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Journal ArticleDOI

On the breakdown of the Koopmans' theorem for nitrogen

15 Feb 1973-Chemical Physics Letters (North-Holland)-Vol. 18, Iss: 4, pp 503-508
TL;DR: In this paper, a perturbation treatment was applied to the nitrogen molecule to predict the vertical ionization potentials of the two lowest ionizations, and it turns out that it is necessary to use a very elaborate form of perturbations in the case of N 2.
About: This article is published in Chemical Physics Letters.The article was published on 1973-02-15. It has received 142 citations till now. The article focuses on the topics: Koopmans' theorem.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors investigated the contribution of higher orders of the self-energy part up to third order and found that the main contributions due to this interaction can be determined by considering the analytic properties of second and third order terms only.
Abstract: The one-body Green's function is investigated by expanding the self-energy part up to third order. On this level some properties of the diagrams of the self-energy part are discussed. To estimate the contribution of higher orders of the self-energy part an effective time dependent interaction is introduced. It is found that the main contributions due to this interaction can be determined by considering the analytic properties of second and third order terms only. The numerical effort required can thus be strongly reduced. The theory is applied to calculate the vertical ionization potentials of B2H6. The calculation of the pole strengths shows that one may expect satellite lines in the photoelectron spectrum of B2H6 with about 10% of the intensity of the principal valence lines due to excitations accompanying ionization.

487 citations

Book ChapterDOI
TL;DR: In this article, a diagrammatic approach to perturbation theory of fermion systems is presented, and the second and third-order excitation energy contributions are given in a simple way without the involvement of the Green function formalism.
Abstract: Publisher Summary The chapter discusses the time-independent diagrammatic approach to perturbation theory of fermion systems. The chapter explores the perturbation theory for a non-degenerate level. The formulas derived serves as a starting point for the subsequent consideration of the excitation and ionization energies. The advantages of the direct calculation of excitation energies, compared with the approach in which the total energies of the pertinent electronic states are calculated separately for each state and then the excitation energies are obtained by subtracting the appropriate state energies, are quite obvious. The Rayleigh-Schrodinger (RS) perturbation theory (PT) for the case of a non-degenerate level of some Hamiltonian operator is discussed. The chapter discusses that even the Rayleigh-Schrodinger perturbation expressions for the direct calculation of the excitation energies may be obtained in a rather simple way without the involvement of the Green function formalism. On the contrary, our simple approach using the ordinary perturbation theory for separate levels presents certain desirable features of the Green function formalism. The chapter explains the diagrammatic representation of Wick's theorem and resulting diagrams. General explicit formulas for the second- and third-order excitation energy contributions are given in the chapter.

420 citations

Journal ArticleDOI
TL;DR: In this article, a theoretical and numerical analysis of the diagrammatic expansion of the self-energy part requires the introduction of a renormalised interaction and renormalized hole and particle lines.
Abstract: Vertical ionization potentials, electron affinities and information about quasi-particles can be obtained by using the technique of the single-particle propagator. The expansion of the self-energy part up to third order perturbation theory can be evaluated numerically, but does not lead, in most cases, to satisfying results. A theoretical and numerical analysis of the diagrammatic expansion of the self-energy part requires the introduction of a renormalized interaction and renormalized hole and particle lines.

249 citations

Journal ArticleDOI
TL;DR: The GW-technology corrects the Kohn-Sham (KS) single particle energies and single particle states for artifacts of the exchange-correlation (XC) functional of the underlying density functional theory (DFT) calculation.
Abstract: The GW-technology corrects the Kohn-Sham (KS) single particle energies and single particle states for artifacts of the exchange-correlation (XC) functional of the underlying density functional theory (DFT) calculation. We present the formalism and implementation of GW adapted for standard quantum chemistry packages. Our implementation is tested using a typical set of molecules. We find that already after the first iteration of the self-consistency cycle, G0W0, the deviations of quasi-particle energies from experimental ionization potentials and electron affinities can be reduced by an order of magnitude against those of KS-DFT using GGA or hybrid functionals. Also, we confirm that even on this level of approximation there is a considerably diminished dependency of the G0W0-results on the XC-functional of the underlying DFT.

