Long‐range corrected density functionals combined with local response dispersion: A promising method for weak interactions

Density functional theory, in general, is considered to underestimate the weak van der Waals type of intermolecular interactions. We optimized parameters of the local response dispersion (LRD) method applied to the long‐range corrected exchange‐correlation functionals (LC‐BOP12+LRD and LCgau‐BOP+LRD) on the interaction energy for the complexes in the recently compiled S66 database and found to be comparable with the high‐level wave function‐based methods reported in ?ezá? et al. (J. Chem. Theory Comput. 2011 , 7, 2427). Our calculations with the S66 intermolecular complexes at equilibrium geometries suggests that the LC‐BOP12+LRD and LCgau‐BOP+LRD are well‐balanced and lower cost alternatives to the methods reported in the database. Further, test on the S66X8 database (with eight nonequilibrium points) and the HBC6 and NBC10 database shows LC+LRD method with newly optimized parameters is a promising candidate for dealing such weak interactions. Finally, the new parameterized LC+LRD method was tested on X40 benchmark halogenated complexes.Copyright © 2013 Wiley Periodicals, Inc.     

Long‐range 19F–15N heteronuclear shift correlation: examination of J‐modulations associated with broad range accordion excitation

The first demonstrated example of ¹⁹F–¹⁵N long‐range heteronuclear shift correlation spectroscopy at natural abundance is reported. Because of the very large variation in the size of ²J(N,F) vs ³J(N,F) long‐range heteronuclear couplings, the utilization of one of the new accordion‐optimized long‐range heteronuclear shift correlations experiments is essential if all possible correlations are to be observed in a single experiment. A modified IMPEACH‐MBC pulse sequence was used in conjunction with an optimization range from 4 to 50 Hz to demonstrate the technique using a mixture of 2‐ and 3‐fluoropyridine, which had ²J(N,F) and ³J(N,F) long‐range couplings of ?52 and 3.6 Hz, respectively. Because of the size of the ²J(N,F) long‐range coupling constant, a J‐modulation of the long‐range correlation response is observed in the spectrum resulting in a ‘doublet’ in F₁ due to amplitude modulation. The size of the ‘doublet’ is shown to be a function of the parameter selection (t_1max,T_max,T_min and spectral width in F₁). This behavior is similar to F₁ ‘skew’ associated with long‐range correlation responses in ACCORD‐HMBC spectra which has been analyzed in detail previously. Copyright © 2002 John Wiley & Sons, Ltd.     

Link between the kinetic‐ and exchange‐energy functionals in the generalized gradient approximation

An approximate kinetic‐energy functional of the generalized gradient approximation form was derived following the “conjointness conjecture” of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange‐energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed‐shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic‐energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

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     

Clusters of hydrogen molecules: Ab initio SCF calculations corrected semiempirically for correlation energies

Stabilization energy of the (H₂) _n clusters (n = 2–8) was calculated as a sum of the SCF interaction energy and the semiempirical interaction correlation energy estimated according to Sinanolu and Pamuk. Optimum successive attachment of hydrogen molecules leads to the formation of a gas-phase solvation shell consisting of seven hydrogen molecules. Basis set effect has been found to be important with all clusters under study. The non-additivity effect was investigated with the (H₂)₄ cluster. Vertical ionization potentials of the clusters considered are predicted to be 0.4–0.6 eV lower than the ionization potential of the parent H₂ molecule.     

