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This article describes a novel approach for the calculation of ionization potentials (IPs), or, more generally, electron-detachment energies, based on a unitary coupled-cluster (UCC) parameterization of the ground-state wave function. Explicit working equations for a scheme referred to as IP-UCC3 are given, providing electron-detachment energies and spectroscopic amplitudes of electron-detached states dominated by one-hole excitations correct through third order. In the derivation, an expansion of the UCC transformed Hamiltonian involving Bernoulli numbers as expansion coefficients is employed. Both the secular matrix and the effective transition moments are shown to be essentially equivalent to the strict third-order algebraic-diagrammatic construction scheme for the electron propagator (IP-ADC). Interestingly, due to the Bernoulli expansion, neglecting triple substitutions in the UCC expansion manifold does not affect the third-order consistency of the IP-UCC effective transition moments. Finally, the equivalence between ADC and UCC excited-state schemes is shown to not hold in fourth or higher order due to a different treatment of the correlated excited-state basis.

Chemical physics 482, 355 - 361(2017). doi:10.1016/j.chemphys.2016.08.001, We present an algebraic, nondiagrammatic derivation of finite-temperature second-order many-body perturbation theory [FT-MBPT(2)], using techniques and concepts accessible to theoretical chemical physicists. We give explicit expressions not just for the grand potential but particularly for the mean energy of an interacting many-electron system. The framework presented is suitable for computing the energy of a finite or infinite system in contact with a heat and particle bath at finite temperature and chemical potential. FT-MBPT(2) may be applied if the system, at zero temperature, may be described using standard (i.e., zero-temperature) second-order many-body perturbation theory [ZT-MBPT(2)] for the energy. We point out that in such a situation, FT-MBPT(2) reproduces, in the zero-temperature limit, the energy computed within ZT-MBPT(2). In other words, the difficulty that has been referred to as the Kohn–Luttinger conundrum, does not occur. We comment, in this context, on a “renormalization” scheme recently proposed by Hirata and He., Published by Elsevier Science, Amsterdam [u.a.]

The equivalence of the direct adc approach and the eco-isr formulation rests on two common key features. The first is the so-called canonical pt order structure of the secular matrix [1], establishing the compactness of the nth-order isr-adc approximation schemes. The other is the separability [2] of the secular matrix with respect to two (or more) non-interacting sub-systems, which warrants size-consistency. While in the adc context these features could have been substantiated using diagrammatic arguments, the eco-isr concept established in the preceding chapter allows for a stringent formulation and rigorous proofs. This is the topic of the present chapter. Section 12.1 (together with Appendix A.6) discusses the order structure of the secular matrix and the characteristic truncation errors thus entailed. The separability property will be treated in Sect. 12.2. Finally, in Sect. 12.3, we take a comparative look at the standard ci method, where the secular structure is simple but neither canonical nor separable.

In the preceding Chap. 9, the algebraic–diagrammatic construction (adc) was established as a procedure to derive systematically higher-order approximations to the \(\varvec{M}^+(\omega )\) and \(\varvec{M}^-(\omega )\) parts of the dynamical self-energy \(\varvec{M}(\omega )\). The respective adc matrices could then be incorporated within a common Dyson secular matrix allowing one to solve the Dyson equation in the form of a hermitian eigenvalue problem. As a characteristic feature, the Dyson approach combines the \((N\!-\!1)\)- and \((N\!+\!1)\)-particle problems as parts of a common computational scheme. The adc procedure, however, is quite general and can be applied to the electron propagator as well, more precisely, to the \(\varvec{G}^-(\omega )\) or \(\varvec{G}^+(\omega )\) parts. Such a direct adc approach, described in this chapter, avoids the Dyson equation altogether and leads to separate adc schemes for the \((N\!-\!1)\)- and \((N\!+\!1)\)-particle problems. The obvious advantage of these direct or non-Dyson schemes is the smaller size of the secular problem, being roughly half the size of a comparable Dyson formulation. Moreover, the lowest ionization energies (or electron affinities) are at the edge of the eigenvalue spectrum (and not in the middle of the joint \((N \pm 1)\)-particle energy spectrum). The price to be paid here is a higher complexity in the pt expansions of the secular matrix elements, which, however, is workable through the third-order adc(3) level.

In the four preceding chapters, we have established the formalism of diagrammatic perturbation theory for the electron propagator, which allows one to derive successively higher-order contributions \(\varvec{G}^{(n)}(\omega )\). However, a finite perturbation expansion, e.g., through third order, $$\begin{aligned} \varvec{G}(\omega ) = \varvec{G}^0(\omega ) + \varvec{G}^{(2)}(\omega ) + \varvec{G}^{(3)}(\omega ) + O(4) \qquad (8.1) \end{aligned}$$ does not result in a useful approximation scheme to determine the physical quantities of interest, that is, ionization energies, electron affinities, and the corresponding spectral factors. The reason is that the components \(G_{pq}(\omega )\) are analytical functions, and a finite perturbation expansion does not recover the proper analytical structure ( 3.17), being a sum over simple poles, from which the desired information could be extracted. So the question is how to translate the diagrammatic perturbation expansion into a viable computational scheme. What is needed here is to sum the perturbation expansion, even if only partially, through infinite order. A possible path toward such infinite partial summations, recovering the proper analytical structure of the electron propagator, is provided by the Dyson equation, which we will address in this chapter.

In the first section, we take a look at the basic ingredients in the quantum-theoretical formulation of many-electron systems: wave functions (states) and operators. For an in-depth discussion of physical aspects relevant here, the reader is referred to Chap. XIV in the textbook by A. Messiah [1]. In dealing with many-particle systems, the handling of matrix elements involving Slater determinants is required. Here, the essential tool is a set of simple rules, referred to as Slater–Condon rules, which will be considered in the second section of this chapter.

