CHEM 3 Midterm
H2(+) ion
(1-0)/2 = 1/2 -stable
He and bonding order
(2-2) / 2 = 0 -molecule is not stable -He gas consists of individual He atoms
Rule for filling shells
(n+1) p follows nd
Two isomer of pentadiene (2)
-1, 3 diene is conjugated like buta 1, 3 diene because there is an unbroken chain of four sp2 hybridized carbon atoms -1, 4 dien is not conjugated because the sp3 hybridized carbon interrupts the chain of sp2 hybridized carbon atoms
sp hybridization
-180 -one s orbital and one p orbital -two effective pairs around an atom will always require sp hybridization of that atom
2s and 2p orbital
-1st maximum significant smaller than 2nd maximum in 2p
B-carotene (C40H56)
-216 valence electrons -11 double bonds - 22 pi electrons -22 C atoms are sp2 hybridized in unbroken ring of conjugation
Buta-1, 3 diene (7)
-22 valence electrons -18 used for 9 sigma bonding, four electrons for pi bonding -4 carbon chain named after butane -two double bonds (diene) -double bonds located at 1, 3 positions, choosing lowest number -carbon atom has one double bond and two singles, all four carbon atoms are sp2 hybridized -one out of plane p-orbital on each atom available for pi type bonding
B2, C2, and N2 energy ordering of molecular orbital energies (2)
-2s and 2p orbitals at the beginning of the row are significantly mixed because their energies are similar -2p(sigma) orbital is destabilized because of the overlap between 2s orbital already places sigma type molecular orbital in the same place
Li2
-2s electrons plugged into similar pair of bonding orbitals
O2
-2s orbitals to form sigma bond and two of its 2p orbitals form a pair of pi bonds = triple bond
**How is 3d different from 3s and 3p? (2)
-3d orbital is much more compact than 3s or 3p -transitional elements have relatively similar properties, whereas main group elements differ significantly in their chemical properties
Penetration effect
-3s orbital spends most of its time far from the nucleus and outside the core electrons (1s, 2s, 2p orbitals) which shields it from the nuclear charge -small but significant probability of being close to the nucleus -significantly penetrates the shield core electron and feels more of the nuclear charge -3p orbital does not have a probability maximum close to the nucleus -penetrates the core electrons to a lesser extent than in the 3s -why an electron prefers the 3s orbital to the 3p or 3d
Actual Bonding in Methane orbital
-4 equivalent atomic orbitals tetrahedrally -combining 2s and 2p orbitals -extra p-electron on carbon will not be used for hybrid formation -carbon can form four bonds: 3 sigma bonds for trigonal planar, remaining pi bond derived from the non-hybrisized p on each carbon atom -sp3 hybridization (large lob and small lobe)
5 membered symmetry (3)
-5 membered ring surrounded by six 5 membered rings gives a non planar structure -lowest pi molecule orbital -bowl shape
#### Assumed B2...
-B = electron configuration is 1s2 2s2 2p1 -six valence electrons -two B atoms have two pairs of p orbitals overlapping in parallel manner and one pair can overlap head-on -two pi bonding orbitals at the same energy (degenerate) from two parallel orbitals -two degenerate pi antibonding orbitals -energy of pi(2p) is higher than sigma(2p) because sigma interactions are stronger than pi interactions -bond order: (4-2)/2 = 1
HF molecule
-H electron configuration 1s1 -F electron configuration 1s2 2s2 2p5 -assume F uses only one of its 2p orbitals to bond to H -MOs composed of fluorine 2p and hydrogen 1s -assume F other VE remain localized on the F atom -F 2p orbital lower energy than 1s orbital of H because F binds its VE more tightly -2p electron on free F atom is at lower energy than the 1s electron of free hydrogen atom, electrons prefer to be closer to F atom -sigma MO containing bonding electron par shows greater probability close to the F, electron pair not equally shared -F has slight excess of negative charge, hydrogen atom partially positive -stable because both electrons are lowered in energy relative to their energies in the free H and F atoms
**4 pi r^2 (2)
-Integrating the volume element over all space at a fixed distance, r -generalize from a single point in space to a spherical shell including all equivalent points at the same radius
##### Sigma bonding of larger molecules (2)
-LE sigma bonds are made between adjacent atoms by overlapping the appropriate atomic orbitals, including hybrids -MO sigma type molecular orbital will spread the electron density through the entire molecules (not limited to interaction between two atoms)
Hydrogen bonding in DNA base pairs (3)
-N atom bonds linearly through its single lone pair -O uses just one of its lone pairs to from an angular bond -the two (AT) or the three (CG) hydrogen bonds keep the unit planar
O2, N2, and magnetism (2)
-O2 - two unpaired electrons in 2p(pi)*, paramagnetic -N2 - electrons paired, diamagnetic
Where and why does electron transition occur? (2)
-UV region, energy separations of electron states typically correspond to energies of photons in UV region -some occur in visible region
B-caroteen
-absorbs most strongly in blue region, resulting color orange/yellow
indigo
-absorbs most strongly in green-red region, color is blue/purple -has two pyrrole like nitrogen atoms
LE model
-accounts for molecular structure -does not accurately describe electron energies -achieve maximum stability and minimum energy
Bonding MO in Pi bonding (2)
-added together, phases match, and constructive interference occurs -electron probability lies above and below the line between the nuclei -pi (2p)
Effective nuclear charge
-apparent nuclear charge, Z(eff) Z(eff) = Z (actual) - (effect of electron repulsion) Z(actual) = Z (atomic number)
