Theory of electronic structure and nuclear quadrupole interactions in the BF3–NH3 complex and methyl derivatives

Magnetic Hyperfine and Nuclear Quadrupole Interactions (HFI and NQI) are now important tools for characterization of systems of interest in materials research and industry. Boron-Trifluoride is an inorganic compound that is very important in this respect as a catalyst in chemical physics research and industry, forming complexes in the process with compounds like ammonia, water and methyl alcohol. The present paper deals with the BF₃–NH₃ complex and methyl derivatives BF₃NH_x(CH₃)_3?x for which we have studied the electronic structures, binding energies, and ¹⁹F* (I?=?5/2) nuclear quadrupole interactions using the first-principles Hartree–Fock–Roothaan procedure combined with electron correlation effects. Our results for the ¹⁹F* nuclear quadrupole coupling constant (e ² qQ/h) in units of MHz compare well with experiment. Trends in the binding energies and NQI parameters between the complexes are discussed.     

Random-phase approximation correlation methods for molecules and solids

Random-phase approximation (RPA) correlation methods based on Kohn–Sham density-functional theory and Hartree–Fock are derived using the adiabatic-connection fluctuation dissipation theorem. It is shown that the correlation energy within the adiabatic-connection fluctuation-dissipation theorem is exact in a Kohn–Sham framework while for Hartree–Fock reference states this is not the case. This shows that Kohn–Sham reference states are probably better suited to describe electron correlation for use in RPA methods than Hartree–Fock reference states. Both, Kohn–Sham and Hartree–Fock RPA methods are related to each other both by comparing the underlying correlation functionals and numerically through the comparison of total energies and reaction energies for a set of small organic molecules.     

Excitons in organic semiconductors

In this article, excitonic effects in organic semiconductors investigated within the framework of many-body perturbation theory are reviewed. As an example for this technologically relevant class of materials the oligoacene series is studied. The electron–hole interaction is included by solving the Bethe–Salpeter equation for the electron–hole Green's function. This approach allows for the evaluation of the exciton binding energies, which are of major interest concerning the application in organic opto-electronic devices. We start the discussion with a comparison of the Kohn–Sham band structure with recent angular resolved photo-emission data. Starting from this one-electron band structure we focus on the impact of the electron–hole interactions on the optical properties by solving the Bethe–Salpeter equation. We demonstrate the dependence of the exciton binding energy on the molecular size and emphasize the effect of the intermolecular interaction on the exciton binding energies by means of pressure investigations. To cite this article: P. Puschnig, C. Ambrosch-Draxl, C. R. Physique 10 (2009).     

The electronic structure of molecules by a many-body approach III. Ionization potentials and one-electron properties of furan and thiophene

The valence ionization potentials (IP's) of furan and thiophene are studied by an ab initio many-body approach which includes the effects of electron correlation and reorganization beyond the Hartree—Fock approximation. For both molecules it is found that the ordering of the IP's as obtained in the Hartree—Fock approximation is correct. The assignment made for furan agrees with the ab initio calculation of Siegbahn, but it does not agree with the ordering proposed by Derrick et al. from their experimental investigations. For thiophene both the ordering of Derrick et al. and the one of Gelius et al. is shown to be incorrect concerning the position of the 1b₁(π) IP. For both molecules the first two IP's are due to the 1a₂(π) and the 2b₁(π) molecular orbitals. For furan four orbitals of σ-type symmetry are placed between the 2b₁ and the 1b₁ π-orbitals, for thiophene there is only one. Several one-electron properties are calculated in the one-particle approximation and compared with experimental and other theoretical data. The localized molecular orbitals are also discussed.     

Existence of Hartree–Fock excited states for atoms and molecules

For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree–Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree–Fock theory, of the famous Zhislin–Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the N-particle linear Schrödinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree–Fock critical points, but with much higher energy. Our main contribution is the proof that the Hartree–Fock functional satisfies the Palais–Smale property below the first energy threshold. We then use minimax methods in the N-particle space, instead of working in the one-particle space.     