As was discussed in the beginning of Chap. 8, a finite perturbation expansion of the electron propagator does not reproduce its correct analytical form. While this applies also to the self-energy part beyond second order, here finite perturbation expansions together with the Dyson equation may provide viable approximations to the electron propagator, as shown by the third-order ovgf approach discussed in Sect. 8.3. The applicability of the ovgf approximation, however, is restricted to the energy region above the highest pole of \(\varvec{M}^-(\omega )\) and below the first pole of \(\varvec{M}^+(\omega )\). For the treatment of ionization energies and electron affinities outside that outer valence regime, the behavior of the self-energy part near its poles matters. This means that one has to recover the proper analytical form ( 8.19) of the dynamical self-energy part. Approximations of that type are obtained as a result of performing infinite summations of a certain class of diagrams. An example of such an infinite partial summation of diagrams in the case of the self-energy part is Hedin’s gw approximation [1] , which, in turn, is based on the famous random-phase approximation (rpa) , being itself an infinite partial summation of diagrams of the polarization propagator (see Chap. 15). An alternative way of generating infinite partial summations in a diagrammatic perturbation expansion is the algebraic–diagrammatic construction (adc) [2, 3]. In the following, we will discuss how the adc procedure can be performed in the case of the dynamic self-energy part. A direct adc approach to the \(\varvec{G}^-(\omega )\) and \(\varvec{G}^+(\omega )\) parts of the electron propagator is presented in Chap. 10.

The direct adc procedure presented in Chap. 10 for the \(\varvec{G}^{\pm }(\omega )\) parts of the electron propagator can essentially be transferred to the polarization propagator, where it suffices to deal with \(\varvec{\Pi }^+(\omega )\) due to the redundancy of the two parts. This will be demonstrated in the following. Moreover, in analogy to Chap. 11, the intermediate-state representation (isr), here based on the correlated excited N-electron states, will be established and discussed.

In this chapter, we will take a look at the famous random-phase approximation (RPA) to the polarization propagator. The computational benefit afforded by the rpa is rather modest, at least for atoms and molecules, as the resulting excitation energies and transition moments are only consistent through first order of perturbation theory.

The direct adc procedure for the electron propagator part \(\varvec{G}^{-}(\omega )\) considered in the preceding chapter allows one to construct successively an in principle exact hermitian secular matrix, \(\varvec{K} + \varvec{C}\), where (i) the eigenvalues are the negative ionization energies \(-I_n\); (ii) the matrix index labels are given by the hf configurations ( 10.9) of \(N\!-\!1\) electrons; (iii) the secular matrix elements can be expanded in regular pt expansions. As already anticipated in Chap. 10, these features suggest that \(\varvec{K} + \varvec{C}\) is essentially a representation of the hamiltonian, or, more specifically, of \(\hat{H} - E_0\), deriving from a set of (\(N\!-\!1\))-electron “intermediate” basis states. But what actually are these presumed intermediate states underlying the adc secular matrix? There is a surprisingly simple solution to this issue, establishing an alternative closed-form version of the adc secular equations, completely independent of the original diagrammatic derivation Schirmer J, Phys Rev A 43:4647, 1991, [1], Mertins F and Schirmer J, Phys Rev A 53:2140, 1996, [2]. Being a wave-function approach, the new formulation overcomes certain limitations inherent to the propagator concept. Of the three sections of this chapter, Sect. 11.1 presents the general procedure for constructing the intermediate states and the consequent intermediate-state representation (isr); Sect. 11.2 demonstrates the explicit derivation of the second-order isr equations; and, finally, Sect. 11.3 discusses how the isr concept can be applied to general operators.

The extension of the coupled-cluster (cc) method, originally devised for ground-states (Coester (1958) Nucl Phys 7:421, [1]), (Cizek (1966) J Phys Chem 45:4256, [2]), to the treatment of (generalized) electronic excitations is based on ce states in which the cc ground-state parametrization is used. To deal with the non-orthogonality of the ce states and, even more importantly, to obtain tractable secular equations, one introduces, as a second expansion manifold, the set of associated biorthogonal states. The corresponding mixed or biorthogonal (b) representation of the (shifted) hamiltonian gives rise to the non-hermitian bcc secular matrix. In this chapter, we give an introduction into the bcc concept and review in particular the order relations and separability properties of the bcc secular equations. We here refer to the extensive analysis given in Ref. [11] which may be consulted for further details.

According to the definition ( 3.3) of the electron propagator, pt expansions come into play in two ways: firstly, via the ground state, and, secondly, in the time-dependent Heisenberg operators. To accomodate both demands, a procedure based on time-dependent perturbation theory (tdpt) has proven advantageous. After a review of tdpt in the ensuing Sect. 4.1, we shall discuss in Sect. 4.2 how this technique can be adapted to the case where the interaction part \(\hat{H}_I\) is slowly “switched on” by applying an appropriate time-dependent function. In the so-called adiabatic limit, a valid pt formulation of the interacting N-electron ground state is obtained, which is the proposition of the Gell-Mann and Low theorem. The Gell-Mann and Low formulation of the ground state can be extended to ground-state expectation values of time-dependent operators and, moreover, to the elements of the electron propagator, as will be discussed in Sect. 4.3.

Algebraic propagator methods, as opposed to methods based on diagrammatic perturbation theory, have been derived within the so-called superoperator formulation [1, 2, 3], in which the respective propagator is written and evaluated in the form of a superoperator resolvent [4]. The resulting secular equations are fully equivalent with those obtained in the context of the eom method [5, 6], originally devised by Rowe [7] in the field of nuclear physics. To some extent, the eom formulation is more general than the algebraic propagator approach since the former provides a genuine wave-function representation of the (generalized) excited states in terms of an extended set of ce states. In this chapter, we briefly review the eom method, emphasizing here in particular its isr characteristics. For a more comprehensive presentation as well as references to the original literature, we refer to the cited review articles and to Ref. [8]. A direct connection to the algebraic propagator methods is established in Sect. 16.2, while the superoperator formulation is reviewed in Appendix A.8.