222 citations

References
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Journal ArticleDOI
TL;DR: In this paper, Fock's Naherungsmethode zur Behandung des quantenmechanischen Mehrelektronenproblems aufgestellten Gleichungen werden auf etwas allgemeinerer Grundlage diskutiert.

5,844 citations

Journal ArticleDOI
TL;DR: In this article, the use of a linear combination of Gaussian type orbitals (CGTO) instead of an individual Gaussian-type orbital (GTO) as a unit of basis functions for large-scale molecular calculations is discussed.
Abstract: The use of a linear combination of Gaussian‐type orbitals (CGTO), instead of an individual Gaussian‐type orbital (GTO), as a unit of basis functions for large‐scale molecular calculations, is discussed. A systematic construction of the CGTO basis functions is attempted and the results for the atoms from Li through Ar are reported.

3,257 citations

Journal ArticleDOI
TL;DR: In this paper, the convergence of a sequence of Hartree-Fock-Roothaan wavefunctions and energy values to the true Hartree Fock results is examined for N2(X1Σg+).
Abstract: The problem of the convergence of a sequence of Hartree—Fock—Roothaan wavefunctions and energy values to the true Hartree—Fock results is examined for N2(X1Σg+). This critical study is based on a hierarchy of Hartree—Fock—Roothaan wavefunctions which differ in the size and composition of the expansion basis set in terms of STO symmetry orbitals. The concluding basis set gives a total Hartree—Fock energy of −108.9956 hartree and Re(HF)=2.0132 bohr for N2(X1Σg+).Results are also presented from direct calculations for three states of the N2+ molecular ion (X2Σg+, A2Πu, B2Σu+) which are also thought to be very close approximations to the true Hartree—Fock values. The results give EHF=−108.4079, −108.4320, and −108.2702 hartree and Re(HF)=2.0385, 2.134, and 1.934 bohr for the X2Σg+, A2Πu, and B2Σu+ states of N2+, respectively. Extensive calculations for various R values establish that the X2Σg+ and A2Πu states are reversed in order relative to experiment, a short‐coming ascribed to the Hartree—Fock approximation.

388 citations

Journal ArticleDOI
TL;DR: In this article, the Hartree-Fock-Roothaan algorithm for homonuclear diatomic molecules is presented and several approaches to calculate the wave function are sketched as well as methods of computing molecular properties from the wavefunction.
Abstract: The analytic and computational framework for Hartree—Fock—Roothaan calculations on homonuclear diatomic molecules is presented. Several approaches to calculating the wavefunction are sketched as well as methods of computing molecular properties from the wavefunction. Emphasis is given to the efficient organization of these calculations for existing digital computers. Typical results obtained through the application of the programs and techniques developed are presented for the fluorine molecule.

200 citations

Journal ArticleDOI
TL;DR: In this article, the spin-orbit fine structure is resolved for the ground 2Πg states of F2+ and Cl2+; values obtained are ζ = 337 ± 40 and 645
Abstract: Photoelectron spectra of valence shell electrons in F2, Cl2, Br2, and I2 yield information on the molecular and electronic structure of the lowest several states of the corresponding positive ions, some of which is not available from previous spectroscopic studies. Spin–orbit fine structure is resolved for the ground 2Πg states of F2+ and Cl2+; values obtained are ζ = 337 ± 40 and 645 ± 40 cm−1, respectively. The first excited states of the ions are identified as 2Πu and approximate values of ζ = 2000–2200 and 6400 cm−1 obtained for Br2+ (A 2Πu) and I2+(A 2Πu), respectively. A state in F2+ reported previously [D. C. Frost, C. A. McDowell, and D. A. Vroom, J. Chem. Phys. 46, 4255 (1967)] to lie at ∼ 17.4 eV is not observed here and is attributed to nitrogen impurity. Vibrational frequencies for F2+ and Cl2+(X 2Πg) are in agreement with spectroscopic work. The corresponding frequencies for Br2+ and I2+ are ωe = 360 ± 40 and ∼ 220 cm−1. A change in bond length to Br2+(2Πg) of Δre ∼ (−)0.095 A is estimated fr...

192 citations