Reducing the Many-Electron Self-Interaction Error in the Second-Order Screened Exchange Method.

The performance of different GW methods is assessed for a set of 24 organic acceptors. Errors are evaluated with respect to coupled cluster singles, doubles, and perturbative triples [CCSD(T)] reference data for the vertical ionization potentials (IPs) and electron affinities (EAs), extrapolated to the complete basis set limit. Additional comparisons are made to experimental data, where available. We consider fully self-consistent GW (scGW), partial self-consistency in the Green's function (scGW0), non-self-consistent G0W0 based on several mean-field starting points, and a "beyond GW" second-order screened exchange (SOSEX) correction to G0W0. We also describe the implementation of the self-consistent Coulomb hole with screened exchange method (COHSEX), which serves as one of the mean-field starting points. The best performers overall are G0W0+SOSEX and G0W0 based on an IP-tuned long-range corrected hybrid functional with the former being more accurate for EAs and the latter for IPs. Both provide a balanced treatment of localized vs delocalized states and valence spectra in good agreement with photoemission spectroscopy (PES) experiments.

The reaction of dimethyl ether (DME) with nitrogen dioxide (NO2), which plays a critical role in the low-temperature oxidation behavior of DME, is employed as prototype for reactions of heavier clean ether fuels to assess different hybrid density functionals and “double-hybrid” density functionals. The reaction energies and barrier heights for the reaction system were computed with CCSD(T) theory extrapolated to the complete basis set limit using augmented cc-pVDZ and cc-pVTZ basis sets. The involved energetics were also improved by the CCSD(T)/6-311+G(2df,2p), QCISD(T)/6-311+G(2df,2p), G3B3, G3MP2B3, CBS-QB3, G4, and G4MP2 calculations. It is shown that “double-hybrid” density functionals with the TZVP basis set can give accurate geometries and principal moments of inertia of reactants and products and the B2PLYP/TZVP level can achieve results for barrier heights comparable in accuracy to the high-level ab initio results, which is identified as an important potential theoretical level for direct kinetics studies on the rates of these and homologous reaction systems. The calculated results indicate that NO2 preferentially captures an out-of-plane hydrogen atom from the DME molecule by the O or the N end via three distinct channels to produce trans-HONO, cis-HONO, and HNO2, respectively, and each channel involves the formation of a van der Waals post-reaction adducts lying lower in energy than their separate products.

The multiconfiguration molecular mechanics (MCMM) algorithm was used to generate potential and vibrationally adiabatic energy surfaces for excited-state tautomerization in the 1:1 7-azaindole:H2O complex. Electronic structures and energies for reactant, product, transition state were computed at the CIS/6-31G(d,p) level of theory. The potential and vibrationally adiabatic energies along the reaction coordinate were generated step by step by using 16 high-level Shepard points, which were computed at the CIS/6-31G(d,p) level. This study shows that the MCMM method was applied successfully to make quite reasonable potential and adiabatic energy curves for the excited-state double proton transfer reaction. No stable intermediates are present in the potential energy curve along the reaction coordinate of the excited-state double proton transfer in the 1:1 7-azaindole:H2O complex, indicating that these two protons are transferred concertedly. The change in the bond distances along the reaction coordinate shows that two protons move very asynchronously to make an H3O + -like moiety at the transition state.

A continuum random phase approximation (RPA) method for evaluating the structure function of nuclear matter is developed, where exchange terms for any particle-hole interaction are explicitly included. The method is applied to the inclusive transverse quasielastic electron scattering response at momentum transfer ranging from q=300 to 550 MeV/c. The interaction employed is a ${\mathit{g}}^{\ensuremath{'}}$ Landau-Migdal constant plus a (\ensuremath{\pi}+\ensuremath{\rho})-meson exchange interaction. A comparison with the standard ring series is made showing that the inclusion of finite range effects in the exchange terms is necessary. \textcopyright{} 1996 The American Physical Society.