The valence shell ionization spectrum of pyridine was studied using the third-order algebraic-diagrammatic construction approximation scheme for the one-particle Green’s function and the outer-valence Green’s function method. The results were used to interpret angle resolved photoelectron spectra recorded with synchrotron radiation in the photon energy range of 17–120 eV. The lowest four states of the pyridine radical cation, namely, 2A2 (1a 2 −1 1a2−1 ), 2A1(7a 1 −1 7a1−1), 2B1(2b 1 −1 2b1−1), and 2B2(5b 2 −1 5b2−1), were studied in detail using various high-level electronic structure calculation methods. The vertical ionization energies were established using the equation-of-motion coupled-cluster approach with single, double, and triple excitations (EOM-IP-CCSDT) and the complete basis set extrapolation technique. Further interpretation of the electronic structure results was accomplished using Dyson orbitals, electron density difference plots, and a second-order perturbation theory treatment for the relaxation energy. Strong orbital relaxation and electron correlation effects were shown to accompany ionization of the 7a1 orbital, which formally represents the nonbonding σ-type nitrogen lone-pair (nσ) orbital. The theoretical work establishes the important roles of the π-system (π-π* excitations) in the screening of the nσ-hole and of the relaxation of the molecular orbitals in the formation of the 7a1(nσ)−1 state. Equilibrium geometric parameters were computed using the MP2 (second-order Moller-Plesset perturbation theory) and CCSD methods, and the harmonic vibrational frequencies were obtained at the MP2 level of theory for the lowest three cation states. The results were used to estimate the adiabatic 0-0 ionization energies, which were then compared to the available experimental and theoretical data. Photoelectron anisotropy parameters and photoionization partial cross sections, derived from the experimental spectra, were compared to predictions obtained with the continuum multiple scattering approach.

The core level photoemission and near edge X-ray photoabsorption spectra of guanine in the gas phase have been measured and the results interpreted with the aid of high level ab initio calculations. Tautomers are clearly identified spectroscopically, and their relative free energies and Boltzmann populations at the temperature of the experiment (600 K) have been calculated and compared with the experimental results and with previous calculations. We obtain good agreement between experiment and the Boltzmann weighted theoretical photoemission spectra, which allows a quantitative determination of the ratio of oxo to hydroxy tautomer populations. For the photoabsorption spectra, good agreement is found for the C 1s and O 1s spectra but only fair agreement for the N 1s edge.

Single reference coupled-cluster (CC) methods for electronic excitation are based on a biorthogonal representation (bCC) of the (shifted) Hamiltonian in terms of excited CC states, also referred to as correlated excited (CE) states, and an associated set of states biorthogonal to the CE states, the latter being essentially configuration interaction (CI) configurations. The bCC representation generates a non-hermitian secular matrix, the eigenvalues representing excitation energies, while the corresponding spectral intensities are to be derived from both the left and right eigenvectors. Using the perspective of the bCC representation, a systematic and comprehensive analysis of the excited-state CC methods is given, extending and generalizing previous such studies. Here, the essential topics are the truncation error characteristics and the separability properties, the latter being crucial for designing size-consistent approximation schemes. Based on the general order relations for the bCC secular matrix and the (left and right) eigenvector matrices, formulas for the perturbation-theoretical (PT) order of the truncation errors (TEO) are derived for energies, transition moments, and property matrix elements of arbitrary excitation classes and truncation levels. In the analysis of the separability properties of the transition moments, the decisive role of the so-called dual ground state is revealed. Due to the use of CE states the bCC approach can be compared to so-called intermediate state representation (ISR) methods based exclusively on suitably orthonormalized CE states. As the present analysis shows, the bCC approach has decisive advantages over the conventional CI treatment, but also distinctly weaker TEO and separability properties in comparison with a full (and hermitian) ISR method.

The valence shell photoelectron spectra of uracil, 1-methyluracil and 6-methyluracil have been studied experimentally and theoretically. Synchrotron radiation has been used to record spectra at photon energies of 40 and 80 eV. Photoelectron angular distributions have been determined and these provide an experimental means of distinguishing between σ- and π-type orbitals. Vertical ionization energies and spectral intensities have been evaluated using the many-body Green’s function approach, thereby enabling theoretical photoelectron spectra to be derived. The calculated spectra display a satisfactory agreement with the experimental data and this has allowed most of the photoelectron bands to be assigned. Two of the outer-valence vertical ionization energies are similar to one another and the vibrational progressions associated with these transitions overlap strongly. Vibronic interaction between these states, induced through the excitation of out-of-plane vibrational modes, may lead to nonadiabatic effects. Preliminary theoretical investigation of this interaction has been performed.

Valence shell photoelectron spectra of the 5-halouracils have been recorded using synchrotron radiation at photon energies of 40 and 80 eV. Photoelectron angular distributions have been determined and these provide an experimental means of deducing the extent to which the molecular orbitals possess predominantly σ, π or halogen np character. In chloro-, bromo- and iodouracil two peaks, associated with the essentially halogen atom lone-pair orbitals, have been observed. The separation between these peaks, and the value of their photoelectron asymmetry parameters at an excitation energy of 40 eV, are compared with results for the corresponding orbitals in the halobenzenes and halothiophenes. Vertical ionisation energies and spectral intensities have been evaluated using the many-body Green’s function approach, thereby enabling theoretical spectra to be derived. Assignments have been proposed for most of the structure observed in the valence shell photoelectron spectra based upon the available experimental and theoretical evidence.

