Lec4Org Chem CCB1013 Alkanes Start May 2011

8/3/2019 Lec4Org Chem CCB1013 Alkanes Start May 2011

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Chapter 1

Atomic structure

Q,E~3 -10 eV...

Nucleus

E1

E2 K, ... x-rays

Auger electrons,

Fluorescence

Gamma-rays

Emission

of photonswith deexcitationof atom

Absorptionof photonswith excitationof atom

Interaction of nucleus

with closest electrons

h = E2 - E1


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Chapter 1

Quantum numbers. Atomic Orbitals

l = 0

ml= 0

ms=+-1/2

l = 0

ml= 0

ms=+-1/2

l = 1

ml= -1 ms

=+-1/2

l = 1

ml= 0

ms=+-1/2

l = 1

ml= +1 ms=+-1/2

l = 0 l = 1 l = 1 l = 1 l=2 l=2 l=2 l=2 l=2

n = 1

3 2 1

n = 2

n = 3

S-orbital

p-orbitals

d-orbitals


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Chapter 1

-

+

+-+

+/-

+/-

+/-

Quantum numbers.

Atomic Orbitals


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Chapter 1

Orbital Filling( 3 Rules)

Electron configurations can be determined using a periodic table and by considering the followingas a guide to how the electrons "fill-up" the orbitals:

Aufbau (Building-Up) Principle. Electrons are placed into the atomic orbitals from lowest to highest

energy. The order of these orbitals is determined using the Schrodinger equation and can be easilydetermined by looking at the periodic table or using a simple mnemonics:

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p etc......

Hund's rule of Maximum Multiplicity. When degenerate orbitals are being filled, single electrons areplaced into each degenerate orbital before they are paired with another electron in the same orbital:

Pauli Exclusion Principle. No two electrons in a atom can have the same four quantum numbers.This means that only two electrons are allowed in the same orbital, and then they have oppositespin, +1/2 and -1/2.

Important distinction:Valence Electronsare the electrons which are involved in bonding between atoms. They possessthe highest energy and are referred to as the 'outermost' electrons.

Core electronsare electrons that under 'normal' reaction conditions are chemically inert. They arethe electrons of an atom which are located in the completely filled energy levels.

1s2s

2p


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The wave description of light describes the effect that thelight has on the space around it. This effect is to generate anoscillating electric and magnetic fields. These fields can vary

in intensity, which is reflected in varying brightness of light.

Photon as wave packet Electron?

wave

bullet = particle

bullet-proof glass


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The De Broglie Hypotesis

After de Broglie we associate behavior of electron with that of photonEphoton = hv (v = c/)

Einsteins special theory of relativity gives the photon energy as Ephoton = mc2

and for photon = h / mc ( impulse, p, of photon is p=mc )

By analogy, de Broglie proposed that a material particle with mass m and speed v wouldhave a wavelength given by = h / mv

(NOTE, that mv = p, where p is the particles momentum). For electron moving in atom with a speed 1.0 x106 m/s we obtain6.6x10-34 J s

= ------------------------------------------------------------ = 7x10-10 m = 7 A( kg 9.1x10-34 kg ) ( 1.0 x 106 m/s )

For macroscopic particle of mass 1.0 g moving at 1.0 cm/s = 7x10-29 m = 7x10-19 Aand quantum effects are unobservable for the motion of macroscopic objects.


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Chapter 1

Electron Probability Density (EPD)How to calculate the probabilityof findingan electronof atom or molecule in the

elementary box dxdydz located at the point x,y,z, with radius vector r(x,y,z)dxdydz ?

The EPD r(x,y,z) can be calculated theoretically from the electronic wave

function, e byintegrating |e|2 over the spin coordinates of all electrons and

over the spatial coordinates of all but one electron and multiplying the result by

the number of electrons in the molecule.

