A short-range correlation energy density functional with multi-determinantal reference

We introduce a short-range correlation density functional defined with respect to a multi-determinantal reference which is meant to be used in a multi-determinantal extension of the Kohn–Sham scheme of density functional theory based on a long-range/short-range decomposition of the Coulomb electron–electron interaction. We construct the local density approximation for this functional and discuss its performance on the He atom.     

An application of correlation energy density functionals to atoms and molecules

Four density functionals — including that recently introduced by Perdew ((1986) Phys Rev B33: 8822)—are tested for first-row atoms, hydrides and dimers. Calculated contributions of the correlation energy to the ionization potentials and electron affinities of atoms and to the dissociation energies of molecules are compared with empirical values which were reevaluated for this purpose. An improvement over Hartree-Fock is found in all cases if the self-interaction or the gradient correction are included in the density functional, although there is a rather large variation in the accuracy of the predictions.     

The performance of density functional theory for LnF (Ln=Nd,Eu, Gd,Yb) and YbH

Different density functional theory (DFT) functionals have been evaluated by studying geometries and bond strengths of YbH, YbF, EuF, GdF, and NdF and compared with accurate CCSD(T) results and, when available, experiment. The agreement between the CCSD(T) results and experiment, when available, is good. The agreement is also good between bond strengths calculated at the DFT level using relativistic effective core potentials and the CCSD(T) results. However, the all-electron ADF calculations systematically overestimate binding energies. The geometries obtained by both the all-electron and the effective-core-potential-based DFT calculations are generally in good agreement with the CCSD(T) results.Contribution to the Björn Roos Honorary Issue     

Exchange and correlation energy in density functional theory

Several different versions of density functional theory (DFT) that satisfy Hohenberg–Kohn theorems are characterized by different definitions of a reference or model state determined by an N‐electron ground state. A common formalism is developed in which exact Kohn–Sham equations are derived for standard Kohn–Sham theory, for reference‐state density functional theory, and for unrestricted Hartree–Fock (UHF) theory considered as an exactly soluble model Hohenberg–Kohn theory. A natural definition of exchange and correlation energy functionals is shown to be valid for all such theories. An easily computed necessary condition for the locality of exchange and correlation potentials is derived. While it is shown that in the UHF model of DFT the optimized effective potential (OEP) exchange satisfies this condition by construction, the derivation shows that this condition is not, in general, sufficient to define an exact local exchange potential. It serves as a test to eliminate proposed local potentials that are not exact for ground states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 521–525, 2000     

On the accuracy of correlation energy calculated by the correlation factor method: first- and second-row atoms

Summary The correlation energy of two- and four-isoelectronic series, a representative example for which the existing spin-density functionals fails, is calculated using the Colle and Salvetti method, considering mono- and multideterminantal wave functions. The results are in agreement with experimental data, and show the potentiality of this method when it is applied to wave functions including the most relevant configurational features. Also, results for the ionization energies and electron affinities of first- and second-row atoms are reported.     

Ab initio and density functional studies on the structure and vibrational spectra of 2-hydroxy-1,4-naphthoquinone-1-oxime derivatives

Structure and vibrational frequencies of lawsoneoxime and its C₃-substituted (R=CH₃, NH₂, Cl, NO₂) derivatives in keto and nitrosophenol forms have been obtained employing the Hartree–Fock and density functional methods. Charge distributions in different conformers have been studied using the molecular electrostatic potential topography as a tool. For all these derivatives except for nitrolawsoneoxime the amphi conformer in the keto form is predicted to be of lowest energy, which can partly be attributed to hydrogen bonding through the oximino nitrogen. In the nitro derivative, however, the preference to form a six membered ring owing to O–H–O hydrogen-bonded interactions makes the anti conformer (keto) the stablest. Further one of the nitrosophenol conformers of nitrolawsoneoxime turns out to be very close in energy (0.21 kJ mol^–1 higher) to this anti conformer. The consequences of hydrogen bonding on charge distribution and vibrational spectra are discussed.     

Electronic and geometrical structures of cyclopropanes, part 51. fluorocyclopropanes. linear correlation of orbital energies with C–C bond lengths. further improvement of the two-orbitals model

The electronic and geometrical structures of fluorocyclopropanes (1–12) have been analysed using DFT B3LYP calculations. A linear relationship, Δɛ_ω=−0.172 Δr−0.171 (n=12, R=0.931), between Δɛ_ω (in eV), the difference of the energies of the Walsh orbitals ω_S and ω_A, and Δr (in pm), the difference of vicinal and distal C–C bond lengths, is established. Correcting the orbital splitting by the basic value at Δr=0.00 pm, an even better linear correlation Δɛ_ω ^eff=0.0720 Δr (n=12, R=0.984) is obtained. The results confirm the general applicability of the two-orbitals model for the relationship between geometrical and electronic structures for substituted cyclopropanes. ¹For Part 4 see Ref. [17].     

