Independent particle theory with electron correlation

We formulate an effective independent particle model where the effective Hamiltonian is composed of the Fock operator and a correlation potential. Within the model the kinetic energy and the exchange energy can be expressed exactly leaving the correlation energy functional as the remaining unknown. Our efforts concentrate on finding a correlation potential such that exact ionization potentials and electron affinities can be reproduced as orbital energies. The equation-of-motion coupled-cluster approach enables us to define an effective Hamiltonian from which a correlation potential can be extracted. We also make the connection to electron propagator theory. The disadvantage of the latter is the inherit energy dependence of the potential resulting in a different Hamiltonian for each orbital. Alternatively, the Fock space coupled-cluster approach employs an effective Hamiltonian which is energy independent and universal for all orbitals. A correlation potential is extracted which yields the exact ionization potentials and electron affinities and a set of associated molecular orbitals. We also describe the close relationship to Brueckner theory.     

Ab initio correlation corrections to the Hartree-Fock quasi band-structure of periodic systems employing Wannier-type orbitals

A size-consistent ab initio formalism to calculate correlation corrections to ionization potentials as well as electron affinities of periodic systems is presented. Our approach is based on a Hartree-Fock scheme which directly yields local orbitals without any a posteriori localization step. The use of local orbitals implies non-zero off-diagonal matrix elements of the Fock operator, which are treated as an additional perturbation and give rise to localization diagrams. Based on the obtained local orbitals, an effective Bloch Hamiltonian is constructed to second order of perturbation theory with all third-order localization diagrams included. In addition, the summation of certain classes of diagrams up to infinite order in the off-diagonal Fock elements as well as the Epstein-Nesbet partitioning of the full Hamiltonian are discussed. The problem of intruder states, frequently encountered in many-body perturbation theory, is dealt with by employing the theory of intermediate Hamiltonians. As model systems we have chosen cyclic periodic structures up to an oligoethylene ring in double-zeta basis; however, the theory presented here straightforwardly carries over to infinite periodic systems. Received: 30 April 1998 / Accepted: 27 July 1998 /  Published online: 7 October 1998     

Ab initio calculation of the electronic structure of TCNQ and its ions

Ab initio SCF-LCAO-MO calculations have been performed for TCNQ and its positive and negative ions in various electronic states. A basis set consisting of 412 primitive Gaussian type orbitals contracted to 180 was used in the investigation. The electron density distribution in TCNQ and the negative ions, and the redistribution upon ionization has been illustrated by plotting difference density contour maps. The quinone structure of the neutral TCNQ system undergoes a transformation to a benzenoid structure when electrons are added. Electronic transitions, ionization potentials and electron affinities have also been calculated.     

Electron densities from the Brueckner Doubles method

Summary The concept of the Brueckner orbital is examined, following a resurgence of interest in wavefunctions constructed from them. The distinction between Self Consistent Field, Natural and Brueckner orbitals are discussed. Total electron densities are calculated for several examples, and correlation densities are studied. It is found that the Brueckner orbitals are more localised than SCF orbitals. The total electron density constructed from the Brueckner reference determinant with Brueckner orbitals gives qualitatively similar pictures as other correlated methods. Brueckner orbitals are found to show dissociation well.     

Overlapping spheres Xα calculatons of the electron affinities and ionization potentials of ethylene, parabenzoquinone and their perfluoro derivatives

It is shown that the overlapping spheres MS Xα method is capable of producing values for the electron affinities, the shape resonances and the ionization potentials of ethylene, parabenzoquinone and their perfluoro derivatives which are in good agreement with available experimental data. The interpretation of the negative ion properties utilizes both Rydberg orbitals and valence orbitals whereas previous approaches have considered only antibonding π* orbitals.     

An examination of the Brueckner condition for the selection of molecular orbitals in correlated wavefunctions

The Brueckner condition is analyzed as an approximation to the condition of stability of the total energy with respect to variations in the orbitals. The recently introduced method of self-consistent electron pairs is used to find Brueckner orbitals and it is shown that the Brueckner condition can give a slightly higher energy wavefunction than with Hartree—Fock orbitals, while a slightly lower energy result is obtained when singly substituted configurations are important.     

Calculation of the brueckner orbitals and generalized natural orbitals

The diagrammatic-perturbation approach for the construction of the one-particle Hermitian pseudoeigenvalue problem determining the Brueckner orbitals and/or generalized natural orbitals is elaborated.     

Investigation of a localised second-order Brueckner correlation method

Local second-order Brueckner correlation potentials have been derived from their non-local counterparts by starting from the assumption that the orbitals generated by these potentials are the same. The structure of the local correlation potentials and its components have been analysed for the neon atom and a range of small molecules, namely HF, HCl, H(2)O, CO and ethyne. The orbitals from the local Brueckner correlation potentials yield first-order electric molecular properties which are close to those inferred from second-order M?ller-Plesset theory and Brueckner coupled cluster doubles with perturbative triples.     

