Johannes Schütt

Quantum delocalization of nuclei and electrons: cyclobutadiene

Abstract A Feynman path integral method for evaluating the quantum delocalization of atomic nuclei is combined with a scheme for calculating electronic delocalization parameters in the correlated electronic ground state. As model system we have selected the cyclobutadiene molecule whose π-electronic structure is discussed in the Pariser-Parr-Pople and Hubbard approaches. The dynamics of the electrons are described by the charge fluctuations as well as by the probabilities P ( n ) of finding n = 0, 1, 2 π-electrons at the respective atomic site. For both Hamiltonians we have compared the π-electron delocalization properties in the fermionic state | Ψ fe 〉 with those realized in the so-called hard core bosonic state | Ψ hcb 〉. The negative sign in | Ψ fe 〉 leads to a suppression of the charge fluctuations in comparison to their | Ψ hcb 〉 va dynamics of the electrons are attenuated by the quantum delocalization of the atomic nuclei. Details of this overall effect depend both on the nature of the π-Hamiltonian and on the nature of the electronic wavefunction.

Resolution of the sign problem in quantum Monte Carlo simulations of annulenes

The applicability of Greens function (GF) and Feynman path-integral quantum Monte Carlo (QMC) methods for the simulation of cyclic networks with (4n + 2) and 4n (n = 1, 2, 3, …) electrons is analysed. Both QMC techniques are employed in simulations on the basis of the simple Huckel Hamiltonian which is exclusively defined by nearest-neighbour hopping elements. In addition we have used the Pariser-Parr-Pople (PPP) Hamiltonian to perform GF QMC simulations. The electronic energies E derived by the QMC methods are compared either with Huckel molecular orbital (HMO) results or exact configuration interaction data where (π) electronic correlations are fully taken into account. A sign problem occurs in QMC simulations of 4n annulenes. This leads to an error in the total energy in the standard formulations of the employed QMC techniques, which is enhanced with decreasing ring size. A simple modification in the QMC formalisms is suggested to avoid the numerical uncertainties caused by the sign problem in 4n annu...

Influence of the Pauli antisymmetry and exclusion principle on the electronic structure of π systems — a combined Green function quantum Monte Carlo and configuration interaction study☆

Abstract It is demonstrated that the Pauli antisymmetry principle (PAP) is a hidden variable in π electron calculations of polyenes and annulenes with 4 n + 2 π electrons ( n = 0, 1, 2,...). Here the π electrons behave as a hard core bosonic ensemble which represents a superposition of fermionic on-site and bosonic intersite properties. In 4 n rings ( n = 1, 2,...) the PAP leads to a destabilization of the π electronic system. With an increasing π electron count the Pauli exclusion principle (PEP) raises the normalized π energy of annulenes. The influence of the PEP and PAP on the π electron localization properties is analyzed in terms of charge fluctuations.

Green's function quantum Monte Carlo method in the presence of topological sign problems: π electronic systems

A Greens function quantum Monte Carlo (GF QMC) method is described which renders possible the determination of the exact ground state energy of any π system in the computational framework of effective π Hamiltonians. An instruction to evaluate the growth estimator in the simultaneous presence of positive and negative phases is suggested. Numerical results for five annulene molecules with 4–12 atomic centres as well as 10 further π molecules with different topology (i.e., monocycles with methylene groups, bi- and polycycles) are given. Negative phases occur in 13 of the 15 π networks considered. The statistical QMC results are compared with data derived by conventional (many-body) diagonalization techniques. The interaction-free Huckel Hamiltonian has been adopted as most simple setup to test the applicability of the Monte Carlo approach. Many-body results have been derived for the Hubbard and Pariser-Parr-Pople variants of the π-electron Hamiltonian. It is demonstrated that GF QMC results can be derived ...

Peculiarities in the quantum statistics of π electron systems

Abstract The peculiarities in the quantum statistics of π electron systems are analyzed by comparing π energies derived for the conventional fermionic (fe) ensemble with so-called hard core bosonic (hcb) energies. hcb ensembles combine fermionic on-site and bosonic intersite properties. They obey the Pauli exclusion principle (PEP) but not the Pauli antisymmetry principle (PAP). In the present study we extend our previous theoretical findings evaluated for one-dimensional (1D) model structures to 2D arrangements realized in hydrocarbon π molecules. Topological electronic ordering principles which have been derived for 1D order can be transferred to 2D networks. It is demonstrated that π systems are destabilized with increasing deviations from the hcb boundary. In the annulene series this destabilization occurs in the 4 n anti-Huckel rings ( n = 1, 2, 3,…). The competition between quantum constraints (PEP, PAP) and the two-electron interaction of π Hamiltonians on the energy of π systems is discussed. Numerical results are given for the Pariser-Parr-Pople, Hubbard and Huckel molecular orbital π Hamiltonians.