The photoelectron spectrum of selenophene has been recorded using synchrotron radiation in the photon energy range 20–80 eV and the inner valence region has been studied in detail for the first time. Green's function methods have been employed to evaluate the energies and spectral intensities of all valence shell ionization transitions and the results have facilitated an interpretation of the experimental spectra. Strong configuration interaction results in a redistribution of the intensity associated with the low lying π1(1b1) orbital amongst several satellite states located in the outer valence region. The continuum multiple scattering approach has been used to calculate photoelectron asymmetry parameters for selenophene, thiophene and hydrogen sulphide, and these theoretical predictions have been compared with the corresponding experimental data to assess the influence of Cooper minima and shape resonances. The comparison indicates that the Se 4p and the S 3p Cooper minima have little effect on the valence shell photoionization dynamics of selenophene and thiophene, respectively. This outcome is discussed in connection with the closely related hydrogen selenide and hydrogen sulphide molecules where strong resonant phenomena are observed.

Ab initio calculations are performed to explain the discrete transitions in experimental C 1s-NEXAFS (near edge X-ray absorption fine structure) spectra of various benzoic acid derivates. Transition energies and oscillator strengths of the contributing C 1s–π * excitations are computed using the ADC(2) (second-order algebraic-diagrammatic construction) method. This method is demonstrated to be well suited for the finite electronic systems represented by these simple organic acids. There is good agreement between experiment and theory reproducing all the relevant spectral features. Some transitions can only be assigned based on a theoretical foundation. Remaining discrepancies between experimental and computed spectra are discussed.

Doubly excited states play important roles in the low-energy region of the optical spectra of polyenes and their investigation has been subject of theoretical and experimental studies for more than 30 years now and still is in the focus of ongoing research. In this work, we address the question why doubly excited states play a role in the low-energy region of the optical spectrum of molecular systems at all, since from a naive point of view one would expect their excitation energy approximately twice as large as the one of the corresponding single excitation. Furthermore, we show that extended-ADC(2) is well suited for the balanced calculation of the low-lying excited 2 1 A g - , 1 1 B u - and 1 1 B u + states of long all-trans polyenes, which are known to possess substantial double excitation character. A careful re-investigation of the performance of TDDFT calculations for these states reveals that the previously reported good performance for the 2 1 A g - state relies heavily on fortuitous cancellation of errors. Finally, the title question is answered such that for short polyenes the lowest excited 2 1 A g - and 1 1 B u - states can clearly be classified as doubly excited, whereas the 1 1 A g - ground state is essentially represented by the (ground-state) HF determinant. For longer polyenes, in addition to increasing double excitation contributions in the 2 1 A g - and 1 1 B u - states, the ground state itself aquires substantial double excitation character (45% in C22H24), so that the transition from the ground state to these excited states should not be addressed as the excitation of two electrons relative to the 1 1 A g - ground state.

A polarization propagator method, referred to as algebraic-diagrammatic construction (ADC), is extended to the treatment of static and dynamic response properties of molecules. The recent intermediate state representation (ISR) concept of the ADC theory, giving direct access to excited states wave functions and properties, allows us to derive simple closed-form expressions for linear and higher response functions. The use of the band-Lanczos algorithm is proposed to evaluate efficiently the resolvent type ADC expressions. The performance of the method is tested in computations of static and dynamic polarizabilities of several small molecules at the second-order (ADC(2)) level of the theory. The ADC(2) results are compared with those of full configuration interaction (FCI), coupled cluster (CC), and SOPPA (second-order polarization propagator approximation) treatments.

The complete valence shell photoelectron spectra of cytosine, thymine and adenine have been investigated experimentally and theoretically. Vertical ionization energies and spectral intensities have been evaluated using the many-body Green's function method, thereby enabling theoretical photoelectron spectra to be derived. In cytosine, the influence of tautomers and rotational conformers has been investigated. The calculated spectra display a satisfactory agreement with the experimental data and this has allowed most of the photoelectron bands to be assigned. Photoelectron asymmetry parameters have been determined from angle resolved spectra recorded with synchrotron radiation. The experimental data show that the electronic configuration of the five outer orbitals in cytosine, thymine and adenine is π, σ, π, σ, π. Vertical ionization energies have been measured for all the outer-valence orbitals even though some of the associated bands overlap significantly.

The photoelectron spectrum of hydrogen selenide has been recorded using synchrotron radiation in the photon energy range 15–110 eV and the inner valence region has been studied in detail for the first time. Green’s function methods have been employed to evaluate the ionisation energies and spectral intensities of all valence states and the results have facilitated an interpretation of the experimental spectra. Two outer valence satellites have been observed at binding energies of ∼17 and ∼18.5 eV. The continuum multiple scattering (CMS-Xα) approach has been used to calculate photoelectron asymmetry parameters and branching ratios for the outer valence orbitals and these have been compared with experimental data. The Se 4p Cooper minimum strongly affects the photoionisation dynamics of the outermost 4b 1 orbital and its influence is evident in both the theoretically predicted and the measured asymmetry parameter for the X ˜ 2 B 1 state. The experimental data for the A ˜ 2 A 1 and B ˜ 2 B 2 state asymmetry parameters also display energy dependent variations in the vicinity of the Cooper minimum. However, for these two states the agreement between the predicted and observed asymmetry parameters is less satisfactory. The present results for H 2 Se have been compared with similar data for the closely related H 2 S molecule.