#### any case where m(l) > 0
-assign a pair of orbitals to a given value of m(l) -for a set of p orbitals px and py can be assigned m(l) +/= but cannot determine which of the two orbital is + and -
Unsaturated molecules
-at least one double bond (at least one pi bond in molecular orbital) -alkenes (C2H4) -aldehydes and ketones (CH3CHO and (CH3)2CO) -conjugated molcules usually have alternating single and double bonds
Molecules containing atoms adjacent to each other in the periodic table
-atoms involved are so similar use the MO diagram for homonuclear molecules
Nucleobases in DNA (2)
-bind as a pair AT with a double link -bind as a pair CG with triple link
NO
-bond order (8-3)/2 = 3.5 -11 valence electrons -paramagnetic
Comparison between bond energies of B2 and F2
-bond order cannot automatically be associated with a particular bond energy -both B2 and F2 have bond order of 1, the bond of B2 is twice as strong as bond in F2
Correlation between bond order, bond energy, and bond length
-bond order increase, bond energy increases, and bond length decreases
Be2
-bonding and antibonding orbitals both contain 2 electrons -bonding order (2-2)/2 = 0 -not more stable than two separated Be atoms = weak bond
Bonding Components in Methane
-bonding involves only valence orbitals -H atoms use 1s orbitals -C atom use one 2s and three 2p orbitals -2p and 2s atomic orbitals two types of C-H
Size of 1s orbital (2p)
-cannot be precisely defined, since the probability is never zero, no distinct size -normally accepted arbitrary definition of the size of the hydrogen 1s orbital is the readies of the sphere that encloses 90% of the total electron probability
Electron correlation problem
-cannot rigorously account for the effect a given electron has on the motions of the other electrons in an atom -all polyelectronic atoms
#### Electron probability of both MOs`
-centered along the line passing thought two nuclei -MO1 greatest electron probability is between the nuclei (matching phases of orbitals produce constructive interference and enhanced electron probability between 2 nuclei) -MO2 centered along the molecular axis but outside the area between the 2 nuclei, mismatched phases produce destructive interference producing a node -electron probability is the same along any line drawn perpendicular to the bond axis at a given point on the axis (simga) -MO1 and MO2 = sigma MOs
#### electron transition (4)
-change from one electron arrangement to another -can absorb or emit a photon (ultraviolet or visible regions) and go from a lower to higher electronic energy state, vice versa -undergo vibrational and rotation energy transitions, quantized vibration energy levels whose spacing correspond to the energies of photons in the microwave region -each vibrational state has a set of rotational states
sp3 hybridization
-chemical environment required to bond with valence electrons from s and p orbitals -steric number four -> tetrahedral -> use all available orbitals -> four lobes (25% s, 75% p)
#### Pi orbitals (3)
-combo of p or higher orbitals in parallel configuration -nodal place passing through the nuclei -weaker than sigma bond because of poorer overlap
Transition metals
-configuration obtained by adding electrons to the five 3d orbitals
#### Electron transition and visible region (2)
-contain transition metal ions -molecules with long chain of carbon molecules that have alternating double bonds (carotene)
Cholesterol (4)
-contains steroid grouping of 4 mostly saturated rings -all carbons are sp3 hybridized expect for one sp2 hybridized -each carbon atom has enough hydrogen to satisfy structure -straight lines indicated terminal methyl groups (CH3) -unit of 4 rings lie roughly in plane
#### Electrons paired in p orbitals affect on bonding
-contribute to non bonded electron pairs -most case involving O, S, F, Cl -presence of paired electrons reduces number of bonds N, O, and F can form -S and Cl have available d orbitals that can increase the bond number
Electron motions
-correlated -electrons repel each other, the movement of a given electron will affect the movements of all the others
ground state
-corresponds to putting all electrons into the lowest available energy levels -any other configuration can be assumed to be temporary (excited state)
#### Sigma bond
-covalent bond, electron pair is shared in an area centered on a line running between the atoms -formed from orbitals whose lobes point toward each other -combine two s orbitals or between s and p orbitals to form a bond that is cylindrically symmetrical about the molecular axis -energy is lower than that of separate orbitals
Benzene (6)
-cyclic, conjugated molecules having 2, 6, 10... electrons in the conjugated pi bonds (4n+2, Huckel rule) -each carbon has sp2 hybridized -sigma bonds us spa hybrids -pi bonds extend over the entire region of conjugation -number of nodes cutting the plane increase with increasing energy -some MO place node atoms and others through bonds
#### Sigma orbitals (2)
-cylindrically symmetric abut the internuclear axis -formed from s, p, d or higher orbitals in any combo
**Energy levels of Na and H (3)
-d and f orbital of Na atom occur at same energy values to the H atom for the same value of "n" -s and p orbitals have significantly lower energies than H atom, electrons experience a significantly larger effective nuclear charge than +1 (s and p orbitals effectively penetrate towards the nucleus) -as n increase and orbitals become larger, the penetration effect is reduced
transition elements
-d shell elements -similar chemical features because they differ only in number of d orbitals, the nd orbitals are filled after the (n+1) orbitals
