Anion Electronic Structure Anion Electronic Structure and Correlated, One-electron and Correlated, One-electron

TheoryTheoryJ. V. Ortiz

Department of Chemistry and Biochemistry

Auburn Universitywww.auburn.edu/cosam/JVOrtiz

Workshop on Molecular Anions and Electron-Molecule Interactions in Honor

of Professor Kenneth Jordan

July 1, 2007Park City, Utah

AcknowledgmentsAcknowledgmentsFunding National Science FoundationNational Science Foundation Defense Threat Reduction Defense Threat Reduction

AgencyAgency

Auburn CoworkersAuburn University• Department of Chemistry and Biochemistry

Symposium Organizers• Jack Simons• Brad Hoffman

UNAM Collaborators:• Ana Martínez• Alfredo Guevara

Quantum Chemistry’s MissionsQuantum Chemistry’s Missions Deductive Deductive

agenda:agenda: Deduce properties of Deduce properties of

molecules from quantum molecules from quantum mechanicsmechanics

Calculate chemical data, Calculate chemical data, especially if experiments especially if experiments are difficult or expensiveare difficult or expensive

Inductive agenda:Inductive agenda: Identify and explain Identify and explain

patterns in structure, patterns in structure, spectra, energetics, spectra, energetics, reactivityreactivity

Deepen and generalize the Deepen and generalize the principles of chemical principles of chemical bondingbonding

E. Schrödinger G. N. Lewis

Electron PropagatorTheory

Molecular OrbitalTheory Applications

Interpretation

Exactness

One-electron EquationsOne-electron Equations Hartree Fock TheoryHartree Fock Theory

Hartree Fock Equations:Hartree Fock Equations:

(T(Tkin kin + U+ Unucl nucl + J+ JCoul Coul - K- Kexchexch))φφiiHF HF ≡≡

F F φφiiHFHF==εεii

HF HF φφiiHFHF

Same potential for all i:Same potential for all i:core, valence, occupied, core, valence, occupied, virtual.virtual.

εεiiHFHF includes Coulomb and includes Coulomb and

exchange contributions to IEs exchange contributions to IEs and EAsand EAs

Electron Propagator Electron Propagator TheoryTheory

Dyson Equation:Dyson Equation:

[F + [F + ∑(∑(εεiiDysonDyson)])]φφii

DysonDyson = = εεiiDyson Dyson φφii

DysonDyson

Self energy, Self energy, ∑(E): ∑(E): Energy Energy dependent, nonlocal potential dependent, nonlocal potential that varies for each electron that varies for each electron binding energybinding energy

εεiiDysonDyson includes Coulomb, includes Coulomb,

exchange, relaxation and exchange, relaxation and correlation contributions to IEs correlation contributions to IEs and EAsand EAs

φφiiDysonDyson describes effect of electron describes effect of electron

detachment or attachment on detachment or attachment on electronic structureelectronic structure

Dyson Orbitals Dyson Orbitals (Feynman-Dyson Amplitudes)(Feynman-Dyson Amplitudes)

Electron Detachment (IEs)Electron Detachment (IEs)

φφiiDysonDyson(x(x11) = ) =

NN-½-½∫∫ΨΨNN(x(x11,x,x22,x,x33,…,x,…,xNN))ΨΨ**i,N-1i,N-1(x(x22,x,x33,x,x44,...,x,...,xNN))

dxdx22dxdx33dxdx44…dx…dxNN

Electron Attachment (EAs)Electron Attachment (EAs)

φφiiDysonDyson(x(x11) =) =

(N+1)(N+1)-½-½∫ ∫ ΨΨi,N+1i,N+1(x(x11,x,x22,x,x33,...,x,...,xN+1N+1))ΨΨ**NN(x(x22,x,x33,x,x44,…,x,…,xN+1N+1) )

dxdx22dxdx33dxdx44…dx…dxN+1N+1

Pole strengthPole strength

PPii = ∫| = ∫|φφiiDysonDyson(x)|(x)|22dxdx

0 ≤ P0 ≤ Pii ≤ 1 ≤ 1

Electron Propagator ConceptsElectron Propagator Concepts

Canonical MO Dyson Orbital

Orbital Energy Correlated Electron Binding Energy

Integer Occupation Numbers

Pole Strengths

Independent-ParticlePotential

Energy-dependent,Self-Energy

Electron Correlation

Accuracy Accuracy versusversus InterpretabilityInterpretability

Does electron Does electron propagator theory propagator theory offer a solution to offer a solution to Mulliken’s Mulliken’s dilemma?dilemma?

