Anion Electronic Structure and Correlated, One-electron Theory

1
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
• Park City, Utah

2
Acknowledgments

• Symposium Organizers
• Jack Simons
• Brad Hoffman

• Funding
• National Science Foundation
• Defense Threat Reduction Agency

• Auburn Coworkers

• Auburn University
• Department of Chemistry and
  Biochemistry

• UNAM Collaborators
• Ana Martínez
• Alfredo Guevara

3
Quantum Chemistrys Missions

• Deductive agenda
• Deduce properties of molecules from quantum
  mechanics
• Calculate chemical data, especially if
  experiments are difficult or expensive

• Inductive agenda
• Identify and explain patterns in structure,
  spectra, energetics, reactivity
• Deepen and generalize the principles of
  chemical bonding

G. N. Lewis
E. Schrödinger
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Electron Propagator Theory
Exactness
Interpretation
Molecular Orbital Theory
Applications
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One-electron Equations

• Hartree Fock Theory
• Hartree Fock Equations
• (Tkin Unucl JCoul - Kexch)fiHF
• F fiHFeiHF fiHF
• Same potential for all i
• core, valence, occupied, virtual.
• eiHF includes Coulomb and exchange contributions
  to IEs and EAs

• Electron Propagator Theory
• Dyson Equation
• F ?(eiDyson)fiDyson eiDyson fiDyson
• Self energy, ?(E) Energy dependent, nonlocal
  potential that varies for each electron binding
  energy
• eiDyson includes Coulomb, exchange, relaxation
  and correlation contributions to IEs and EAs
• fiDyson describes effect of electron detachment
  or attachment on electronic structure

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Dyson Orbitals (Feynman-Dyson Amplitudes)

• Electron Detachment (IEs)
• fiDyson(x1)
• N-½??N(x1,x2,x3,,xN)?i,N-1(x2,x3,x4,...,xN)
• dx2dx3dx4dxN
• Electron Attachment (EAs)
• fiDyson(x1)
• (N1)-½? ?i,N1(x1,x2,x3,...,xN1)?N(x2,x3,x4,,x
  N1) dx2dx3dx4dxN1
• Pole strength
• Pi ?fiDyson(x)2dx
• 0 Pi 1

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Electron Propagator Concepts
Electron Correlation
Dyson Orbital
Canonical MO
Correlated Electron Binding Energy
Orbital Energy
Integer Occupation Numbers
Pole Strengths
Independent-Particle Potential
Energy-dependent, Self-Energy
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Accuracy versus Interpretability

• Does electron propagator theory offer a solution
  to Mullikens dilemma?

The more accurate the calculations become, the
more the concepts vanish into thin air. - R. S.
Mulliken
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Substituent Effects U and T
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Dyson Orbitals for U and T IEs
Uracil
p1
s-
p2
s
p3
Thymine
Methyl (CH3) participation
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Uracil versus Thymine

• Methyl group destabilizes p orbitals with large
  amplitudes at nearest ring atom
• Therefore, IE(T) lt IE(U)
• Valid principles for substituted DNA bases,
  porphyrins and other organic molecules

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A Self-Energy for Large Molecules P3

• Neglect off-diagonal elements of S(E) in
  canonical MO basis fiDyson(x) Pi½ fiHF-CMO(x)
• Partial summation of third-order diagrams
• Arithmetic bottleneck oN4 (MP2 partial integral
  transformation)
• Storage bottleneck o2v2 in semidirect mode
• Abelian, symmetry-adapted algorithm in G03

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Formulae for SP3(E)

• SP3pq(E)
• ½Siab ltpiabgtltabqigt ?(E)-1iab
• ½Saij ltpaijgt(ltijqagt Wijqa) ?(E)-1aij
• ½Saij Upaij(E)ltijqagt?(E)-1aij
• where
• ?(E)-1pqr (E ep eq er)-1
• Wijqa ½Sbcltbcqagtltijbcgt ?-1ijbc
• (1-Pij)Sbkltbiqkgtltjkbagt ?-1jkab
• Upaij(E) - ½Sklltpaklgtltklijgt ?(E)-1akl
• - (1 Pij) Sbkltpbjkgtltakbigt ?(E)-1bjk

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P3 Performance

• 31 Valence IEs of Closed-Shell Molecules
• (N2,CO,F2,HF,H2O,NH3,C2H2,C2H4,CH4,HCN,H2CO)
• MAD (eV) 0.20 (tz)
• 10 VEDEs of Closed-Shell Anions
• (F-,Cl-,OH-,SH-,NH2-,PH2-,CN-,BO-,AlO-,AlS-)
• MAD (eV) 0.25 (a-tz)
• Arithmetic bottleneck o2v3 for Wijqa
• Storage bottleneck ltiabcgt for Wijqa

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Recent Applications Porphyrins and Fullerenes