Atomic radius trend
-decreases going from left to right across a period -increasing effective nuclear charge from left to right (valence electron drawn closer to nucleus) -increase down a group (increases in orbital sizes in successive principal quantum level
Methane electrons
-delocalized and do not have the same energy `
electron configuration
-determined from position of an element in a particular row -exception: filled shell = special stability
diatomic molecule
-different combination of atomic orbital can overlap to form chemical bonds -overlapping different types of orbitals to form different types of bonds
C60 (4)
-don't need any hydrogen atoms -carob sp2 hybridized -pi MO extend through whole surface -icosahedron
O3 and NO3- bonds
-double bond changes position in the resonance structures -double bond involves one sigma bond and one pi bond, sigma bond between all bound atoms in each resonance structure (localized) -pi bond has different locations in various resonance structures (delocalized)
#### Repulsions between electron1 and other electrons
-each point in space from the sum of the average electron densities corresponding to [wave function2]^2, [wave function3]^3....[wave functionN]^N in volume element dv around the point -electron 2 [wave function1], [wave function2]....[wave functionN]
ionization energies
-ease with which the first few electrons are displaced A + Ionization energy -> A+ + e- (zero excess energy) -electron most easily released is one at the top of the stack of filled energy levels
#### Energy of the bonding MO is lower than for the individual atomic orbitals... (3)
-effective shielding of the nuclei by the electron density placed between them -attraction of the electrons to the opposite nuclei, allowance for electron-electron repulsion -principal contribution is from delocalization of electrons, allowing electron to occupy a greater region of space is stabilizing
Li2 MO diagram (3)
-electron configuration for VE is sigma (2s)^2 -bond order is (2-0)/2 = 1 -stable
Explain Li2's 1s orbitals (4)
-electron configuration is 1s2 2s1 -logical for Li 1s and 2s orbitals to form MOs of Li2 -1s orbitals are much smaller than 2s orbitals, do not overlap in space -two electrons in each 1s orbital can be assumed to be localized on a given atom, do not participate in bonding
N, P, and As atoms
-electron configuration is ns2np3 so that unpairing the s-electron will not help -usually a non-bonded pair of electrons -NO3- nitrogen atom has a positive formal charge, having lost a valence electron so that it can form 4 bonds
####Problem with LE model of carbon dioxide (4)
-electron density is cylindrically symmetric (homogenous all around the O-C-O molecular axis) -not consistent with two C-O bonds have pi electron densities centered in 2 perpendicular planes -incorrectly assumes that electrons localized, concept of resonance must be added -no info about bond energies
Apply Aufbau principle to H2+
-electron is placed in the bonding orbital (more stable arrangement than for separate nuclei) -more stability by adding another electron, neutral H2 (stable) -adding another election (H2-) would decrease stability (electron go into antibonding molecular orbital)
Source of large difference in energies required to remove one electron from ion vs neutral atom
-electron-electron repulsions in neutral atoms -effectiveness of positively charged nucleus in binding the electrons has been decreased by the repulsions between electrons -effect of the electron repulsions can be thought of as reducing the number charge
Solar Radiation Spectrum (3)
-electronic absorption by O3 prevents short wavelength UV from reaching sea level -electronic absorption of O2 partially blocks narrow band outside visible region -absorption by water and CO2 is not electronic, due to molecular vibrations
Stable hydrocarbon
-electrons in bonding MO and leave all antibonding MO vacant
promotion energy
-energy cost when electron are paired s orbital will promoted to the next higher p orbital (2s -> 2p, 3s -> 3p third row main group elements) or sometimes to the next available d orbitals (4s -> 3d first row transition elements) -compensated by formation of chemical bonds
Sigma bond interactions in O2 and F2
-energy of the sigma(2p) orbital drop below pi(2p)
electron affinity
-energy released when an electron is added to an atom B + e- -> B- + energy (electron affinity) -largest electron affinity is always less than the smallest ionization energy
B2 and magnetism
-even if B2 is expected to have only has paired electrons (diamagnetic) it is actually paramagnetic with two unpaired electrons -each of the last two electrons goes into one of the degenerate pi(2p) orbitals, making it paramagnetic
B-carotene and indigo
-extended conjugated double bond systems are a characteristic of strong absorbers of visible light
For higher orbitals than 3p...
-filling order does not go strictly according to the principle quantum number -K suggests strong similarity to Na, single outer electron is contained in a large s orbital
#### Lanthanide series
-filling seven 4f orbitals -sometimes one electron occupies a 5d instead of 4f orbitals (energies of 4f and 5f orbitals)
#### Actinide series
-filling seven 5f orbitals -sometimes one or two electrons occupy the 6d orbitals instead of the 5 f orbitals (orbitals have very similar energies)
##### Hybridization of F or Cl (2)
-form bonds with just a single p orbital -middle of structure use sp3 hybridization
#### electron transitions (2)
-from bonding to antibonding molecular orbitals -when a molecule absorbs light in the UV-Vis region -PE curve for ground state is different from excited state because less bonding density is found in excited state