The more accurate thecalculations become, the more the conceptsvanish into thin air.- R. S. Mulliken

88.5

99.510

10.511

11.512

12.513

Uracil Thymine

IEs

(eV)

Pi1 P3Pi1 PESSg- P3Sg- PESPi2 P3Pi2 PESSg+ P3Sg+ PESPi3 P3Pi3 PES

Substituent Effects: U and TSubstituent Effects: U and T

Dyson Orbitals for U and T IEsDyson Orbitals for U and T IEs

Uracil

Thymine

π1 σ- π2 σ+ π3

Methyl (CH3) participation

Uracil Uracil versusversus Thymine Thymine

Methyl group destabilizes Methyl group destabilizes ππ orbitals orbitals with large with large amplitudes at nearest ring amplitudes at nearest ring atomatom

Therefore, IE(T) < IE(U)Therefore, IE(T) < IE(U) Valid principles for substituted DNA Valid principles for substituted DNA

bases, porphyrins and other organic bases, porphyrins and other organic moleculesmolecules

A Self-Energy for A Self-Energy for Large Molecules: P3Large Molecules: P3

Neglect off-diagonal elements of Neglect off-diagonal elements of ΣΣ(E) in (E) in canonical MO basis: canonical MO basis: φφii

DysonDyson(x) = P(x) = Pii½½ φφii

HF-CMOHF-CMO(x)(x) Partial summation of third-order diagramsPartial summation of third-order diagrams Arithmetic bottleneck: oNArithmetic bottleneck: oN44 (MP2 partial (MP2 partial

integral transformation)integral transformation) Storage bottleneck: oStorage bottleneck: o22vv22 in semidirect mode in semidirect mode Abelian, symmetry-adapted algorithm in G03Abelian, symmetry-adapted algorithm in G03

Formulae for Formulae for ΣΣP3P3(E)(E) ΣΣP3P3

pqpq(E) = (E) =

½½ΣΣiabiab <pi||ab><ab||qi> <pi||ab><ab||qi> ΔΔ(E)(E)-1-1iabiab + +

½½ΣΣaijaij <pa||ij>(<ij||qa> + W <pa||ij>(<ij||qa> + Wijqaijqa) ) ΔΔ(E)(E)-1-1aijaij + +

½½ΣΣaijaij U Upaijpaij(E)<ij||qa>(E)<ij||qa>ΔΔ(E)(E)-1-1aijaij

wherewhere

ΔΔ(E)(E)-1-1pqrpqr = (E + = (E + εεpp – – εεqq – – εεrr))-1-1

WWijqaijqa = ½ = ½ΣΣbcbc<bc||qa><ij||bc> <bc||qa><ij||bc> ΔΔ-1-1ijbcijbc

+ (1-P+ (1-Pijij))ΣΣbkbk<bi||qk><jk||ba> <bi||qk><jk||ba> ΔΔ-1-1jkabjkab

UUpaijpaij(E) = - ½(E) = - ½ΣΣklkl<pa||kl><kl||ij> <pa||kl><kl||ij> ΔΔ(E)(E)-1-1aklakl

- (1 – P- (1 – Pijij) ) ΣΣbkbk<pb||jk><ak||bi> <pb||jk><ak||bi> ΔΔ(E)(E)-1-1bjkbjk

P3 PerformanceP3 Performance

31 Valence IEs of Closed-Shell 31 Valence IEs of Closed-Shell Molecules:Molecules:(N(N22,CO,F,CO,F22,HF,H,HF,H22O,NHO,NH33,C,C22HH22,C,C22HH44,CH,CH44,HCN,H,HCN,H22CO)CO)

MAD (eV) = 0.20 (tz)MAD (eV) = 0.20 (tz) 10 VEDEs of Closed-Shell Anions:10 VEDEs of Closed-Shell Anions:

(F(F--,Cl,Cl--,OH,OH--,SH,SH--,NH,NH22--,PH,PH22

--,CN,CN--,BO,BO--,AlO,AlO--,AlS,AlS--))

MAD (eV) = 0.25 (a-tz)MAD (eV) = 0.25 (a-tz) Arithmetic bottleneck: oArithmetic bottleneck: o22vv3 3 for Wfor Wijqaijqa

Storage bottleneck: <ia||bc> for WStorage bottleneck: <ia||bc> for W ijqaijqa

Recent Applications: Recent Applications: Porphyrins and FullerenesPorphyrins and Fullerenes

0

2

4

6

8

10

Ioniz

ati

on E

nerg

y (e

V)

2-A2 2-A1 2-B1 2-A1

Cationic States

OEP Photoelectron Spectra

KoopmansEPT-P3Expt.

0

2

4

6

8

10

12

14

Ioniz

ati

on E

nerg

y

(eV)

2Hu 2Hg 2Gg 2Gu 2T2u

Cationic States

C60 Photoelectron Spectra

KoopmansEPT-P3+Expt.

Input to Gaussian 03

Invitation to PropagateInvitation to Propagate

# OVGF 6-311G** iop(9/11=10000)

P3 Electron Propagator for Water

0 1OH 1 0.98H 1 0.98 2 105.

Available diagonal approximations for Σ(E):Second order, Third order, P3, OVGF (versions A, B & C)

Nucleotides: Gaseous SpectraNucleotides: Gaseous Spectra

Nucleotides: phosphate-sugar-base DNA Nucleotides: phosphate-sugar-base DNA fragmentsfragments

Electrospray ion sourcesElectrospray ion sources Magnetic bottle detectionMagnetic bottle detection High resolution laser spectroscopy of ions, High resolution laser spectroscopy of ions,

mass spectrometrymass spectrometry Goal: predict photoelectron spectra of Goal: predict photoelectron spectra of

anionic nucleotides (vertical electron anionic nucleotides (vertical electron detachment energies or VEDEs)detachment energies or VEDEs)

Photoelectron Spectra of Photoelectron Spectra of 2’-deoxybase 5’-monophosphate 2’-deoxybase 5’-monophosphate

AnionsAnionsDAMP

DCMP

DGMP

DTMP

Base = adenine

Base = cytosine

Base = guanine

Base = thymine

L-S.Wang, 2004

Anomalous peak for dGMP

G: lowest IEof DNA bases

Dyson orbitals forlowest VEDEs:

phosphate or base?

DAMP Isomers and EnergiesDAMP Isomers and Energies

0 kcal/mol

4.62

4.66

DAMP VEDEs (eV) DAMP VEDEs (eV) and Dyson Orbitalsand Dyson Orbitals

DODO KTKT P3P3 PESPES

PP 7.847.84 6.076.07 6.056.05

A A ππ11 6.166.16 6.156.15

PP 8.218.21 6.396.39 ~6.~6.44

PP 8.388.38 6.626.62 ~6.~6.77

PP 8.438.43 6.766.76

A A ππ22 7.757.75 6.896.89 ~6.~6.99

A nA n11 8.938.93 7.247.24 ~7.~7.11

DGMP Isomers and EnergiesDGMP Isomers and Energies

0 kcal/mol

5.1

9.2

DGMP VEDEs (eV) DGMP VEDEs (eV) and Dyson Orbitalsand Dyson Orbitals

DODO KTKT P3P3 PESPES

G G ππ11 5.255.25 5.015.01 5.055.05

PP 7.947.94 6.186.18 ~6.~6.11

PP 8.318.31 6.546.54 ~6.~6.44

PP 8.548.54 6.756.75 ~6.~6.88

G nG n11 8.658.65 6.846.84 ~6.~6.99

G G ππ22 8.128.12 6.966.96 ~7.~7.00

Hydrogen Bonds: DGMP vs Hydrogen Bonds: DGMP vs DAMPDAMP

DGMP: G amino to DGMP: G amino to Phosphate oxygen Phosphate oxygen

DAMP: Sugar DAMP: Sugar hydroxy to hydroxy to Phosphate oxygenPhosphate oxygen

Nucleotide Electronic StructureNucleotide Electronic Structure

Phosphate anion reduces Base VEDEs Phosphate anion reduces Base VEDEs by several eVby several eV

