We performed a diabatization of the mutually perturbed $1^1Pi$ and $2^1Pi$ states of KRb based on both electronic structure calculation and direct coupled-channel deperturbation analysis of experimental energies. The potential energy curves (PECs) of the diabatic states and their scalar coupling were constructed from the textit{ab initio} adiabatic PECs by analytically integrating the radial $langle psi_1^{ad}|partial /partial R|psi_2^{ad}rangle$ matrix element obtained by a finite-difference method. The diabatic potentials and electronic coupling function were refined by the least squares fitting of the rovibronic termvalues of the $1^1Pisim 2^1Pi$ complex. The empirical PECs combined with the coupling function as well as the diabatized spin-orbit coupling and transition dipole matrix elements are useful for further deperturbation treatment of both singlet and triplet states manifold.
We investigate the linear behavior in the 2+ ion concentration observed in the double photoionization of a variety of aromatic molecules. We show it arises when the photoelectrons are emitted simultaneously. Neglecting the momentum of the incoming photon and the momentum transferred to the molecule, it follows that the momenta of the individual photoelectrons are oppositely directed and equal in magnitude. Under steady-state conditions, the ion concentration is proportional to the rate at which the ions are created which, in turn, varies as the product of the densities of states of the individual electrons. The latter vary as the square root of the kinetic energy, leading to overall linear behavior. The origin of the linear behavior in pyrrole and related molecules is attributed to the presence of atoms that destroy the periodicity of a hypothetical carbon loop. In contrast, the resonant behavior observed in pyridine and related molecules, where a fraction of the CH pairs is replaced by N atoms, is associated with electron transfer between the nitrogen atoms and carbon atoms that preserves the periodicity of the closed loop.
Reliable quantum chemical methods for the description of molecules with dense-lying frontier orbitals are needed in the context of many chemical compounds and reactions. Here, we review developments that led to our newcomputational toolbo x which implements the quantum chemical density matrix renormalization group in a second-generation algorithm. We present an overview of the different components of this toolbox.
We make use of supersymmetric quantum mechanics (SUSY QM) to find three sets of conditions under which the problem of a planar quantum pendulum becomes analytically solvable. The analytic forms of the pendulums eigenfuntions make it possible to find analytic expressions for observables of interest, such as the expectation values of the angular momentum squared and of the orientation and alignment cosines as well as of the eigenenergy. Furthermore, we find that the topology of the intersections of the pendulums eigenenergy surfaces can be characterized by a single integer index whose values correspond to the sets of conditions under which the analytic solutions to the quantum pendulum problem exist.
The stationary nonempirical simulations of Na+(H2O)n clusters with n in a range of 28 to 51 carried out at the density functional level with a hybrid B3LYP functional and the Born-Oppenheimer molecular dynamics modeling of the size selected clusters reveal the interrelated structural and energetic peculiarities of sodium hydration structures. Surface, bulk, and transient configurations of the clusters are distinguished with the different location of the sodium nucleus (close to either the spatial center of the structure or one of its side faces) and its consistently changing coordination number (which typically equals five or six). The <rNaO> mean Na-O distances for the first-shell water molecules are found to depend both on the spatial character of the structure and the local coordination of sodium. The <rNaO> values are compared to different experimental estimates, and the virtual discrepancy of the latter is explained based on the results of the cluster simulations. Different coordination neighborhoods of sodium are predicted depending on its local fraction in the actual specimens.
The Ramachandran plot is a potent way to understand structures of biomolecules, however, the original formulation of the Ramachandran plot only considers backbone conformations. We formulate a new interpretation of the original Ramachandran plot ($phi-psi$) that can include a description of the weaker interactions including both the hydrogen bonds and H$---$H bonds as a new way to derive insights into the phenomenon of peptide folding. We use QTAIM (quantum theory of atoms in molecules) to interpret the Ramachandran plot. Specifically, we show that QTAIM analysis permits identifying key regions of the Ramachandran plot without the need for massive data sets. A highly non-linear relationship is found between the QTAIM vector-derived interpreted Ramachandran plot and the conventional Ramachandran plot ($phi-psi$) demonstrating that this new approach is not a trivial coordinate transformation. An investigation of both the backbone and the weaker bonds within the framework of the QTAIM interpreted Ramachandran plot was found to be in line with physical intuition. The least-preferred directions calculated for the hydrogen bonds and H$---$H bonds were found to coincide with the unlikely regions of the Ramachandran plot.
S. V. Kozlov
,E. A. Pazyuk
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(2016)
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"The twofold diabatization of the KRb $(1sim 2)^1Pi$ complex in the framework of emph{ab initio} and deperturbation approaches"
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Stolyarov Andrey V.
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