#### Arrangement of electrons in molecules attempt to...
-give each atom a noble gas configuration where possible -minimuze electron pair repulsions
#### electron density for antibonding orbital (3)
-goes to zero in a plane midway between the nuclei -negative cross term exactly cancels the sum of the square terms -there will be a node at some position between the nuclei
Comparing 1s, 2s, 3s (3)
-great difference in effective size -wave functions normalized (area under each curve is the same, integral over all space is unity) -define any 2 values can estimate the fractional probability of finding the electron in that region
#### antibonding MO (5)
-higher in energy than the atomic orbitals of which it is composed -favor separated atoms -shielding is much less if there is a node present -forced to occupy the higher energy MO -electrons are mainly outside the space between the nuclei (H2)
#### Molecular orbitals
-hold two electrons wit opposite spins -square of the molecular orbital wave function indicates the electron probability -requires a structure to be estimated in advance (structures predicted by VSEPR)
#### Antibonding MO in sigma bonding
-if two orbital are combined directly the positive phase of the left orbital overlaps with the negative phase of the right orbital -destructive interference of orbitals produces a node between the nuclei, decreasing electron probability -electrons are concentrated outside the area between the two nuclei
Pauli exclusion principle
-in a given atom no two electrons can have the same set of four quantum numbers (n, l, m(l), m(s)) -an orbital can hold only two electrons and they must have opposite spins -helps offset the natural coulomb repulsion
####Molecular orbital model (4)
-in terms of quantum mechanics -cannot account for the details of the electron movements -two electrons, electron spin opposite -orbtals conserved, number of MOs always the same as number of atomic orbitals used to construct them
Probability distribution diagram (2p)
-intensity of color is used to indicated the probability value at a given point in space -darkness of a point indicates the probability of finding an electron at that position
spectroscopy
-interaction of electromagnetic radiation with matter -nondestructive way to find identity, structure, and properties of substance
START Strong electronic transitions in larger molecules (3)
-involved moving bonding electron to an antibonding orbital -absorbing visible region tend to involve pi electrons -apprx. energy of electronic transition from energy gap between the molecular orbitals labeled HOMO and LUMO -spin tends to be conserved when the electron is excited
Why does a molecule form?
-it has lower energy than the separated atoms -MO model = number of bonding electrons is greater than the number of antibonding electrons = stable
N2 bond energy
-large bond energy -a bond order of 3, triple bond
Molecular fluorescence demonstrated by...
-laser or black light excitation -photon absorbed, energy rapidly relaxes within the electronically excited states to lowest vibrational level -spectra of most molecules independent of the wavelength of the exciting state
#### bonding MO (6)
-lower in energy than the atomic orbitals of which it is composed (energy minimum, stabilizing) -effective shielding of nuclei by the electron density placed between them -attraction of electrons to opposite nuclei (electron-electron replusions) -delocalization of electrons, allowing an electron to occupy greater region of space is stabilizing -favor bonding -mainly between nuclei (H2)
Penetration toward the nucleus of 4s orbital ...
-lowers the energy of this orbital below 3d -3d orbital does not penetrate vey well -following the completion of the p shell, the next element is an alkali metal where electrons occupy s orbital
Orbitals
-mathematical functions -no physical reality
radii atoms and ions
-measured from crystals -radii of atoms and their derived ions are often different -ratios of radio of the constituent ions determine crystal structures -hydration causes the effective diameter of an on to be much larger than the examples presented in this table -effective radii of ions are different in many solids and fluids
atomic radii
-measuring the distance between atoms in chemical compounds -covalent atomic radii -significantly smaller than might be expected from the 90% electron density volumes of isolated atoms because when atoms from bonds their electron clouds interpenetrate
#### Hybridization (4)
-mixing of native atomic orbitals to form special orbitals for bonding -easier way than compute calculating molecular structure -electron configuration, promoton (unpairing) of electrons to maximize sharing, set up of different types of hybrid (molecular geometry) -hybrid orbitals form sigma bonds, p orbitals form pi bonds
#### Coronene C24H12 (3)
-molecule is planar -extended pi electron system -6 fold symmetry, lowest energy pi MO
F orbitals
-more compact than d orbitals -chemical properties similar
To participate in molecular orbitals, atomic orbitals... (2)
-must overlap in space -only valence orbitals contribute significantly to MOs
#### Elements with 2p electrons in relation to s orbitals
-neglect 2s electrons, influence is seen from the ordering of the orbitals formed from the overlap of 2p orbitals
#### saturated molecules (4)
-neither double nor triple bonds -usually second row atom with steric number 4 -tetrahedrally coordinated -sp3 hybrid orbital
Daylight spectrum (2)
-normal daylight exact spectrum depends on the wearer and time of day -up to 60% of sunlight in this region is absorbed by atmospheric O2
Orbitals that correspond to a given value of n must fill in the order
-ns, np, nd, and nf -energies of the one electron SCF orbital to vary in the order ns < np < nd < nf
##### electronic spectrum (4)
-occurs in ultraviolet or visible region -information about the spacing of electronic energy levels -plots the quantity of radiation absorbed vs the wavelength of radiation (peaks at wavelengths where the photon has an energy that matches an energy gap) -deliver large quantities of energy in precise wavelengths and power in short burst (observe molecule decay)
SF6