Modeling water exchange on monomeric and dimeric Mn centers

Water exchange on Mn centers in proteins has been modeled with density functional theory using the B3LYP functional. The reaction barrier for dissociative water exchange on [Mn^IV(H₂O)₂(OH)₄] is only 9.6 kcal mol^–1, corresponding to a rate of 6×10⁵ s^–1. It has also been investigated how modifications of the model complex change the exchange rate. Three cases of water exchange on Mn dimers have been modeled. The reaction barrier for dissociative exchange of a terminal water ligand on [(H₂O)₂(OH)₂Mn^IV(-O)₂Mn^IV(H₂O)₂(OH)₂] is 8.6 kcal mol^–1, while the bridging oxo group exchange with a ring-opening mechanism has a barrier of 19.2 kcal mol^–1. These results are intended for interpretations of measurements of water exchange for the oxygen evolving complex of photosystem II. Finally, a tautomerization mechanism for exchange of a terminal oxyl radical has been modeled for the synthetic O₂ catalyst [(terpy)(H₂O)Mn^IV(-O)₂Mn^IV(O)(terpy)]³⁺ (terpy=2,2:6,2-terpyridine). The calculated reaction barrier is 14.7 kcal mol^–1.Contribution to the Björn Roos Honorary Issue     

Adiabatic integration formula for the correlation energy functional of the Hartree–Fock density

An adiabatic integration formula for the quantum chemistry correlation energy functional of the Hartree–Fock density, E _c ^QC[n], is presented. The functional E _c ^QC[n] is meant to be added to the completed Hartree–Fock energy to produce the exact ground-state energy of the system under consideration. The initial slope of the integrand in this connection formula is identified as a second-order energy and an explicit expression for the initial slope of the integrand is presented. Our expression should be useful for arriving at new improved approximations to E _c ^QC[n]. Previous numerical results by Huang and Umrigar (1997) Phys Rev A 56:290, for two-electron densities are proved, and a generalization to more than two electrons is presented. Results obtained by means of the present density functional theory correlation energy functionals, when used to approximate the initial slope in our adiabatic integration formula for E _c ^QC[n], are compared against exact numbers. Received: 10 September 1998 / Accepted: 3 February 1999 / Published online: 21 June 1999     

A theoretical study of radical-only and combined radical/carbocationic mechanisms of arachidonic acid cyclooxygenation by prostaglandin H synthase

Prostaglandin H synthase catalyzes the oxygenation of arachidonic acid into the cyclic endoperoxide, prostaglandin G₂ (PGG₂), and the subsequent reduction of PGG₂ to the corresponding alcohol, prostaglandin H₂ (PGH₂), the precursor of all prostaglandins and thromboxanes. Both radical abstraction by a neighboring tyrosyl radical and combined radical/carbocationic models have been proposed to explain the cyclooxygenase part of this reaction. We have used density functional theory calculations to study the mechanism of the formation of the cyclooxygenated product PGG₂. We found an activation free energy for the initial hydrogen abstraction by the tyrosine radical of 15.6 kcal/mol, and of 14.5 kcal/mol for peroxo bridge formation, in remarkable agreement with the experimental value of 15.0 kcal/mol. Subsequent steps of the radical-based mechanism were found to happen with smaller barriers. A combined radical/carbocation mechanism proceeding through a sigmatropic hydrogen shift was ruled out, owing to its much larger activation free energy of 36.5 kcal/mol. Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00214-003-0476-9. Electronic Supplementary MaterialSupplementary material is available in the online version of this article at Electronic Supplementary Material: Supplementary material is available in the online version of this article at     

Calculation of correlation energy by many-body diagrammatic perturbation theory

The many-body diagrammatic perturbation theory is used for calculation of the correlation energy of closed-shell molecular systems. We apply Brueckner's concept of the two-particle renormalized interaction defined by a non-linear diagrammatic expression containing all possible (diagonal and/or non-diagonal) particle-particle, hole-hole and particle-hole intermediate elementary processes. Then, a “second-order” simple diagrammatic expression for the correlation energy can be formed, where the correlation energy is approximated by all the diagrams with biexcited intermediate states. An illustrative numerical application for the LiH molecule is presented. This article is dedicated to the memory of our friends and colleagues Dr. Jarka Surá and Dr. Marta Černayová, who tragically died in July 1976.     

Method for evaluation of density functional integrals in molecular calculations

Numerical methods for computing variationally optimized molecular orbitals within the Hartree–Fock approximation are augmented to include correlation functionals of the density in the energy and the numerical methods for carrying this out are described. The approach is applied explicitly to the Colle–Salvetti correlation energy functional. It is found that the gradient terms in the Colle–Salvetti functional present numerical problems associated with the low-density behavior, but also that they make a relatively small contribution to the correlation energy. In the three cases considered, HF, H₂O and N₂, it is found that the Colle–Salvetti correction considerably underestimates the correlation energies obtained in coupled-cluster theory.     

