anion electronic structure and correlated, one-electron theory
DESCRIPTION
Anion Electronic Structure and Correlated, One-electron Theory. J. V. Ortiz Department of Chemistry and Biochemistry Auburn University www.auburn.edu/cosam/JVOrtiz Workshop on Molecular Anions and Electron-Molecule Interactions in Honor of Professor Kenneth Jordan July 1, 2007 - PowerPoint PPT PresentationTRANSCRIPT
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