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.     

The exact Fermi potential yielding the Hartree–Fock electron density from orbital‐free density functional theory

The exact expression for the Fermi potential yielding the Hartree–Fock electron density within an orbital‐free density functional formalism is derived. The Fermi potential, which is defined as that part of the potential that depends on the particles’ nature, is in this context given as the sum of the Pauli potential and the exchange potential. The exact exchange potential for an orbital‐free density functional formalism is shown to be the Slater potential.     

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.     

A semiempirical long-range corrected exchange correlation functional including a short-range Gaussian attenuation (LCgau-B97)

We applied an improved long‐range correction scheme including a short‐range Gaussian attenuation (LCgau) to the Becke97 (B97) exchange correlation functional. In the optimization of LCgau‐B97 functional, the linear parameters are determined by least squares fitting. Optimizing μ parameter (0.2) that controls long‐range portion of Hartree‐Fock (HF) exchange to excitation energies of large molecules (Chai and Head‐Gordon, J Chem Phys 2008, 128, 084106) and additional short‐range Gaussian parameters (a = 0.15 and k = 0.9) that controls HF exchange inclusion ranging from short‐range to mid‐range (0.5–3 Å) to ground state properties achieved high performances of LCgau‐B97 simultaneously on both ground state and excited state properties, which is better than other tested semiempirical density functional theory (DFT) functionals, such as ωB97, ωB97X, BMK, and M0x‐family. We also found that while a small μ value (～0.2) in LC‐DFT is appropriate to the local excitation and intramolecular charge‐transfer excitation energies, a larger μ value (0.42) is desirable in the Rydberg excitation‐energy calculations. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Accurate potential energy surfaces for hydrogen abstraction reactions: A benchmark study on the XYG3 doubly hybrid density functional

The potential energy surface (PES) for the H + CH₄ system has been constructed with the recently developed XYG3 doubly hybrid functional, while those with the standard B3LYP hybrid functional, and the Møller–Plesset perturbation theory up to the second order (MP2) are also presented for comparison. Quantum dynamics studies demonstrated that satisfactory results on the reaction probabilities and the rate coefficients can be obtained on top of the XYG3‐PES, as compared to the results based on the highly accurate, yet expensive, CCSD(T)‐PES (Li et al., J. Chem. Phys. 2015, 142, 204302). Further investigation suggested that the XYG3 functional is useful in providing accurate rate coefficients for some larger systems involving H atom abstractions. © 2017 Wiley Periodicals, Inc.     

A density functional theory study on the Diels‐Alder reactions with vinylallenes as dienes

The Diels‐Alder (DA) reactions of vinylallenes (VA) with ethylenes were investigated using the global electrophilicity and nucleophilicity of the corresponding reactants as global reactivity indexes defined within the conceptual density functional theory. The reactivity and regioselectivity of these reactions were predicted by analysis of the energies, geometries, and electronic nature of the transition‐state structures. In general, substitution by the electron‐accepting acetyl group favors the reaction, whereas substitution by the electron‐releasing methoxy group provides the opposite effect, regardless of being on VA or ethylene. However, the substitution effect in ethylene is apparently greater than that in VA. It has also been disclosed that substitution by electron‐accepting group on both reactants accelerates the reaction, and the reaction may give different regioselectivity from that between VA and acetyl‐substituted ethylene. This has also been verified by our experiments. It seems that the DA reactions with VAs as the diene components can generally be classified as nonpolar asynchronous with the endo product formation (wherever possible) being more pronounced. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Excited states of OsO4: A comprehensive time‐dependent relativistic density functional theory study

A large number of scalar as well as spinor excited states of OsO₄, in the experimentally accessible energy range of 3–11 eV, have been captured by time‐dependent relativistic density functional linear response theory based on an exact two‐component Hamiltonian resulting from the symmetrized elimination of the small component. The results are grossly in good agreement with those by the singles and doubles coupled‐cluster linear response theory in conjunction with relativistic effective core potentials. The simulated‐excitation spectrum is also in line with the available experiment. Furthermore, combined with detailed analysis of the excited states, the nature of the observed optical transitions is clearly elucidated. It is found that a few scalar states of ³T₁ and ³T₂ symmetries are split significantly by the spin‐orbit coupling. The possible source for the substantial spin‐orbit splittings of ligand molecular orbitals is carefully examined, leading to a new interpretation on the primary valence photoelectron ionization spectrum of OsO₄. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Regional self-interaction correction of density functional theory

We propose a new simple scheme for self-interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self-interactions for exchange functionals in regions of self-interaction. To classify the regions of self-interaction, we take advantage of the property of the total kinetic energy density approaching the Weizs?cker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional "pure" functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals.     

