Correlated Wave Functions Research Articles

Feshbach-like study of He resonant states in Debye plasmas using explicitly correlated wave functions

We present a study on the 1,3Se, 1,3P° and 1,3 De He resonant states below the He+ (N = 2) threshold under the influence of a plasma environment, when the Debye screening length is varied. The interaction between all charged particles is modeled with Yukawa-like screened Coulomb potentials. We make use of the Feshbach projector method to characterize resonant states, implemented by using explicitly correlated CI-wave functions.

Symmetry-adapted perturbation theory study for some magnesium complexes

A systematic theoretical study on Mg–ligand interactions has been carried out employing both ab initio correlated wave function and density functional methods. The interactions of the Mg(CH3N2)2moiety with BF, CO, N2, NH3, and H2O ligands have been investigated by performing calculations at the B3LYP, MP2, MP4, and CCSD(T)/6–311++G(3df,3pd) levels of theory. Results indicate that the interaction energies of the Mg(CH3N2)2–L complexes increase in the order NH3 > H2O > BF > CO > N2. Symmetry-adapted perturbation theory (SAPT) analysis has been carried out to understand the nature of the forces involved in the bonding. The SAPT results indicate that the stabilities of the Mg–L interactions are attributed mainly to electrostatic effects, while induction and dispersion forces also play a significant role. The evaluated SAPT interaction energies for the Mg(CH3N2)2–L complexes are generally in good agreement with those obtained using the supermolecule CCSD(T) methods, suggesting that SAPT is a proper method to study the intermolecular interactions in these complexes. The results also suggest an explanation for the unique role of Mg2+as a carrier of water molecules that mediate enzymatic hydrolysis reactions.

Enhanced asymmetry in few-cycle attosecond pulse ionization of He in the vicinity of autoionizing resonances

By solving the two-active-electron, time-dependent Schrödinger equation in its full dimensionality, we investigate the carrier-envelope phase (CEP) dependence of single ionization of He to the He+(1s) state triggered by an intense few-cycle attosecond pulse with carrier frequency ω corresponding to the energy ℏω = 36 eV. Effects of electron correlations are probed by comparing projections of the final state of the two-electron wave packet onto field-free highly correlated Jacobi matrix wave functions with projections onto uncorrelated Coulomb wave functions. Significant differences are found in the vicinity of autoionizing resonances. Owing to the broad bandwidths of our 115 and 230 as pulses and their high intensities (1–2 PW cm−2), asymmetries are found in the differential probability for ionization of electrons parallel and antiparallel to the linear polarization axis of the laser pulse. These asymmetries stem from interference of the one- and two-photon ionization amplitudes for producing electrons with the same momentum along the linear polarization axis. Whereas these asymmetries generally decrease with increasing ionized electron kinetic energy, we find a large enhancement of the asymmetry in the vicinity of two-electron doubly excited (autoionizing) states on an energy scale comparable to the widths of the autoionizing states. The CEP dependence of the energy-integrated asymmetry agrees very well with the predictions of time-dependent perturbation theory (Pronin et al 2009 Phys. Rev. A 80 063403).

Dynamical correlation effects in the transition probability: A study for the atoms Li to Ar

Explicitly correlated wave functions constructed as a Jastrow correlation factor times a model function have been obtained for the ground and the first excited state of opposite parity of the atoms Li to Ar. Single and restricted multi-configuration model functions are employed. Line strength, oscillator strength and transition probabilities have been obtained. An analysis of the different correlation mechanisms considered, single particle excitations and dynamical correlations, on these quantities is carried out. All calculations have been done by using Variational Monte Carlo, except when no Jastrow is involved where calculations have been performed using the Optimized Effective Potential method.

