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Hybridization and hypervalency in transition-metal and main-group bonding. (The Absence of ) Radial Nodes of Atomic Orbitals, an Important Aspect in Bonding Throughout the Periodic Table Consequences for p-Block Elements: Hybridization Defects ,

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slide1

Hybridization and hypervalency

in transition-metal and main-group bonding

  • (The Absence of) Radial Nodes ofAtomic Orbitals,
  • an ImportantAspect in BondingThroughoutthePeriodic Table
  • Consequencesfor p-Block Elements: HybridizationDefects,
  • Hypervalency, Bond Polarity, etc….
  • Consequencesfür the Transition Metal Elements
  • Non-VSEPR Structuresof d0Complexes

Martin Kaupp, Winter School on Quantum Chemistry, Helsinki, Dec. 13-17, 2009

slide2

Analogybetween Wave Functionsand

Classical Standing Waves

Note thenodes (zerocrossings)!!

Theyresultfromthenecessary

orthogonalityofthemodes.

x=l

x=0

Vibrationsof a stringfixedatboth

ends. Base tone andthefirsttwo

harmonicsareshown.

2. harmonic

1. harmonic

base tone

slide3

The Nodes ofthe Radial Solutions

R istheproductof an exponential e-(1/2)randof an

associatedLaguerrepolynomial; r = 2Zr/na0

1s, 2p, 3d, 4f: no „primogenicrepulsion“ (Pekka Pyykkö)

slide4

1s

2p

2p

3d

4f

See also: J. Comput. Chem.2007, 28, 320.

slide5

2p

2p

P-Block Main-Group Elements

See also: J. Comput. Chem.2007, 28, 320.

slide7

X-H Binding Energiesof Monohydrides XH,

andof „Saturated“ Hydrides MHn

W. KutzelniggAngew. Chem.1984, 96, 262.

slide8

Radial ExtentandEnergiesofValence Orbitals

W. Kutzelnigg Angew. Chem.1984, 96, 262.

AO-Energies from Moore Tables

26-55%

20-33%

24-40%

10%

r-expectationvaluesfromDesclauxtables (DHF)

slide9

ReasonsforHybridization (1)

better bonding overlap

(radial)

reduced antibonding overlap

(angular)

slide10

ReasonsforHybridization (2)

W. Kutzelnigg, Einführung in die

Theoretische Chemie, Vol. 2

slide11

HybridizationDefects (1)

Mulliken gross populations

for valence AOs in XHn hydrides

without free electron pairs

W. Kutzelnigg Angew. Chem.1984, 96, 262.

slide12

HybridizationDefects (2)

cos(180-) = a2/(1-a2) (a2 = s-character, 1-a2 = p-character)

Holdsonlyfor orthogonal hybrids!

*A posteriori hybridizationanalysesfromDFT calculations (BP86/TZVP)

slide13

Explanationsofthe Inert-Pair Effect

1) Promotion energies increase down the group

2) Drago: Binding energies decrease down the group

 promotion energies are not overcompensated anymore

3) Extension following Kutzelnigg:

Promotion does not take place anymore 

no good hybrids and weakened covalent bonds in

higher oxidation state

slide14

decreasing stability:

R4Pb > R3PbX > R2PbX2 > RPbX3 > PbX4

(R = alkyl, aryl; X = halogen, OR, NR2, OOCR, etc……)

Why is Inorganic Lead Chemistry Dominated by PbII,

but Organolead Chemistry by PbIV?

(J. Am. Chem. Soc.1993, 115, 1061)

slide15

Substituent Effects on 1,1

-

Elimination Reactions of Pb(IV) Compounds

PbMe

F

PbMe

F

+F

160

n

4

-

n

n

2

-

n

2

140

)

120

1

-

100

(kJ mol

80

60

40

react.

PbMe

F

PbMe

F

+MeF

n

4

-

n

n

-

1

3

-

n

20

E

D

0

PbMe

F

PbMe

F

+C

H

-

20

n

4

-

n

n

-

2

4

-

n

2

6

-

40

-

60

PbMeF

PbMe

F

PbF

PbMe

F

PbMe

3

3

4

2

2

4

1993

J. Am. Chem. Soc.

,

115

, 1061.

