scholarly journals Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

2015 ◽  
Vol 11 (2) ◽  
pp. 415-422 ◽  
Author(s):  
Raffaele Borrelli ◽  
Andrea Peluso
Keyword(s):  
Quantum Dynamics ◽  
Normal Modes ◽  
Second Order ◽  
Electronic Transitions

Second-Order Fourier Synthesis of Broadband Acoustic Signals Using Normal Modes

1997 ◽  
Vol 05 (04) ◽  
pp. 355-370 ◽  
Author(s):  
E. K. Skarsoulis
Keyword(s):  
Time Domain ◽  
Normal Modes ◽  
Acoustic Signals ◽  
Second Order ◽  
Single Frequency ◽  
Closed Form Expression ◽  
Fourier Synthesis ◽  
Eigenvalues And Eigenfunctions ◽  
Intermediate Order ◽  
The Time Domain

A scheme for approximate normal-mode calculation of broadband acoustic signals in the time domain is proposed based on a second-order Taylor expansion of eigenvalues and eigenfunctions with respect to frequency. For the case of a Gaussian impulse source a closed-form expression is derived for the pressure in the time domain. Using perturbation theory, analytical expressions are obtained for the involved first and second frequency-derivatives of eigenvalues and eigenfunctions. The proposed approximation significantly accelerates arrival-pattern calculations, since the eigenvalues, the eigenfunctions and their frequency-derivatives need to be calculated at a single frequency, the central frequency of the source. Furthermore, it offers a satisfactory degree of accuracy for the lower and intermediate order modes. This is due to the fact that essential wave-theoretic mechanisms such as dispersion and frequency dependence of mode amplitudes are contained in the representation up to a sufficient order. Numerical results demonstrate the efficiency of the method.

Quantum Chemical Studies on the Spectroscopic, Electronic Structural and Nonlinear Properties of an Organic N-Methyl-N- (2,4,6-Trinitrophenyl) Nitramide Energetic Molecule

2019 ◽  
Vol 9 (1) ◽  
pp. 5-21
Author(s):  
Anbu Veerappan ◽  
Vijayalakshmi Karattadipalayam Arumugam
Keyword(s):  
Reference Material ◽  
Structural Properties ◽  
Quantum Chemical ◽  
Energy Gap ◽  
Normal Modes ◽  
Lone Pair ◽  
Second Order ◽  
Potential Energy Distribution ◽  
Nlo Response ◽  
Ft Ir

Background: Earlier studies on the energetic molecule MTNPN show a small HOMO-LUMO energy gap. In general, the material which acquires small energy gap exhibits NLO response and identical counterparts in both IR and Raman spectra. Hence, the combined experimental and theoretical studies were performed to explore the fundamental properties of the molecule. Objective: The objective of this study was to explore the fundamental structural properties of an energetic molecule MTNPN in addition to its application as a nonlinear optical material. Methods: FT-IR technique and quantum chemical methods were used to analyze the vibrational normal modes and structural properties of the molecule. Kurtz and Perry technique is used to find second harmonic generation efficiency in comparison to the standard NLO reference material. Results: The potential energy distribution was used to assign the vibrational normal modes of the molecule. The second order perturbation energies between the lone pair and anti-bonding species were predicted to understand the driving forces of molecular stability. The chemical reactivity of the molecule was determined from the molecular electrostatic potential surface and global reactivity descriptor results. The second-order hyperpolarizability of MTNPN and SHG efficiency of MTNPN were studied to find its NLO response and it was found from the results that MTNPN exhibits high NLO response than the standard NLO reference material. Conclusion: The vibrational degrees of freedom of MTNPN molecule were assigned and the experimental FT-IR spectra were compared with the scaled harmonic frequencies. The predicted second-order hyperpolarizability of MTNPN was about 6.46 times greater than the standard NLO reference urea. The interacting species between the lone pair orbitals and antibonding orbitals such as n3O8→ π*(N7-O9), n3O11→ π*(N10-O12) and n3O14→ π*(N13-O15) stabilized the molecule to a greater extent.

scholarly journals Normal modes of a laterally heterogeneous body: A one-dimensional example