Ab Initio Reaction Kinetics of Hydrogen Abstraction from Methyl Formate by Hydrogen, Methyl, Oxygen, Hydroxyl, and Hydroperoxy Radicals

Combustion of renewable biofuels, including energy-dense biodiesel, is expected to contribute significantly toward meeting future energy demands in the transportation sector. Elucidating detailed reaction mechanisms will be crucial to understanding biodiesel combustion, and hydrogen abstraction reactions are expected to dominate biodiesel combustion during ignition. In this work, we investigate hydrogen abstraction by the radicals H·, CH(3)·, O·, HO(2)·, and OH· from methyl formate, the simplest surrogate for complex biodiesels. We evaluate the H abstraction barrier heights and reaction enthalpies, using multireference correlated wave function methods including size-extensivity corrections and extrapolation to the complete basis set limit. The barrier heights predicted for abstraction by H·, CH(3)·, and O· are in excellent agreement with derived experimental values, with errors ≤1 kcal/mol. We also predict the reaction energetics for forming reactant complexes, transition states, and product complexes for reactions involving HO(2)· and OH·. High-pressure-limit rate constants are computed using transition state theory within the separable-hindered-rotor approximation for torsions and the harmonic oscillator approximation for other vibrational modes. The predicted rate constants differ significantly from those appearing in the latest combustion kinetics models of these reactions.

What are the most efficient basis set strategies for correlated wave function calculations of reaction energies and barrier heights?

As electronic structure methods are being used to obtain quantitatively accurate reaction energies and barrier heights for increasingly larger systems, the choice of an efficient basis set is becoming more critical. The optimum strategy for achieving basis set convergence can depend on the way that electron correlation is treated and can take advantage of flexibility in the order in which basis functions are added. Here we study several approaches for estimating accurate reaction energies and barrier heights from post-Hartree-Fock electronic structure calculations. First and second, we evaluate methods of estimating the basis set limit of second order Møller-Plesset perturbation theory and of coupled cluster theory with single and double excitations and a quasiperturbative treatment of connected triple excitations by using explicitly correlated basis functions (in the F12a implementation) along with valence, polarization, and diffuse one-electron basis functions. Third, we test the scheme of adding a higher-order correction to MP2 results (sometimes called MP2∕CBS + ΔCCSD(T)). Finally, we evaluate the basis set requirements of these methods in light of comparisons to Weizmann-3.2, Weizmann-4, and CCSDT(2)(Q)∕CBS+CV+R results.

PERI-CC2: A Polarizable Embedded RI-CC2 Method.

We present a combination of the polarizable embedding (PE) method with the resolution-of-the-identity implementation of the approximate coupled-cluster singles and doubles method CC2. The new approach, termed PERI-CC2, allows one to study excited state phenomena of large solvated molecular systems with an accurate correlated wave function method. Central to the PE approach is the advanced description of the environmental electrostatic potential and inclusion of polarization, and the quintessence of RI-CC2 is efficient access to excited state properties while retaining the accuracy associated with CC theory. To maintain efficiency, an approximate truncated CC2 density is introduced to calculate the PE contributions. Explicitly, we derive the central equations and outline an implementation of polarizable embedding for the RI-CC2 approach. The new method is tested against previous PE-CC2 and PE-CCSD results for solvatochromic shifts, demonstrating how the important effects of polarization are incorporated well with PERI-CC2 but with a dramatically reduced overall computational cost. A follow-up investigation of the solvatochromic shift of uracil in aqueous solution further illustrates the potential of PERI-CC2. We discuss the need to explicitly incorporate several water molecules into the region treated by quantum mechanics in order to obtain a reliable and accurate description of the physical effects when specific solute/solvent interactions as, e.g., hydrogen-bonds are involved.

Improved definition of bond orders for correlated wave functions

The definition of bond orders for singlet correlated wave functions is improved by adding a term providing the correct dissociation behaviour if the system dissociates into open-shell fragments.

