Photophysical Deactivation Mechanisms of the Pyrimidine Analogue 1-Cyclohexyluracil

The photophysical relaxation mechanisms of 1-cyclohexyluracil, in vacuum and water, were investigated by employing the Multi-State CASPT2 (MS-CASPT2, Multi-State Complete Active-Space Second-Order Perturbation Theory) quantum chemical method and Dunning’s cc-pVDZ basis sets. In both environments, our results suggest that the primary photophysical event is the population of the S11(ππ*) bright state. Afterwards, two likely deactivation pathways can take place, which is sustained by linear interpolation in internal coordinates defined via Z-Matrix scans connecting the most important characteristic points. The first one (Route 1) is the same relaxation mechanism observed for uracil, its canonical analogue, i.e., internal conversion to the ground state through an ethylenic-like conical intersection. The other route (Route 2) is the direct population transfer from the S11(ππ*) bright state to the T23(nπ*) triplet state via an intersystem crossing process involving the (S11(ππ*)/T23(nπ*))STCP singlet-triplet crossing point. As the spin-orbit coupling is not too large in either environment, we propose that most of the electronic population initially on the S11(ππ*) state returns to the ground following the same ultrafast deactivation mechanism observed in uracil (Route 1), while a smaller percentage goes to the triplet manifold. The presence of a minimum on the S11(ππ*) potential energy hypersurface in water can help to understand why experimentally it is noticed suppression of the triplet states population in polar protic solvent.

Where Quantum Biochemistry Meets Structural Bioinformatics: Excited Conformationally-Tautomeric States of the Classical A·T DNA Base Pair

This Chapter summarizes recent quantum-chemical (QM) investigations of the novel conformational and tautomeric states on the potential energy hypersurface of the classical A·T/A·U nucleobase pairs. For the first time, it was observed 28 local minima for each base pair excluding enantiomers - planar, non-planar base pairs and structures with wobble geometry. Considered excited conformationally-tautomeric states of the classical A·T DNA base pair have been revealed in the Nucleic Acid Database by structural bioinformatics. These data shed light on the biological significance of the unusual A·T/A·U nucleobase pairs for the functioning of the nucleic acids at the quantum level.

Computational Study of the C-H∙∙∙H-C Contacts in Valine-Methane Complexes.

<div> <p>A series of complexes between neutral Valine and methane that feature potential homopolar C-H∙∙∙H-C contacts were located on the MP2/aug-cc-pVTZ potential energy hypersurface. In order to better estimate the strength of this contacts, the interaction energies were improve by single-point calculations at different levels of theory (MP2, CCSD(T), SAPT2, SAPT2+3) together with Dunning’s basis sets (aug-cc-pVXZ; X=T,Q,5). Topological analysis of the electron density within the QTAIM framework, NCI plots and energy decomposition within the SAPT framework were used to discuss the nature of this interactions. The complexes whose monomers only interact though C-H∙∙∙H-C contacts indicate that these interactions are entirely due to dispersion forces, are not directional and are much stronger than expected (the interaction energies of the complexes range from -0.7 to -1.0 kcal/mol). This large value is remarkable considering the small size of the interacting groups herein considered (methane, and one or two Valine’s methyl groups), and indicates that in biological systems, where those interactions can be very numerous in the presence of multiple aliphatic amino acids, if those interactions are not properly model, magnitudes as ligand-receptor affinities, protein-protein interaction energies and protein stabilities might be grossly misestimated. Finally, since some of the computed complexes also include stronger interactions than homopolar C-H∙∙∙H-C contacts, we analyzed if the potential C-H∙∙∙H-C contacts in these complexes are really contributing to stabilize the complexes or are just a geometrical artifact arising from the maximization of stronger interactions.</p> </div>

Computational Study of the C-H∙∙∙H-C Contacts in Valine-Methane Complexes.

