Electronic excitation of sulfur-organic compounds – performance of time-dependent density functional theory

 To define the scope and limitations of the time-dependent density functional theory (TDDFT) method, spectral absorption data of a series of about 100 neutral or charged sulfur-organic compounds with up to 24 non-hydrogen atoms and up to four sulfur atoms were calculated in the near-UV, visible and IR regions. Although the theoretical vertical transition energies correspond only approximately to experimental absorption band maxima, the mean absolute deviation was calculated to be 0.21 eV (1600 cm⁻¹). The main absorption features of various compounds with monocoordinated or dicoordinated sulfur atoms are well reproduced. As far as possible TDDFT results were compared with those of semiempirical Zerner's intermediate neglect of differential overlap (ZINDO/S) and of Pariser–Parr–Pople (PPP) calculations. TDDFT also works well in cases where the semiempirical methods fail. Limitations of TDDFT were encountered with calculations of spectral absorptions of dye molecules. The “vinylene shift” of polymethine dyes is not reproduced by TDDFT. Whereas electronic excitation energies delocalized polar and betainic chromophores are reasonably well reproduced, excitation energies of charge-transfer-type and charge-resonance-type transitions of weakly interacting composite chromophores are significantly underestimated. Received: 30 October 2000 / Accepted: 29 November 2000 / Published online: 22 May 2001     

Improved supermolecular second order Møller-Plesset intermolecular interaction energies using time-dependent density functional response theory

The supermolecular second order Moller-Plesset (MP2) intermolecular interaction energy is corrected by employing time-dependent density functional (TDDFT) response theory. This is done by replacing the uncoupled second order dispersion contribution contained in the supermolecular MP2 energy with the coupled dispersion energy obtained from the TDDFT approach. Preliminary results for the rare gas dimers He2, Ne2, and Ar2 and a few structures of the (HF)2 and (H2O)2 dimers show that the conventional MP2 interaction energies are considerably improved by this procedure if compared to coupled cluster singles doubles with perturbative triples [CCSD(T)] interaction energies. However, the quality of the interaction energies obtained in this way strongly depends on the exchange-correlation potential employed in the monomer calculations: It is shown that an exact exchange-only potential surprisingly often performs better than an asymptotically corrected hybrid exchange-correlation potential. Therefore the method proposed in this work is similar to the method by Cybulski and Lytle [J. Chem. Phys., 127, 141102 (2007)] which corrects the supermolecular MP2 energies with a scaled dispersion energy from time-dependent Hartree-Fock. The results in this work are also compared to the combination of density functional theory and intermolecular perturbation theory.     

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     

Excitation energies expressed as orbital energies of Kohn–Sham density functional theory with long-range corrected functionals

A new simple and conceptual theoretical scheme is proposed for estimating one-electron excitation energies using Kohn–Sham (KS) solutions. One-electron transitions that are dominated by the promotion from one initially occupied orbital to one unoccupied orbital of a molecular system can be expressed in a two-step process, ionization, and electron attachment. KS with long-range corrected (LC) functionals satisfies Janak's theorem and LC total energy varies almost linearly as a function of its fractional occupation number between the integer electron points. Thus, LC reproduces ionization energies (IPs) and electron affinities (EAs) with high accuracy and one-electron excitation energies are expressed as the difference between the occupied orbital energy of a neutral molecule and the corresponding unoccupied orbital energy of its cation. Two such expressions can be used, with one employing the orbital energies for the neutral and cationic systems, while the other utilizes orbital energies of just the cation. Because the EA of a molecule is the IP of its anion, if we utilize this identity, the two expressions coincide and give the same excitation energies. Reasonable results are obtained for valence and core excitations using only orbital energies.     

The importance of Colle–Salvetti for computational density functional theory

The purpose of this presentation is to show the importance of the Colle–Salvetti (Theor Chim Acta 37:329, 1975) paper in the development of modern computational density functional theory. To do this we cover the following topics (1) the Bright Wilson understanding (2) the Kohn–Sham equations (3) local density exchange (4) the exchange-hole (5) generalised gradient approximation for exchange (Becke and Cohen) (6) left–right correlation and dynamic correlation (7) the development of the Lee–Yang–Parr dynamic correlation functional from the Colle–Salvetti paper (8) the early success of GGA DFT. Finally we observe that the the BLYP and OLYP exchange-correlation functionals are not semi-empirical; this may explain their great success.     

