The effect of the nuclear motion on harmonic spectral structure

2019 ◽  
Vol 33 (17) ◽  
pp. 1950186 ◽  
Author(s):  
Cai-Ping Zhang ◽  
Chang-Long Xia ◽  
Xiang-Yang Miao
Keyword(s):  
Vibrational State ◽  
Electronic States ◽  
Time Dependent ◽  
Symmetric System ◽  
Nuclear Motion ◽  
Spectral Structure ◽  
Vibrational States ◽  
Coupling Region ◽  
Electronic Distribution ◽  
Even Harmonics

The harmonic emissions from hydrogen molecular ion at different initial vibrational states have been simulated by numerically solving the time-dependent Schrödinger equation. The results show that the nuclear motion exhibits different effects on the spectral structure for different vibrational states. For lower vibrational state, the odd harmonics experience obvious harmonic shifting; however, for higher vibrational state, the even harmonics are emitted from the symmetric system due to the asymmetric electronic distribution in the coupling region of two lowest electronic states.

Nuclear Quadrupole Hyperfine Structure of the Direct /-Type Transitions of the Fulminic Acid Isotopomers H12C14N16O and H13C14N16O

1996 ◽  
Vol 51 (3) ◽  
pp. 207-214
Author(s):  
Jürgen Preusser ◽  
Manfred Winnewisser
Keyword(s):  
Hyperfine Structure ◽  
Vibrational State ◽  
Line Broadening ◽  
Frequency Range ◽  
Vibrational States ◽  
Contour Fitting ◽  
Splitting Parameter ◽  
Nuclear Quadrupole ◽  
Significant Line ◽  
Large Amplitude Motion

The direct I- type transitions of H133C14N16O in the vibrational states (υ4,υ5) = (01) and (03) were measured in the frequency range from 18 to 40 GHz. These transitions show a nuclear quadrupole hyperfine structure caused by the 14N nucleus, which could partially be resolved at Doppler-limited resolution. The analogous transitions of the parent species. H12C14N16O, were remeasured. They displayed a very similar hyperfine structure, also partially resolved. The hyperfine patterns of both H12C14N16O and H13C14N16O were analysed by means of contour fitting s to the absorption profiles. The parameter ηseQq, which is responsible for the splittings, is determined to be 645(20) kHz for the vibrational state (01) and 890(44) kHz for the vibrational state (03) for H12C14N16O and 642(32) kHz for (01) and 898(22) kHz for (03) for H13C14N16O. This unexpectedly large splitting parameter for states involving the large amplitude motion υ5 (HCN bending) is discussed as another consequence of the quasilinearity of fulminic acid, in view of the fact that the analogous transitions for the vibrational state (10) (NCO bending) do not split or even show a significant line broadening at the resolution used for the present measurements

scholarly journals X-ray spectroscopy study of ThO2 and ThF4

2010 ◽  
Vol 25 (1) ◽  
pp. 8-12
Author(s):  
Anton Teterin ◽  
Mikhail Ryzhkov ◽  
Yury Teterin ◽  
Ernst Kurmaev ◽  
Konstantin Maslakov ◽  
...  
Keyword(s):  
Binding Energy ◽  
Energy Range ◽  
Density Distribution ◽  
Electronic State ◽  
Electronic States ◽  
State Density ◽  
Molecular Orbitals ◽  
Spectral Structure ◽  
X Ray ◽  
Electronic State Density

