Feynman Path Integral Quantum Monte Research Articles

On the influence of vibrational modes and intramolecular isomerization processes on the NMR parameters of bullvalene: A Feynman path integral – ab initio investigation

The absolute isotropic shieldings and chemical shifts at the 13C and 1H nuclei of bullvalene have been theoretically studied under the conditions of thermal equilibrium. For temperatures T ⩽ 400 K the present Monte Carlo simulations predict a bare vibrational nuclear dynamics. T values > 400 K allow the superposition of vibrational modes and an intramolecular isomerization, i.e. the so-called Cope rearrangement. This result can be correlated with the “slow” and “fast” isomerization regime of bullvalene. In the slow regime nuclear magnetic resonance (NMR) measures four different 13C and 1H signals, a splitting that is in line with the molecular C 3v symmetry at the minimum of the potential energy surface (PES). In the fast regime only a single signal for the 13C and 1H nuclei is measured by NMR indicating that all bullvalene carbons and protons are equivalent in the NMR time-scale. To derive the NMR parameters of bullvalene we have combined the Feynman path integral quantum Monte Carlo (PIMC) formalism with a tight-binding (TB) Hamiltonian and the Gauge including atomic orbital (GIAO) approach in an ab initio Hartree–Fock formulation. The TB model has been used to calculate the ground state PES, the free energy barrier of the Cope rearrangement, the statistical weight of the nuclear configurations in thermal equilibrium as well as the radial distribution functions of the nuclei. The vibrational modes in a highly anharmonic potential cause an elongation of all bond lengths in thermal equilibrium. This leads to a topology dependent deshielding of the bullvalene nuclei. The T dependence of the deshielding is characteristic for dominating zero-point fluctuations for all temperatures studied. The GIAO based chemical shifts at the 13C and 1H nuclei are compared with experiment. The PIMC – ab initio approach leads to theoretical results of good quality. The T gradient of the 13C and 1H chemical shifts can be reproduced qualitatively by the present PIMC – ab initio approach.

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.

Theoretical study of the nuclear degrees of freedom in the isotropic and anisotropic hyperfine coupling constants of the C2H5 radical: a Feynman path integral–density functional approach

The isotropic and anisotropic hyperfine coupling (hfs) constants of the C2H5 radical have been theoretically studied under the conditions of thermal equilibrium, i.e. under the explicit consideration of the nuclear degrees of freedom. For this purpose the Feynman path integral quantum Monte Carlo (PIMC) formalism has been combined with an electronic Hamiltonian of the B3LYP–EPRIII type. The density functional operator has been used to derive both the distribution functions for the isotropic and anisotropic hfs constants of the ethyl radical as well as the thermal mean values. The electron paramagnetic resonance (EPR) timescale enables only the measurement of the thermal averages. The underlying distribution functions of these mean values, however, offer insight into the nature and strength of the nuclear degrees of freedom contributing to the observable thermal averages. The EPR parameters of C2H5 have been studied between 25 and 1000 K. This temperature (T ) window is large enough to consider nuclear fluctuations beyond zero-point effects. The deviations between the thermally averaged hfs constants and the values at the minimum of the potential energy surface (PES) are caused by (i) enlargements of the bond lengths in thermal equilibrium under the influence of anharmonicities in the internuclear potential, and (ii) by the intramolecular methylene rotation. The latter degree of freedom leads to a planar CH2 unit in thermal equilibrium. At the minimum of the PES the methylene fragment exhibits a certain pyramidalization. The ensemble corrections as well as the T dependence of the isotropic hfs constants are larger than the ensemble shifts and T dependence of the anisotropic parameters. The non-validity of the crude Born–Oppenheimer approximation for the theoretical evaluation of physically meaningful isotropic hfs constants of the ethyl radical has been explained on the basis of specific nuclear degrees of freedom. Theoretical results of the ensemble averaged Monte Carlo type as well as single-nuclear configuration data are compared with experiment whenever available.

Nuclear degrees of freedom in calculated isotropic hyperfine coupling constants of the ethyl radical: a Feynman path integral – ab initio study

The Feynman path integral quantum Monte Carlo formalism has been combined with an electronic Hamiltonian of the B3LYP-EPRIII type to study the isotropic hyperfine coupling (hfs) constants of the ethyl radical in thermal equilibrium ( T=25 K). The nuclear vibrations and the intramolecular rotation around the C–C bond have a sizeable influence on the hfs parameters. The thermally averaged numbers differ from single-nuclear configuration values calculated at the minimum of the potential energy surface. The analysis of the distribution functions for the isotropic hfs constants of C 2H 5 offers insight into the strong coupling between calculated hfs parameters and the nuclear configuration adopted.