QCISD/DZ+P data

slide16

160

140

120

100

80

60

40

20

0

-20

-40

-60

Substituent Effects on 1,1-Elimination Reactions of Pb(IV) Compounds

PbMenF4-n→ PbMenF2-n +F2

DEreact. (kJ mol-1)

PbMenF4-n→ PbMen-1F3-n +MeF

PbMenF4-n→ PbMen-2F4-n +C2H6

PbMeF3

PbMe3F

PbF4

PbMe2F2

PbMe4

J. Am. Chem. Soc.1993, 115, 1061.

QCISD/DZ+P data

slide17

HybridizationDefects (3)

h(E): NPA/NLMO Hybridization

results from DFT calculations (BP86)

slide19

Bent‘sRule: Basic Principles

e.g.:

larger angles between

more electropositive substituents

more s-character of central atom is directed

towards less electronegative substituent,

more p-character to more electronegative substituent

H. A. Bent Chem. Rev.1961, 61, 275; H. C. Allen at al. J. Am. Chem. Soc.1958, 80, 2673.

exceptions: a) large steric effects, b) very different sizes of substituent orbitals (e.g. H vs. Hg),

c) counteracting effects for very light central atoms d) transition metal systems (cf. also Huheey text book)

slide20

Bent‘sruleeffects in organoleadfluorides

101.10

Pb

115.50

Pb

116.40

102.80

101.40

104.10

Pb

134.80

Quasirelativistic ab initio calculations, J. Am.Chem. Soc.1993, 115, 1061.

slide21

Bent‘sRule: CounteractingEffects

negative hyperconjugation

„switched off“

negative hyperconjugation

counteracts EN effects

negative hyperconjugation

small for heavier elements

slide22

Bent‘sRuleand Lone Pairs

h: NPA/NLMO Hybridization

results from DFT calculations (BP86)

slide23

Inversion BarriersandHybridization

TS

pure p-character of LP

high s-character in bonds

high s-character of LP

high p-character in bonds

  • everything that enhances hybridization defects increases inversion barrier

and decreases angles!

  • e.g. NH3 << PH3 < AsH3 < SbH3 < BiH3
  • NLi3 << NH3 << NF3
  • NH3 << NH2F << NHF2 << NF3
slide24

Further Pecularitiesof 1st-Row (2. Period) Elements (p-Block)

important: size, electronegativity, hybridizationdefects

particularlyweakbondsfor F2, H2O2, N2H4, ..........

e.g. BDE (kJ mol‑1): F2 155, Cl2 240, Br2 190, I2 149.

(cf. also low EA offluorineatom!)

explanation: „lone-pair bondweakeningeffect“ (Sanderson),

(lesspronouncedforheavierhomologues)

preferencefor- multiple bondingcomparedtochain-linkedsinglebonds

e.g.: O2vs S8, CO2 vs. SiO2, ketones vs. silicones

e.g. BDE (kJ mol‑1):

slide26

BDEs (kJ mol‑1):

also: bond ionicity

cf. silicates, etc…!

X

C-X

Si-X

F

485

565

Cl

327

381

Br

285

310

I

213

234

Preference for- multiple bondingcomparedtochain-linkedsinglebonds

increments (/, in kJ mol‑1):

slide27

Pauling

Allred-Rochow

slide28

Silicon-Oxygen Bonds

Electronegativity

Si: 1.74 O: 3.50

154o

111o

Electron-Localisation-Function

Electron-Localisation-Function

The Si-O Bond has a Strong Ionic Character

summary hybridization defects and related phenomena in p block main group chemistry
Summary: HybridizationDefectsandRelatedPhenomena in p-Block Main-Group Chemistry
  • 2p shellhasnoprimogenicrepulsionandisthuscompact
  • thisfavorsisovalenthybridization in the 2nd period
  • electronegativesubstituentsenhancehybridizationdefects
  • fortheheavier p-block elements, hybridizationdefectsareimportantfor inert-pair effect, inversionbarriers, Bent‘sruleeffects, double-bondrule…..
  • large electronegativityof 2p-elements also arisesfromcompact 2p shell
slide31

covalency increases

ionicity increases

certainly no

hypervalency

hypervalency ?