The EPD r(x,y,z) can be also found experimentally by analyzing x-ray diffraction

data of crystals. The EPD calculated from WF agrees well with experimentallydetermined densities.

z

dxdy

dz

x

ynucleus

electron


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Chapter 1

Schrdinger wave equation

The Schrdinger equation is the fundamental equation of physics fordescribing quantum mechanical behavior. It is also often called the

Schrdinger wave equation, and is a partial differential equation thatdescribes how the wave function of a physical system evolves over time.The time-dependent one-dimensional Schrdinger equation is given by

(3)

F= mad2rF = m ------ ,dt2

F = m(d2x/dt2) if one-dimensional

Heisenberg, 1927.

x px0 y py 0 z pz 0


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Chapter 1

General formula for Hydrogenlike Wave Functions(r,,)=Rnl (r) Ylm(,)

Radial part, anassociatedLaguerre function

Angular factor,

spherical harmonic

x

z

y

+Ze

-e

1s(1,0)(r,,) = (1/)1/2(Z/a0)

3/2e-Zr/a0

R(1,0) = (Z/a0)3/22e-Zr/a0

The ground-state WF of hydrogen atom,

ra0=the Bohr radius = 0.529A

Y0,0(,) = (1/4)1/2


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Chapter 1

2s(2,0)(r,,) = (1/4)(1/2)1/2(Z/a0)

3/2(2 Zr/a0 ) e-Zr/2a0

2pz(2,1,m=0)(r,,) = (1/4)(1/2)1/2(Z/a0)

5/2r e-Zr/2a0 cos

2px(2,1,m=+1)(r,,) = (1/4)(1/2)1/2(Z/a0)

5/2r e-Zr/2a0 sin cos

2py(2,1,m= -1)(r,,) = (1/4)(1/2)1/2(Z/a0)

5/2r e-Zr/2a0 sin sin


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Chapter 1

Pr (a x b) = | (r,t)|2dxa

b

| (r,t)|2 dxdydz = 1---

+++

z

dxdy

dz

x

ynucleus

electron


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Chapter 1

-

+

+-+

+/-

+/-

+/-

O bit l Filli ( 3 R l )


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Chapter 1

Orbital Filling( 3 Rules)

Electron configurations can be determined using a periodic table and by considering the followingas a guide to how the electrons "fill-up" the orbitals:

Aufbau (Building-Up) Principle. Electrons are placed into the atomic orbitals from lowest to highestenergy. The order of these orbitals is determined using the Schrodinger equation and can be easilydetermined by looking at the periodic table or using a simple mnemonics:

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p etc......

Hund's rule of Maximum Multiplicity. When degenerate orbitals are being filled, single electrons areplaced into each degenerate orbital before they are paired with another electron in the same orbital:

Pauli Exclusion Principle. No two electrons in a atom can have the same four quantum numbers.This means that only two electrons are allowed in the same orbital, and then they have oppositespin, +1/2 and -1/2.

Important distinction:Valence Electronsare the electrons which are involved in bonding between atoms. They possessthe highest energy and are referred to as the 'outermost' electrons.

Core electronsare electrons that under 'normal' reaction conditions are chemically inert. They arethe electrons of an atom which are located in the completely filled energy levels.

1s2s

2p


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Chapter 1

Chemical Bonding

Simplistically, chemistry is about the interaction of molecules with other molecules.

But what is a molecule ?

But why do atoms form bonds ?

What makes bonding favourable ?

A molecule is a collection of atoms held together by bonds due to the interaction of the atomic electronclouds.

One of the principle driving forces that makes bonding favourable is an atoms desire to obtain a stablevalence electron configuration (i.e. a valence energy level that contains a complete set of electrons)For the atoms that are most important in organic chemistry (with the exception of H), this is an octet ofelectrons, which is similar to the valence electron configuration of the nearest noble gas (e.g. 2s2 2p6).

There are two ways in which this octet can be achieved, either

ransfer of electrons which results in ionic bonds, or,

by sharing electrons which result in covalent bonds.