On the influence of nuclear fluctuations on calculated NMR shieldings of benzene and ethylene: a Feynman path integral–ab initio investigation*

AbstractThe absolute magnetic shieldings of benzene and ethylene have been theoretically studied under the conditions of thermal equilibrium, i.e., under explicit consideration of the nuclear degrees of freedom. For this purpose we have combined the Feynman path integral quantum Monte Carlo (PIMC) formalism with the gauge‐including atomic orbital (GIAO) approach in the Hartree–Fock (HF) approximation. The HF operator has been employed to derive the NMR parameters of the two hydrocarbons via an ensemble averaging over large sets of molecular configurations that are populated in thermal equilibrium. The nuclear fluctuations are responsible for a deshielding of the nuclei relative to the shieldings at the vibrationless minimum of the potential energy surface (PES). The influence of the nuclear degrees of freedom is largest for the isotropic part of the 13C shielding tensor. The theoretical results can be explained on the basis of simple geometrical considerations. The bond lengths in thermal equilibrium are larger than the bond lengths at the minimum of the PES. This length enhancement is the prerequisite for a deshielding of the nuclei in thermal equilibrium. The vibrational corrections of the nuclear magnetic resonance (NMR) parameters of benzene and ethylene are quantum driven; classical thermal degrees of freedom of the nuclei are of minor importance. Conceptual problems of theoretical studies of NMR parameters on the basis of a single molecular geometry are emphasized. The influence of the spatial uncertainty of the nuclei becomes decisive in molecules with light atoms. It is pointed out that the combination of the PIMC formalism with electronic Hamiltonians of state‐of‐the‐art quality renders possible accurate determinations of NMR parameters. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem 86: 280–296, 2002

Electrons and nuclei of ethylene isomers; a Feynman path integral – ab initio study

The finite temperature properties of the ethylene isomers C 2H 4, C 2D 4, C 2 13H 4 and C 2 13D 4 have been studied by a Feynman path integral quantum Monte Carlo (PIMC) approach which has been combined with different electronic Hamiltonians. The nuclear potential V ( R ) in the PIMC step of the present formalism has been modeled by an efficient tight-binding one-electron Hamiltonian. Electronic expectation values in thermal equilibrium have been evaluated by ab initio Hartree–Fock and Møller–Plesset calculations. The quantum degrees of freedom of the ethylene nuclei as well as the anharmonicities in V ( R ) cause sizable elongations of the bond lengths relative to the hypothetical vibrationless values at the minimum of the potential energy surface. The PIMC results demonstrate impressively the wave-packet character of the nuclear wave function. This effect is neglected in the crude Born–Oppenheimer approximation which forms the basis of the large majority of electronic structure calculations of molecules. The nuclear degrees of freedom have a strong influence on the expectation values of the electronic Hamiltonian. The isotope and temperature dependence of these quantities has been analyzed. The nuclear fluctuations attenuate the nuclear–nuclear and electron–electron repulsions and lower the electronic kinetic energy. These stabilizing shifts in thermal equilibrium compete with a destabilization of the electron–nuclear attraction. The analysis of the ensemble averaged electronic quantities offers insight into the modifications of covalent bonding under the conditions of thermal equilibrium. Conceptual problems of classical Monte Carlo simulations as well as the shortcomings of electronic structure calculations on the basis of a single nuclear configuration in molecules with light atoms are emphasized. It is demonstrated that the nuclear degrees of freedom up to room temperature of the ethylene isomers studied are caused by quantum tunneling. Physical implications which follow from the present PIMC – ab initio investigation are mentioned concisely.

Isotope Effect in the Mott Transition; a Prediction on the Basis of Molecular All-Quantum Simulations

We have linked an ab initio Hartree-Fock Hamiltonian to the Feynman path integral quantum Monte Carlo formalism in order to derive electronic expectation values under consideration of nuclear degrees of freedom. This approach yields electronic expectation values which depend on the atomic masses. On the basis of combined path integral – ab initio calculations we predict an isotope effect in the correlation driven Mott transition. The nuclear degrees of freedom lead to an enhancement in the electronic correlation strength, an effect which supports the transition conditions. This enhancement is negatively correlated with the atomic masses. Implications of an isotope effect in the Mott transition for the explanation of the superconducting pairing are mentioned concisely.