Strong renormalization of the Fermi-surface topology close to the Mott transition

The underlying Fermi surface is a key concept for strongly-interacting electron models and has been introduced to generalize the usual notion of the Fermi surface to generic (superconducting or insulating) systems. By using improved correlated wave functions that contain backflow and Jastrow terms, we examine the two-dimensional $t{-}t^\prime$ Hubbard model and find a non-trivial renormalization of the topology of the underlying Fermi surface close to the Mott insulator. Moreover, we observe a sharp crossover region, which arises from the metal-insulator transition, from a weakly interacting metal at small coupling to a resonating valence-bond superconductor at intermediate coupling. A violation of the Luttinger theorem is detected at low hole dopings.

Shape resonance in the Ps−system

We have searched for $S$-wave shape resonances in the Ps${}^{\ensuremath{-}}$ system. The calculations are carried out in the framework of the complex-coordinate rotation method using both Hylleraas-type wave functions involving powers of interparticle coordinates, and the exponential correlated wave functions. We have located an $S$-wave shape resonance lying above the Ps ($N$ $=$ 2) threshold. By changing the mass of the positively charged particle from one unit of the electron mass to infinitely heavy, we have traced this resonance pole from Ps${}^{\ensuremath{-}}$ to H${}^{\ensuremath{-}}$. Results for the shape resonance in H${}^{\ensuremath{-}}$ are comparable with the available results in the literature.

Complex-Scaling Treatment for Doubly Excited Inter-Shell Resonances in H− Interacting with Screened Coulomb (Yukawa) Potentials

The doubly-excited inter-shell resonance states of the hydrogen negative ion with screened Coulomb potentials are investigated in the framework of complex-scaling method. Highly correlated wave functions with terms up to 1078 in Hylleraas coordinates are used. The resonance parameters for the 2s3s 1 S e associated with the H (N = 2) threshold and the 3s4s 1 S e state associated with the H (N = 3) threshold for various screening strengths are reported. Comparisons are made with other available data in the literature.

Doubly excited non-autoionizing 1,3Pe and 1,3Do states of two-electron highly stripped atoms

We have investigated the doubly excited 1,3Pe and 1,3Do non-autoionizing states of two-electron highly stripped atoms within the framework of the Ritz variational principle. Highly correlated wave functions are used to represent the correlation effect between the charge particles. Precise non-relativistic energy eigenvalues of 2pnp 1Pe(n = 3–7), 2pnp 3Pe(n = 2–6) and 2pnd 1,3Do(n = 3–7) states for the systems N5+, O6+, F7+, Ne8+, Na9+ and Mg10+ are reported. The present results for 2pnp 1,3Pe state energies of O6+ and 2pnd 1,3Do state energies of N5+ are accurate in precision compared with the available theoretical results. The wavelengths for 2pnp 1Pe → 2pn′ d1Do (n, n′ ⩽ 6) and 2pnp 3Pe → 2pn′d 3Do (n, n′ ⩽ 6) transitions and the effective quantum numbers (n*) for 2pnp 1,3Pe and 2pnd 1,3Do states have been calculated.

Short-range nuclear effects on axion emissivities by nucleon–nucleon bremsstrahlung

The rates of axion emission by nucleon–nucleon (NN) bremsstrahlung are reconsidered by taking into account the NN short-range correlations. The analytical formulas for the neutron–neutron, proton–proton and neutron–proton processes with the inclusion of the full momentum dependence of one- and two-pion exchange nuclear potentials, in the non-degenerate limit, are explicitly given. We find that the two-pion exchange (short-range) effects can give a significant contribution to the emission rates, and are temperature dependent. Also, other short-range nuclear effects such as effective nucleon mass, polarization effects and use of correlated wave functions are discussed. The trend of all these nuclear effects is to diminish the corresponding axion emission rates. Furthermore, we estimate that the values of the emission rates calculated with the inclusion of all these effects can differ from the corresponding ones derived with constant nuclear matrix elements by a factor of ∼24. This leads to an uncertainty factor of ∼4.9 when extracting bounds of the axion parameters.