The complete valence shell photoelectron spectrum of tetrafluoromethane has been recorded using synchrotron radiation and the observed structure has been interpreted using ionisation energies and relative spectral intensities computed using the third-order algebraic-diagrammatic-construction (ADC(3)) scheme for the one-particle Green’s function and the outer valence Green’s function (OVGF) method. The ADC(3) calculations were performed using both the original variant based on the Dyson equation and the recently proposed non-Dyson scheme. The theoretical predictions for the single-hole ionic states due to outer valence shell ionisation agree satisfactorily with the experimental results. Ionisation from the inner valence 2t2 and 3a1 orbitals is strongly influenced by reorganisation effects and the intensity is spread amongst numerous satellites. Highly resolved spectra have been measured for the C ∼ 2 T 2 and the D ∼ 2 A 1 states, and the vibrational structure has been associated primarily with excitation of the ν 1 + ( a 1 ) mode. However, the analyses also provide evidence for excitation of the Jahn-Teller active ν 2 + ( e ) mode in the C ∼ 2 T 2 state, and the ν 3 + ( t 2 ) mode in the D ∼ 2 A 1 state. Excitation of this latter mode can be explained in terms of vibronic coupling between the C ∼ 2 T 2 and the D ∼ 2 A 1 states. Photoelectron angular distributions and branching ratios have been determined and demonstrate that shape resonances affect the outer valence shell photoionisation dynamics. The experimental results are compared with previous theoretical predictions but a consistent interpretation has not been obtained. The major difficulty concerns the uncertainty in the locations of valence shell transitions into the 5a1 and the 5t2 virtual orbitals.

International audience; The excitation spectra and molecular dynamics of furan associated with its low-lying excited singlet states 1A2(3s), 1B2(V), 1A1(V'), and 1B1(3p) are investigated using an ab initio quantum-dynamical approach. The ab initio results of our previous work [J. Chem. Phys. 119, 737 (2003)] on the potential energy surfaces (PES) of these states indicate that they are vibronically coupled with each other and subject to conical intersections. This should give rise to complex nonadiabatic nuclear dynamics. In the present work the dynamical problem is treated using adequate vibronic coupling models accounting for up to four coupled PES and thirteen vibrational degrees of freedom. The calculations were performed using the multiconfiguration time-dependent Hartree method for wave-packet propagation. It is found that in the low-energy region the nuclear dynamics of furan is governed mainly by vibronic coupling of the 1A2(3s) and 1B2(V) states, involving also the 1A1(V') state. These interactions are responsible for the ultrafast internal conversion from the 1B2(V) state, characterized by a transfer of the electronic population to the 1A2(3s) state on a time scale of approximately 25 fs. The calculated photoabsorption spectrum of furan is in good qualitative agreement with experimental data. Some assignments of the measured spectrum are proposed.

The valence shell photoelectron spectra of BrCN and ICN have been studied using synchrotron radiation. In addition to the main bands associated with the single-hole states, complex satellite structure due to many-electron effects has been observed in the inner valence region. The Green’s function method has been employed to evaluate the ionisation energies and pole strengths of all valence states and the results have facilitated an interpretation of the experimental spectra. Photoelectron angular distributions and branching ratios for the valence shell, the Br 3d level in BrCN and the I 4d level in ICN have been measured in the photon energy range 14–120 eV. The continuum multiple scattering (CMS-Xα) approach has been used to calculate photoelectron asymmetry parameters and branching ratios for the valence orbitals of ClCN, BrCN and ICN. These have been used to assess the influence of Cooper minima and shape resonances on the photoionisation dynamics. In ICN, the experimental and theoretical results provide evidence of core-valence shell coupling at energies above the I 4d threshold. The experimentally determined asymmetry parameters and branching ratios for the spin–orbit split Br 3d 5/2,3/2 and I 4d 5/2,3/2 components have been compared to those for Kr and Xe, and a strong atomic-like behaviour is evident. The calculated spin–orbit averaged β -parameters for the Br 3d and I 4d levels confirm this interpretation. Hartree–Fock (HF) calculations have been carried out to study the evolution of the valence orbital characteristics through the series of halogen-substituted XCN (X=H, Cl, Br, I) molecules.

We report on a new implementation and first numerical tests of the fourth-order algebraic–diagramatic construction [ADC(4)] propagator method for K-shell ionization in molecules. The theory, which has been presented in a preceding paper (paper I) [J. Chem. Phys. 115, 10621 (2001)], is based on an intermediate state representation (ISR) or non-Dyson reformulation of the general ADC approach and uses the core–valence separation approximation to specialize the method to the case of core-level ionization. The ISR form offers the possibility to go beyond the finite perturbation-theoretical expressions of the previous (strict) ADC(4) scheme, and several such modifications are considered. The general aim of the present development is to establish a practical “frozen” orbital method that can be applied equally well to systems with and without equivalent core levels. A set of small model calculations has been carried out on the 1s ionization in CO and N2 allowing us to compare the ADC results with those of large-s...

2 (V), 1 A 1 (V8), respectively, at the C 2v ground-state molecular configuration# have been studied using the equation-of-motion coupled-cluster singles and doubles method ~EOM-CCSD!. Full geometry optimizations with subsequent computation of harmonic vibrational frequencies have been performed in order to locate and characterize stationary points on the potential energy surfaces ~PES!. The latter optimization work was enabled by the availability of analytic energy gradient techniques for the EOM-CCSD approach. A major new finding is that both the 1 B2(V) and 1 A1(V8) valence states are unstable with respect to non-totally symmetric distortions at the C2v configuration. The symmetry breaking in the 1 B2(V) state involves an in-plane coordinate of b2 symmetry. The relaxation process begins on the S2 adiabatic PES and, after passing through a conical intersection of the S2 and S1 PES, continues on the S1 surface, taking the system finally to the adiabatic minimum ofS1 ( 1 A2 state!. The 1 A1(V8) valence state is found to be unstable with respect to the out-of-plane bending coordinates of b1 and a2 symmetry. The resulting relaxed molecular structures have Cs and C2 symmetry, respectively. The present findings are analyzed in terms of a linear vibronic coupling model and spectroscopic implications are discussed. © 2003 American Institute of Physics. @DOI: 10.1063/1.1578051#

The valence shell photoelectron spectrum of purine has been studied experimentally and theoretically. Synchrotron radiation has been used to record spectra at photon energies of 45 and 85 eV. Photoelectron angular distributions have been determined and these provide an experimental means of distinguishing between σ-and π-type orbitals. Vertical ionization energies and photoelectron spectral intensities have been evaluated using the many-body Green function method. The calculated spectra agree well with the experimental results in the outer valence region and have proved to be indispensable for interpreting the structure at higher binding energies where the single particle model of ionization breaks down. The photoelectron spectrum of pyrimidine has also been studied and is compared to that of purine.