<div> <p>A series of complexes between neutral Valine and methane that feature potential homopolar C-H∙∙∙H-C contacts were located on the MP2/aug-cc-pVTZ potential energy hypersurface. In order to better estimate the strength of this contacts, the interaction energies were improve by single-point calculations at different levels of theory (MP2, CCSD(T), SAPT2, SAPT2+3) together with Dunning’s basis sets (aug-cc-pVXZ; X=T,Q,5). Topological analysis of the electron density within the QTAIM framework, NCI plots and energy decomposition within the SAPT framework were used to discuss the nature of this interactions. The complexes whose monomers only interact though C-H∙∙∙H-C contacts indicate that these interactions are entirely due to dispersion forces, are not directional and are much stronger than expected (the interaction energies of the complexes range from -0.7 to -1.0 kcal/mol). This large value is remarkable considering the small size of the interacting groups herein considered (methane, and one or two Valine’s methyl groups), and indicates that in biological systems, where those interactions can be very numerous in the presence of multiple aliphatic amino acids, if those interactions are not properly model, magnitudes as ligand-receptor affinities, protein-protein interaction energies and protein stabilities might be grossly misestimated. Finally, since some of the computed complexes also include stronger interactions than homopolar C-H∙∙∙H-C contacts, we analyzed if the potential C-H∙∙∙H-C contacts in these complexes are really contributing to stabilize the complexes or are just a geometrical artifact arising from the maximization of stronger interactions.</p> </div>

Rare Energy-Conservative Attractors on Global Invariant Hypersurfaces and Their Multistability

A general formalism describing a type of energy-conservative system is established. Some possible dynamic behaviors of such energy-conservative systems are analyzed from the perspective of geometric invariance. A specific 4D chaotic energy-conservative system with a line of equilibria is constructed and analyzed. Typically, an energy-conservative system is also conservative in preserving its phase volume. The constructed system however is conservative only in energy but is dissipative in phase volume. It produces energy-conservative attractors specifically exhibiting chaotic 2-torus and quasiperiodic behaviors including regular 2-torus and 3-torus. From the basin of attraction containing a line of equilibria, the hidden nature of chaotic attractors generated from the system is further discussed. The energy hypersurface on which the attractors lie is determined by the initial value, which generates complex dynamics and multistability, verified by energy-related bifurcation diagrams and Poincaré sections. A new type of coexistence of attractors on the equal-energy hypersurface is discovered by turning the system parameter values to their opposite. The basins of attraction under three sets of parameter values demonstrate that the Hamiltonian is the leading factor predominating the dynamic behaviors of the system with a closed energy hypersurface. Finally, an analog circuit is designed and implemented to demonstrate the consistent theoretical and simulation results.

A prelude to building mathematical models for polypeptide folding: analysis on the conformational potential energy hypersurface cross-sections of N-acetyl-glycyl-glycine-N′-methylamide

Finding a relationship on how a three-dimensional protein folds from its linear amino acid chain gets more complex with increasing chain length, so working on a smaller peptide conformational problem can provide initial ideas on what are the main molecular forces and how these influence the folding process. Following the study of conformations of amino acid units entering the proteins to understand the secondary structure of small peptides, this paper proposes mathematical models for the several two-rotor cross-sections of the five-dimensional N-acetyl-glycyl-glycine-N′-methylamide potential energy hypersurface (PEHS). These cross-sections are extracted along the first glycine subunit, with its coordinates fixed at the five energy minima of the glycine diamide. The resulting mathematical models yield an average RMSE of 1.36 kJ mol−1 and an average R2 of 0.9923 with respect to energy values obtained from DFT calculations. The minima geometries obtained from these models are also in good agreement with DFT-optimized energy minima conformers. An important aspect of this study also tackles the relationship between the PEHS of the glycyl-glycine diamide and its glycine subunits. It has been observed that there are deviations up to 28.35 kJ mol−1 and 29.52 kJ mol−1 between the PEHS cross-sections along γL and γD conformations, respectively, in the first glycine subunit. This may suggest that there are significant backbone–backbone intermolecular forces acting on the dipeptide. The abovementioned findings can help in developing more complex mathematical models for polypeptide folding from amino acid subunits.

Dynamical convexity of the Euler problem of two fixed centers

We give thorough analysis for the rotation functions of the critical orbits from which one can understand bifurcations of periodic orbits. Moreover, we give explicit formulas of the Conley–Zehnder indices of the interior and exterior collision orbits and show that the universal cover of the regularised energy hypersurface of the Euler problem is dynamically convex for energies below the critical Jacobi energy.

The Conley–Zehnder indices of the rotating Kepler problem

We determine the Conley–Zehnder indices of all periodic orbits of the rotating Kepler problem for energies below the critical Jacobi energy. Consequently, we show the universal cover of the bounded component of the regularized energy hypersurface is dynamically convex. Moreover, in the universal cover there is always precisely one periodic orbit with Conley–Zehnder index 3, namely the lift of the doubly covered retrograde circular orbit.