On the Definition of Hyper-(co)-Valency

MgF64-SiF62-SF6

slide32

A Working Definition of Hypervalency

We regard a molecule as hypervalent

if at least for one atom the bonding situation

requires more valence orbitals

than available for the free atom

slide33

The Early History of Hypervalency, Part 1

electron pair theory, octet rule

Lewis 1916; Kossel 1916; Langmuir 1919

directed valency, spmdn hybrids,

electroneutrality principle

Pauling 1931, 1940, 1948

3-center-4-electron-bond

Pimentel 1951; Hach, Rundle 1951

slide34

F Xe F

F - Xe+ F

F Xe + F -

F - Xe2+ F -

LimitingBondingSituations:

Exampleof Different Lewis Structuresfor XeF2

covalent, hypervalent

partially ionic,

delocalized

ionic

slide35

3-Center-4-Electron MO Model

F - Xe+ F

F Xe + F -

pa

pn

pb

sa

sn

sb

slide36

F - Xe+ F

F Xe + F -

pa

pn

pb

sa

sn

sb

Modified 3-Center-4-Electron MO Model

slide37

The Early History of Hypervalency, Part 2

discovery of noble-gas compounds

Chernik et al.; Claasen et al.; Bartlett,

Hoppe; since 1962:

first ab initio calculations

since ca. 1970

first improved wave functions,

Mulliken population analyses

since ca. 1975:

slide38

+ l

=

electric field

The Roleof d-Polarization-Functions

pp + l dp = polarized pp

slide39

weak points of Mulliken population analysis:

strong basis-set dependence

unphysical (partly negative) populations

failure for transition to ionic bonding

slide40

ImprovedAnalysesofAccurate Wave Functions

modifiedRoby/Davidson populationanalysis

Ahlrichs et al. 1976, 1985;

Wallmeier, Kutzelnigg1979

„Natural Population Analysis“ (NPA),

„Natural Bond Orbital Analysis“ (NBO)

Reed, Weinhold 1986; Reed, Schleyer 1990

„Natural ResonanceTheory“ (NRT)

Weinhold et al., 1995

energycontributionsfrom d-orbitals

Magnusson 1986, 1990, 1993

topologicalanalysisofelectrondensity (QTAIM)

Cioslowski, Mixon 1993

„GeneralizedValence Bond“ (GVB) theory

  • Hay 1977, Cooper et al. 1994 (full-GVB)

one-centerexpansionofone-particledensitymatrix

  • Häser 1996
  • Sincelate 1990‘s
  • QTAIM based on experimental densities
  • (e.g. D. Stalke et al.)
slide41

NRT-Analysis of Sulfate Ion

NRT weight:

O

0%

- O S O -

O

O -

- O S2+O -

66.2%

O -

O

12x1.9% = 22.8%

- O S2+ O -

O 2-

11%

NRT at HF/6-31G* level

Weinhold et al., 1995

further ionic structures:

slide42

Which NRT-Lewis StructureDescribesthe Perchlorate Ion Best?

NRT weight:

O

0%

O Cl O -

O

O -

60.9%

- O Cl3+O -

O -

O

- O Cl3+O -

12x2.0% = 24.0%

O 2-

further ionic structures:

15%

NRT at HF/6-31G* level

Weinhold et al., 1995

slide43

C

C

C

C

C

C

H+

H

H+

C

C

C-

C

C

C

C-

C

C

H

H

H

HyperconjugationExemplifiedbyCyclopentadiene

......

H

C

C

p3*

su

C

C

C

H

slide44

F

F

F+

F-

F-

F+

C

C

C

H

H

H

H

H

H

Negative HyperconjugationExemplifiedbyDifluoromethane

......

p(F)

F

F

s*(C-F)

C

H

H

slide45

F

P

O

F

F

Negative Hyperconjugation in F3PO

F

F-

F

P+

O-

P+

O

P+

O

F

F

F

......