Base also increases Phosphate VEDEsBase also increases Phosphate VEDEs Therefore, Base and Phosphate VEDEs Therefore, Base and Phosphate VEDEs

are closeare close Differential correlation effects are largeDifferential correlation effects are large Koopmans ordering is not reliableKoopmans ordering is not reliable

A Simple, Renormalized Self-A Simple, Renormalized Self-Energy: P3+Energy: P3+

ΣΣP3+P3+pqpq(E) = (E) =

½½ΣΣiabiab <pi||ab><ab||qi> <pi||ab><ab||qi> ΔΔ(E)(E)-1-1iabiab + +

[1+Y(E)][1+Y(E)]-1-1 ½ ½ΣΣaijaij<pa||ij>(<ij||qa> + W<pa||ij>(<ij||qa> + Wijqaijqa) ) ΔΔ(E)(E)-1-1

aijaij + ½ + ½ΣΣaijaij U Upaijpaij(E)<ij||qa>(E)<ij||qa>ΔΔ(E)(E)-1-1aijaij

wherewhere

Y(E) = {-½Y(E) = {-½ΣΣaijaij<pa||ij>W<pa||ij>Wijqa ijqa ΔΔ(E)(E)-1-1aijaij} }

{½{½ΣΣaijaij<pa||ij><ij||qa> <pa||ij><ij||qa> ΔΔ(E)(E)-1-1aijaij}}-1-1

P3+ PerformanceP3+ Performance

31 Valence IEs of Closed-Shell 31 Valence IEs of Closed-Shell Molecules:Molecules:(N(N22,CO,F,CO,F22,HF,H,HF,H22O,NHO,NH33,C,C22HH22,C,C22HH44,CH,CH44,HCN,H,HCN,H22CO)CO)

MAD (eV) = 0.19 (tz), 0.19 (qz)MAD (eV) = 0.19 (tz), 0.19 (qz) 10 VEDEs of Closed-Shell Anions:10 VEDEs of Closed-Shell Anions:

(F(F--,Cl,Cl--,OH,OH--,SH,SH--,NH,NH22--,PH,PH22

--,CN,CN--,BO,BO--,AlO,AlO--,AlS,AlS--))

MAD (eV) = 0.11 (a-tz), 0.13 (a-qz)MAD (eV) = 0.11 (a-tz), 0.13 (a-qz)

Reactivity of AlReactivity of Al33OO33-- with H with H22OO

Wang: first anion Wang: first anion photoisomerizationphotoisomerization

Jarrold: AlJarrold: Al33OO33--(H(H22O)O)nn

photoelectron photoelectron spectra n=0,1,2spectra n=0,1,2

Distinct profile for Distinct profile for n=1n=1

Similar spectra for Similar spectra for n=2 and n=0n=2 and n=0

AlAl33OO33- - Photoelectron Photoelectron SpectrumSpectrum

Book Kite-0.8

0.2

0.8

-0.6

AnioAnionn

Final Final StateState

KTKT P3 P3 P3P3++

ExpExp..

BooBookk

22BB22 2.952.95 2.852.85 2.842.84 2.962.96

22AA11 3.573.57 3.493.49 3.483.48 3.73.7

KiteKite 22AA11 2.102.10 2.022.02 2.012.01 2.252.25

22BB22 7.207.20 5.735.73 5.305.30 5.25.2

22AA22 6.946.94 5.725.72 5.405.40 5.25.2

22AA11 6.026.02 6.056.05 6.066.06

Cluster VEDEs and Dyson OrbitalsCluster VEDEs and Dyson Orbitals

ClusterCluster P3+P3+ Expt. Expt. (eV)(eV)

