Correlated Wave Functions Research Articles

Dynamic dipole polarizabilities of H− and Ps− in weakly coupled plasmas

The effects of weakly coupled plasmas on the dynamic dipole polarizabilities of the H− and Ps− ions are investigated using highly correlated exponential wave functions. The Debye-Hückel shielding approach of plasma modeling is used to represent weakly coupled plasma environments. In free-atomic cases, results obtained from the present study for H− are in agreement with the available calculations and results for Ps− are reported for the first time. Frequency-dependent polarizabilities of H− and Ps− as functions of screening parameter are also presented for the first time.

A possibility of high spin hole states in doped CoO2 layered systems

We introduce and investigate an effective five-band model for t2g and eg electrons to describe doped cobalt oxides with Co3+ and Co4+ ions in two-dimensional CoO2 triangular lattice layers, as in Na1−xCoO2. The effective Hamiltonian includes anisotropic kinetic energy (due to both direct Co–Co and indirect Co–O–Co hoppings), on-site Coulomb interactions parameterized by intraorbital Hubbard repulsion U and full Hund’s exchange tensor, crystal field terms and Jahn–Teller static distortions. We study it using correlated wave functions on 6 × 6 clusters with periodic boundary conditions. The computations indicate a low S = 0 spin to high S = 2 spin abrupt transition in the undoped systems when increasing strength of the crystal field, while intermediate S = 1 spins are not found. Surprisingly, for the investigated realistic Hamiltonian parameters describing low-spin states in CoO2 planes, doping generates high spins at Co4+ ions that are pairwise bound into singlets, seen here as pairs of up and down spins. It is found that such singlet pairs self-organize at higher doping into lines of magnetic ions with coexisting antiferromagnetic and ferromagnetic bonds between them, forming stripe-like structures. The ground states are insulating within the investigated range of doping because computed HOMO–LUMO gaps are never small enough.

Efficient antisymmetrization algorithm for the partially correlated wave functions in the free complement-local Schrödinger equation method

We propose here fast antisymmetrization procedures for the partially correlated wave functions that appear in the free complement-local Schrödinger equation (FC-LSE) method. Pre-analysis of the correlation diagram, referred to as dot analysis, combined with the determinant update technique based on the Laplace expansion, drastically reduces the orders of the antisymmetrization computations. When the complement functions include only up to single-correlated terms, the order of computations is O(N(3)), which is the same as the non-correlated case. Similar acceleration is obtained for general correlated functions as a result of dot analysis. This algorithm has been successfully used in our laboratory in actual FC-LSE calculations for accurately solving the many-electron Schrödinger equations of atoms and molecules. The proposed method is general and applicable to the sampling-type methodology of other partially correlated wave functions like those in the quantum Monte Carlo and modern Hylleraas-type methods.

Mesoscopic behavior of the transmission phase through confined correlated electronic systems

We investigate the effect of electronic correlations on the transmission phase of quantum coherent scatterers, considering quantum dots in the Coulomb blockade regime connected to two single-channel leads. We focus on transmission zeros and the associated \pi-phase lapses that have been observed in interferometric experiments. We numerically explore two types of models for quantum dots: (i) lattice models with up to eight sites, and (ii) resonant level models with up to six levels. We identify different regimes of parameters where the presence of electronic correlations is responsible for the increase or the decrease of the number of transmission zeros vs. electrochemical potential on the dot. However, we show that interaction effects cannot reproduce the universal behavior of alternating resonances and phase lapses, experimentally observed in many-electron Coulomb blockaded dots. Our numerical results strongly suggest that the main experimentally observed features are captured by the theory for chaotic ballistic dots of Molina et al., [Phys. Rev. Lett. 108, 076803 (2012)] incorporating one-particle wave-function correlations but ignoring many-particle electronic correlations.

Density-Functional Theory with Dispersion-Correcting Potentials for Methane: Bridging the Efficiency and Accuracy Gap between High-Level Wave Function and Classical Molecular Mechanics Methods.