-octahedral arrangement of pairs, set of six hybrid orbitals -d2sp3 hybridization -d2sp3 orbital on S atom is used to bond to F atom -four pairs on F atom, assumed to sp3 hybridized
#### sp2 hybridization
-one 2s and two 2p orbital -plane is determined by which p orbitals are used -in formation of 2 sp2 orbital, one 2p orbital is not used and is oriented perpendicular to the plane of the sp2 orbitals -whenever an atom is surrounded by three effective pairs -steric number is tree -use three of the four available orbitals -> make three lobes (33% s, 67% p) -120
dsp3 hybridization
-one d orbital, one s orbital, three p orbitals -the orbitals pointing to the vertices of the triangle (equatorial hybrid orbitals) are slightly different than other two (axial orbitals) -a set of five effective pairs around a given atom always requires a trigonal bipyramidal arrangement
#### Use of the established model based on s, p, d orbitals makes sense (4)
-only a few of the electrons in most atoms actually in chemical bonds, rest remaining associated with atoms -share electrons, 50% with original atom -electron is lost/gain (ionic bond), ion modeled using hydrogen based orbital scheme -mathematical models of orbitals
Electron spin quantum number (ms)
-only one of two values +1/2 and -1/2
Extending sp2 hybridization to much larger molecules examples (5)
-other aromatic molecules extended from benzene, hydrocarbons which definite edges capped by H -graphene - signle large sheet 1 atom thick -graphite - many planar graphene like sheets, loosely bonded -bucky ball - pure hydrocarbon C60 -nanotubes -cylinder
Expected Bonding in Methane
-overlap of C 2p orbital and 1s orbital of H -2p orbitals perpendicular, 3 C-H bonds are at 90 degrees
O2 and magnetism
-paramagnetic -MO model predicts paramagnetism
Bonding MO in sigma bonding (2)
-phase of the right orbital is reversed, constructive interference results, giving enhanced electron probability between the nuclei -electrons are concentrated between the nuclei
#### LCAO Theory (think orbitals)
-place valence electrons of a molecule in molecular orbitals -core electrons do not contribute significantly to the chemical bonds -pictorially more straightforward to show the electron distribution of a molecule using molecular orbital theory -only consider atomic orbitals containing valence electrons
Benzene bonds
-planar hexagon of carbon atoms -all six C-C bonds are known to be equivalent (resonance) -each carbon sp2 hybridized, p orbital perpendicular to the plane of the ring remains on each carbon atom -six p orbitals used to form pi molecular orbitals (delocalized above and below the plane of the ring) -delocalized pi bonding
#### Absorption spectrum (3)
-plots extinction coefficient against wavelength -electronic spectrum often measured in visible region -absorbance is equal to ECL
**Radial Probability Distribution (4)
-predict relative sizes of orbitals -provide important clues of chemical behavior -as the energy of a type of orbital increases so does the number of nodes -because of r^2 weighting of wave function and the more gradual exponential term (exp(-r / nap)) the orbital become substantially more diffuse as n increases
**Maximum in the curve (3)
-probability of finding an electron at a particular position is greatest near the nucleus -the volume of the spherical shell increases with the distance from the nucleus -the total probability increase to a certain radius and then decreases as the electron probability at each position becomes very small
Different types of energy changes
-pure rotational transition -vibrational transition that may involve simultaneous rotational transition -simultaneous vibration and/or rotational change
Bond order (4)
-quantitative indicator of molecular stability for an atomic molecule -the difference between the number of bonding electrons and the number of antibonding electrons, divided by 2 (bonds as pairs of electrons) -strength it reflects the quantity of energy released when the molecule is formed from its atom -larger bond order indicates greater bond strength
m(l)
-quantum number distinguishes between differently oriented/shaped sub orbitals -three possible m values l=1 (-1, 0, 1) may also be termed px, py, pz
#### 2s orbital affects its bonding (5)
-radial node causes 2s orbital to apear -in sigma bond, presence of radial node has little effect on the bond formation -outer region has large diameter than inner one, overlapping only a small part of wave function -bonding between 2s orbital same as 1s -3p same as 2p
phosphorescence
-relatively slow process and rarely seen because molecular excited states are so highly reactive that they will not survive for longer than a microsecond -small chance that a photon could be emitted and at the same time spin could flip which usually lasts on a very long time scale -triplet excited molecules will usually undergo chemical reaction faster than they emit phosphorescence -ion electron recombination -chemiluminescence
#### Pi bond
-result from parallel orbitals -p orbital interact in a sideways arrangement where both phases interfere constructively
#### Actual B2 MO... (6)
-s and p orbital are allowed to mix n the same MO -even though s and p contributions to the MOs are no longer separated, retain the simple orbital designations -mixing of p and s orbitals occurs only in sigma MO -energy of sigma(2p) orbital is changed by p-s mixing, the energies of pi(2p) and sigma (2p) orbitals are reversed -p-s mixing changes energies of sigma(2s) and sigma (2s)*, no longer equally spaced relative to the energy of the free 2s orbital -bond order (4-2)/2 = 1
Elements in the same group
-same valence electron configuration -similar chemical behavior
#### Schrodinger equation for polyelectronic atoms
-self consistent field method -electron is assumed to be moving in a potential energy field that is a result of both the nucleus and the average "electron density" of all other electrons -electron equation to separate into set of one electron equation -orbitals have angular properties same as H orbitals and radial characteristic different from H orbitals -orbitals for polyelectronic atoms depend on both n and l,
Sigma vs Pi bond energy (2)
-sigma bond has lower energy since the electrons are closest to the two nuclei -sigma interactions are typically stronger than pi interactions
Effects of p-s mixing (3)
