Anion Electronic Structure and Correlated, One-electron Theory J. V. Ortiz Department of Chemistry and Biochemistry Auburn University Workshop on Molecular Anions and Electron- Molecule Interactions in Honor of Professor Kenneth Jordan July 1, 2007 Park City, Utah

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

Quantum Chemistry’s Missions Deductive agenda: Deductive agenda: Deduce properties of molecules from quantum mechanics Deduce properties of molecules from quantum mechanics Calculate chemical data, especially if experiments are difficult or expensive Calculate chemical data, especially if experiments are difficult or expensive Inductive agenda: Inductive agenda: Identify and explain patterns in structure, spectra, energetics, reactivity Identify and explain patterns in structure, spectra, energetics, reactivity Deepen and generalize the principles of chemical bonding Deepen and generalize the principles of chemical bonding E. Schrödinger G. N. Lewis

Electron Propagator Theory Molecular Orbital Theory Applications Interpretation Exactness

One-electron Equations Hartree Fock Theory Hartree Fock Theory Hartree Fock Equations: (T kin + U nucl + J Coul - K exch )φ i HF ≡ F φ i HF =ε i HF φ i HF F φ i HF =ε i HF φ i HF Same potential for all i: core, valence, occupied, virtual. ε i HF includes Coulomb and exchange contributions to IEs and EAs Electron Propagator Theory Electron Propagator Theory Dyson Equation: [F + ∑(ε i Dyson )]φ i Dyson = ε i Dyson φ i Dyson Self energy, ∑(E): Energy dependent, nonlocal potential that varies for each electron binding energy ε i Dyson includes Coulomb, exchange, relaxation and correlation contributions to IEs and EAs φ i Dyson describes effect of electron detachment or attachment on electronic structure

Dyson Orbitals (Feynman-Dyson Amplitudes) Electron Detachment (IEs) Electron Detachment (IEs) φ i Dyson (x 1 ) = N -½ ∫Ψ N (x 1,x 2,x 3,…,x N )Ψ * i,N-1 (x 2,x 3,x 4,...,x N ) dx 2 dx 3 dx 4 …dx N Electron Attachment (EAs) Electron Attachment (EAs) φ i Dyson (x 1 ) = (N+1) -½ ∫ Ψ i,N+1 (x 1,x 2,x 3,...,x N+1 )Ψ * N (x 2,x 3,x 4,…,x N+1 ) dx 2 dx 3 dx 4 …dx N+1 Pole strength Pole strength P i = ∫|φ i Dyson (x)| 2 dx 0 ≤ P i ≤ 1

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

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

Substituent Effects: U and T

Dyson Orbitals for U and T IEs Uracil Thymine π1π1 σ-σ- π2π2 σ+σ+ π3π3 Methyl (CH 3 ) participation

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

A Self-Energy for Large Molecules: P3 Neglect off-diagonal elements of Σ(E) in canonical MO basis: φ i Dyson (x) = P i ½ φ i HF-CMO (x) Neglect off-diagonal elements of Σ(E) in canonical MO basis: φ i Dyson (x) = P i ½ φ i HF-CMO (x) Partial summation of third-order diagrams Partial summation of third-order diagrams Arithmetic bottleneck: oN 4 (MP2 partial integral transformation) Arithmetic bottleneck: oN 4 (MP2 partial integral transformation) Storage bottleneck: o 2 v 2 in semidirect mode Storage bottleneck: o 2 v 2 in semidirect mode Abelian, symmetry-adapted algorithm in G03 Abelian, symmetry-adapted algorithm in G03

Formulae for Σ P3 (E) Σ P3 pq (E) = ½Σ iab Δ(E) -1 iab + ½Σ aij ( + W ijqa ) Δ(E) -1 aij + ½Σ aij U paij (E) Δ(E) -1 aij where Δ(E) -1 pqr = (E + ε p – ε q – ε r ) -1 W ijqa = ½Σ bc Δ -1 ijbc + (1-P ij )Σ bk Δ -1 jkab U paij (E) = - ½Σ kl Δ(E) -1 akl - (1 – P ij ) Σ bk Δ(E) -1 bjk

P3 Performance 31 Valence IEs of Closed-Shell Molecules: 31 Valence IEs of Closed-Shell Molecules: (N 2,CO,F 2,HF,H 2 O,NH 3,C 2 H 2,C 2 H 4,CH 4,HCN,H 2 CO) MAD (eV) = 0.20 (tz) 10 VEDEs of Closed-Shell Anions: 10 VEDEs of Closed-Shell Anions: (F -,Cl -,OH -,SH -,NH 2 -,PH 2 -,CN -,BO -,AlO -,AlS - ) MAD (eV) = 0.25 (a-tz) MAD (eV) = 0.25 (a-tz) Arithmetic bottleneck: o 2 v 3 for W ijqa Arithmetic bottleneck: o 2 v 3 for W ijqa Storage bottleneck: for W ijqa Storage bottleneck: for W ijqa

Recent Applications: Porphyrins and Fullerenes

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

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

Photoelectron Spectra of 2’-deoxybase 5’-monophosphate Anions DAMP DCMP DGMP DTMP Base = adenine Base = cytosine Base = guanine Base = thymine L-S.Wang, 2004 Anomalous peak for dGMP G: lowest IE of DNA bases Dyson orbitals for lowest VEDEs: phosphate or base?