Large clusters of noncovalently bonded molecules can only be efficiently modeled by classical mechanics simulations. One prominent challenge associated with this approach is obtaining force-field parameters that accurately describe noncovalent interactions. High-level correlated wave function methods, such as CCSD(T), are capable of correctly predicting noncovalent interactions, and are widely used to produce reference data. However, high-level correlated methods are generally too computationally costly to generate the critical reference data required for good force-field parameter development. In this work we present an approach to generate Lennard-Jones force-field parameters to accurately account for noncovalent interactions. We propose the use of a computational step that is intermediate to CCSD(T) and classical molecular mechanics, that can bridge the accuracy and computational efficiency gap between them, and demonstrate the efficacy of our approach with methane clusters. On the basis of CCSD(T)-level binding energy data for a small set of methane clusters, we develop methane-specific, atom-centered, dispersion-correcting potentials (DCPs) for use with the PBE0 density-functional and 6-31+G(d,p) basis sets. We then use the PBE0-DCP approach to compute a detailed map of the interaction forces associated with the removal of a single methane molecule from a cluster of eight methane molecules and use this map to optimize the Lennard-Jones parameters for methane. The quality of the binding energies obtained by the Lennard-Jones parameters we obtained is assessed on a set of methane clusters containing from 2 to 40 molecules. Our Lennard-Jones parameters, used in combination with the intramolecular parameters of the CHARMM force field, are found to closely reproduce the results of our dispersion-corrected density-functional calculations. The approach outlined can be used to develop Lennard-Jones parameters for any kind of molecular system.

Algebraic connectivity analysis in molecular electronic structure theory II: total exponential formulation of second-quantised correlated methods

The fundamentality of the exponential representation of a second-quantised correlated wave function is emphasised with an accent on the physical sense of cluster amplitudes as cumulants of the correlated ansatz. Three main wave function formalisms, namely, the configuration-interaction theory, the coupled-cluster approach, and the many-body perturbation theory (as well as their extensions, e.g. the equation-of-motion coupled-cluster method, multireference schemes, etc.), are represented in an exponential form, leading to a formulation of the working equations in terms of cluster amplitudes. By expressing the corresponding many-body tensor equations in terms of cluster amplitudes, we could unambiguously check connectivity types and the asymptotic behaviour of all tensors/scalars involved (in the formal limit of an infinite number of correlated particles). In particular, the appearance of disconnected cluster amplitudes corresponds to unphysical correlations. Besides, we demonstrate that the equation-of-motion coupled-cluster approach, as well as certain excited-state configuration-interaction methods, can be recast in a fully connected (exponential) form, thus breaking the common belief that all truncated configuration-interaction methods violate connectivity. Our work is based on the recently developed algebraic framework which can be viewed as a complement to the classical diagrammatic analysis.

Precise estimation of the energy levels of two-electron atoms under spherical confinement

The effect of spherical confinement on the ground state of helium-like ions (Z = 1–5) and the first four (1Se) excited states for Z = 2–5 have been analyzed in detail by using correlated Hylleraas basis sets within the variational framework. The correlated wave functions used here are consistent with the finite boundary conditions due to spherical confinement. The present energy values and the thermodynamic pressure generated for the confined ions as well as the critical values of the confining radii close to the fragmentation limit can be set as a benchmark for future references.

Doubly-Excited States of Two-Electron Systems in Lorentzian Astrophysical Plasmas

The nonthermal effects on the doubly-excited resonance states of two-electron positive ions are investigated in Lorentzian astrophysical plasma environments using highly correlated Hylleraas-type wave functions in the framework of the stabilization method. Resonance parameters (resonance position and width) for Li+, Be2+ and B3+ are reported for the first time as functions of the spectral index and plasma parameter.

