Integral Hellmann‐Feynman computations on H3ABHn—H2ABHn+1 rearrangements

Subjecting a galactic potential to (possibly damped) nearly periodic, time-dependent variations can lead to large numbers of chaotic orbits experiencing systematic changes in energy, and the resulting chaotic phase mixing could play an important role in explaining such phenomena as violent relaxation. This paper focuses on the simplest case of spherically symmetric potentials subjected to strictly periodic driving with the aim of understanding precisely why orbits become chaotic and under what circumstances they will exhibit systematic changes in energy. Four unperturbed potentials V 0(r) were considered, each subjected to a time dependence of the form V(r, t) = V 0(r)(1 + m0 sin ωt). In each case, the orbits divide clearly into regular and chaotic, distinctions which appear absolute. In particular, transitions from regularity to chaos are seemingly impossible. Over finite time intervals, chaotic orbits subdivide into what can be termed ‘sticky’ chaotic orbits, which exhibit no large-scale secular changes in energy and remain trapped in the phase-space region where they started; and ‘wildly’ chaotic orbits, which do exhibit systematic drifts in energy as the orbits diffuse to different phase-space regions. This latter distinction is not absolute, transitions corresponding apparently to orbits penetrating a ‘leaky’ phase-space barrier. The three different orbit types can be identified simply in terms of the frequencies for which their Fourier spectra have the most power. An examination of the statistical properties of orbit ensembles as a function of driving frequency ω allows us to identify the specific resonances that determine orbital structure. Attention focuses also on how, for fixed amplitude m0, such quantities as the mean energy shift, the relative measure of chaotic orbits and the mean value of the largest Lyapunov exponent vary with driving frequency ω; and how, for fixed ω, the same quantities depend on m0.

The use of the mutual information (MI) as a measure of the entanglement in quantum systems has gained a consensus in recent years, even if there is an ongoing effort to distinguish the classical and quantum contributions contained therein. This quantity has been first introduced in condensed matter physics, in particular, in studies based on the density matrix renormalization group method. This method has been successfully adapted to quantum chemistry problems, opening the way to compute MI also in molecular systems. A key aspect of this quantity is its dependence on the one-electron (orbital) basis set, even for wave functions that are invariant under unitary transformation of the orbitals. In this work, we investigate the role of the orbital basis set (delocalized or localized, following different strategies) for wave functions expressed as linear combinations of Slater determinants and we give the analytic expression for the MI for a few special cases. This study aims to improve the knowledge of the relationship between the characteristics of the chemical bond (considering a few paradigmatic molecules, H2, F2, N2, and short linear polyenes) and the properties of interest in the field of quantum information theory.

A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calculations conducted for molecular crystals to test structures (including cell volumes) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calculations. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust "high-speed" computational tool in theoretical chemistry and physics.

The performance of Atomic Natural Orbital (ANO) basis sets for calculations involving nonempirical core pseudopotentials has been studied by comparing the results for atomic and molecular nitrogen obtained using contracted ANO basis sets with those obtained using both the primitive set and a segmented one. The primitive set has been optimized at the SCF level for atomic N treated as a five-electron pseudo-atom, and consists of 7s and 7p primitive GTOs supplemented by 2d and 1f GTOs optimized at the CI level. From this primitive set three contracted [3s 3p 2d 1f] sets have been obtained. The first one has been derived from the ANOs of the neutral atom, the second has been obtained from an averaged density matrix and the third one is a segmented set. For the atom, the segmented set gives a zero contraction error at the SCF level as it must be in valence-only calculations. The ANO basis sets show some small contraction error at the SCF level but perform better in CI calculations. However, for the diatomic N2 molecule the ANO basis sets exhibit a rather large contraction error in the calculated SCF energy. A detailed analysis of the origin of this error is reported, which shows that the conventional strategy used to derive ANO basis sets does not work very well when pseudopotentials are involved.

The performance of many-body perturbation theory (MBPT) and coupled-cluster (CC) methods in the calculation of nuclear magnetic shielding constants for BH is analyzed by comparison with results from full configuration interaction (FCI) calculations. Low-order MBPT computations are shown to be inadequate for BH, while the coupled-cluster ansatz, in particular, in its singles and doubles (CCSD) approximation, provides an efficient treatment of electron correlation, overestimating correlation effects to the 11B shielding by only 3-4 ppm (1.5%). Based on this comparison, CCSD calculations with large atomic natural orbital (ANO) basis sets are used to estimate accurate theoretical values for the isotropic and anisotropic shielding constants of BH. © 1995 John Wiley & Sons, Inc.