The structure of the X-ray photoelectron, X-ray O(F)Ka-emission spectra from ThO2 and ThF4 as well as the Auger OKLL spectra from ThO2 was studied. The spectral structure was analyzed by using fully relativistic cluster discrete variational calculations of the electronic structure of the ThO8 D4h) and ThF8 (C2) clusters reflecting thorium close environment in solid ThO2 and ThF4. As a result it was theoretically found and experimentally confirmed that during the chemical bond formation the filled O(F)2p electronic states are distributed mainly in the binding energy range of the outer valence molecular orbitals from 0-13 eV, while the filled O(F)2s electronic states - in the binding energy range of the inner valence molecular orbitals from 13-35 eV. It was shown that the Auger OKLL spectral structure from ThO2 characterizes not only the O2p electronic state density distribution, but also the O2s electronic state density distribution. It agrees with the suggestion that O2s electrons participate in formation of the inner valence molecular orbitals, in the binding energy range of 13-35 eV. The relative Auger OKL2-3L2-3 peak intensity was shown to reflect quantitatively the O2p electronic state density of the oxygen ion in ThO2.

QUANTUM DYNAMICS OF WAVE PACKET IN HARMONIC POTENTIAL

2005 ◽  
Vol 19 (24) ◽  
pp. 3745-3754
Author(s):  
ZHAN-NING HU ◽  
CHANG SUB KIM
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Quantum Dynamics ◽  
Schrodinger Equation ◽  
Analytic Solution ◽  
Nonlinear Differential Equations ◽  
Time Dependent ◽  
Dimensional System ◽  
Two Dimensional ◽  
Vibrational States

In this paper, the analytic solution of the time-dependent Schrödinger equation is obtained for the wave packet in two-dimensional oscillator potential. The quantum dynamics of the wave packet is investigated based on this analytic solution. To our knowledge, this is the first time we solve, analytically and exactly this kind of time-dependent Schrödinger equation in a two-dimensional system, in which the Gaussian parameters satisfy the coupled nonlinear differential equations. The coherent states and their rotations of the system are discussed in detail. We find also that this analytic solution includes four kinds of modes of the evolutions for the wave packets: rigid, rotational, vibrational states and a combination of the rotation and vibration without spreading.

Millimeter Wave Rotational Transitions of 16O12C32S and 16O13C32S

1974 ◽  
Vol 29 (8) ◽  
pp. 1213-1215 ◽  
Author(s):  
N. W. Larsen ◽  
B. P. Winnewisser
Keyword(s):  
Excited States ◽  
Millimeter Wave ◽  
Vibrational Spectra ◽  
Vibrational State ◽  
Vibrational States ◽  
Ground Vibrational State ◽  
Wave Region ◽  
Rotational Transitions ◽  
Good Agreement

Rotational transitions of 16012C32S and 16013C32S in the ground vibrational state and of 16012C32S in several excited states have been accurately measured in the millimeter wave region for a minimum of four different J values. The analysis of the measured frequencies leads to rotational constants for the following vibrational states: 0 00 0 of 16O13C32S and 0 00 0, 0 1 1c 0, 0 1 1d 0, 0 20 0, 0 22c 0, 0 22d 0, 0 00 1 of 16O12C32S. Since the two components of the 0 22 0 transitions were resolved, an analysis of the l-type resonance was carried out and the interval 0 22 0 - 0 20 0 has been determined to be -4.63(10) cm-1. The result is in good agreement with the presently available determination of this level from vibrational spectra.

scholarly journals The interaction of atoms and molecules with solid surfaces - X-The activation of adsorbed atoms by metallic electrons

1937 ◽  
Vol 163 (912) ◽  
pp. 101-127 ◽  
Keyword(s):  
Vibrational State ◽  
Simple Calculation ◽  
Solid Surfaces ◽  
Adsorbed Atom ◽  
Vibrational States ◽  
Free Electrons ◽  
Atoms And Molecules ◽  
Vibrational Levels ◽  
Adsorbed Atoms ◽  
Thermal Vibrations