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Chapter 1

SUMMARY OF CONCEPTS UNDERLAYING THESTRUCTURAL FORMULAS OF ORGANIC COMPOUNDS

Structural Theory

(A. Kekule, A,S.Couper,A.M.Butlerov, 1858-1861

J.H. vant Hoff, J.A.Le Bel, 1874)

| fixed number of

-- C -- -- O H -- Cl chemical bonds

|

| carbon-carbon

-- C C-- >C = C< -- C C -- bonds can be

| single, double, triple

The nature of chemicalbonds (Octet Rule, Formal

Charge)

(G.N.Lewis, W.Kossel, 1916)

Ionic (electrovalent) bonds - (transfer of electrons)

Covalent bonds - (sharingof electrons)


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Chapter 1


Resonance theory

resonance structures(RS)/resonance contributors areonly limited representations;actual structure is a hybrid(average)of RS; only electrons (pi&nonbonding) can bemoved in RS; RS must be proper Lewis structures;resonance stabilization (in terms of energy gain);contribution depends on stabiliry of RS; more covalentdtructure more stable;

VSERP model (valence shellelectron pair repulsion)

covalenly bonded atoms; bonding/nonbonding(unsharedpairs; orbitals tend to stay as far apart as possible; optimalgeometry as minimum energy

Quantum Theories (MOLCAO: Huckel, SCF Theory, ab

initio calculations)


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Chapter 1





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Chapter 1





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Chapter 1

One common approximation that allows us to generate molecular orbitaldiagrams for some small diatomic molecules is called the LinearCombination of Atomic Orbitals (LCAO) approach. The following

assumptions lie at the core of this model:

1) Molecular orbitals are formed from the overlap of atomicorbitals.

2) Only atomic orbitals of about the same energy interact toa significant degree.

3) When two atomic orbitals overlap, they interact in two

extreme ways to form two molecular orbitals, a bondingmolecular orbital and an antibonding molecular orbital.


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Chapter 1


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Chapter 1


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Chapter 1

IMPORTANT: Only orbitals containingelectrons contribute to the stability ofthe molecule, so the empty *-orbitalhas no impact here.

Hatomic

orbital

Hatomic

orbital

The electrons are "placed" in themolecular orbitals following thesame rules as for filling orbitals in

atoms (i.e. lowest energy first).

This means the two 1s electronsboth go into the bonding molecularorbital, this results in stabilisationof the system.

Hence, two H atoms combine tobecome more stable as a H2molecule.

H2molecular

orbital

anti-bonding orbital


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Chapter 1

The following procedure is used to draw molecular orbitaldiagrams.

1) Determine the number of electrons in the molecule. Weget the number of electrons per atom from their atomicnumber on the periodic table. (Remember to determine

the total number of electrons, not just the valenceelectrons.)

2) Fill the molecular orbitals from bottom to top until all

the electrons are added. Describe the electrons witharrows. Put two arrows in each molecular orbital, with the

first arrow pointing up and the second pointing down.

3) Orbitals of equal energy are half filled with parallelspin before they begin to pair up.


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Chapter 1

In theory of MO we describe the stability of the molecule withbond order.

bond order = 1/2 (#e- in bonding MO's - #e- in antibonding MO's)

We use bond orders to predict the stability of molecules.If the bond order for a molecule is equal to zero, the

molecule is unstable.A bond order of greater than zero suggests a stable

molecule.The higher the bond order is, the more stable the bond.

We can use the molecular orbital diagram to predict whetherthe molecule is paramagnetic or diamagnetic. If all the

electrons are paired, the molecule is diamagnetic. If one ormore electrons are unpaired, the molecule is paramagnetic.


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Chapter 1

1. The molecular orbital diagram for a diatomic hydrogenmolecule, H2, is

The bond order is 1. Bond Order = 1/2(2 - 0) = 1

The bond order above zero suggests that H2 is stable.Because there are no unpaired electrons, H2 isdiamagnetic.


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Chapter 1

2. The molecular orbital diagram for a diatomic helium

molecule, He2, shows the following.

The bond order is 0 for He2. Bond Order = 1/2(2 - 2) = 0

The zero bond order for He2 suggests that He2 is unstable.

If He2 did form, it would be diamagnetic.