The valence shell photoelectron spectrum of 2-iodothiophene (2-I-Th) has been studied experimentally and calculations have been carried out to characterize the main bands due to single-hole ionized states for both 2- and 3-iodothiophene. The importance of electron correlation in the formation of satellite states has also been assessed. The vertical ionization energies and spectral intensities of the entire valence shell photoelectron spectrum have been computed using the third-order algebraic–diagrammatic construction approximation for the one-particle Green function. These theoretical predictions have allowed assignments to be proposed for all the prominent structure observed in the experimental spectra, and have highlighted the breakdown of the molecular orbital model of ionization for the π1-orbital. By comparing the present theoretical and experimental results for iodothiophene with similar data for chloro-and bromothiophene, it has been found that the binding energies and intensities of the satellites associated with the π1-orbital form a pattern which is common to all three monohalothiophenes. Relativistic Hartree–Fock calculations have been carried out to investigate the importance of such effects on the valence shell ionization of iodothiophene. Synchrotron radiation has been used to measure photoelectron angular distributions and branching ratios of 2-I-Th. The spectral behaviour of the asymmetry parameters has provided an experimental means of distinguishing photoelectron bands due to σ-orbitals from those associated with π-orbitals. A high-resolution photoelectron spectrum of the outer valence shell of 2-I-Th has been recorded using HeI radiation, and vibrational structure has been observed and analysed in the 2A'', A 2A'', 2A' and 2A'' state bands.

A recently developed consistent third-order propagator method for the treatment of electronic excitation in molecules is tested in first applications. The method referred to as third-order algebraic-diagrammatic construction [ADC(3)] extends the existing second-order approximation and aims at a more accurate computation of excitation energies and transition moments than afforded at the second-order level. For a stringent test of the method we compare the ADC(3) energies for over 40 singlet and triplet vertical transitions in H2O, HF, N2, and Ne with the results of recent full configuration interaction (FCI) and coupled cluster (CC) computations. The ADC(3) results reflect a substantial and uniform improvement with respect to the second-order description. The mean absolute deviation of the single excitation energies from the FCI results is below 0.2 eV. Although this does not equal the accuracy of the third-order CC3 model, the ADC(3) method, scaling as N6 with the number of orbitals, may be viewed as a good compromise between accuracy and computational cost.

The complete valence shell photoelectron spectrum of silicon tetrafluoride has been studied both experimentally and theoretically. Photoelectron angular distributions and branching ratios have been measured in the photon energy range 17-120 eV, using synchrotron radiation, and compared with previous theoretical predictions. The spectra demonstrate that shape resonance phenomena affect the photoionization dynamics of the outer valence shell orbitals, and the predicted shape resonance in the a1 channel, close to threshold, has been confirmed experimentally. At higher energies, the effects of the e and t2 symmetry shape resonances have been observed, for the first time, in the photoelectron asymmetry parameters. Partial photoionization cross sections have been derived by combining the experimental branching ratios with the total ion yield curve and normalizing the results to the absolute photoabsorption cross section. The partial cross sections so obtained have been compared with theoretical curves reported in two earlier studies. The vertical ionization energies and spectroscopic factors for the entire valence shell photoelectron spectrum have been computed using the third-order algebraic-diagrammatic construction approximation scheme for the one-particle Green function.

The general intermediate state representation (ISR) for single-electron ionization is adapted to the case of K-shell (or core-level) ionization in molecules. The development is based on the so-called core–valence separation (CVS) approximation leading to a considerable simplification of the ISR secular equations. Using the CVS approximation the core-level ISR can be formulated entirely in terms of the intermediate states of the valence electron excitation problem, which allows one to construct consistent nth-order approximation schemes for the (single-hole) ionization energies by a specific extension of the (n−2)-nd order ISR approximation for electronic excitation. In particular, the CVS-ISR concept is used to derive a consistent fourth-order approximation for core-level ionization based on the existing second-order algebraic-diagrammatic construction [ADC(2)] approximation to electron excitation. The computational scheme combines the diagonalization of a Hermitian secular matrix with finite perturbation...

The valence shell photoelectron spectra of thiophene, 2-chlorothiophene (2-Cl-Th) and 3-chlorothiophene (3-Cl-Th) have been investigated theoretically and experimentally. The third-order algebraic-diagrammatic construction approximation scheme for the one-particle Green’s function has been employed to evaluate the vertical ionisation energies and spectral intensities. The ground state geometrical parameters of the three molecules have been optimised at the level of the second order Moller–Plesset perturbation theory, and standard cc-pvDZ basis sets have been used throughout. The results for the outer valence region of thiophene agree well with available experimental and theoretical data. Very satisfactory agreements have been obtained between the theoretical predictions for the photoelectron spectra of 2-Cl-Th and 3-Cl-Th and the corresponding experimental data recorded in the present study. Assignments have been proposed for the major spectral structures. In all three molecules the breakdown of the molecular orbital ionisation picture associated with the π1 molecular orbital is discussed. Synchrotron radiation has been used to record the complete valence shell photoelectron spectra of 2-Cl-Th and 3-Cl-Th. Photoelectron angular distributions and branching ratios have been determined in the photon energy range 13–115 eV, and those for the chlorine and sulphur 3p orbitals show effects that can be attributed to Cooper minima. A high resolution photoelectron spectrum of the outer valence shell of 2-Cl-Th has been recorded using HeI radiation, and vibrational structure has been observed and analysed in the X 2 A ′′ , A 2 A ′′ , B 2 A ′ , C 2 A ′′ and I 2 A ′ state bands.

