Superconductivity from repulsive electronic correlations on alternant cuprate and iron‐based lattices

A key question in the theory of high‐temperature superconductivity is whether off‐diagonal long‐range order can be induced wholly or in large part by repulsive electronic correlations. Electron pairs on cuprate and the iron‐based pnictide and chalcogenide alternant lattices may interact with a strong short‐range Coulomb repulsion and much weaker longer range attractive tail. Here, we show that such interacting electrons can cooperate to produce a superconducting state in which time‐reversed electron pairs effectively avoid the repulsive part but reside predominantly in the attractive region of the potential. The alternant lattice structure is a key feature of such a stabilization mechanism leading to the occurrence of high‐temperature superconductivity with or sign alternating s‐wave or s± condensate symmetries. © 2013 Wiley Periodicals, Inc.     

Scaling relations,virial theorem,and energy densities for long‐range and short‐range density functionals

Decomposition of the Coulomb electron–electron interaction into a long‐range and a short‐range part is described within the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study the behavior of the local density approximation in the high‐density limit for the long‐range and the short‐range functionals by carrying out a detailed analysis of the correlation energy of a uniform electron gas interacting via a long‐range‐only electron–electron repulsion. Possible definitions of exchange and correlation energy densities are discussed and clarified with some examples. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Theory of strongly correlated electron systems. II. Including correlation effects into electronic structure calculations

We have previously shown that a division of the f‐shell into two subsystems gives a better understanding of the cohesive properties as well the general behavior of lanthanide systems. In this article, we present numerical computations, using the suggested method. We show that the picture is consistent with most experimental data, e.g., the equilibrium volume and electronic structure in general. Compared with standard energy band calculations and calculations based on the self‐interaction correction and LDA + U, the f‐(non‐f)‐mixing interaction is decreased by spectral weights of the many‐body states of the f‐ion. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Long‐range analysis of density fitting in extended systems

Density fitting scheme is analyzed for the Coulomb problem in extended systems from the correctness of long‐range behavior point of view. We show that for the correct cancellation of divergent long‐range Coulomb terms it is crucial for the density fitting scheme to reproduce the overlap matrix exactly. It is demonstrated that from all possible fitting metric choices the Coulomb metric is the only one which inherently preserves the overlap matrix for infinite systems with translational periodicity. Moreover, we show that by a small additional effort any non‐Coulomb metric fit can be made overlap‐preserving as well. The problem is analyzed for both ordinary and Poisson basis set choices. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Multiscale fast summation of long‐range charge and dipolar interactions

Here we present a linear order multiscale method for the fast summation of long range forces in a system consisting of a large number of charge and dipolar particles. For a N‐body system, our algorithm requires an order of work that is proportional to O(N), in comparison to order O(N²) of the direct pairwise computation. Our method is demonstrated on two‐dimensional homogeneous point‐charge and dipolar systems, and a combined heterogeneous particle system, for the calculation of the induced electrostatic potential and energy. The electrostatic interaction is decomposed into a local part and a smooth part. The method thus, has several potential advantages over other O(N log N) or O(N) techniques, especially for calculation with moving particles or implicit charges locations. This approach is beneficial to large‐scale problems such as molecular statics, molecular dynamics, equilibrium statistics (Monte‐Carlo simulations), molecular docking, and in areas such as magnetism and astrophysics. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 717–731, 2001     

Efficient measurement of the sign and the magnitude of long‐range proton‐carbon coupling constants from a spin‐state‐selective HSQMBC‐COSY experiment

A spin state‐selective Heteronuclear Single‐Quantum Multiple‐Bond Connectivities (HSQMBC‐COSY) experiment is proposed to measure the sign and the magnitude of long‐range proton‐carbon coupling constants (ⁿJ(CH); n > 1) either for protonated or for non‐protonated carbons in small molecules. The simple substitution of the selective 180° ¹H pulse in the original selHSQMBC pulse scheme by a hard one allows the simultaneous evolution of both proton‐proton and proton‐carbon coupling constants during the refocusing period and enables a final COSY transfer between coupled protons. The successful implementation of the IPAP principle leads to separate mixed‐phase α/β cross‐peaks from which ⁿJ(CH) values can be easily measured by analyzing their relative frequency displacements in the detected dimension. Copyright © 2012 John Wiley & Sons, Ltd.     

Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long‐range and/or empirical dispersion corrections, including LC‐ωPBE, B97‐D, ωB97X‐D, M06‐2X, B2PLYP‐D, and mPW2PLYP‐D functionals, are assessed for their ability to describe the conformational preferences of Ac‐Ala‐NHMe (the alanine dipeptide) and Ac‐Pro‐NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22–0.40 kcal/mol in conformational energy and 2.0–3.2° in torsion angles ? and ψ using these functionals with the 6‐311++G(d,p) basis set against the reference values calculated at the MP2/aug‐cc‐pVTZ//MP2/aug‐cc‐pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP‐D ≈ mPW2PLYP‐D > ωB97X‐D ≈ M06‐2X > MP2 > LC‐ωPBE > B3LYP with the 6–311++G(d,p) basis set. The SMD model at the M06‐2X/6‐31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP‐D/6‐311++G(d,p)//SMD M06‐2X/6‐31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

BASHD‐J‐resolved‐HMBC,an efficient method for measuring proton–proton and heteronuclear long‐range coupling constants

Natural products often possess various spin systems consisting of a methine group directly bonded to a methyl group (e.g. –CH_a–CH_b(CH₃)–CH_c–). The methine proton H_b splits into a broadened multiplet by coupling with several vicinal protons, rendering analysis difficult of ⁿJ_C–H with respect to H_b in the J‐resolved HMBC‐1. In purpose of the reliable and easy measurements of ⁿJ_C–H and ⁿJ_H–H in the aforesaid spin system, we have developed a new technique, named BASHD‐J‐resolved‐HMBC. This method incorporates band selective homo decoupled pulse and J‐scaling pulse into HMBC. In this method, high resolution cross peaks can be observed along the F₁ axis by J‐scaling pulse, and band selective homo decoupled pulse simplified multiplet signals. Determinations of ⁿJ_C–H and ⁿJ_H–H of multiplet signals can easily be performed using the proposed pulse sequence. Copyright © 2013 John Wiley & Sons, Ltd.     

Probing long‐range spin–spin coupling constants in 2‐halo‐substituted cyclohexanones and cyclohexanethiones: The role of solvent and stereoelectronic effects

Earlier studies with 2‐bromocyclohexanone demonstrated a measurable long‐range coupling constant (⁴J_H2,H6) for the equatorial conformer, although ⁴J_H2,H4 and ⁴J_H4,H6 were not observed; as a consequence, it is inferred that the carbonyl group plays an important role particularly due to hyperconjugative interactions σ_C2H2→π*_C═O and σ_C6H6→π*_C═O. In the present study, NBO analysis and coupling constant calculations were performed to cyclohexanone and cyclohexanethione alpha substituted with F, Cl, and Br, aiming to evaluate the halogen effect and acceptor character of the π* orbital on the long‐range coupling pathway. The σ_C2H2→π*_C1═Y and σ_C6H6→π*_C1═Y (Y═O and S) hyperconjugative interactions for the equatorial conformer indeed contribute for the ⁴J_H2,H6 transmission mechanism_. Surprisingly, the ⁴J_H2,H6 value is higher for the carbonyl compounds, although the interactions σ_C2H2→π*_C═Y and σ_C6H6→π*_C═Y are more efficient for the thiocarbonyl compounds. Accordingly, the Fermi contact (FC) contribution for the thiocarbonyl compounds decays deeper than in ketones, thus reducing more the ⁴J_H2,H6 values. Moreover, both π_C═S→σ*_C─X and π_C═S→σ*_C─H interactions seem to be stronger in thiocarbonyl than in carbonylic compounds. The implicit solvent effect (DMSO and water) on the coupling constant values was negligible when compared with the gas phase. On the other hand, an explicit solvent effect was found and ⁴J_H2,H6 for the thiocarbonyl compounds appeared to be more sensitive than for the cyclohexanones.     

Electronic spectra and intersystem spin‐orbit coupling in 1,2‐ and 1,3‐squaraines

The main photophysical properties of a series of recently synthetized 1,2‐ and 1,3‐squaraines, including absorption electronic spectra, singlet‐triplet energy gaps, and spin‐orbit matrix elements, have been investigated by means of density functional theory (DFT) and time‐dependent DFT approaches. A benchmark of three exchange‐correlation functionals has been performed in six different solvent environments. The investigated 1,2 squaraines have been found to possess two excited triplet states (T₁ and T₂) that lie below the energy of the excited singlet one (S₁). The radiationless intersystem spin crossing efficiency is thus enhanced in both the studied systems and both the transitions could contribute to the excited singlet oxygen production. Moreover, they have a singlet‐triplet energy gap higher than that required to generate the cytotoxic singlet oxygen species. According to our data, these compounds could be used in photodynamic therapy applications that do not require high tissue penetration. © 2014 Wiley Periodicals, Inc.     

Relationship between orbital energy gaps and excitation energies for long‐chain systems

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time‐dependent (TD) density functional theory (DFT) for long‐chain systems: all‐trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long‐range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two‐electron interactions between occupied and unoccupied orbitals through the Coulomb‐exchange‐correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long‐range exchange interactions are involved. Spin‐flip (SF) TDDFT calculations are then carried out to clarify double‐excitation effects in these excitation energies. The calculated SF‐TDDFT results indicate that double‐excitation effects significantly contribute to the excitations of long‐chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP–EA) values and the HOMO–LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least‐square fits to estimate the exciton binding energy of infinitely long systems. It is found that long‐range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long‐range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long‐chain systems, while double‐excitation correlation effects are also significant to hold the energy balance of the excitations. © 2016 Wiley Periodicals, Inc.     