The extended Koopmans' theorem Fock operator and the generalized overlap amplitude one-electron operator

The wave function of a system may be expanded in terms of eigenfunctions of the N −1 electron Hamiltonian times one-particle functions known as generalized overlap amplitudes (GOAS). The one-electron operator whose eigenfunctions are the GOAS is presented, without using an energy-dependent term as in the one-particle Green function or propagator approach. It is shown that this operator and the extended Koopmans' theorem (EKT) one-electron operator are of similar form, but perform complementary roles. The GOA operator begins with one-electron densities and total energies of N −1 electron states to generate the two-matrix and total energy of an N-electron state. The EKT operator begins with the two-matrix of an N-electron state to generate one-electron densities and ionization potentials (or approximations thereto) for N −1 electron states. However, whereas the EKT orbitals must be linearly independent, no such restriction applies to the GOAS. © 1996 John Wiley & Sons, Inc.     

Natural energy orbitals and the one-particle Green's function

It is shown how the properties of the one-particle Green's function lead naturally to the definition of the so-called natural energy orbitals. These orbitals allow the fully correlated total energy of a system to be written in Hartree–Fock-like fashion and might therefore provide a bridge between sophisticated correlated wave functions and approximate theories of chemical structure and reactivity based on a Hartree–Fock-like energy expression. Moreover these orbitals form the basis for a self-consistent scheme to calculate the one-particle Green's function. The relation between these natural energy orbitals and the extended Koopmans' theorem is considered. Finally it is shown that the exactness of the lowest extended Koopmans' ionization potential implies the linear independence of the corresponding Dyson orbital from all other Dyson orbitals.     

Theoretical study of electron affinities,ionization potentials and photoionization cross-sections of chalcogen heterocyclopentadienes

The first electron affinities, valence ionization potentials and photoionization cross-sections of furan, thiophene, selenophene and tellurophene have been studied by application of one-particle Green's function technique and plane-wave theory, respectively, within the framework of the CNDO approximation. The results are compared with the available experimental values and some sophisticated ab initio predictions.     

Equivalent orbitals for multiconfigurational spin‐tensor electron propagator method (MCSTEP): The vertical ionization potentials of B,NO, CF,and OF

The multiconfigurational spin tensor electron propagator method (MCSTEP) was developed as an implementation of electron propagator/single particle Green's function methods for ionization potentials (IPs) and electron affinities (EAs). MCSTEP was specifically designed for open shell and highly correlated (nondynamically correlated) initial states. For computational efficiency the initial state used in MCSTEP is typically a small complete active space (CAS) multiconfigurational self‐consistent field (MCSCF) state. If in a molecule there are some degenerate orbitals which are not fully or half occupied, usual MCSCF calculations will make these orbitals inequivalent, i.e., the occupied ones will be different from the nonoccupied ones, so that the degeneracy is broken. In this article, we use a state averaged MCSCF method to get equivalent orbitals for the initial state and import the integrals into the subsequent MCSTEP calculations. This gives, in general, more reliable MCSTEP vertical IPs. © 2008 Wiley Periodicals, Inc., 2008     

The self-consistent determination of the ion and neutral molecule wavefunctions in a theory of electron affinities and ionization potentials

In this paper, we discuss the validity of our earlier derivation of a theory of molecular electron affinities and ionization potentials. We show how one can improve upon our original derivation, which was not entirely consistent, by iteratively calculating both the ion and neutral molecule wavefunctions. Most importantly, we demonstrate that the electron affinities and ionization potentials which are obtained by using our original theory are correct through third order, even though the derivation of this theory contains an inconsistency.     

Theoretical determination of electron affinity and ionization potential of DNA and RNA bases

The ionization potentials and electron affinities of thymine, cytosine, adenine, guanine, and uracil were determined at density functional level using different exchange‐correlation functionals and basis sets. Results showed that the computed ionization potentials are very close to the experimental counterparts. The sign of adiabatic electron affinities of adenine, thymine, and uracil is unaffected by the used level of theory while that for guanine and cytosine depends on both the used potential and basis set. Vertical electron affinities are always negative in agreement with the experimental indications. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1243–1250, 2000     

On the use of effective core potentials in the calculation of magnetic properties, such as magnetizabilites and magnetic shieldings

State-of-the art effective core potentials (ECPs) that replace electrons of inner atomic cores involve non-local potentials. If such an effective core potential is added to the Hamiltonian of a system in a magnetic field, the resulting Hamiltonian is not gauge invariant. This means, magnetic properties such as magnetisabilities and magnetic shieldings (or magnetic susceptibilities and nuclear magnetic resonance chemical shifts) calculated with different gauge origins are different even for exact solutions of the Schro?dinger equation. It is possible to restore gauge invariance of the Hamiltonian by adding magnetic field dependent terms arising from the effective core potential. Numerical calculations on atomic and diatomic model systems (potassium mono-cation and potassium dimer) clearly demonstrate that the standard effective core potential Hamiltonian violates gauge invariance, and this affects the calculation of magnetisabilities more strongly than the calculation of magnetic shieldings. The modified magnetic field dependent effective core potential Hamiltonian is gauge invariant, and therefore it is the correct starting point for distributed gauge origin methods. The formalism for gauge including atomic orbitals (GIAO) and individual gauge for localized orbitals methods is worked out. ECP GIAO results for the potassium dimer are presented. The new method performs much better than a previous ECP GIAO implementation that did not account for the non-locality of the potential. For magnetic shieldings, deviations are clearly seen, but they amount to few ppm only. For magnetisabilities, our new ECP GIAO implementation is a major improvement, as demonstrated by the comparison of all-electron and ECP results.     