The valence shell photoelectron spectrum of cyanogen chloride has been studied using HeI and synchrotron radiation. In the outer valence region the molecular orbital model of ionization holds, and the main bands can be associated with single-hole states. However, in the inner valence region electron correlation effects become important, and these result in complex satellite structure being observed. Vertical ionization energies and spectral intensities have been computed using the Green's function approach, and the results have facilitated an interpretation of the experimental spectra. Photoelectron angular distributions and branching ratios have been measured and have been used to assess the bonding characteristics of the outer valence molecular orbitals. The experimental data for the 8σ orbital display an energy dependence which suggests that photoionization from this orbital may be influenced by the chlorine 3p Cooper minimum. The extent to which the 8σ orbital can be considered as a chlorine atom lone...

The group of three lowest singlet C 1s-excited states of formaldehyde H2CO is studied theoretically. The equilibrium geometries are determined at the restricted open-shell Hartree–Fock (ROHF) level and refined total energies are obtained using the multireference configuration interaction (MRCI) approach. In agreement with an earlier prediction [Chem. Phys. 122, 9 (1988)] the second lowest singlet state, 1B2, is characterized by a doubly excited, “two particle–two hole” (2p–2h), configuration C 1s,n→π*2. Our calculations predict that H2CO in the 1B2(2p–2h) state has a stable pyramidal equilibrium structure with a barrier to inversion of 0.28 eV, the valence angle being close to 107°. The calculated length of the CO bond is 1.390 A. The 1B2(2p–2h) state is shown to be also bound with respect to all possible dissociation and rearrangement processes. The lowest predicted dissociation energy for the 1B2 state (H2CO*→H2+CO* reaction) is 0.29 eV (6.69 kcal/mol). The rationalization of the great stability of the ...

An effective ab initio approach to core-level electronic spectral studies is discussed. The approach uses polarization propagator theory in a second-order algebraic diagram construction ADC(2) approximation for calculating the characteristics of electron transitions; it also uses the linear vibronic model LVM for investigating the vibrational structure of transitions. The core excitation specialization of ADC(2) is achieved by introducing the core valence separation (CVS) approximation. K-excitation spectra of CO and N2 molecules are calculated to examine the potential of the approach. The calculated spectra and the available experimental data are analyzed to characterize the method. A number of additional facts of methodological and practical value are found, and new transitions are predicted. It is concluded that ADC(2)/CVS/LVM is a promising approach to problem solving in core level spectroscopy, which requires qualitatively reliable theoretical estimations.

A propagator method referred to as third-order algebraic–diagrammatic construction [ADC(3)] for the direct computation of electronic excitation energies and transition moments is presented. This approach is based on a specific reformulation of the diagrammatic perturbation expansion for the polarization propagator, and extends the existing second-order [ADC(2)] scheme to the next level of perturbation theory. The computational scheme combines diagonalization of a Hermitian secular matrix and perturbation theory for the matrix elements. The characteristic properties of the method are compact configuration spaces, regular perturbation expansions, and size-consistent results. The configuration space is spanned by singly and doubly excited states, while the perturbation expansions in the secular matrix extend through third order in the p-h block, second order in the p-h/2p-2h coupling block, and first order in the 2p-2h block. While the simpler ADC(2) method, representing a counterpart to the MP2 (second-orde...

An efficient third-order propagator method to compute ionization potentials and electron affinities of atoms and molecules is presented. The development is based on the algebraic diagrammatic construction (ADC) representing a specific reformulation of the diagrammatic perturbation series of the electron propagator G(ω). In contrast with previous approximation schemes, relying on the Dyson equation and approximations for the self-energy part, the ADC procedure here is applied directly to the (N∓1)-electron parts G−(ω) and G+(ω), respectively, of the electron propagator. This leads to decoupled secular equations for the ionization energies ((N−1)-electron part) and electron affinities ((N+1)-electron part), respectively. In comparison with the Dyson-type approach, there is a substantial reduction of the secular matrix dimension opposed by a small additional expense in computing some second- and third-order contributions to the secular matrix elements. The relationship of the non-Dyson ADC(3) method to coupl...

The 2A2 and 2B1 states formed in the ionization of the outermost π orbitals in furan, pyrrole and thiophene are shown to interact vibronically via nontotally symmetric b2 vibrational modes. The interaction is strongest in pyrrole and thiophene, where the conical intersection between the two adiabatic surfaces occurs near the minimum of the upper (2B1) state. The resulting nonadiabatic effects manifest themselves in the 2B1 bands by a lack of resolved structure in case of pyrrole and thiophene, and by a line broadening in case of furan. The spectra are investigated using a linear vibronic coupling model. All totally symmetric a1 (tuning) modes and nontotally symmetric b2 (coupling) modes describing the ring motion are taken into account. The parameters of the model are obtained with the aid of ab initio calculations. The ground state optimized geometries and vibrational frequencies are computed at the level of the second-order Mo/ller–Plesset perturbation theory, while the dependence of the ionization ener...