Long‐range interactions in embedded ionic cluster calculations

The effect of long‐range Coulomb interactions on bulk properties is studied for the ionic solids NaBr and NaCl. The embedded cluster approach in the framework of density functional theory is employed. The Madelung potential is calculated with the Evjen cube summation method. To explore the effects of the long‐range interactions on the electron densities and the Madelung constant, the Evjen cube size is varied from 310 to 19650 point charges for 33 atom clusters. To study the size effect of the quantum region, all‐electron clusters with 33 to 87 atoms, embedded in Evjen cubes of 6859 point charges, are investigated. The results show that for the 81 and 87 atom clusters the Madelung potential is constant from the center up to the second neighbor shell. For the same atoms, in all clusters, the electron density at the nuclei has nearly the same value. The largest difference found for the positive ions was 0.54%, and for the negative ions, 0.14%. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Selective J‐resolved‐HMQC‐1 and ‐2, new methods for measuring proton–proton coupling constants in strongly coupled spin systems

Efficient pulse sequences for measuring ¹H–¹H coupling constants (J_HH) in strongly coupled spin systems, named selective J‐resolved‐HMQC‐1 and ‐2, have been developed. In the strongly coupled spin systems such as ‐CH₂‐CH_A(OH)‐CH_B(OH)‐CH₂‐, measurements of ³J_HAHB are generally difficult owing to the complicated splitting caused by the adjacent CH₂ protons. For easier and accurate measurements of ³J_HAHB in such a spin system, a selective excitation pulse is incorporated into the J‐resolved HMQC pulse sequence. In the proposed methods, only two strongly coupled protons, H_A and H_B which are excited by a selective pulse, are observed as J‐resolved HMQC signals. The cross peaks of H_A and H_B appear as doublets owing to ³J_HAHB along the F₁ dimension in the selective J‐resolved HMQC‐1 and ‐2 experiments. The efficiency of the proposed pulse sequences has been demonstrated in application to the stereochemical studies of the complicated natural product, monazomycin. Copyright © 2011 John Wiley & Sons, Ltd.     

Slow relaxation of longitudinal multispin orders in weakly and strongly coupled two‐spin systems

Longitudinal multispin order (LOMO) corresponds to a nonequilibrium population distribution in spin systems that exhibit scalar (J), dipolar, or quadrupolar coupling. We investigated the relaxation of longitudinal two‐spin order (2‐LOMO) in systems that had either weakly or strongly J‐coupled spins. Our results indicated longer relaxation times for the 2‐LOMO state compared with the corresponding longitudinal single‐spin state (1‐LOMO). Accessing nuclear spin states that have relaxation times longer than T₁, without the use of external contrast agents, is potentially useful for in vivo imaging and also for studying systems using dynamically hyperpolarized nuclear spins where longer life times are sought to increase the time available to study (bio)chemical events. Copyright © 2012 John Wiley & Sons, Ltd.     

Natural bond orbital‐based energy density analysis for correlated methods: Second‐order Møller–Plesset perturbation and coupled‐cluster singles and doubles

Natural bond orbital‐based energy density analysis (NBO‐EDA), which split energies into atomic and bonding contributions, is proposed for correlated methods such as coupled‐cluster singles and doubles (CCSD) and second‐order Møller–Plesset (MP2) perturbation. Applying NBO‐EDA for CCSD and MP2 to ethylene and the Diels–Alder reaction, we are successful in obtaining useful knowledge regarding electron correlation of π‐ and σ‐type orbitals, and clarifying the difference of the reaction barriers and heat of reaction calculated by CCSD and MP2. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Interesting properties of Thomas–Fermi kinetic and Parr electron–electron‐repulsion DFT energy functional generated compact one‐electron density approximation for ground‐state electronic energy of molecular systems

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N‐dimensions to a (nonlinear, approximate) density functional of three spatial dimension one‐electron density for an N‐electron system, which is tractable in the practice, is a long desired goal in electronic structure calculation. If the Thomas‐Fermi kinetic energy (～∫ρ^5/3d r ₁) and Parr electron–electron repulsion energy (～∫ρ^4/3d r ₁) main‐term functionals are accepted, and they should, the later described, compact one‐electron density approximation for calculating ground state electronic energy from the 2nd Hohenberg–Kohn theorem is also noticeable, because it is a certain consequence of the aforementioned two basic functionals. Its two parameters have been fitted to neutral and ionic atoms, which are transferable to molecules when one uses it for estimating ground‐state electronic energy. The convergence is proportional to the number of nuclei (M) needing low disc space usage and numerical integration. Its properties are discussed and compared with known ab initio methods, and for energy differences (here atomic ionization potentials) it is comparable or sometimes gives better result than those. It does not reach the chemical accuracy for total electronic energy, but beside its amusing simplicity, it is interesting in theoretical point of view, and can serve as generator function for more accurate one‐electron density models. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009