Photoionization of helium by attosecond pulses: Extraction of spectra from correlated wave functions

We investigate the photoionization spectrum of helium by attosecond XUV pulses both in the spectral region of doubly excited resonances as well as above the double ionization threshold. In order to probe for convergence, we compare three techniques to extract photoelectron spectra from the wavepacket resulting from the integration of the time-dependent Schroedinger equation in a finite-element discrete variable representation basis. These techniques are: projection on products of hydrogenic bound and continuum states, projection onto multi-channel scattering states computed in a B-spline close-coupling basis, and a technique based on exterior complex scaling (ECS) implemented in the same basis used for the time propagation. These methods allow to monitor the population of continuum states in wavepackets created with ultrashort pulses in different regimes. Applications include photo cross sections and anisotropy parameters in the spectral region of doubly excited resonances, time-resolved photoexcitation of autoionizing resonances in an attosecond pump-probe setting, and the energy and angular distribution of correlated wavepackets for two-photon double ionization.

A Correlated Electron View of Singlet Fission

Singlet fission occurs when a single exciton splits into multiple electron-hole pairs, and could dramatically increase the efficiency of organic solar cells by converting high energy photons into multiple charge carriers. Scientists might exploit singlet fission to its full potential by first understanding the underlying mechanism of this quantum mechanical process. The pursuit of this fundamental mechanism has recently benefited from the development and application of new correlated wave function methods. These methods-called restricted active space spin flip-can capture the most important electron interactions in molecular materials, such as acene crystals, at low computational cost. It is unrealistic to use previous wave function methods due to the excessive computational cost involved in simulating realistic molecular structures at a meaningful level of electron correlation. In this Account, we describe how we use these techniques to compute single exciton and multiple exciton excited states in tetracene and pentacene crystals in order to understand how a single exciton generated from photon absorption undergoes fission to generate two triplets. Our studies indicate that an adiabatic charge transfer intermediate is unlikely to contribute significantly to the fission process because it lies too high in energy. Instead, we propose a new mechanism that involves the direct coupling of an optically allowed single exciton to an optically dark multiexciton. This coupling is facilitated by intermolecular motion of two acene monomers that drives nonadiabatic population transfer between the two states. This transfer occurs in the limit of near degeneracies between adiabatic states where the Born-Oppenheimer approximation of fixed nuclei is no longer valid. Existing theories for singlet fission have not considered this type of coupling between states and, therefore, cannot describe this mechanism. The direct mechanism through intermolecular motion describes many experimentally observed characteristics of these materials, such as the ultrafast time scale of photobleaching and triplet generation during singlet fission in pentacene. We believe this newly discovered mechanism provides fundamental insight to guide the creation of new solar materials that exhibit high efficiencies through multiple charge generation.

Electron scattering from trans 1,3-butadiene molecule: cross-sections, oscillator strength and VUV photoabsorption cross-sections

Electron energy-loss spectra for the butadiene molecule were measured in the scattering angular range of 2.0° to 8.0°, in an energy-loss range from 2 to 50 eV, using 1000 eV incident electrons. The absolute generalized oscillator strength (GOS) and inelastic cross section have been determined for the \hbox{$\tilde{\rm X}^{1}$}˜X1A g → 11B u transition. The absolute elastic differential cross section was also determined spanning an angular range from 2.0° to 40.0°. From a small angle electron energy-loss spectrum, the optical oscillator distribution (photoabsorption spectrum) for the butadiene molecule was obtained in the 2 to 100 eV photon energy range. Accurate ab initio calculations have been performed, within the First Born Approximation, for generalized oscillator strength (GOS) and excitation energies for the \hbox{$\tilde{\rm X}^{1}$}˜X1A g → 11B u and \hbox{$\tilde{\rm X}^{1}$}˜X1A g → 21A g transitions. Our results emphasize the importance of using highly correlated wavefunctions and accurate methodologies in the calculation of the GOS for electron impact-induced electronic transitions in molecules.