We present an extension of the frozen-core Hartree - Fock (FCHF) approach to molecular photoionization, allowing us to study the effect of ground-state correlation on the cross sections and photoelectron angular distributions in both a practical and a systematic way. The extended FCHF model is obtained by augmenting the usual FCHF scattering equation by a simple first-order perturbation theoretical expression for the transition moment involving merely bound-state terms. In addition we describe a numerical method for the treatment of the FCHF scattering problem. Our method makes use of the usual (single-centre) partial wave expansion techniques. The local scattering equations are solved by means of numerical integration and asymptotic matching to the Coulomb (or free) scattering solutions. Subsequently, the non-local exchange potential and the orthogonality constraints are taken into account by using a basis set approach based on the Schwinger variational method. The method has been tested in applications to the photoionization of He, , , and . These examples show that ground-state correlation can affect quite substantially both the magnitude and the shape of the cross sections. The correlation effect is particularly pronounced at the shape resonances in and CO. In the case of CO a distinct effect is seen also in the photoelectron angular distribution. For the two-electron systems, He and , the agreement between the length and velocity formulation is distinctly improved at the extended FCHF level. In cases with more than one ionization channel, the length-form version is no longer appropriate, reflecting a failure of the single-channel approximation rather than a shortcoming of the FCHF extension.

The vibrational fine structure of the prominent C1s-π* absorption band of ethylene and some of its isotopomers has been investigated theoretically with the aid of a specific (linear) vibronic coupling model. The presence of two equivalent C1s levels gives rise to two nearly degenerate electronic states of g and u symmetry, respectively, which can interact vibronically via the (planar) antisymmetric C–H stretching and bending modes (ν11 and ν12). In addition to these states of immediate interest, the present model comprises three more pairs of “effective” states at higher energy allowing one to describe the excitation of additional asymmetric (nonplanar) modes as a result of linear vibronic coupling. To a good approximation the intrapair vibronic coupling can be eliminated by using a representation in terms of localized C1s hole states. As a further result, the in-plane and out-of-plane modes become separable. The required vibronic coupling constants have been determined with the aid of ab initio calculati...

The electronic spectrum of furan is investigated theoretically beyond the previous vertical-electronic description. A polarization propagator method referred to as second-order algebraic-diagrammatic construction (ADC(2)) has been used in the electronic structure calculations. The vibrational excitation accompanying the electronic transitions is described with the aid of a linear electron-vibrational coupling model. The spectral information thereby obtained permits extensive comparison with experiment. The average accuracy of the present method, estimated by comparing adiabatic transition energies, is better than 0.4 eV. Only for the lowest π-π ∗ valance transition, V′( 1 A 1 ) and V′( 1 B 2 ), and for the Rydberg excitations agree The results for the other π-π ∗ valence transitions, V( 1 B 2 ), and for the Rydberg excitations agree well with findings of previous experimental and theoretical work. A (multistate) vibronic coupling effect involving the V′( 1 A 1 ) and V( 1 B 2 ) valence transitions and the 3s( 1 A 2 Rydberg excitation is suggested as the reason for the highly diffuse character of the 5.7–6.7 eV photoabsorption band.

With the aim of obtaining a practical approach to molecular photoionization continua, a new formulation is given for the random phase approximation (RPA). This development is based on the so-called algebraic-diagrammatic construction (ADC) used previously to derive higher-order approximations to the polarization and other propagators. In the ADC reformulation the RPA pseudo-eigenvalue equations split into two equivalent, generally Hermitian, secular problems of half dimension. Here the elements of the resulting ADC secular matrices are given in the form of `regular' perturbation expansions. Similar perturbation expansions result for the `effective' transition amplitudes required to calculate spectral intensities. Approximation schemes converging to the full RPA are obtained by truncating these perturbation expansions at successively higher-order n. For the lowest orders n = 1 and 2 the ADC(n)/RPA schemes are specified explicitly. In addition to the perturbation-theoretical approach, direct closed-form expressions are given for the ADC secular matrix and effective transition amplitudes relating these quantities to the RPA eigenvalues and eigenvectors. As shown by these relations, the ADC reformulation can be viewed as a specific form of quasi-degenerate perturbation theory (QDPT) applied to the RPA pseudo-eigenvalue problem. In the single-channel (SC) approximation the ADC secular equations reduce to a one-electron eigenvalue problem for an energy-independent non-local potential. A particularly useful method is the single-channel ADC(1) scheme combining the scattering solutions of the familiar frozen-core Hartree - Fock (FCHF) model with a simple first-order expression for the transition moments. Illustrative applications of the SC-ADC(1) method to the photoionization in and are reported. These calculations show that ground state correlation can quite substantially influence both the magnitude and the shape of the cross sections as a function of energy.

As a general common concept, underlying diverse methods used to compute generalized electronic excitations in atoms and molecules, intermediate-state representations (ISR's), are considered and analyzed. Essentially, an ISR results by representing the excitation energy operator in terms of so-called correlated excited states (CES's) or states derived thereof. Three different ISR schemes are compared, namely the biorthogonal coupled-cluster (BCC) representation used in both the coupled-cluster linear response and equation-of-motion coupled-cluster methods, a unitary coupled-cluster (UCC) representation, and the excitation class orthogonalized (ECO) representation resulting from a Gram-Schmidt orthogonalization procedure for the CES. Moreover, the relationship between the BCC scheme and the symmetry-adapted-cluster--configuration-interaction method is discussed. The relevance of the ISR schemes, as opposed to the much simpler configuration-interaction (CI) expansions, arises from two basic properties referred to as separability and compactness. The former property is a sufficient condition for size-consistent results, while the latter allows one to use smaller explicit configuration spaces than in comparable CI treatments. We show that the ECO and UCC representations are both separable and compact, whereas a somewhat restricted compactness property applies in the BCC case. \textcopyright{} 1996 The American Physical Society.