Structure–antioxidant activity relationships of dendrocandin analogues determined using density functional theory

Structural Chemistry - Quantum-chemical calculations based on the density functional theory (DFT) at the B3LYP/6–311?+?+?G(2d,2p)//B3LYP/6–31G(d,p) level were employed...     

Calculation of weakly polar interaction energies in polypeptides using density functional and local Møller-Plesset perturbation theory

The interaction energies of ubiquitous weakly polar interactions in proteins are comparable with those of hydrogen bonds, consequently, they stabilize local, secondary, and tertiary structures. However, the most widely-used density functionals fail to describe the weakly polar interactions. Thus, it is important to find and test functionals which adequately describe and quantify the energetics of such interactions. For this purpose, interaction energies in the hydrophobic core of rubredoxin (PDB id: 1rb9) and in the S22 subset of the JSCH-2005 benchmark database were computed with the BHandHLYP and PWPW91 functionals and with the pseudospectral implementation of the local MP2 (PS-LMP2) method. The cc-pVDZ, cc-pVTZ(-f), cc-pVTZ, cc-pVQZ(-g), aug-cc-pVDZ, aug-cc-VTZ(-f), and aug-cc-pVTZ basis sets were used for the calculations. In the S22 subset the PS-LMP2 results were extrapolated to the complete basis set limit. Furthermore, the a posteriori counterpoise method of Boys and Bernardi was used to correct the basis set superposition errors in the calculation of interaction energies. Calculations using the BHandHLYP functional, both for the various weakly polar interactions in rubredoxin and for the dispersion interactions in the S22 subset, were in good agreement with those using the coupled cluster (CCSD(T)) and the resolution of identity MP2 (RIMP2) methods and clearly outperformed both the PWPW91 functional and the PS-LMP2 method. The results for the S22 hydrogen bonded subset, obtained with PWPW91 calculations, were closest to those of the reference high level calculations. For the "mixed" (hydrogen bonded and dispersive) interactions in the S22 subset, results obtained with the BHandHLYP and PS-LMP2 calculations agreed well with the reference calculations.     

Camphor-based α-bromoketones for the asymmetric darzens reaction: Insights into the mechanism using density functional theory

Density functional theory (DFT) calculations at B3LYP/6-31G(d,p) level were carried out to investigate the mechanism of the reaction of benzaldehyde (BA) or acetaldehyde (AD) with (1R)-2-endo-bromoacetyl-1,7,7-trimethylbicyclo[2.2.1]heptan-2-ol (endo-2-bromoacetylisoborneol) 1 (Scheme 1). The calculations indicate that the reactions are diastereoselective, in good agreement with the experimental results [1]. Moreover, the calculations show that these reactions proceed via two steps: (1) an aldol-like reaction and (2) the formation of an epoxide. Our calculation study of the transition states demonstrates that the terminal hydroxyl group in compound 1 is vital for the stereoselectivity of the reactions.     

Influence of Hartree-Fock exchange on the calculated Mössbauer isomer shifts and quadrupole splittings in ferrocene derivatives using density functional theory

Influence of molecular geometry, type of exchange-correlation functional, and contraction scheme of basis set applied at the iron nuclei have been tested in the calculation of 57Fe M?ssbauer isomer shifts and quadrupole splittings for a wide range of ligand types, as well as oxidation and spin states, in inorganic and organometallic systems. It has been found that uncontraction of the s-part of Wachter's full-electron basis set at the iron nuclei does not appreciably improve the calculated isomer shifts. The observed correlations for all tested sets of geometries are close to each other and predominantly depend on the employed exchange-correlation functional with B3LYP functional being slightly better as compared to BPW91. Both hybrid (B3LYP) and pure (BPW91) exchange-correlation functionals are suitable for the calculation of isomer shifts in organometallic compounds. Surprisingly, it has been found that the hybrid B3LYP exchange-correlation functional completely fails in accurate prediction of quadrupole splittings in ferrocenes, while performance of the pure BPW91 functional for the same systems was excellent. This observation has been explained on the basis of relationship between the amount of Hartree-Fock exchange involved in the applied exchange-correlation functional and the calculated HOMO-LUMO energy gap in ferrocenes. On the basis of this explanation, use of only pure exchange-correlation functionals has been suggested for accurate prediction of M?ssbauer spectra parameters in ferrocenes.     

