Homoclinic orbits for first order Hamiltonian systems with some twist conditions

In this paper, we study the nonperiodic first-order Hamiltonian system ù = J L(t)u +J H(t, u), where H ∈ C1(R × R2n). With some assumptions on L, the corresponding Hamiltonian operator has only discrete spectrum. By using the index theory for self-adjoint operator equation,we establish the existence of multiple homoclinic orbits for the asymptotically quadratic nonlinearty satisfying some twist conditions between infinity and origin.     

On the Solvent‐free Structure of a Jäger‐type Cobalt(II) N2O2‐Chelate Complex

A combined synchrotron X‐ray and density functional theory (DFT) study on the structure of a Jäger‐type N₂O₂ chelate complex was carried out. The ethoxy‐substituted bis(3‐oxo‐enaminato)cobalt(II) complex ( 1 ) was an original sample from the laboratory of the late Professor Ernst‐G. Jäger (University of Jena, Germany). Single‐crystal X‐ray analysis revealed essentially flat molecules of 1 , which are unsolvated and coordinatively unsaturated. The DFT calculations on the isolated molecule predict a planar structure for the non‐hydrogen atoms, which is a local minimum on the energy surface. The crystal packing is achieved through off‐set stacking (staircase arrangement), resulting in a herringbone pattern in the space group P2₁2₁2₁. The structure of 1 is compared to known structures of related bis(3‐oxo‐enaminato)cobalt(II) complexes ( 2 – 4 ). Original bulk material of 1 was investigated by scanning electron microscopy (SEM), powder X‐ray diffraction (PXRD), melting point determination, and infrared (IR) spectroscopy.     

The photoisomerization of 11‐cis‐retinal protonated schiff base in gas phase: Insight from spin‐flip density functional theory

This extensive theoretical study employed the spin‐flip density functional theory (SFDFT) method to investigate the photoisomerization of 11‐cis‐retinal protonated Schiff base (PSB11) and its minimal model tZt‐penta‐3,5‐dieniminium cation (PSB3). Our calculated results indicate that SFDFT can perform very well in describing the ground‐ and excited‐state geometries of PSB3 and PSB11. We located the conical intersection (CI) point and constructed the photoisomerization reaction path of PSB3 and PSB11 by using the SFDFT method. To further verify the SFDFT results, we computed the energy profiles along the constructed linearly interpolated internal coordinate (LIIC) pathways by using high‐level theoretical methods, such as the EOM‐CCSD, CR‐EOM‐CCSD(T), CASPT2, NEVPT2, and XMCQDPT2 methods. The SFDFT method predicts that the photoisomerization of PSB3 is barrierless, in accordance with previous complete‐active‐space self‐consistent‐field (CASSCF) results. However, an energy barrier is predicted along the LIIC pathways of PSB11. This finding is different from previous CASSCF results and may indicate that the photoisomerization of PSB11 in gas phase is similar to that in solution. However, the higher spin contamination of the SFDFT method in the vicinity of the CI point caused the located CI geometry to deviate from that of the real CI. In addition, the LIIC pathways are only approximations to the minimum energy path (MEP). Thus, further experimental and theoretical studies are needed to verify the existence of an energy barrier along the photoisomerization reaction path of PSB11 in gas phase. © 2013 Wiley Periodicals, Inc.     

KiSThelP: A program to predict thermodynamic properties and rate constants from quantum chemistry results†

Kinetic and Statistical Thermodynamical Package (KiSThelP) is a cross‐platform free open‐source program developed to estimate molecular and reaction properties from electronic structure data. To date, three computational chemistry software formats are supported (Gaussian, GAMESS, and NWChem). Some key features are: gas‐phase molecular thermodynamic properties (offering hindered rotor treatment), thermal equilibrium constants, transition state theory rate coefficients (transition state theory (TST), variational transition state theory (VTST)) including one‐dimensional (1D) tunnelling effects (Wigner, and Eckart) and Rice‐Ramsperger‐Kassel‐Marcus (RRKM) rate constants, for elementary reactions with well‐defined barriers. KiSThelP is intended as a working tool both for the general public and also for more expert users. It provides graphical front‐end capabilities designed to facilitate calculations and interpreting results. KiSThelP enables to change input data and simulation parameters directly through the graphical user interface and to visually probe how it affects results. Users can access results in the form of graphs and tables. The graphical tool offers customizing of 2D plots, exporting images and data files. These features make this program also well‐suited to support and enhance students learning and can serve as a very attractive courseware, taking the teaching content directly from results in molecular and kinetic modelling. © 2013 Wiley Periodicals, Inc.     

