Ab initio density functional theory: the best of both worlds?

Density functional theory (DFT), in its current local, gradient corrected, and hybrid implementations and their extensions, is approaching an impasse. To continue to progress toward the quality of results demanded by today's ab initio quantum chemistry encourages a new direction. We believe ab initio DFT is a promising route to pursue. Whereas conventional DFT cannot describe weak interactions, photoelectron spectra, or many potential energy surfaces, ab initio DFT, even in its initial, optimized effective potential, second-order many-body perturbation theory form [OEP (2)-semi canonical], is shown to do all well. In fact, we obtain accuracy that frequently exceeds MP2, being competitive with coupled-cluster theory in some cases. Furthermore, this is accomplished within a relatively fast computational procedure that scales like iterative second order. We illustrate our results with several molecular examples including Ne2,Be2,F2, and benzene.     

How to obtain accurate results with molecular iodine and density functional theory?

Molecular iodine is found in many organic synthetic methodologies, both as reagent and as catalyst. Naturally, many groups have carried out computational studies involving this element. However, the choice of computational method proves to be more challenging than for other non-metals. We quantify herein the errors that some common theory levels can introduce in terms of both structural and energetic deviations. We also evaluate multiple post hoc corrections, namely, vibrational entropy, dispersion, and counter-poise corrections. Our results indicate the triple- $$ basis sets are essential to obtain quality results and that post hoc corrections are overall detrimental.     

Phase-space relative Rényi entropy in density functional theory

The phase-space relative Rényi entropy is introduced using the information theoretical and thermodynamic view of density functional theory. In the special case of constant inverse temperature the phase-space relative Rényi entropy is a sum of the position-space relative Rényi entropy and a term arising from the momentum space. This quantity can be considered as a measure of similarity. It includes more information than the position-space measures, since it also incorporates momentum-space knowledge.     

Are electrophilicity and electrofugality related concepts? A density functional theory study

It is proposed that the electrofugality of a fragment within a molecule is determined by its group nucleophilicity. The variation of electrofugality should be tightly related to the electron releasing ability of the substituent attached to the electrofuge moiety. This contribution closes the set of relationships between philicity and fugality quantities: while nucleofugality appears related to the group electrophilicity of the leaving group, electrofugality is related to the group nucleophilicity of the permanent group.     

Application of capillary affinity electrophoresis and density functional theory to the investigation of valinomycin–lithium complex

Capillary affinity electrophoresis (CAE) and quantum mechanical density functional theory (DFT) have been applied to the investigation of interactions of valinomycin (Val), a macrocyclic dodecadepsipeptide antibiotic ionophore, with lithium cation Li⁺. Firstly, from the dependence of effective electrophoretic mobility of Val on the Li⁺ ion concentration in the background electrolyte (BGE) (methanolic solution of 50 mM chloroacetic acid, 25 mM Tris, pH_MeOH 7.8, 0–40 mM LiCl), the apparent binding (stability) constant (K_b) of Val–Li⁺ complex in methanol was evaluated as log K_b = 1.50 ± 0.24. The employed CAE method include correction of the effective mobilities measured at ambient temperature, at different input power (Joule heating) and at variable ionic strength of the BGEs to the mobilities related to the reference temperature 25 °C and to the constant ionic strength 25 mM. Secondly, using DFT calculations, the most probable structures of the non-hydrated Val–Li⁺ and hydrated Val–Li⁺·3H₂O complex species were predicted.     

Exchange kernel of density functional response theory from the common energy denominator approximation (CEDA) for the Kohn–Sham Green's function