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Chapter 1


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Chapter 1


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Chapter 1


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Chapter 1

Hybrid Orbitals and Molecular Shape

sp3 hybridizationCH4

The ground state electron configuration ofC is

1s2 2s22p2 or1s 2s 2px 2py 2pz

valence level

This electron configuration explains

neither the bonding capacity of C

nor the shape ofCH4.


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Chapter 1

Hybrid Orbitals

Step One

ground state of C

1s 2s 2px 2py 2pz

Electron Promotion 2s

1s 2s 2px 2py 2pz

excited state

2p

+energy

Step Two

This set of valenceorbitals does not

explain the molecular

shape of methane.

1s 2s 2px 2py 2pz 1s sp3 sp3 sp3 sp3

Orbital Hybridization

hybrid orbitals


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Chapter 1

Overviewelectron promotion

+ energy

excited state

1s 2s 2px 2py 2pz

1s

2s

2px 2py 2pz

hybrid orbitals

orbital hybridization

1s sp3 sp3 sp3 sp3

sp3 sp3 sp3 sp3

1s

ground state for C

1s

2s

2px 2py 2pz

energy

1s 2s 2px 2py 2pz

Th Th Di i l S t f 3 H b id O bit l


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Chapter 1

The Three-Dimensional Symmetry of sp3 Hybrid Orbitals

x

z

y

2s orbital

+

2px orbital

mixing of the

2s, 2px,2py and 2pz orbitals

2py orbital

2pz orbital yields four sp3 hybrid

orbitals directed

towards the corners

of a tetrahedron


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Chapter 1

The Tetrahedral Shape of Methane

In 1874 J.H. Van't Hoff and J.A. Le Bel proposed that the four bonds

to tetravalent carbon point to the corners of a tetrahedron. A regular

four-sided geometric figure.

a tetrahedron

In methane, CH4, each

bond angle is a perfect

109o 28'.

This geometry at carbon

accounts for the overall shapes

of organic structures


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Chapter 1

SigmaBonds

Becausesp3 orbital has the character of ap orbital, the positive lobe of the

sp3orbital is large and extends out far from the carbon nucleus.

Si B d


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Chapter 1

SigmaBonds

The positive lobe of the sp3 orbital overlaps with the 1s orbital of hydrogen to

form the bonding molecular orbital of a carbon-hydrogen bond. The two

orbitals have a large overlap due to their size and shape. This large overlap

results in a very strong bond.

high internuclear

electron density


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Chapter 1

.

The bond formed from the overlap of ansp3 orbital and a 1s orbital is a

sigma () bond. Sigma bonds are bonds in which the orbital overlap gives abond that has a circular, symmetric cross section when viewed along the

bond axis. ALL PURELY SINGLE BONDS ARE SIGMA BONDS


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Chapter 1


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Chapter 1

The Shape of CH4

sp3

sp3

sp3

sp3

C

1s

1s

1s

1s

H

H

H

H

In-phase combination of

atomic orbitals yields

bonding molecular orbitals.

four sigma bonds

C

H

HH

H

109.5o

a tetrahedral geometry

C

H

HH

H

Th St t f Eth


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Chapter 1

C

H

H

H

H H C

H

H

H

CH

H

H CH

H

H

The Structure of Ethane

Ethane, C2H6, is the second member of the alkane family. The four

covalent bonds around each carbon are projected towards the corners of

a tetrahedron, as in methane. This shape of ethane may be predicted by

removing a C-H bond from two methanes and joining the carbons

through a C-C bond.

This geometryfollows from the sp3

hybridization at

each carbon.sigma

C-C bond

C C

HHH

HH

HH

The C-C sigma bond resultsfrom the in-phase combination

of sp3 orbitals. Each C-H bond is

formed from the in-phase

combination of an sp3 orbital at

carbon with the hydrogen 1s

orbital.


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Chapter 1

C C

HH

HH

HH

All sigma type bonds have circular symmetry along the bond which means

that there is no loss of orbital overlap when one atom is rotated.Consequently, there is no significant energy barrier (no increase in

energy) with rotation.