Medium polarization and pairing in asymmetric nuclear matter

The many-body theory of asymmetric nuclear matter is developed beyond the Brueckner–Hartree–Fock approximation to incorporate the medium polarization effects. The extension is performed within the Babu–Brown induced interaction theory. After deriving the particle–hole interaction in the form of Landau–Migdal parameters, the effects of the induced component on the symmetry energy are investigated along with the screening of ¹ S ₀ proton–proton and ³ PF ₂ neutron–neutron pairing, which are relevant for the neutron-star cooling. The crossover from repulsive (screening) to attractive (anti-screening) interaction going from pure neutron matter to symmetric nuclear matter is discussed.     

First principles electronic structure investigation of order of singlet and triplet states of oxyhemoglobin and analysis of possible influence of muon trapping

Interest in the possibility of magnetic character for oxyhemoglobin (OxyHb) has been recently stimulated by the observations of muon spin-lattice relaxation effects studied (Nagamine et al., Proc Jpn Acad Ser B Phys Biol Sci 83:120–126, 2007) with the muon-spin rotation (μSR) technique. In view of this, we have carried out first-principles electronic structure investigations involving Hartree–Fock theory combined with many body perturbation effects for the singlet and triplet states of OxyHb. Our results indicate that using two recent x-ray structural data (Paoli et al., J Mol Biol 256:775, 1996; Park et al., J Mol Biol 360:690, 2006) for OxyHb, for only Hartree–Fock theory without many-body effects included, the singlet state lies above the triplet state by energies of about 0.08 and 0.13 a.u. for the two structures in Paoli et al. (J Mol Biol 256:775, 1996) and Park et al. (J Mol Biol 360:690, 2006). Incorporation of many-body effects by the perturbation method reverses the order, with the triplet state located 0.18 and 0.14 a.u. above the singlet state for the structures in Paoli et al. (J Mol Biol 256:775, 1996) and Park et al. (J Mol Biol 360:690, 2006). Physical reasons for these relative orderings of the singlet and triplet states will be discussed. It is clear that OxyHb by itself would be in a singlet state at room temperature or below, since from our calculation, the triplet state lies about KT above the singlet state with T having the value of 44,098 K and 56,449 K for the two structural data in Paoli et al. (J Mol Biol 256:775, 1996) and Park et al. (J Mol Biol 360:690, 2006). As regards the muon spin-lattice relaxation effects obtained by recent μSR measurements (by Nagamine et al., Proc Jpn Acad Ser B Phys Biol Sci 83:120–126, 2007) at room temperature, the sensitive dependence of the singlet-triplet separation on many-body effects in our investigation suggests that it is possible that the singlet-triplet separation could be reversed or reduced significantly when a muon is trapped near an oxygen atom of the oxygen molecule, allowing the triplet to be occupied at room temperature and lead to significant muon spin-lattice relaxation.     

New massively parallel linear-response coupled-cluster module in ACES III: application to static polarisabilities of closed-shell molecules and oligomers and of open-shell radicals

ABSTRACT

Stemming from our implementation of parallel coupled-cluster (CC) capabilities for electron spin resonance properties [J. Chem. Phys. 139, 174103 (2013)], we present a new massively parallel linear response CC module within ACES III. Unlike alternative parallel CC modules, this general purpose module evaluates any type of first- and second-order CC properties of both closed- and open-shell molecules employing restricted, unrestricted and restricted-open-shell Hartree–Fock (HF) references. We demonstrate the accuracy and usefulness of this module through the calculation of static polarisabilities of large molecules. Closed-shell calculations are performed at the following levels: second-order many-body perturbation theory [MBPT(2)], CC with single- and double-excitations (CCSD), coupled-perturbed HF and density functional theory (DFT), and open-shell calculations at the unrestricted CCSD (UCSSD) one. Applications involve eight closed-shell organic-chemistry molecules (Set I), the first four members of the closed-shell thiophene oligomer series (Set II), and five open-shell radicals (Set III). In Set I, all calculated average polarisabilities agree reasonably well with experimental data. In Set II, all calculated average polarisabilities vs. the number of monomers show comparable values and saturation patterns and demonstrate that experimental polarisabilities may be inaccurate. In Set III, UCCSD perpendicular polarisabilities show a reasonable agreement with previous UCCSD(T) and restricted-open-shell-MBPT(2) values.     