A complete and explicit expression for the exchange kernel f _x of density functional response theory (DFRT) is derived in terms of the occupied Kohn-Sham (KS) orbitals _i. It is based on the common energy denominator approximation (CEDA) for the KS Green's function (O. V. Gritsenko and E. J. Baerends, Phys. Rev. A 64, 042506 (2001)). The kernel f _x ^CEDA is naturally subdivided into the Slater f _S ^CEDA and the 'response' f _resp ^CEDA parts, which are the derivatives of the Slater _S and response _resp potentials, respectively. While f _S ^CEDA is obtained with a straightforward differentiation of _S , some terms of f _resp ^CEDA are obtained from the solution of linear equations for the corresponding derivatives. All components of f _x ^CEDA are explicitly expressed in terms of the products _i ^* _j of the occupied KS orbitals taken at the positions r ₁ and r ₂, as well as the potentials of these products at r ₃. The coefficients in these expressions are obtained by inversion of the matrix, associated with the overlap matrix of the products _i ^* _j and _k ^* _l . Terms are indicated, which generate in an external electric field an ultra-nonlocal potential _x , counteracting an external field, and possible approximations to f _x ^CEDA are considered.     

Concurrent cyclopropanation by carbenes and carbanions? A density functional theory study on the reaction pathways

The mechanisms for the addition reactions of phenylhalocarbenes and phenyldihalomethide carbanions with acrylonitrile (ACN) and trimethylethylene (TME) have been investigated using an ab initio BH and HLYP/6-31G (d, p) level of theory. Solvent effects on these reactions have been explored by calculations that included a polarizable continuum model (PCM) for the solvent (THF). These model calculations show that for the addition of phenylhalocarbenes, a TME species may readily undergo addition reactions with carbenes while ACN has a high-energy barrier to overcome. It was also found that phenyldihalomethide carbanions do not readily add to the electron-rich TME. The cyclopropane yields only appear to occur via addition of PhCBr to TME. However, the cyclopropanation proceeds not only via slow addition of phenylhalocarbenes to ACN but also forms through the stepwise reaction of phenyldihalomethide carbanions with ACN. Our calculation results are in good agreement with experimental observations (Moss, R.A.; Tian, J.-Z. J. Am. Chem. Soc. 2005, 127, 8960) that indicate that the cyclopropanation of phenylhalocarbenes and phenyldihalomethide carbanions with ACN are concurrent in THF.     

Half or full core hole in density functional theory X-ray absorption spectrum calculations of water?

We analyze the performance of two different core-hole potentials in the theoretical modeling of XAS of ice, liquid and gas phase water; the use of a full core-hole (FCH) in the calculations, as suggested by Hetenyi et al. [B. Hetenyi, F. De Angelis, P. Giamozzi and R. Car, J. Chem. Phys., 2004, 120(18), 8632], gives poor agreement with experiment in terms of intensity distribution as well as transition energies, while the half core hole (HCH) potential, in the case of water, provides a better compromise between initial and final state effects, leading to good agreement with the experimental data.     

Molecular electronegativity in density functional theory (VI) --Atom-bond electronegativity equalization model

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A density functional theory study of the ��mythic�� Lindlar hydrogenation catalyst

A Lindlar catalyst is a popular heterogeneous catalyst that consists of 5?wt.% palladium supported on porous calcium carbonate and treated with various forms of lead and quinoline. The additives strategically deactivate palladium sites. The catalyst is widely used for the partial hydrogenation of acetylenic compounds in organic syntheses. Alkyne reduction is stereoselective, occurring via syn addition to give the cis-alkene. Even if it has been employed for about 60?years, there is a lack of molecular level understanding of the Lindlar catalyst. We have applied density functional theory simulations to understand the structure and the nature of the interplay between the multiple chemical modifiers in the Lindlar catalyst. Indeed, the poisons influence different parameters controlling selectivity to the alkene: Pb modifies the thermodynamic factor and hinders the formation of hydrides, while quinoline isolates Pd sites thus minimizing oligomerization.     

How accurate is the density functional theory combined with symmetry-adapted perturbation theory approach for CH-pi and pi-pi interactions? A comparison to supermolecular calculations for the acetylene-benzene dimer