Molecular structural formulas as one-electron density and hamiltonian operators: the VIF method extended

The valency interaction formula (VIF) method is given a broader and more general interpretation in which these simple molecular structural formulas implicitly include all overlaps between valence atomic orbitals even for interactions not drawn in the VIF picture. This applies for VIF pictures as one-electron Hamiltonian operators as well as VIF pictures as one-electron density operators that constitute a new implementation of the VIF method simpler in its application and more accurate in its results than previous approaches. A procedure for estimating elements of the effective charge density-bond order matrix, Pmunu, from electron configurations in atoms is presented, and it is shown how these lead to loop and line constants in the VIF picture. From these structural formulas, one finds the number of singly, doubly, and unoccupied molecular orbitals, as well as the number of molecular orbitals with energy lower, equal, and higher than -1/2Eh, the negative of the hydrogen atom's ionization energy. The VIF results for water are in qualitative agreement with MP2/6311++G3df3pd, MO energy levels where the simple VIF for water presented in the earlier literature does not agree with computed energy levels. The method presented here gives the simplest accurate VIF pictures for hydrocarbons. It is shown how VIF can be used to predict thermal barriers to chemical reactions. Insertion of singlet carbene into H2 is given as an example. VIF pictures as one-electron density operators describe the ground-state multiplicities of B2, N2, and O2 molecules and as one-electron Hamiltonian operators give the correct electronegativity trend across period two. Previous implementations of VIF do not indicate singly occupied molecular orbitals directly from the pictorial VIF rules for these examples. The direct comparison between structural formulas that represent electron density and those that represent energy is supported by comparison of a simple electronegativity scale, chiD=N/n2, with well-known electronegativity scales of Pauling, Mulliken, and Allen. This scale comes from the method used to calculate Pmumu for sp3 hybridized period-two elements and is comparable to electronegativity because it has the same form as <1/r> for hydrogenic orbitals. It therefore provides a physical basis for the representation of one electron density and Hamiltonian operators by the same VIF picture.     

Construction of an effective hamiltonian for open-shell molecular systems

An effective Hamiltonian for open-shell molecular systems is constructed. The unrestricted Hartree–Fock orbitals are applied as a basis set of one-particle functions. This effective Hamiltonian is determined as a simple product of the original total Hamiltonian and the spin annihilator. The second-quantization formalism and the Feynman–Goldstone diagrammatic technique are used. The resulting effective hamiltonian is composed of zero- to four-particle terms. A possibility of applying the nondegenerate diagrammatic perturbation theory constructed over this effective Hamiltonian is discussed.     

Application of one-particle Green functions technique for calculation of vertical ionization potentials of closed-shell molecules described by CNDO/2 semiempirical Hamiltonian

A simple method of infinite summations of some dominant diagrams in the framework of the one-particle Green functions technique is suggested. This method for the calculation of the lowlying vertical ionization potentials of some simple closed-shell molecules described by CNDO/2 semiempirical Hamiltonian is applied. The obtained results are in quite-satisfactory agreement with the experimental values of the vertical ionization potentials measured by the photo-electron spectroscopy technique.     

Correlation study of Franck-Condon barriers associated with electron self-exchange reactions with ionization potentials and electron affinities and experimental Born-Oppenheimer potentials

An accurate theoretical scheme for obtaining directly the Franck-Condon barrier associated with the electron self-exchange reaction from ionization potentials and electron affinities is presented. Applicability is tested using some diatomic molecular redox couples. The corresponding ionization potentials and electron affinities are obtained from the Born-Oppenheimer potential energy curves which are directly determined from the experimental vibration-rotational spectroscopic data. The Franck-Condon barriers are calculated for the electron self-exchange reactions and are also compared with those from other theoretical methods.     

Relativistic all-electron configuration interaction calculations on the gold atom

We present the results of relativistic and non-relativistic self-consistent field and configuration interaction calculations for the gold atom, using the spin-free no-pair Hamiltonian in a basis set expansion. A new basis set for the gold atom is discussed and its results in relativistic and non-relativistic self-consistent field calculations are compared to those of numerical Dirac-Hartree-Focic and Hartree-Fock calculations, respectively. Excitation energies, electron affinities and ionization potentials were calculated using a multi-reference configuration interaction technique and are in reasonable agreement with experiment in the relativistic case.