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Invitation to Propagate
Input to Gaussian 03
OVGF 6-311G iop(9/1110000) P3 Electron
Propagator for Water 0 1 O H 1 0.98 H 1 0.98 2
105.
Available diagonal approximations for
S(E) Second order, Third order, P3, OVGF
(versions A, B C)
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Nucleotides Gaseous Spectra

• Nucleotides phosphate-sugar-base DNA fragments
• Electrospray ion sources
• Magnetic bottle detection
• High resolution laser spectroscopy of ions, mass
  spectrometry
• Goal predict photoelectron spectra of anionic
  nucleotides (vertical electron detachment
  energies or VEDEs)

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Photoelectron Spectra of 2-deoxybase
5-monophosphate Anions
DAMP
Anomalous peak for dGMP
Base adenine
DCMP
G lowest IE of DNA bases
Base cytosine
DGMP
Base guanine
Dyson orbitals for lowest VEDEs phosphate or
base?
DTMP
Base thymine
L-S.Wang, 2004
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DAMP Isomers and Energies
0 kcal/mol
4.62
4.66
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DAMP VEDEs (eV) and Dyson Orbitals
DO KT P3 PES
P 7.84 6.07 6.05
A p1 6.16 6.15
P 8.21 6.39 6.4
P 8.38 6.62 6.7
P 8.43 6.76
A p2 7.75 6.89 6.9
A n1 8.93 7.24 7.1
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DGMP Isomers and Energies
0 kcal/mol
5.1
9.2
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DGMP VEDEs (eV) and Dyson Orbitals
DO KT P3 PES
G p1 5.25 5.01 5.05
P 7.94 6.18 6.1
P 8.31 6.54 6.4
P 8.54 6.75 6.8
G n1 8.65 6.84 6.9
G p2 8.12 6.96 7.0
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Hydrogen Bonds DGMP vs DAMP

• DGMP G amino to Phosphate oxygen
• DAMP Sugar hydroxy to Phosphate oxygen

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Nucleotide Electronic Structure

• Phosphate anion reduces Base VEDEs by several eV
• Base also increases Phosphate VEDEs
• Therefore, Base and Phosphate VEDEs
• are close
• Differential correlation effects are large
• Koopmans ordering is not reliable

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A Simple, Renormalized Self-Energy P3

• SP3pq(E)
• ½Siab ltpiabgtltabqigt ?(E)-1iab
• 1Y(E)-1 ½Saijltpaijgt(ltijqagt Wijqa)
  ?(E)-1aij ½Saij Upaij(E)ltijqagt?(E)-1aij
• where
• Y(E) -½SaijltpaijgtWijqa ?(E)-1aij
  ½Saijltpaijgtltijqagt ?(E)-1aij-1

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P3 Performance

• 31 Valence IEs of Closed-Shell Molecules
• (N2,CO,F2,HF,H2O,NH3,C2H2,C2H4,CH4,HCN,H2CO)
• MAD (eV) 0.19 (tz), 0.19 (qz)
• 10 VEDEs of Closed-Shell Anions
• (F-,Cl-,OH-,SH-,NH2-,PH2-,CN-,BO-,AlO-,AlS-)
• MAD (eV) 0.11 (a-tz), 0.13 (a-qz)

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Reactivity of Al3O3- with H2O

• Wang first anion photoisomerization
• Jarrold Al3O3-(H2O)n photoelectron spectra
  n0,1,2
• Distinct profile for n1
• Similar spectra for n2 and n0

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Al3O3- Photoelectron Spectrum
Book
Kite
Anion Final State KT P3 P3 Exp.
Book 2B2 2.95 2.85 2.84 2.96
2A1 3.57 3.49 3.48 3.7
Kite 2A1 2.10 2.02 2.01 2.25
2B2 7.20 5.73 5.30 5.2
2A2 6.94 5.72 5.40 5.2
2A1 6.02 6.05 6.06
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Cluster VEDEs and Dyson Orbitals
Al3O3-
Cluster P3 Expt. (eV)
Al3O3- 2.84 2.96
3.48 3.7
Al3O4H2- 2.72 2.7 2.8
3.80 3.8 4.0
Al3O5H4- 3.23 3.3
3.63 3.8
Al3O4H2-
Al3O5H4-
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Strong Initial State Correlation

• Need better reference orbitals for
• diradicaloids, bond dissociation, unusual
  bonding
• Generate renormalized self-energy with
  approximate Brueckner reference determinant

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A Versatile Self-Energy BD-T1

• Asymmetric Metric
• (XY)
• ltBruecknerX,Y(1T2)Bruecknergt
• Galitskii-Migdal energy
• BD (Brueckner Doubles, Coupled-Cluster)
• Operator manifold faaaf3
• Discard only 2ph-2hp couplings

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Applications of theBD-T1 Approximation