Five different orientations of the acetylene-benzene dimer including the T-shaped global minimum structure are used to assess the accuracy of the density functional theory combined with symmetry adapted perturbation theory (DFT-SAPT) approach in its density-fitting implementation (DF-DFT-SAPT) for the study of CH-pi and pi-pi interactions. The results are compared with the outcome of counterpoise corrected supermolecular calculations employing second-order M?ller-Plesset (MP2), spin-component scaled MP2 (SCS-MP2) and single and double excitation coupled cluster theory including perturbative triple excitations (CCSD(T)). For all considered orientations MP2 predicts much deeper potential energy curves with considerably shifted minima compared to CCSD(T) and DFT-SAPT. In spite of being an improvement over the results of MP2, SCS-MP2 tends to underestimate the well depth while DFT-SAPT, employing an asymptotically corrected hybrid exchange-correlation potential in conjunction with the adiabatic local density approximation for the exchange-correlation kernel, is found to be in excellent agreement with CCSD(T). Furthermore, DFT-SAPT provides a detailed understanding of the importance of the electrostatic, induction and dispersion contributions to the total interaction energy and their repulsive exchange corrections.     

Intermolecular potentials of the methane dimer calculated with Møller-Plesset perturbation theory and density functional theory

We have calculated the intermolecular interaction potentials of the methane dimer at the minimum-energy D(3d) conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order M?ller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with the Perdew-Wang (PW91) functional as the exchange or the correlation part. The HF calculations yield unbound potentials largely due to the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater-type orbitals fitted with Gaussian functions (STO-nG) (n=3-6) [Quantum Theory of Molecular and Solids: The Self-Consistent Field for Molecular and Solids (McGraw-Hill, New York, 1974), Vol. 4], Pople's medium size basis sets of Krishnan et al. [J. Chem. Phys. 72, 650 (1980)] [up to 6-311++G(3df,3pd)] to Dunning's correlation consistent basis sets [J. Chem. Phys. 90, 1007 (1989)] (cc-pVXZ and aug-cc-pVXZ) (X=D, T, and Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(2d,2p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy (approximately 0.01 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the destined C6 value from molecular polarizability calculations. The slow convergence could indicate the inefficacy of using the MP2 calculations with Gaussian-type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the destined potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energy calculated using the PW91PW91 functional and the equilibrium bond length calculated using the PW91VP86 functional are close to the MP2 results at the basis set limit.     

A profound density functional theory study to unravel the spectroscopic and molecular properties of two Flavanols differing in α-pyrone ring position

A comprehensive theoretical model was designed for two new flavanols that have been reported from Glycosmis pentaphylla, differing in the placement of α-pyrone ring. The density functional theory (DFT) approach was utilized for computing different properties of these compounds to validate the experimental findings and stereochemical assignments. Electronic properties, geometric parameters, frontier molecular orbitals (FMOs), molecular electrostatic potential (MESP), and natural bond orbital analysis were performed for the first time at the PBE0-D3BJ/def2-TZVP level of theory for the compounds under study. The simulated vibrational frequencies for compounds 1 and 2 were computed and compared with the experimental results. nuclear magnetic resonance (NMR) (¹H and ¹³C) chemical shift values were computed at the PBE0-D3BJ/def2-TZVP/SMD_DMSO level of theory and showed a very good agreement with the experimental results for both the compounds. The electronic circular dichroism (ECD) and ultraviolet–visible (UV) spectra for both the compounds were obtained using time-dependent DFT in methanol, whose results exhibited excellent correlation with experimental data. The intermolecular interaction effect on geometric parameters, vibrational frequencies, and electronic properties were studied for the first time.     

Evaluation of potential reaction mechanisms leading to the formation of coniferyl alcohol α-linkages in lignin: a density functional theory study

Five potential reaction mechanisms, each leading to the formation of an α-O-4-linked coniferyl alcohol dimer, and one scheme leading to the formation of a recently proposed free-radical coniferyl alcohol trimer were assessed using density functional theory (DFT) calculations. These potential reaction mechanisms were evaluated using both the calculated Gibbs free energies, to predict the spontaneity of the constituent reactions, and the electron-density mapped Fukui function, to determine the most reactive sites of each intermediate species. The results indicate that each reaction in one of the six mechanisms is thermodynamically favorable to those in the other mechanisms; what is more, the Fukui function for each free radical intermediate corroborates with the thermochemical results for this mechanism. This mechanism proceeds via the formation of two distinct free-radical intermediates, which then react to produce the four α-O-4 stereoisomers.