An energy decomposition scheme applicable to strongly interacting systems

An energy decomposition scheme useful for the analysis of the coupled types of interactions in strongly interacting systems is developed within the Hartree-Fock approximation. A dominant characteristic of the scheme is that it involves the interactions between vacant orbitals of component molecules, as can be justified from the third-order perturbation theory. On the basis ofab initio molecular orbital calculations, the utility of the scheme is illustrated for the BH₃-NH₃ complexation and the S_N2 reaction of CH₄ with H^–. It is found that the charge transfer from electron donor (i.e. NH₃ or H^–) to acceptor (i.e. BH₃ or CH₄) is strongly coupled with the polarization of the acceptor, to contribute appreciably to the stabilization of the entire system. A specific role of this coupling mode in the progress of reactions is discussed.     

Molecular states of atoms. I. Orbital energy parameters

Atomic valence state energies are analyzed to obtain values of orbital energy parameters that may be used in semiempirical molecular orbital calculations. Difficulty in defining the interaction between orbitals with non-integer electron populations is systematically avoided by distinguishing between a valence state and a molecular state of an atom, only the latter state having non-integer spin paired orbital occupancy. Application of the virial theorem to the molecular state enables a value for the orbital kinetic energy to be obtained from the valence state orbital energy parameters once an arbitrary configuration is defined as reference. The orbitals then are eigenfunctions of the atomic Fock operator for that reference molecular state and, with their energy parameters, may be employed as a fixed basis set for molecular orbital calculations.     

Kinetic energy decomposition scheme based on information theory

We proposed a novel kinetic energy decomposition analysis based on information theory. Since the Hirshfeld partitioning for electron densities can be formulated in terms of Kullback–Leibler information deficiency in information theory, a similar partitioning for kinetic energy densities was newly proposed. The numerical assessments confirm that the current kinetic energy decomposition scheme provides reasonable chemical pictures for ionic and covalent molecules, and can also estimate atomic energies using a correction with viral ratios.     

CASSCF and multireference CI with singles and doubles study of low-lying valence and Rydberg states of 2H-tetrazole

Complete active space self-consistent field (CASSCF) and multireference CI with singles and doubles (MR-CISD) calculations [including extensivity corrections, at MR-CISD+Q and multireference averaged quadratic coupled cluster (MR-AQCC) levels] have been performed to characterize the low-lying valence and the Rydberg states of 2H-tetrazole. The highest level results (MR-AQCC/d'-aug'-cc-pVDZ) indicate the following ordering of the valence singlet excited states: S(1) (n-pi*), 6.06 eV; S(2) (n-pi*), 6.55 eV; S(3) (pi-pi*), 6.55 eV. The MR-CISD+Q/d'-aug'-cc-pVDZ results indicate the same ordering, but at slight higher energies: 6.16, 6.68, and 6.69 eV, respectively. According to our MR-CISD+Q/d'-aug'-cc-pVDZ results, the next two states are Rydberg states, at 7.69 eV (pi-3s) and 7.89 eV (n-3s). The calculated energies of these two states, as well as their proximity, are consistent with the conclusion reached by Palmer and Beveridge (Chem Phys 1987, 111, 249) that the first band of the photoelectron spectrum of 2H-tetrazole is likely to be associated to the first two ionizations processes (of pi and N lone pair electrons), at energies close to 11.3 eV.     

A hybrid approach combining energy density analysis with the interaction energy decomposition method

We propose a new analysis technique for characterizing molecular interactions that combines an energy decomposition scheme, such as the Kitaura-Morokuma decomposition method, with energy density analysis, which partitions the total energy of the system into atomic contributions. The combined scheme, termed Interaction-EDA, enables us to estimate the local contribution of interaction energy components, such as electrostatic, exchange, polarization, and charge transfer. The evaluation of the local interaction energy is rather important in large systems. For a numerical assessment, the Interaction-EDA method is applied to the process of CO adsorption on Si(100) - (2 x 1) surface.     

On the usefulness of generalised quantum chemical valence parameters in monitoring the course of a chemical reaction: A case study of the photochemical decomposition of HNO in excited states

A variant of the orthogonal gradient method of orbital optimization in the INDO-MCSCF framework has been used to study the photochemical decomposition of the HNO molecule into H + NO in the lowest^1.3A″ states. A complete geometry optimization has been carried out at all points of the reaction path which appears to be almost barrierless. The one-electron density matrix extracted from the optimized wavefunction at each point has been used to generate the relevant sets of quantum chemical valence parameters. A sharp transition is noted in the N-H bond order and hydrogen free valence index when plotted as functions of r_NH. This enables us to locate the transition region easily.     