F-

F

F

p(O)

(to e-MO)

s*(P-F)

(to e*-MO)

slide46

F

P

M

s*(P-F)

p(M)

F

F

…….andforp-backbonding in phosphanecomplexes…….

slide47

Musher’sClassificationof

„Hypervalent“ Compounds

(Musher 1969)

summary hypervalency d orbital participation in p block main group chemistry
Summary: Hypervalency, d-Orbital-Participationin p-Block Main-Group Chemistry
  • in normal valent and „hypervalent“ p-block main-groupsystems, d-functionsserveas „polarizationfunctions“ but not astruevalenceorbitals
  • hypervalent Lewis structuresusuallyobtainsmallornoweight!
  • ionicbondingcontributionsdominate, assistedbydelocalization (3-c-4-el.-bonding, negative hyperconjugation)
  • in PF5, SF6, etc., delocalizationismorecomplex due to s-orbital participationsignificant hypervalent populations
slide50

3d

Transition Metal Systems

slide51

Radial Orbital DensitiesoftheManganese Atom

r f(r) in a.u.

r in a.u.

J. Comput. Chem.2007, 28, 320

slide52

M

L

(n-1)d

(n-1)s,p

outermost

core shell

Pauli repulsion

 stretched bond

The problemoftheoutermostcoreshells in transition-metalatoms

The problem is most pronounced for the 3d elements

(nodelessness of the 3d shell)

 weak bonds, low-lying excited states, strong (nondynamical) correlation effects

The 4d shell is already better suited for bonding overlap.

The 5d shell even more so due to its relativistic expansion.

M. Kaupp J. Comput. Chem.2007, 28, 320.

See also: M. A. Buijse, E. J. Baerends J. Chem. Phys.1990, 93, 4129.

slide53

M

M

(n-1)d

(n-1)s,p

outermost

core shell

Pauli repulsion

 stretched bond

The problemoftheoutermostcoreshells in transition-metalatoms

The problem is most pronounced for the 3d elements

(nodelessness of the 3d shell)

 weak bonds, low-lying excited states, strong (nondynamical) correlation effects

The 4d shell is already better suited for bonding overlap.

The 5d shell even more so due to its relativistic expansion.

M. KauppJ. Comput. Chem.2007, 28, 320.

See also: M. A. Buijse, E. J. BaerendsJ. Chem. Phys.1990, 93, 4129.

slide54

M

L

(n-1)d

(n-1)s,p

outermost

core shell

Pauli repulsion

 stretched bond

The problemoftheoutermostcoreshells in transition-metalatoms

The problem is most pronounced for the 3d elements

(nodelessness of the 3d shell)

 weak bonds, low-lying excited states, strong (nondynamical) correlation effects

The 4d shell is already better suited for bonding overlap.

The 5d shell even more so due to its relativistic expansion.

M. Kaupp J. Comput. Chem.2007, 28, 320.

See also: M. A. Buijse, E. J. Baerends J. Chem. Phys.1990, 93, 4129.

slide55

Non-VSEPR Structures

andBondingford0-Systems

slide56

VSEPR = valence-shell electron-pair-repulsion model

Non-VSEPR Structures of d0-Systems

slide58

ZrO2,

ferroelectric perovskites

e.g. materials

PracticalRelevanceof d0-Systems

e.g. catalysis

e.g. bioinorganicchemistry

Mo-Cofactor (after Rajagopalan, Johnson)

slide59

F

F

Mg

Ba

F

F

1230

The QuestionofBending

oftheAlkaline Earth

Dihalides

linearization energies in kJ/mol from SDCI calculations

(J. Am. Chem. Soc.1991, 113, 6012)

slide60

M

X

X

Factors Controlling theStructuresof d0 Systems

mutual repulsionandpolarizationoftheligands

maximizationof d-orbital participation in -bonding

distorted, „non-VSEPR“ structures

regular, „VSEPR“ structures

polarization of central-atom semi-core orbitals by the ligands, „inverse polarization“ of cation

maximization of -bonding

(??)