AlAl33OO33-- 2.842.84 2.962.96

3.483.48 3.73.7

AlAl33OO44HH22-- 2.722.72 2.7 – 2.82.7 – 2.8

3.803.80 3.8 – 4.03.8 – 4.0

AlAl33OO55HH44-- 3.233.23 3.33.3

3.633.63 3.83.8

Al3O3-

Al3O4H2-

Al3O5H4-

Strong Initial State CorrelationStrong Initial State Correlation

Need better reference orbitals for:Need better reference orbitals for:

diradicaloids, bond dissociation, diradicaloids, bond dissociation, unusual bonding …unusual bonding …

Generate renormalized self-energy Generate renormalized self-energy with approximate Brueckner with approximate Brueckner reference determinantreference determinant

A Versatile Self-Energy: BD-A Versatile Self-Energy: BD-T1T1

Asymmetric Metric:Asymmetric Metric:(X|Y)=(X|Y)=

<Brueckner|[X<Brueckner|[X††,Y],Y]++(1+T(1+T22)|Brueckner>)|Brueckner> Galitskii-Migdal energy = Galitskii-Migdal energy =

BD (Brueckner Doubles, Coupled-BD (Brueckner Doubles, Coupled-Cluster) Cluster)

Operator manifold: f~aOperator manifold: f~a††aa=faa=f33

Discard only 2ph-2hp couplingsDiscard only 2ph-2hp couplings

Applications of theApplications of theBD-T1 ApproximationBD-T1 Approximation

Vertical Electron Detachment Energies Vertical Electron Detachment Energies of Anions: MAD=0.03 eVof Anions: MAD=0.03 eV

1s Core Ionization Energies: MAD = 1s Core Ionization Energies: MAD = 0.2%0.2%

Valence IEs of Closed-Shell Molecules:Valence IEs of Closed-Shell Molecules:

MAD = 0.15 eVMAD = 0.15 eV IEs of Biradicaloids: MAD = 0.08 eVIEs of Biradicaloids: MAD = 0.08 eV

x300

X

A

B

X: H-(NH3)NH3 increases H- VEDE

A: H- detachment with vibrational

excitation of NH3

B: Mysterious low-VEDE peak

Not due to hot NH4-

Variable relative intensity

Another isomer of NH4-?

Bowen’s Photoelectron Spectrum of NH4

-

Computational Search: Computational Search: NHNH44

- - StructuresStructures

Hydride anion: HHydride anion: H--

HH--(NH(NH33) constituents:) constituents:

Ammonia molecule: NH3

Lewis: 3 electron pairs shared in polar NH bonds

+ 1 unshared pair on N→

Partial + charge on H’sPartial – charge on N

Lewis: 1 electron pairH nucleus has 1+ chargeNegative charge attracts+ end of polar NH bondAnion(molecule)

structureaccounts for

dominant peaks

Computational Search:Computational Search:What is the structure for the What is the structure for the

low-VEDE peak?low-VEDE peak?Idea: NH2

-(H2) anion-molecule complexReject: spectral peak would be high-VEDE, not low

Idea: NH4- has 5 valence e- pairs

Deploy in 4 N-H bonds and 1 unshared pairat the 5 vertices of a trigonal biprism or

square pyramid

Calculations find no such structures!Instead, they spontaneously rearrange ….

…….to a heretical structure!.to a heretical structure!

Tetrahedral NH4- has 4

equivalent N-H bonds

Defies Lewis theory

Defies valence shellelectron pair

repulsion theory

Structure similar to that of NH4+

So where are the 2 extra electrons?

Structural Confirmation:Structural Confirmation:Experiment and TheoryExperiment and Theory

NHNH44- -

StructureStructureEPTEPT ExperimentExperiment

HH--(NH(NH33)) 1.07 1.07 1.11 1.11 ± 0.02 ± 0.02 eVeV

TetrahedronTetrahedron 0.480.48 0.47 0.47 ± 0.02± 0.02

Predicted VEDEs from Electron Propagator Theoryfor Anion(molecule) and Tetrahedral forms of NH4

-

coincide with peaks from photoelectron spectrum

Dyson Orbitals for VEDEs of Dyson Orbitals for VEDEs of NHNH44

--

H-(NH3) has 2 electronsin hydride-centered orbital

with minor N-H delocalization.VEDE is 1.07 eV

Tetrahedral NH4- has 2

diffuse electrons locatedchiefly outside of NH4

+ core.VEDE is 0.47 eV

16.1actE

R 11.1E

Ene

rgy

(au)