Isotope Effect in the Mott Transition; a Prediction on the Basis of Molecular All-Quantum Simulations

We have linked an ab initio Hartree-Fock Hamiltonian to the Feynman path integral quantum Monte Carlo formalism in order to derive electronic expectation values under consideration of nuclear degrees of freedom. This approach yields electronic expectation values which depend on the atomic masses. On the basis of combined path integral – ab initio calculations we predict an isotope effect in the correlation driven Mott transition. The nuclear degrees of freedom lead to an enhancement in the electronic correlation strength, an effect which supports the transition conditions. This enhancement is negatively correlated with the atomic masses. Implications of an isotope effect in the Mott transition for the explanation of the superconducting pairing are mentioned concisely.

Electrons and nuclei of C 6H 6 and C 6D 6; a combined Feynman path integral – ab initio approach

We have linked an ab initio approach of the Hartree–Fock (HF) type to the Feynman path integral quantum Monte Carlo (PIMC) formalism in order to study C 6H 6 and C 6D 6 under consideration of the quantum character of the nuclei and electrons. The combination of the statistical Monte Carlo approach with an electronic Hamiltonian offers the possibility to study the influence of the quantum and classical (=thermal) nuclear degrees of freedom on electronic expectation values. The PIMC technique has been used to derive the finite-temperature properties of the nuclei of both π rings. We discuss the temperature ( T) dependence of the energy of the C 6H 6 and C 6D 6 nuclei, their spatial delocalization properties as well as the radial and angular distribution functions. The nuclear configurations generated by the PIMC formalism have been used as input for ab initio HF calculations. Electronic expectation values have been derived as ensemble averages over 6000 different nuclear configurations which are populated in thermal equilibrium. As a result of the large quantum effects of the C 6H 6 and C 6D 6 nuclei, we derive ensemble averaged electronic expectation values which differ sizeable from the corresponding single-configuration quantities at the energy minimum. This difference is mainly caused by nuclear quantum effects; thermal degrees of freedom are of minor importance only. The electronic origin of the potential energy part of the total vibrational energy is emphasized. It is largely determined by the raise in the electron–core attraction under the influence of the spatial uncertainty of the nuclei. The all-quantum approach yields a temperature and isotope dependence of bare electronic quantities already in the framework of the Born–Oppenheimer approximation (BOA). The principal findings of the all-quantum study have been used to reconsider certain solid state problems. We mention theoretical difficulties to reproduce Compton profiles and consider metal–insulator transitions of the Mott type as well as superconductivity. On the basis of the present all-quantum results we have to emphasize, that there is no unambiguous justification to adopt an observed isotope shift in the superconducting transition temperature T c as an indicator of an electron–phonon-coupled superconducting pairing mechanism.

Specific Heat of the Half-Filled One-Dimensional Hubbard Model: Feynman Path-Integral Simulations

The Feynman path-integral quantum Monte Carlo (PI QMC) approach has been employed to study the specific heat C of the one-dimensional (1D) half-filled Hubbard chain as a function of temperature. For not too strong many-body interactions C exhibits a single maximum only. With increasing correlation strength the C curve shows an intermediate minimum separating a sharp low-temperature maximum and a broad high-temperature profile. The first peak is caused by spin excitations and the high-temperature values of C are determined by charge degrees of freedom. The contribution of both quantities to the net specific heat curve has been quantified in the present theoretical setup. The specific heat data are interpreted with the aid of calculated charge fluctuations, probabilities Pi(n) to find n = 2, 1, 0 electrons at the respective lattice sites, a spin density wave (SDW) order parameter and the electronic chemical potential μ. Die Wärmekapazität C der halbgefüllten eindimensionalen (1D) Hubbard-Kette wurde mit Hilfe von Feynman-Pfadintegral-Quanten-Monte-Carlo (PI-QMC)Simulationen als Funktion der Temperatur untersucht. Für nicht zu starke Vielteilchen-Wechselwirkungen zeigt C nur ein Maximum. Mit zunehmender Korrelationsstärke bildet sich ein intermediäres Minimum in der C-Kurve aus, die ein Tieftemperatur-Maximum und eine Hochtemperatur-Flanke trennt. Der erste Peak wird durch Spin-Anregungen verursacht, während die Hochtemperatur-Flanke von C durch Ladungs-Freiheitsgrade hervorgerufen wird. Die Beiträge beider Größen zu den Netto-Wärmekapazitätskurven werden in der vorliegenden Arbeit diskutiert. Die Wärmekapazitäts-Daten werden auf der Basis von Besetzungswahrscheinlichkeiten Pi(n) interpretiert, die die Wahrscheinlichkeit angeben, an Gitterplatz i n = 2, 1 oder 0 Elektronen zu finden. Weitere Hilfsgrößen sind ein Ordnungsparameter für Spindichtewellen (SDW) sowie das elektronische chemische Potential μ.