A solvation‐free‐energy functional: A reference‐modified density functional formulation

The three‐dimensional reference interaction site model (3D‐RISM) theory, which is one of the most applicable integral equation theories for molecular liquids, overestimates the absolute values of solvation‐free‐energy (SFE) for large solute molecules in water. To improve the free‐energy density functional for the SFE of solute molecules, we propose a reference‐modified density functional theory (RMDFT) that is a general theoretical approach to construct the free‐energy density functional systematically. In the RMDFT formulation, hard‐sphere (HS) fluids are introduced as the reference system instead of an ideal polyatomic molecular gas, which has been regarded as the appropriate reference system of the interaction‐site‐model density functional theory for polyatomic molecular fluids. We show that using RMDFT with a reference HS system can significantly improve the absolute values of the SFE for a set of neutral amino acid side‐chain analogues as well as for 504 small organic molecules. © 2015 Wiley Periodicals, Inc.     

Dissociation constants of 2‐azidoethanamines in aqueous solution

Aqueous‐phase dissociation constants (K_a) for the conjugate acids of a series of 2‐azidoethanamine bases: R¹N(R²)CH₂CH₂N₃ ( 1 , R¹ = CH₃, R² = H; 2 , R¹ = CH₃, R² = CH₃; 3 , R¹ = CH₂CH₃, R² = CH₂CH₃; 4 , R¹/R² =  CH₂CH₂CH₂CH₂ ; 5 , R¹/R² =  CH₂CH₂OCH₂CH₂ ; 6 , R¹ = CH₂CH₃, R² = CH₂CH₂N₃) were measured and found to fall between those for analogous unfunctionalized and cyano‐functionalized ethanamines. To explore the possibility of a relationship existing between the constants and molecular geometry, a theoretically based study was conducted. In it, the Gibbs free energies of aqueous‐phase (equilibrium) conformers of the bases and their conjugate acids were determined via a density functional theory/polarizable continuum model method. The results indicate that an attractive interaction between the amine and azide groups that underlies the lowest‐energy gas‐phase conformer of 2 is negated in an aqueous environment by solvent–solute interactions. The magnitudes of the free energy changes of solvation and −TS (entropic) energies of the conformers of the 2‐azidoethanamines and their conjugate acids are observed to correlate with the magnitude of the separation between the conformers' amine and azide groups. However, those correlations are not by themselves sufficient to predict the relative free energies of a molecule's conformers in an aqueous environment. That insufficiency is due to the influence of the correlations being mitigated by three other parameters that arise within the thermodynamic framework employed to compute the observable. The nature of those parameters is discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Novel method of self‐interaction corrections in density functional calculations

It is demonstrated that the commonly applied self‐interaction correction (SIC) used in density functional theory does not remove all self‐interaction. We present as an alternative a novel method that, by construction, is totally free from self‐interaction. The method has the correct asymptotic 1/r dependence. We apply the new theory to localized f electrons in praseodymium and compare with the old version of SIC, the local density approximation (LDA) and with an atomic Hartree–Fock calculation. The results show a lowering of the f level, a contraction of the f electron cloud and a lowering of the total energy by 13 eV per 4 f electron compared to LDA. The equilibrium volume of the new SIC method is close to the ones given by LDA and the older SIC method and is in good agreement with experiment. The experimental cohesive energy is in better agreement using the new SIC method, both compared to LDA and another SIC method. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 247–252, 2001     

Fully ab initio protein‐ligand interaction energies with dispersion corrected density functional theory

Dispersion corrected density functional theory (DFT‐D3) is used for fully ab initio protein‐ligand (PL) interaction energy calculation via molecular fractionation with conjugated caps (MFCC) and applied to PL complexes from the PDB comprising 3680, 1798, and 1060 atoms. Molecular fragments with n amino acids instead of one in the original MFCC approach are considered, thereby allowing for estimating the three‐body and higher many‐body terms. n > 1 is recommended both in terms of accuracy and efficiency of MFCC. For neutral protein side‐chains, the computed PL interaction energy is visibly independent of the fragment length n. The MFCC fractionation error is determined by comparison to a full‐system calculation for the 1060 atoms containing PL complex. For charged amino acid side‐chains, the variation of the MFCC result with n is increased. For these systems, using a continuum solvation model with a dielectricity constant typical for protein environments (? = 4) reduces both the variation with n and improves the stability of the DFT calculations considerably. The PL interaction energies for two typical complexes obtained ab initio for the first time are found to be rather large (?30 and ?54 kcal/mol). © 2012 Wiley Periodicals, Inc.     