The calculation of accurate reaction energies and barrier heights is essential in computational studies of reaction mechanisms and thermochemistry. To assess methods regarding their ability to predict these two properties, high-quality benchmark sets are required that comprise a reasonably large and diverse set of organic reactions. Due to the time-consuming nature of both locating transition states and computing accurate reference energies for reactions involving large molecules, previous benchmark sets have been limited in scope, the number of reactions considered, and the size of the reactant and product molecules. Recent advances in coupled-cluster theory, in particular local correlation methods like DLPNO-CCSD(T), now allow the calculation of reaction energies and barrier heights for relatively large systems. In this work, we present a comprehensive and diverse benchmark set of barrier heights and reaction energies based on DLPNO-CCSD(T)/CBS called BH9. BH9 comprises 449 chemical reactions belonging to nine types common in organic chemistry and biochemistry. We examine the accuracy of DLPNO-CCSD(T) vis-a-vis canonical CCSD(T) for a subset of BH9 and conclude that, although there is a penalty in using the DLPNO approximation, the reference data are accurate enough to serve as a benchmark for density functional theory (DFT) methods. We then present two applications of the BH9 set. First, we examine the performance of several density functional approximations commonly used in thermochemical and mechanistic studies. Second, we assess our basis set incompleteness potentials regarding their ability to mitigate basis set incompleteness errors. The number of data points, the diversity of the reactions considered, and the relatively large size of the reactant molecules make BH9 the most comprehensive thermochemical benchmark set to date and a useful tool for the development and assessment of computational methods.

Density functional theory (DFT) has emerged as one of the most versatile and lucrative approaches in electronic structure calculations of many-electron systems in past four decades. Here we give an account of the development of a variational DFT method for atoms and molecules completely in a Cartesian grid. The non-relativistic Kohn–Sham equation is solved by using an LCAO-MO ansatz. Atom-centered localized basis set, electron density, molecular orbitals, two-body potentials are directly constructed on the grid. We adopt a Fourier convolution method for classical Coulomb potentials by making an Ewald-type decomposition technique in terms of short- and long-range interactions. It produces quite accurate and competitive results for various properties of interest, such as component energy, total energy, ionization energy, potential energy curve, atomization energy, etc. Both local and non-local functionals are employed for pseudopotential as well as full calculations. While most results are offered in a uniform grid, initial exploratory attempts are made in a non-uniform grid, which can significantly reduce the computational overhead. This offers a practical, viable alternative to atom-centered grid-based implementations, currently exploited by the majority of programs available world-wide.