An application of second-order n-electron valence state perturbation theory to the calculation of excited states

n–electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory where all the zero-order wave functions are of multireference nature, being generated as eigenfunctions of a two–electron model Hamiltonian. The absence of intruder states makes NEVPT an interesting choice for the calculation of electronically excited states. Test calculations have been performed on several valence and Rydberg transitions for the formaldehyde and acetone molecules; the results are in good accordance with the best calculations and with the existing experimental data.Contribution to the Jacopo Tomasi Honorary Issue     

A novel method to prepare metal oxide electrode:Spin-coating with thermal decomposition

In this work,we propose a new spin-coating method coupling with high thermal decomposition,to prepare the tin-antimony(Sn-Sb) oxide electrode.The character of the spin-coating electrode was compared with the dip-coating electrode through X-ray diffraction(XRD),scanning electron microscopy(SEM),accelerated life test,cyclic voltammetry,and electrolytic degradability. The results showed that the spin-coating electrode had a better defined crystal form,a smoother and more compact surface than that of the dip-coating electrode.Service time of the spin-coating electrode was determined to be longer than 15 h,and it was less than 2 min for the dip-coating electrode.Electrochemical characterization analysis showed that the electrolytic degradability of the spin-coating electrode is better than that of the dip-coating electrode.     

Bonding character of intermediates in on-surface Ullmann reactions revealed with energy decomposition analysis

On-surface synthesis has become a thriving topic in surface science. The Ullmann coupling reaction is the most applied synthetic route today, but the nature of the organometallic intermediate is still under discussion. We investigate the bonding nature of prototypical intermediate species (phenyl, naphthyl, anthracenyl, phenanthryl, and triphenylenyl) on the Cu(111) surface with a combination of plane wave and atomic orbital basis set methods using density functional theory calculations with periodic boundary conditions. The surface bonding is shown to be of covalent nature with a polarized shared-electron bond supported by π-back donation effects using energy decomposition analysis for extended systems (pEDA). The bond angle of the intermediates is determined by balancing dispersion attraction and Pauli repulsion between adsorbate and surface. The latter can be significantly reduced by adatoms on the surface. We furthermore investigate how to choose computational parameters for pEDA of organic adsorbates on metal surfaces efficiently and show that bonding interpretation requires consistent choice of the density functional.     

Thermal decomposition kinetics of natural fibers: Activation energy with dynamic thermogravimetric analysis

Dynamic TG analysis under nitrogen was used to investigate the thermal decomposition processes of 10 types of natural fibers commonly used in the polymer composite industry. These fibers included wood, bamboo, agricultural residue, and bast fibers. Various degradation models including the Kissinger, Friedman, Flynn-Wall-Ozawa, and modified Coats-Redfern methods were used to determine the apparent activation energy of these fibers. For most natural fibers approximately 60% of the thermal decomposition occurred within a temperature range between 215 and 310 °C. The result also showed that an apparent activation energy of 160-170 kJ/mol was obtained for most of the selected fibers throughout the polymer processing temperature range. These activation energy values allow developing a simplified approach to understand the thermal decomposition behavior of natural fibers as a function of polymer composite processing.     

Anionic behavior and single-molecule crystal in fullerene confinements: A contribution from DFT energy decomposition and cooperativity analyses

The recently proposed systems of various anions (A) confined inside C₆₀ , A⁻ @ C₆₀ , which in turn behave as large and stable anions, (A @ C₆₀)⁻ , can find potential applications in various fields. On the other hand, it has earlier been shown that from the dihalogens (X₂ ) encapsulated C₆₀ , X₂ @ C₆₀ , only F₂ @ C₆₀ can be introduced as a system in which the cage acts as a cation C₆₀⁺ and interacts with an endohedral anion, F₂⁻ , forming the F₂⁻ @ C₆₀⁺ as a single-molecule crystal compound. In this work, two density functional theory energy decomposition analysis (EDA) schemes, where in one of them the noninteracting kinetic, electrostatic, and exchange-correlation energies come into play while another scheme, called as EDA-SBL, includes the steric, electrostatic, and quantum effects as essential ingredients (S. Liu, J. Chem. Phys. 2007 , 126, 244103), are utilized to find out what energetic components govern the unique characteristics of the (A @ C₆₀)⁻ and X₂ @ C₆₀ confinements. It is shown that the noninteracting kinetic energy and steric energies have important contributions to the total interaction energies for the considered systems. However, there are other confinements for which the electrostatic and exchange-correlation contributions play also imperative roles. Furthermore, we find reasonable correlations between interaction energies and their components as well as the energetic components themselves, leading to an alternative EDA scheme including the noninteracting kinetic, steric, and electrostatic energies for investigations on other endohedral fullerenes. Extending our analyses to large size confinements, Cl⁻ @ C_n with n up to 90 as illustrative examples, the quantitative cooperativity concept is also explored, where the positive and negative cooperativity profiles unveil a specific size of the anionic confinements to form the most stable large anion.     

Recasting wave functions into valence bond structures: A simple projection method to describe excited states

A method is proposed to obtain coefficients and weights of valence bond (VB) determinants from multi configurational wave functions. This reading of the wave functions can apply to ground states as well as excited states. The method is based on projection operators. Both energetic and overlap‐based criteria are used to assess the quality of the resulting VB wave function. The approach gives a simple access to a VB rewriting for low‐lying states, and it is applied to the allyl cation, to the allyl radical and to the ethene (notably to the V‐state). For these states, large overlap between VB and multi reference wave functions are easily obtained. The approach proves to be useful to propose an interpretation of the nature of the V‐state of ethene. © 2015 Wiley Periodicals, Inc.     

