Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.

Non-antisymmetric versions of Nambu-Poisson and Lie algebroids

Abstract: We show that one can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi identity must be skew-symmetric. A similar result holds for a non-antisymmetric version of Lie algebroids.

Clarification of the electronic asymmetry of Λ doublets in 3Π electronic states of diatomic molecules

Abstract: The reflection symmetry of the spatial part of the electronic wave function for 3Π diatomic molecular states is examined carefully for the individual Λ doublet levels by means of an approach presented earlier [M. H. Alexander and P. J. Dagdigian, J. Chem. Phys. 80, 4325 (1984)]. The results are: For a 3Π molecule in Hund’s case (a) the electronic wave function in the Ω=1 (F2) e levels will be antisymmetric and, in the the f levels, symmetric with respect to reflection of the spatial coordinates of the electrons in the plane of rotation of the molecule. The electronic wave functions in the F1 and F3 levels will not have a defined plane of symmetry. By contrast, in the Hund’s case (b) high J limit, the electronic wave function in the F1e, F2 f, and F3e levels will be antisymmetric and, in the F1 f, F2e, and F3 f levels, symmetric with respect to reflection. Thus, the symmetry of the wave functions in the F2Λ‐doublet levels reverses with the passage from case (a) to case (b). In the case (b) limit, the main ...

Accelerating Convergence in the Antisymmetric Product of Strongly Orthogonal Geminals Method

Abstract: Antisymmetric product of strongly orthogonal geminals (APSG) method is a wavefunction theory that can effectively treat the static electron correlation using twoelectron wavefunctions, called geminals. However, the APSG method has the problem of slow convergence in the optimization of the geminal function. In this study, we introduced the direct inversion in the iterative subspace (DIIS) method, for both closed- and open-shell systems, for accelerating its convergence. Two types of error vectors, that is, unitary transformation and orbital gradient, were examined for the DIIS procedure. Numerical assessments revealed that the orbital-gradient error vector shows better performance than the unitary-transformation one. V C 2012

An antisymmetric neural network to predict free energy changes in protein variants

Abstract: The prediction of free energy changes upon protein residue variations is an important application in biophysics and biomedicine. Several methods have been developed to address this problem so far, including physical-based and machine learning models. However, most of the current computational tools, especially data-driven approaches, fail to incorporate the antisymmetric basic thermodynamic principle: a variation from wild-type to a mutated form of the protein structure ( XW→XM ) and its reverse process ( XM→XW ) must have opposite values of the free energy difference: ΔΔGWM=−ΔΔGMW . Here, we build a deep neural network system that, by construction, satisfies the antisymmetric properties. We show that the new method (ACDC-NN) achieved comparable or better performance with respect to other state-of-the-art approaches on both direct and reverse variations, making this method suitable for scoring new protein variants preserving the antisymmetry. The code is available at: https://github.com/compbiomed-unito/acdc-nn.