Review:

Angew. Chemie 2001, 113, 642.

slide63

BaH2: ElectronLocalizationFunction (ELF, colorscale)

projected on electrondensity (cloudofpoints)

slide64

Bending Force Constants (at Linear Structure)

for Molecular Alkaline Earth Dihalides

J. Am. Chem. Soc. 1991, 113, 6017

forceconstantsfrompolarizedion

model toolowforBeand Mg

complexes but toohighfor

Ca, Sr, andBacomplexes

slide65

Radial Distribution of (Pseudo)-Valence Orbitals of Barium

0.20

5p

0.15

6p

5d

0.10

r f(r) (a.u.)

0.05

6s

0.00

-0.05

0

2

4

6

r (Å)

outer-corepolarizationand d-orbital participationcannotbeseparatedcompletely!

slide66

Factors Controlling theStructuresof d0 Systems

M

X

X

maximization of d-orbital participation in -bonding

mutual repulsion and polarization of the ligands

distorted, „non-VSEPR“ structures

regular, „VSEPR“ structures

polarization of central-atom semi-core orbitals by the ligands, „inverse polarization“ of cation

maximization of -bonding

(??)

Review:

Angew. Chemie 2001, 113, 642.

slide67

Low Ligand-Ligand Repulsion for Neutral Ligands

J. Phys. Chem.1992, 96, 7316

Ba2+(H2O)2

Ba

O

O

DE(MP2)Lin= 0.6 kJ/Mol

1170

Ba2+(H2O)3

Ba

O

O

O

DE(HF)Plan= 0.4 kJ/Mol

980

slide68

Cs+(H2O)2

Cs

O

O

1220

DE(MP2)Lin= 0.2 kJ/Mol

slide69

M

X

X

Factors Controlling theStructuresof d0 Systems

maximization of d-orbital participation in -bonding

mutual repulsion and polarization of the ligands

distorted, „non-VSEPR“ structures

regular, „VSEPR“ structures

polarization of central-atom semi-core orbitals by the ligands, „inverse polarization“ of cation

maximization of -bonding

(??)

Review:

Angew. Chemie 2001, 113, 642.

slide70

30

25

20

15

10

5

0

X: Li BeH BH2 CH3 NH2 OH F

Effectsofp-Bonding

C2v(in-plane)

DElin/

kJ mol-1

Cs

C2v(out-of-plane)

Ba

Ba

N

N

N

N

128.8º

118.4º

C2v(in-plane)

DE(HF)= 0.0 kJ mol-1

C2v(out-of-plane)

DE(HF)= +15.7 kJ mol-1

slide71

MR2 (M = Ca, Yb, Eu; R = C[Si(CH3)3]3 )

Eaborn et al. Organomet.1996, 15, 4783.

J. Chem. Soc., Chem. Commun.1997, 1961.

slide72

StructuralPreferencesof d0 MX3Complexes

Sc

H

H

H

F

Sc

F

F

C. A. Jolly, D. S. MarynickInorg. Chem.1989, 28, 2893.

slide73

X

X

M

X

X

X

X

p-Acceptor-Type d-Orbitals for Linear and Bent MX2 d0Complexes

‘pip’, ‘b2’

‘pop’, ‘a2’

‘pip’, a1

‘pop’, a2

‘pop’, b1

slide76

117.30

107.50

Cl

Cl

Cl

Cl

Ti

Si

C

C

C

C

102.80

114.20

Inversion ofBent’srulefor d0-Systems

(CH3)2SiCl2

(CH3)2TiCl2

GED data, Haaland et al., 1996.