Refractive indices of organo‐metallic and ‐metalloid compounds: A long‐range corrected DFT study

Refractive indices of metal‐ and metalloid‐containing compounds are systematically evaluated using the Lorentz–Lorenz equation with polarizabilities obtained via density functional theory (DFT). Among exchange‐correlation functionals studied, the long‐range corrected (LC) fuctionals yield the lowest errors for the polarizabilities of gaseous compounds and refractive indices of liquids. The LC‐DFT predicts very well the wavelength dependence of refractive indices. A scheme for computing Abbe numbers of organometallic and organometaloid compounds is proposed and a refractive index – Abbe number plot for 80 compounds is constructed. The compounds containing heavier metals tend to have higher refractive index and lower Abbe number, but several outliers, among them Te(CH₃)₂, Ni(PF₃)₄, Sb(C₂F₃)₃, Hg(C₂F₃)₂, are found. For Hg(C₂F₃)₂, also the effect of intramolecular and intermolecular degrees of freedom on polarizability is investigated. The absolute relative error in polarizability decreases from 5.7% for monomer model to 1.7% when a dimer model (derived from the available experimental crystal data) is employed. © 2016 Wiley Periodicals, Inc.     

Molecular dynamics in ion‐irradiated poly(ether ether ketone) investigated by two‐dimensional correlation dielectric relaxation spectroscopy

This paper reports the first use of temperature–temperature 2D correlation dielectric relaxation spectroscopy (2D COS‐DRS) to study the molecular relaxation dynamics in ion‐irradiated poly(ether ether ketone) (PEEK). With the help of the high resolution and high sensitivity of 2D COS‐DRS, it was possible to locate the position of the motion of water molecules in the dielectric spectrum of PEEK. This occurred at −20°C and increased in intensity on increasing water contents. On irradiation, a new relaxation was observed at −75°C and −85°C for proton and helium ion‐irradiated samples, respectively. This increased in intensity on increasing radiation dose and was assigned to main‐chain phenyl motions of the cross‐linked units of the polymer. 2D COS‐DRS was also successfully applied to resolve the overlap in molecular events in the region of glass transition. Three processes that change in different directions with respect to ion irradiation dose were identified. These were at 160°C, 175°C, and 240°C and were assigned to the α relaxation, second α relaxation, and the onset of conductivity, respectively. In addition, hybrid 2D COS‐DRS was used to investigate the effect of the so‐called linear energy transfer effect, and the results showed that helium ions were more effective in cross‐linking PEEK. Copyright © 2013 John Wiley & Sons, Ltd.     

Energy and capacity time correlation functions for investigation of vibrational energy relaxation

Vibrational energy relaxation of a diatomic solute in a liquid solvent is investigated by means of the generalized Langevin equation. The vibrational energy, velocity and capacity time correlation functions (TCFs) are considered. It is shown that the detailed structure of the energy TCF contains an initial fast (subpicosecond) decay segment that is followed by weak oscillations on the background of an exponential relaxation curve. The direct method for evaluating the relaxation rate constant from equilibrium molecular dynamics simulations of a flexible solute is proposed and implemented. The closed form expressions for the memory function and for the relaxation rate constant in terms of quantities accessible from the simulations are derived. The simulation results for rigid and flexible solutes are compared and analyzed.     

Scaling factors for vibrational frequencies and zero-point vibrational energies of some recently developed exchange-correlation functionals

The scaling factors for the vibrational frequencies and zero-point vibrational energies evaluated at various combinations of recently developed exchange-correlation functionals and various basis sets are reported. The exchange-correlation functionals considered are B972, B98, HCTH, OLYP, O3LYP, G96LYP, PBE0 and VSXC functionals; the basis sets employed are 3-21G, 6-31G*, 6-31G**, 6-31+G, 6-311G*, 6-311G**, 6-311G(df,p), 6-311+G(df,p), cc-pVDZ and aug-cc-pVDZ. The experimental harmonic frequencies of 122 small molecules and the zero-point vibrational energies of 39 small molecules are used to determine the scaling factors through the least-square fitting procedure. It was found that the scaling factors do not depend significantly on the basis sets considered. The vibrational frequency scaling factors evaluated by using the B98 and PBE0 functionals are recommended on the basis of smallest root mean square error. The zero-point vibrational energy scaling factors evaluated from the B972 functional with Pople's double-zeta basis set and the HCTH functional with Pople's triple-zeta basis set are recommended on the basis of smallest root mean square error.     