Many-particle effects in the bond length alternation of alternant hydrocarbons

The local approach (LA) method has been employed to investigate the correlated ground state wavefunction in alternant monocyclic and linear hydrocarbon π systems as a function of the bond length alternation δ. The LA has been supplemented by a simple model-Hamiltonian developed in the ZDO (zero differential overlap) approximation. The integrals have been calculated ab initio in a Slater-type basis. To quantify many-particle effects in the studied systems we have determined the interatomic π correlation energy E corr and a π electron localization parameter Δi as a function of δ. Δi measures the reduction of the charge fluctuations due to electronic correlations and is thus a convenient measure for the atomic electron density localization. It is demonstrated that monocyclic 4n + 2 (n = 1,2,3, …) Huckel rings allow for a coincidence of increasing |E corr| numbers and increasing atomic electron density delocalization with enlarged δ values. The δ variation of Δi reflects in a transparent form that hydrocarbon...

On the localization of π-electrons in linear and cyclic hydrocarbons

The localization properties of π-electrons in alternant and nonalternant hydrocarbons are investigated by calculating the mean-square deviation corr of the electronic charge at the ith π-centre in the correlated ground state |Ψcorr> The interatomic π-correlations are determined by the method of the local approach (LA) in the framework of a zero differential overlap (ZDO) model-Hamiltonian supplemented by the tight-binding approximation. The necessary integrals are calculated parameter-free, i.e. ab initio, in a Slater-type basis. Comparison of the corr numbers with the charge fluctuations predicted in the independent-particle picture |ΨSCF> allows for the definition of correlation-strength parameters Δ i , Σ i which measure the many-particle character of π-bonding. It is demonstrated that electronic correlations are sizeable in the π-network of hydrocarbons. This is also valid for conjugated polyenes and cyclic (4n + 2) systems. The π-electron localization exceeds throughout th...

Convergence behaviour of Green's function quantum Monte Carlo simulations of pi electron systems

Greens function quantum Monte Carlo (GF QMC) simulations of fermionic ensembles require the definition of a so-called spectral parameter W to yield trustworthy estimates of the fully correlated ground state energy E. In the present work we discuss the influence of the shift parameter, W, on the convergence behaviour of GF QMC simulations. As model systems we have considered some π molecules which are studied in the framework of the Pariser–Parr–Pople (PPP) Hamiltonian. The influence of the W parameter on the convergence of the GF QMC simulations in many-electron systems with an odd number of electronic permutations within one spin direction exceeds the influence observed in systems without such odd permutations. They do not occur in polyenes and Huckel annulenes with an electron count of (4n + 2) (n = 0, 1, 2…). The GF QMC technique adopted as a computational tool has been developed to study π molecules with fermionic sign problems owing to odd electronic interchanges within one spin direction.

On the Role of the Pauli Antisymmetry Principle in Pericyclic Reactions

Abstract In the present work we discuss the role of the Pauli antisymmetry principle (PAP) in synchronous pericyclic reactions. These reactions are allowed in the electronic ground state whenever the PAP does not act as a quantum constraint in the transition state. The possible suppression of the influence of the PAP is a peculiarity of π electron systems. The PAP is a hidden (= deactivated) variable in the π electron subspace of polyenes and (4n + 2) annulenes (n = 0, 1, 2,...). In 4n annulenes (n = 1, 2, 3,...) it leads to minority signs in the kinetic hopping matrix of the π electronic wave function and thus to an energetic destabilization. The quantum statistical difference between the above families of π systems renders possible a microscopical definition of the quantities “aromaticity” and “antiaromaticity”. The sign behaviour of the kinetic hopping elements is used in the discussion of pericyclic reactions. The present quantum statistical description of these reactions is related to the Dewar-Zimmermann and Woodward-Hoffmann rules.

Electronic Structure of the C60 Fragment in Alkali- and Alkaline-earth-doped Fullerides

Abstract The electronic structure of the C50 fragment in alkali-and alkaline-earth-doped fullerides is studied theoretically. With increasing metal-to-C 60 charge transfer (CT) the n electronic properties of the soccerball are changed. In the undoped solid and for not too high a concentration of doping atoms the hexagon-hexagon (6-6) bonds show sizeable double bond character while the hexagon-pentagon (6-5) bonds are essentially of single bond type. In systems with a high concentration of doping atoms this relative ordering is changed. Now the 6-5 bonds have partial double bond character and the 6-6 bonds are essentially single bonds. The high ability of the C 60 unit to accomodate excess electrons prevents any sizeable weakening of the overall n bonding in systems with up to 12 excess electrons on the soccerball. A crystal orbital (CO) formalism on the basis of an INDO (intermediate neglect of differential overlap) Hamiltonian has been employed to derive solid state results for potassium-and barium-doped C 60 fullerides. For both types of doping atoms an incomplete metal-to-C 60 CT is predicted. In the potassium-doped fullerides the magnitude of the CT depends on the interstitial site of the dopant. The solid state data have been supplemented by INDO and ab initio calculations on molecular C 60 , and C^, 2 , -. The calculated bondlength alternation in the neutral molecule is changed in C 6 ö~ where the length of the 6-6 bonds exceeds the length of the 6-5 bonds. The geometries of the three molecular species have been optimized with a 3-21 G* basis. The theoretically derived modification of the C 60 (7r) electronic structure as a function of the electron count is explained microscopically in the framework of two quantum statistics accessible for n electronic ensembles. In the 7r ensemble of the C W) fragment so-called hard core bosonic properties are maximized where the Pauli antisymmetry principle has the character of a hidden variable only. Here the electronic degrees of freedom are attenuated only by the Pauli exclusion principle. This behaviour leads to the changes in the ir electronic structure mentioned above.