A theoretical study of receptor site models for trimethylammonium group interaction

We present a series of auxiliary basis sets, for the elements Na to Ar, for use in density‐fitted Hartree–Fock calculations with the correlation consistent cc‐pV(n + d)Z orbital basis sets. Benchmarking on total molecular energies, reaction energies and the spectroscopic constants of the SO molecule demonstrate that the new sets address the deficiencies of using existing auxiliary sets in combination with these orbital basis sets. We also report auxiliary basis sets for Na and Mg matched to cc‐pVnZ, along with recommendations for pairing auxiliary basis sets to the cc‐pVnZ‐F12 basis sets for Hartree–Fock calculations.

In this work, we extend the selected columns of the density matrix (SCDM) methodology [J. Chem. Theory Comput. 2015, 11, 1463-1469]─a non-iterative and real-space procedure for generating localized occupied orbitals for condensed-phase systems─to the construction of local molecular orbitals (LMOs) in systems described using non-orthogonal atomic orbital (AO) basis sets. In particular, we introduce three different theoretical and algorithmic variants of SCDM (referred to as SCDM-M, SCDM-L, and SCDM-G) that can be used in conjunction with the AO basis sets used in standard quantum chemistry codebases. The SCDM-M and SCDM-L variants are based on a pivoted QR factorization of the Mulliken and Löwdin representations of the density matrix and are tantamount to selecting a well-conditioned set of projected atomic orbitals (PAOs) and projected (symmetrically-) orthogonalized atomic orbitals, respectively, as proto-LMOs that can be orthogonalized to exactly span the occupied space. The SCDM-G variant is based on a real-space (grid) representation of the wavefunction, and therefore has the added flexibility of considering a large number of grid points (or δ functions) when selecting a set of well-conditioned proto-LMOs. A detailed comparative analysis across molecular systems of varying size, dimensionality, and saturation level reveals that the LMOs generated by these three non-iterative/direct SCDM variants are robust, comparable in orbital locality to those produced with the iterative Boys or Pipek-Mezey (PM) localization schemes, and completely agnostic toward any single orbital locality metric. Although all three SCDM variants are based on the density matrix, we find that the character of the generated LMOs can differ significantly between SCDM-M, SCDM-L, and SCDM-G. In this regard, only the grid-based SCDM-G procedure (like PM) generates LMOs that qualitatively preserve σ-π symmetry (in systems such as s-trans alkenes), and are well-aligned with chemical (i.e., Lewis structure) intuition. While the direct and standalone use of SCDM-generated LMOs should suffice for most chemical applications, our findings also suggest that the use of these orbitals as an unbiased and cost-effective (initial) guess also has the potential to improve the convergence of iterative orbital localization schemes, in particular for large-scale and/or pathological molecular systems.

We propose a novel method of calculation of free energy for coarse grained models of proteins by combining our newly developed multibody potentials with entropies computed from elastic network models of proteins. Multi-body potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Combining four-body non-sequential, four-body sequential and pairwise short range potentials with optimized weights for each term, our coarse-grained potential improved recognition of native structure among misfolded decoys, outperforming all other contact potentials for CASP8 decoy sets and performance comparable to the fully atomic empirical DFIRE potentials. By combing statistical contact potentials with entropies from elastic network models of the same structures we can compute free energy changes and improve coarse-grained modeling of protein structure and dynamics. The consideration of protein flexibility and dynamics should improve protein structure prediction and refinement of computational models. This work is the first to combine coarse-grained multibody potentials with an entropic model that takes into account contributions of the entire structure, investigating native-like decoy selection.

The tumor suppressor gene p16INK4a is commonly found altered in numerous and different types of cancer. The encoded protein arrests cell cycle in G1 phase by binding to CDK4 and CDK6, inhibiting their kinase function. In 1995, a 20-residue peptide, extracted from p16INK4a protein sequence, was discovered that retains the cell cycle inhibition properties of the endogenous tumor suppressor. However, its structure has not been determined yet. In this article, the features of a theoretical structure of the peptide bound to CDK6 are reported. The complex was modeled from CDK6-p16INK4a X-ray crystal structure and through molecular dynamics. Final structure was assessed by comparing computed binding free energy changes, when single-alanine substitutions were brought about on the peptide, to experimental data. Better concordance was obtained when including a high level of solvation effects. Solute-solvent vdW energy and electrostatic energy between solute and first shells of water, computed through a force field and considering explicit waters, were also to be included to achieve reasonably good concordance between theoretical and experimental data.