Correlation energy,correlated electron density,and exchange‐correlation potential in some spherically confined atoms

We report correlation energies, electron densities, and exchange‐correlation potentials obtained from configuration interaction and density functional calculations on spherically confined He, Be, Be²⁺, and Ne atoms. The variation of the correlation energy with the confinement radius R_c is relatively small for the He, Be²⁺, and Ne systems. Curiously, the Lee–Yang–Parr (LYP) functional works well for weak confinements but fails completely for small R_c. However, in the neutral beryllium atom the CI correlation energy increases markedly with decreasing R_c. This effect is less pronounced at the density‐functional theory level. The LYP functional performs very well for the unconfined Be atom, but fails badly for small R_c. The standard exchange‐correlation potentials exhibit significant deviation from the “exact” potential obtained by inversion of Kohn–Sham equation. The LYP correlation potential behaves erratically at strong confinements. © 2016 Wiley Periodicals, Inc.     

Performance of DFT hybrid functionals in the theoretical treatment of H‐bonds: Analysis term‐by‐term

The performance of DFT to reproduce noncovalent interactions like H‐bonds was assessed. Three DFT hybrid functionals (B3LYP, BHandHLYP from Jaguar5.5, and BHandHLYP from G03) were used to calculate the interaction energies and H‐bond distances of several host–guest complexes theoretically designed. Two reference systems (whose experimental data were available) were also calculated at the same levels of theory. In all the cases B3LYP and BHandHLYP from G03 gave rather the same results of interaction energy and distances, whereas the functional BHandHLYP from Jaguar5.5 overestimated the interaction energies and underestimated the H‐bond distances. Considering the construction of each functional, the terms responsible for such differences are the gradient correction to the exchange functional (Becke88) and the correlation functional (VWN, LYP) and not the Hartree–Fock contribution. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Assessment of dispersion‐improved exchange‐correlation functionals for the simulation of CO2 binding by alcoholamines

In this study, 12 bound complexes were selected to construct a database for testing 15 dispersion‐improved exchange‐correlation (XC) functionals, including hybrid generalized gradient approximation (GGA), modified using the Grimme's pairwise strategy, and double hybrid XC functionals, for specifically characterizing the CO₂ binding by alcoholamines. Bound complexes were selected based on the characteristics of their hydrogen bonds, dispersion, and electrostatic (particularly between the positive charge of CO₂ and the lone pair of N of alcoholamines) interactions. The extrapolated binding energy from the aug‐cc‐pVTZ (ATZ) to aug‐cc‐pVQZ (AQZ) basis set at the CCSD(T)/CBS(MP2+DZ) level was used as the reference for the XC functional comparison. M06‐2X produced the optimal agreement if the optimized geometries at MP2/ATZ level were chosen for all the test bound complexes. However, M06‐L, ωB97X, and ωB97, and were preferred if the corresponding density functional theory (DFT) optimized geometries were adapted for the benchmark. Simple bimolecular reaction between CO₂ and monoethanolamine simulated using polarizable continuum solvation model confirmed that ωB97, ωB97X, and ωB97XD qualitatively reproduced the energetics of MP2 level. The inconsistent performance of the tested XC functionals, observed when using MP2 or DFT optimized geometries, raised concerns regarding using the single‐point ab initio correction combined with DFT optimized geometry, particularly for determining the nucleophilic attack by alcoholamines to CO₂. © 2014 Wiley Periodicals, Inc.     

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.     

Enhanced second‐order treatment of electron pair correlation

Ab initio calculations have been performed for F₂, HCCH, H₂O, HF, (HF)₂, and (H₂O)₂, comparing certain electron pair correlation methods, or methods for doubly substituted configurations. In these model systems, the reweighting of substituted configurations that occurs beyond a second‐order perturbative treatment of electron correlation can be partly built into the second‐order analysis in a computationally trivial step. Specific means for doing this are explored, and they offer improvement in certain cases or else very little change. A consistent improvement in the correlation energy when judged against treatment with double substitution coupled cluster theory for the test species is obtained through one of these schemes. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 226–236, 2000     