-sigma(2s) and sigma(2p) significant electron probability in the area between the nuclei and the bonded atoms, electrons in sigma(2s) orbital will repel any electrons placed in sigma(2p) orbitals, making orbital less attractive to electrons -sigma (2p) pushed to higher energy level than the pi(2p) orbitals, which do not have electron probability between the nuclei and are not affected by electrons in the sigma(2s) orbital -repulsion effects between sigma(2s) and sigma(2p) decrease in going across the period because the increasing nuclear charge pulls the sigma(2s) electrons in closer, making the sigma(2s) smaller and decreasing sigma(2s)-sigma(2p) interactions
Why would Li2 MO neglect 1s electrons? (1)
-significantly less overlap between the tightly bound 1s of Li than the diffuse 2s orbitals -the 1s orbitals are full, so there is no net bonding results
Be2 MO (4)
-similar to He2 -little bonding -proximity of 2p orbitals weakens approx. -more complete picture must account for 2p orbitals
**Sodium atom
-single electron interacting with net charge of +1 centered at the nucleus, 10 core electrons effectively shield most of the nucleus charge
Two types of electronically excited states in larger molecules
-singlet state involves having all electron spins parallel -triplet state involves two unpaired electrons, lower energy state in excited molecules but usually accessible directly from the ground state
Carbon dioxide
-sp hybrid orbital are used to form the sigma bonds between carbon and oxygen atoms -two 2p orbital remain unchanged on the sp hybridized carbon, used to form pi bonds to the oxygen atoms -each oxygen atom has three effective pairs around it, requiring trigonal plan arrangement of the pairs, each oxygen can be assumed to have sp2 hybridized -orbital on each oxygen is used for the pi bond to the carbon -sp hybridized carbon atom has two un-hybridized p orbitals, used to form a pi bond with oxygen atom
Ethylene
-sp2 hybridization -in formation of 2 sp2 orbital, one 2p carbon orbital is not used and is oriented perpendicular to the plane of the sp2 orbitals -three sp2 orbital on each carbon are used to share electrons -sigma bonds are formed using sp2 orbitals on each carbon atom and the 1s orbital on each hydrogen atom (occupies space between carbon atoms) -double bond result from sharing an electron pair in the space above and below the sigma bond (using 2p orbital perpendicular to the sp2 hybrid orbitals on each carbon atom) -parallel p orbitals can share an electron par (occupies space above and below line joining atoms) to form a pi bond
triplet state
-spin of one or other of the electrons will flip so that two spins are parallel -cannot directly relax to the ground state by just emitting a photon (Pauli principle) -chemical reaction must occur -example: oxygen
SF4 (3)
-steric number 5 -hybridization same as PCL5 -S has 6 VE, non bonded pair involved
Paramagnetism (2)
-substance to be attracted toward the inducing magnetic field -associated with unpaired electrons
Diamagnetism (2)
-substance to be repelled from the inducing magnetic field -associated with paired electrons
Valence electron
-the electrons in the outermost principle quantum level of atom -involved in bonding -different elements are closely connected with the number -determine the oxidation numbers for metallic elements (simple ion the oxidation # is same as the charge of ion, metallic/non metallic elements other rules apply)
Hund's rule
-the lowest-energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals -if their is a choice of equivalent orbitals to place more than one electrons if possible go into different orbitals with parallel spin
How is paramagnetism measured?
-the sample is weighed with the electromagnet turned off and then weighed again with the electromagnet turned on -increase in weight when the field is turned on indicates that the sample is paramagnetic -increase in weight can be used to estimate the number of unpaired electrons per molecule of sample
##### purine (3)
-three N atoms replace C - H units like the ones in pyrimidine -other N atom is like the one in pyrrole, and donates two electrons to the pi electron system -all N are sp2
#### Result of effective nuclear charge
-treat each electron individually, each electron is viewed as moving under the influence of a positive nuclear charge Z(eff) -simplified atom has one electron with a positive nuclear charge of Z(eff)
##### pyrimidine (3)
-two N atoms replace C - H units in benzene ring -N atoms are naturally sp2 hybridized -non bonded pairs on N atoms lie in place and are not involved in pi electron system
d2sp3 hybridization
-two d orbitals, one s orbital, three p orbitals -six electron pairs around an atom are always arranged octahedrally
He + He(2+)
-two electrons are lowered in energy and only one is raised in energy -(2-1)/2 = 1/2 -stable
B2 and Hund's Rule (3)
-two electrons in two identical 2p(pi) orbitals placed in parallel spins -paramagnetic -evidence that 2p(sigma) and 2p(pi) orbitals are inverted since bonding pair of 2p(sigma) is diamagnetic
H2
-two protons and two electrons -constructed using hydrogen 1s orbitals (basis set, radial part of the atomic orbital vary to achieve lowest energy MOs) -1s orbital no longer exist in H2 molecule (own set of new orbitals) -MO1 lower energy than 1s orbitals of free H atom -MO2 higher energy than 1s orbitals -if 2 electrons occupy the lower energy MO will have lower energy than they have in two separate H atoms (favor molecule) -both MOs have sigma symmetry and constructed from H 1s orbitals
H2(-)
-unstable, immediately decomposing to H2 and free electrons -even if bond order is (2-1)/2 = 1/2
PCl5
-use of the 3d orbitals for bonding -5 electron pairs, require trigonal bipyramidal arrangement -dsp3 hybridization -Cl atom is surrounded by four electron pairs, requires tetrahedral arrangement (set of four sp3 orbital on each Cl atom) -five P-Cl sigma bonds are formed by sharing electron between dsp3 orbital on the P atom and sp3 orbital on each Cl, other sp3 orbitals on Cl hold lone pairs
O3 Absorption Spectrum (4)
-vertical axis in the spectrum is cross section per molecule -scale is logarithmic to show the wide range of values -<290 nm atmospheric oxen begins to strongly -<242 nm molecular oxygen beings to absorb strongly