Chirality and activity relationships are paramount to pharmaceutical design and synthesis. Generally, point chirality (enantiomeric R and S configurations) is emphasized most in molecules and drugs; however, axis chirality (present when structures adopt conformations with asymmetrical distributions of electron density) must also be considered as a stereogenic unit of interest. Together, stereogenic units and optical isomerism describe the chiral disposition of electron density about nuclei. In this essence, different components of chirality are always present in molecular systems. In assessing the different chiral parameters of pharmaceuticals, the cardiovascular drug carvedilol serves as an ideal example because both enantiomers produce different physiological effects. In the current study, R- and S-4-(2-hydroxypropoxy)carbazol (carvedilol fragment A), along with prochiral and chiral analogues, are studied to investigate the chiral components of carvedilol. Further, the effects of substituent variation about a stereocenter are investigated and discussed using conformational energy as a surrogate of structure (based on the fact that energy is a function of molecular spatial orientation) to determine the energetic equivalency of prochiral and chiral structures. Multidimensional conformational analysis (MDCA) was performed on selected structures using restricted Hartree−Fock (RHF) and density functional theory (DFT with the Becke 3LYP hybrid exchange-correlation functional) molecular orbital computations to elucidate the structural and energetic basis of chirality. The analogues had the following prochiral and chiral structures: R−CH2−OH, [R] and [S] R−CHMe−OH, and R−CMe2−OH, with substituent R being either MeCH2- or ArCH2-, where Ar is the carbazole moiety. Potential energy curves (PECs) of torsional angles χ1, χ2, χ3, and χ10 for R- and S-4-(2-hydroxypropoxy)carbazol verified that all torsional angles are indeed enantiomeric. Correspondingly, the potential energy hypersurfaces (PEHSs) of R- and S-4-(2-hydroxypropoxy)carbazol were also enantiomeric, as illustrated with optimizations of conformational minima; converged minima occurred in equivalent point chiral and axis chiral pairs. Similarly to R- and S-4-(2-hydroxypropoxy)carbazol, achiral and chiral analogues analyzed by MDCA displayed axis chirality while chiral structures displayed both axis and point chirality. As such, the presence of point and axis chirality in molecular systems allows predictions to be made concerning the orientations of viable conformations of a respective PEHS. Further, the data indicate that chirality induced by an asymmetric distribution of electron density (axis chirality) is always present whenever a structure adopts asymmetric conformations. Like enantiomers of point chirality, axis chiral conformers also occur in pairs. Potential energy surfaces (PESs) were generated about the prochiral and chiral centers for all structures at the RHF/3-21G level of theory and used to test the equivalency of conformational energy between sufficiently constructed achiral and chiral structures. It is hypothesized that, with regard to conformational energy, the addition of two chiral enantiomers minus the addition of two achiral structures will give a zero result (assuming the only structural differences occur at the stereocenters). The combination of prochiral and chiral potential energy surfaces, according to an equation describing two consecutive and concerted methyl substitutions, gave a practically flat, virtually zero surface, indicating that sufficiently constructed achiral structures are energetically equivalent to chiral enantiomers. Thus, solely on the basis of molecular structure, chiral properties such as energy, number of converged conformers in a PEHS, conformations of corresponding point chiral and axis chiral pairs, and intramolecular interactions can be predicted from achiral structures. It remains to be seen how this can be utilized in drug research and development.

The electronic and geometric structure of various substituted borylenes BR (where R = H, F, Cl, Br, CH(3), Ph, NH(2), NHMe, and NMe(2)) in their lowest singlet and triplet electronic states was investigated by computational means using hybrid density functional (B3LYP) and second-order Møller-Plesset perturbation theories combined with 6-311+G** and cc-pVTZ basis sets. The reactivity of singlet borylenes towards prototypical saturated and unsaturated hydrocarbons was examined by the MP2 method in conjugation with the cc-pVTZ basis set and also by coupled cluster [CCSD(T)] computations in combination with the aug-cc-pVTZ basis set. To study the energetics and the mechanism of the addition reaction of borylenes to unsaturated CC bonds, ethyne and ethene are chosen as model compounds. The insertion reaction of borylene into a C-H bond of methane was also investigated. The addition reactions of borylenes to multiple C-C bonds are strongly exothermic. In case of the BH molecule the reactions proceed without barrier and are the most exothermic. For the insertion reaction of borylenes into methane, two approaches could be identified. Again, the smallest reaction barriers and highest reaction energies were computed for the BH insertion, while the highest barriers and the smallest exothermicities were obtained for the BF molecule. On the basis of frontier molecular orbital energies, barrier heights, reaction energies, and transition state geometries BH is the most electrophilic borylene, followed by BPh, while aminoborylenes and BF are the most nucleophilic ones among the investigated derivatives. Accordingly, reactions of BH have the smallest barriers (if there is one at all) and the largest reaction energies, while the reactions of BF have the highest barriers and the smallest reaction energies.