Carbondioxide rare‐gas systems: Sensitivity of basis sets and double‐hybrid density functionals

This study emphasizes on the performance of six newly developed double‐hybrid density functionals (DHDF) in explaining the potential energy curves of different carbondioxide rare‐gas systems. The basis set sensitivity has also been explored with the use of three basis sets. Our results suggest that for lighter He/Ne‐CO₂ complexes, proper choice of DHDF and basis set lead to results those matches exactly with earlier calculations and also with the experiment. On the other hand, for heavier Ar/Kr‐CO₂ complexes although the equilibrium separation distance matches exactly with earlier observations, the interaction energy values lie far apart. The overall investigation emphasizes on the fact that one has to tune the methods and basis sets properly to achieve good and satisfactory results. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Toward the complete range separation of non‐hybrid exchange–correlation functional

In this study, we use a very simple scheme to achieve range separation of a total exchange–correlation functional. We have utilized this methodology to combine a short‐range pure density functional theory (DFT) functional with a corresponding long‐range pure DFT, leading to a “Range‐separated eXchange–Correlation” (RXC) scheme. By examining the performance of a range of standard exchange–correlation functionals for prototypical short‐ and long‐range properties, we have chosen B‐LYP as the short‐range functional and PBE‐B95 as the long‐range counterpart. The results of our testing using a more diverse range of data sets show that, for properties that we deem to be short‐range in nature, the performance of this prescribed RXC‐DFT protocol does resemble that of B‐LYP in most cases, and vice versa. Thus, this RXC‐DFT protocol already provides meaningful numerical results. Furthermore, we envisage that the general RXC scheme can be easily implemented in computational chemistry software packages. This study paves a way for further refinement of such a range‐separation technique for the development of better performing DFT procedures. © 2015 Wiley Periodicals, Inc.     

Harmonic vibrational frequencies: scale factors for pure, hybrid, hybrid meta, and double-hybrid functionals in conjunction with correlation consistent basis sets

Scale factors for (a) low (<1000 cm(-1)) and high harmonic vibrational frequencies, (b) thermal contributions to enthalpy and entropy, and (c) zero-point vibrational energies have been determined for five hybrid functionals (B3P86, B3PW91, PBE1PBE, BH&HLYP, MPW1K), five pure functionals (BLYP, BPW91, PBEPBE, HCTH93, and BP86), four hybrid meta functionals (M05, M05-2X, M06, and M06-2X) and one double-hybrid functional (B2GP-PLYP) in combination with the correlation consistent basis sets [cc-pVnZ and aug-cc-pVnZ, n = D(2),T(3),Q(4)]. Calculations for vibrational frequencies were carried out on 41 organic molecules and an additional set of 22 small molecules was used for the zero-point vibrational energy scale factors. Before scaling, approximately 25% of the calculated frequencies were within 3% of experimental frequencies. Upon application of the derived scale factors, nearly 90% of the calculated frequencies deviated less than 3% from the experimental frequencies for all of the functionals when the augmented correlation consistent basis sets were used.     

Hadamard Homonuclear Broadband Decoupled TOCSY NMR: Improved Efficacy in Detecting Long‐range Chemical Shift Correlations

The importance of Hadamard encoding pulses in one‐dimensional pure shift yielded by the chirp excitation version of selective total correlation spectroscopy (1D PSYCHE–TOCSY) experiments is discussed for chemical‐shift analysis of complex natural products at ultrahigh resolution. Herein, we adapted H_n Hadamard matrices to 1D PSYCHE–TOCSY and observed an overall circa square root of n‐fold enhancement in the signal‐to‐noise (S/N) ratio when compared to conventional 1D PSYCHE–TOCSY recorded by refocusing only one spin at a time. This enhancement in S/N facilitates the observation of very weak long‐range chemical‐shift correlations from Hadamard‐encoded PSYCHE–TOCSY (HE–PSYCHE–TOCSY). The proposed method will have a significant impact on structure determination of complex isolated/ synthetic natural products.