First-principles dynamical calculation of a pump-probe scenario for the spin flip on NiO: Dynamical vs static calculation of the susceptibility tensor

Using a fully ab initio approach we calculate in a dynamic way the susceptibility through the time-dependent probe signal of a spin-flip scenario on the antiferromagnetic NiO (001) surface using linear-response theory. To this end we obtain the highly correlated wave function of the system and we propagate it under the influence of both a pump and a probe pulse of the same frequency, a situation usually encountered in experiment. Thus we treat both pulses on equal footing and, for the first time, consider the effects of the electronic nonequilibrium on the susceptibility due to the concurrent presence of the pulses. Our time-resolved calculations reveal the subtle influence of the probe pulse itself on the detection signal, which cannot be completely accounted for solely by the time propagation of the pump pulse and the subsequent static calculation of the susceptibility tensor. We calculate the dynamical Stark effect, a broadening of the peaks, optical interference effects, and satellite peaks.

Quantum Monte Carlo ionization potential and electron affinity for transition metal atoms

Non-relativistic all-electron Quantum Monte Carlo ground state energies of the neutral atoms K to Zn and positive and negative ions are calculated starting from explicitly correlated wave functions. The accuracy obtained for these atoms and ions in the fourth period is similar to that reached for those in the second and third periods. For the atoms and ions for which the 4s–4p near degeneracy effect can be important a restricted multi-configuration expansion has been employed. Ionization potentials and electron affinities have been calculated showing a good agreement with the experimental values.

Doubly excited states of the hydrogen negative ion and helium atom in astrophysical plasmas

The nonthermal effects on the doubly excited resonance states of the hydrogen negative ion and helium atom are investigated in Lorentzian astrophysical plasma environments using highly correlated Hylleraas-type wave functions in the framework of the stabilization method. Resonance parameters (resonance position and width) are reported for the first time as functions of the spectral index and plasma parameter. The screening effects are more pronounced in the stronger screening region.

Benchmarks for 0–0 transitions of aromatic organic molecules: DFT/B3LYP, ADC(2), CC2, SOS-CC2 and SCS-CC2 compared to high-resolution gas-phase data

In the present study a benchmark set of medium-sized and large aromatic organic molecules with 10-78 atoms is presented. For this test set 0-0 transition energies measured in supersonic jets are compared to those calculated with DFT and the B3LYP functional, ADC(2), CC2 and the spin-scaled CC2 variants SOS-CC2 and SCS-CC2. Geometries of the ground and excited states have been optimized with these methods in polarized triple zeta basis sets. Zero-point vibrational corrections have been calculated with the same methods and basis sets. In addition the energies have been corrected by single point calculations with a triple zeta basis augmented with diffuse functions, aug-cc-pVTZ. The deviations of the theoretical results from experimental electronic origins, which have all been measured in the gas phase with high-resolution techniques, were evaluated. The accuracy of SOS-CC2 is comparable to that of unscaled CC2, whereas ADC(2) has slightly larger errors. The lowest errors were found for SCS-CC2. All correlated wave function methods provide significantly better results than DFT with the B3LYP functional. The effects of the energy corrections from the augmented basis set and the method-consistent calculation of the zero-point vibrational corrections are small. With this benchmark set reliable reference data for 0-0 transition energies for larger organic chromophores are available that can be used to benchmark the accuracy of other quantum chemical methods such as new DFT functionals or semi-empirical methods for excitation energies and structures and thereby augments available benchmark sets augments present benchmark sets which include mainly smaller molecules.

Dynamic dipole polarizability of the helium atom with Debye-Hückel potentials

In the present study, we investigate the effect of Debye-H\uckel potentials on the frequency-dependent dipole polarizability of the helium atom using highly correlated wave functions within the framework of the pseudostate summation technique. The dynamic dipole polarizability of He (1${s}^{2}$ ${}^{1}\phantom{\rule{-0.16em}{0ex}}S$) as a function of the scaled number density of the plasma electrons for arbitrary plasma temperature is presented. Screening effects on the resonance frequencies are also presented. In a free-atomic system, our calculated results are in agreement with the available theoretical and experimental predictions.