Mean Field Evolution of Fermions with Coulomb Interaction

We study the many body Schrödinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles. For initial data describing approximate Slater determinants, we prove convergence of the many-body evolution towards Hartree–Fock dynamics. Our result holds under a condition on the solution of the Hartree–Fock equation, that we can only show in a very special situation (translation invariant data, whose Hartree–Fock evolution is trivial), but that we expect to hold more generally.     

Approximation of the electron density of Aluminium clusters in tensor-product format

The tensor-structured methods developed recently for the accurate calculation of the Hartree and the non-local exchange operators have been applied successfully to the ab initio numerical solution of the Hartree–Fock equation for some molecules. In the present work, we show that the rank-structured representation can be gainfully applied to the accurate approximation of the electron density of large Aluminium clusters. We consider the Tucker-type decomposition of the electron density of certain Aluminium clusters originating from finite element calculations in the framework of the orbital-free density functional theory. Numerical investigations of the Tucker approximation of the corresponding electron density reveal the exponential decay of the approximation error with respect to the Tucker rank. The resulting low-rank tensor representation reduces dramatically the storage needs and the computational complexity of the consequent tensor operations on the electron density. As main result, the rank of the Tucker approximation for the accurate representation of the electron density is small and only weakly dependent on the system size for the systems studied here. This shows good promise for resolving the electronic structure of materials using tensor-structured techniques.     

Numerical solution of the Sinanoǧlu equation using a multicentre radial-angular grid

ABSTRACT

The pair functions that minimise the correlation energy of second-order many-body perturbation (MP2) theory (the Hylleraas functional) are obtained as solutions to the corresponding Sinano?lu equation by expanding them on a six-dimensional, multicentre, radial-angular grid of two electrons. Cusps in the pair functions at the nuclei are described numerically accurately by the multicentre grid. A cusp in each singlet pair function at the coalescence of the two electrons is taken into account analytically by a correlation factor. With a grid of approximately 10,000 points per atom, the MP2 correlation energies for atoms and polyatomic molecules are obtained usually within 0.1 mE _h of the complete-basis-set results. The correlation factor, auxiliary basis functions, and a judicious choice of integration algorithms are all necessary to stabilise the grid-based MP2 and underlying Hartree–Fock (HF) calculations. The auxiliary basis set, in particular, largely restores the hermiticity and diagonal dominance of the Fock matrix as well as furnishes virtual orbitals used in a resolution-of-the-identity approximation to lower the dimension of some integrals. The results of the grid-based HF and MP2 calculations without a correlation factor are found to suffer from large, nonsystematic errors frequently.     

Self-Consistent Solutions for the Scattering State with Two Free Electrons

Wave functions for the scattering states with two free electrons in the field of an ion core are explicitly calculated by the self-consistent, continuum Hartree–Fock (CHF) theory. Typically, such states are associated with the three-body recombination, collisional ionization and photo-double ionization, but have never been directly studied previously. The calculated continuum orbitals are found to be predominantly of the plane-wave forms, as though the system is translation invariant, in the context of many-body HF theory. The symmetry is mildly broken by the presence of the core ion, at about fifteen-percents level, indicating that the orbitals are largely delocalized and the effect of the core potential is an important but minor perturbation. The properties of channel orthogonality and completeness are preserved by the nearly plane wave forms. To test the validity of this finding and the CHF, the continuum orbitals are used to evaluate the amplitudes for the electron impact ionization, and the amputation procedure, that is crucial in the theory, is also critically re-examined.     

Do Dyson Orbitals resemble canonical Hartree–Fock orbitals?