Isoelectronic analogue of oxywater: a parametric two-electron reduced-density-matrix study of ammonia oxide

A parametrization of the two-electron reduced density matrix (2-RDM) provides energies that improve on the accuracy of coupled electron-pair theories including coupled cluster with single-double excitations at the computational cost of configuration interaction with single-double excitations [Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. This parametric 2-RDM method was recently employed to study the isomerization of oxywater to hydrogen peroxide where it predicted a lower energy barrier from oxywater (2.1 kcal mol−1) than coupled cluster methods (4.2 kcal mol−1). In this paper we study an isoelectronic analogue, the isomerization of ammonia oxide to hydroxylamine. In the extrapolated basis-set limit, using the augmented correlation-consistent polarized valance quadruple-zeta (aug-cc-pVQZ) basis set, the parametric 2-RDM method predicts a 27.5 kcal mol−1 barrier from ammonia oxide to hydroxylamine. We report reaction energies, barriers, geometries, and natural-orbital occupation numbers for the ammonia-oxide reaction and compare them to those from the oxywater reaction. We find that the parametric 2-RDM method agrees with dynamic correlation wavefunction methods when the multi-reference character of the system is small as in the ammonia-oxide isomerization computed here but that it captures additional multi-reference correlation, usually requiring a multi-reference method, when such correlation increases as in the oxywater isomerization.

Relativistic explicit correlation: Coalescence conditions and practical suggestions

To set up the general framework for relativistic explicitly correlated wave function methods, the electron-electron coalescence conditions are derived for the wave functions of the Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG), Dirac-Coulomb-Breit (DCB), modified Dirac-Coulomb (MDC), and zeroth-order regularly approximated (ZORA) Hamiltonians. The manipulations make full use of the internal symmetries of the reduced two-electron Hamiltonians such that the asymptotic behaviors of the wave functions emerge naturally. The results show that, at the coalescence point of two electrons, the wave functions of the DCG Hamiltonian are regular, while those of the DC and DCB Hamiltonians have weak singularities of the type r(12)(ν) with ν being negative and of O(α(2)). The behaviors of the MDC wave functions are related to the original ones in a simple manner, while the spin-free counterparts are somewhat different due to the complicated electron-electron interaction. The behaviors of the ZORA wave functions depend on the chosen potential in the kinetic energy operator. In the case of the nuclear attraction, the behaviors of the ZORA wave functions are very similar to those of the nonrelativistic ones, just with an additional correction of O(α(2)) to the nonrelativistic cusp condition. However, if the Coulomb interaction is also included, the ZORA wave functions become close to the large-large components of the DC wave functions. Note that such asymptotic expansions of the relativistic wave functions are only valid within an extremely small convergence radius R(c) of O(α(2)). Beyond this radius, the behaviors of the relativistic wave functions are still dominated by the nonrelativistic limit, as can be seen in terms of direct perturbation theory (DPT) of relativity. However, as the two limits α → 0 and r(12) → 0 do not commute, DPT is doomed to fail due to incorrect descriptions of the small-small component Ψ(SS) of the DC wave function for r(12) < R(c). Another deduction from the possible divergence of Ψ(SS) at r(12) = R(c) is that the DC Hamiltonian has no bound electronic states, although the last word cannot be said. These findings enrich our understandings of relativistic wave functions. On the practical side, it is shown that, under the no-pair approximation, relativistic explicitly correlated wave function methods can be made completely parallel to the nonrelativistic counterparts, as demonstrated explicitly for MP2-F12. Yet, this can only be achieved by using an extended no-pair projector.

Toward a Unique Definition of the Local Spin.

In this work, we demonstrate that there is a continuum of different formulations for the decomposition of ⟨Ŝ(2)⟩ that fulfills all physical requirements imposed to date. We introduce a new criterion based upon the behavior of single-electron systems to fix the value of the parameter defining that continuum, and thus we put forward a new general formula applicable for both single-determinant and correlated wave functions. The numerical implementation has been carried out in the three-dimensional physical space for several atomic definitions. A series of representative closed-shell and open-shell systems have been used to illustrate the performance of this new decomposition scheme against other existing approaches. Unlike other decompositions of ⟨Ŝ(2)⟩, the new scheme provides very small local-spin values for genuine diamagnetic molecules treated with correlated wave functions, in conformity with the physical expectations.