Which Ab Initio Wave Function Methods Are Adequate for Quantitative Calculations of the Energies of Biradicals? The Performance of Coupled-Cluster and Multi-Reference Methods Along a Single-Bond Dissociation Coordinate.

We examine the accuracy of single-reference and multireference correlated wave function methods for predicting accurate energies and potential energy curves of biradicals. The biradicals considered are intermediate species along the bond dissociation coordinates for breaking the F-F bond in F2, the O-O bond in H2O2, and the C-C bond in CH3CH3. We apply a host of single-reference and multireference approximations in a consistent way to the same cases to provide a better assessment of their relative accuracies than was previously possible. The most accurate method studied is coupled cluster theory with all connected excitations through quadruples, CCSDTQ. Without explicit quadruple excitations, the most accurate potential energy curves are obtained by the single-reference RCCSDt method, followed, in order of decreasing accuracy, by UCCSDT, RCCSDT, UCCSDt, seven multireference methods, including perturbation theory, configuration interaction, and coupled-cluster methods (with MRCI+Q being the best and Mk-MR-CCSD the least accurate), four CCSD(T) methods, and then CCSD.

Biofuel Combustion. Energetics and Kinetics of Hydrogen Abstraction from Carbon-1 inn-Butanol by the Hydroperoxyl Radical Calculated by Coupled Cluster and Density Functional Theories and Multistructural Variational Transition-State Theory with Multidimensional Tunneling

Multistructural canonical variational transition-state theory with small-curvature multidimensional tunneling (MS-CVT/SCT) is employed to calculate thermal rate constants for hydrogen-atom abstraction from carbon-1 of n-butanol by the hydroperoxyl radical over the temperature range 250-2000 K. The M08-SO hybrid meta-GGA density functional was validated against CCSD(T)-F12a explicitly correlated wave function calculations with the jul-cc-pVTZ basis set. It was then used to compute the properties of all stationary points and the energies and Hessians of a few nonstationary points along the reaction path, which were then used to generate a potential energy surface by the multiconfiguration Shepard interpolation (MCSI) method. The internal rotations in the transition state for this reaction (like those in the reactant alcohol) are strongly coupled to each other and generate multiple stable conformations, which make important contributions to the partition functions. It is shown that neglecting to account for the multiple-structure effects and torsional potential anharmonicity effects that arise from the torsional modes would lead to order-of-magnitude errors in the calculated rate constants at temperatures of interest in combustion.

Quadrupole Oscillator Strengths of Helium Interacting with Debye Potentials

The influence of Debye potentials on the quadrupole oscillator strengths of helium atom is investigated using highly correlated wave functions within a framework of a variational method. The quadrupole oscillator strengths for the 1,3S–1,3D, 1,3P–1,3P and 1,3D–1,3D transitions of He for various screening parameters are reported for the first time in the literature. In free atomic case, our calculated results are in good agreement with the available results.

Origin of the Energy Barrier to Chemical Reactions ofO2on Al(111): Evidence for Charge Transfer, Not Spin Selection

Dissociative adsorption of molecular oxygen on the Al(111) surface exhibits mechanistic complexity that remains surprisingly poorly understood in terms of the underlying physics. Experiments clearly indicate substantial energy barriers and a mysteriously large number of adsorbed single oxygen atoms instead of pairs. Conventional first principles quantum mechanics (density functional theory) predicts no energy barrier at all; instead, spin selection rules have been invoked to explain the barrier. In this Letter, we show that correct barriers arise naturally when embedded correlated electron wave functions are used to capture the physics of the interaction of O(2) with the metal surface. The barrier originates from an abrupt charge transfer (from metal to oxygen), which is properly treated within correlated wave function theory but not within conventional density functional theory. Our potential energy surfaces also identify oxygen atom abstraction as the dominant reaction pathway at low incident energies, consistent with measurements, and show that charge transfer occurs in a stepwise fashion.