1978 ◽  
Vol 68 (1) ◽  
pp. 103-116
Author(s):  
Robert J. Geller ◽  
Seth Stein
Keyword(s):  
Perturbation Theory ◽  
Variational Method ◽  
Normal Modes ◽  
Second Order ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Transient Solution ◽  
Eigenvalues And Eigenfunctions ◽  
One Dimensional ◽  
Second Order Perturbation Theory

abstract Various methods, including first- and second-order perturbation theory and variational methods have been proposed for calculating the normal modes of a laterally heterogeneous earth. In this paper, we test all three of these methods for a simple one-dimensional example for which the exact solution is available: an initially homogeneous “string” in which the density and stiffness are increased in one half and decreased in the other by equal amounts. It is found that first-order perturbation theory (as commonly applied in seismology) yields only the eigenvalues and eigenfunctions for a string with the average elastic properties; second-order perturbation theory is worse, because the eigenfunction is assumed to be the original eigenfunction plus small correction terms, but actually may be almost completely different. The variational method (Rayleigh-Ritz), using the unperturbed modes as trial functions, succeeds in giving correct eigenvalues and eigenfunctions even for modes of high-order number. For the example problem only the variational solution correctly yields the transient solution for excitation by a point force, including correct amplitudes for waves reflected by and transmitted through the discontinuity. Our result suggests but does not demonstrate, that the variational method may be the most appropriate method for finding the normal modes of a laterally heterogeneous earth model, particularly if the transient solution is desired.

scholarly journals Non-adiabatic Matsubara Dynamics and Non-adiabatic Ring Polymer Molecular Dynamics

2020 ◽  
Author(s):  
Sutirtha N. Chowdhury ◽  
Pengfei Huo
Keyword(s):  
Molecular Dynamics ◽  
Correlation Function ◽  
Quantum Dynamics ◽  
General Framework ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics

We present the non-adiabatic Matsubara dynamics, a general framework for computing the time-correlation function (TCF) of electronically non-adiabatic systems. This new formalism is derived based on the generalized Kubo-transformed time-correlation function, using the Wigner representation for both the nuclear degrees of freedom (DOF) and the electronic mapping variables. By dropping the non-Matsubara nuclear normal modes in the quantum Liouvillian and explicitly integrate these modes out of the TCF, we derived the non-adiabatic Matsubara dynamics approach. Further making the approximation to drop the imaginary part of the Matsubara Liouvillian and enforce the nuclear momentum integral to be real, we arrived at the non-adiabatic ring-polymer molecular dynamics (NRPMD) approach. We have further justified the capability of NRPMD for simulating the non-equilibrium time-correlation function. This work provides the rigorous theoretical foundation for several recently proposed state-dependent RPMD approaches and offers a general framework for developing new non-adiabatic quantum dynamics approaches in the future.

scholarly journals Non-adiabatic Matsubara Dynamics and Non-adiabatic Ring Polymer Molecular Dynamics

2020 ◽  
Author(s):  
Sutirtha N. Chowdhury ◽  
Pengfei Huo
Keyword(s):  
Molecular Dynamics ◽  
Correlation Function ◽  
Quantum Dynamics ◽  
General Framework ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics

We present the non-adiabatic Matsubara dynamics, a general framework for computing the time-correlation function (TCF) of electronically non-adiabatic systems. This new formalism is derived based on the generalized Kubo-transformed time-correlation function, using the Wigner representation for both the nuclear degrees of freedom (DOF) and the electronic mapping variables. By dropping the non-Matsubara nuclear normal modes in the quantum Liouvillian and explicitly integrate these modes out of the TCF, we derived the non-adiabatic Matsubara dynamics approach. Further making the approximation to drop the imaginary part of the Matsubara Liouvillian and enforce the nuclear momentum integral to be real, we arrived at the non-adiabatic ring-polymer molecular dynamics (NRPMD) approach. We have further justified the capability of NRPMD for simulating the non-equilibrium time-correlation function. This work provides the rigorous theoretical foundation for several recently proposed state-dependent RPMD approaches and offers a general framework for developing new non-adiabatic quantum dynamics approaches in the future.

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