• Vertical Electron Detachment Energies of Anions
  MAD0.03 eV
• 1s Core Ionization Energies MAD 0.2
• Valence IEs of Closed-Shell Molecules
• MAD 0.15 eV
• IEs of Biradicaloids MAD 0.08 eV

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Bowens Photoelectron Spectrum of NH4-
B Mysterious low-VEDE peak Not due to hot
NH4- Variable relative intensity Another isomer
of NH4-?
A H- detachment with vibrational excitation of
NH3
X H-(NH3) NH3 increases H- VEDE
X
B
x300
A
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Computational Search NH4- Structures

• H-(NH3) constituents

Ammonia molecule NH3

• Hydride anion H-

Lewis 1 electron pair H nucleus has 1
charge Negative charge attracts end of polar NH
bond
Lewis 3 electron pairs shared in polar NH
bonds 1 unshared pair on N ? Partial charge
on Hs Partial charge on N
Anion(molecule) structure accounts for dominant
peaks
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Computational SearchWhat is the structure for
the low-VEDE peak?
Idea NH2-(H2) anion-molecule complex Reject
spectral peak would be high-VEDE, not low
Idea NH4- has 5 valence e- pairs Deploy in 4 N-H
bonds and 1 unshared pair at the 5 vertices of a
trigonal biprism or square pyramid
Calculations find no such structures! Instead,
they spontaneously rearrange .
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.to a heretical structure!
Tetrahedral NH4- has 4 equivalent N-H bonds
Defies Lewis theory
Defies valence shell electron pair repulsion
theory
Structure similar to that of NH4 So where are
the 2 extra electrons?
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Structural ConfirmationExperiment and Theory
NH4- Structure EPT Experiment
H-(NH3) 1.07 1.11 0.02 eV
Tetrahedron 0.48 0.47 0.02
Predicted VEDEs from Electron Propagator
Theory for Anion(molecule) and Tetrahedral forms
of NH4- coincide with peaks from photoelectron
spectrum
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Dyson Orbitals for VEDEs of NH4-
H-(NH3) has 2 electrons in hydride-centered
orbital with minor N-H delocalization. VEDE is
1.07 eV
Tetrahedral NH4- has 2 diffuse electrons
located chiefly outside of NH4 core. VEDE is
0.47 eV
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IRC Td NH4- -gt H-(NH3)
Energy (au)
Intrinsic Reaction Coordinate
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Double Rydberg Anions

• Highly correlated motion of two diffuse (Rydberg)
  electrons in the field of a positive ion (NH4 ,
  OH3)
• United atom limit is an alkali anion Na-
• Extravalence atomic contributions in Dyson
  orbitals

NH4-
OH3-
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IRC C3v OH3- -gt H-(H2O)
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Bowens Photoelectron Spectrum of N2H7-
X H-(NH3)2 e- detachment
B C two low EBEs!
B
C
X
x500
A
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Calculated N2H7- Structures

• H-(NH3)2 anion-
• molecule complex
• NH4-(NH3) anion-
• molecule complex
• with tetrahedral NH4-
• N2H7- with hydrogen bond (similar to N2H7 )

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N2H7- VEDEs and Dyson Orbitals
H-(NH3)2 has hydride centered Dyson orbital EPT
predicts 1.49 eV for VEDE Peak observed in
spectrum at 1.46 0.02 eV
Dyson orbital concentrated near NH4- EPT predicts
0.60 eV for VEDE Peak observed at 0.58 0.02 eV
Dyson orbital concentrated near 3 hydrogens EPT
predicts 0.42 eV for VEDE Peak observed at 0.42
0.02 eV
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Assignment of N3H10- EBEs to Double Rydberg
Anions

• (NH4-)(NH3)2 0.66 (Expt.) 0.68 (EPT)
• (N2H7-)(NH3) 0.49 (Expt.) 0.49 (EPT)
• (N3H10-) 0.42 (Expt.) 0.40 (EPT)

x800
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O2H5- and N2H7- Structures
Bridge
Ion-dipole
Molecule-Hydride
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O2H5- VEDEs and Dyson Orbitals
H-(H2O)2 VEDE 2.36 eV
H-bridged VEDE 0.48 eV
Ion-dipole VEDE 0.74 eV
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Electron Pair Concepts Old and New
Chemical bonds arise from pairs of electrons
shared between atoms
G.N. Lewis
I. Langmuir
W.N. Lipscomb
Unshared pairs localized on single atoms affect
bond angles
Molecular cations may bind an e- pair peripheral
to nuclear framework Double Rydberg Anions
R.J. Gillespie
R.S. Nyholm
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Electron Propagator Theory and Quantum
Chemistrys Missions

• Deductive, quantitative theory
• Prediction and interpretation enable dialogue
  with experimentalists requiring accurate data
• Inductive, qualitative theory
• Orbital formalism generalizes and deepens
  qualitative notions of electronic structure,
  relating structure, spectra and reactivity