A density functional theory study on the catalytic mechanism of hydroxycinnamoyl‐CoA hydratase‐lyase

Hydroxycinnamoyl‐CoA hydratase‐lyase (HCHL), a particular member of the crotonase superfamily, catalyzes the bioconversion of feruloyl‐CoA to the important flavor and fragrance compound vanillin. In this article, the catalytic mechanism of HCHL has been studied by using hybrid density functional theory method with simplified models. The calculated results reveal that the mechanism involves the hydration of the C?C double bond of feruloyl‐CoA and thence the cleavage of C? C single bond of β‐hydroxythioester. The hydration step is a typical concerted process, whereas C? C bond cleavage follows a concerted but asynchronous mechanism. The calculated energy barrier of hydration reaction is only slightly lower than that of cleavage process, implying both of two processes are rate limiting. By using three substrate analogs, the substrate specificity of HCHL was further examined. It is found that the p‐hydroxyl group of aromatic ring is necessary for the catalytic reaction. © 2013 Wiley Periodicals, Inc.     

A density functional theory study on diazotization and nitration of 3,5‐diamino‐1,2,4‐triazole

The reaction mechanism, thermodynamic and kinetic properties for diazotization and nitration of 3,5‐diamino‐1,2,4‐triazole were studied by a density functional theory. The geometries of the reactants, transition states, and intermediates were optimized at the B3LYP/6‐31G (d, p) level. Vibrational analysis was carried out to confirm the transition state structures, and the intrinsic reaction coordinate (IRC) method was used to explore the minimum energy path. The single‐point energies of all stagnation points were further calculated at the B3LYP (MP2)/6‐311+G (2d, p) level. The statistical thermodynamic method and Eyring transition state theory with Wigner correction were used to study the thermodynamic and kinetic characters of all reactions within 0–25°C. Two reaction channels are computed, including the diazotization and nitration of 3‐NH₂ or 5‐NH₂, and there are six steps in each channel. The reaction rate in each step is increased with temperature. The last step in each channel is the slowest step. The first, second, and fifth steps are exothermic reactions, and are favored at lower temperature in the thermodynamics. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Density functional study of the conformers of Co4‐based single‐molecule magnet

We present a detailed density functional theory‐based investigation on the geometry and electronic structure of the [Co₄(hmp)₄(MeOH)₄Cl₄] molecule. It is experimentally found to behave as a molecular magnet. The all‐electron electronic structure calculations and geometry optimization of the 88‐atom molecule were carried out within the generalized gradient approximation to the exchange correlation energy. We also study the electronic structures and geometries of a few low‐lying conformers of this molecule. It is found that the magnetic anisotropy energy is highly sensitive to the geometric structure of the molecule. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 324–331, 2003     

Applications of density functional theory methods in millimeter‐wave spectroscopy

Density functional theory (DFT), using the most common functionals, and ab initio quantum chemistry methods are used to calculate the rotational constants and dipole moments of the astrophysically important molecules HCN, CH₃CN, CH₃CNH⁺, HCCCN, and HCCNC. As far as millimeter‐wave spectroscopy is of interest the DFT methods performed well with most functionals, giving results within ±1% of experiments for rotational constants and ±3% for dipole moments. Analyzing the results obtained with all theoretical models, it may be concluded that the Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three‐parameter functional with Perdew–Wang correlational functional [B3PW91/6‐31G(d, p)] give the best performances. A detailed analysis of the electron correlation effects shows that HCCCN is more stable than is HCCNC, by 1.16 eV, with important contribution arising from triple excitations. This result is also compared with those obtained with DFT methods. Despite occasional difficulties, DFT with the currently available functionals are of great utility in quickly assessing spectroscopic parameters of astrophysical interest. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

First‐order correlation‐kinetic contribution to Kohn–Sham exchange charge density function in atoms,using quantal density functional theory approach

Using the static exchange‐correlation charge density concept, the total integrated exchange‐charge density function is calculated within the nonrelativistic spin‐restricted exchange‐only (i) optimized effective potential model, and (ii) nonvariational local potential derived from the exchange‐only work potential within the quantal density functional theory, for the ground‐state isoelectronic series: Ga⁺, Zn, Cu^?; In⁺, Cd, Ag^?; and Tl⁺, Hg, Au^?. The difference between the exchange charge density function derived from these potentials is employed to evaluate the first‐order correlation‐kinetic contribution to the integrated exchange charge density. This contribution is found to be important for both the intra‐ and inter‐shell regions. Screening effects on the contribution due to the nd¹⁰ (n = 3–5) subshells are discussed through comparisons with similar calculations on Ca, Sr, and Ba, wherein nd¹⁰ electrons are absent. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005