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Anion Electronic Structure and Correlated, One-electron Theory

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

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Anion Electronic Structure and Correlated, One-electron Theory

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  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. Funding National Science Foundation Defense Threat Reduction Agency Acknowledgments • Symposium Organizers • Jack Simons • Brad Hoffman • Auburn University • Department of Chemistry and Biochemistry • Auburn Coworkers • UNAM Collaborators: • Ana Martínez • Alfredo Guevara

  3. 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 Quantum Chemistry’s Missions G. N. Lewis E. Schrödinger

  4. Electron Propagator Theory Exactness Interpretation Molecular Orbital Theory Applications

  5. Hartree Fock Theory Hartree Fock Equations: (Tkin + Unucl + JCoul - Kexch)φiHF ≡ F φiHF=εiHF φiHF Same potential for all i: core, valence, occupied, virtual. εiHF includes Coulomb and exchange contributions to IEs and EAs Electron Propagator Theory Dyson Equation: [F + ∑(εiDyson)]φiDyson = εiDyson φiDyson Self energy, ∑(E): Energy dependent, nonlocal potential that varies for each electron binding energy εiDyson includes Coulomb, exchange, relaxation and correlation contributions to IEs and EAs φiDyson describes effect of electron detachment or attachment on electronic structure One-electron Equations

  6. Dyson Orbitals (Feynman-Dyson Amplitudes) • Electron Detachment (IEs) φiDyson(x1) = N-½∫ΨN(x1,x2,x3,…,xN)Ψ*i,N-1(x2,x3,x4,...,xN) dx2dx3dx4…dxN • Electron Attachment (EAs) φiDyson(x1) = (N+1)-½∫ Ψi,N+1(x1,x2,x3,...,xN+1)Ψ*N(x2,x3,x4,…,xN+1) dx2dx3dx4…dxN+1 • Pole strength Pi = ∫|φiDyson(x)|2dx 0 ≤ Pi ≤ 1

  7. 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

  8. Accuracy versus Interpretability • Does electron propagator theory offer a solution to Mulliken’s dilemma? The more accurate the calculations become, the more the concepts vanish into thin air. - R. S. Mulliken

  9. Substituent Effects: U and T

  10. Dyson Orbitals for U and T IEs Uracil π1 σ- π2 σ+ π3 Thymine Methyl (CH3) participation

  11. Uracil versus Thymine • Methyl group destabilizes π orbitals with large amplitudes at nearest ring atom • Therefore, IE(T) < IE(U) • Valid principles for substituted DNA bases, porphyrins and other organic molecules

  12. A Self-Energy for Large Molecules: P3 • Neglect off-diagonal elements of Σ(E) in canonical MO basis: φiDyson(x) = Pi½φiHF-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

  13. Formulae for ΣP3(E) ΣP3pq(E) = ½Σiab <pi||ab><ab||qi> Δ(E)-1iab + ½Σaij <pa||ij>(<ij||qa> + Wijqa) Δ(E)-1aij + ½Σaij Upaij(E)<ij||qa>Δ(E)-1aij where Δ(E)-1pqr = (E + εp – εq – εr)-1 Wijqa = ½Σbc<bc||qa><ij||bc> Δ-1ijbc + (1-Pij)Σbk<bi||qk><jk||ba> Δ-1jkab Upaij(E) = - ½Σkl<pa||kl><kl||ij> Δ(E)-1akl - (1 – Pij) Σbk<pb||jk><ak||bi> Δ(E)-1bjk

  14. 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: <ia||bc> for Wijqa

  15. Recent Applications: Porphyrins and Fullerenes

  16. Invitation to Propagate Input to Gaussian 03 # OVGF 6-311G** iop(9/11=10000) P3 Electron Propagator for Water 0 1 O H 1 0.98 H 1 0.98 2 105. Available diagonal approximations for Σ(E): Second order, Third order, P3, OVGF (versions A, B & C)

  17. 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)

  18. 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

  19. DAMP Isomers and Energies 0 kcal/mol 4.62 4.66

  20. DAMP VEDEs (eV) and Dyson Orbitals

  21. DGMP Isomers and Energies 0 kcal/mol 5.1 9.2

  22. DGMP VEDEs (eV) and Dyson Orbitals

  23. Hydrogen Bonds: DGMP vs DAMP • DGMP: G amino to Phosphate oxygen • DAMP: Sugar hydroxy to Phosphate oxygen

  24. 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

  25. A Simple, Renormalized Self-Energy: P3+ ΣP3+pq(E) = ½Σiab <pi||ab><ab||qi> Δ(E)-1iab + [1+Y(E)]-1 ½Σaij<pa||ij>(<ij||qa> + Wijqa) Δ(E)-1aij + ½Σaij Upaij(E)<ij||qa>Δ(E)-1aij where Y(E) = {-½Σaij<pa||ij>Wijqa Δ(E)-1aij} {½Σaij<pa||ij><ij||qa> Δ(E)-1aij}-1

  26. 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)

  27. Reactivity of Al3O3- with H2O • Wang: first anion photoisomerization • Jarrold: Al3O3-(H2O)n photoelectron spectra n=0,1,2 • Distinct profile for n=1 • Similar spectra for n=2 and n=0

  28. Al3O3- Photoelectron Spectrum Book Kite

  29. Cluster VEDEs and Dyson Orbitals Al3O3- Al3O4H2- Al3O5H4-

  30. Strong Initial State Correlation • Need better reference orbitals for: diradicaloids, bond dissociation, unusual bonding … • Generate renormalized self-energy with approximate Brueckner reference determinant

  31. A Versatile Self-Energy: BD-T1 • Asymmetric Metric: (X|Y)= <Brueckner|[X†,Y]+(1+T2)|Brueckner> • Galitskii-Migdal energy = BD (Brueckner Doubles, Coupled-Cluster) • Operator manifold: f~a†aa=f3 • Discard only 2ph-2hp couplings

  32. Applications of theBD-T1 Approximation • Vertical Electron Detachment Energies of Anions: MAD=0.03 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

  33. Bowen’s 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

  34. Computational Search: NH4- Structures Hydride anion: H- H-(NH3) constituents: Ammonia molecule: NH3 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 H’s Partial – charge on N Anion(molecule) structure accounts for dominant peaks

  35. Computational Search:What 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 ….

  36. ….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?

  37. Structural Confirmation:Experiment and Theory Predicted VEDEs from Electron Propagator Theory for Anion(molecule) and Tetrahedral forms of NH4- coincide with peaks from photoelectron spectrum

  38. 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

  39. IRC: Td NH4- -> H-(NH3) Energy (au) Intrinsic Reaction Coordinate

  40. 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-

  41. Eact = 5.1 Erx = -39.9 IRC: C3v OH3- -> H-(H2O)

  42. Bowen’s Photoelectron Spectrum of N2H7- X: H-(NH3)2 e- detachment B & C: two low EBEs! C B X x500 A

  43. Calculated N2H7- Structures • H-(NH3)2 anion- molecule complex • NH4-(NH3) anion- molecule complex with tetrahedral NH4- • N2H7- with hydrogen bond (similar to N2H7+ )

  44. 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

  45. 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

  46. O2H5- and N2H7- Structures Molecule-Hydride Bridge Ion-dipole

  47. O2H5- VEDEs and Dyson Orbitals H-(H2O)2 VEDE: 2.36 eV H-bridged VEDE: 0.48 eV Ion-dipole VEDE: 0.74 eV

  48. Electron Pair Concepts: Old and New Chemical bonds arise from pairs of electrons shared betweenatoms 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

  49. Electron Propagator Theory and Quantum Chemistry’s 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

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