Joachim Schulte

Nuclear quantum effects in calculated NMR shieldings of ethylene; a Feynman path integral – ab initio study

Abstract The Feynman path integral Monte-Carlo formalism has been combined with the gauge-including atomic orbital (GIAO) approach to study the absolute magnetic shieldings of C 2 H 4 under consideration of the thermal and quantum degrees of freedom of the nuclei. An ab initio Hamiltonian has been employed for the statistical averaging of NMR parameters. The spatial fluctuations of the atoms around their equilibrium positions lead to a deshielding of both types of nuclei relative to their shieldings at the minimum of the potential energy surface. This behavior is caused by quantum mechanical effects. It is supported by bondlength elongations in thermal equilibrium.

Charge distribution in K3C60 revisited: Incomplete alkali-to-C60 electron transfer

Abstract The charge distribution in K 3 C 60 has been calculated in the theoretical framework of a crystal orbital formalism based on an INDO (intermediate neglect of differential overlap) Hamiltonian. We predict a non-integral potassium-to-C 60 charge transfer (CT) with a clear discrimination between tetrahedral (t) and octahedral (o) alkali atoms. The CT from the o sites exceeds the CT from the t positions. The influence of the incomplete alkali ionization on the binding energy of core electrons is discussed. It is demonstrated that the present theoretical results provide a straightforward explanation of photoemission experiments on K 3 C 60 .

NUCLEAR QUANTUM EFFECTS IN THE ELECTRONIC STRUCTURE OF C2H4 : A COMBINED FEYNMAN PATH INTEGRAL-AB INITIO APPROACH

Abstract A tight-binding equipped Feynman path integral Monte Carlo formalism has been linked to a Hartree–Fock Hamiltonian to derive the electronic properties of C 2 H 4 considering the quantum character of the nuclei. Configurationally averaged electronic quantities are compared with single-configuration results. The potential energy of the vibrational problem is caused by an energetic up-shift of the electron-nuclear interaction of the electronic Hamiltonian under the influence of nuclear quantum fluctuations. Relative to the values optimized by bare electronic Hamiltonians, calculated bond lengths are elongated by nuclear quantum effects. This elongation becomes more pronounced with decreasing atomic masses. Nuclear quantum properties are discussed via the radial distribution function, projected probability distributions and spatial fluctuations.

Electronic structure of C60: from the molecular to the solid state

The electronic structure of fullerides is discussed in the theoretical framework of an INDO (intermediate neglect of differential overlap) Hamiltonian defined for molecules and, in the basis of Bloch orbitals, for crystalline solids. In the C60 molecule the strength of the symmetry allowed π/σ and π*/σ* interaction is quantified by using localized molecular orbitals (MOs) as well as a so-called precanonical MO basis confined to decoupled π,π* and σ,σ* MO spaces. Consequences for the solid state electronic structure of C60 are given. The theoretical determination of the electronic transition energies in the C60 molecule in a CI (configuration interaction) calculation shows the importance of the two-electron interaction in this system. This behaviour is confirmed by Greens function calculations that are employed to derive the ionization potentials (IPs) and the electron affinity of the C60 molecule. Pair-relaxation effects in the cationic hole-states lead to significant many-body corrections to calculated ...

ALL-QUANTUM DESCRIPTION OF MOLECULES : ELECTRONS AND NUCLEI OF C6H6

Abstract Feynman path integral (FPI) quantum Monte Carlo simulations have been combined with electronic ab initio calculations of Hartree-Fock (HF) type to achieve an all-quantum description of the benzene molecule. The linking of these two quantum approaches allows the consideration of the quantum character of the atomic nuclei and electrons. The FPI formalism has been employed to generate 6000 different nuclear configurations of the benzene molecule which are populated in thermal equilibrium (canonical ensemble statistics). In a second step the ab initio HF Hamiltonian has been used to calculate (electronic) expectation values as ensemble averages over these configurations. The influence of the nuclear dynamics on the kinetic and potential energy of the electronic Hamiltonian is discussed. The spatial nuclear degrees of freedom of benzene are largely determined by quantum fluctuations which exceed the thermal fluctuations even at room temperature. The importance of the quantum delocalization of the nuclei is emphasized on the basis of calculated radial and angular distribution functions.

Material properties of one-dimensional systems studied by path-integral quantum Monte Carlo simulations and an analytical many-body model

Feynman path-integral quantum Monte Carlo (QMC) simulations and an analytic many-body approach are used to study the ground state properties of one-dimensional (1D) chains in the theoretical framework of model Hamiltonians of the Hubbard type. The QMC algorithm is employed to derive position-space quantities, while band structure properties are evaluated by combining QMC data with expressions derived in momentum (k) space. Bridging link between both representations is the quasi-chemical approximation (QCA). Electronic charge fluctuations and the fluctuations of the magnetic local moments are studied as a function of the on-site density and correlation strength, which is given by the ratio between two-electron interaction and kinetic hopping. Caused by the non-analytic behaviour of the chemical potential μ = ∂E/∂ (with E denoting the electronic energy), strict 1D systems with an on-site density of 1·0 do not exhibit the properties of a conductor for any non-zero ...