For a C-H bond,

there is nochange in energy

with rotation

around the

sigma bond.

For a C-C bond, there

are small energychanges with rotation

around the bond that

lead to significant

structural properties.

Rotation Around the C-C Bond


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Chapter 1


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Chapter 1

Quiz Chapter 1 Section 12


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Chapter 1

The bonding in ammonia, NH3, may be explained by using a set ofsp3hybrid

molecular orbitals in the central nitrogen as follows:

The ground state electron configuration

of atomic N is

1s 2s 2p

The occupancy of the atomic orbitals is2s

2p

1s

Formation of a set of sp3 hybrid orbitals

in the valence or bonding level gives

The spatial projection of these

hybrid atomic orbitals is

The in-phase combination of these

hybrid atomic orbitals of N with the 1s

atomic orbitals of 3 H form the bonding

orbitals in NH3

as shown:


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Chapter 1


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Chapter 1


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Chapter 1

Ethene (ethylene) molecule


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Chapter 1


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Chapter 1

Li G t f Eth


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Chapter 1

Linear Geometry of Ethynee

The Hybrid Orbital Model

sp hybridized carbon

1s

spx spx

py pzvalencelevel

spx spx

py

pz

bonding orbitals

C

The Carbon-Carbon Triple Bond


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Chapter 1

The Carbon-Carbon Triple Bond

spx spx

py

pz

spx spx

py

pz

The carbon-carbon triple bond is formed from in-phase overlap of the

orbitals of two sp-hybridized carbons positioned along the x-axis as

shown.

C C

x-axis

A sigma bond forms from overlap of two spx orbitals.

C C

z

y

Two separate -bonds form from overlap of the py and pz orbitals.

In ethyne, C2H2, the remaining spxorbitals overlap with the 1s orbital

of H.

H-C C-H

Orbital Hybridization Bond Lengths


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Chapter 1

Orbital Hybridization, Bond Lengths

and Bond Strengths

The greater the degree ofs-character in a hybrid orbital that

overlaps with another atomic orbital to form a covalent bond, theshorter the covalent bond and the stronger the bond.

hydrocarbon hybridization bond lengths

C-C C-HHo (C-H)

(kJ/mol)

H

H

H

H

H

H

H

H

H

H

H H

410

452

523

sp3 1.54 1.10 (sp3 - 1s)

sp2 1.34 1.09 (sp2- 1s)

sp 1.20 1.06(sp- 1s)

O bit l H b idi ti I fl


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Chapter 1

Orbital Hybridization Influences on

C-C Bond Lengths and Bond Strengths

orbitals C-C Bond Length Ho (C-C)(kJ/mol)

C CH3

H3C CH3

CH2=CHCH

3

HC C CH3

Shorter bonds are generally stronger bonds.

sp3 sp3 1.54 368

sp sp3 1.46 490sp

2

sp

3

1.50 385

accomodate other geometries. The table below


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Chapter 1

provides a list of common geometries and sets of

hybrid orbitals having this geometry.

GeometryHybrid

Orbitals

Number of

Orbitals

Atomic Orbitals used to

form Hybrid Orbitalslinear sp 2 s, pz

trigonalplanar

sp2 3 s, py, pz

tetrahedral sp3 4 s, px, py, pz

trigonalbipyramidal

dsp3 5 s, px, py, pz, dz2

octahedral d2sp3 6 s, px, py, p

z, d

z

2, dx

2

-y

2

squareplanar

dsp2 4 s, px, py, dx2-y

2The electron density plots below compare the sp, sp2, and sp3 orbitals.Notice that these orbitals are all very similar, in that the majority of the

orbital is oriented in a particular direction. A p orbital is distributed

equally in two opposite directions (e.g., half in the positive z direction


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Chapter 1

+ +

-bond -bond

HH C C


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SUMMARY OF IMPORTANT CONCEPTS OF

QUANTUM CHEMISTRY

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Lec4Org Chem CCB1013 Alkanes Start May 2011