quantum confinement
-very small particles on the order of a few nm in size emit wavelengths that depend on the size -3D particle in a box example -the larger the dimensions, the smaller the energy spacing, so that larger particles emit longer wavelengths of light -each cuvette was irradiated with a black light
Consequence of absorbing visible light
-vision -simple molecule retinal changes shape when light is absorbed, conformational change leads to triggering a response in the optic nerve -irradiation of 11-cis retinal in rhodopsin causes geometrical change to the lower energy all trans conformer
**4 pi r^2 dr describes (3)
-volume -thickness of the sphere -r is the radius
#### H2 (EQUATIONS)
-wave function is a linear combination of 1s atomic orbital function -WF(MO) = C(a) WF(1sa) + C(b) WF(1sb) -mixing coefficients Ca and Cb have the same magnitude but could have different sings -produce as many molecular orbitals as the number of atomic orbitals used -sigma(1s) = C1(WF(1sa) + WF(1sb)) -sigma(1s)* = C2(WF(1sa) - WF(1sb))
Chromium
-weird configuration -[Ar] 4s1 3d5 -both 4s and 3d orbitals half filled
Antibonding MO in Pi bonding (2)
-when the phase of the right orbital is reversed and combined with the left orbital, destructive interference occurs -electron probability lies above and below the line between the nuclei -pi (2p)*
Molecule that forms a tetrahedral set of bonds
-whenever a set of equivalent tetrahedral atomic orbitals is required by an atom, this model assumes that the atom forms a set of sp3 orbitals -109.5
Main group
1A, 2A, 3A, 4A, 5A, 6A, 7A, 8A -members of these groups have the same valence electron configuration -only the principal quantum number of the occupied orbitals changes in going down a particular group -incompletely filled p-orbitals
Na atom ground state
1s^2 2s^2 2p^6 3s^1
3s and 3p oribtal
1st, 2nd, and 3rd maximum continuously become bigger from left to right
**Helium and energy
2 protons, 2 electrons -kinetic energy of electrons as they move around nucleus -potential energy of attraction between the nucleus and the electrons -potential energy of repulsion between electrons
Simple ions of transition metals
2+, 3+ except such as Cu+
as atomic number increases (in relation to 2s and 2p orbitals)...
2s orbital penetrates closer to the nucleus than 2p, shrinks and drops down in energy so that it influences the 2p orbitals much less
#### Filling of shells
3d shell (end of first transition series) 4p shell 5s shell (penetrate better toward nucleus than 4d) 4d (second transition row) 5p (4f significantly higher energy than 5p, main group) 6s (Cs, Ba) 5d (La-no f orbital but included in lanthanides) 4f (next 14 after La) 5d (resumes when f shell complete, 3rd row transition) 6p
**Radial probability distribution
4 pi r^2 R^2 vs r
Maximum radius of 1s
5.29 x 10^ -2 nm = .539 A from nucleus same distance of the innermost orbit in the Bohr model (Bohr radius ao)
B2 model similar to...
C2 and N2
alcohol, ethers and simple amino compounds
CH2OH, (CH3)2O, CH3NH
Copper
Expected: [Ar] 4s2 3d9 Actual: [Ar] 4s1 3d10 -half filled 4s orbital and filled set 3d orbitals
Approximation treatment of hydrogen molecule
MO1 = 1sa + 1 sb MO2 = 1sa - 1 sb 1sa, 1sb = 1s orbitals from two separated hydrogen atoms
pro bonding
Mo available to two electrons in lower energy than atomic orbitals these electrons occupy in separated atoms
Complete filling...
a set of equivalent orbitals before moving into next one (1s, 2s, 2p, 3s, 3p)
**Reality of sodium and hydrogen
actual effective nuclear charge also depends on the orbital occupied by the single valence electron different orbitals penetrate the core electron shell to different degrees
singlet
all spins are paired
Conjugated molecules
alternating single and (usually) double bond
(n+1) s orbitals
always fill before the nd orbitals
Filling a p shell
always gives a noble gas element, next element if always an alkali metal
neutral atom
as many electrons in the orbitals as there are protons in the nucleus
quantum number l increases...
as n increases the average distance of the electron from the nucleus
Aufbau principle
as protons are added one by one to the nucleus to build up the elements, electrons are similarly added to these atomic orbitals
Explain conjugated molecules and energy
as system gets longer the electron energies get closes together, and light absorbed correspond to longer wavelength
Single valence electron
assumes that the valence electron do not penetrate into the core
Square of the wave function...
at a particular point in space indicate the probability of finding an electron near the point
Only the MOs...
available for occupation by electrons
At liquid nitrogen phosphorescence can...
be observed because competing chemical reactions usually cannot occur in a frozen sample
Other ways of finding probability distribution
calculate the probability at points along a line drawn outward in any direction from the nucleus (R^2 vs r^2)
Role of filled shells
common properties to elements having similar numbers of electrons relative to rare-gas configuration
Double bonds
consist of one sigma bond, where electron pair is located directly between the atoms, and one pi bond, where the shared pair occupies the space above and below the sigma bond
Heteronuclear diatomic molecules
containing two different atoms
Steriods
cyclic alkanes
2s wave function
decays exponenially, modified by a node in the radial function the term (2-r/ ao) takes the wave function to zero at r = 2ao
1s wave function
decays exponentially
**small cubic volume of space
dr = dx, dy, dx, = r^2 dr sin (theta) d(phi) d(theta)
When atom combine to form a chemical bond...
driving force is to lower the energy
Molecules absorb...
electromagnetic radiation to furnish energy for many different process, quantized energy levels
Electron correlation problem --> approximation
electron has a field of charge that is the net result of the nuclear attraction and the average repulsions of all the other electrons
similarity of 6s, 5d, 4s
energies
Substance with both paired and unpaired electrons
exhibit net paramagnetism, effect of paramagnetism is much stronger than diamagnetism
halogens
five p-electrons
Strong transitions reach the excited singlet state causing..