1′-Acetylferrocene amino acid esters and amides. A simple model for parallel β-helical peptides

In this study we present a synthesis and conformational analysis of 1′-acetylferrocene amino acid derivatives of type Ac–Fn–CO–AA–Y (Fn=ferrocene-1,1-diyl; AA=Gly, Ala or Val; Y=OMe or NHMe) as a simple model for parallel β-helical peptides. Derivatives with only one amino acid adopt a reduced number of total conformations and allow a more exact analysis of intramolecular hydrogen bonds (IHB) close to the ferrocene unit. Conformational analysis of these bioconjugates was performed by a combination of spectroscopic techniques (IR, NMR and CD) and corroborated by solution-phase DFT calculations. The investigation of ester conjugates 1–3 indicates the coexistence of non-bonded (an open forms) and hydrogen bonded NH_a group forming a 7-membered ring (γ-turn). The amide derivatives 4–6 with an additional NH_b hydrogen bond donor are mostly constituted of conformers with a 10-membered ring (β-turn) as a single IHB pattern or the β-turn accompanied by a 7-membered ring (γ-turn) containing NH_a group. The exchange of the amino acid side-chain does not significantly affect the conformational properties and IHB pattern of the studied conjugates 1–6.     

A new size extensive multireference perturbation theory

A new multireference perturbation series is derived based on the Rayleigh–Schrödinger perturbation theory. It is orbitally invariant. Its computational cost is comparable to the single reference Møller–Plesset perturbation theory. It is demonstrated numerically that the present multireference second‐ and third‐order energies are size extensive by two types of supermolecules composed of H₂ and BH monomers. Spectroscopic constants of as well as the ground state energies of H₂O, NH₂, and CH₂ at three bond lengths have been calculated with the second multireference perturbation theory. The dissociation behaviors of CH₄ and HF have also been investigated. Comparisons with other approximate theoretical models as well as the experimental data have been carried out to show their relative performances. © 2013 Wiley Periodicals, Inc.     

Kinetics of radical‐molecule reactions in aqueous solution: A benchmark study of the performance of density functional methods

The performance of 18 density functional approximations has been tested for a very challenging task, the calculations of rate constants for radical‐molecule reactions in aqueous solution. Despite of the many difficulties involved in such an enterprise, six of them provide high quality results, and are recommended to that purpose. They are LC‐ωPBE, M06‐2X, BMK, B2PLYP, M05‐2X, and MN12SX, in that order. This trend was obtained using experimental data as reference. The other relevant aspects used in this benchmark are: (i) the SMD model for mimicking the solvent; (ii) the conventional transition state, the zero‐curvature tunneling correction, and the limit imposed by diffusion for the calculation of the rate constants. Even though changing any of these aspects might alter the trend in performance, at least, when using them, the aforementioned functionals can be successfully used to obtain high quality kinetic data for the kind of reactions investigated in this work. © 2014 Wiley Periodicals, Inc.     

Exploiting space‐group symmetry in fragment‐based molecular crystal calculations

Recent developments in fragment‐based methods make it increasingly feasible to use high‐level ab initio electronic structure techniques to molecular crystals. Such studies remain computationally demanding, however. Here, we describe a straightforward algorithm for exploiting space‐group symmetry in fragment‐based methods which often provides computational speed‐ups of several fold or more. This algorithm does not require a priori specification of the space group or symmetry operators. Rather, the symmetrically equivalent fragments are identified automatically by aligning the individual fragments along their principle axes of inertia and testing for equivalence with other fragments. The symmetry operators relating equivalent fragments can then be worked out easily. Implementation of this algorithm for computing energies, nuclear gradients with respect to both atomic coordinates and lattice parameters, and the nuclear hessian is described. © 2014 Wiley Periodicals, Inc.     

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2)2 and (PCCP)2

This work characterizes eight stationary points of the P₂ dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second‐order Møller–Plesset (MP2) electronic structure method and six different basis sets: aug‐cc‐pVXZ, aug‐cc‐pV(X+d)Z, and aug‐cc‐pCVXZ where X = T, Q. A new L‐shaped structure with C₂ symmetry is the only minimum for the P₂ dimer at the MP2 level of theory with these basis sets. The previously reported parallel‐slipped structure with C_2h symmetry and a newly identified cross configuration with D₂ symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2‐F12 and CCSD(T)‐F12 methods and the aug‐cc‐pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2‐F12 significantly overbind the P₂ and PCCP dimers relative to the CCSD(T) and CCSD(T)‐F12 binding energies by as much as 1.5 kcal mol^?1 for the former and 5.0 kcal mol^?1 for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry‐adapted perturbation theory analyses. © 2014 Wiley Periodicals, Inc.