One object of this series of papers (Lennard-Jones and others 1935-7) is to consider in detail the mechanism of condensation, migration and evaporation of atoms and molecules at solid surfaces and to try to find the processes which govern the transition from one state to another. It has been shown that under certain conditions the thermal vibrations of a solid may activate an adsorbed atom from one vibrational state to a higher one or even eject it from the surface altogether. But the theory there developed is limited in the sense that it deals only with the transfer of single quanta to or from the solid, and consequently the quantized vibrational levels of the adsorbed atom must be closer together than the largest single quantum of energy which the solid can emit. An attempt has been made (Strachan 1937) to find the probability of the simultaneous emission or absorption of several quanta by the solid, and the indication is that the probability of several such simultaneous events is small. Now when atoms are bound to solid surfaces by valency forces, the vibrational levels are widely spaced compared with those of the solid, and many thermal quanta must be transferred simultaneously to the adsorbed atom to change its state of vibration. While this process may occur in nature, it seemed desirable to look for other possible processes whereby adsorbed atoms could be activated to higher vibrational states. One such possible mechanism, in metals at any rate, is by the transfer of energy from the conduction electrons. A simple calculation by classical methods indicates that in a typical case a surface atom may suffer as many as 10 15 collisions per second with the “free” electrons of a metal, and as, according to modern views, these electrons are moving with an energy of several volts, there is here an ample reservoir of energy from which adsorbed atoms may absorb energy or to which they can re-emit it, and thus change their vibrational state, or indeed, also their electronic state.

scholarly journals Model of daytime emissions of electronically-vibrationally excited products of O<sub>3</sub> and O<sub>2</sub> photolysis: application to ozone retrieval

2006 ◽  
Vol 24 (11) ◽  
pp. 2823-2839 ◽  
Author(s):  
V. A. Yankovsky ◽  
R. O. Manuilova
Keyword(s):  
Atomic Oxygen ◽  
Energy Exchange ◽  
Electronic States ◽  
Vibrational States ◽  
Vibrationally Excited ◽  
Proposed Model ◽  
Vibrational Levels ◽  
Electronically Excited ◽  
Basic Facts ◽  
Kinetics Of

Abstract. The traditional kinetics of electronically excited products of O3 and O2 photolysis is supplemented with the processes of the energy transfer between electronically-vibrationally excited levels O2(a1Δg, v) and O2(b1Σ+g, v), excited atomic oxygen O(1D), and the O2 molecules in the ground electronic state O2(X3Σg−, v). In contrast to the previous models of kinetics of O2(a1Δg) and O2 (b1Σ+g), our model takes into consideration the following basic facts: first, photolysis of O3 and O2 and the processes of energy exchange between the metastable products of photolysis involve generation of oxygen molecules on highly excited vibrational levels in all considered electronic states – b1Σ+g, a1Δg and X3Σg−; second, the absorption of solar radiation not only leads to populating the electronic states on vibrational levels with vibrational quantum number v equal to 0 – O2(b1Σ+g, v=0) (at 762 nm) and O2(a1Δg, v=0) (at 1.27 µm), but also leads to populating the excited electronic–vibrational states O2(b1Σ+g, v=1) and O2(b1Σ+g, v=2) (at 689 nm and 629 nm). The proposed model allows one to calculate not only the vertical profiles of the O2(a1Δg, v=0) and O2(b1Σ

Odd–even harmonic generation from oriented CO molecules in linearly polarized laser fields and the influence of the dynamic core-electron polarization

2019 ◽  
Vol 21 (43) ◽  
pp. 24177-24186 ◽  
Author(s):  
Ngoc-Loan Phan ◽  
Cam-Tu Le ◽  
Van-Hung Hoang ◽  
Van-Hoang Le
Keyword(s):  
Harmonic Generation ◽  
Theoretical Study ◽  
Polar Molecule ◽  
Time Dependent ◽  
Laser Fields ◽  
Core Electron ◽  
Electron Polarization ◽  
Linearly Polarized ◽  
Active Electron ◽  
Even Harmonics

We present a detailed theoretical study of the odd–even harmonics generated from the polar molecule CO by the method based on numerically solving the time-dependent Schrödinger equation within the single-active-electron approximation.

