Semiclassical theory of Fermi resonance between stretching and bending modes in polyatomic molecules

Approximate semiclassical solutions are developed for a system of a Morse oscillator coupled to a harmonic oscillator via a nonlinear perturbation. This system serves as a model for the interaction of an excited stretching mode with a bending mode in a polyatomic molecule. Three semiclassical methods are used to treat this model. In particular, a matrix diagonalization, a two‐state model, and a uniform semiclassical approximation (USC) based on Mathieu functions are each used to determine the splittings and state mixing involved in these stretch–bend Fermi resonances. For small perturbations, approximate analytic semiclassical expressions are obtained for the system treated. These analytic expressions are given for the splittings using a two‐state or USC method and for the overlaps of the zeroth order states with the eigenstates of the molecule using a USC method

The highly excited C-H stretching states of CHD_3, CHT_3, and CH_3D

Unlike many other molecules having local modes, the highly excited C-H stretching states of CHD_3 show well resolved experimental spectra and simple Fermi resonance behavior. In this paper the local mode features in this prototype molecule are examined using a curvilinear coordinate approach. Theory and experiment are used to identify the vibrational state coupling. Both kinetic and potential terms are employed in order to characterize the coupling of the C-H stretch to various other vibrational modes, notably those including D-C-H bending. Predictions are also made for CHT_3 and the role of dynamical coupling on the vibrational states of CH_3D explored. Implications of these findings for mode-specific and other couplings are discussed

A Fully Self-Consistent Treatment of Collective Fluctuations in Quantum Liquids

The problem of calculating collective density fluctuations in quantum liquids is revisited. A fully quantum mechanical self-consistent treatment based on a quantum mode-coupling theory [E. Rabani and D.R. Reichman, J. Chem. Phys.116, 6271 (2002)] is presented. The theory is compared with the maximum entropy analytic continuation approach and with available experimental results. The quantum mode-coupling theory provides semi-quantitative results for both short and long time dynamics. The proper description of long time phenomena is important in future study of problems related to the physics of glassy quantum systems, and to the study of collective fluctuations in Bose fluids.Comment: 9 pages, 4 figure

Ordered Clusters and Dynamical States of Particles in a Vibrated Fluid

Reports the discovery and explanation of ordered arrangements of particles that are immersed in a fluid. When they move with respect to the fluid, dynamical forces arise that are mediated by the fluid. These forces lead to self-assembly of structures. --author-supplied descriptio

Adiabatically reduced coupled equations for intramolecular dynamics calculations

"Adiabatically reduced" coupled equations are derived to obtain an approximate quantum mechanical solution for the dynamics of nonstationary states in isolated polyatomic molecules. Under suitable conditions, the number of such equations is considerably less than the number of coupled equations needed in practice for the exact calculation. The relationship of the present technique to several other methods, including the partitioning method, is discussed, and specific applications of the present treatment are given

Immature HIV-1 assembles from Gag dimers leaving partial hexamers at lattice edges as potential substrates for proteolytic maturation

The CA (capsid) domain of immature HIV-1 Gag and the adjacent spacer peptide 1 (SP1) play a key role in viral assembly by forming a lattice of CA hexamers, which adapts to viral envelope curvature by incorporating small lattice defects and a large gap at the site of budding. This lattice is stabilized by intrahexameric and interhexameric CA-CA interactions, which are important in regulating viral assembly and maturation. We applied subtomogram averaging and classification to determine the oligomerization state of CA at lattice edges and found that CA forms partial hexamers. These structures reveal the network of interactions formed by CA-SP1 at the lattice edge. We also performed atomistic molecular dynamics simulations of CA-CA interactions stabilizing the immature lattice and partial CA-SP1 helical bundles. Free energy calculations reveal increased propensity for helix-to-coil transitions in partial hexamers compared to complete six-helix bundles. Taken together, these results suggest that the CA dimer is the basic unit of lattice assembly, partial hexamers exist at lattice edges, these are in a helix-coil dynamic equilibrium, and partial helical bundles are more likely to unfold, representing potential sites for HIV-1 maturation initiation

Local Variational Principle

A generalization of the Gibbs-Bogoliubov-Feynman inequality for spinless particles is proven and then illustrated for the simple model of a symmetric double-well quartic potential. The method gives a pointwise lower bound for the finite-temperature density matrix and it can be systematically improved by the Trotter composition rule. It is also shown to produce groundstate energies better than the ones given by the Rayleigh-Ritz principle as applied to the groundstate eigenfunctions of the reference potentials. Based on this observation, it is argued that the Local Variational Principle performs better than the equivalent methods based on the centroid path idea and on the Gibbs-Bogoliubov-Feynman variational principle, especially in the range of low temperatures.Comment: 15 pages, 5 figures, one more section adde