Differential Correlation Effects Research Articles

New-Generation Electron-Propagator Methods for Molecular Electron-Binding Energies.

A new generation of electron-propagator methods for the calculation of electron binding energies has surpassed its antecedents with respect to accuracy, efficiency, and interpretability. No adjustable parameters are introduced in these fully ab initio procedures. Numerical tests versus several databases of valence, vertical electron binding energies of closed-shell molecules and atoms have been performed. Easily interpreted self-energy approximations with cubic arithmetic scaling produce mean absolute errors (MAEs) of 0.2 and 0.3 eV for electron detachments and attachments, respectively. The most accurate explicitly renormalized methods with fifth-power arithmetic scaling yield MAEs below 0.1 eV for detachments and attachments. Approximate renormalization leads to more efficient fifth-power alternatives for electron detachments that achieve similar accuracy with fewer bottleneck operations. Composite protocols generate excellent predictions versus highly accurate basis-extrapolated standards and experiments. The validity of the diagonal self-energy approximation and the accuracy of the approximate renormalizations are confirmed. The success of these perturbative methods based on canonical Hartree-Fock orbitals rests on a Hermitized, intermediately normalized superoperator metric. The results of all of the new-generation calculations may be analyzed in terms of final-state orbital relaxation and differential correlation effects.

Assessment of density functional theory based ΔSCF (self-consistent field) and linear response methods for longest wavelength excited states of extended π-conjugated molecular systems.

Computational investigation of the longest wavelength excitations in a series of cyanines and linear n-acenes is undertaken with the use of standard spin-conserving linear response time-dependent density functional theory (TD-DFT) as well as its spin-flip variant and a ΔSCF method based on the ensemble DFT. The spin-conserving linear response TD-DFT fails to accurately reproduce the lowest excitation energy in these π-conjugated systems by strongly overestimating the excitation energies of cyanines and underestimating the excitation energies of n-acenes. The spin-flip TD-DFT is capable of correcting the underestimation of excitation energies of n-acenes by bringing in the non-dynamic electron correlation into the ground state; however, it does not fully correct for the overestimation of the excitation energies of cyanines, for which the non-dynamic correlation does not seem to play a role. The ensemble DFT method employed in this work is capable of correcting for the effect of missing non-dynamic correlation in the ground state of n-acenes and for the deficient description of differential correlation effects between the ground and excited states of cyanines and yields the excitation energies of both types of extended π-conjugated systems with the accuracy matching high-level ab initio multireference calculations.

Hybrid Ab initio/EFP approach for calculating d‐d absorption spectrum of hexaammineruthenium(II) ion in aqueous solutions

AbstractAb initio quantum chemical strategies for quantitatively predicting the lowest (1Ag → 1T1g) vertical d‐d excitation energy of hexaammineruthenium(II) ion in aqueous solution are discussed. The scalar‐relativistic ECP/valence basis set on Ru atom developed by the Stuttgart group in a combination with the state‐average CASSCF(d) approach, followed by multiconfigurational quasi‐degenerate second‐order perturbation theory (MCQDPT2) to account for differential correlation effects is proved to be an adequate tool to reproduce the experimental absorption spectrum of the complex for a variety of AO basis sets on ligand atoms. In addition, different ab initio methodologies are examined in order to predict the ground state geometry which is consistent with the follow‐up excitation spectrum calculations. It is observed that the use of the optimized structures of a hypothetical gas‐phase complex lead to substantial underestimation of excitation energies. Solvent effects strongly influence the excitation energy though indirectly, mainly by means of changing the ground state geometry of the solvated complex when compared with the vacuum one. In particular, the ground state structure of the complex surrounded by effective fragments simulating water molecules provides the lowest CASSCF/MCQDPT excitation energy estimate to be within 25,500–26,400 cm−1, in a fair agreement with the experimentally measured value of 25,600 cm−1. At the same time, direct incorporation of solvation effects causes only minor change in the estimated transition energies, within several hundred cm−1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Development and applications of a relaxation-inducing cluster expansion theory for treating strong relaxation and differential correlation effects

We present in this paper a multi-reference coupled cluster (MRCC) formulation for energy differences which treats orbital relaxation and correlation effects on the same footing, by invoking a novel cluster ansatz of the valence portion of the wave operator Ωv. Unlike in the traditional normal-ordered exponential representation of Ωv, our new relaxation-inducing ansatz, represented symbolically as Er(S), allows contractions between the spectator lines and also certain other special contractions. By an extensive theoretical analysis, taking as an example the case of one-hole model space (the IP problem), we demonstrate that our ansatz incorporates in a manifestly spin-free form the orbital relaxation to all orders. The traditional Thouless-type of exponential transformation via one-body excitations can induce the same effect, as is done in the valence-specific or the quasi-valence-specific MRCC formalisms, but they have to be done in the spin-orbital basis – making the spin adaptation of the problem a complicated exercise. In contrast, we use a spin-free representation of the cluster operators right from start, but expand the rank of the cluster operators by involving spectator orbitals to distinguish the various spin possibilities. The combinatorial factors entering the contracted power series in Er(S) are chosen in such a way that they correspond to what we would have obtained if we had used a Thouless-like transformation to induce the orbital relaxation. Our working equations generally have only finite powers of the cluster operators S, resulting in a very compact formulation of the relaxation problem. Pilot numerical applications for the IP computations of HF and H2O in the core, the inner valence and the outer valence regions show very good performance of the method vis-a-vis those obtained using the traditional normal ordered ansatz for Ωv. The improvement in the core IP value is particularly impressive, although even for the valence regions there is an overall improvement of the IP values.