Ene

rgy

(au)

Intrinsic Reaction CoordinateIntrinsic Reaction Coordinate

IRC: TIRC: Tdd NH NH44-- -> H -> H--(NH(NH33))

Double Rydberg AnionsDouble Rydberg Anions

Highly correlated motion Highly correlated motion of two diffuse (Rydberg) of two diffuse (Rydberg) electrons in the field of electrons in the field of a positive ion (NHa positive ion (NH44

+ + , , OHOH33

++)) United atom limit is an United atom limit is an

alkali anion: Naalkali anion: Na--

Extravalence atomic Extravalence atomic contributions in contributions in Dyson orbitalsDyson orbitals

NHNH44--

OHOH33--

Erx = -39.9

Eact = 5.1

IRC: CIRC: C3v3v OH OH33-- -> H -> H--(H(H22O)O)

X

x500

A

BC

Bowen’s Photoelectron Spectrum Bowen’s Photoelectron Spectrum of Nof N22HH77

--

X: H-(NH3)2 e- detachmentB & C: two low EBEs!

Calculated NCalculated N22HH77- - Structures Structures

HH--(NH(NH33))2 2 anion-anion-molecule complexmolecule complex

NHNH44--(NH(NH33) anion-) anion-

molecule complex molecule complex with tetrahedral NHwith tetrahedral NH44

--

NN22HH77- - with hydrogen with hydrogen

bond (similar to Nbond (similar to N22HH77+ + ) )

NN22HH77- - VEDEs and Dyson VEDEs and Dyson

OrbitalsOrbitalsH-(NH3)2 has hydride centered Dyson orbital

EPT predicts 1.49 eV for VEDEPeak observed in spectrum at 1.46 ± 0.02 eV

Dyson orbital concentrated near NH4-

EPT predicts 0.60 eV for VEDEPeak observed at 0.58 ± 0.02 eV

Dyson orbital concentrated near 3 hydrogensEPT predicts 0.42 eV for VEDE

Peak observed at 0.42 ± 0.02 eV

Assignment of NAssignment of N33HH1010-- EBEs to EBEs to

Double Rydberg AnionsDouble Rydberg Anions (NH(NH44

--)(NH)(NH33))2 2 : 0.66 : 0.66 (Expt.) 0.68 (EPT) (Expt.) 0.68 (EPT)

(N(N22HH77--)(NH)(NH33) : 0.49 ) : 0.49

(Expt.) 0.49 (EPT)(Expt.) 0.49 (EPT)

(N(N33HH1010--) : 0.42 ) : 0.42

(Expt.) 0.40 (EPT)(Expt.) 0.40 (EPT)

x800

BridgeBridge Ion-dipoleIon-dipoleMolecule-HydrideMolecule-Hydride

OO22HH55-- and N and N22HH77

- - StructuresStructures

OO22HH55-- VEDEs and Dyson VEDEs and Dyson

OrbitalsOrbitalsH-(H2O)2 VEDE: 2.36 eV

H-bridged VEDE: 0.48 eV

Ion-dipole VEDE: 0.74 eV

Electron Pair Concepts: Old and Electron Pair Concepts: Old and NewNew

G.N. LewisG.N. Lewis I. LangmuirI. Langmuir

Chemical bonds arise from pairs of electrons shared between atoms

Unshared pairs localized on single atoms

affect bond angles

Molecular cations maybind an e- pair peripheral

to nuclear framework: Double Rydberg Anions

W.N. Lipscomb

R.J. GillespieR.S. Nyholm

Electron Propagator Theory Electron Propagator Theory and Quantum Chemistry’s and Quantum Chemistry’s

MissionsMissions Deductive, quantitative theory:Deductive, quantitative theory:

Prediction and interpretation enable Prediction and interpretation enable dialogue with experimentalists dialogue with experimentalists requiring accurate datarequiring accurate data

Inductive, qualitative theory:Inductive, qualitative theory:Orbital formalism generalizes and Orbital formalism generalizes and deepens qualitative notions of deepens qualitative notions of electronic structure, relating structure, electronic structure, relating structure, spectra and reactivityspectra and reactivity