Explanation via p-contributions: Chem. Eur. J.1999, 5, 3632.

slide78

typical ligand types:

S-

S-

S-

S-

S

S

H

H

H2

H2

H

H

ExamplesforNonoctahedralComplexeswith Sulfur Ligands

See, e.g.:

Can. J. Chem. 1989, 67, 1914

Inorg. Chem. 1993, 32, 2085

Inorg. Chem. 1989, 28, 773, etc.....

slide80

The Structureof W(CH3)6

95.60

2.15 Å

W

W

2. 18 Å

2.21 Å

75.60

84.60

D3

C3

transition state

minimum

+17 kJ/mol

CCSD(T)

M. Kaupp J. Am. Chem. Soc. 1996, 118, 3018.

slide82

MO Rationalization of Nonoctahedral d0 Structures

S. K. Kang, H. Tang, T. A. Albright J. Am. Chem. Soc.1993, 115, 1971.

slide83

Landis’ sd-Hybridization Model (1)

(J. Am. Chem. Soc. 1998, 120, 1842)

slide84

Landis’ sd-Hybridization Model (2)

(J. Am. Chem. Soc. 1998, 120, 1842)

Preferred coordination arrangements for sd5 hybrids.

slide85

EnergeticsofBaylar Twist for MX6 d0Complexes

D3h

M

M

transition state

Oh

minimum

Relative energies (kJ mol—1) between D3h and Oh

structures of group 6 hexahalide complexes

aDFT-BP86 results, Angew. Chem., Int. Ed. Engl.2001, 40, 3534.

No convergence for CrBr6, CrI6, MoI6.

slide86

S

S

S

2.414 Å

88.7º

Mo

2.406 Å

S

S

S

83.5º

dihedral d = 26º

40

35

30

25

20

15

10

5

0

0

5

10

15

20

25

30

35

40

45

50

55

60

Mo(SH)6:

intermediate

betweenoctahedral

andtrigonalprismatic

Erel /

kJ mol-1

d / deg

slide87

Importanceoftrigonalprismatic intermediates andtransitionstructures

ofcertainmolybdenumenzymes

Review: M. Kaupp Angew. Chemie, Int. Ed. Engl. 2004, 43, 546.

slide88

The Structureof WCl5CH3

79.90

83.30

C

Cl3

2.19 Å

2.32 Å

Cl2

C

78.10

Cl4

102.10

2.35 Å

2.22 Å

W

81.10

Cl2

Cl1

W

Cl3

2.33 Å

75.60

2.39 Å

2.34 Å

2.35 Å

81.90

2.35 Å

Cl5

Cl1

Cl5

Cl4

85.30

<Cl1-W-Cl5 = 97.90

<Cl1-W-Cl2 = 179.80

<Cl3-W-Cl4 = 166.30

<Cl1-W-Cl3 = 87.00

Cs trig. prism

Cs oct.

transition state

minimum

+19 kJ/mol

BP86/A

BP86 data, relative energies in kJ/mol

Angew. Chemie 1999, 111, 3219

slide89

The Structureof WCl4(CH3)2

tp “same face”, Cs

(TS +14.5)

cis oct. C2v

(TS +25.7)

cis tp “other face”, C2v

(TS +8.5)

“intermediate” C2

(min. +6.5)

trans oct. C2

(min. 0.0)

BP86 data, relative energies in kJ/mol

Angew. Chemie 1999, 111, 3219

slide90

The Structureof WCl3(CH3)3

oct. fac. C3v

(TS +61.2)

oct. merid. Cs

(TS +26.0)

tp “across” C1

(min. 0.0)

tp “same face” C3

(min. +2.3)

BP86 data, relative energies in kJ/mol

Angew. Chemie 1999, 111, 3219

slide91

Examples of Unsymmetrical Metal Coordination in Oxide Materials

*5d vs. 4d comparisons:

KTaO3 is regular octahedral (cubic) and paraelectric, KNbO3 is distorted (rhombohedral)

and ferroelectric at lower temperatures.

LiTaO3 has a ferroelectric transition at lower temperature (950 K) than LiNbO3 (1480 K).