On the invariance of the configuration interaction energy with respect to orbital rotations

Summary The invariance of the configuration interaction (CI) energy with respect to orbital rotation is considered. The inclusion of all spin couplings versus only those from the first-order interacting space is considered. A definition for the analog of a second-order CI calculation when inactive electrons are present is proposed.     

An extended dead-end elimination algorithm to determine gap-free lists of low energy states

Proteins are flexible systems and commonly populate several functionally important states. To understand protein function, these states and their energies have to be identified. We introduce an algorithm that allows the determination of a gap-free list of the low energy states. This algorithm is based on the dead-end elimination (DEE) theorem and is termed X-DEE (extended DEE). X-DEE is applicable to discrete systems whose state energy can be formulated as pairwise interaction between sites and their intrinsic energies. In this article, the computational performance of X-DEE is analyzed and discussed. X-DEE is implemented to determine the lowest energy protonation states of proteins, a problem to which DEE has not been applied so far. We use X-DEE to calculate a list of low energy protonation states for two bacteriorhodopsin structures that represent the first proton transfer step of the bacteriorhodopsin photocycle.     

Toward deformation densities for intramolecular interactions without radical reference states using the fragment,atom, localized,delocalized, and interatomic (FALDI) charge density decomposition scheme

A novel approach for calculating deformation densities is presented, which enables to calculate the deformation density resulting from a change between two chemical states, typically conformers, without the need for radical fragments. The Fragment, Atom, Localized, Delocalized, and Interatomic (FALDI) charge density decomposition scheme is introduced, which is applicable to static electron densities (FALDI‐ED), conformational deformation densities (FALDI‐DD) as well as orthodox fragment‐based deformation densities. The formation of an intramolecular NH⋅⋅⋅N interaction in protonated ethylene diamine is used as a case study where the FALDI‐based conformational deformation densities (with atomic or fragment resolution) are compared with an orthodox EDA‐based approach. Atomic and fragment deformation densities revealed in real‐space details that (i) pointed at the origin of density changes associated with the intramolecular H‐bond formation and (ii) fully support the IUPAC H‐bond representation. The FALDI scheme is equally applicable to intra‐ and intermolecular interactions. © 2017 Wiley Periodicals, Inc.     

Spinodal decomposition with varying chain lengths and its application to designing polymer blends

The diffusion equations of spinodal decompositions with unique diffusivities for each species are derived for binary systems and ternary systems. These dynamic equations are linearized to show that the minimum size for growth is independent of diffusivity and is identical to the thermodynamic minimum on phase volume. Increases in chain length will destabilize mixtures and increase quench depth. Numerical simulations were conducted for two-dimensional systems. The considerable influences of chain lengths on morphology represent a competition between smaller diffusivities and larger quench depth when chain length is increased. These influences on several important morphologies in binary and ternary systems are described. The understanding of independent variable chain lengths represents one further step towards the systematical design of polymer blends. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 897–907, 1997     

Ab initio and density functional theory study of the electronic structure of rhenium complexes with noninnocent dioxolene ligands: Localized vs delocalized valence states

The dioxolene type ligands (Diox) derived from ortho-quinones are the most widely studied redox noninnocent ligands existing in the dianionic (Cat), anion radical (SQ) or neutral (Q) forms although a highly delocalized electronic structure is also possible. For [ReO(Diox)₂PPh₃]⁻ ( 2 ) and [ReCl₃(Diox)PPh₃] ( 3 ) complexes, the Re^V-Cat₂ and Re^IV-SQ localized valence states were proposed on the basis of their XRD structures. To understand in detail the electronic structure of these complexes, we performed a series of the all-electron calculations at the DKH2-CASSCF/CASPT2 and DKH2-CASSCF/NEVPT2 levels taking into account scalar relativistic and spin-orbit effects. All calculations predicted that 2 has a singlet ground state with a predominant contribution of a single electronic configuration with doubly occupied molecular orbitals being pure o-quinone LUMOs of both Diox ligands that corresponds to the Re^V-Cat₂ valence state. Complex 3 has a triplet ground state with four electronic configurations contributing mainly into its wavefunction and differing by the occupation of bonding and antibonding combinations of the o-quinone LUMO and rhenium d-AO with nearly equal contributions. This leads to the empirical “metrical oxidation state” of dioxolene ligand being −1 that is usually referred to the Re^IV-SQ oxidation state. However, in fact, the negative charge on the Diox ligand is mainly provided by a pair of electrons on the bonding MO. The standard DFT calculations entirely fail to correctly predict the ground state multiplicity for 3 .     

A short-range correlation energy density functional with multi-determinantal reference

We introduce a short-range correlation density functional defined with respect to a multi-determinantal reference which is meant to be used in a multi-determinantal extension of the Kohn–Sham scheme of density functional theory based on a long-range/short-range decomposition of the Coulomb electron–electron interaction. We construct the local density approximation for this functional and discuss its performance on the He atom.