fluorescence back to ground state
#### Homonuclear diatomic molecules
formed by elements in period 2
electron spin
fourth quantum number was necessary to account for details of the emission spectra of atom
#### What determines transitions?
geometric structure and electronic structure of molecule
Color
give by the sum of the colors that remain unabsorbed
Probability of finding electron at a given point (distance)
greatest close to the nucleus and drops off rapidly at the distance from the nucleus increases
Corresponding antibonding orbital
higher energy than the constituent atomic orbitals, principally from #1 above-shielding is much less if there is a node present
Describe He orbitals in relation to attractions and repulsions of H atom
increased nuclear charge is more important than the repulsions between two electrons, electrons more tightly bound than electrons in H atom
given value of quantum number l
increasing n increases the average distance of the electron from nucleus
Graphene
inflated 2D sheet of sp2 hybridized carbon atoms
Core electrons
inner electrons
**quantum numbers n and 1
l angular nodes n-l-1 radial nodes
quantum numbers n and l
l angular nodes and n-l-1 radial nodes, giving total n-1 nodes
half-filled shells
lesser ole because ionization energies are discontinuous
hydrocarbon
linear and branched
2p and 3d orbital
looks like 1s orbital
pz
m(l) = 0
photochemistry
molecules absorbs a photon, resulting in an excited state much more chemically reactive than the molecule in ground state
**Polyelectronic atoms
more than one electron
Penetration effect with 4s and 3d electrons
most probable distance from the nucleus for a 3d electron s less than that for a 4s electron 4s electron has a significant probability of penetrating close to the nucleus Potassium = 1s2 2s2 2p6 3s2 3p6 4s1 NOT 1s2 2s2 2p6 3s2 3p6 3d1
##### pyrrole
non bonded pair on the spa hybridized nitrogen atom adds to the other 4 pi electrons to provided benzene like aromatic properties
alkali metals
one s-electron
When reaching oxygen...
ordering of MO assume the expected ordering
#### Atomic s orbitals cannot form pi bond because...
overlap integral with a p-orbital in pi configuration is zero
3D structure of molecules
p and d orbitals contribute
Electrons in 3s and 3p orbitals compared to 3d (effect of charge)
penetrate closer to the nucleus than 3d
Linear combinations of 2s and 2p orbitals
phi1 = .5[(s) + (px) + (py) + (pz)] phi2 = .5[(s) + (px) - (py) - (pz)] phi3 = .5[(s) - (px) + (py) - (pz)] phi4 = .5[(s) - (px) - (py) + (pz)] (s) represents 2s (p) represents 2p -1/2 represent boundary condition that total probability is 1 for each orbital -each function represents a separate sp3 hybrid orbital
Squaring of wave function is necessary because
probability is always a positive quantity, whereas the wave function itself can be both negative and positive
wave function ^2 dr
probability per unit volume at a certain distance from the nucleus
#### Different l orbitals having the same n...
same energy in hydrogen but in larger atoms and in the presence of external electric or magnetic fields energies differ
Probability of finding an electron
sigma 1s^2 = C1^2 [(WF1sa)^2 + (WF1sb)^2 + 2(WF1sa)(WF1sb)] bonding sigma 1s*^2 = C2^2 [(WF1sa)^2 + (WF1sb)^2 - 2(WF1sa)(WF1sb)] anti-bonding -squares of the orbital wave functions are always positive and are the same for sigma and sigma* orbitals -difference lies "cross-terms" (same magnitude but opposite sign)
Hydrogen atom
single electron interacting with single proton of charge +1
noble gases
six p-electrons
Valence electrons and sigma bonding
small fraction of valence electrons are used in pi bonding
Expectations of sodium and hydrogen
sodium and hydrogen electron should experience the sam effective nuclear charge of 1, the same as H atom energy levels n = 3, 4, 5 would be similar to those for the H atom
**Total probability in radial probability distribution
space around hydrogen nucleus is made up of a series of thin spherical shells, the total probability of finding the electron in each spherical shell is plotted verses the distance from the nucleus
How to find wave function?
substituting Z(eff) in place of Z=1 in hydrogen wave mechanical equation
**The relative probability of finding an electron near positions 1 and 2 is determined by...
substituting the values r, theta, phi for two positions into the wave function, squaring the function value, and computing into ratio: 8 (r1, theta 1, phi 1)^2 dv / 8 (r2, theta 2, phi 2)^2 dv = N1 / N2
N1 / N2 and what it fails to tell?
the ratio of probabilities of finding the electron in the infinitesimally small volume elements dv around points 1 and 2 no information about position or how it moves between the positions consistent with Heisenberg uncertainty principle
**R^2
the square of the radial part (depends on r)
Problem with the physical meaning of wave function ...
the uncertainty principle indicates that there is not way of knowing the detailed movements of the election in a hydrogen atom
r -> 0
the wave function (r, theta, phi) vanishes for all orbitals except s orbitals (only have significant probability of being found close to the nucleus)
if electron spin flips in excited state...
triplet stat will arse, which blocked from emitting fluorescence
alkaline earth elements
two s-electrons
#### How to achieve a minimum energy
uses one set of atomic orbitals in free state and different set in a molecule
r -> 0
wave function (r, theta, phi) for all orbitals except s-orbitals, only s-orbital electrons have a significant probability of being found close to the nucleus