scholarly journals Structure in the secondary hydrogen spectrum—Part V

1926 ◽  
Vol 113 (764) ◽  
pp. 368-419 ◽  
Keyword(s):  
Quantum Number ◽  
Vibrational State ◽  
Final States ◽  
Vibrational Quantum Number ◽  
Vibrational States ◽  
Rydberg Constant ◽  
Infra Red ◽  
Preliminary Account ◽  
Before And After ◽  
State Of Affairs

In a previous paper entitled “Structure in the Secondary Hydrogen Spectrum,” Part IV, it was shown that there were a number of bands associated with Fulcher’s bands. It now appears that these and other related bands form a set of band systems whose null lines are connected by a Rydberg-Ritz formula. This formula has the normal value of the Rydberg constant, as is the case with the formula found by Fowler to connect the heads of some of the helium bands. This discovery makes it possible to apportion the effects observed as between electron jumps and vibration jumps, a matter which had to be left open in the previous paper (p. 740). The present paper deals only with the Q branches which are the most strongly developed and have been investigated most fully. A preliminary account of some of the results has been published a letter to ‘Nature,’ but the numbering of the vibrational states of the H α bands proposed therein has since been abandoned. It will be shown that all the lines of Fulcher’s red bands arise as a result of transitions in which the total quantum number (electron jump) changes from 3 to 2 and the vibrational quantum number is unchanged. In the part of the band denoted by A in “Structure,” Part IV, the vibrational state has the lowest possible quantum number both before and after the transition. I shall indicate this state of affairs by the symbol 0 → 0. The corresponding vibrational states in the parts denoted by B, C, D, E and F are, both initially and finally, 1, 2, 3, 4 and 5, and I shall denote these transitions by 1 →1, 2 → 2 , 3 → 3 , 4 → 4 and 5 → 5 respectively. The different lines in part A all have the same electron jump (3 → 2) and the same vibration state (0 → 0) but have different rotational jumps either of the molecule as a whole or of the emitting electron or of both. This statement will be equally true if the letter A is replaced by any of the letters B, C, D, E or F, except that the vibrational jump 0 0 is replaced by 1 → 1, 2 → 2, etc. In the present paper I shall confine my attention to the Q branches so that all the rotational transitions here dealt with are of the type m + ½ → m + ½ , m = 1, 2, 3, 4, 5, etc. (see Part IV, p. 749). Fulcher’s green bands also have the same electron jumps (3 → 2), but in these bands the vibrational quantum number is higher by unity in the initial than in the final states. Thus for the various green bands denoted by the letters A, B, C, D, E and F the vibrational transitions are 1 → 0, 2 → 1, 3 → 2, 4 → 3, 5 → 4 and 6 → 5 respectively. In addition to these, bands with the same electron jump (3 → 2) can be found in the infra-red with the vibrational jumps 0 → 1, 1 → 2, 2 → 3, 3 → 4 and 4 → 5 and others on the side of the green towards the violet which correspond to the vibration jumps 2 → 0, 3 → 1, 4 → 2, 5 → 3 and 6 → 4, and a few lines which may correspond to the vibration jumps 3 → 0 and 5 → 2. All these lines have the electron jump 3 → 2 and are the band analogue of the single line H α in the line spectrum of the hydrogen atom. For this reason it is convenient to refer to this system of bands as the H α bands.

Vibronic energy relaxation approach highlighting deactivation pathways in carotenoids

2015 ◽  
Vol 17 (29) ◽  
pp. 19491-19499 ◽  
Author(s):  
Vytautas Balevičius ◽  
Arpa Galestian Pour ◽  
Janne Savolainen ◽  
Craig N. Lincoln ◽  
Vladimír Lukeš ◽  
...  
Keyword(s):  
Electronic States ◽  
Energy Relaxation ◽  
Vibrational States

Energy relaxation between two electronic states of a molecule is mediated by a set of relevant vibrational states.

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