Finite-temperature properties of the muonium substituted ethyl radical CH2MuCH2: nuclear degrees of freedom and hyperfine splitting constants

The finite-temperature (T) properties of the muonium substituted ethyl radical CH2MuCH2 have been theoretically studied by Feynman path integral quantum Monte Carlo (PIMC) simulations. To derive the ensemble averaged expectation values we have combined the PIMC formalism with an efficient tight-binding (TB) Hamiltonian and a density functional operator of the B3LYP type in the EPRIII basis. The TB operator has been used to calculate the potential energy surface (PES) of the ethyl radical in the doublet ground state, the harmonic and anharmonic vibrational wave numbers as well as several probability density functions of the nuclei. The harmonic linear response approximation, which makes use of the Feynman centroid density, has been adopted to evaluate the anharmonic wave numbers. The large anharmonicities in the nuclear potential lead to bond lengths in thermal equilibrium which exceed the vibrationless parameters at the PES minimum. This enhancement is particularly strong for the C–Mu bond. It is responsible for the suppression of the intramolecular rotation for temperatures below room temperature. In C2 H5 the rotation is allowed down to 10 K. The dissimilar rotational dynamics for H2MuCH2 and C2 H5 has been studied with the help of TB-based probability density functions. The nuclear configurations of CH2MuCH2 and C2 H5, which are populated in thermal equilibrium, have been used to evaluate the isotropic and anisotropic hyperfine splitting (hfs) constants under explicit consideration of the nuclear vibrations and the internal rotation. The hfs constants have been determined with the help of the B3LYP-EPRIII Hamiltonian. The hindered low-temperature rotation in the Mu isomer is responsible for roto-vibrational corrections to the isotropic hfs constants which are smaller than the corrections in C2 H5. The shortcomings of single-configuration approaches for the evaluation of isotropic hfs constants have been demonstrated for both radicals. The ensemble corrections to the isotropic hfs parameters are correlated with fluctuations in the atomic spin densities. Differences in the absolute values of the isotropic hfs parameters in CH2MuCH2 and C2 H5 can be traced back to differences in the nuclear degrees of freedom. The ensemble shift for each isotropic hfs parameter can be explained by characteristic nuclear motions. For this discussion we make use of the distribution functions of the isotropic hfs constants. Roto-vibrational corrections to the anisotropic hfs constants are rather small. PIMC simulations have been performed between 25 and 1000 K, i.e. in a T interval that is large enough to consider nuclear effects beyond zero-point motions. The TB and B3LYP-EPRIII based physical quantities of CH2MuCH2 and C2 H5 have been compared with experimental findings whenever possible.

Nuclear quantum effects in calculated NMR shieldings of benzene; a Feynman path integral study

The Feynman path integral Monte Carlo approach has been coupled to the gauge including atomic orbital formalism in order to analyse the absolute magnetic shieldings of the benzene nuclei under the conditions of thermal equilibrium. The Hamiltonian employed in the derivation of ensemble averaged NMR quantities is of the Hartree-Fock type. The basis set used is of 6–31G quality. The spatial delocalization of the atoms leads to a deshielding of both types of benzene nuclei relative to the shieldings experienced at the minimum of the potential energy surface. This deshielding has to be traced back to bond length elongations in thermal equilibrium. The influence of the nuclear fluctuations on the NMR parameters of benzene is quantum driven up to temperatures of 400 K; classical fluctuations are of minor importance in this low-temperature window.

Feynman path integral–ab initio investigation of the excited state properties of C2H4

Abstract A tight binding based Feynman path integral Monte-Carlo approach has been combined with an ab initio configuration interaction scheme to study the excited singlet states of C 2 H 4 under consideration of the nuclear degrees of freedom. Transition energies and oscillator strengths, which have been averaged over manifolds of nuclear configurations, are compared with single-point values calculated at the minimum of the potential energy. The quantum fluctuations of the nuclei cause a reduction of the transition energies and a complete redistribution in the transition intensities. Transitions, which are dipole allowed in the rigid D 2h geometry of ethylene, lose intensity under the influence of the nuclear fluctuations; vice versa for transitions that are dipole forbidden under D 2h symmetry.

Electronic structure of endohedral Y@C82; an ab initio Hartree-Fock investigation

Abstract Parts of the potential energy surface of endohedral Y@C 82 have been studied in a three-dimensional configuration space confined to the spatial degrees of freedom of Y. The optimized position of the endohedral atom is strongly off-center and corresponds to a pyracylene topology with Y located above a 6-6 bond connecting two pentagons. The calculated minimum is explained by the pocket structure of the C 82 cage and the high acceptor capability of fullerence pentagons. We have employed a Hartree-Fock ab initio approach defined by a split-valence 3-21G double zeta basis to search for the optimized position of Y embedded in a C 82 shell of C 2 symmetry. The present computational results are compared with experimental data and findings of other quantum chemical calculations.