Incorporating self-interaction corrections (SIC) significantly improves chemical reaction barrier height predictions made using density functional theory methods. We present a detailed orbital-by-orbital analysis of these corrections for three semi-local density functional approximations (DFAs) situated on the three lowest rungs of Jacob's ladder of approximations. The analysis is based on Fermi-Löwdin Orbital Self-Interaction Correction (FLOSIC) calculations performed at several steps along the reaction pathway from the reactants (R) to the transition state (TS) to the products (P) for four representative reactions selected from the BH76 benchmark set. For all three functionals, the major contribution to self-interaction corrections of the barrier heights can be traced to stretched bond orbitals that develop near the TS configuration. The magnitude of the ratio of the self-exchange-correlation energy to the self-Hartree energy (XC/H) for a given orbital is introduced as an indicator of one-electron self-interaction error. XC/H = 1.0 implies that an orbital's self-exchange-correlation energy exactly cancels its self-Hartree energy and that the orbital, therefore, makes no contribution to the SIC in the FLOSIC scheme. For the practical DFAs studied here, XC/H spans a range of values. The largest values are obtained for stretched or strongly lobed orbitals. We show that significant differences in XC/H for corresponding orbitals in the R, TS, and P configurations can be used to identify the major contributors to the SIC of barrier heights and reaction energies. Based on such comparisons, we suggest that barrier height predictions made using the strongly constrained and appropriately normed meta-generalized gradient approximation may have attained the best accuracy possible for a semi-local functional using the Perdew-Zunger SIC approach.

Abstract— The importance of charge transfer(CT) between the retinal chromophore and the protein environment in the ground state of bacteriorhodopsin(BR) has been verified by using ab initio and semiempirical molecular orbital methods. We hypothesize that the chromophore is stabilized in BR by highest occupied molecular orbital‐lowest unoccupied molecular orbital(HOMO‐LUMO) interaction with the protein environment. If sufficient charge is transferred between two sites due to the strong HOMO‐LUMO interaction, the chromophore might be treated as a one‐electron reduced species(when it behaves as an electron acceptor), or as a one‐electron oxidized one (when it acts as an electron donor).In both optimized geometries, the ‐conjugated systems exhibit a drastic decrease in bond alternation. To estimate the rotational barrier for thermal isomerization between the al‐trans and the 13,15‐dicis form, the potential energy curve around these two bonds was computed. The first ‐* transition energy was also calculated for an inspection of the opsin shift. The barrier height and the transition energy became much lower as a result of the chromophore reduction. The site selectivity in photo‐ and thermal isomerization and the opsin shift in BR can be well explained by considering CT from the protein environment to the chromophore.

Potential energy curves, surfaces and hypersurfaces. A model to follow and understand the conformational transformations in amino acids

Electronic excitations: Ab initio calculations of electronic spectra and application to zirconia ZrO 2, titania TiO 2 and cuprous oxide Cu 2O

The suitability of one-particle energies from the generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA) method for electron affinities of molecules is investigated. It is shown that the GKS-spPRA effective potential includes exact exchange and polarizability-dependent correlation terms that are necessary for the correct description of anionic systems. An implementation that enables fast computation of electron affinities is presented. For model systems, I show that the GKS-spRPA approach is applicable for valence and nonvalence type anions with a maximum error of 0.13 eV for valence anionic states and 0.03 eV for nonvalence anionic states compared to equation of motion coupled cluster methods. For a series of perhalobenzene molecules, C6X6 (X= F, Cl, Br, and I), GKS-spRPA predicts that the ground-state character changes from a nonvalence-σ* type in C6F6- to valence-π* in C6Cl6- and valence-σ* in C6Br6- and C6I6-. Experimental implications of these findings are discussed.

Two vacua particle number projected random phase approximation

Recent angle-resolved photoemission spectroscopy (ARPES) experiments have suggested that BiS2-based superconductors are at very low electron doping. Using random phase approximation (RPA) and functional renormalization group (FRG) methods, we find that g-wave pairing symmetry belonging to the irreducible representation is dominant at electron doping . The pairing symmetry is determined by inter-pocket nesting and orbital characters on the Fermi surfaces and is robust in a two-orbital model including both Hund's coupling J, and Hubbard-like Coulomb interactions U and with relatively small . With the increasing electron doping, the g-wave state competes with both the s-wave and d-wave states and no pairing symmetry emerges dominantly.