Application of density functional theory and optical spectroscopy for the prediction of the photophysical properties of Р-pyridylphospholanes

Russian Chemical Bulletin - The spatial and electronic structure of a series of pyridyl-containing phospholanes, which are potential ligands for the synthesis of luminescent transition metal...     

Aqueous Diels–Alder reactions for thermochemical storage and heat transfer fluids identified using density functional theory

Thermal storage and transfer fluids have important applications in industrial, transportation, and domestic settings. Current thermal fluids have relatively low specific heats, often significantly below that of water. However, by introducing a thermochemical reaction to a base fluid, it is possible to enhance the fluid's thermal properties. In this work, density functional theory (DFT) is used to screen Diels–Alder reactions for use in aqueous thermal fluids. From an initial set of 52 reactions, four are identified with moderate aqueous solubility and predicted turning temperature near the liquid region of water. These reactions are selectively modified through 60 total functional group substitutions to produce novel reactions with improved solubility and thermal properties. Among the reactions generated by functional group substitution, seven have promising predicted thermal properties, significantly improving specific heat (by as much as 30.5%) and energy storage density (by as much as 4.9%) compared to pure water.     

Conventional strain energies of azetidine and phosphetane: Can density functional theory yield reliable results?

The conventional strain energies for azetidine and phosphetane are determined within the isodesmic, homodesmotic, and hyperhomodesmotic models. Optimum equilibrium geometries, harmonic vibrational frequencies, and corresponding electronic energies and zero‐point vibrational energies are computed for all pertinent molecular systems using self‐consistent field theory, second‐order perturbation theory, and density functional theory and using the correlation consistent basis sets cc‐pVDZ, cc‐pVTZ, and cc‐pVQZ. Single point fourth‐order perturbation theory, CCSD, and CCSD(T) calculations using the cc‐pVTZ and the cc‐pVQZ basis sets are computed using the MP2/cc‐pVTZ and MP2/cc‐pVQZ optimized geometries, respectively, to ascertain the contribution of higher order correlation effects and to determine if the quadruple‐zeta valence basis set is needed when higher order correlation is included. In the density functional theory study, eight different functionals are used including B3LYP, wB97XD, and M06‐2X to determine if any functional can yield results similar to those obtained at the CCSD(T) level. © 2012 Wiley Periodicals, Inc.     

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.     

Anisotropy of the elastic properties of crystalline cellulose Iβ from first principles density functional theory with Van der Waals interactions

In spite of the significant potential of cellulose nanocrystals as functional nanoparticles for numerous applications, a fundamental understanding of the mechanical properties of defect-free, crystalline cellulose is still lacking. In this paper, the elasticity matrix for cellulose I_β with hydrogen bonding network A was calculated using ab initio density functional theory with a semi-empirical correction for van der Waals interactions. The computed Young’s modulus is found to be 206 GPa along [001] (c-axis), 98 GPa along [010] (b-axis), and 19 GPa along [100] (a-axis). Full compliance matrices are reported for 1.0, 1.5 and 2.0 % applied strains Color contour surfaces that show variations of the Young’s modulus and average Poisson’s ratio with crystallographic direction revealed the extreme anisotropies of these important mechanical properties. The sensitivity of the elastic parameters to misalignments in the crystal were examined with 2D polar plots within selected planes containing specific bonding characteristics; these are used to explain the substantial variability in the reported experimental Young’s moduli values. Results for the lattice directions [001], [010] and [100] are within the range of reported experimental and other numerical values.     

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.