Pseudospectral calculation of the gas-phase acidities of aliphatic alcohols

The acidity of aliphatic alcohols in gas phase is reinvestigated with the aim at establishing the simplest, yet reliable, level of description to be used for the solute in a solution-phase acidity calculation. It is shown that a procedure which includes only the differential correlation effects arising from the O–H bond being broken and its first neighbor bonds can generate reliable results for a comparative study of gas-phase and solution-phase acidities, thus considerably reducing the computational effort to obtain such a property in solution. Preliminary pKa results for alcohols in water solution show a reasonable agreement with the available experimental data. Also, the fact that the pseudospectral formulation of both Hartree–Fock (HF) and the local Moller–Plesset second-order perturbation theory (L-MP2) have been used, makes the procedure applicable to much larger molecules. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 417–422, 1999

The electroaffinity of O 2 by DFT and coupled MCSCF/peturbation approaches. A computational experiment

The electroaffinity of the O 2 molecule is revisited using density functional theory (DFT) and perturbation treatments built on a MCSCF wavefunction that includes most of the non-dynamic correlation effects (MC/P approach). Using a standard 6–31 + G ∗ basis set, DFT treatments based on BLYP or B3LYP functionals provide electroaffinities of the order of +0.6 eV that compare favorably to experiment. Coupled MCSCF/perturbation treatments using an Epstein-Nesbet partition of the molecular Hamiltonian give a more accurate value of +0.492 eV in excellent agreement with the most recent experimental data (+0.431 eV) as well as with highest-level purely variational ab initio treatments which are far less tractable for larger systems. The analysis of the results in terms of differential correlation effects made it possible to identify the failure of the previous MCSCF-limited treatments as arising from the dynamic correlation of the electron pair describing the σ O:O bond.

An MCSCF+CI calculation of the H 3CAlH and H 3CAlH bond dissociation energies

Results of MCSCF(GVB)+CI calculations are presented for the H 3CAlH and H 3CAlH bond dissociation energies. Using the AlH 2 molecule as a test case it is shown that reliable bond energies can be obtained by considering only the differential correlation effects on the chemical bond being broken and the relaxation effects on its neighbouring bonds. The AlH bond (39.32 kcal mol −1) is found to be stronger than the AlC bond (33.36 kcal mol −1), but both bonds are weaker than the HAlH bond.

Second-order Møller-Plesset perturbation theory calculations with relativistic effective core potentials including spin-orbit operators

The two-component Hartree-Fock method using relativistic effective core potentials (RECP) is extended to include electron correlations by second-order Møller-Plesset perturbation theory (MP2). The present method simultaneously treats electron correlation and all the relativistic effects in REP including spin-orbit effects. It is possible to estimate differential correlation effects on molecular properties due to the relativity and/or the spin-orbit interactions at the MP2 level using the present method. Test calculations have been performed for HX, X 2, XY (X, YBr, I), and PbH 4 molecules. Spin-orbit and electron-correlation effects are rather small for the equilibrium bond lengths and dissociation energies of the tested molecules, but exhibit interesting trends.

Differential correlation effects in chemisorption cluster model calculations: an FCI study

The interaction of atomic hydrogen with Cu 5 and Ag 5 cluster models simulating the Cu(100) and Ag(100) surfaces has been studied at the full configuration interaction (FCI) level in order to establish the transferability of differential correlation arising from the valence shell. It is shown that pseudopotentials that deal explicitly with one electron or eleven electrons lead to differential correlation effects which agree to within 1–2 mhartree when a localization procedure is used to separate d-shell MOs from the valence ones.

A new nonperturbative theory of core-hole ionizations: a compact cluster-expansion technique for treating relaxation effects

We have introduced in this paper a new cluster-expansion ansatz for the wave-operator Ω that incorporates orbital relaxation and differential correlation effects in a compact and efficient manner. The ansatz utilizes a Thouless-type transformation inducing these effects via a seminormal ordered exponential-type cluster operator, denoted as exp r[ T+ S c+ S r], with T, S c and S r as the core-correlation, valence-correlation and relaxation-cum-differential-correlation cluster operators, respectively. The theory is illustrated by using the example of one-valence core ionizations. Numerical applications illustrate both the superiority of the method to the normal-ordered ansatz for Ω, and the relative unimportance of S c for this problem.