DAMP Isomers and Energies 0 kcal/mol

DAMP VEDEs (eV) and Dyson Orbitals DAMP VEDEs (eV) and Dyson Orbitals DOKTP3PES P A π P ~6.4 P ~6.7 P A π ~6.9 A n ~7.1

DGMP Isomers and Energies 0 kcal/mol

DGMP VEDEs (eV) and Dyson Orbitals DGMP VEDEs (eV) and Dyson Orbitals DOKTP3PES G π P ~6.1 P ~6.4 P ~6.8 G n ~6.9 G π ~7.0

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

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

A Simple, Renormalized Self- Energy: P3+ A Simple, Renormalized Self- Energy: P3+ Σ P3+ pq (E) = ½Σ iab Δ(E) -1 iab + [1+Y(E)] -1 ½Σ aij ( + W ijqa ) Δ(E) -1 aij + ½Σ aij U paij (E) Δ(E) -1 aij where Y(E) = {-½Σ aij W ijqa Δ(E) -1 aij } {½Σ aij Δ(E) -1 aij } -1

P3+ Performance 31 Valence IEs of Closed-Shell Molecules: 31 Valence IEs of Closed-Shell Molecules: (N 2,CO,F 2,HF,H 2 O,NH 3,C 2 H 2,C 2 H 4,CH 4,HCN,H 2 CO) MAD (eV) = 0.19 (tz), 0.19 (qz) 10 VEDEs of Closed-Shell Anions: 10 VEDEs of Closed-Shell Anions: (F -,Cl -,OH -,SH -,NH 2 -,PH 2 -,CN -,BO -,AlO -,AlS - ) MAD (eV) = 0.11 (a-tz), 0.13 (a-qz) MAD (eV) = 0.11 (a-tz), 0.13 (a-qz)

Reactivity of Al 3 O 3 - with H 2 O Wang: first anion photoisomerization Wang: first anion photoisomerization Jarrold: Al 3 O 3 - (H 2 O) n photoelectron spectra n=0,1,2 Jarrold: Al 3 O 3 - (H 2 O) n photoelectron spectra n=0,1,2 Distinct profile for n=1 Distinct profile for n=1 Similar spectra for n=2 and n=0 Similar spectra for n=2 and n=0

Al 3 O 3 - Photoelectron Spectrum Book KiteAnion Final State KTP3P3+Exp.Book 2B22B22B22B A12A12A12A Kite 2A12A12A12A B22B22B22B A22A22A22A A12A12A12A

Cluster VEDEs and Dyson Orbitals Cluster VEDEs and Dyson Orbitals ClusterP3+ Expt. (eV) Al 3 O Al 3 O 4 H – – 4.0 Al 3 O 5 H Al 3 O 3 - Al 3 O 4 H 2 - Al 3 O 5 H 4 -

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

A Versatile Self-Energy: BD-T1 Asymmetric Metric: Asymmetric Metric:(X|Y)= Galitskii-Migdal energy = Galitskii-Migdal energy = BD (Brueckner Doubles, Coupled-Cluster) Operator manifold: f~a † aa=f 3 Operator manifold: f~a † aa=f 3 Discard only 2ph-2hp couplings Discard only 2ph-2hp couplings

Applications of the BD-T1 Approximation Vertical Electron Detachment Energies of Anions: MAD=0.03 eV Vertical Electron Detachment Energies of Anions: MAD=0.03 eV 1s Core Ionization Energies: MAD = 0.2% 1s Core Ionization Energies: MAD = 0.2% Valence IEs of Closed-Shell Molecules: Valence IEs of Closed-Shell Molecules: MAD = 0.15 eV IEs of Biradicaloids: MAD = 0.08 eV IEs of Biradicaloids: MAD = 0.08 eV

x300 X A B X: H - (NH 3 ) NH 3 increases H - VEDE A: H - detachment with vibrational excitation of NH 3 B: Mysterious low-VEDE peak Not due to hot NH 4 - Variable relative intensity Another isomer of NH 4 - ? Bowen’s Photoelectron Spectrum of NH 4 -

Computational Search: NH 4 - Structures Hydride anion: H - H - (NH 3 ) constituents: Ammonia molecule: NH 3 Lewis: 3 electron pairs shared in polar NH bonds + 1 unshared pair on N → Partial + charge on H’s Partial – charge on N Lewis: 1 electron pair H nucleus has 1+ charge Negative charge attracts + end of polar NH bond Anion(molecule) structure accounts for dominant peaks

Computational Search: What is the structure for the low- VEDE peak? Idea: NH 2 - (H 2 ) anion-molecule complex Reject: spectral peak would be high-VEDE, not low Idea: NH 4 - 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 ….