More ionic bonding and larger band gap with 5d vs. 4d, due to relativistic effects!

slide92

Structures of the Dihydride Dimers M2H4 (M = Mg, Ca, Sr, Ba)

(relative MP2 Energies in kJ/Mol)

C2h

D2h

+19.2

+35.5

0.0

0.0

+20.1

+56.0

C2v

C3v

+115.0

+5.9

0.0

0.0

D4h

+507.0

+130.4

+86.5

+33.4

C2v

J. Am. Chem. Soc. 1993, 115, 11202

slide93

Summary: Understanding Non-VSEPR Structures in d0-Complexes

-d0complexeswithpurely-bondedligandstendtoviolate VSEPR

andrelatedmodels, in spiteofincreasedligandrepulsion.

-whileextended VSEPR modelsare not useful in rationalizingthedistorted

structures, both MO and VB modelsaresuccessfulfor simple homoleptic

complexes.

--bondingismuchmoreimportant in d0complexesthan in related p-block

complexes, due totheavalabilityofinner d-orbitals.

-the interrelationbetween-bondingandbondanglesiscomplicated, due to

theinvolvementof different d‑orbitals.

-the “anti-Bent’s-rule” structureof TiCl2(CH3)2is due toTi‑Cl-bonding!

-additional -donorligandsinfluencetheanglesbetween-donorligands in

heterolepticcomplexes.

slide95

“Natural Population Analysis”

“Natural Bond Orbital Analysis”

Weinhold et al. 1984, 1988

AO basis

NAO basis

NHO basis

NBO basis

original basis set

occupancy-weighted Löwdin orthogonalization

“natural atomic orbitals”

“natural minimal basis set” (strongly occupied)

“natural Rydberg basis set” (sparsely occupied)

“natural hybrid orbitals”

“natural bond orbitals”

NBO-Lewis-structure

“natural resonance theory” (NRT)

superposition of NBO-Lewis structures

Weinhold et al. 1995

NLMO basis

“natürliche lokalisierte Orbitale”

slide96

NRT Weights (w) forVarious Lewis Structures

in Oxo Anions and Sulfur Oxides

species

NRT at HF/6-31G* (MP2/6-31G*) level

Weinhold et al., 1995

slide97

H2

H1

H3

C1

C2

M

M

C2A

Structure of Mo(butadiene)3

slide98

Limits oftheIsolobalPrinciple

+

+

Zr

H

Si

H

H

H

H

H

.

.

Zr

Si

H

H

H

H

H

H

-

-

H

Si

Zr

H

H

H

H

H

d(Zr-H)=1.800Å, <H-Zr-H=104.8º

d(Si-H)=1.488Å, <H-Si-H=120.0º

d(Si-H)=1.500Å, <H-Si-H=110.9º

d(Zr-H)=1.862Å, <H-Zr-H=116.6º

d(Si-H)=1.563Å, <H-Si-H=93.3º

d(Zr-H)=1.902Å, <H-Zr-H=120.0º

Review: M. KauppAngew. Chemie2001, 113,3642.

slide99

Extreme Resonance Structures for

tris(Butadiene)-Molybdenum and Related Complexes

slide101

5p

a‘‘,e‘

a‘‘

Y4

e‘‘

a‘

5s

3e‘

2e‘‘

a‘

3a‘

Y3

e‘

2a‘

4d

a‘,e‘,e‘‘

2e‘

e‘‘

Y2

1a‘‘

a‘‘

1e‘‘

e‘

1e‘

Y1

a‘

1a‘

(C4H6)3

Mo(C4H6)3

C3h

Mo

slide105

Trends of the s- and d-valence orbitals in the transition metal series

a) radial size

from Dirac-Fock calculations (Desclaux)

slide106

Trends of the s- and d-valence orbitals in the transition metal series

b) orbital energies

from Dirac-Fock calculations (Desclaux)

slide109

On the relative energies of 3d- and 4s orbitals

The 3d orbitals are always lower in energy (and smaller!) than 4s.

Stronger electron repulsion in 3d may nevertheless favor 4s occupation.

slide110

3p orbital (outermost core shell)

3d orbital (valence shell)

Ca atom:

radial orbital densities

Malrieu et al.Chem. Phys. Lett.1983, 98, 433.