ABSTRACT

Dyson orbitals are overlaps between states with N and N±1 electrons and provide conceptual links between transition probabilities of electron detachment or attachment, density matrices, total energies and general principles of chemical bonding. Canonical, Hartree–Fock orbitals are compared with Dyson orbitals obtained with electron–propagator calculations that retain all elements of the self–energy matrix, wherein all orbital–relaxation and electron–correlation corrections to Koopmans results reside. For valence ionization energies and electron affinities of representative closed–shell molecules, canonical, Hartree–Fock orbitals usually are excellent approximations to Dyson orbitals, although there are some notable cases where the resemblance is not as strong. Numerical relationships between pole strengths and the Koopmans contributions to Dyson orbitals also are inferred from the data.     

On the thermodynamics of degenerate Bose gas with delta-shaped interaction potential

Within the self-consistent Hartree–Fock approximation, the equilibrium weakly nonideal Bose gas with a delta-shaped interaction potential in the presence of the Bose–Einstein condensate is considered without using quasi-averages. On this basis, using the virial theorem and diagram techniques of the perturbation theory for the equilibrium system in a macroscopic volume, the equation of state providing the isothermal compressibility finiteness, including the Bose–Einstein condensate domain of existence, is obtained.     

Hydrogen bonding in liquid water: An ab initio QM/MM MD simulation study

Pattern and dynamics of hydrogen bonds in liquid water were investigated by a quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulation at Hartree–Fock (HF) level of theory. A large subregion of the whole system comprising two complete coordination shells was treated quantum mechanically in order to include all polarization and charge transfer effects and to obtain accurate data about structure and dynamics of the intermolecular bonds. The results of this investigation are in agreement with recent experimental findings and suggest that in liquid water every molecule forms in average 2.8, but almost as a rule less than four intermolecular hydrogen bonds.     

DFT simulations and Vibrational spectra of 4‐chloro and 4‐bromophenylboronic acid molecules

The experimental and theoretical vibrational spectra of 4‐chloro‐ and 4‐bromophenylboronic acids (abbreviated as 4Clpba and 4Brpba) were studied. The Fourier transform Raman and Fourier transform infrared (FTIR) spectra of 4Clpba and 4Brpba molecules were recorded in the solid phase. The structural and spectroscopic analyses of the molecules were made by using Hartree–Fock and density functional harmonic calculations. In both 4Clpba and 4Brpba only one form was most stable using B3LYP level with the 6–311 + + G(d,p) basis set. Selected experimental bands were assigned and characterized on the basis of the scaled theoretical wavenumbers by their total energy distribution (TED). Finally, geometric parameters as well as infrared (IR) and Raman bands were compared with the experimental data of the molecules. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimized auxiliary basis sets for density fitted post-Hartree–Fock calculations of lanthanide containing molecules

Optimised auxiliary basis sets for lanthanide atoms (Ce to Lu) for four basis sets of the Karlsruhe error-balanced segmented contracted def2 - series (SVP, TZVP, TZVPP and QZVPP) are reported. These auxiliary basis sets enable the use of the resolution-of-the-identity (RI) approximation in post Hartree–Fock methods – as for example, second-order perturbation theory (MP2) and coupled cluster (CC) theory. The auxiliary basis sets are tested on an enlarged set of about a hundred molecules where the test criterion is the size of the RI error in MP2 calculations. Our tests also show that the same auxiliary basis sets can be used together with different effective core potentials. With these auxiliary basis set calculations of MP2 and CC quality can now be performed efficiently on medium-sized molecules containing lanthanides.     

First-principles cluster study of electronic structures, locations and hyperfine interactions of isolated atoms and ions in silicon

The electronic structures of the dilute transition metal (TM) impurities, V^2?+?, Cr^?+?, Mn^2?+?, and Mn⁰ in silicon have been studied using the Hartree–Fock (HF) procedure combined with many-body perturbation theory (MBPT). The systems studied involved the TM impurities at the hexagonal interstitial (H _i ), tetrahedral interstitial (T _i ) and substitutional (S) locations. Investigations of the binding energy and local potential energy surface of the TM impurity-Si systems indicate that the TM impurities are binding at the T _i location. Hyperfine interaction constants (A) of the TM impurities at the T _i and S sites are presented and compared with available experimental results (Woodbury and Ludwig, J Phys Rev 117:102, 1960a, Phys Rev Lett 5:98, b) from Electron Paramagnetic Resonance (EPR) measurements.