A b i n i t i o calculations on the positive ions of the alkaline-earth oxides, fluorides, and hydroxides

Theoretical spectroscopic parameters are presented at the self-consistent-field and singles-plus-doubles configuration-interaction (SDCI) levels for the ground states of the positive ions of the alkaline-earth fluorides, oxides, and hydroxides. The alkaline-earth fluoride and hydroxide ions are found to have X 1Σ+ ground states corresponding to a M+2X−1 structure. The alkaline-earth oxide positive ions, on the other hand, undergo a change in ground state symmetry between CaO+(X 2Π) and SrO+(X 2Σ+), whereas the analogous alkali oxides undergo the change one row higher between NaO and KO. The greater stability of the 2Π states for the alkaline-earth oxide positive ions is due to the increased electrostatic field created by the larger metal ion charge and reduced bond lengths. Calculations on the 3Π states of BeF+, MgF+, BeOH+, and MgOH+ indicate that these states, corresponding to the M+1X structure, lie much higher in energy. The bond distances of the positive ions are uniformly 0.07±0.02 Å shorter than the analogous electronic states of the neutral. By correcting for the relatively small errors in the theoretical bond distances for the neutrals, bond distances accurate to about 0.005 Å are obtained for the ions where experimental values are available for the neutral species. Since extensive one-particle basis sets are employed and differential correlation effects are minimized by dissociating directly to ions, theoretical dissociation energies and ionization potentials (I.P.) accurate to about 0.15 eV can be obtained. The dissociation energies (D0) in eV for the ground states at the SDCI level are found to be: BeO+(4.04), MgO+(2.31), CaO+(3.29), SrO+(3.28), BeF+(6.25), MgF+(4.46), CaF+(5.67), SrF+(5.71), BeOH+(6.00), MgOH+(3.62), CaOH+(4.73), and SrOH+(4.67). For all of the systems studied, the bonding is dominated by electrostatic interactions. However, the molecules containing Be show some covalent character owing to the large I.P. of Be+. We have found that the constrained space orbital variation analysis, which decomposes the bonding into intrafragment polarization and interfragment donations, is an excellent method for delineating the degree of ionic bonding in a molecular system.

Theoretical dissociation energies for the alkali and alkaline-earth monofluorides and monochlorides

A b initio calculations using self-consistent-field and correlated wave functions are used to determine accurate spectroscopic parameters (re, ωe, D0) for the alkali and alkaline-earth monofluorides and monochlorides. Numerical Hartree–Fock (NHF) calculations are performed on selected systems to ensure that the extended Slater basis sets employed are near the Hartree–Fock limit. Because the bonding is predominantly electrostatic in origin, there is a strong correlation between the dissociation energy (to ions) and re. By dissociating to the ionic limits, most of the differential correlation effects can be embedded in the accurate experimental electron affinities and ionization potentials. With this model, correlation effects are relatively small (0.0–0.4 eV), but invariably increase D0. The importance of correlating the electrons on both the anion and the metal is discussed. For the heavier alkali chlorides, RbCl and CsCl, we show that a core-valence treatment, which excludes the double excitations out of the metal (n−1) shell, gives significantly better re and D0 parameters than does the full singles plus doubles configuration-interaction CI(SD) calculation. The theoretical studies combined with the experimental literature allow us to recommend D0 values that are accurate to 0.1 eV for all systems considered.

Differential correlation effects for states of the 3dnand 3dn4smconfigurations. II. A complete study of the energy splittings for the nickel atom

For pt.I, see ibid., vol.18, p.2133-46 (1985). The approximate ab initio approach for the evaluation of electron correlation effects on atomic energy differences, formulated in part I, (1985), has been applied to a complete study of the splittings of the energies corresponding to the 3d10-m4sm (m=0, 1, 2) configurations of the Ni atom. The results are modified to take into account the leading relativistic corrections. If both non-dynamical and all-external correlation effects are accounted for, good agreement with experiment is found. The analysis of the impact of various types of correlation effects further confirmed the findings of part I.

Differential correlation effects for states of the 3dnand 3dn4smconfigurations. I. The copper and zinc atoms and their ions

The recently formulated approximate ab initio method for the evaluation of electron correlation effects on atomic energy differences, which has been tested for the first-row atoms, has been slightly modified to become applicable to transition-metal atoms and ions. Pilot calculations have been performed for: (a) the excitation energies in Cu, Cu+, Zn+ and Zn2+; (b) the electron affinity of Cu; and (c) the ionisation potentials for Cu, Cu+, Zn, Zn+ and Zn2+. The results indicate that the present approach leads to a satisfactory agreement with the observed values. The impact of various types of correlation effects is carefully studied. It turns out that for some of the energy differences even the correlation effects involving the 2p electrons may be important. The results are modified to take into account the leading relativistic corrections, which further improve the results.

MINDO/2 calculations on the reaction of methyl radicals with ethylene and butadiene

Semiempirical calculations using the MINDO/2 procedure have been carried out on the potential surface for the reaction of a methyl radical with ethylene and trans-butadiene. The transition state is predicted to be reactant-like in character and no evidence of resonance stabilization of the activated complex is found for butadiene. It is conjectured that the experimentally observed lowering of the activation energy for butadiene relative to ethylene may be attributed to differential correlation effects.