Report

Application of equation-of-motion coupledcluster theory to photodetachment cross section calculations Takatoshi Ichino and John F. Stanton The University of Texas at Austin June 18, 2012 Why do we care about photodetachment cross section? ex. photoelectron spectrum of NO3‾ Interpretation of photoelectron spectra can be facilitated with knowledge of cross sections. Weaver et al., J. Chem. Phys. 94, 1740 (1991) Two approaches to photodetachment cross section calculations 1. Plane wave approximation of scattering electrons • Transition of the electron from the Dyson orbital obtained with equationof-motion coupled-cluster theory (EOMIP-CC) cf. Reed et al., J. Chem. Phys. 64, 1368 (1976). Öhrn and Born, Adv. Quantum Chem. 13, 1 (1981). Oana and Krylov, J. Chem. Phys. 131, 124114 (2009). 2. Direct ab initio calculations of electronic transition dipole moments for pseudostates • Equation-of-motion coupled-cluster calculations of oscillator strengths (EOMEE-CC) to obtain the associated moments cf. Langhoff and Corcoran, J. Chem. Phys. 61, 146 (1976). Reinhardt, Comp. Phys. Comm. 17, 1 (1979). Müller-Plathe and Diercksen in “Electronic Structure of Atoms, Molecules and Solids” (1990). First approach: Plane wave approximation differential cross section: : plane wave photodetachment from an orbital How to choose the orbital: 1) : SCF orbital → Koopmans’ theorem 2) : Dyson orbital (EOMIP-CC) Feynman-Dyson amplitudes : CC wavefunction : EOMIP-CC wavefunction First approach: Plane wave approximation differential cross section: : plane wave photodetachment from an orbital (SCF, Dyson) Adjustments of the plane wavefunction: 1) Partial orthogonalization: 2) Full orthogonalization: orthogonalized against orthogonalized against all natural orbitals First approach: Plane wave approximation Choice of the operator in transition moment calculations: 1) Dipole length: 2) Momentum: Steps in cross section calculations: 1) EOMIP-CCSD calculations of Feynman-Dyson amplitudes 2) Analytic calculations of integrals (overlap, dipole, derivative) 3) Analytic evaluation of angular integrals of transition moments First approach: Plane wave approximation Result 1: Photodetachment from H anion SCF Dyson (dipole length) Dyson (momentum) EOMIP-CCSD aug-pVQZ + diffuse functions Transition dipole length calculations with the Dyson orbital give an excellent match with the experimental results. Experiment (dots): Branscomb and Smith, Phys. Rev. 98, 1028 (1955) Smith and Burch, Phys. Rev. 116, 1125 (1959) First approach: Plane wave approximation Result 2: Photodetachment from Li anion SCF EOMIP-CCSD/aug-pVTZ Dyson/partial orthogonalization Dyson/full orthogonalization (dipole length) Dyson/full orthogonalization (momentum) Transition dipole length calculations with the Dyson orbital and the fully orthogonalized plane wave give an excellent match with the experimental results. Experiment (dots) : Kaiser et al., Z. Phys. 270, 259 (1974) First approach: Plane wave approximation Result 3: Photodetachment from O radical anion Dyson/partial orthogonalization Dyson/full orthogonalization (momentum) SCF Dyson/full orthogonalization (dipole length) EOMIP-CCSD aug-pVTZ + diffuse functions Transition dipole length calculations with the Dyson orbital and the fully orthogonalized plane wave give an excellent match with the experimental results. Experiment (dots): Branscomb et al., Phys. Rev. 111, 504 (1958); J. Chem. Phys. 43, 2906 (1965) First approach: Plane wave approximation Result 4: Photodetachment from F anion Dyson/partial orthogonalization SCF Dyson/full orthogonalization (momentum) Dyson/full orthogonalization (dipole length) EOMIP-CCSD aug-pVTZ + diffuse functions Higher correlation effects? Wrong experimental results? Experiment (dots): Mandl, Phys. Rev. A 3, 251 (1971) Second approach: Electronic excitation to pseudostates The moments of the oscillator strength for the continuum states: approximated by the oscillator strengths for pseudostates Photodetachment cross sections calculated from the oscillator strength density: Steps in cross section calculations (Stieltjes imaging): 1) EOMEE-CCSD calculations of oscillator strengths for pseudostates 2) Quadrature calculations utilizing the relation between moments and orthogonal polynomials 3) Differentiation to obtain the oscillator strength density Second approach: Electronic excitation to pseudostates Result 1: Photodetachment from H anion Dyson (dipole length) ▲: Stieltjes imaging EOMEE-CCSD aug-pVQZ + diffuse functions Stieltjes imaging gives an excellent match with the experimental results. Experiment (dots): Branscomb and Smith, Phys. Rev. 98, 1028 (1955) Smith and Burch, Phys. Rev. 116, 1125 (1959) Second approach: Electronic excitation to pseudostates Result 2: Photodetachment from Li anion ▲: Stieltjes imaging EOMEE-CCSD aug-pVQZ + diffuse functions Dyson/full orthogonalization (dipole length) Stieltjes imaging gives an excellent match with the experimental results. Experiment (dots) : Kaiser et al., Z. Phys. 270, 259 (1974) Second approach: Electronic excitation to pseudostates Result 3: Photodetachment from O radical anion Dyson/full orthogonalization (dipole length) ▲: Stieltjes imaging EOMEE-CCSD aug-pVQZ + diffuse functions Stieltjes imaging gives a good match with the experimental results. Experiment (dots): Branscomb et al., Phys. Rev. 111, 504 (1958); J. Chem. Phys. 43, 2906 (1965) Second approach: Electronic excitation to pseudostates Result 4: Photodetachment from F anion Dyson/full orthogonalization (dipole length) ▲: Stieltjes imaging EOMEE-CCSD aug-pVQZ + diffuse functions Stieltjes imaging gives cross sections consistent with those from Dyson orbital calculations. Experiment (dots): Mandl, Phys. Rev. A 3, 251 (1971) Conclusions • • • The Dyson orbitals obtained from equation-of-motion coupled-cluster calculations (EOMIP-CCSD) can successfully represent the initial states of photodetachment processes for atomic anions in the cross section calculations. The scattering electrons are described as plane waves orthogonalized against all natural orbitals of the anions. The transition moment calculations should be performed with the dipole length operator. The oscillator strengths for photoexcitation to discrete pseudostates of atomic anions obtained from equation-of-motion coupled-cluster calculations (EOMEE-CCSD) can successfully be utilized for the moments for the photodetachment processes. The associated quadrature calculations provide “smoothed” oscillator strength density, based on which photodetachment cross sections can be evaluated. It may be worth reexamining the photodetachment cross section of the F anion experimentally. Thanks to: Professor John F. Stanton NSF, DOE, The Welch Foundation Feynman-Dyson amplitude in EOMIP (ex) EOMIP-CCSD Stanton and Gauss, J. Chem. Phys. 101, 8938 (1994) Oana and Krylov, J. Chem. Phys. 127, 234106 (2007); 131, 124114 (2009) Brauman’s treatment Koopmans’ theorem reference orbital from which an electron is detached continuum orbital Partially orthogonalized plane wave Slater functions Reed et al., J. Chem. Phys. 64, 1368 (1976) What the program does … integral evaluation for the transition moment angular integration to collect all electrons Öhrn and Born, Adv. Quantum Chem. 13, 1 (1981)