic TablePeriodic Table

1.1. Can obtain Group A valence electron Can obtain Group A valence electron configurationsconfigurations

2.2. Can determine individual electron Can determine individual electron configurations.configurations.This information can be used to:This information can be used to:

a.a. Predict the physical properties and Predict the physical properties and general chemical behavior of the elements.general chemical behavior of the elements.

b.b. Identify metals and nonmetals. Identify metals and nonmetals.