Accuracy of geometries: influence of basis set,exchange–correlation potential,inclusion of core electrons,and relativistic corrections

The geometries of a set of small molecules were optimized using eight different exchange–correlation (xc) potentials in a few different basis sets of Slater-type orbitals, ranging from a minimal basis (I) to a triple-zeta valence basis plus double polarization functions (VII). This enables a comparison of the accuracy of the xc potentials in a certain basis set, which can be related to the accuracies of wavefunction-based methods such as Hartree–Fock and coupled cluster. Four different checks are done on the accuracy by looking at the mean error, standard deviation, mean absolute error and maximum error. It is shown that the mean absolute error decreases with increasing basis set size, and reaches a basis set limit at basis VI. With this basis set, the mean absolute errors of the xc potentials are of the order of 0.7–1.3 pm. This is comparable to the accuracy obtained with CCSD and MP2/MP3 methods, but is still larger than the accuracy of the CCSD(T) method (0.2 pm). The best performing xc potentials are found to be Becke–Perdew, PBE and PW91, which perform as well as the hybrid B3LYP potential. In the second part of this paper, we report the optimization of the geometries of five metallocenes with the same potentials and basis sets, either in a nonrelativistic or a scalar relativistic calculation using the zeroth-order regular approximation approach. For the first-row transition-metal complexes, the relativistic corrections have a negligible effect on the optimized structures, but for ruthenocene they improve the optimized Ru–ring distance by some 1.4–2.2 pm. In the largest basis set used, the absolute mean error is again of the order of 1.0 pm. As the wavefunction-based methods either give a poor performance for metallocenes (Hartree–Fock, MP2), or the size of the system makes a treatment with accurate methods such as CCSD(T) in a reasonable basis set cumbersome, the good performance of density functional theory calculations for these molecules is very promising; even more so as density functional theory is an efficient method that can be used without problems on systems of this size, or larger.     

Excited state geometries within time-dependent and restricted open-shell density functional theories

Singlet excited state geometries of a set of medium sized molecules with different characteristic lowest excitations are studied. Geometry optimizations of excited states are performed with two closely related restricted open-shell Kohn–Sham methods and within linear response to time-dependent density functional theory. The results are compared to wave-function based methods. Excitation energies (vertical and adiabatic) calculated from the open-shell methods show systematic errors depending on the type of excitation. However, for all states accessible by the restricted methods a good agreement for the geometries with time-dependent density functional theory and wave-function based methods is found. An analysis of the energy with respect to the mixing angle for the singly occupied orbitals reveals that some states (mostly [n→π^*]) are stable when symmetry constraints are relaxed and others (mostly [π→π^*]) are instable. This has major implications on the applicability of the restricted open-shell methods in molecular dynamics simulations.     

Correlation energies in the spin-density functional formalism

It has been shown recently that dynamical correlation effects can be adequately described by using an electron-gas expression for correlation between electrons of different spins. In this paper the method is applied to the calculation of excitation energies for the first- and second-row atoms and to the determination of ground-state properties for small polyatomic molecules, such as CH₂, CH₄, CH ₄ ⁺ , CH ₅ ⁺ . Additionally, deficiencies of the method for cases with few electrons and strongly varying electron density are investigated and an empirical correction to the electron-gas approximation is proposed. This correction is based on atomic data and gives an overall improvement for test molecules with two to four electrons.     

Alternative Representations of the Correlation Energy in Density‐Functional Theory: A Kinetic‐Energy Based Adiabatic Connection

The adiabatic‐connection framework has been widely used to explore the properties of the correlation energy in density‐functional theory. The integrand in this formula may be expressed in terms of the electron–electron interactions directly, involving intrinsically two‐particle expectation values. Alternatively, it may be expressed in terms of the kinetic energy, involving only one‐particle quantities. In this work, we explore this alternative representation for the correlation energy and highlight some of its potential for the construction of new density functional approximations. The kinetic‐energy based integrand is effective in concentrating static correlation effects to the low interaction strength regime and approaches zero asymptotically, offering interesting new possibilities for modeling the correlation energy in density‐functional theory     

Ab initio and density functional theory based studies on collagen triplets

An understanding of the amino acid sequence dependent stability of polypeptides is of renowned interest to biophysicists and biochemists, in order to identify the nature of forces that stabilize the three-dimensional structure of proteins. In this study, the role of various collagen triplets influencing the stability of collagen has been addressed. It is found from this study that proline can stabilize the collagen triplet only when other residues are also in the polyproline II conformation. Solvation studies of various triplets indicate that the presence of polar residues increases the free energy of solvation. Especially the triplets containing arginine residues displays a higher solvation free energy. The chemical hardness of all the triplets in collagen-like conformation has been found to be higher than that in the extended conformation. Studies on Gly–X–Y, Gly–X–Hyp, and Gly–Pro–Y triplets confirm that there will be local variations in the stability of collagen along the entire sequence.