Dynamics of the Carbon Nuclei in C60 Studied by Feynman Path-Integral Quantum Monte Carlo Simulations

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTDynamics of the Carbon Nuclei in C60 Studied by Feynman Path-Integral Quantum Monte Carlo SimulationsMichael C. Boehm and Rafael RamirezCite this: J. Phys. Chem. 1995, 99, 33, 12401–12408Publication Date (Print):August 1, 1995Publication History Published online1 May 2002Published inissue 1 August 1995https://doi.org/10.1021/j100033a007RIGHTS & PERMISSIONSArticle Views82Altmetric-Citations17LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (980 KB) Get e-Alerts

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

The applicability of Green's 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...

Analysis of static and dynamic electron and spin properties within the interaction space of the one-dimensional Hubbard chain; a path-integral quantum Monte Carlo approach

Feynman path-integral quantum Monte Carlo (QMC) simulations have been performed to investigate electronic structure properties of the one-dimensional (1D) Hubbard chain. On the basis of the calculated on-site densities 〈 n i 〉 the following electronic configurations can be discriminated: (i) symmetry nonbroken 〈 n i 〉 distributions, (ii) on-site charge density waves (CDWs), (iii) clusters, (iv) statistical 〈 n i 〉 distributions resulting from chaotic QMC trajectories. The stability region for the different configurations is discussed as a function of the average electron density 〈 n〉 and the parameters of the extended Hubbard Hamiltonian, the two-electron elements U, V and the kinetic hopping t. It is suggested that the formation of cluster structures is a position-space concomitant of superconducting configurations in the 1D chain. The role of attractive on-site elements U and attractive intersite couplings V are analyzed in detail. The conditions stabilizing on-site CDWs are compared with the conditions favouring cluster formation. The static and dynamic electronic properties are discussed in terms of the on-site densities 〈 n i 〉 of the monoatomic 1D chain, electronic charge and spin fluctuations 〈Δ n 2)〉, 〈(Δ s 2)〉 and the probability of double occupancy P(2). Prerequisites leading to simultaneous and nonsimultaneous occurrence of charge and spin degrees of freedom are formulated. The possible violation of particle—hole (ph) symmetry in the presence of attractive on-site elements U is discussed. Consequences emerging from ph violation in charge transfer salts are also considered. It is suggested that low-temperature superconductivity in these materials is supported by attractive intersite interactions.

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 ...

On-site charge-density wave formation in one-dimensional chains investigated by Feynman path-integral quantum Monte Carlo calculations

The formation of on-site charge-density waves (CDWs) in the one-dimensional (1D) Hubbard chain is studied by path-integral quantum Monte Carlo (QMC) simulations as a function of the band filling, the ratio between on-site and nearest-neighbor intersite interaction as well as the net Coulomb interaction and kinetic hopping. The dynamics of the electrons of the 1D system are quantified by the charge fluctuations 〈(Δ n 2 i )〉 and the probability of double occupancy P(2) averaged over all lattice sites i. Electronic conditions favouring CDWs are summarized. It is shown that one quarter, one half and three quarter filled bands are optimum conditions for on-site CDWs.

Electronic and spin dynamics in one-dimensional chains studied by path-integral quantum Monte Carlo simulations

Feynman path-integral quantum Monte Carlo (QMC) simulations have been employed to evaluate the charge and spin fluctuations in quasi one-dimensional chains as well as the probabilities to find 0, 1, 2 electrons at the associated ith lattice-site. The QMC data have been derived as a function of the on-site density 〈 n i 〉 and the ratio between the two-electron repulsion and kinetic hopping. An extended Hubbard—Hamiltonian has been used as underlying model-operator. Increasing electronic correlations in the neighborhood of the half-filled band sector cause a decoupling of charge and spin degrees of freedom.