A density functional theory computational study of the role of ligand on the stability of CuI and CuII species associated with ATRP and SET‐LRP

Atom transfer radical polymerization (ATRP) and single electron‐transfer living radical polymerization (SET‐LRP) both utilize copper complexes of various oxidation states with N‐ligands to perform their respective activation and deactivation steps. Herein, we utilize DFT (B3YLP) methods to determine the preferred ligand‐binding geometries for Cu/N‐ligand complexes related to ATRP and SET‐LRP. We find that those ligands capable of achieving tetrahedral complexes with Cu^I and trigonal bipyramidal with axial halide complexes with [Cu^IIX]⁺ have higher energies of stabilization. We were able to correlate calculated preferential stabilization of [Cu^IIX]⁺ with those ligands that perform best in SET‐LRP. A crude calculation of energy of disproportionation revealed that the same preferential binding of [Cu^IIX]⁺ results in increased propensity for disproportionation. Finally, by examining the relative energies of the basic steps of ATRP and SET‐LRP, we were able to rationalize the transition from the ATRP mechanism to the SET‐LRP mechanism as we transition from typical nonpolar ATRP solvents to polar SET‐LRP solvents. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4950–4964, 2007     

A partial differential equation which describes an interatomic surface

In this work we present a first-order partial differential equationwhich defines the topology of single ‘atomic entities’in multiatomic systems. Such an equation, obtained by R. F.W. Bader, is here analysed and discussed from a general mathematicalpoint of view; a method is then proposed for defining the initialor boundary condition. With this contribution we would liketo promote and stimulate a more detailed analysis which goesbeyond practical purposes and basic mathematical analysis inorder to have a deeper understanding of the theory behind theequation and its consequences for practical applications.     

An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

Calculation of the proton affinities of polyfluorobenzenes and the activation energies for 1,2-hydrogen shifts in their carbocations

Isolated polyfluorobenzene (PFB) molecules and their protonated forms are investigated by the AM1 method with full geometry optimization. The proton affinities of PFB are estimated for different protonated positions. The proton affinity of PFB averaged over all isomers is shown to decrease monotonically as the number of fluorine atoms in the molecule increases. The relative populations of different isomers of arenonium ions (AI) formed by PFB protonation are determined. From the calculated data, the value of ⁺ for the F atom in theipso-position is estimated as 1.00. The activation energies of the 1,2-hydrogen shifts in AI are calculated. The dependences of the proton affinity and the activation energies of 1,2-hydrogen shifts on the number of halogen atoms are found to have distinct characters for PFB and polychlorobenzenes. The physical reasons for these difference are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1878–1882, November, 1993.     

Evaluation of Multicenter Electronic Attraction, Electric Field and Electric Field Gradient Integrals with Screened and Nonscreened Coulomb Potentials over Integer and Noninteger n Slater Orbitals

By the use of complete orthonormal sets of -exponential-type orbitals, where ( = 1, 0, –1, –2,...) the multicenter electronic attraction (EA), electric field (EF) and electric field gradient (EFG) integrals of nonscreened and Yukawa-like screened Coulomb potentials are expressed through the two-center overlap integrals with the same screening constants and the auxiliary functions introduced in our previous paper (I.I. Guseinov, J. Phys. B, 3 (1970) 1399). The recurrence relations for auxiliary functions are useful for the calculation of multicenter EA, EF and EFG integrals for arbitrary integer and noninteger values of principal quantum numbers, screening constants, and location of slater-type orbitals. The convergence of the series is tested by calculating concrete cases.     

Basis Set Orbital Relaxation in Atomic and Molecular Hydrogen Systems

Orbital relaxation (OR) amounts to variation of the orbital exponents in hydrogen molecules and ions relative to the exponents of the isolated atom; it is represented as the sum of the one- and two-center contributions depending on the effective atomic charge and on the presence of other atoms in the molecule. The procedure for isolating the contributions of the exponent includes treatment of the OR of hydrogen in a special set of neutral and charged atoms and molecules with certain multiplicities of their electronic states. Within the framework of the spin-unrestricted Hartree-Fock method, we found and discussed the optimal values of the exponents of the basis orbitals of hydrogen atoms and molecules using the minimal split valence-shell basis set, the basis set that includes the polarization function, and the expanded set of grouped natural orbitals. A simple energy model is suggested for OR. Expressions are derived for evaluating the exponents of the relaxed orbitals in hydrogen-containing systems.Original Russian Text Copyright © 2004 by A. I. Ermakov, A. E. Merkulov, A. A. Svechnikova, and V. V. Belousov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 973–978, November–December, 2004.     

The complete symmetrization of quantum operators: new thoughts on an old problem

The complete symmetrization with respect to x, p _x,... of the operators associated with dynamical properties can sometimes lead to results different from those obtained by the conventional quantum formalism based on the rule op (A ²)=(op A)². For example, angular momentum operators M _z ² and M ² are modified by the additive constants ²/2 and 3 ²/2 respectively (M ²0 for electron in the ground state of H atom, rotator never at rest, but spectra unchanged); the average quadratic dispersion of energy is different from zero. These results can be interpreted by assuming that the system is never strictly isolated but communicates with the other systems of the universe by means of electromagnetic interactions. Quantum mechanics would give only average values over a sufficiently long time and would exhibit a quasi-ergodic character. Examples supporting this possibility are given, in particular that of arsines for which quantum forecasts correspond to average values over one year.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Quantum Information Entropies on Hyperbolic Single Potential Wells

In this work, we study the quantum information entropies for two different types of hyperbolic single potential wells. We first study the behaviors of the moving particle subject to two different hyperbolic potential wells through focusing on their wave functions. The shapes of these hyperbolic potentials are similar, but we notice that their momentum entropy densities change along with the width of each potential and the magnitude of position entropy density decreases when the momentum entropy magnitude increases. On the other hand, we illustrate the behaviors of their position and momentum entropy densities. Finally, we show the variation of position and momentum entropies Sx and Sp with the change of the potential well depth u and verify that their sum still satisfies the BBM inequality relation.     

Quantum-Inspired Complex-Valued Language Models for Aspect-Based Sentiment Classification

Aiming at classifying the polarities over aspects, aspect-based sentiment analysis (ABSA) is a fine-grained task of sentiment analysis. The vector representations of current models are generally constrained to real values. Based on mathematical formulations of quantum theory, quantum language models have drawn increasing attention. Words in such models can be projected as physical particles in quantum systems, and naturally represented by representation-rich complex-valued vectors in a Hilbert Space, rather than real-valued ones. In this paper, the Hilbert Space representation for ABSA models is investigated and the complexification of three strong real-valued baselines are constructed. Experimental results demonstrate the effectiveness of complexification and the outperformance of our complex-valued models, illustrating that the complex-valued embedding can carry additional information beyond the real embedding. Especially, a complex-valued RoBERTa model outperforms or approaches the previous state-of-the-art on three standard benchmarking datasets.