Energies and transition wavelengths for Li II, Be III, B IV, C V embedded in Debye plasmas

We have carried out non-relativistic calculations to investigate the effect of Debye plasmas screening on the doubly excited nonautoionizing 1,3Pe and 1,3Do states of Li II, Be III, B IV, and C V using highly correlated exponential wave functions within the framework of Ritz variational principle. The 2p2 3Pe, 2p3p 1Pe, and 2p3d 1,3Do states energies, and wavelengths for the 2p3p 1Pe → 2p3d 1Do, 2p2 3Pe→ 2p3d 3Do, 2p3p 3Pe → 2p3d 3Do, and 2p3p 3Pe → 2p3d 3Do transitions for different Debye lengths are reported. Comparisons are made with the existing results. Results for B IV and C V for different screening parameters are reported for the first time in the literature. Transition wavelengths show interesting behavior with increasing screening parameters and nuclear charge.

Complex-Scaling Calculations for Doubly Excited Resonances in Ps− Interacting with Screened Coulomb (Yukawa) Potentials

We have investigated the effect of screened Coulomb potentials on the high-lying doubly excited resonance states of the positronium negative ion in the framework of complex-scaling method. Highly correlated wave functions in Hylleraas coordinates are used. The resonance parameters below the Ps (2s2S) and Ps (3s2S) thresholds, for various screening parameters, are reported.

Calculation of two-photon absorption strengths with the approximate coupled cluster singles and doubles model CC2 using the resolution-of-identity approximation

An implementation of two-photon absorption matrix elements using the approximate second-order coupled-cluster singles and doubles model CC2 is presented. In this implementation we use the resolution-of-the-identity approximation for the two-electron repulsion integrals to reduce the computational cost. To avoid storage of large arrays we introduce in addition a numerical Laplace transformation of orbital energy denominators for the response of the doubles amplitudes. The error due to the numerical Laplace transformation is found to be negligible. Using this new implementation, we performed a series of benchmark calculations on substituted benzene and azobenzene derivatives to get reference values for TD-DFT results. We show that results obtained with the Coulomb-attenuated B3LYP functional are in reasonable agreement with the coupled-cluster results, whereas other density functionals which do not have a long-range correction give considerably less accurate results. Applications to the AF240 dye molecule and a weakly bound molecular tweezer complex demonstrate that this new RI-CC2 implementation allows for the first time to compute two-photon absorption cross sections with a correlated wave function method for molecules with more than 70 atoms and to apply this method for benchmarking TD-DFT calculations on molecules which are of particular relevance for experimental studies of two-photon absorption.

On the discrepancy between theory and experiment for the F–F spin–spin coupling constant of difluoroethyne

The vicinal indirect nuclear spin-spin coupling constant (SSCC) between the two fluorine atoms in difluoroethyne has been reinvestigated. This coupling has previously proved to be difficult to calculate accurately. In this study we have therefore systematically investigated the dependence of this coupling on the choice of one-electron basis set, the choice of correlated wave function method and the inclusion of zero-point vibrational and temperature corrections. All terms of the SSCC have been evaluated at the second-order polarization propagator, SOPPA and SOPPA(CCSD), and coupled cluster singles and doubles (CCSD) levels of theory and for the most correlation dependent term, the paramagnetic spin-orbit contribution (PSO), also at the very accurate CC3 level. We find that in order to get results that are well converged with respect to the basis set, one needs to use special SSCC optimized basis sets of at least quadruple zeta quality and with added diffuse functions. Furthermore, the PSO term is not yet converged at the CCSD level as shown by the CC3 calculations. Finally, it is shown that vibrational effects are very important, as they are in this case of the same order of magnitude as the equilibrium geometry value of the coupling constant. Only by using a converged basis set and including both vibrational and higher order correlation effects can we obtain agreement with the experimental value for this coupling.