Quantized Vibrational Motion

2020 ◽  
pp. 281-305
Author(s):  
Jochen Autschbach
Keyword(s):  
Angular Momentum ◽  
Harmonic Oscillator ◽  
Potential Function ◽  
Vibrational Spectroscopy ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Atoms In Molecules ◽  
Vibrational Motion ◽  
Morse Oscillator ◽  
Internal Degrees Of Freedom

The harmonic oscillator of chapter 2 is visited again, now in its quantum theoretical version. The solution of the Schrodinger equation (SE) is shown step-by step, as it features steps that are very similar to those used in solving the equations for the angular momentum and hydrogen-like orbitals in later chapters. The Morse oscillator has a potential function that is much more representative of the vibrations of atoms in molecules as the harmonic potential. The solutions of the harmonic and Morse oscillator are compared. It is then shown how nuclear vibrations in poly-atomic molecules are treated at the harmonic level. This requires the separation of internal degrees of freedom from the overall translation and rotation of a molecule, leading to the normal modes. The chapter also discusses basic aspects of vibrational spectroscopy and the selection rules of infrared and Raman vibrational spectroscopy.

scholarly journals Structured 3D linear space–time light bullets by nonlocal nanophotonics

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Cheng Guo ◽  
Meng Xiao ◽  
Meir Orenstein ◽  
Shanhui Fan
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Pulse Shaping ◽  
Propagation Distance ◽  
Space Time ◽  
Spatial Modulation ◽  
Simultaneous Control ◽  
Modulation Techniques ◽  
Light Bullets ◽  
Internal Degrees Of Freedom

AbstractWe propose the generation of 3D linear light bullets propagating in free space using a single passive nonlocal optical surface. The nonlocal nanophotonics can generate space–time coupling without any need for bulky pulse-shaping and spatial modulation techniques. Our approach provides simultaneous control of various properties of the light bullets, including the external properties such as the group velocity and the propagation distance, and internal degrees of freedom such as the spin angular momentum and the orbital angular momentum.

Reversibly Sampling Conformations and Binding Modes Using Molecular Darting

2020 ◽  
Author(s):  
Samuel C. Gill ◽  
David Mobley
Keyword(s):  
Monte Carlo ◽  
Ligand Binding ◽  
Binding Sites ◽  
Degrees Of Freedom ◽  
Dynamics Simulation ◽  
Hiv Integrase ◽  
Binding Modes ◽  
System A ◽  
Multiple Binding ◽  
Internal Degrees Of Freedom

<div>Sampling multiple binding modes of a ligand in a single molecular dynamics simulation is difficult. A given ligand may have many internal degrees of freedom, along with many different ways it might orient itself a binding site or across several binding sites, all of which might be separated by large energy barriers. We have developed a novel Monte Carlo move called Molecular Darting (MolDarting) to reversibly sample between predefined binding modes of a ligand. Here, we couple this with nonequilibrium candidate Monte Carlo (NCMC) to improve acceptance of moves.</div><div>We apply this technique to a simple dipeptide system, a ligand binding to T4 Lysozyme L99A, and ligand binding to HIV integrase in order to test this new method. We observe significant increases in acceptance compared to uniformly sampling the internal, and rotational/translational degrees of freedom in these systems.</div>

Triatomic molecules

2018 ◽  
Author(s):  
John H. D. Eland ◽  
Raimund Feifel
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Electronic States ◽  
Triatomic Molecules ◽  
Doubly Charged Ions ◽  
Spectral Bands ◽  
Valence Electrons ◽  
Doubly Charged ◽  
Charged Ions ◽  
Double Ionisation

Double ionisation of the triatomic molecules presented in this chapter shows an added degree of complexity. Besides potentially having many more electrons, they have three vibrational degrees of freedom (three normal modes) instead of the single one in a diatomic molecule. For asymmetric and bent triatomic molecules multiple modes can be excited, so the spectral bands may be congested in all forms of electronic spectra, including double ionisation. Double photoionisation spectra of H2O, H2S, HCN, CO2, N2O, OCS, CS2, BrCN, ICN, HgCl2, NO2, and SO2 are presented with analysis to identify the electronic states of the doubly charged ions. The order of the molecules in this chapter is set first by the number of valence electrons, then by the molecular weight.

scholarly journals A novel class of translationally invariant spin chains with long-range interactions

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
B. Basu-Mallick ◽  
F. Finkel ◽  
A. González-López
Keyword(s):  
Long Range ◽  
Degrees Of Freedom ◽  
Spin Chains ◽  
Open Chain ◽  
New Class ◽  
Spin Interactions ◽  
Long Range Interactions ◽  
Spin Reversal ◽  
Twisted Yangian ◽  
Internal Degrees Of Freedom

Abstract We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case. The new class is characterized by the fact that the Hamiltonian is invariant under “twisted” translations, combining an ordinary translation with a spin flip at one end of the chain. It includes a remarkable model with elliptic spin-spin interactions, smoothly interpolating between the XXX Heisenberg model with anti-periodic boundary conditions and a new open chain with sites uniformly spaced on a half-circle and interactions inversely proportional to the square of the distance between the spins. We are able to compute in closed form the partition function of the latter chain, thereby obtaining a complete description of its spectrum in terms of a pair of independent su(1|1) and su(m/2) motifs when the number m of internal degrees of freedom is even. This implies that the even m model is invariant under the direct sum of the Yangians Y (gl(1|1)) and Y (gl(0|m/2)). We also analyze several statistical properties of the new chain’s spectrum. In particular, we show that it is highly degenerate, which strongly suggests the existence of an underlying (twisted) Yangian symmetry also for odd m.

scholarly journals Dissipative dynamics of a particle coupled to a field via internal degrees of freedom

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Kanupriya Sinha ◽  
Adrián Ezequiel Rubio López ◽  
Yiğit Subaşı
Keyword(s):  
Degrees Of Freedom ◽  
Dissipative Dynamics ◽  
Internal Degrees Of Freedom

scholarly journals Optimal Relabeling of Water Molecules and Single-Molecule Entropy Estimation

Biophysica ◽  
2021 ◽  
Vol 1 (3) ◽  
pp. 279-296
Author(s):  
Federico Fogolari ◽  
Gennaro Esposito
Keyword(s):  
Single Molecule ◽  
Degrees Of Freedom ◽  
Water Molecules ◽  
Maximum Information ◽  
Nearest Neighbours ◽  
Biomolecular Simulations ◽  
Solvent Molecules ◽  
Solvation Entropy ◽  
Dynamics Simulations ◽  
Internal Degrees Of Freedom

Estimation of solvent entropy from equilibrium molecular dynamics simulations is a long-standing problem in statistical mechanics. In recent years, methods that estimate entropy using k-th nearest neighbours (kNN) have been applied to internal degrees of freedom in biomolecular simulations, and for the rigorous computation of positional-orientational entropy of one and two molecules. The mutual information expansion (MIE) and the maximum information spanning tree (MIST) methods were proposed and used to deal with a large number of non-independent degrees of freedom, providing estimates or bounds on the global entropy, thus complementing the kNN method. The application of the combination of such methods to solvent molecules appears problematic because of the indistinguishability of molecules and of their symmetric parts. All indistiguishable molecules span the same global conformational volume, making application of MIE and MIST methods difficult. Here, we address the problem of indistinguishability by relabeling water molecules in such a way that each water molecule spans only a local region throughout the simulation. Then, we work out approximations and show how to compute the single-molecule entropy for the system of relabeled molecules. The results suggest that relabeling water molecules is promising for computation of solvation entropy.

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