….to a heretical structure! Tetrahedral NH 4 - has 4 equivalent N-H bonds Defies Lewis theory Defies valence shell electron pair repulsion theory Structure similar to that of NH 4 + So where are the 2 extra electrons?

Structural Confirmation: Experiment and Theory NH 4 - Structure EPTExperiment H - (NH 3 ) ± 0.02 eV Tetrahedron ± 0.02 Predicted VEDEs from Electron Propagator Theory for Anion(molecule) and Tetrahedral forms of NH 4 - coincide with peaks from photoelectron spectrum

Dyson Orbitals for VEDEs of NH 4 - H - (NH 3 ) has 2 electrons in hydride-centered orbital with minor N-H delocalization. VEDE is 1.07 eV Tetrahedral NH 4 - has 2 diffuse electrons located chiefly outside of NH 4 + core. VEDE is 0.47 eV

Energy (au) Intrinsic Reaction Coordinate IRC: T d NH 4 - -> H - (NH 3 )

Double Rydberg Anions Highly correlated motion of two diffuse (Rydberg) electrons in the field of a positive ion (NH 4 +, OH 3 + ) Highly correlated motion of two diffuse (Rydberg) electrons in the field of a positive ion (NH 4 +, OH 3 + ) United atom limit is an alkali anion: Na - United atom limit is an alkali anion: Na - Extravalence atomic contributions in Dyson orbitals Extravalence atomic contributions in Dyson orbitals NH 4 - OH 3 -

 E rx =  E act = 5.1 IRC: C 3v OH 3 - -> H - (H 2 O)

X x500 A BC Bowen’s Photoelectron Spectrum of N 2 H 7 - X: H - (NH 3 ) 2 e - detachmentB & C: two low EBEs!

Calculated N 2 H 7 - Structures H - (NH 3 ) 2 anion- H - (NH 3 ) 2 anion- molecule complex NH 4 - (NH 3 ) anion- NH 4 - (NH 3 ) anion- molecule complex molecule complex with tetrahedral NH 4 - with tetrahedral NH 4 - N 2 H 7 - with hydrogen bond (similar to N 2 H 7 + ) N 2 H 7 - with hydrogen bond (similar to N 2 H 7 + )

N 2 H 7 - VEDEs and Dyson Orbitals H - (NH 3 ) 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 NH 4 - 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

Assignment of N 3 H 10 - EBEs to Double Rydberg Anions (NH 4 - )(NH 3 ) 2 : 0.66 (Expt.) 0.68 (EPT) (NH 4 - )(NH 3 ) 2 : 0.66 (Expt.) 0.68 (EPT) (N 2 H 7 - )(NH 3 ) : 0.49 (Expt.) 0.49 (EPT) (N 2 H 7 - )(NH 3 ) : 0.49 (Expt.) 0.49 (EPT) (N 3 H 10 - ) : 0.42 (Expt.) 0.40 (EPT) (N 3 H 10 - ) : 0.42 (Expt.) 0.40 (EPT) x800

BridgeIon-dipoleMolecule-Hydride O 2 H 5 - and N 2 H 7 - Structures

O 2 H 5 - VEDEs and Dyson Orbitals H - (H 2 O) 2 VEDE: 2.36 eV H-bridged VEDE: 0.48 eV Ion-dipole VEDE: 0.74 eV

Electron Pair Concepts: Old and New G.N. Lewis I. Langmuir Chemical bonds arise from pairs of electrons shared between atoms Unshared pairs localized on single atoms affect bond angles Molecular cations may bind an e - pair peripheral to nuclear framework: Double Rydberg Anions W.N. Lipscomb R.J. GillespieR.S. Nyholm

Electron Propagator Theory and Quantum Chemistry ’ s Missions Deductive, quantitative theory: Deductive, quantitative theory: Prediction and interpretation enable dialogue with experimentalists requiring accurate data Inductive, qualitative theory: Inductive, qualitative theory: Orbital formalism generalizes and deepens qualitative notions of electronic structure, relating structure, spectra and reactivity