A direct generalized Bloch approach: ground and excited states of C 2

Elastic grain-boundary responses in copper and aluminium

Morphing aircraft are multi-role aircraft that use innovative actuators, effectors, and mechanisms to change their state to perform select missions with substantially improved system performance. State change in this study means a change in the cross-sectional shape of the wing itself, not chord extension or span extension. Integrating actuators and mechanisms into an effective, light weight structural topology that generates lift and sustains the air loads generated by the wing is central to the success of morphing, shape changing wings and airfoils. The objective of this study is to explore a process to link analytical models and optimization tools with design methods to create energy efficient, lightweight wing/structure/actuator combinations for morphing aircraft wings. In this case, the energy required to change from one wing or airfoil shape to another is used as the performance index for optimization while the aerodynamic performance such as lift or drag is constrained. Three different, but related, topics are considered: energy required to operate articulated trailing edge flaps and slats attached to flexible 2D airfoils; optimal, minimum energy, articulated control deflections on wings to generate lift; and, deformable airfoils with cross-sectional shape changes requiring strain energy changes to move from one lift coefficient to another. Results indicate that a formal optimization scheme using minimum actuator energy as an objective and internal structural topology features as design variables can identify the best actuators and their most effective locations so that minimal energy is required to operate a morphing wing. Background

Aims:The objective of the present work is to understand the structural stability (i.e., H-bonding and other weak noncovalent interactions) and electronic features of new model substrates, such as methyl orange (MO), vanadium oxide (V), surfactants as Triton-X100 (TX-100), and their allied substrate-surfactant model complexes (MO-V, MO-TX100, V-TX100, and (MO-V)-X100) with the deployment of density functional theory (DFT) method followed by electronic structure calculations and quantum theory of atoms in molecules (QTAIM) approaches.Background:Significant interactions appear to play a major role in reducing the energy gap between the model substrates Methyl Orange (MO)/Vanadium Oxide (V)/MO-V) and surfactant/catalyst Tri-ton-X100 (TX-100) and enhancing the catalytic behaviour of the surfactant/catalyst TX-100.Objective:The main objective of the present report is to conduct computational experiments on the designing, characterization, structure, stability, and electronic feature analyses of substrates-surfac-tant model complexes constituted from Methyl Orange (MO), Vanadium Oxide (V), Triton-X100 (TX-100) units which could indeed help in synthesizing novel materials as a catalyst, controlling the reaction path by tuning such interesting interactions between a catalyst/surfactant and substrate.Methods of Computational Calculations:The quantum chemical calculations have been performed using Gaussian 09 electronic structure calculations program. B3LYP exchange-correlation functional in conjunction with 6-31G(d,p) basis set has been employed along with the incorporation of the ef-fective core potential (ECP) based basis set for vanadium ‘V’ atom.Results:In the present report, the computational experiments have been conducted to probe the struc-tural, stability, and electronic features of four substrates-surfactant model complexes (SSMC) [MO-V, MO-TX-100, V-TX-100, and (MO-V)-TX-100] acquired from the substrates MO and V or the combination of both as MO-V and surfactant/catalyst TX-100. The HOMO-LUMO energy gap of the (MO-V)-TX-100 SSMC complex (0.679 eV) is found to be the lowest among all [MO-V (3.691 eV), MO-TX-100 (3.321 eV), and V-TX-100 (3.125 eV)] SSMCs, which appears mainly due to the presence of surfactant/catalyst (TX-100), thus showing its high reactivity/catalytic behaviour.Conclusion:The calculated binding energy, change in Gibbs free energy, natural charges, and the QTAIM based topological parameters show the most favourable stabilization (H-bonding and non-covalent interactions, including metal/non-metal bonding) and interactions in the (MO-V)-TX-100 SSMC, indicating the presence of the TX-100 surfactant.

The Bergman reaction of the hex-3-ene-1,5-diyne molecule (enediyne) to form the singlet biradical p-benzyne structure under ring closure has been studied by ab initio methods. The complete active space (CAS) SCF method was used for geometry optimizations at five points along the reaction path of the Bergman reaction. Subsequent calculations using the multireference second-order perturbation theory based on a CASSCF reference (CASPT2) established the energetics along the reaction path, especially for the reactant, transition state, and product. The energetics were further corrected for zero point vibrational energy at the CASSCF level of theory. The study incorporated four different basis sets: a double-zeta plus polarization (DZP), a triple-zeta plus double polarization (TZ2P), and two different average atomic natural orbital (ANO) basis sets. The study predicts the energy barrier to ring closure to be 25.0 +/- 3.1 kcal/mol and the enthalpy of reaction to be 4.9 +/- 3.2 kcal/mol. The latter value deviates significantly from the value estimated on the basis of group additivity and the Born-Haber cycle. The enediyne moiety is the main functional group of a new class of anticancer agents. The activation of the Bergman reaction in these drugs has been argued to be due to a small structural change in the terminal-terminal carbon distance of about -0.5 Angstrom originating from an epoxide conversion in the rest of the drug. The present study indicates that such a structural change is not sufficient for the Bergman autoaromatization to proceed at an appreciable rate. A new reaction path involving no biradical formation, resulting in the same products, is suggested.